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wiley/fff2407c_b944_49e2_9739_985c13298e70.md | # Water Resources Research
Research Article
10.1029/2024 WR037068
A Fully Coupled Numerical Solution of Water, Vapor, Heat, and Water Stable Isotope Transport in Soil
[PERSON]
1 College of Hydraulic and Civil Engineering, Luding University, Yantai, Shandong Province, China, 1 Department of Soil Science, College of Agriculture and Bioresources, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
[PERSON]
1 College of Hydraulic and Civil Engineering, Luding University, Yantai, Shandong Province, China, 1 Department of Soil Science, College of Agriculture and Bioresources, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
[PERSON]
1 College of Hydraulic and Civil Engineering, Luding University, Yantai, Shandong Province, China, 1 Department of Soil Science, College of Agriculture and Bioresources, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
[PERSON]
1 College of Hydraulic and Civil Engineering, Luding University, Yantai, Shandong Province, China, 1 Department of Soil Science, College of Agriculture and Bioresources, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
###### Abstract
Modeling water stable isotope transport in soil is crucial to sharpen our understanding of water cycles in terrestrial ecosystems. Although several models for soil water isotope transport have been developed, many rely on a semi-coupled numerical approach, solving isotope transport only after obtaining solutions from water and heat transport equations. However, this approach may increase instability and errors of model. Here, we developed an algorithm that solves one-dimensional water, heat, and isotope transport equations with a fully coupled method (MOIST). Our results showed that MOIST is more stable under various spatial and temporal discretization than semi-coupled method and has good agreement with semi-analytical solutions of isotope transport. We also validated MOIST with long-term measurements from a lysimeter study under three scenarios with soil hydraulic parameters calibrated by HYDRUS-1D in the first two scenarios and by MOIST in the last scenario. In scenario 1, MOIST showed an overall _NSE_, _KGE_, and _MAE_ of simulated 8\({}^{18}\)O of 0.47, 0.58, and 0.92%, respectively, compared to the 0.31, 0.60, and 1.00% from HYDRUS-1D; In scenario 2, these indices of MOIST were 0.33, 0.52, and 1.04%, respectively, compared to the 0.19, 0.58, and 1.15% from HYDRUS-1D; In scenario 3, calibrated MOIST exhibited the highest _NSE_ (0.48) and _KGE_ (0.76), the smallest _MAE_ (0.90) among all scenarios. These findings indicate MOIST has better performance in simulating water flow and isotope transport in simplified ecosystems than HYDRUS-1D, suggesting the great potential of MOIST in furthering our understandings of ecohydrological processes in terrestrial ecosystems.
1
[PERSON], [PERSON], H.
theory to model isotopic signals in soil water. This simplification facilitates computations, making the models easily applicable at large scales, but may overlook the influence of physical mechanisms on isotope transport, such as phase changes and vapor diffusion.
Physical processes associated with isotope transport within soil receive greater attention at smaller scales, such as one-dimensional isotope movement. Based on [PERSON] et al. (1996), [PERSON] et al. (2005) developed the \"SiSPAT-Isotope\" (Simple Soil-Plant-Atmosphere Transfer) model, which incorporated the resistance to isotope transport between the soil surface and atmosphere ([PERSON], et al., 2009, 2009b). Subsequently, [PERSON] and [PERSON] (2010) developed \"Soil-Litter-Iso,\" which is also a one-dimensional model for the transport of heat, water, and stable isotopes in soil containing surface litter and actively transpiering vegetative cover. This model extended the linearization method of [PERSON] (2003) to vapor transport and emphasized the importance of isotope vapor transport, which is later supported by [PERSON] et al. (2018) using a SWIS model ([PERSON] et al., 2014). Compared to SiSPAT-Isotope, Soil-Litter-Iso is more efficient for thicker soil layers and larger time steps because of the implementation of the special linearization scheme in the model framework. However, Soil-Litter-Iso does not consider liquid and vapor heat capacity variation and the changes in vapor volume during heat transport, which may substantially bias the estimation of heat flux transport within the soil ([PERSON] et al., 2006), thereby resulting in biased isotope transport fluxes.
Another approach capitalizes on the capability of the well-known model, HYDRUS-1D, for simulating water flow and chemical transport. [PERSON] et al. (2012) simulated oxygen-18 movement in soil by modifying a solute transport module of HYDRUS-1D. However, [PERSON] et al. (2012) originally neglected fractionation and thus, their model was only applicable in situations where the slope of the isotopic evaporation line from soil water was close to the local meteoric water line ([PERSON] et al., 2012). The latest version of HYDRUS-1D incorporated isotopic fractionation by integrating with the SiSPAT-Isotope model ([PERSON] et al., 2021).
A common problem of these models related to isotope simulation is that each of these modeling approaches considers water and isotope transport separately, where the isotope transport is solved after solving the water and heat transport at each time step (semi-coupled method). This is reasonable because isotope transport does not affect soil water and heat transport. However, numerical errors and instabilities from soil, water and heat transport equations can be transferred into isotope transport equations at each time step (step 2 and three in Figure 1). Thus,
Figure 1: Demonstration of semi-coupled and fully coupled numerical solution method for water, heat, and isotope transport in soil at each time step. For the semi-coupled method, step 1 is to obtain the water and heat solutions at time step \(t+\Delta t\) from \(t\). Then, the soil water contents and temperature from \(t\) and \(t+\Delta t\) are used as inputs in the isotope transport equation (step 2). Finally, the isotope transport is solved in step 3. By contrast, the fully coupled method solves the three transport equations simultaneously.
either a tiny spatial discretization at the soil surface (\(10^{-6}\) m, [PERSON] et al., 2005) for extremely small mass balance errors (in the magnitude of \(10^{-16}\), [PERSON] et al., 2021), or complicated discretization schemes ([PERSON] & [PERSON], 2010) were required to protect the isotope solutions from numerical oscillation. We hypothesize that steps 2 and 3 from the semi-coupled method can be incorporated into step 1 in a fully coupled method (Figure 1) and thus, the fully coupled method reduces the impact of mass balance errors from soil water and heat transport equations on the isotope transport equation (step 2, Figure 1) compared to the semi-coupled method. Consequently, the fully coupled method should be more accurate and less affected by numerical instability than semi-coupled methods.
Therefore, the objectives of this study are: (a) to develop a one-dimensional model which can solve fully coupled soil water, heat, vapor, and isotope transport simultaneously and (b) to validate MOIST through analytical simulations with specific boundary conditions and field measurements. MOIST was written in MATLAB programming language and it is expected to be more efficient for simulating isotope transport within soil under various spatial and temporal scales than existing models by solving fully coupled soil water, heat, vapor, and isotope transport equations.
## 2 Materials and Methods
### Model Description
#### 2.1.1 Soil Water and Heat Transport
One-dimensional water and heat transport within soil can be described by mass and energy conservation equations with a downward-positive coordinate system ([PERSON], 2017; [PERSON] et al., 2006):
\[\frac{\partial(\theta+\theta_{v})}{\partial t}=-\frac{\partial(q_{t}+q_{v})}{ \partial z}-S_{p} \tag{1}\]
\[\frac{\partial C_{v\alpha\beta}T}{\partial t}+\lambda_{k}\frac{\partial\theta _{v}}{\partial t}=\frac{\partial\left(K_{H}\frac{\partial T}{\partial z} \right)}{\partial z}-C_{v}\frac{\partial(q_{t}T)}{\partial z}-C_{v\alpha} \frac{\partial(Tq_{v})}{\partial z}-\rho_{k}\frac{\partial q_{v}}{\partial z }-C_{v}S_{p}T \tag{2}\]
where \(\theta\) and \(\theta_{v}\) are the volumetric soil water (\(\mathrm{m^{3}\ m^{-3}}\)) and vapor content (\(\mathrm{m^{3}\ m^{-3}}\)); \(t\) is the time (s); \(q_{t}\) is the liquid flux (\(\mathrm{m\ s^{-1}}\)) and \(q_{v}\) is the vapor flux (\(\mathrm{m\ s^{-1}}\)); \(z\) is the spatial distance (m); \(S_{p}\) is the sink term (\(\mathrm{s^{-1}}\)), which is zero when there is no sink during simulation (e.g., root water uptake); \(C_{v\alpha\beta}\) is the soil volumetric heat capacity (J \(\mathrm{m^{-3}\ K^{-1}}\)); T is the soil temperature (K); \(\lambda_{k}\) is the latent heat of vapourization (J \(\mathrm{kg^{-1}}\)); \(K_{H}\) is the soil thermal conductivity (\(\mathrm{W\ m^{-1}\ K^{-1}}\)); \(C_{v\alpha}\) and \(C_{v\alpha}\) are the heat capacities of liquid water (J \(\mathrm{m^{-3}\ K^{-1}}\)) and vapor (\(\mathrm{J\ m^{-3}\ K^{-1}}\)); and \(\rho\) is the water density (\(\mathrm{kg\ m^{-3}}\)). Detailed explanations of these variables can be found in the Supporting Information S1.
The liquid flux, \(q_{p}\) is calculated by [PERSON]'s law (positive downwards) ([PERSON], 2010):
\[q_{t}=-K(h)\,\frac{dh}{dz}+K(h) \tag{3}\]
where \(K(h)\) is the unsaturated hydraulic conductivity (\(\mathrm{m\ s^{-1}}\)) as a function of \(h\). The vapor flux, \(q_{v}\), is calculated by the [PERSON]'s law ([PERSON] et al., 2009):
\[q_{v}=-D_{v\alpha}\frac{\partial c_{v}}{\partial z} \tag{4}\]
where \(D_{v\alpha}\) is the diffusivity of vapor within soil (\(\mathrm{m^{2}\ s^{-1}}\)). Note that \(c_{v}\) is the function of \(h\) and \(T\). Thus, the thermal vapor conduction is implicitly considered. Detailed derivations can be found in the Supporting Information S1.
Note that Equation 1 is the mixed form of [PERSON] equation. However, the current study uses the head-based Richards' equation:\[(1-c_{v,sat}R_{H})\frac{\partial\theta}{\partial h}\frac{\partial h}{\partial t}+( \theta_{sat}-\theta)\frac{\partial(c_{v,sat}R_{H})}{\partial t}=-\frac{\partial (q_{t}+q_{t})}{\partial z}-S_{p} \tag{5}\]
where \(c_{v,sat}\) is the saturated vapor concentration within soil air (m\({}^{3}_{\text{liquid water}}\) m\({}^{-3}_{\text{air}}\)); and \(R_{H}\) is the relative humidity in soil. Equations for \(c_{v}\), \(D_{\text{ex}}\), \(c_{v,sat}\), and \(R_{H}\) can be found in the Supporting Information S1.
Both the head-based and the mixed forms of [PERSON] equation are commonly used for modeling water flow in porous media. The current study utilizes the head-based form of [PERSON] equation because the head is continuous across the soil interface under typical natural conditions, especially for the layered soils ([PERSON] et al., 2019). However, \(\frac{\partial\theta}{\partial h}\frac{\partial h}{\partial t}\) may not be numerically equal to \(\frac{\partial\theta}{\partial t}\)([PERSON] et al., 1990; [PERSON] et al., 2021) because \(\frac{\partial\theta}{\partial t}\) could introduce mass balance errors during linearization. Nevertheless, the mass balance of head-based Richards' equation can be significantly improved by a second-order approximation to the time derivative ([PERSON] et al., 1990) and effectively controlled by adaptive time-stepping schemes ([PERSON] et al., 2023). MATLAB provides well-tested ordinary differential equations solvers, which implement adaptive time stepping schemes. As such, these solvers effectively meet the criteria.
#### 2.1.2 Soil Water Isotope Transport
The abundance of oxygen and hydrogen stable isotopes is conventionally expressed as \(\delta\) values, in units of per mil (%). However, for convenience, the abundances in MOIST were presented as concentrations (kg m\({}^{-3}\)), \(c_{i}\), where the relationship between isotopic ratio (\(R_{i}\)) and concentration (\(c_{i}\)) can be expressed as ([PERSON] et al., 2005; [PERSON] et al., 1996):
\[c_{i}=\frac{M_{i}}{M_{w}}R_{i}\rho \tag{6}\]
where \(M_{i}\) and \(R_{i}\) are the molar mass (kg mol\({}^{-1}\)) and the isotopic ratio of isotopic species \(i\), respectively, for a given isotope species; \(R_{i}\) can be calculated by:
\[R_{i}=\delta\frac{R_{ref}}{1000}+R_{ref} \tag{7}\]
where \(R_{ref}\) is the reference value for the isotopic ratio, which is 155.76 \(\times\) 10\({}^{-6}\) and 2,005.2 \(\times\) 10\({}^{-6}\) for HDO and H\({}_{2}\)\({}^{18}\)O, respectively ([PERSON], 1978).
The isotope mass conservation equation for both liquid and vapor phases is:
\[\frac{\partial(c_{i}\theta+c_{i}^{\prime}(\theta_{sat}-\theta))}{\partial t} =-\frac{\partial q_{t}}{\partial z}-c_{i}^{\prime}S_{p} \tag{8}\]
where \(c_{i}^{\prime}\) and \(c_{i}^{\prime}\) are the concentrations of isotope species \(i\) in liquid (kg m\({}^{-3}\)) and vapor phases (kg m\({}^{-3}\)). Assuming an instantaneous equilibrium between liquid and vapor phases ([PERSON] et al., 2017), a relationship between liquid and vapor isotopic concentration can be expressed as ([PERSON] et al., 2005; [PERSON] and [PERSON], 2010):
\[c_{i}^{\prime}=c_{v}\:a_{i}^{*}c_{i}^{\prime} \tag{9}\]
where \(a_{i}^{*}\) is the equilibrium fractionation coefficient of isotope species \(i\), which can be written as ([PERSON] et al., 2005):
\[a_{i}^{*}=e^{\left(\frac{c_{i}^{\prime}}{(\theta+\lambda_{i})^{2}}\frac{c_{i}^ {\prime}}{\tau^{2}\lambda_{i}-c_{i}^{\prime}}\right)} \tag{10}\]where \(a^{*}\), \(b^{*}\), \(c^{*}\) have values of 24,844, \(-\)76.248, and 0.052612 for \({}^{2}\)H, and 1,137, \(-\)0.4156, and \(-\)0.0020667 for \({}^{18}\)O.
The total isotopic flux, \(q_{i}\) (positive downwards), consists of liquid isotopic flux, \(q_{i}^{I}\), and vapor isotopic flux, \(q_{i}^{I}\):
\[q_{i}^{I}=c_{i}^{I}q_{i}-D_{i,a}^{I}\frac{\partial c_{i}^{I}}{\partial z} \tag{11}\]
\[q_{i}^{r}=-D_{i,a}^{r}\frac{\partial c_{i}^{r}}{\partial z} \tag{12}\]
where \(D_{i,a}^{I}\) and \(D_{i,a}^{r}\) are the liquid (m\({}^{2}\) s\({}^{-1}\)) and vapor (m\({}^{2}\) s\({}^{-1}\)) diffusivity in soil for isotope species \(i\), respectively. Detailed equations of \(D_{i,a}^{I}\) and \(D_{i,a}^{r}\) can be found in the Supporting Information S1.
Combing Equations 4 and 9 (Equation S3-10 in Supporting Information S1), and (Equation S3-11 in Supporting Information S1) with Equation 12 leads to ([PERSON] & [PERSON], 2010):
\[q_{i}^{r}=-(\alpha_{diff})^{D}\ a_{i}^{*}c_{i}^{I}q_{i}-D_{i,a}^{r}c_{i}\left( a_{i}^{r}\frac{\partial c_{i}^{I}}{\partial z}+c_{i}^{I}\frac{\partial a_{i}^{r}}{ \partial z}\right) \tag{13}\]
Equation 13 illustrates that the isotope transport in vapor phase consists of convection and diffusion terms, where the latter can be expressed as a concentration gradient in the liquid phase (first term within the brackets), and an equilibrium fractionation coefficient gradient (second term within the brackets). Detailed derivations can be found in Supporting Information S1.
#### 2.1.3 Root Water Uptake
Root water uptake is modeled as a sink term in Equations 1 and 8 ([PERSON] et al., 2001):
\[S_{p}=\frac{\Omega F_{i}P_{i}}{\Delta z} \tag{14}\]
where \(\Omega\) is the efficiency coefficient (between 0 and 1), which can be obtained from a prescribed stress function; \(\Delta z\) is the thickness of the considered layer (\(m\)) and \(P_{i}\) is the potential transpiration rate (m s\({}^{-1}\)), which can be obtained from the Penman-Monteith equation ([PERSON] et al., 1999) and the leaf area index. The current version of MOIST does not account for isotope fractionation during root water uptake. Root water uptake in MOIST is described by the [PERSON] model ([PERSON] et al., 1978). Essentially, potential evapotranspiration (\(pET\)) is calculated using the Penman-Monteith equation ([PERSON] et al., 1999). Following this, \(pET\) partitioned into potential evaporation and potential transpiration based on leaf area index ([PERSON] et al., 2013). The potential transpiration is then distributed across individual soil layers by multiplying root proportion (\(F_{i}\)) of each layer. Ultimately, the actual root water uptake flux from each layer is determined by multiplying the allocated potential root water uptake flux by the stress factor (Equations 14 and 15, Figure 2).
As demonstrated by Figure 2, \(\Omega\) is a function of pressure head, \(h\), and can be modeled with four critical pressure heads (\(h_{I}\), \(h_{2}\), \(h_{y}\), \(h_{\Delta}\)) that may vary among different plant species:
\[\Omega=\begin{cases}0,h<h_{4}\ \text{or}\ h>h_{1}\\ \frac{h-h_{4}}{h_{3}-h_{4}},h_{4}\leq h\leq h_{3}\\ \frac{h-h_{1}}{h_{2}-h_{1}},h_{2}\leq h\leq h_{1}\\ 1,h_{3}\leq h\leq h_{2}\end{cases} \tag{15}\]
\(F_{i}\) is the fraction of root length in the depth interval of \(z\) to \(z+\Delta z\), defined as:\[F_{i}=\frac{\int_{z}^{z+\Delta z}R(x)\,dx}{\int_{0}^{z}R(x)\,dx} \tag{16}\]
where \(z\) is the depth (\(m\)) of the upper boundary of layer \(i\); \(z+\Delta\)\(z\) is the depth of the lower boundary (m); \(Z_{i}\) is the maximum depth of the soil column (m); and \(R(x)\) is a predefined root length density distribution function which can be obtained by fitting to fine root length density measurements. For convenience, here we define \(R(z)\) as ([PERSON] et al., 1988):
\[R(z)=RD_{0}\left[1-\frac{1}{1+e^{-\Delta z}}+\frac{e^{-\Delta z}}{2}\right] \tag{17}\]
where \(RD_{0}\) is root length density at \(z=0\) and it is canceled out when calculating \(F_{i}\); \(b\) is an empirical root distribution parameter (m\({}^{-1}\)), and the equation was given by [PERSON] et al. (2001).
Note that \(R(z)\) can be static or treated as dynamic with \(Z_{r}\) being described as the classical Verhulst-Pearl logistic growth function ([PERSON], 2001):
\[Z_{r}(t)=L_{m}\frac{L_{0}}{L_{0}+\left(L_{m}-L_{0}\right)e^{-\alpha t}} \tag{18}\]
where \(L_{0}\) is the initial value of the rooting depth at the beginning of the growing season (m); \(L_{m}\) is the maximum rooting depth during the growing season (m); \(r\) is the growth rate (day\({}^{-1}\)) ([PERSON] et al., 2013).
#### 2.1.4 Boundary Conditions
#### 2.1.4.1 Boundary Conditions for Soil Water Flow
According to the Soil-Litter-Iso model ([PERSON], 2010), the coupled energy and water mass conservation equations were solved at the soil-air interface:
\[\frac{1}{r_{bw}}[c_{av}(T_{s},R_{hi})-c_{un}]=-D_{v}\frac{\partial c_{v,att}R _{hi}}{\partial z}-K\frac{\partial h}{\partial z}+K \tag{19}\]
\[R_{net}= \frac{C_{p}}{r_{hh}}(T_{s}-T_{a})+\frac{\rho\lambda_{E}}{r_{bw}}[c_{ av}(T_{s},R_{hi})-c_{un}]-K_{H}\frac{\partial T}{\partial z} \tag{20}\]
Figure 2: Illustration of a stress function, based on [PERSON] et al. (1978).
where \(r_{bw}\) and \(r_{hb}\) are the resistance to vapor (s m\({}^{-1}\)) and heat (s m\({}^{-1}\)) transfer at the soil-air interface, respectively; \(c_{vis}\) and \(c_{uu}\) are the vapor concentrations (m\({}^{3}\)\({}_{\text{water}}\) m\({}^{-3}\)\({}_{\text{air}}\)) at the soil surface and in the atmosphere, respectively; \(R_{ant}\) is the net radiation (W m\({}^{-2}\) K\({}^{-1}\)); \(C_{p}\) is the volumetric heat capacity of air at constant pressure (J m\({}^{-3}\) K\({}^{-1}\)); and \(T_{a}\) is the air temperature (K).
Equations 19 and 20 were used only in the top half of the soil surface layer for obtaining the unknown soil surface temperature (\(T_{s}\)) and surface relative humidity (\(R_{th}\)) by using a Jacobian iteration method at the beginning of each time step. \(T_{s}\) and \(R_{th}\) are required to calculate surface evaporation flux, surface liquid and vapor fluxes, surface sensible heat flux, surface latent heat flux and heat flux into the soil ([PERSON] & [PERSON], 2010).
The lower boundary condition for soil water flow can be set to free drainage (zero gradient of soil water pressure head at the lower boundary), seepage surface (constant soil water pressure head at the lower boundary), or zero water flux. The lower boundary condition for heat transport can be set to zero temperature gradient.
#### 2.1.4.2 Boundary Conditions for Isotope Transport
Isotopic evaporation fluxes through the soil surface to the atmosphere were calculated using the [PERSON] (1965) model:
\[E_{i}=\frac{\alpha_{k}}{r_{bw}}[c_{v}c_{i,u}^{l}\sigma_{i}^{*}(T_{s})-c_{i}^{ uu}] \tag{21}\]
where \(\alpha_{k}\) is the kinetic fractionation coefficient; \(c_{i}^{uu}\) is the isotopic concentration of the atmospheric water vapor (kg m\({}^{-3}\)); \(c_{i,u}^{l}\) is the isotopic concentration at the soil surface (kg m\({}^{-3}\)); and \(E_{i}\) is the surface soil isotopic flux (m s\({}^{-1}\)) and can be specified as:
\[E_{i}=-p_{i}^{c}\frac{\partial(c_{v}c_{i}^{l}\alpha_{i}^{*}T)}{\partial z}-D_{ i}^{c}\frac{\partial c_{v}^{l}}{\partial z}+q_{h}c_{v,u}^{l} \tag{22}\]
where \(q_{h}\) is the liquid flux at the soil surface (m s\({}^{-1}\)).
The kinetic fractionation coefficient, \(\alpha_{k}\), can be written as ([PERSON], 2010; [PERSON], 1996):
\[\alpha_{k}=(\alpha_{diff})^{nk} \tag{23}\]
with
\[nk=\frac{(\theta_{s}-\theta_{res})\,n_{a}+(\theta_{sat}-\theta_{s})\,n_{s}}{ \theta_{sat}-\theta_{res}} \tag{24}\]
where \(n_{a}\) and \(n_{s}\) are coefficients with values of 0.5 and 1.0, respectively, and \(\theta_{s}\) is the soil surface water content (m\({}^{3}\) m\({}^{-5}\)). There are several equations available to calculate \(\alpha_{k}\). In the current study, a sensitivity analysis was conducted on these equations (Supporting Information S1), which revealed that MOIST was not sensitive to available formulations. Thus, we chose Equation 21 for its relatively simple formulation, and it considers the influence of surface soil water content on isotope fractionation.
Combining Equations 21 and 22 leads to the final expression for surface soil isotopic concentration, \(c_{i,u}^{l}\) (kg m\({}^{-3}\)):
\[\frac{\alpha_{k}}{r_{bw}}[c_{i,u}^{l}\alpha_{k}(T_{s})-c_{i}^{uu}]=-D_{i}^{c }\frac{\partial(c_{v}c_{i}^{l}\alpha_{i}^{*}T)}{\partial z}-D_{i}^{l}\frac{ \partial c_{v}^{l}}{\partial z}+q_{h}c_{v,u}^{l} \tag{25}\]
Using this relationship, \(c_{i,u}^{l}\) can be readily solved as it is the only unknown quantity.
It is important to note that energy, water, and isotope mass conservation equations (Equations 19, 20 and 25) at the air-soil interface are identical to that of [PERSON] and [PERSON] (2010), except that the influence of litter layer is not considered. This means that the fluxes from the center of the top-soil layer to the soil-air interface are balanced by the fluxes from the soil-air interface to the atmosphere (Equations 19, 20 and 25). The lower boundary conditions for isotope transport are determined by soil water flux or can be customized. Normally, the lower boundary condition for isotope transport is zero gradient or zero flux.
#### 2.1.5 Numerical Implementations
MOIST adopts a cell-centered spatial discretization scheme along with the finite volume method (FVM). While the finite element method (FEM) is another commonly used approach for solving partial differential equations, it is particularly advantageous for complex problems such as two- and three-dimensional water transport in intricate geometries with complex boundary conditions. However, this study focuses on one-dimensional soil water movement, where the simplicity of the scenario reduces performance differences between FVM and FEM, making the choice of method less impactful on the performance of the fully coupled scheme. Furthermore, compared to FEM, FVM is inherently suited to conservation law problems, as it conserves fluxes both locally and globally, and it also offers simpler mathematical implementation. Therefore, FVM is used in MOIST.
To solve Equations 1, 2 and 8 simultaneously, we expand them into:
\[\left[\left(1-c_{s,sat}R_{H}\right)\frac{\partial\theta}{\partial t }+\left(\theta_{sat}-\theta\right)c_{s,sat}\frac{\partial R_{H}}{\partial t} \right]\frac{\partial t}{\partial
\[B=\ C_{s,sat}+\rho\lambda_{E}\left[\left(\theta_{sat}-\theta\right)c_{s,sat}\frac{ \partial h_{r}}{\partial T}+\left(\theta_{sat}-\theta\right)R_{H}\frac{\partial c _{s,sat}}{\partial T}\right] \tag{33}\]
\[\mathrm{C}=\left(1-c_{s,sat}R_{H}\right)\frac{\partial\theta}{\partial h}+ \left(\theta_{sat}-\theta\right)c_{s,sat}\frac{\partial R_{H}}{\partial h} \tag{34}\]
\[\mathrm{D}=\left(\theta_{sat}-\theta\right)c_{s,sat}\frac{\partial R_{H}}{ \partial T}+\left(\theta_{sat}-\theta\right)R_{H}\frac{\partial c_{s,sat}}{ \partial T} \tag{35}\]
\[\mathrm{E}=\theta+\alpha_{c}^{*}c_{s,sat}R_{H}(\theta_{sat}-\theta) \tag{36}\]
\[\mathrm{F}=-\frac{\partial q_{i}}{\partial z}-c_{i}^{*}S_{p}-c_{i}^{ \dagger}\frac{\partial\theta}{\partial h}\frac{\partial h}{\partial h}-c_{i}^ {\dagger}\theta_{sat}\left[c_{s,sat}R_{H}\frac{\partial\sigma}{\partial T} \frac{\partial T}{\partial t}+\alpha_{i}^{*}R_{H}\frac{\partial\sigma_{s,sat} }{\partial T}\frac{\partial T}{\partial t}+\alpha_{i}^{*}c_{s,sat}\left(\frac {\partial R_{H}}{\partial h}\frac{\partial h}{\partial t}+\frac{\partial R_{H}} {\partial T}\frac{\partial T}{\partial t}\right)\right]\] \[\quad\quad+c_{i}^{*}\left[c_{s,sat}R_{H}\theta\frac{\partial \alpha_{i}^{*}}{\partial T}\frac{\partial T}{\partial t}+\alpha_{i}^{*}R_{H} \theta\frac{\partial c_{s,sat}}{\partial T}\frac{\partial\sigma}{\partial t}+ \alpha_{i}^{*}c_{s,sat}\theta\left(\frac{\partial R_{H}}{\partial h}\frac{ \partial h}{\partial t}+\frac{\partial R_{H}}{\partial T}\frac{\partial T}{ \partial t}\right)+\alpha_{i}^{*}c_{s,sat}R_{H}\frac{\partial\theta}{\partial h }\frac{\partial h}{\partial t}\right] \tag{37}\]
Equations 26-28 are expressed as a system of coupled ordinary differential equations of Equations 29-37. This system of equations (\(\frac{\partial T}{\partial t}\), \(\frac{\partial T}{\partial t}\), and \(\frac{\partial^{*}}{\partial t^{*}}\)) are solved at the center of each layer (cell-centered discretization) by MATLAB solver ode113 (or ode23 tb). Furthermore, the semi-coupled scheme (Figure 1) is also incorporated in MOIST, where the derivative vector of the soil water and heat transport equations (Equations 29 and 30) are constructed by Equations 32-35 and passed to the solver first. Then, Equation 31 is rewritten as:
\[\frac{\partial C_{i}^{\dagger}}{\partial t}=\frac{-\frac{\partial q_{i}}{ \partial z}-H}{I} \tag{38}\]
with
\[H=\ c_{i}^{\dagger}\left[\frac{\partial\theta}{\partial t}-c_{s,sat}R_{H}\ \alpha_{i}^{*}\frac{\partial\theta}{\partial t}+\frac{\partial\left(c_{s,sat}R _{H}\ \alpha_{i}^{*}\ \theta_{sat}\right)}{\partial t}-\theta\frac{\partial\left(c_{s,sat}R_{H}\ \alpha_{i}^{*}\ \right)}{ \partial t}\right] \tag{39}\]
\[I=\theta+c_{s,sat}R_{H}\alpha_{i}^{*}\left(\theta_{sat}-\theta\right) \tag{40}\]
The solutions from the coupled soil water and heat transport equation (\(h\) and \(T\)) at new time point are used to update parameter values (\(c_{s,sat}\), \(R_{H}\), \(\alpha_{i}^{*}\), \(\theta\)) in Equations 39 and 40. Subsequently, the derivative vector of isotope transport can be constructed and solved (Equations 38-40).
#### 2.1.5.1 MATLAB Solver ode113
The ode113 solver uses an adaptive, variable-order, variable-step-size (VOVS) method ([PERSON], 2002). This is implemented with a variable order Adams-Bashforth-Moulton (ABM) method, which is a combination of an explicit type of the Adams-Bashforth (AB) and an implicit type of Adams-Moulton (AM) methods. Specifically, the AB method is used to obtain the solution at the new time step by taking multiple previous time steps into account, while the AM method is used to make corrections.
The ode113 selects automatically between the first and twelfth order approximation during the computation based on the estimation errors. This is helpful for minimizing the estimated errors and for achieving high efficiency in time. Moreover, the time step size is adjusted according to the estimation error. Therefore, ode113 can handle a wide range of problems with high accuracy and efficiency. The ode113 is well suited to transport in relatively uniform media but is susceptible to numerical oscillation when hydraulic conductivities between layers differ greatly.
#### 2.1.5.2 MATLAB Solver ode23 tb
Ode23 tb is a solver specifically designed for solving ordinary differential equations with highly oscillatory solutions, such as those arising from heterogeneity in hydraulic conductivities between soil layers. The solver combines a trapezoidal rule (sometimes referred as the second order AM method) with a second order backward differentiation formula (BDF), hence the \"tb\" suffix. As an implicit solver, ode23 tb is generally more computationally expensive than other solvers that adopt explicit numerical schemes. However, because it adopts the trapezoidal BDF method, it is more efficient than other types of implicit methods, such as the fully implicit Euler method or the backward Euler method. Therefore, ode23 tb is better suited than ode113 when the soil physical properties differed greatly between layers. Like ode113, ode23 tb can adjust the step size automatically based on the oscillatory behavior of the solution. Thus, ode23 tb is an efficient and accurate solver for stiff systems, making it less likely to have numerical instability.
#### 2.1.6 Modeling Efficiency
To evaluate the model performance quantitatively, the Nash-Sutcliffe efficiency (_NSE_) (Nash & Sutcliffe, 1970) is used:
\[NSE=1-\frac{\sum_{t=1}^{T_{cl}}\left[M_{0}(t)-M_{m}\right]^{2}}{\sum_{t=1}^{T _{cl}}\left[M_{0}(t)-\overline{M_{0}}\right]^{2}} \tag{41}\]
where \(M_{0}\) and \(M_{m}\) are observations (measurements) and modeling values (simulations) respectively. \(\overline{M_{0}}\) is the average of the observations over time, \(t\) is the temporal point, and \(T_{cl}\) is the total number of temporal steps. _NSE_ ranges between negative infinity to 1. _NSE_ of one is indicative of excellent performance of the model in predicting the temporal variations of variables, while an _NSE_ of 0 suggests the model can only reflect average values. A negative _NSE_ implies poor performance of the model in regenerating the temporal variations of variables.
Moreover, Kling-Gupta efficiency (_KGE_, [PERSON] et al., 2009) has become popular in recent years to evaluate the model performance ([PERSON] et al., 2019; [PERSON] et al., 2022). _KGE_ considers correlation, bias, and variability between simulations and measurements, providing a more comprehensive assessment of the model performance and can be written as:
\[KGE=1-\sqrt{(\text{cor}-1)^{2}+\left(\frac{\sigma_{m}}{\sigma_{o}}-1\right)^{ 2}+\left(\frac{\mu_{m}}{\mu_{o}}-1\right)^{2}} \tag{42}\]
where _cor_ is the linear correlation between observations and simulations, \(\sigma_{m}\) and \(\sigma_{o}\) are standard deviations of simulations and observations, respectively; \(\mu_{m}\) and \(\mu_{o}\) are mean of simulations and observations, respectively. Like _NSE_, _KGE_ = 1 indicates perfect agreement between simulations and observations. A model had a negative _KGE_ is generally considered as \"not satisfactory\" ([PERSON] et al., 2017).
Sometimes, _NSE_ and _KGE_ may disagree with each other during model comparisons ([PERSON] et al., 2019). A third index, the absolute error (_MAE_), is used to evaluate the model performance. Here, we decided to use _MAE_ rather than the root mean square error (_RMSE_) because the residuals between simulations and measurements are non-normally distributed ([PERSON], 2014; [PERSON] et al., 2018). _MAE_ is given as:
\[MAE=\frac{1}{T_{cl}}\sum_{t=1}^{T_{cl}}\left|M_{0}(t)-M_{m}(t)\right| \tag{43}\]
### Model Validation
To validate MOIST, we conducted sensitivity analysis on various temporal and spatial discretization, through theoretical, semi-analytical, and long-term field tests. However, we mainly reported the findings of sensitivity under various temporal and spatial discretization, semi-analytical tests under unsaturated and non-isothermal conditions, and a long-term field test. This is because the results from other semi-coupled models are readily available for comparison. Detailed information about the theoretical tests, and the semi-analytical test under saturated isothermal conditions, can be found in Supporting Information S1.
The current test assumes a 1 m soil column containing Yolo light clay. The relationships between soil water content, pressure head, and unsaturated hydraulic conductivity for the Yolo light clay were described by the Brooks-Corey ([PERSON] & Corey, 1964) model:
\[S=\frac{\theta-\theta_{res}}{\theta_{sat}-\theta_{res}}=\left\{\begin{array}{ ll}\left(\frac{h}{h_{c}}\right)^{-\lambda},h\leq he\\ 1\quad h\geq he\end{array}\right. \tag{44}\]
\[S^{\eta}=\left\{\begin{array}{ll}K_{sat},h\leq he\\ 1\quad h\geq he\end{array}\right. \tag{45}\]
where \(S\) is the effective saturation; \(h_{c}\) is the air-entry value (m); and \(\lambda\) and \(\eta\) are the shape coefficients, where \(\eta=2\gamma\)\(\lambda+3\) (Table 1).
The initial conditions assume the soil water content as 70% of its saturated value and the net radiation as a constant value of 200 W m\({}^{-2}\) at the soil surface. The air temperature and relative humidity during the simulation period remained at 30\({}^{\circ}\)C and 0.2, respectively. Water in the soil column can escape only through evaporation from the top of the column. The upper boundary conditions for soil water and isotope transport were calculated by Equations 19, 20 and 25. For the lower boundary, the rate of water supply from the bottom of the profile is equivalent to the evaporation rate at each time step. The simulation length was 700 hr.
Three spatial steps, \(\Delta z=0.01\) m, \(\Delta z=0.02\) m, and \(\Delta z=0.005\) m were used. The fixed initial temporal step was 25 s. By contrast, for the various temporal steps, three initial steps, \(\Delta t=100\) s, \(\Delta t=50\) s, and \(\Delta t=25\) s, were used and the spatial step was fixed at 0.01 m. Note that if a large temporal step is used, the result may be affected by the time-adaption, which could reduce the difference between semi-coupled and fully coupled methods. Thus, we used small temporal steps to approximately transform the time-adaptive solver into a fixed time step solver. This is because the solver can obtain a satisfactory solution within the provided initial time step without the need for time adjustments when boundary conditions are stable.
#### 2.2.2 Semi-Analytical Test Under Unsaturated Non-Isothermal Conditions
[PERSON] and [PERSON] (1984) developed a semi-analytical solution to predict \(\delta^{2}\)H and \(\delta^{18}\)O profiles under unsaturated, non-isothermal conditions as:
\[\frac{d\delta_{i}}{dz}+\frac{\delta_{i}-\delta_{i,\text{sup}}}{z_{i}+R_{i}z_{ e}}=\frac{R_{i}\sigma_{z}(\alpha_{k}-\alpha_{i}^{\ast})}{z_{i}+R_{i}z_{e}}\, \frac{d\left[ln(\rho R_{tt}c_{v,\text{sat}}(\alpha_{k}-\alpha_{i}^{\ast})) \right]}{dz} \tag{46}\]
\[z_{i}=\frac{D_{i,t}^{l}}{q_{\text{crop}}} \tag{47}\]
\[z_{v}=\frac{D_{i,t}^{l}c_{v,\text{sat}}}{q_{\text{crop}}} \tag{48}\]where \(z_{i}\) and \(z_{v}\) are the liquid and vapor characteristic lengths (m), respectively. Note that all modeling conditions were the same as that described in Section 2.2.1, except the 1 m soil column was divided uniformly at a step of 0.01 m and the total simulation length was 250 days to ensure that steady state is achieved.
#### 2.2.3 Long-Term Simulations at HBLFA Raumberg-Gumpenstein, Austria
#### 2.2.3.1 Site Description
Precipitation and seepage water from lysimeters were collected from May 2002 to February 2007 by [PERSON] et al. (2012) at the HBLFA Raumberg-Gumpenstein, Austria. During the experiment, the air temperature exhibited ainuous variation, ranging between \(-15^{\circ}\)C and \(27^{\circ}\)C (Figure 3a), with a mean of 8.2\({}^{\circ}\)C. Similarly, the atmospheric relative humidity showed seasonal fluctuations and varied between 0.30 and 0.99 (Figure 3b), with a mean of 0.89. In addition, most precipitation events occurred during the summer (Figure 3c), with a daily mean rainfall of 2.8 mm day\({}^{-1}\).
Five lysimeters were used to investigate the influence of land cover and fertilization on soil water and solute transport by [PERSON] et al. (2012). For simplicity, the current study used only lysimeter-3 for the comparison of numerical simulations. Lysimeter-3 had a surface area of 1 m\({}^{2}\), depth of 1.5 m, and was filled with three soil horizons (0-0.25 m, 0.25-1.0 m, 1.0-1.5 m) of undisturbed Dystric Cambisol ([PERSON] et al., 2012) (Figure 4).
Each year the lysimeter was planted with winter rye, which had a maximum rooting depth of 1 m. Weekly precipitation and drainage water samples from the bottom of Lysimeter-3 were collected between May 2002 and February 2007. Isotopic compositions were analyzed by using dual-inlet mass spectrometry. Further information about the site and experimental procedures can be obtained from [PERSON] et al. (2012).
#### 2.2.3.2 Model Setup
The MOIST simulations adopted the solute transport and soil hydraulic parameter values provided by [PERSON] et al. (2012). The soil hydraulic properties were described by the [PERSON] (1980) model. Because the measured saturated hydraulic conductivities varied greatly within different soil horizons ([PERSON] et al., 2012), water flux at the interface of different soil layers may vary drastically. Therefore, to minimize the oscillation of numerical solutions, the ode23 tb solver, which is designed for stiff problems, was used in this simulation.
The initial soil water content and \(8^{13}\)O profiles were provided by [PERSON] et al. (2012). The upper boundaries of soil water and heat transport were calculated by Equations 14 and 16, while the upper boundary of isotope transport was calculated by Equation 25. The lower boundary condition for soil water flow was defined as seepage
Figure 3: Air temperature, relative humidity, and precipitation events at HBLFA Raumberg-Gumpenstein in Austria: (a) air temperature (T), (b) air relative humidity (RH), and (c) daily precipitation (P). Data from [PERSON] et al. (2012).
surface. Zero temperature and zero isotopic concentration gradients were set as the lower boundary conditions of heat and isotope transport, respectively.
The root distribution of winter ye at the site varied during the growing season and has been described in HYDRUS-1D ([PERSON] et al., 2012), along with the water stress function described by the [PERSON] model ([PERSON] et al., 1978). Following this approach, the water stress function parameters \(h_{t}\), \(h_{2}\), \(h_{t}\), and \(h_{t}\) were set as 0, 0.01, 5, and 160 m, respectively ([PERSON] et al., 2012).
Environmental parameters such as air temperature, air relative humidity, and precipitation were assumed to be constant within each hour. Regarding the isotopic compositions of atmospheric vapor, \(\delta_{\alpha}\), it is expressed as following equation when rainfall occurs ([PERSON] et al., 2015):
\[\delta_{\alpha}=\frac{\delta_{min}\ -\left(\alpha^{+}+1\right)1000}{\alpha^{+}} \tag{49}\]
where \(\alpha^{+}\) is the equilibrium fractionation factor.
Obviously, Equation 49 cannot be used when there is a rain-free period. However, the field measurements of \(\delta_{\alpha}\) (oxygen-18) in Austria (where the lysimeter study conducted) ranged between \(-27\%\epsilon\) and \(-13\%\epsilon\) annually ([PERSON] et al., 2012), with an average of \(-20\%\epsilon\)([PERSON] et al., 2016). Therefore, we used \(-20\%\epsilon\) as the value of \(\delta_{\alpha}\) for the rain-free period. Values \(-27\%\epsilon\) and \(-13\%\epsilon\) were used to explore the influence of \(\delta_{\alpha}\) values on the simulated outflow isotopic signals.
Soil hydraulic parameters were calibrated by both [PERSON] et al. (2012) and [PERSON] et al. (2022) with this data set (Table 2). We obtained a new set of hydraulic parameters by calibrating MOIST using the same data set. Consequently, simulations were conducted in three scenarios: Scenario 1, calibrated parameters from [PERSON] et al. (2012) were utilized in MOIST; Scenario 2, calibrated parameters from [PERSON] et al. (2022) were employed in MOIST; Scenario 3, parameters calibrated by MOIST were used. In the first two scenarios, we aimed to highlight the advantages of the coupling scheme because the parameters are independent of MOIST, allowing for a comparison that reflects model differences. In Scenario 3, we aimed to demonstrate that model calibration can further enhance the performance of MOIST.
The soil column was divided into 150 layers with a spatial step of 0.01 m in the model simulation. The simulation length was 1,736 days, and the initial temporal step was 86,400 s. The minimum time step was \(1\times 10^{-8}\) s and the maximum time step was 86,400 s. The time step can be automatically adjusted within the range between minimum and maximum. Lastly, the lysimeter simulation (including Sections 2.2.1 and 2.2.2) was completed by MATLAB R2022a on a personal computer with an Intel processor (i7-10700k).
\begin{table}
\begin{tabular}{l c c c c c c} \hline & Layers (m) & \(\alpha\) (m\({}^{-1}\)) & \(n\) & \(\theta_{max}\) (m\({}^{3}\) m\({}^{-3}\)) & \(\theta_{max}\) (m\({}^{3}\) m\({}^{-3}\)) & \(K_{max}\) (m s\({}^{-1}\)) \\ \hline [PERSON] et al. (2012) & 0–0.30 & 2.3 & 1.14 & 0.30 & 0 & \(1.27\times 10^{-5}\) \\ & 0.31–0.90 & 7.6 & 1.07 & 0.32 & 0 & \(6.94\times 10^{-4}\) \\ & 0.91–1.50 & 1.6 & 1.07 & 0.32 & 0 & \(1.27\times 10^{-5}\) \\ [PERSON] et al. (2022) & 0–0.30 & 2.0 & 1.15 & 0.30 & 0 & \(2.55\times 10^{-5}\) \\ & 0.31–0.90 & 30.0 & 1.11 & 0.41 & 0 & \(3.32\times 10^{-5}\) \\ & 0.91–1.50 & 8.2 & 1.10 & 0.30 & 0 & \(2.55\times 10^{-5}\) \\ \hline \end{tabular}
\end{table}
Table 2 Calibrated Soil Hydraulic Parameters by [PERSON] et al. (2012) and [PERSON] et al. (2022)
Figure 4.— Illustration of the Lysimeter-3 setup from the long-term simulations at HBLFA Raumberg-Gumpenstein, Austria.
#### 2.2.3.3 Model Calibration
Three soil horizons were defined in this lysimeter study ([PERSON] et al., 2012). Limited by the computation time of MOIST, we did not calibrate all 13 parameters (4 parameters of van Genuchten model of each horizon plus the longitude dispersivity). Instead, we calibrated the saturated hydraulic conductivity of each horizon because \(K_{sat}\) are generally prone to large uncertainties ([PERSON] and [PERSON], 2019) and highly sensitive to the choice of models (Table 2). Moreover, the longitude dispersivity was also calibrated because it directly affects the isotope transport ([PERSON] et al., 2022). One dispersivity for three horizons can be estimated because only the isotopic composition of the drainage water was measured in the [PERSON] et al. (2012) data set. The remaining soil hydraulic parameters, such as \(\alpha\), \(n\), \(\theta_{sat}\), and \(\theta_{res}\) were identical to that from [PERSON] et al. (2012).
The calibrated saturated hydraulic conductivities from [PERSON] et al. (2012) served as base values, and each was assigned a coefficient ranging between 0.1 and 10 for scaling purposes. These coefficients were uniformly sampled through a Monte Carlo simulation. Then, the Nash-Sutcliffe Efficiency (_NSE_) of simulated outflow isotope signals, along with the disparity between modeled and measured total outflow amount, was calculated. In cases where MOIST failed to produce results under specific coefficients, a negative _NSE_ was assigned. The set of coefficients yielding the highest _NSE_ and the smallest difference between modeled and measured total outflow was selected. The calibration was conducted on Cedar, a heterogeneous high-performance cluster (HPC) within the Digital Research Alliance of Canada. Note that the validation is simplified, but it provided valuable insights into the potential impact of calibration on the performance of MOIST when applied to real-world situations.
## 3 Results
MOIST was validated against semi-coupled solutions under various temporal and spatial discretization, theoretical solutions, semi-analytical solutions under saturated isothermal conditions, semi-analytical solutions under unsaturated non-isothermal conditions, and long-term field measurements. Here we focused primarily on the validation of MOIST against semi-coupled solutions under various temporal and spatial discretization, semi-analytical tests under unsaturated non-isothermal conditions and the long-term field measurements. Validations against theoretical tests and semi-analytical tests under saturated isothermal conditions can be found in the Supporting Information S1.
Comparison Between Fully Coupled and Semi-Coupled Methods Under Various Spatial and Temporal Discretization
The feasibility and stability of fully coupled and semi-coupled methods were assessed. The initial \(\delta^{2}\)H profile was uniformly distributed with a value of 0%. Given that water (\(\delta^{2}\)H = 0%) was continuously supplied from the bottom of the profile, and water escaped the column through evaporation only at the soil surface, \(\delta^{2}\)H of soil water in the column at any point in space and time is unlikely to be \(\gtrsim\)0%, especially at its lower boundary. However, considering numerical errors, a negative value of \(-\)0.3% was set as the threshold for the largest acceptable deviation from 0% (\(\delta^{2}\)H of the bottom-supplied water) because the largest error of simulated \(\delta^{2}\)H from MOIST in the semi-analytical test is 0.31% (Table 4). Additionally, a 0.1% threshold was used as the maximum acceptable absolute deviation between the fully coupled and semi-coupled methods, recognizing that the two methods cannot produce identical numerical solutions.
\begin{table}
\begin{tabular}{l c c} \hline & MOIST & Semi-analytical solution \\ \hline Maximum \(\delta^{2}\)H (\%) & 40.34 & 40.65 \\ Maximum \(\delta^{10}\)O (\%) & 21.15 & 22.13 \\ Slope of HDO/H\({}_{1}\)SO in vapor dominated region & 3.55 & 3.31 \\ Slope of HDO/H\({}_{2}\)SO in liquid dominated region & 1.91 & 1.90 \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of Maximum \(\delta^{2}\)H, \(\delta^{10}\)O, and the Slope of \({}^{2}\)H/\({}^{10}\)O in Liquid Dominated Regions Estimated From MOIST and the Analytical Solution Under Unsaturated and Non-isothermal Conditions
\begin{table}
\begin{tabular}{l c c} \hline & MOIST & Semi-analytical solution \\ \hline Maximum \(\delta^{3}\)H (\%) & 40.34 & 40.65 \\ Maximum \(\delta^{10}\)O (\%) & 21.15 & 22.13 \\ Slope of HDO/H\({}_{1}\)SO in vapor dominated region & 3.55 & 3.31 \\ Slope of HDO/H\({}_{2}\)SO in liquid dominated region & 1.91 & 1.90 \\ \hline \end{tabular}
\end{table}
Table 4: Difference of Maximum Isotopic Composition Between Numerical and Analytical Solutions With a Layer Thickness of 0.01 m
#### 3.1.1 Various Temporal Discretization
Under different temporal discretization, the fully coupled method consistently displayed \(\delta^{2}\)H values greater than \(-0.3\%\)e (see Figures 5a-5c). By contrast, the semi-coupled method exhibited unreasonable negative \(\delta^{2}\)H values (depicted by dark blue areas in Figures 5d-5f) across all temporal step lengths. This discrepancy can be attributed to errors originating from soil water and heat equations being incorporated into the isotope transport equation. Consequently, noticeable disparities in the estimated transient \(\delta^{2}\)H between the two methods emerged (highlighted by pink areas in Figures 5g-5i), and these differences became more pronounced with increasing temporal steps (Figures 5g-5i). This highlights the robustness of the fully coupled method, which is less sensitive to temporal discretization and capable of accommodating larger time steps compared to the semi-coupled method.
Solver CPU times of both fully coupled and semi-coupled methods were presented in Figure 6. For the fully coupled method, solver CPU times were 14.4 s, 7.2 s, and 3.5 s under temporal discretization of 100 s, 50 s, and 25 s, respectively (Figure 6). By contrast, the corresponding times for the semi-coupled method were 29.2 s, 15.2 s, and 7.7 s, respectively (Figure 6). Notably, the fully coupled method reduced solver CPU time by approximately 50% compared to the semi-coupled method. This gained efficiency can be attributed to the fact that all equations were solved simultaneously in the fully coupled method, requiring the solver to be called only once within a single iteration. On the other hand, the semi-coupled method involved solving water and heat transport equations before addressing the isotope equation,
Figure 5: Comparison of simulated transient hydrogen isotope ratio (\(\delta^{2}\)H) profiles using fully coupled and semi-coupled numerical methods under unsaturated non-isothermal conditions at three spatial discretization, including 100 s (left), 50 s (center), and 25 s (right). Panels (a) to (c) show the \(\delta^{2}\)H profiles from the fully coupled method. Panels (d) to (f) show the \(\delta^{2}\)H profiles from the semi-coupled method. Panels (g) to (i) show the absolute differences in the \(\delta^{2}\)H profiles between the fully coupled and semi-coupled method. FC, SC, and D represent fully coupled solutions, semi-coupled solutions, and the differences between two solutions, respectively. A threshold of \(-0.3\%\)e was set as the largest acceptable deviation from 0 to 0.1% as the maximum deviation between the fully coupled and semi-coupled methods because they cannot produce identical numerical solutions.
Figure 6: The solver CPU time of fully coupled and semi-coupled version of MOIST under a spatial discretization of 0.01 m and temporal discretization of 25 s, 50 s, and 100 s, respectively.
leading to the solver being called twice within one iteration (Figure 6). Additionally, the solver CPU time approximately decreased linearly with the initial step increased (Figure 6), which supports that employing a small initial time step can effectively alleviate the need for a time-adaptive solver.
#### 3.1.2 Various Spatial Discretization
The comparison between fully coupled and semi-coupled method was also conducted under various spatial discretization (Figures 7a-7f). The semi-coupled method exhibited similar \(\delta^{\mathrm{5}}\)H transit profiles as the fully coupled method. The difference between these two methods was diminished as spatial step decreased (Figures 7g-7i). However, the unreasonable negative \(\delta^{\mathrm{2}}\)H values can be observed again at the bottom from semi-coupled method (Figures 7d-7f), as appeared under various temporal discretization (Figure 5). This illustrated that the semi-coupled method is more sensitive to spatial discretization than the fully coupled method.
Again, the solver CPU times for both fully coupled and semi-coupled methods under various spatial discretization were presented in Figure 8. Specifically, with spatial discretization of \(\Delta z\) = 0.005 m, 0.01 m, and 0.05 m, the solver CPU times for the fully coupled method were 21.0 s, 14.4 s, and 14.5 s, respectively (Figure 8). By contrast, the corresponding times for the semi-coupled method were 29.9 s, 29.2 s, and 28.9 s under the same conditions. The consistently lower CPU times from the fully coupled method than the semi-coupled method confirms the enhanced efficiency of the fully coupled approach.
Figure 8: The solver CPU time of fully coupled and semi-coupled version of MOIST under a temporal discretization of 25 s and spatial discretization of 0.005 m, 0.01 m, and 0.02 m, respectively.
Figure 7: Comparison of simulated transient hydrogen isotope (\(\delta^{\mathrm{5}}\)H) profiles using fully coupled and semi-coupled solute transport methods under unsaturated, non-isothermal conditions at three spatial discretization, including 0.02 m (left), 0.01 m (center), and 0.005 m (right). Panels (a) to (c) show the \(\delta^{\mathrm{5}}\)H profiles from the fully coupled method. Panels (d) to (f) show the \(\delta^{\mathrm{5}}\)H profiles from the semi-coupled method. Panels (g) to (i) show the absolute differences in the \(\delta^{\mathrm{5}}\)H profiles between the fully coupled and semi-coupled methods. FC, SC, and D represent fully coupled solutions, semi-coupled solutions, and the differences between two solutions, respectively. A threshold of \(-0.3\%\) was set as the largest acceptable deviation from 0 to 0.1\(\%\) as the maximum deviation between the fully coupled and semi-coupled methods because they cannot produce identical numerical solutions.
### Semi-Analytical Tests Under Unsaturated Non-Isothermal Conditions
Under unsaturated conditions, a drying layer appeared at the soil surface (Figure 9a) and water flow in this region was dominated by upward vapor diffusion (Figure 9b). The total water flux within the column was uniform with depth (Figure 9b) because a steady state flow was achieved. \(\delta^{2}\)H and \(\delta^{18}\)O increased sharply with depth until reaching their peak values at approximately 0.02 m below the soil surface, which is the location of the bottom of the drying layer (Figures 9c and 9d). This differs from the saturated conditions (Supporting Information S1), where the maximum \(\delta^{2}\)H and \(\delta^{18}\)O appeared at the soil surface. This is because in the unsaturated system the soil water content at the air-soil interface was close to residual soil water content: when a drying layer forms, the air invades into the drying layer, resulting in a downward shift of the isotope peak values as compared to the saturated system.
Visually, the analytical solution and the estimates from MOIST agreed very well across the entire soil profile (Figures 9c and 9d). If numeric models are biased, they tend to be biased at locations where sharp changes of isotope occur. Therefore, we compared the simulated peak concentrations obtained from the MOIST and the analytical solutions. Quantitatively, the approaches agreed well at the maximum \(\delta^{2}\)H and \(\delta^{18}\)O (Table 3). They also agreed in terms of the slopes of HDO/H\({}_{2}\)\({}^{18}\)O in the liquid and vapor dominated regions (Table 3). This demonstrates that MOIST is robust with respect to the accuracy of calculating isotope transport within soil.
[PERSON] et al. (2021) presented the simulated maximum \(\delta^{3}\)H and \(\delta^{18}\)O from a revised HYDRUS-1D model (rHZ for short) under unsaturated non-isothermal conditions with fine (\(\Delta z=1\times 10^{-6}\) m), medium (\(\Delta z=0.005\) m), and coarse (\(\Delta z=0.01\) m) spatial discretization. However, their spatial intervals were not uniformly distributed, except in the coarse spatial discretization scenario. Because MOIST currently does not support adaptive spatial steps (which will be addressed in the future), its results were compared with those of rHZ under the coarse scenario.
Table 4 showed that the largest differences in \(\delta^{2}\)H and \(\delta^{18}\)O between MOIST and the analytical solution were 0.31 and 0.98\(\%\)e, respectively. By contrast, these values were 34.68 and 24.88\(\%\)e from rHZ. Compared to rHZ, MOIST significantly reduced the numerical error of the maximum isotopic compositions between numerical and analytical solutions (Table 4), illustrating that MOIST offered better accuracy under the same spatial
Figure 9: Comparison of the semi-analytical test results from MOIST after steady state evaporation was reached under unsaturated and non-isothermal conditions. (a) Volumetric soil water content; (b) liquid and vapor flux; (c) simulated \(\delta^{2}\)H as a function of depth from numerical and semi-analytical solutions; and (d) simulated \(\delta^{18}\)O as a function of depth by numerical and semi-analytical solutions.
discretization scheme as compared to rHZ. Many factors could lead to the superior performance of MOIST. The most striking difference is that MOIST is based on the fully coupled method while rHZ is based on the semi-coupled method. In the semi-coupled method, mass balance errors from soil water and heat transport can be inflated by coarse spatial resolutions and transferred into isotope transport at each time step. This is reflected in the fact that fine spatial discretization is needed for rHZ to pass this analytical test. By contrast, there was little error transfer from the soil water and heat equations to the isotope equation in MOIST, because all the equations were integrated by the fully coupled method. These findings illustrated that the fully coupled method has the potential to improve numerical accuracy and stability under large spatial steps.
### Validation by the Long-Term Experiment at HBLFA Raumber-Gumpenstein
In the long-term validation, MOIST modeled the isotopic signals of drainage water under three scenarios: Soil hydraulic parameters calibrated by [PERSON] et al. (2012) (Scenario 1, Figure 10a), [PERSON] et al. (2022) (Scenario 2, Figure 10b), and MOIST (Scenario 3, Figure 10c).
In scenario 1, the MOIST model, as well as the HYDRUS-1D revised by [PERSON] et al. (2012) (rHS for short), reproduced temporal variations of measured \(8^{18}\)O in drainage water (Figure 10). However, the _NSE_, _KGE_, and _MAE_ of rHS were 0.35, 0.60, and 1.00%, respectively. By contrast, these indices from MOIST were 0.47, 0.58, and 0.92%, respectively, suggesting that MOIST slightly outperformed rHS when using parameters calibrated by
Figure 10: \(8^{\mathrm{rd}}\)O from seepage water over the course of the experiment at HBLFA Raumberg-Gumpenstein in Austria. Included are the measurement values, (a) simulations from MOIST (with and without fractionation) based on the parameters calibrated by [PERSON] et al. (2012) and simulations from [PERSON] et al. (2012), (b) simulations from MOIST based on parameters calibrated [PERSON] et al. (2022) under various isotopic compositions of atmospheric water vapor and results from [PERSON] et al. (2022); (c) simulations from MOIST after calibration. _NSE_, _KGE_, and _MAE_ are Nash-Sutcliffe Efficiency, Kling-Guppa Efficiency, and Mean Absolute Error, respectively.
rHS. Interestingly, although fractionation would typically result in more enriched isotopic compositions, this was not observed between the curves generated by rHS (without fractionation, represented by the blue solid line in Figure 10) and MOIST (with fractionation, represented by the red solid line in Figure 10). This discrepancy may be attributed to the possibility that the calibrated parameters do not precisely match MOIST. However, when the fractionation process was removed from MOIST, as expected, the temporal isotopic compositions became more depleted (red dash line in Figure 10). This underscores the significance of incorporating fractionation when modeling isotope transport within soil. In scenario 2, parameters calibrated by another version of revised HYDRUS-1D ([PERSON] et al., 2022, rHZ for short) were employed in MOIST for comparison. It can be observed that rHZ and MOIST generated comparable temporal patterns of drainage water isotopic compositions, especially after 1,500 days (Figure 10b). Quantitively, _NSE_, _KGE_, and _MAE_ of rHZ were 0.19, 0.58, and 1.15%, respectively. By contrast, these indices from MOIST were 0.33, 0.52, and 1.04%, respectively. The smaller errors (_MAE_) from MOIST supported the fully coupled method outperformed the semi-coupled method. Moreover, simulated isotopic signals of outflow from MOIST under various \(\delta_{u}\) values illustrated a marginal influence of \(\delta_{u}\) on the time series of outflow isotopic signals (Figure 10b).
Results from scenario 3 demonstrated that accuracy of predictions from MOIST benefited significantly from calibration (Figure 10c). The temporal trend of 8\({}^{18}\)O of drainage water fitted well to the measurements, especially from the first 600 days. Moreover, the highest _NSE_ (0.48), _KGE_ (0.76), and the smallest _MAE_ (0.90) among the three scenarios not only confirmed the outperformance of MOIST, but also underscored the importance of calibration when applying a hydrological model into real conditions.
### Calibrated Soil Hydraulic Conductivities and the Longitude Dispersivity
Only saturated hydraulic conductivity (\(K_{sat}\)) and longitudinal dispersivity were calibrated in MOIST (Table 5) and the remaining parameters were maintained as calibrated by [PERSON] et al. (2012). This is because MOIST exhibited better accuracy with [PERSON] et al. (2012) calibrated parameters compared to those calibrated by [PERSON] et al. (2022) (Figure 10).
MOIST yielded \(6.08\times 10^{-2}\) m for longitudinal dispersivity, which is close to initial values (\(4.70\times 10^{-2}\) m, Table 5). For saturated hydraulic conductivities (\(K_{sat}\)), initial values (from rHS) were \(1.27\times 10^{-5}\), \(6.94\times 10^{-4}\), and \(1.27\times 10^{-5}\) m s\({}^{-1}\) for three horizons, with corresponding _MAE_ values of estimated \(K\) were \(1.83\times 10^{-6}\), \(4.7\times 10^{-5}\), and \(3.47\times 10^{-6}\) m s\({}^{-1}\), and the overall _MAE_ is \(1.8\times 10^{-5}\) m s\({}^{-1}\). By contrast, MOIST calibrated \(K_{sat}\) values for three horizons to \(4.20\times 10^{-6}\), \(5.80\times 10^{-4}\), and \(5.72\times 10^{-6}\) m s\({}^{-1}\), with respective _MAE_ values of estimated \(K\) were \(5.37\times 10^{-7}\), \(3.92\times 10^{-5}\), and \(3.89\times 10^{-7}\) m s\({}^{-1}\), and the overall _MAE_ is \(1.48\times 10^{-5}\) m s\({}^{-1}\). In comparison to initial values from rHS, MOIST exhibited smaller errors of \(K\) that calculated from calibrated \(K_{sat}\). This suggested that the results from MOIST were acceptable, although the calibration of MOIST was simplified (fewer objective functions than rHS).
\begin{table}
\begin{tabular}{c c c c c c c} \hline & Layers (m) & Longitude dispersivity (m) & \(K_{sat}\) (m s\({}^{-1}\)) & _MAE_ of \(K\) (m s\({}^{-1}\)) & Overall _MAE_ of \(K\) (m s\({}^{-1}\)) & Objective functions \\ \hline [PERSON] et al. (2012) & 0–0.30 & \(4.70\times 10^{-2}\) & \(1.27\times 10^{-5}\) & \(1.83\times 10^{-6}\) & \(1.80\times 10^{-5}\) & _SW_; \(\delta_{Bt}\); \(K\); \(BC\); \(BF\)-\(t\) \\ & 0.31–0.90 & & \(6.94\times 10^{-4}\) & \(4.70\times 10^{-5}\) & & \\ & 0.91–1.50 & & \(1.27\times 10^{-5}\) & \(3.47\times 10^{-6}\) & & \\ MOIST & 0–0.30 & \(6.08\times 10^{-2}\) & \(4.20\times 10^{-6}\) & \(5.37\times 10^{-7}\) & \(1.48\times 10^{-5}\) & \(\delta_{Bt}\); \(BF\)-\(T\) \\ & 0.31–0.90 & & \(5.80\times 10^{-4}\) & \(3.92\times 10^{-5}\) & & \\ & 0.91–1.50 & & \(5.72\times 10^{-6}\) & \(3.89\times 10^{-7}\) & & \\ \hline \end{tabular} _Note._ The calibration of longitude dispersivity is not evaluated because the measurements are not available. _SW_, \(\delta_{Bt}\), \(K\), _RC_, \(BF\)-\(t\), and _BF-\(T\)_ are soil water content measurements, isotopic compositions of bottom flow, unsaturated hydraulic conductivities, soil water retention curve measurements, time series bottom flow, and total bottom flow, respectively. _MAE_ of \(K\) is calculated by averaging errors between modeled \(\mathcal{K}\) (estimated by the measured \(K(h)\) and calibrated \(K_{sat}\)) and measured \(\mathcal{K}\).
\end{table}
Table 5: _Initial Longitude Dispersivity and Saturated Hydraulic Conductivities From [PERSON] et al., (2012) and Calibrated by MOIST_
## 4 Discussion
### Difference Between the Fully Coupled Method and the Semi-Coupled Method
The semi-coupled variation of MOIST exhibited unfeasible \(\delta^{2}\)H values across various spatial and temporal discretization, a problem not encountered by the fully coupled version of MOIST (Figures 5 and 7). This discrepancy can be attributed to the fact that mass balance errors arising from solving soil water and heat transport equations are introduced into the isotope transport equation within the semi-coupled method. By contrast, the fully coupled method avoids this issue by analytically integrating the soil water and heat transport equations into the isotope transport equation (Equations 36 and 37). This aligns with the findings of [PERSON] and [PERSON] (2019), who also observed that the fully coupled method excels in capturing coupled physical processes, mitigating errors, and delivering more precise outcomes when compared to the semi-coupled approach.
Moreover, it is worth noting that the disparities between the fully coupled and semi-coupled methods diminished as finer temporal and spatial steps were employed (Figure 5). This phenomenon can be attributed to the fact that the finer spatial and temporal discretization leads to reduced mass balance errors in solving the soil water and heat transport equations ([PERSON] et al., 2005; [PERSON] et al., 2018; [PERSON] et al., 2021). However, a surprising trend can be observed that as the layer thickness decreased in the semi-coupled simulations, a longer dark blue band appeared at the bottom of the column (Figures 6(d)-6(f)). This phenomenon can be attributed to numerical instability in the differential equations. To ensure numerical stability, adherence to CFL (Courant-Friedrichs-Lewy) condition is essential ([PERSON] et al., 1967):
\[\left|\frac{\zeta\Delta t}{\Delta z}\right|<\ \varepsilon_{max} \tag{50}\]
where \(\varepsilon_{max}\) is typically set to 1. This equation stipulates that the spatial step (\(\Delta z\)) should not be excessively small compared to the temporal step (\(\Delta t\)), as excessively small \(\Delta z\) values can lead to numerical oscillations. In the case of the semi-coupled method, where \(\Delta t\) was 25 s, decreasing \(\Delta z\) resulted in a larger \(\left|\frac{\zeta\Delta t}{\Delta z}\right|\) value, increasing the likelihood of instabilities. However, in the fully coupled method, as shown in Figures 5 and 7, the relationship between instability and spatial step size was less evident. This could be due to the scaling down of \(\varsigma\) by coefficients from the soil water and temperature equations (Equations 26 and 27), which may reduce the value of \(\left|\frac{\zeta\Delta t}{\Delta z}\right|\). Consequently, compared to the semi-coupled method, the fully coupled method demonstrated greater stability across a range of spatial step sizes, highlighting its superior reliability in predicting temporal variations in the isotopic compositions of soil water.
While our tests were conducted under ideal boundary conditions, the results aligned with the findings presented in [PERSON] and [PERSON] (2004). They further underscore the fact that the fully coupled method effectively minimizes errors and displays reduced sensitivity to variations in spatial and temporal step sizes. This attribute enhances the accuracy of one-dimensional isotope transport simulations. However, the semi-coupled method has advantages in steady-state systems. By assuming linear changes in the water and heat solution within the time step, the isotope equation in the semi-coupled method can use a smaller time step, improving the stability of the isotope solution, although at the cost of increased computation time. In our simulations (Sections 2.2.1), to ensure consistency, the time step for the isotope equation in the semi-coupled method was kept the same as that for the water and heat equations, but the time consumption of semi-coupled method was doubled compared to the fully coupled method, as shown in Figure 6. This contrasts with the theoretical expectation that the semi-coupled method should generally be faster due to its lower memory and computational requirements per iteration ([PERSON] and [PERSON], 2021; [PERSON] and [PERSON], 2019). Several factors can contribute to this discrepancy.
First, the choice between using the semi-coupled method and the fully coupled method depends on the degree of coupling exhibited by the variables involved ([PERSON] and [PERSON], 2019). In our study, all variables are tightly coupled due to intricate interactions between water and heat transport, which concurrently influence the movement of isotopes. Solving a coupled system in a segregated manner may lead to increased computational time, as it may require more iterations for convergence to occur ([PERSON] and [PERSON], 2004). Notably, the semi-coupled method consumed more time because it necessitates two solver calls within a single time step, whereas thefully coupled method requires only one call. This observation is supported by the solver CPU time (Figures 6 and 8).
Second, it is essential to consider the scale of the problem. In our tests, we examined a relatively small-scale problem, with the minimum spatial discretization (\(\Delta z\)) is 0.005 m. This means that the semi-coupled method processed two matrices with sizes of \(400\times 400\) and \(200\times 200\), respectively (Figure 10(a)). By contrast, the fully coupled method handled a single matrix with a size of \(600\times 600\) (Figure 10(a)). Both matrix size and quantity are critical factors influencing solver CPU times. With a smaller matrix size (resulted from a larger \(\Delta z\)), the fully coupled method can be faster than the semi-coupled method because both methods require similar CPU time per solver call, but the semi-coupled method calls the solver twice. However, for a larger matrix size (resulted from a smaller \(\Delta z\)), the efficiency of the fully coupled method may decrease, as processing a single large matrix can significantly increase RAM usage and processing time compared to handling two sub-matrices in the semi-coupled method (Figure 10(a)). For example, the solver CPU times of the semi-coupled method were 2 times larger than that of the fully coupled method when \(\Delta z\) = 0.02 and 0.01 m, but 1.4 times larger when \(\Delta z\) = 0.005 m (Figure 8). This suggested that the efficiency of fully coupled method depends on the scale of the problem (e.g., the number of soil layers) ([PERSON] & [PERSON], 2019).
To better illustrate the influence of problem scale (\(\Delta z\)) on the solver CPU time, we attempted finer simulations, such as \(\Delta z\) = 0.001 m, but non-convergence of the upper boundary solutions occurred in MOIST. To resolve this, \(\Delta t\) must be reduced but reducing the initial \(\Delta t\) alters the simulation conditions, making the solver CPU time non-comparable. Although the current version of MOIST cannot explicitly explore larger simulation problems without
Figure 11: Illustration of matrices sizes from fully coupled method and semi-coupled method (Panel a); Panel b is the solver CPU time comparison between fully coupled method and semi-coupled method across various spatial discretization.
modifying initial \(\Delta t\), we developed a simplified example (codes are available from the Supporting Information S1) with six different \(\Delta z\) levels (0.0005 m, 0.001 m, 0.005 m, 0.01 m, 0.05 m, and 0.1 m) to compare time consumption of the fully coupled method and semi-coupled method across different problem scales (\(\Delta z\)). It can be found that the solver CPU times for the fully coupled and semi-coupled methods followed the same trend as seen in Figure 8 when \(\Delta z>0.005\) m (Figure 11b). For smaller \(\Delta z\) values, the solver CPU time for both methods increased sharply due to larger matrix sizes. When \(\Delta z\) was 0.0005 m, the time consumption of both methods was similar (Figure 11b). Consequently, it is expected that for even finer discretization, such as \(\Delta z=0.0005\) m, the fully coupled method may spend more time than the semi-coupled method ([PERSON] & [PERSON], 2021; [PERSON] & [PERSON], 2019). However, such a fine spatial discretization is uncommon in practice, and the resulting matrix size is extremely large (60,000 \(\times\) 60,000 for the fully coupled method, 40,000 \(\times\) 40,000 and 20,000 \(\times\) 20,000 for the semi-coupled method), potentially causing an \"out of memory\" error. Presently, research on isotope transport in soil and plant root water uptake typically focuses on depths around 2 m ([PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2004; [PERSON], 2017) with a spatial interval of \(\Delta z=0.01\) m (e.g., the lysimeter simulation in this study). Under these conditions, the matrix to be solved typically has a size of 600 \(\times\) 600. Therefore, the fully coupled method offers advantages in terms of computation time when compared to the semi-coupled method.
### Outperformance of MOIST Under the Semi-Analytical Test and the Long-Term Lysimeter Simulation
The fully coupled approach empowers MOIST to exhibit superior accuracy in theoretical tests when compared to the revised HYDRUS-1D (rHZ, [PERSON] et al., 2021). There are several distinctions between MOIST and rHZ, including model structure and algorithms. However, theoretical testing scenarios with fixed boundary conditions and parameters, as well as known true values, provide a controlled environment that isolates model differences and underscores the impact of the fully coupled and semi-coupled methodologies on the results.
It is worth noting that numerical errors originating from the soil water flow equation can be propagated to the isotope transport equations, potentially leading to the observed numerical oscillations (Figures 5 and 7). This issue has prompted previous models like SiSPAT-Isotope ([PERSON] et al., 2005) and the revised HYDRUS-1D ([PERSON] et al., 2021) to necessitate an extremely small thickness for the first soil layer (e.g., 1 \(\times\) 10\({}^{-6}\) m) to pass theoretical tests (Supporting Information S1).
However, in semi-analytical tests where spatial discretization is 0.01 m, error control of rHZ may not be as effective as it is under a finer spatial discretization of 1 \(\times\) 10\({}^{-6}\) m. This discrepancy resulted in a significant difference between rHZ and the semi-analytical solution. Therefore, it is crucial for a semi-coupled method to rigorously manage mass balance errors ([PERSON] et al., 2019). By contrast, when equations are solved using the fully coupled method, fewer mass balance errors are transferred between equations ([PERSON] & [PERSON], 2004; [PERSON], 2004; [PERSON] et al., 1996), a fact that has been verified through temporal and spatial discretization tests (Figures 5 and 7). Consequently, MOIST outperformed rHZ under a coarse spatial discretization in the semi-analytical test (Table 3).
Under the long-term lysimeter simulation, the fully coupled method outperforms the semi-coupled method in simulating isotope transport. Both MOIST and rHZ consider fractionation. Notably, MOIST utilizes parameters that have been calibrated by rHZ, and it exhibits a slight but discernible advantage in performance over rHZ (Figure 10). Moreover, the calibrated parameters from [PERSON] et al. (2012) were applied to rHZ, the resulting Nash-Sutcliffe Efficiency (NSE) was 0.19 ([PERSON] et al., 2021), while MOIST achieved a notably higher NSE of 0.47. This discrepancy, with rHZ yielding a smaller NSE compared to MOIST, supports the idea that the semi-coupled method may introduce more mass balance errors into the process of isotope transport when compared with the fully coupled method. Additionally, as demonstrated by the theoretical test, under the spatial step of 0.01 m (used in the lysimeter simulation), the maximum errors between the semi-analytical solution and the semi-coupled method from rHZ exceeded those from MOIST (Table 4). This evidence, along with the above-mentioned discrepancy underscores the robustness and effectiveness of the fully coupled approach as adopted in MOIST.
### Applications for MOIST
As a one-dimensional isotope transport simulator, MOIST contributes to enhancing the precision of calibrated model parameters, such as saturated hydraulic conductivities and isotopic longitudinal dispersivity, as demonstrated in this study (Table 5). This improvement is attributed to the fact that the fully coupled method employed in MOIST reduces errors of simulated isotopic signals. Previous studies confirmed that incorporating isotopic and soil water information can enhance the accuracy of model calibration ([PERSON] and [PERSON], 2020; [PERSON] et al., 2022). However, model accuracy is a fundamental requirement. When the model itself generates numerical errors, these errors are compensated by calibrated parameters, potentially leading to biased parameter values. For instance, [PERSON] et al. (2022) obtained the calibrated soil saturated hydraulic conductivity was two orders of magnitude smaller than that reported by [PERSON] et al. (2012). The greater \(K_{\text{sat}}\) from [PERSON] et al. (2012) is a result of ignoring fractionation. As is known, fractionation reduces the evaporative isotopic flux. To achieve a satisfactory fit between observations and predictions of outflow isotopic signals, neglecting fractionation forces longitudinal dispersivity to increased and downward convection to decreased ([PERSON] et al., 2022). However, it is worth noting that the spatial step used in [PERSON] et al. (2022) was 0.01 m, which could produce significant numerical errors (Table 3). Such errors can lead to overly enriched isotopic signals, thereby amplifying the influence of fractionation ([PERSON] et al., 2016). Consequently, it remains unclear whether the impact of fractionation on model calibration results from fractionation itself or from compensation for numerical errors. By contrast, the fully coupling scheme of MOIST leads to more accurate isotope simulations and consequently has a smaller impact on parameter calibration compared to the semi-coupled method (Table 5). This not only enables MOIST to derive more accurate model parameters but also potentially offers a better understanding of the impact of evaporative fractionation on model calibration.
Moreover, MOIST can be used to test assumptions and validate methods in water transit time estimations ([PERSON] et al., 2022) and evaporation estimation studies ([PERSON] et al., 2017; [PERSON] et al., 2021; [PERSON] et al., 2021). This is because MOIST can construct high-precision and high-resolution spatial-temporal distributions of isotopic species, which is crucial for studying water transit time ([PERSON] et al., 2022). Understanding water transit time, also known as water age distribution, is essential for comprehending the connectivity between sources of transpiration, streamflow, groundwater recharge ([PERSON] et al., 2022), and the water cycles in the critical zone ([PERSON] et al., 2022). However, challenges persist in obtaining high-precision soil and plant water isotope data ([PERSON] et al., 2022), despite related research efforts ([PERSON] et al., 2016; [PERSON] et al., 2017). Additionally, various methods for water age estimation based on discrete isotopic measurements often exhibit discrepancies and large uncertainties ([PERSON] et al., 2022; [PERSON] et al., 2023). For instance, in the Bruntland Burn catchment, [PERSON] et al. (2018a) simulated a watershed water age of approximately 2 years (using the instantons age mixing method), contrasting with 1.2 years (using flux tracing) reported by [PERSON] et al. (2015) and approximately 1 year (using StorAge Selection) reported by [PERSON] et al. (2017). Due to the absence of true values, the accuracy and effectiveness of different methods remain unknown. Addressing this issue, MOIST can generate high-resolution spatial-temporal isotopic profiles, enabling the derivation of transit time from these profiles to serve as ground truth, especially incorporating with recent developed continuous plant water sourcing models, such as CrisPy ([PERSON] et al., 2024) and PRIME ([PERSON] et al., 2024). While other semi-coupled method-based numerical models can perform similar tasks, the accuracy of isotopic profiles may be affected by numerical oscillations (Figures 5 and 7), leading to increased uncertainties. Although MOIST is a one-dimensional model and water transit time studies are primarily conducted at the watershed scale ([PERSON] et al., 2022), smaller-scale experiments coupled with accurate modeling serve as the foundation for upscaling ([PERSON] et al., 2021; [PERSON] et al., 2019). Therefore, MOIST holds promise for transit time studies and cross-validating various water transit time estimation methods.
Regarding the evaporation estimation, MOIST can validate methods for calculating short-term and long-term evaporation based on measured isotopic compositions of soil water. For example, [PERSON] et al. (2017) determined evaporation rates from measured soil water isotopic compositions, while [PERSON] et al. (2021) computed long-term evaporation rates from deep soil isotopic compositions. Both approaches rely on the assumption that sampled soil isotopic compositions at specific depths (shallow or deep soil) retain the evaporation signal. Understanding how much evaporation signal is preserved by the isotopic composition at a given depth is crucial for assessing the accuracy of calculated evaporation rates from methods such as those of [PERSON] et al. and [PERSON] et al. This assessment necessitates high-resolution (both temporal and spatial) data on soil evaporation rates and soil water isotopic compositions, which can be challenging to obtain. MOIST can bridge this gap through simulations.
### Limitations and Future Work
First, in the long-term lysimeter study simulation (Figure 10), a notable observation emerged regarding the simulated \(\delta^{18}\)O values. Regardless of whether the model is calibrated or not, or whether it considers fractionation, there was a consistent underestimation of \(\delta^{18}\)O between the 1,200 th and 1,500 th days. This discrepancy can likely be attributed to the phenomenon of preferential flow. During this period, there was a significant influx of precipitation that was relatively enriched in \(\delta^{18}\)O, occurring between the 1,050 th and 1,300 th days. This enriched rainfall contributed to the \(\delta^{18}\)O enrichment of water reaching the bottom of the lysimeter. Consequently, a portion of this enriched water was transported to the bottom of the soil column via preferential flow pathways, resulting in an overall increase in \(\delta^{18}\)O of drainage water. It is worth noting that in the MOIST, rHZ, and rHS models, preferential flow is not considered for isotope transportation. This omission leads to the systematic underestimation of \(\delta^{18}\)O.
Previous research has demonstrated that different modes of soil water mobility, such as preferential and piston flow, as well as mobile and immobile soil water, can significantly influence the isotopic composition of bulk soil water ([PERSON] et al., 2022; [PERSON] et al., 2018). This effect becomes particularly pronounced when substantial rainfall infiltration occurs, potentially giving rise to significant preferential flow events that closely mirror the isotopic signals of the input water. By contrast, the current version of MOIST does not account for preferential flow, resulting in incomplete simulations. To rectify this limitation and better understand hydraulic processes, it is imperative to incorporate preferential flow and its impact on isotopic variations in bulk soil water. Neglecting these factors in isotope simulations can lead to biased interpretations of runoff generation and evaporation ([PERSON] et al., 2015). Therefore, future iterations of MOIST should consider implementing a two-pore domain model to provide a more comprehensive simulation of isotope transport processes within the soil. Such enhancements are likely to result in improved simulation accuracy ([PERSON] et al., 2018).
Second, the current version of MOIST relies on field measurements from [PERSON] et al. (2012) to represent \(\delta_{a}\) during rain-free period when simulating the long term lysimeter study. By contrast, the approach presented by [PERSON] et al. (2021) for estimating \(\delta_{a}\) is locally suitable. However, this local method was unable to be applied in MOIST because in [PERSON] et al. (2021), the isotope value of topmost soil layer can be computed from the solution of each time step and used in this local method directly. By contrast, MOIST operates on a cell-centered scheme, resulting in the surface soil water isotopic compositions being unknown at the commencement of each time step. Deriving the isotope concentrations of surface soil water in MOIST necessitates computation based on isotope mass balance between the top-half layer and the isotope value in the atmosphere (refer to Equation 25). Consequently, the formula proposed by [PERSON] et al. (2021) is inapplicable in MOIST as one equation cannot resolve two unknowns simultaneously. In the future iterations of MOIST, we aim to incorporate the equations for local \(\delta_{a}\) to better describe isotope transport processes.
Lastly, the primary objective of this study is to assess the performance of MOIST under various conditions and demonstrate the performance of the fully coupled method. Consequently, during the model comparison, we refrained from conducting an exhaustive calibration for MOIST. Notably, with the inclusion of calibrated saturated hydraulic conductivities, our model exhibited smaller errors compared to other models. Furthermore, the calibrated ranges of saturated hydraulic conductivities were smaller than the initial values (as shown in Table 5), aligning with the findings of [PERSON] et al. (2022) under the same data set. This alignment underscores the acceptability of the calibrated saturated hydraulic conductivities and longitudinal dispersivity. It instills confidence that a more comprehensive calibration process could further enhance the capacity of MOIST for accurate simulations.
We concur with the notion that for practical model applications, comprehensive calibration using independent data is indispensable ([PERSON] et al., 2018; [PERSON] et al., 2021). This necessity arises due to the inherent uncertainties associated with many parameters. Calibration serves the purpose of refining the model by imposing constraints, resulting in a more accurate representation of potential hydrological processes. Therefore, in forthcoming iterations, we intend to implement comprehensive calibration as an integral step toward practical applications.
## 5 Conclusions
We developed MOIST, a novel soil water and isotope transport model using MATLAB programming language. MOIST is unique in that it solves water, vapor, heat, and isotope transport simultaneously with a fully coupledmethod and with a cell-centered numerical approximation to the derivatives. MOIST successfully passed well-known theoretical tests, and semi-analytical solutions. Due to its adoption of fully coupled solution method, MOIST can predict isotope profiles under various temporal and spatial discretization with greater accuracy and stability than the existing semi-coupled models. We also tested MOIST against well-controlled long-term lysimeter studies at HBLFA Raumberg-Gumpenstein in Austria. Results showed good agreement between measured and predicted values and outperformed HYDRUS-1D. Given the evidence accrued in this study, it can be concluded that MOIST can be a robust tool for simulating one-dimensional isotope transport within soil. Moreover, the model is open-source and thus can be customized according to different requirements. As such, the adopted equations and parameters can be easily updated as our knowledge about isotope fractionation and transport continues to expand, making MOIST a suitable tool for current and future exploration of isotope transport in the soil-vegetation-atmosphere continuum.
## Data Availability Statement
Source codes of MOIST ([PERSON] & Si, 2023) used for semi-analytical tests, theoretical tests, calibration, and the long term lysimeter study tests were developed by MATLAB R2022a and available via Creative Commons Attribution 4.0 International license through [[https://zenodo.org/records/8397416](https://zenodo.org/records/8397416)]([https://zenodo.org/records/8397416](https://zenodo.org/records/8397416)). The long term lysimeter measurements are available in [PERSON] et al. (2012).
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wiley/ffea1893_168d_4360_9077_d9071300eca6.md | ([PERSON] & [PERSON], 1981; [PERSON] & [PERSON], 2018) is inconsistent with the elastic properties reported so far for solid iron phases ([PERSON] et al., 2007; [PERSON] et al., 2022; [PERSON], 2007; [PERSON] & [PERSON], 2022; [PERSON] et al., 2001), an observation that requires the introduction of other mechanisms such as interstitial impurities ([PERSON] et al., 2022), melt ([PERSON], 2007) and/or polycrystallinity ([PERSON] et al., 2007; [PERSON] & [PERSON], 2022) in quantitative microscopic models of the inner core.
On the theory side, atomistic simulations have attempted to shed light on the phase diagram of solid iron at core conditions, but simulations are challenged by the large sizes and long times required to explore the complex phase space of possible configurations and by the necessity to retain _ab-initio_ energetic accuracy in order to distinguish between the different structures. The \(T_{m}\) determined by atomistic methods at ICB pressures ranges from 5,400 ([PERSON] et al., 2000) to 6,900 K ([PERSON] & [PERSON], 2009), depending on the simulation size, method, and interatomic potential employed. The dependence of the thermodynamical properties on the size of the simulation is especially problematic in the case of bcc iron, whose thermodynamical and mechanical stability (including elastic stability, i.e. stability against strain distortions) are still debated. Although bcc iron is mechanically unstable at low temperature ([PERSON] et al., 2003), _ab-initio_ lattice dynamics ([PERSON] et al., 2010) and molecular dynamics (MD) ([PERSON] et al., 2003; [PERSON] et al., 2003) studies with small simulation cells found that vibrational anharmonicities make bcc iron mechanically stable at high temperatures, and contribute to lower its free energy to values that are close to that of hcp iron at core conditions ([PERSON] & [PERSON], 2023; [PERSON] et al., 2023; [PERSON] et al., 2003). A recent _ab-initio_ study with 2,000 atoms has confirmed that bcc iron is mechanically stable at 360 GPa and 6,600 K ([PERSON] et al., 2022). However, earlier simulations conducted with up to 180 atoms ([PERSON] et al., 2015) found that bcc iron violates the Born stability criteria, and thus is elastically unstable at Earth's core conditions. Therefore, it appears that the mechanical stability of bcc iron is remarkably sensitive to the simulation size.
More importantly, anomalously fast self-diffusion has been observed in large-scale MD simulations for bcc iron ([PERSON] et al., 2017), while no self-diffusion has been reported in simulations involving small cells ([PERSON] & [PERSON], 2023; [PERSON] et al., 2023; [PERSON] et al., 2003). Large self-diffusion, if confirmed, invalidates the use of most theoretical methods used so far to determine the free energies of solid iron at core conditions. For example, phonon-based methods are based on the principle that the direct use of the ideal crystal acts as a reference state, but the principle is clearly violated in the presence of substantial atomic self-diffusion. In addition, it casts doubt on the accuracy of simulations carried out with cell sizes and time-scales that may not be sufficiently large to show self-diffusion ([PERSON] & [PERSON], 2023; [PERSON] et al., 2023; [PERSON] et al., 2003), as already pointed out in [PERSON] et al. (2017).
In this Letter, we determine the properties and relative stability of different structures of iron at Earth's core conditions based on an approach that retains the accuracy of _ab-initio_ methods but where the statistical sampling is accelerated with the help of a deep-learning model. The approach allows us to include atomic self-diffusion in the crystalline phases and more generally to overcome the limits on the system size and temporal scales faced by standard _ab-initio_ methods. Our results indicate that Gibbs free-energy differences between competing structures for pure Fe are small enough to open the possibility that the stability ordering of phases could be overturned by the presence of impurities, whose role is therefore crucial not only to account for the density deficit and for geochemical observations, but also to stabilize the correct crystal structure of Fe in the Earth's inner core. Different competing phases however differ substantially in terms of elastic properties and seismic velocities, with bcc Fe coming much closer to seismic data for the shear wave velocity of the inner core than all other considered structures.
## 2 Methodology
### The Deep-Learning Interatomic Potential
Although the accuracy of _ab-initio_ methods based on density-functional theory (DFT) ([PERSON], 1964; [PERSON], 1965; [PERSON], 1965) in describing the potential energy surface of a large system of atoms is unsurpassed, _ab-initio_ simulations are challenged by the large simulation sizes and times that are required to obtain free energies and elastic constants that are precise enough to solve the most relevant geophysical questions such as the crystal structure of the inner core and its shear wave velocities. Deep-learning interatomic potentials (DLP), based on deep neural networks, have emerged as an efficient method to accurately describe the DFT potential energy surface in a computationally cost-effective manner. In our recent work ([PERSON] & [PERSON], 2024),we constructed and validated a set of potentials for iron that cover hcp, fcc, and bcc structures as well as the liquid phase. These potentials exhibit accuracy comparable to DFT within the temperature range of 4,000-7,600 K and in the pressure range of 75-650 GPa. Due to the significant role played by temperature-dependent thermal electronic excitation, five DLP models have been established at temperatures of 4,000, 5,000, 6,000, 7,000, and 7,600 K. We exclusively utilize DLP-6000, trained at 6,000 K, for simulations conducted at the same temperature. Rigorous validation tests demonstrate their accuracy in large-scale simulations and in the presence of extended defects. Additionally, we benchmarked their Gibbs free energy difference compared to the DFT potential, which is found to be less than 6 meV/atom or 1% of the thermal energy. Remarkably, this difference is shown to be independent of pressure, temperature, and the number of atoms, further confirming the applicability of these models to large-scale simulations. In addition, we obtain elastic constants and self-diffusion coefficients that are essentially indistinguishable from the _ab-initio_ results, in those situations where a comparison is possible. More details on the construction of the deep-learning models and their validation can be found in [PERSON]. [PERSON] and [PERSON] (2024) and in the Supporting Information (Texts S1-S8 in Supporting Information S1).
### Molecular Dynamics Simulations
Molecular dynamics (MD) simulations with the DLP models were performed using LAMMPS([PERSON], 1995). Except for the thermodynamic integration calculations to determine the free energy (see below), the Nose-Hoover thermostat ([PERSON], 1985) and Martyna-Tobias-Klein barostat ([PERSON] et al., 1994) were used to control temperature and pressure, respectively. The timestep was set to 1 fs below 7,000 K and 0.5 fs at 7,600 K. Simulations lasted for more than 100 ps to reduce the statistical uncertainty. We used the Langevin thermostat in these thermodynamic integration calculations since the Nose-Hoover thermostat has difficulties in achieving ergodicity when the system is close to be harmonic, as discussed below.
### Free Energy Calculations
To determine the phase stability and melting line, we calculated free energies for hcp, fcc, bcc and liquid iron using the thermodynamic integration method (TDI) method, which involves computing the free energy difference between the system of interest and a reference system with known free energy (also see Texts S3-5 in SI). We used the Einstein crystal as the reference for solids and the ideal gas for the liquid phase. The free energy calculations followed a three-step sequence. First, we applied TDI to compute the free energy difference between the reference system and a Lennard-Jones (LJ) model developed using the force-matching algorithm ([PERSON] et al., 2004). Next, we determined the free energy difference between the LJ and DLP models. Finally, we applied a correction from DLP based on free energy perturbation theory to achieve DFT accuracy, with the correction typically as low as 6 meV/atom ([PERSON] et al., 2000; [PERSON] & [PERSON], 2024). Error bars on melting lines include all statistical uncertainties arising from the calculation of free energies.
Special consideration is required when determining the free energy for the bcc phase. Since direct TDI simulations from a diffusive system to the Einstein crystal are not physically feasible, we tuned the parameters of the LJ potential to ensure that it has no self-diffusion and then determined its free energy. Subsequently, we transitioned from LJ to the DLP model for the bcc phase. We have thoroughly checked the continuity of the transformation and found the absence of first-order transitions by monitoring self-diffusivity as the coupling constant varied from the LJ to DLP sides. It should be noted that a similar method has been employed to determine the free energy of a superionic phase ([PERSON] & [PERSON], 2018). We have performed extra tests based on the coexistence method ([PERSON] et al., 1994) to obtain the free energy for bcc iron, and the resulting free energy shows good agreement with the TDI method (see Text S4 in SI). Additionally, we have verified the DFT correction based on perturbation theory is converged with system size by using a simulation cell up to 1,024 atoms, where the correction is typically less than 3 meV/atom ([PERSON] & [PERSON], 2024). The effects of self-diffusion have been properly taken into account by the configurations extracted from MD simulations using DLP models that exhibit self-diffusion.
### Mechanical Stability and Elastic Constants
The mechanical stability and the elastic constants of bcc and fcc iron were calculated using the stress-strain method as in our previous studies ([PERSON] & [PERSON], 2022). In this method, the deviatoric stress on a distorted simulation cell after applying a small strain was estimated by performing MD simulations in the canonical diffusion in the bcc structure, independent of the simulation size (Figure 1). However, diffusion events are more rare in the 128-atom system where more than 100 ps are required to observe a few diffusion events. The calculated self-diffusion coefficient for bcc iron \(\left(2\times 10^{-10}\mathrm{m^{2}/s}\right)\) agrees with previous _ab-initio_ results \(\left(1.8\times 10^{-10}\mathrm{m^{2}/s}\right)\)([PERSON] et al., 2019), which further confirms the accuracy of the DLP employed in our study, and is only an order of magnitude smaller than in the liquid ([PERSON] et al., 2000).
We found that diffusion takes place primarily by cooperative atomic hopping to the nearest lattice sites along the \(\left(111\right)\) crystallographic direction. In rare cases, iron atoms also move along the \(\left(100\right)\) or \(\left(110\right)\) directions (see Figures S2-2 in Supporting Information S1). It should be noted that the observed diffusion direction differs from that reported in ([PERSON] et al., 2017), where diffusion was observed only along the \(\left(110\right)\) direction.
Large and cooperative self-diffusion at high temperatures has been observed in other bcc metals (Kadkhodaei and Davariashtiyani, 2020). We find that atomic diffusion is the result of rapid and temporally well-defined concerted events during which all atoms exchange their positions cooperatively in a loop. In some cases the diffusion event starts with the creation of a vacancy-interstitial pair and terminates with the annihilation of the defect (see Figures S2-2 in Supporting Information S1) We stress that, from a practical point of view, the presence of self-diffusion invalidates the use of approaches for the calculation of free energies directly based on the ideal crystal as a reference, such as anharmonic phonon approximations ([PERSON] et al., 2017) and direct thermodynamic integration from the [PERSON] crystal ([PERSON] et al., 2003).
As a necessary condition for thermodynamic stability, the local mechanical stability of bcc iron at Earth's core conditions was investigated by performing molecular dynamics simulations with up to 128,000 atoms at different pressure and temperature conditions. In addition to monitoring the presence of bcc long-range order in the simulation cell, the stability of bcc iron against elastic instabilities was checked by determining the elastic constants with the stress-strain method. We found that bcc iron becomes mechanically stable in a narrow range of temperatures close to the melting point (Figure 1). Below the Born stability line, bcc iron transforms, in our simulations, into an fcc structure (see Figures S6-4 and S6-5 in Supporting Information S1), instead of the hcp iron at 360 GPa. In a previous study ([PERSON] et al., 2015), the transformed structure from bcc iron was classified as hcp. However, their analysis was based on a comparison of pair-distribution functions and on the use of a small 216-atom simulation cell. The fcc and hcp structures exhibit nearly identical pair-distribution functions below 5 A ([PERSON] and [PERSON], 2024), and a correct assignment becomes challenging with small cells.
It has been argued, based on self-consistent anharmonic lattice dynamics calculations, that the temperature-induced mechanical stability of bcc iron is due to phonon anharmonicity ([PERSON] et al., 2010). We calculated the
Figure 1: Calculated melting lines for the solid phases considered in this work. Rec iron is mechanically unstable below the instability line (light blue). The inset shows the atomic mean-squared displacements for bcc iron from simulations at 360 GPa and 7,000 K, with 128 and 1,024 atoms, averaged over initial times. The slope of the mean square displacement with 1,024 atoms corresponds to a diffusion coefficient of \(2\times 10^{-10}\mathrm{m^{2}/s}\).
second-order derivative of the free energy of bcc iron with respect to atomic displacements from the ideal crystal positions and found the presence of unstable modes with negative curvature at all temperatures from 4,000 to 7,000 K (see Figures S6-6 in Supporting Information S1). Contrary to previous claims ([PERSON] et al., 2010), and in agreement with more recent MD simulations ([PERSON] et al., 2017), we conclude that anharmonic contributions to the lattice free energy are not sufficient to stabilize bcc iron mechanically, and that therefore self-diffusion is crucial to explain the mechanical stability of bcc iron at 6,000 K.
### Relative Phase Stability at Earth's Core Conditions
Having demonstrated the mechanical stability of bcc iron at core conditions, we calculated the Gibbs free energies for bcc, hcp, fcc and liquid iron, and determined the phase diagram of iron from 100 GPa to 4,000 K up to 550 GPa and 7,600 K. Gibbs free energies were determined by the thermodynamic integration method ([PERSON] et al., 1999). Although the maximal discrepancy between the DLP model and the DFT energies is only 6 meV/atom ([PERSON] & [PERSON], 2024), Gibbs free energies determined with the DLP model were nonetheless corrected to achieve _ab-initio_ accuracy through free energy perturbation theory ([PERSON] et al., 2002; [PERSON] & [PERSON], 2024).
The results, shown in Figure 2, confirm that hcp iron is the only thermodynamically stable solid phase of iron at Earth's core conditions. Consistently, hcp iron melts at higher temperatures than all other solid structures, and the hypothetical melting lines of fcc and bcc iron follow their relative stability order (bcc \(<\) fcc \(<\) hcp). Our calculated melting curve for hcp iron compares well with recent initio studies ([PERSON], 2009; [PERSON] et al., 2002) with a maximal difference of 80 K, which is less than the uncertainty of 100 K in these studies. The melting temperature of \(6450\pm 25\) K at the Earth's inner core boundary (330 GPa), agrees well with previous experimental studies with shock waves (\(6230\pm 540\) K) ([PERSON] et al., 2022) and fast X-ray diffraction (\(6230\pm 500\) K) ([PERSON] et al., 2013) but differs from the resistance-heated diamond anvil cell studies (\(5120\pm 390\) K) ([PERSON] et al., 2019). A large discrepancy is present compared to the previous classical-potential-based MD simulations ([PERSON] et al., 2000; [PERSON] et al., 2000), which we attribute to the inaccuracy of these classical potentials ([PERSON] et al., 2002). There is a good agreement between our calculated hcp melting points at 360 GPa (6,715 \(\pm\) 20 K) and those reported in more recent work by ([PERSON] et al., 2023) (6,692 \(\pm\) 45 K), suggesting that different DFT implementations yield a similar accuracy of the reported thermophysical properties. However, the reported bcc melting point (6,519 \(\pm\) 80 K) in their study is much higher than in our study (6,164 \(\pm\) 30 K). Once again, we believe that the difference might be caused by the large simulation sizes required to converge the free energy of the bcc structure.
The Gibbs free energies at Earth's inner core conditions of the three structures considered here, namely hcp, fcc, and bcc, are all within a narrow range of about 30 meV/atom, more than an order of magnitude smaller than at
Figure 2: (a) Calculated melting line of hcp iron, compared to previous theoretical ([PERSON], 2009; [PERSON] et al., 2002; [PERSON] et al., 2000; [PERSON] et al., 2000; [PERSON] & [PERSON], 2009) and experimental results ([PERSON] et al., 2013; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2019). (b) Gibbs free energy difference between different structures of Fe at 400 GPa, with respect to hcp.
ambient temperature (700 meV/atom). We also find that temperature-induced electronic excitations provide a significant contribution to this reduction ([PERSON] & [PERSON], 2024).
There is a strong debate in the literature about the thermodynamic and mechanical stability of bcc iron due to the lack of an accurate and consistent approach to reach DFT accuracy with the large cell sizes required to capture the effects of self-diffusion. In this study, we employ a single, consistent, and extensively validated deep-learning-based approach, as thoroughly described in ([PERSON] & [PERSON], 2024), to clarify the role played by self-diffusion. Thanks to this new approach, we are in a position to rationalize and place on a much stronger and coherent basis a collection of mutually inconsistent earlier results. We found that self-diffusion is not sufficient to stabilize bcc iron thermodynamically over other competing phases. The finding disagrees with the only other study where self-diffusion was reported ([PERSON] et al., 2017). However the entropic contribution to the free energy in [PERSON] et al. (2017) was determined on a qualitative basis only. In addition, [PERSON] et al. (2017) propose that self-diffusion deactivates a soft-mode driven transition from bcc to hcp along the \(\left\langle 110\right\rangle\) direction. In our study, we found that the self-diffusion mechanism is more complicated and occurs not only along the \(\left\langle 110\right\rangle\) direction. Additionally, in our phonon simulations we find a low-temperature soft mode that drives the bcc phase into the fcc structure instead of hcp.
We also found that the melting line of bcc iron rises above its elastic instability limit at pressures above 260 GPa, indicating that bcc iron is locally mechanically stable at core conditions, although in a narrow range of temperatures. In a previous theoretical study by ([PERSON] et al., 2015), bcc iron was found to be mechanically unstable even at 7000 K along the Bain deformation path, suggesting that bcc iron lies at a saddle point rather than at a local minimum in the potential energy surface. With our new data, we can reinterpret their findings. At lower temperatures, the phase transition is driven by mechanical instability, while at 7000 K, it is driven by free energy.
There is a strong debate in the literature about the thermodynamic and mechanical stability of bcc iron due to the lack of an accurate and consistent approach to reach DFT accuracy with the large cell sizes required to capture the effects of self-diffusion. In this study, we employ a single, consistent, and extensively validated deep-learning-based approach, as thoroughly described in [PERSON] and [PERSON] (2024), to clarify the role played by self-diffusion. Thanks to this new approach, we are in a position to rationalize and place on a much stronger and coherent basis a collection of mutually inconsistent earlier results. We found that self-diffusion is not sufficient to stabilize bcc iron thermodynamically over other competing phases. The finding disagrees with the only other study where self-diffusion was reported ([PERSON] et al., 2017). However the entropic contribution to the free energy in ([PERSON] et al. (2017)) was determined on a qualitative basis only. In addition, [PERSON] et al. (2017) propose that self-diffusion deactivates a soft-mode driven transition from bcc to hcp along the \(\left\langle 110\right\rangle\) direction. In our study, we found that the self-diffusion mechanism is more complicated and occurs not only along the \(\left\langle 110\right\rangle\) direction. Additionally, in our phonon simulations we find a low-temperature soft mode that drives the bcc phase into the fcc structure instead of hcp.
## 4 The Origin of the Low Shear Velocity in the Earth's Inner Core
Among the observed physical properties on the Early inner core, the low shear velocity remains difficult to reconcile with the intrinsic elastic properties of hcp iron. It has been proposed that grain boundaries might play an important role, and previous simulations have demonstrated a very low shear velocity due to viscous grain boundaries ([PERSON] et al., 2007; [PERSON]. [PERSON] & [PERSON], 2022) or the premelting effects ([PERSON] et al., 2013). However, it remains unclear whether this mechanism will work for geophysically relevant grain sizes. The role of light impurities in interstitial sites might also be significant ([PERSON] et al., 2022), but future studies are needed to understand whether they affect the stability of the solid phases.
Except for the above possibilities, we have found that a striking feature of bcc iron is its low shear velocity compared to other phases, as shown in Figure 3. The anomaly is caused by soft transverse acoustic phonons that lead to a small value for \(c^{\prime}=c_{11}-c_{12}\) and to the result that the shear velocity is essentially controlled by \(c_{44}\). The calculated shear velocity of bcc iron at its melting point and at 360 GPa is 3.60 km/s, in remarkable agreement with seismic observations (3.68 km/s ([PERSON] & [PERSON], 1981) or 3.58 km/s ([PERSON] & [PERSON], 2018)), which makes of bcc iron a strong candidate for the structure of iron in the inner core. For comparison, the calculated shear velocities of hcp and fcc iron at their melting points and 360 GPa are 4.4 and 4.5 km/s, respectively.
atomic self-diffusion, and it is the only structure whose shear sound velocity matches seismic data. Future work is needed to clarify the role played by light elements in the thermodynamic stability of the different iron phases at core conditions.
## Data Availability Statement
The first-principles calculations were performed using the Quantum ESPRESSO package ([PERSON] et al., 2009). The DeePMD package was used to train the deep-learning interatomic potential ([PERSON] et al., 2018). The raw data supporting the findings of this study are available on Zenodo ([PERSON], 2024b). The DFT data set and interatomic potentials can be accessed on Zenodo ([PERSON], 2024a).
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Figure 3: Shear velocities of bcc and fcc iron at Earth’s inner core conditions (360 GPa), compared to previous theoretical studies ([PERSON] et al., 2022; [PERSON]. [PERSON] & [PERSON], 2022; [PERSON] et al., 2013, 2015, [PERSON] & [PERSON], 2009). The velocity of shear seismic waves in the Earth’s inner core as reported in the preliminary reference Earth model (PREM) is also shown ([PERSON] & [PERSON], 1981).
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wiley/ffe1c238_a022_40fc_9746_b2de1a036adc.md | In this study, we focus on an end-member type of detachment faulting observed along almost magmatic sections of ultraslow MORs, such as the narrow corridors of highly serpentinized seafloor between 62\({}^{\circ}\)E and 65\({}^{\circ}\)E at the Southwest Indian Ridge (SWIR). In the absence of melt supply, extension in the hanging wall of a detachment cannot be accommodated by magmatic accretion. The entire fault zone of the active detachment therefore migrates across the ridge axis into thicker lithosphere until the formation of a new on-axis fault in the footwall is energetically more favorable. This new fault is most likely dipping in the opposite direction (i.e., is of opposite polarity) and is oriented along weak zones in the footwall resulting from strain induced by its rotation and flexure. [PERSON] and [PERSON] (2011) proposed this so-called \"flip-flop\" detachment mode to be responsible for large areas of exhumed, extensively serpentinized mantle rocks at magma-poor margins and ultraslow-spreading MORs. This extension mode produces regions of unusually smooth seafloor, large ridges that are oriented parallel to the spreading axis, and a pattern of off-axis dipping fault zones that is symmetrical on a large-scale ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2006; [PERSON] et al., 2013).
A recent numerical study by [PERSON] et al. (2020) explores the processes causing the flip-flop kinematics. They find that fault zone weakening through mantle serpentinization and grain size reduction in mechanically stressed regions in the lower lithosphere play fundamental roles in stabilizing active tectonic zones and triggering new faults of opposite polarity. A crucial assumption in the aforementioned model is that the near-ridge lithosphere is in a thermal quasi-steady state with prescribed temperature maximum at the ridge axis and fixed depth-dependent temperature profiles. However, gaining further insights into the multifaceted thermo-mechanical interplay of the processes involved in this spreading mode requires a dynamically evolving temperature field. In this study we therefore investigate which processes predominantly shape the near-ridge thermal structure and how the evolving temperature field, in turn, affects the faulting sequence through rheological changes.
The thermal state of (ultra)slow magmatic ridges is not as well understood as at faster spreading ridges with strong magmatism. A nearly continuous axial melt lens with minor depth variation, for example, at the fast-spreading East Pacific Rise ([PERSON] et al., 1987; [PERSON] et al., 2018), indicates a rather stable thermal regime in both space and time. The hot, weak axial region serves as a thermal and mechanical anchor that stabilizes the ridge axis position and focuses deformation. In contrast, magmatic ridge sections without a significant melt budget are in a more transient thermal state that is controlled, at least partly, by its faulting dynamics and history (e.g., [PERSON] and [PERSON], 2008). Here, in the absence of strong magmatic processes, advection of hot mantle material into the footwall of detachments and subsequent cooling by heat conduction and hydrothermal circulation become the main heat distribution mechanisms.
Indirect evidence for hydrothermal cooling is the more than 15 km thick axial brittle lithosphere at ultraslow-spreading ridges (e.g., [PERSON] et al., 2019), which is incompatible with solely conductive cooling (see also our model without hydrothermal cooling; Section 3.2.1). Mapping of thermal plumes in the water column point at a reduced yet still significant hydrothermal activity along sections of the ultraslow Gakkel Ridge and SWIR ([PERSON] et al., 2004). Direct observations of hydrothermal venting in magmatic settings are limited to the recently discovered low temperature Old City hydrothermal field in the eastern magma-poor corridor of the SWIR ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2021). Additional evidence of potentially widespread hydrothermal activity is the inactive ultramafic-hosted Tianzuo hydrothermal field ([PERSON] et al., 2021), located on a detachment surface in a smooth seafloor area between the two corridors investigated by [PERSON] et al. (2013). Further indicators are the seismically imaged \(\sim\)5 km thick layer of partially serpentinized material exhumed by the successive detachments ([PERSON] et al., 2021; [PERSON] et al., 2017, 2020; [PERSON] et al., 2013) and conclusions of other petrological studies ([PERSON] et al., 2023; [PERSON] et al., 2021; [PERSON] et al., 2020). Observed correlations between fault and vent field positions at more magmatic ridge sections (e.g., TAG, [PERSON] et al. (2007); [PERSON], [PERSON] et al. (2009); [PERSON], [PERSON] et al. (2020)) suggest that hydrothermal circulation presumably occurs along highly permeable fault zones ([PERSON] et al., 2007). Potential driving forces for hydrothermal activity at magma-poor ridges are exothermic heat from serpentinization reactions, magmatic heat from sporadic intrusions into the footwall (indicated in recent seismic data; [PERSON] et al., 2020), and possibly heat mined from deep hot rocks through thermal contraction cracks ([PERSON], 1974). [PERSON] et al. (2021) suggest that the observed lithosphere thickness results from a thermal balance between deep periodic sill intrusions and hydrothermal circulation in the upper lithosphere driven by their heat. More details on spreading-related processes including hydrothermal activity can be found in the excellent reviews by [PERSON] (2023) and [PERSON] et al. (2022).
Our study is motivated by these recently published data and models, and associated advances in the understanding of the structure and thermal regime of this complex end-member tectonic setting. The key question is, how can the interplay of tectonic, magmatic and hydrothermal processes explain a thermal structure that will lead to flip-flop detachment faulting during ultraslow, magma-poor oceanic spreading. To address this question, we present a thermo-mechanical numerical model for magmatic oceanic spreading that includes refined implementations of serpentinization and grain size evolution, parametrized hydrothermal cooling (enhanced along active fault zones) and the thermal and rheological effects of sill intrusions into the detachment footwall. Starting with a setup similar to the model by [PERSON] et al. (2020) with an imposed temperature structure, we increase complexity by calculating the dynamically evolving thermal structure including the effects of hydrothermal fault zone cooling and magmatic intrusions.
## 2 Numerical Model
### Numerical Method and Constitutive Equations
The numerical model used in this study applies the finite element method on unstructured meshes to solve for the thermal and mechanical evolution of lithosphere and underlying mantle. The program M2 TRI_vep ([PERSON] and [PERSON], 2024, see Data Availability Statement for more information) is a successor of the mantle convection code M2 TRI ([PERSON], 2010), into which elastic and plastic deformation behavior, serpentinization of mantle rocks and a simple hydrothermal cooling parametrization have been implemented as discussed in previous studies ([PERSON] et al., 2017; [PERSON] and [PERSON], 2017). For the present study, we have further advanced the model by improving the visco-elasto-plastic rheology formulation, which now considers diffusion creep as well as non-linear dislocation creep mechanisms and a viscoplastic regularization ([PERSON] et al., 2021). Furthermore, we have implemented processes that are critical for lithosphere and upper mantle deformation such as strain softening, deformation-controlled serpentinization, dynamic grain size evolution, periodic emplacement of magmatic intrusions and an advanced hydrothermal cooling parametrization that takes into account the deformation state of the lithosphere. In the following, the relevant equations are written using index notation and Einstein summation convention. All parameters and variables introduced in this section are listed in Table 1.
We solve the conservation equations for mass, Equation 1, and momentum, Equation 2, for an incompressible medium using the Boussinesq approximation. The solution variables are displacement velocity components \(u_{i}\) and total pressure \(P\):
\[\frac{\partial u_{i}}{\partial x_{i}}=0, \tag{1}\]
\[\frac{\partial\tau_{ij}}{\partial x_{j}}-\frac{\partial P}{\partial x_{i}}+ \rho g_{i}=0, \tag{2}\]
where \(x_{i}\) are the spatial coordinates, \(\tau_{ij}\) are the deviatoric stresses, \(\rho\) is the density and \(g_{i}\) are the components of the gravitational acceleration.
Density in the Stokes Equation 2 is assumed to vary with temperature \(T\) and degree of serpentinization \(s\). The latter is used to calculate the volumetric mean between two end-member rock types: mantle peridotite (for which we assume olivine properties; subscript \(ol\)) and serpentine (subscript \(srep\)). This averaging is done for all rock parameters for which two values--one for olivine and one for serpentine--are given in Table 1.
\[\rho(T,s)=\rho_{ol}(T)\cdot(1-s)+\rho_{srep}(T)\cdot s,\qquad\rho_{c}(T)=\rho _{c,0}(1-\alpha_{c}(T-T_{0})) \tag{3}\]
Densities \(\rho_{c,0}\), with \(c\in[ol\), \(srep\)], are defined at the reference temperature \(T_{0}=0^{\circ}\)C and \(\alpha_{c}\) are the thermal expansion coefficients. Note that volume changes associated with serpentinization as well as other volume changing processes such as the formation of a fracture network (cf. Section 2.2.3) and magmatic sill emplacement (cf. Section 2.4) are disregarded in this incompressible formulation.
\begin{table}
\begin{tabular}{l c c c} \hline Parameter & Description & Unit & Value \\ \hline \(g_{i}\) & Gravitational acceleration & m s\({}^{-2}\) & [0, 0, \(-\)9.81] \\ \(P\) & Total pressure & Pa & \\ \(P_{h}\) & Lithostatic pressure & Pa & \\ \(Q\) & Plastic flow potential & Pa & \\ \(R\) & Gas constant & J kg\({}^{-1}\) mol\({}^{-1}\) & 8.314472 \\ \(t\) & Time & s & \\ \(\Delta t\) & Time step & kyr & 0.5–5 \\ \(T\) & Temperature & \({}^{\circ}\)C & \\ \(T_{bol}\) & Temperature of brittle-ductile transition & \({}^{\circ}\)C & 750 \\ \(u_{i}\) & Advection velocity & m s\({}^{-1}\) & \\ \(x_{i}\) & Spatial coordinates & m & \\ \(\dot{k}_{\theta}\) & Deviatoric strain rate & s\({}^{-1}\) & \\ \(e_{H\rho}\) & Accumulated plastic strain & & \\ \(e_{P,aw}\) & Accumulated plastic strain for full strain weakening & & 1.0 \\ \(\eta\) & Viscosity & Pa s & \(10^{18}-10^{23}\) \\ \(\eta_{\pi\rho}\) & Viscoplastic viscosity for regularization & Pa s & \(5\times 10^{19}\) \\ \(\dot{\lambda}\) & Plastic multiplier & s\({}^{-1}\) & \\ \(\tau_{\dot{q}}\) & Deviatoric stresses & Pa & \\ \(\tau_{\dot{u},ud}\) & Yield stress & Pa & \\ & _Thermo-mechanical properties_ & _Mantile\({}^{a}\)_ & _Sperpineb\({}^{a}\)_ \\ \(C\) & Cohesion & MPa & 60(6)\({}^{c}\) & 40(4) \\ \(\frac{\Delta C}{c_{0}}\) & Max. relative cohesion loss & & 0.9 \\ \(C_{\rho}\) & Specific heat capacity & J kg\({}^{-1}\) K\({}^{-1}\) & 1,200 & 1,200 \\ \(G\) & Shear modulus & GPa & 30 & 30 \\ \(a\) & Thermal expansion coefficient & \(10^{-5}\) K\({}^{-1}\) & 3.0 & 2.65 \\ \(\kappa_{0}\) & Thermal conductivity & W m\({}^{-1}\) K\({}^{-1}\) & 3.3 & 2.7 \\ \(\rho_{0}\) & Reference density & kg m\({}^{-3}\) & 3,300 & 2,600 \\ \(\Phi\) & Friction angle & \(\circ\) & 30 & 15 \\ \multicolumn{4}{c}{_Diffusion creep_} \\ \(A_{d\sigma}\) & Pre-exponential factor & MPa\({}^{-\alpha}\)s\({}^{-1}\) & \(1.5\times 10^{9}\) \\ \(n_{d\sigma}\) & Stress exponent & & 1 \\ \(E_{d\sigma}\) & Activation energy & kJ mol\({}^{-1}\) & 375 \\ \(V_{d\sigma}\) & Activation volume & \(10^{-6}\) m\({}^{3}\) mol\({}^{-1}\) & 6 \\ & _Dislocation creep_ & & \\ \(A_{d\sigma}\) & Pre-exponential factor & MPa\({}^{-\alpha}\) s\({}^{-1}\) & \(1.1\times 10^{5}\) \\ \(m\) & Grain size exponent & & 3 \\ \(n_{d\sigma}\) & Stress exponent & & 3.5 \\ \(E_{d\sigma}\) & Activation energy & kJ mol\({}^{-1}\) & 530 \\ \(V_{d\sigma}\) & Activation volume & \(10^{-6}\) m\({}^{3}\) mol\({}^{-1}\) & 13 \\ & _Sperpineb_ & & \\ \(s\) & Sperpineb\({}^{a}\) & & \\ \(S\) & Sperpineb\({}^{a}\) & & \\ \(S_{0}\) & Reaction rate scaling factor & s\({}^{-1}\) & \(3\times 10^{-13}\) \\ \hline \end{tabular}
\end{table}
Table 1: Description and Values of Model Parameters and Variables Used for This StudyThe conservation equation of heat is solved to obtain the temperature \(T\):
\[\rho C_{p}\frac{DT}{Dt}=\frac{\partial}{\partial x_{t}}\left(\kappa\,\frac{ \partial T}{\partial x_{t}}\right)+H_{ud}+H_{acep}+H_{lat}, \tag{4}\]where \(C_{p}\) is the specific heat capacity and \(\kappa\) is the thermal conductivity. \(H\)-terms represent the heat sources and sinks introduced in the next sections, that is, viscous dissipation \(H_{sw}\) exothermic heat of serpentination \(H_{sw}\) and latent heat of crystallization \(H_{tar}\). Radiogenic heat production is neglected in this study, since for the case of magmatic spreading investigated here, we assume the lithosphere will mainly consist of mantle rocks with a low concentration of radioactive elements.
### Rheology
#### 2.2.1 Visco-Elasto-Plastic Behavior
On geological time scales, the mechanical deformation of lithosphere and upper mantle rocks occurs through three different mechanisms: reversible elastic deformation, irreversible viscous flow and irreversible plastic deformation simulating brittle failure. All three mechanisms act at strongly variable quantitative proportions depending mainly on the ambient temperature-pressure conditions and stresses. A numerical model for lithosphere dynamics has to be able to resolve these processes, and different theoretical descriptions of visco-elasto-plastic rheology have been suggested (e.g., [PERSON] et al., 2019; [PERSON], 2019; [PERSON], 2010; [PERSON], 2002). In line with these studies we follow the approach by [PERSON] et al. (2003) and assume elastic, viscous and plastic (superscripts \(e\), \(v\), and \(p\), resp.) deformation processes to be active simultaneously so that the respective strain rates are additive. This allows to adopt an additive decomposition of the total deviatoric strain rate, \(\dot{\epsilon}_{ij}\):
\[\dot{\epsilon}_{ij} =\ddot{\epsilon}_{ij}^{\prime}+\dot{\epsilon}_{ij}^{\prime}+\dot {\epsilon}_{ij}^{\prime\prime} \tag{5}\] \[=\frac{\pi_{ij}}{2\eta_{v}}+\frac{\dot{\tau}_{ij}}{2G}+\dot{ \lambda}\,\frac{\partial Q}{\partial\tau_{ij}}, \tag{6}\]
where \(\eta_{v}\) is the effective viscous creep viscosity, \(G\) is the elastic shear modulus, \(\dot{\lambda}\) is the plastic multiplier and \(Q\) is the plastic flow potential. The stress-strain rate relation is based on the visco-elastic Maxwell-model:
\[\tau_{ij}=\eta_{off}\left(2\dot{\epsilon}_{ij}+\frac{\dot{\tau}_{ij}}{G\Delta t }\right), \tag{7}\]
where \(\eta_{off}\) is an effective visco-elasto-plastic viscosity (discussed below), \(\dot{\tau}_{ij}\) are the Jaumann-rotated old deviatoric stresses (for a detailed description see [PERSON] et al., 2019, and references therein), and \(\Delta t\) is the model time step. The second term on the right side represents the elastic deformation memory.
Viscous deformation includes diffusion (subscript _dif_) and dislocation creep (subscript _dis_) and we assume both creep mechanisms to be simultaneously active. The effective creep viscosity \(\eta_{v}\) is thus given by
\[\eta_{v}=\left(\frac{1}{\eta_{off}}+\frac{1}{\eta_{dis}}\right)^{-1}. \tag{8}\]
All rocks are assumed to be isotropic, which allows use of a scalar measure for the strain rate magnitude in the dislocation creep law. Following [PERSON] (2019) we use the second invariant of the viscous strain rate tensor, \(\dot{\epsilon}_{\mathbf{t},s}=\sqrt{1/2}\ \dot{\epsilon}_{ij,s}\cdot\dot{\epsilon}_{ij,s}\), to describe the non-Newtonian behavior of dislocation creep. Diffusion and dislocation creep viscosities are defined as
\[\eta_{df}=\frac{1}{3}\big{(}A_{df}\cdot B_{meth}\cdot r^{-m}\big{)}^{-\frac{ 1}{\alpha_{0}}}\exp\left(\frac{E_{df}+PV_{df}}{n_{df}RT}\right) \tag{9}\]
\[\eta_{dis}=\frac{1}{2^{\frac{\kappa^{-1}}{2^{\frac{\kappa^{-1}}{2^{\frac{ \kappa^{-1}}{2^{\frac{\kappa^{-1}}{2^{\frac{\kappa^{-1}}{
experiment parameters ([PERSON], 2019). Mantle peridotite forms the largest fraction of lithosphere at amagmatic ridges, and olivine is the most abundant and weakest mineral of this rock type. We therefore use a dry olivine rheology in our model ([PERSON], 2003). \(B_{melt}\) incorporates the effect of partial melts in intrusion regions on the rock's viscosity (see Section 2.4).
To include the plastic deformation into the viscous formulation we adopt the Prandtl-Reuss flow rule which, upon yielding, reduces the rock's stress state to the yield stress. The standard plasticity formulation is known to cause a mesh resolution dependent shear band width of \(\sim\)3 elements ([PERSON] et al., 2000). To reduce this unwanted numerical effect we implemented a viscoplastic regularization following [PERSON] et al. (2021). This allows the model to build up overstress to a certain level controlled by the viscoplastic viscosity \(\eta_{sp}\). We implemented a yield criterion \(\tau_{yield}\) similar to a Drucker-Prager criterion, however, we use the local lithostatic pressure \(P_{h}\) instead of the total pressure \(P\) from Equation 2. We prefer this so-called \"depth-dependent von Mises\" criterion over the Drucker-Prager criterion because the latter is known to potentially cause numerical convergence problems ([PERSON] et al., 2016). The resulting yield function is given by
\[F=\tau_{\mathbf{I}}-\tau_{yield}-\dot{\lambda}_{\eta_{sp}}=\tau_{\mathbf{I}}-C\cdot \cos\Phi-\sin\Phi\cdot P_{h}-\dot{\lambda}_{\eta_{sp}}, \tag{11}\]
with \(C\) and \(\Phi\) being the cohesive strength and the friction angle, respectively. The rock's stress state is quantified using the second invariant of the deviatoric stress tensor \(\tau_{H}\).
In summary, the effective viscosity including the effect of plastic yielding can be expressed by
\[\eta_{df}=\begin{cases}\left(\frac{1}{\eta_{s}}+\frac{1}{G\Delta t}\right)^{ -1},&\text{if }\tau_{\mathbf{I}}<\tau_{yield}.\\ \frac{\tau_{yield}+\dot{\lambda}_{\eta_{sp}}}{2\dot{\mathbf{I}}},&\text{if }\tau_{\mathbf{I}} \geq\tau_{yield}.\end{cases} \tag{12}\]
Using Equations 8-11 with the parameters of the dry olivine rheology and a geothermal gradient of 0.05\({}^{\circ}\)C m\({}^{-1}\), we find that the transition from elastic-brittle to ductile behavior occurs at \(\sim\)750\({}^{\circ}\)C at a depth of \(\sim\)15 km. This is in agreement with the temperature assumed for the lower end of the seismogenic zone at (ultra-)slow spreading ridges ([PERSON] et al., 2019) and we refer to the \(T_{hd}=750^{\circ}\)C isotherm from here on as the base of the brittle lithosphere. For numerical stability reasons, viscosity is limited between \(10^{18}\) and \(10^{23}\) Pa s.
#### 2.2.2 Strain Weakening
Strain weakening of fractured rocks is a critical process that needs to be considered in numerical models for lithosphere faulting. It parametrizes the weakening effects of pore fluids, gauge materials and mineral transformations in regions of strong plastic deformation, that is, shear zones. Strain weakening should thus scale with the deformation that a rock has experienced. It is incorporated in our model by reducing rock cohesion by \(\frac{\Delta C}{C_{0}}\) = 0.9 over the range of accumulated plastic strain \(\varepsilon_{L_{sp}}\) from 0 to \(\varepsilon_{p,sw}=1.0\):
\[C=C_{0}\cdot\left(1-\min\left\{1,\frac{\varepsilon_{L_{sp}}}{\varepsilon_{p,sw }}\right\}\cdot\frac{\Delta C}{C_{0}}\right) \tag{13}\]
To calculate plastic strain accumulated in yielding regions, the plastic strain rate, which corresponds to the total strain rate minus the visco-elastic strain rate, is integrated over time, following
\[\varepsilon_{L_{sp}}(t+\Delta t)=\varepsilon_{L_{sp}}(t)+\dot{\varepsilon}_{L _{sp}}(t)\cdot\Delta t. \tag{14}\]
#### 2.2.3 Serpentinization
To investigate the lithosphere-scale influence of the reaction of olivine and water to form serpentine at temperatures below 350\({}^{\circ}\)C, we adopt the temperature-dependent kinetic rate used by Rupke and Hasenclever (2017):\[S(T)=S_{0}\cdot a\cdot\exp\left(-\frac{b}{T}\right)\cdot\left[1-\exp\left(-c\left( \frac{1}{T}-\frac{1}{T_{0}}\right)\right)\right], \tag{15}\]
with \(S_{0}=10^{-13}\) s\({}^{-1}\)([PERSON], 2017) and \(a=808.3\), \(b=3,640\) K, \(T_{0}=623.6\) K, and \(c=8,759\) K ([PERSON] et al., 2012). Note that we do not incorporate grain size effects on the kinetic rate ([PERSON] et al., 2012). This rate describes the relative change of olivine mass per rock volume \(\rho_{\beta e}\), thus allows to calculate the serpentinization degree \(s\) of the rock by
\[\frac{\partial\rho_{\beta t}}{\partial t} =-S(T)\rho_{\beta t} \tag{16}\] \[s =1-\frac{\rho_{\beta t}}{\rho}. \tag{17}\]
Furthermore, this representation directly allows to calculate the exothermic heat released during the reaction ([PERSON] et al., 2010) by:
\[H_{app}=-Q_{app}\frac{\partial\rho_{\beta t}}{\partial t}, \tag{18}\]
where \(Q_{app}\) is the heat produced per unit mass of olivine of \(2.9\times 10^{5}\) J kg\({}^{-1}\) (value for forsterite from [PERSON] et al. (2010)).
Since we do not explicitly resolve the dynamics of hydrothermal fluid flow through a porous medium, we follow the approach of [PERSON] et al. (2020) to asses the availability of water for the reaction. The product of stress and accumulated strain, representing the volumetric work done to the rock by deformation, is used as a proxy for the formation of a fracture network giving water access to the rock. The threshold for this work, above which temperature-controlled serpentinization is activated, is set to \(10^{8}\) J m\({}^{-3}\).
Serpentine properties are listed in Table 1 and are used to derive effective rock properties by calculating the volumetric mean between olivine and serpentine properties using the serpentinization degree (cf. Equation 3). Mechanical weakening due to serpentinization is incorporated by reducing cohesion and friction angle ([PERSON] et al., 1997). The occurrence of serpentine in the oceanic spreading context is limited to shallow and cold regions. We therefore refrain from adjusting the viscous flow law parameters for serpentine, as serpentinized regions are expected to deform predominantly elasto-plastically.
#### 2.2.4 Dynamic Grain Size Evolution
Grain size reduction occurs through dynamic recrystallization at sufficiently high applied stresses and results in a decrease of the diffusion creep viscosity (Equation 9). We adopt the dynamic grain size evolution model by [PERSON] et al. (2022), which is based on the palaeo-wattmeter ([PERSON] & [PERSON], 2007):
\[\frac{Dr}{Dr}=\frac{K_{g}f_{\text{H,O}}\exp\left(-\frac{E_{G}+P\text{I}_{ \text{E}}}{RT}\right)}{pt^{p-1}}-\frac{\lambda r^{2}}{\gamma\pi}\dot{\Psi} \tag{19}\]
Equation 19 describes the change of grain size \(r\) under the influence of grain growth driven by surface energy (first term) and grain size reduction through dynamic recrystallization (second term). \(K_{g}\) is the growth rate constant,\(\dot{H}_{\text{t,O}}\) is the water fugacity, \(E_{G}\) and \(V_{G}\) are activation energy and volume, respectively, and \(p\) is the growth exponent. \(\gamma\) is the grain boundary energy, the geometrical factor \(\pi\) results from the assumption of spherical grains. \(\dot{\Psi}=\tau_{g}\dot{x}_{\beta t,dis}\) is the mechanical work rate from dislocation creep, of which the portion \(\dot{\lambda}\) goes into grain size reduction. This reduces the heat from viscous dissipation, which takes the form of
\[H_{d}=\tau_{g}\dot{x}_{\dot{\phi}}-\dot{\Psi}_{2}. \tag{20}\]Experimentally derived model parameters are from [PERSON] et al. (2020) and listed in Table 1. For numerical stability we limit the grain size from 1 um to 10 mm consistent with observations (e.g., [PERSON] et al., 2021).
### Hydrothermal Cooling
To incorporate the large-scale cooling effect of fluid circulation, we implemented an enhanced thermal conductivity. The enhancement factor is commonly referred to as the Nusselt number Nu in this context--not to confuse with its classical definition--as it up-scales conductive heat transfer to account for the missing cooling effect from the advection of hydrothermal fluids (e.g., [PERSON] et al., 2009; [PERSON] et al., 1987; [PERSON] et al., 2011). Here we adapt the approach of [PERSON] et al. (2009), in which thermal conductivity additionally depends on temperature and depth. We have modified this formulation by using lithostatic pressure instead of depth and applying a linear taper of the conductivity-scaling across the brittle-ductile transition between 600 and 750\({}^{\circ}\)C. The latter avoids the temperature dependence in the exponential term and reduces non-linear feedbacks. Thus, we obtain:
\[\kappa=\kappa_{0}\cdot\text{Nu}\] (21a) \[\text{with}\quad\text{Nu}=1+\theta(\text{Nu}_{0}-1)\,\exp\left(\beta\left(1- \frac{P_{it}}{P_{it}}\right)\right)\cdot K_{HZ},\] (21b) \[\text{and}\quad\theta=\text{max}\left\{0,\,\min\left\{1,\,1-\frac{T-600\,^{ \circ}\text{C}}{750\,^{\circ}\text{C}-600\,^{\circ}\text{C}}\right\}\right\},\] (21c) \[\kappa_{0}\] is a rock type dependent reference conductivity, \[\text{Nu}_{0}\] is a reference Nusselt number, \[\theta\] is the temperature-dependent taper, \[\beta=0.75\] a smoothing factor, and \[P_{it}=330\] MPa the scaling lithostatic pressure for hydrothermal activity. For a flat topography, \[P_{it}\] corresponds to 10 km depth. Since our models always form an axial valley and lithostatic pressure laterally balances at relatively shallow depths, this value corresponds to approximately 6 km depth below the ridge axis, which is a typical assumption for the maximum depth of vigorous hydrothermal convection (e.g., [PERSON] et al., 2009).
Motivated by the approach of [PERSON] and [PERSON] (2002), who enhance cooling around active faults, we have incorporated the factor \(K_{FZ}\) into Equation 21b. We use this factor to account for enhanced hydrothermal fluid circulation in damaged regions, that is, fault zones, where highly permeable pathways are likely to form. \(K_{FZ}\) is a function of the product \(W=\tau_{\mathbf{t}}\cdot\epsilon_{\mathbf{t}_{Z}}\cdot\hat{\mathbf{e}}_{\mathbf{t}}\) of the second invariants of stress \(\tau\), accumulated plastic strain \(\epsilon_{p}\) and strain rate \(\hat{\mathbf{\lambda}}\). \(K_{FZ}\) follows a logarithmic increase between the activation threshold of \(W_{1}=4\times 10^{-6}\,\text{Is}^{-1}\,\text{m}^{-3}\) and the upper limit of \(W_{2}=10^{-3}\,\text{Js}^{-1}\,\text{m}^{-3}\):
\[K_{HZ}=\begin{cases}1&,\text{ if }W<W_{1}\\ \left(\frac{W}{W_{1}}\right)^{\frac{P_{it}}{\text{Nu}_{0}\left(W_{2}\,W_{1} \right)}}&,\text{ if }W_{1}\leq W\leq W_{2}\\ 10^{F_{\text{max}}}&,\text{ if }W_{2}<W\end{cases} \tag{22}\]
Analogously to the activation of serpentinization, \(K_{FZ}\) parametrizes the formation of a connected fracture network (\(\tau\cdot\epsilon_{p}\)) but additionally favors active fault zones \(\left(\hat{\mathbf{\lambda}}\right)\), where processes clogging the tectonically opened pore space, such as mineral precipitation from hydrothermal fluids, mineral transformations in the rock and consolidation of fractured rocks, have not yet closed the fracture network again. The activation threshold \(W_{1}\) is derived from the serpentinization threshold of \(10^{8}\,\text{Nm}^{-3}\) and a typical fault zone strain rate of \(4\times 10^{-14}\,\text{s}^{-1}\), while the upper limit \(W_{2}\) has been defined empirically to have maximum cooling in the center of the most active shear zone. \(F_{\text{max}}\) is the exponent of maximum cooling intensity, which we vary in our parameter study to test the influence of hydrothermal fault zone cooling.
### Magmatic Intrusions
Magmatic intrusions are periodically emplaced as sills of variable size and periodicity. Based on the strategy by [PERSON] et al. (2021) and consistent with thermal models by [PERSON] et al. (2022), emplacement is assumed to occur instantaneously below the shallowest point of the 1000\({}^{\circ}\)C isotherm, representing the basaltic solids \(T_{sol}\). This corresponds to a mean depth of about 18 km, below seafloor, however, the exact positions of individual intrusions depend on the model dynamics. The emplacement temperature is a basaltic liquidus temperature \(T_{life}\) of 1200\({}^{\circ}\)C. Upon cooling, latent heat of crystallization is assumed to be evenly released between liquidus and solidus temperature:
\[H_{lat}=-\rho\,\frac{Q_{lat}}{T_{life}-T_{sol}}\,\frac{DT}{Dt}\qquad\text{for} \qquad T_{life}\geq T\geq T_{sol}, \tag{23}\]
where \(\rho\) is the density, \(\frac{DT}{Dt}\) is the total derivative of temperature with respect to time, and \(Q_{lat}\) = 335 kJ kg\({}^{-1}\) is the latent heat per kilogram of melt. Numerically this is implemented by increasing the specific heat capacity in intrusion regions between liquidus and solidus temperatures (\(C_{p}\) in Equation 4). To account for the effect of partial melts on the viscosity of crystallizing intrusions, we adopt the exponential formulation by [PERSON] and [PERSON] (2003) and multiply an additional factor \(B_{melt}\) to the pre-exponential flow law parameters (\(A_{dis}\), \(A_{dif}\) in Equations 9 and 10). For simplicity, we do not track melt content, but assume melt fraction \(\xi\) to be a linear function from 0 to 1 between solidus and liquidus temperature. This yields
\[B_{melt}=\exp(k\xi)=\begin{cases}1,&\text{if }T<T_{sol}\\ \exp\left(k\cdot\frac{T-T_{sol}}{T_{life}-T_{sol}}\right),&\text{if }T_{sol} \leq T\leq T_{life}\\ \exp\left(k\right),&\text{if }T_{life}<T\end{cases} \tag{24}\]
We use a moderate pre-exponential factor \(k=35\) so that the intrusion viscosity remains at the lower cut-off viscosity of 10\({}^{18}\) Pa s until intrusions have crystallized to about 25%. From then on, viscosity increases until complete crystallization. For simplicity we do not consider rheological differences between solidified basaltic intrusions and other lithospheric rocks so that any rheological effect of intrusions vanishes once they have cooled below the solidus temperature. Further mechanical aspects of intrusions such as volume changes and related effects on the stress field are not considered here as they require a compressible mechanical model ([PERSON] et al., 2019).
### Code Structure
We use the 2-D Galerkin finite element method (FEM) with unstructured triangular elements to solve the system of equations in a Lagrangian reference frame (i.e., the mesh is advected according to the calculated deformation). All meshes are generated using the mesh generator _Triangle_ by [PERSON] (2002). Mechanical and thermal parts of the model are solved sequentially over every time step. The mechanical solver uses Crouzeix-Raviart elements with continuous quadratic order shape functions to approximate the deformation field and linear, discontinuous shape functions to approximate the pressure. We employ the so-called penalty method ([PERSON], 2003, and references therein) to derive an incompressible deformation field by iteratively solving Equations 1 and 2.
Next, we solve for heat diffusion and heat sources using a fully implicit FEM with quadratic order (6-node) triangles. The converged flow field is then converted to a displacement field using the current time step to advect the nodes of the finite element mesh. This step accounts for advective heat transport. Last, the second-order variables such as accumulated strain, serpentinization degree, grain size, lithostatic pressure and rock properties are calculated for the new configuration.
Between two time steps, mesh quality is checked to decide whether or not a remesh procedure is necessary. If so, a new mesh is created that preserves the high resolution regions near the ridge axis and that is adaptively refined along the active fault zones and in regions where intrusions are emplaced. To save computation time, these high resolution mesh regions are coarsened again once the intrusion temperature falls below the solidus temperature. After a remesh, all important variables are transferred from the old to the new mesh by interpolation using the finite element shape functions. The transfer of variables only stored at integration points requires an intermediatemapping step from integration points to nodes before interpolating to the location of integration points in the new mesh (see Figure 3 in de [PERSON] et al. (2019)).
The time step size dynamically adjusts to the model dynamics, for example, flow field and temperature changes, between 0.5 and 5 Kyr. Upon intrusion emplacement, the thermal solver sub-iterates with time steps down to 100 years in order to properly resolve the heat transfer from the intrusion to its surroundings where high temperature gradients exist. The model is written in MATLAB (ver. R2020a, www.mahworks.com) and uses a vectorized element assembly for an improved performance as suggested by [PERSON] et al. (2008). In addition we make use of the libraries SuiteSparse ([PERSON] and [PERSON], 2009) and MUTILS ([PERSON] and [PERSON], 2010). Data visualizations are done using MATLAB and Tecopt 360 EX (ver. 2021 R1, www.tecpilot.com).
### Model Setup
The model setup is illustrated in Figure 1. The model domain is \(200\times 80\) km, discretized with a triangular finite element mesh and variable mesh resolution. The mean node spacing in the region of the axial lithosphere is 375 m and increases to up to 1,250 m toward the bottom boundary. Additionally, the mesh is adaptively refined along actively deforming regions during each remesion procedure with a node spacing of 250 m in the fault zones. The model has a free surface ([PERSON] et al., 2015) with \(z=0\) km corresponding to a water depth of 4,650 m and constant mantle inflow along the bottom boundary that balances the lateral extension of 7 mm yr\({}^{-1}\) on both sides. Spreading rate and water depth represent the amangmatic segments of the SWIR at 62\({}^{\circ}\)E-65\({}^{\circ}\)E ([PERSON] et al., 2006, 2008). To stabilize the initial model phase, we trigger the first fault by imposing a linear profile of accumulated strain (Figure 1).
The initial temperature field is based on [PERSON] et al. (2020), however, we assume a slightly thinner axial brittle lithosphere of 15 km in agreement with recently reported data ([PERSON] et al., 2023). The geometry of the initial temperature field has been adjusted accordingly, see Figure 1. At the domain top and bottom, isothermal boundary conditions are set to 4 and 1,400\({}^{\circ}\)C respectively. The lateral domain boundaries are insulating.
For our parameter study, we use one configuration without magmatic input and five configurations with intrusion geometries and periodicities ranging from \(0.14\times 1.4\) km sized sills every 40 Kyr to \(0.5\times 5\) km sized sills every 100 Kyr ([PERSON] et al., 2021). The ratio of intrusion volume flux (average over time) to brittle lithosphere flux (15 km \(\times\) 14 km/Myr) serves as a proxy for the fraction of lithosphere extension that is potentially compensated by magma input through disks, commonly referred to as the \(M\)-factor ([PERSON] et al., 2005). Assuming that the melt budget provided by the intrusions could go into diking, the above intrusion scenarios correspond to equivalent hypothetical values of \(M\) between 0.02 and 0.12. Note, however, that spreading in our models is always magmatic and the actual \(M\)-factor in all calculations is zero because neither the volume flux of intrusions nor diking
Figure 1: Initial temperature field, finite element mesh and mechanical boundary conditions. The geometry of the temperature field is controlled by the axial depth to the 750 and 1,260\({}^{\circ}\)C isotherms (brittle-ductile transition at 15 km and lithosphere-asthenosphere boundary 35 km, respectively), the off-axis depth of the 1,260\({}^{\circ}\)C isotherm of 60 km, and the width of the axial thermal structure of 55 km.
are considered. To investigate the effect of hydrothermal cooling, we vary the magnitude of enhanced hydrothermal fault zone cooling using six values of \(F_{\text{max}}\) ranging from 0 to 2.5. In each setup, Nu\({}_{0}\) in Equation 21b is adjusted to \(F_{\text{max}}\) and \(M\) and take values between 6.4 and 10.2 to obtain a similar average axial brittle lithosphere thickness for all setups. The exact model parameters for each setup can be found in Figure S1 and Table S1 of the Supporting Information S1. For all experiments, we set the maximum simulation time to 40 Myr.
## 3 Results
Lithosphere deformation is controlled by several feedback mechanisms between thermal and rheological subprocesses. In our model calculations we observe various faulting modes that are illustrated in Figure 2. We distinguish between the formation of individual faults (e.g., a detachment of opposite polarity or an accommodating footwall fault) and the fault sequence (e.g., successive parallel faults or flip-flop). To facilitate a comparison between our model calculations and the ones by [PERSON] et al. (2020)--despite using different numerical techniques and parametrizations of key processes--we first investigate a setup that is very similar to theirs. To do so we analyze the faulting dynamics of a model with imposed temperature structure, where the initial temperature field is modified only by the vertical movement of the domain top representing seafloor relief. We analyze the faulting dynamics of this model in Section 3.1.
Figure 2: (a) Kectches illustrating the different faulting modes observed in our simulations. The numbering indicates the order of the sequences. Colored arrows on top indicate direction of increasing age of the respective seafloor section. Abnormal age gradients (increasing age toward ridge axis) are indicated by an asterisk. In the chaotic mode, seafloor structures are frequently dismantled by the underlying faults, making a classification practically impossible. (b) Interpretation of fault zones and seafloor relief of the eastern magmatic corridor of the SWIR by [PERSON], [PERSON], et al. (2019) (D3\({}^{\circ}\) from [PERSON] et al. (2021)); vertical exaggeration 2:1; B— Breakaway, E—Emergence, #1 is the currently active detachment, C5—magnetic anomaly #5. Modified after [PERSON], [PERSON], et al. (2019).
In Section 3.2 we present the fully coupled models with a dynamically evolving temperature field. We first show one calculation without any hydrothermal cooling (Section 3.2.1) to emphasize the importance of this additional cooling mechanism for reproducing the observed lithosphere thickness. Afterward we present the different faulting modes observed in the parameter study.
### Model With Imposed Temperature Structure
Tests with this simplified thermal model show particular sensitivity to weakening parameters and the prescribed thermal structure, similar to the findings of [PERSON] et al. (2020). We observe a very stable and uniform sequence of flip-flop faults (Figures 3 and 4). The shown faulting sequence starts at 11.1 Myr, after nine flip-flop detachment faults have already formed in the same manner. Each detachment starts as a high angle normal fault (Figure 3a). With increasing vertical displacement, the footwall rolls back under its own weight. Thereby it experiences large flexure, indicated by the formation of a region with increased strain rate pointing from the central footwall to the emergence of detachment D10 (Figure 3b), consistent with the dynamics suggested by [PERSON] and [PERSON] (2011). Since the temperature field evolves with the seafloor relief, the upward movement of the footwall results in a shallow temperature maximum in the central footwall close to the center of the incipient solid-block rotation. The resulting rheological weakening focuses flexural strain (Figure 3c) and acts as a trigger for the new fault D11 with a polarity opposite to its predecessor D10, in agreement with the assumption that a new fault cuts the hinge of its predecessors footwall ([PERSON], 2018). Eventually, a shear-localizing feedback loop between deformation and grain size reduction/serpentinization is activated. This leads to the formation of a new fault accounting for a major portion of extension and the cycle starts over again (D11 in Figure 3d).
The stability of the flip-flop cycles are shown in Figure 4. We find that successive strain rate increase and focusing occur simultaneously with grain size reduction prior to the \"activation\" of the new fault zone, which from then on accommodates a major part of the deformation (dashed vertical lines in the left panel of Figure 4). For evaluating each fault's lifetime we take the time span between the activation of one detachment to the next. Thus, the mean fault duration is also obtained by dividing the total duration of a faulting sequence by the number of faults, allowing for comparison with the SWIR data by [PERSON], [PERSON], et al. (2019). The results of this simulation are in perfect agreement with the data from the SWIR.
The strain rate of each fault peaks at around \(3\times 10^{-13}\) s\({}^{-1}\), while fault zone width and minimum grain size converge to 1 km and 1.5 \(\upmu\)m, respectively, in agreement with seismic and petrological data ([PERSON] et al., 2020, 2021; [PERSON] et al., 2020).
Besides the similarities between our simulation, SWIR observations and the classical flip-flop mechanism ([PERSON], 2018; [PERSON] et al., 2013), we also see some differences. From the theoretical model, we would expect the new fault to cut its predecessors exhumed shear plane a few kilometers away from its emergence. Also, with the formation of the new fault, the predecessor should successively fade out as it reaches the colder and thicker off-axis lithosphere. Instead, new faults in our simulations often cut the shear plane around the emergence, and the preceding fault remains active and continues to exhume mantle material to the seafloor. The two simultaneously active faults enclose a central hosst with predominantly vertical motion, until it tilts toward the older fault and initiates the mechanism discussed above. Slip on the old detachment ends with the formation of the second next fault with same polarity (D9 becomes inactive when D11 forms; see Figure 3d). Interestingly, this faulting sequence can also explain the segments of abnormal seafloor age pattern at the SWIR ([PERSON], [PERSON], et al., 2019). To observe more classical flip-flop detachments with more pronounced roll-back, a stronger reorientation of the fault zone from initially straight to curved would be required. Tests have shown that a lower yield stress, that is, lower friction angle and/or cohesion, or an increase of \(\eta_{sp}\) in the visco-plastic regularization lead to faster yielding and wider fault zones, both allowing for more efficient fault zone reorientation and roll-back.
Our model with imposed temperature structure generally confirms the conclusion of [PERSON] et al. (2020)--despite the differences in modeling techniques and parameterizations--that grain size reduction allows for strain focusing in the deep lithosphere at the root of the incipient detachment fault, which in turn facilitates flip-flop faulting. An important prerequisite for triggering a new fault of opposite polarity is, however, a higher temperature in the footwall relative to the colder active fault zone(s) (cf. Figures 2a and 3b). In the next sections we investigate how such a thermal structure can dynamically evolve through the interplay of tectonic, magmatic and hydrothermal processes.
### Models With Dynamic Thermal Evolution
We conducted 36 simulations with a dynamically evolving temperature field to test the effects of hydrothermal cooling--widespread plus enhanced to a certain level within and around active fault zones (see Equation 21b)--and magmatic input in form of sill intrusions that can be converted into a hypothetical M-factor. In all model simulations, the mean axial brittle lithosphere thickness, defined as the minimum depth of the 750\({}^{\circ}\)C isotherm below the seafloor, is in the range of 15.1 \(\pm\) 1.0 km, which matches observations and facilitates a good comparison of the different model calculations. These simulations are labeled using an index of 1-36 to refer to them
Figure 3: Central model region displaying flip-flop dynamics in the model with imposed temperature structure. Left: strain rate and white isotherms, vector colors show advection velocity. Fault numbering as in Figure 4. Right: grain size in μm (blue to white) overlain by serpentinization degree (green to yellow) and black isotherms. The same graphical framework is used for all related figures. The full sequence can be seen in Movie S2.
later in the summarizing parameter space plot (Figure 11). Additionally, we show simulation 0 in the next section, which has no magmatic input and no hydrothermal cooling at all. Over the following sections we will present the different faulting modes observed in our simulations.
#### 3.2.1 Miniature Flip-Flop (No Hydrothermal Cooling)
Without the additional cooling effect of hydrothermal circulation (Nu = 1), the upwelling hot mantle reduces brittle lithosphere thickness (defined by the 750\({}^{\circ}\)C isotherm) to less than 4 km (Figure 5). This result is incompatible with micro-seismicity data indicating a thickness of around 15 km ([PERSON] et al., 2023; [PERSON] et al., 2019). Also, the seafloor topography is much smoother than observed at the SWIR. We show this calculation to emphasize the importance of hydrothermal cooling not only at predominantly magmatic fast- and intermediate spreading ridges but also at paramagnetic slow- and ultraslow ridges. Interestingly, the faulting pattern is very similar to that of the model with imposed temperature structure and could be considered a miniature version of flip-flop faulting. However, such a thin lithosphere is typical for much faster spreading ridges or for sections of slow spreading ridges with a significantly increased melt budget. We therefore consider this setup to be unrealistic for an magmatic slow spreading ridge.
#### 3.2.2 Long-Lived Detachment Mode
Each of the simulations of the parameter study shows several faulting modes (cf. Figure 2). There is no calculation that maintains a single faulting mode throughout the 40 Myr simulation time. However, certain faulting modes clearly dominate depending on the intensity of fault zone cooling and magmatic input. Note that all calculations include a wide-spread background hydrothermal cooling to achieve a realistic lithosphere thickness.
We first focus on simulation 1 (Figures 6a and 6b), which has neither enhanced cooling of fault zones nor magmatic input (\(M=0\), \(F_{\rm max}=0\), i.e. \(K_{F2}\)= 1 in Equation 21b). With increasing displacement on the fault plane, hot mantle material is pulled up with the footwall. The advective velocity and thus the pull-up is largest close to the active fault zone resulting in a temperature maximum at this position (Figure 6a)--similar to the findings of [PERSON] and [PERSON] (2008). With ongoing fault activity, the temperature maximum then moves together with the fault zone toward the hanging wall side (Figure 6b). Thereby, the fault remains in a hot, weak environment instead of migrating into
Figure 4: Fault zone analysis of the model with imposed temperature structure showing the evolution of strain rate, fault width and grain size. Strain rate and fault width are evaluated in the brittle lithosphere, grain size at the detachment root around the brittle-ductile transition between 500 and 1000\({}^{\circ}\)C. Left panel: Time series of subsequent faults. Dashed vertical lines indicate the activation of a new detachment. Right panel: Same data for all detachments in the simulation but as a function of their life time, that is, shifted so that their point of activation (vertical lines in the left panel) match. The second vertical line indicates the onset of the following detachment, giving a mean fault period duration of \(1.1\pm 0.1\) Myr (SWIR: 1.1 \(\pm\) 0.3 Myr; [PERSON], [PERSON], et al., 2019).
thicker, stronger lithosphere. This generally allows the fault to stay active significantly longer than a typical flip-flop detachment and leads to a _long-lived detachment_ that may be accompanied by accommodating football faults.
For most simulations with low hydrothermal fault zone cooling and low magmatic input, we observe a behavior similar to that of simulation 1. Long-lived detachment faults and their accommodating faults are the dominant faulting mode. We observe three variations of long-lived detachments: (a) _rolling-hinge detachments_, (b) detachments with _synthetic accommodating football faults_, and (c) detachments with _antithetic accommodating football faults_. The different modes are illustrated by sketches in Figure 2a and by snapshots from two different simulations in Figure 6.
_Rolling-hinge detachments_ (Figures 6a and 6b) are characterized by a rotation of the football that transitions into a horizontal plate motion further off-axis ([PERSON], 1988; [PERSON] et al., 1999). This goes along with stretching and shearing in the football, but the emerging shear bands do not become focused enough to form a new fault zone (Figure 6a). At the seafloor, a very smooth and kilometer-long shear plane is exhumed.
_Synthetic accommodating faults_ are secondary faults of the same orientation as the detachment but opposite curvature in the upper part (Figures 6c and 6d). Similar faults have been observed by [PERSON] et al. (2000) and [PERSON] et al. (2021). In-between this fault pair, a closed solid-block rotation with very little shear deformation
Figure 5.— Sequence showing a model without any hydrothermal cooling (Nu = 1) and no magmatic input. The full sequence can be seen in Movie S3.
Figure 6.— Sequences illustrating the different types of long-lived detachments observed in the simulations. Labels: B—breakaway of the long-lived detachment; Id—long-lived detachment; sa—synthetic accommodating fault; na—antithetic accommodating fault. The full sequences can be seen in Movies S4 (a,b,e,f), and S5 (c,d).
begins. The accommodating fault either fades out after some time or realigns its curvature and may become the major active detachment fault itself.
_Antithetic accommodating faults_ (Figures 5(e) and 5(f)) cut the footwall of the active detachment with opposite polarity. The general deformation in the footwall remains dominated by the curved long-lived detachment. After producing significant relief, but before experiencing major roll-back, the accommodating fault fades out instead of becoming a full-grown detachment. We find that one long-lived detachment fault can cause and survive multiple antithetic accommodating faults. Interestingly, the resulting fault zone pattern and seafloor topography closely resembles that of flip-flop faulting.
#### 3.2.3 Detachments With Opposite Polarity
One characteristic of flip-flop faulting is the alternating polarity of successive detachments, each of which accommodates a significant amount of extension. A sequence of such detachments with alternating polarity is thus required for considering a simulation to exhibit flip-flop faulting.
Figures 7 and 8 show a temporal evolution from simulation 28 (\(M=0.1\), \(F_{\mathrm{max}}=1.5\)), which is an example for such a sequence and shares many characteristics discussed above for the model with imposed temperature structure. With increasing displacement on the detachment fault, the footwall experiences roll-back (Figures 6(a) and 6(b) left column). At the same time, the increased cooling of the active fault zone(s) shifts the isotherms around the detachment to slightly greater depth (Figures 6(a) and 6(b) right column). This cooling effect increases the temperature difference between active fault zone and footwall and thereby pushes the temperature maximum further into the footwall. The emplacement of intrusions (size: \(4.000\times 400\) m every 80 Kyr) near the temperature maximum further weakens the footwall, which eventually allows for enough focusing of flexural strain to initiate the feedback loop between grain size reduction and strain rate increase (Figures 6(b) and 6(c)). After the new detachment fault of opposite polarity has formed (Figure 6(c)), heat is extracted from its root by (in our case parametrized) hydrothermal circulation. The heat extraction causes the temperature maximum again to move into the footwall of the new detachment (Figure 6(d)) and the next cycle begins.
In the model with a dynamic thermal evolution, footwall roll-back is more pronounced and takes longer compared to that with an imposed temperature structure. This is reflected in a smoother seafloor relief and longer fault life times. The stronger roll-back is possibly related to slightly wider fault zones. Compared to the model with imposed thermal structure (Figure 4), the strain rate of individual faults (Figure 8) does not drop as significantly at the activation of the next detachment, indicating a different partitioning of the total deformation between the active detachments. Furthermore, within the dynamic thermal model flip-flop sequences are shorter and faulting is generally more diverse including cross-cutting faults and more variable fault dips and life times.
While single detachments of opposite polarity are initiated at lower hydrothermal fault zone cooling, it requires \(F_{\mathrm{max}}\geq 1.5\) to achieve stable sequences of alternating polarity in the absence of intrusions (simulation 4). A similar trend is observed in simulations without enhanced cooling of fault zones, where a magmatic input equivalent to \(M=0.095\) (simulation 25) or more is required to achieve such stable sequences. Combinations of both, moderately enhanced fault zone cooling and moderate magmatic input, also reveal stable sequences of alternating polarity. This indicates that a combination of hydrothermal activity in fault zones and magmatic still intrusions below the footwall may favor flip-flop faulting.
#### 3.2.4 Deep-Cutting Faults: Criss-Cross and Spider Modes
Another type of faults that we observe in many simulations are _deep-cutting faults_. The name refers to the case where a new fault of opposite polarity cuts its predecessor several kilometers below the seafloor. The two faults then form an X-shape that encloses a large central block with significant surface relief (Figure 9). After the formation of such a deep-cutting fault pair, we observe two different faulting pattern evolutions.
The first mode is what [PERSON] et al. (2020) have named _spider mode_, where both deep-cutting faults remain active almost symmetrically. For geometrical reasons, this configuration requires an alternating activity of the faults below the crossing point, which temporarily induces strain and weak regions in both footwalls. These regions of accumulated strains migrate upwards and form the \"spider legs\" faintly visible in the strain rate plots (Figures 8(b) and 8(c)). While magmatic intrusions are not necessarily required to activate spider mode, they support and stabilize this mode by weakening the region below the intersection of the two faults. Spider mode typically ends after some million years when one fault becomes more dominant due to an emerging asymmetry.
_Criss-cross mode_ is a new mode identified in our simulations. It represents the second option for the evolution of deep-cutting faults, in which the two faults migrate through the central block by slicing it in several discrete steps. Each step is a short-lived normal fault that offsets a part of the central block (Figure 9e). The name _criss-cross_ refers to the alternating, almost perpendicular normal faults that cut-off sections of the central block. The number of dissecting normal faults during the criss-cross phase varies, and so does the impact on the enclosed surface relief. Criss-cross mode ends when the intersection point of the two deep-cutting faults reaches the seafloor allowing them to separate and migrate off-axis in opposite directions, similar to \"detachments of opposite polarity\".
We find criss-cross faults to become more frequent with stronger fault zone cooling. At increased \(F_{\rm{max}}\) (Equation 21b), new faults tend to form at a higher frequency. Thus, there is less time for shifting the temperature maximum away from the root of a fault into its footwall, and the next fault is more likely to form as a deep-cutting
Figure 7.— Flip-flop sequence from simulation 28 including hydrothermal fault zone cooling and magmatic intrusions (\(M=0.095,F_{\rm{max}}=1.5\)). First and second column: see Figure 3. Intrusions are marked in red in the central panels. Third column: Nusselt number on a logarithmic scale, maximum value \(\rm{Nu}_{\rm{max}}\approx 200\). Intrusions are marked in red in the central panels and by temperature in the right panels. The full sequence can be seen in Movie S6.
fault close to the root of its predecessor. The more spontaneous fault initiation also facilitates the formation of the sequence of dissecting normal faults.
#### 3.2.5 Chaotic Faulting Patterns
At the largest values of \(F_{\rm max}\) that we tested, fault formation becomes mostly chaotic. New faults form at high frequency, can be scattered around the axial region and possess variable fault dip and curvature. In this mode, more than two faults may be active simultaneously and accommodate comparable portions of total extension. Since each fault is repeatedly dissected by new faults, the surface relief is continuously reworked, which renders an interpretation of seafloor topography rather complicated. An exemplary sequence from simulation 24 (\(M=0.07\), \(F_{\rm max}=2.5\)) displaying this _chaotic mode_ is shown in Figure 10. Simulations featuring this mode do not resemble any observations from magmatic ridges and we therefore consider this setup to be unrealistic.
#### 3.2.6 Faulting Mode Summary
The faulting modes resulting from varying fault zone cooling and magmatic input are summarized in Figure 11 and we observe several trends. The occurrence of long-lived detachments and their accommodating faults is mainly limited to simulations with relatively low fault zone cooling (\(F_{\rm max}\leq 1\)), while criss-cross mode evolving from deep-cutting faults mainly occurs for \(F_{\rm max}\geq 1\). Chaotic mode is limited to the largest values of \(F_{\rm max}\geq 2.0\). Spider mode is observed almost equally over the whole range of \(F_{\rm max}\) that we tested, however it occurs more frequently with increasing \(M\). Consequently, the number of observed long-lived detachments and criss-cross faults slightly decreases with increasing \(M\). detachments of opposite polarity are the most abundant faulting mode in our simulations with \(F_{\rm max}\leq 2.0\).
Over the next sections, we will discuss the mechanisms that produce flip-flop detachment faulting in our model and evaluate different fault sequences from our results in the scope of observations from the SWIR.
## 4 Discussion
### Thermal Structure of the Football
Our simulations demonstrate that a crucial prerequisite for sequences of alternating detachments that constitute flip-flop faulting is a temperature maximum in the central footwall. In the model with an imposed temperature structure this automatically evolves as the footwall is uplifted. In the fully coupled model with a dynamic thermal
Figure 8: Fault zone analysis of a flip-flop sequence from simulation 28 including hydrothermal fault zone cooling and magmatic intrusions (\(M=0.095\), \(F_{\rm max}=1.5\)). Analysis strategy as described for Figure 4.
Figure 12 shows how the parametrized hydrothermal activity efficiently cools the currently active D7 and, to a lesser extent, the preceding fault zone D6 (Figure 12a). This shifts the temperature maximum at the brittle-ductile transition away from the active fault zone up 3 km into the central football (Figure 12b). The emplacement of
Figure 12. Analysis of the influence of different parameter combinations on the temperature field using the deformation from simulation 28. (a) Temperature difference between simulation 28 and its evolution when setting \(F_{\rm max}=0\) and \(M=0\) (same snapshot and fault numbers as in Figure 7b). White isotherms are from simulation 28, black ones are for \(F_{\rm max}=0\) and \(M=0\). The horizontal bars illustrate the meaning of the parameters plotted in panels (b) and (c). (b) Horizontal shift of the shallowest point of the 750\(\circ\)-isotherm compared to the setup with \(F_{\rm max}=0\) and \(M=0\). Dashed vertical black lines indicate the formation of a new fault. Note that the temperature field is reset at 30.6 Myr when the new fault forms to facilitate this comparison. (c) Width of the 750\(\circ\)C-isotherm, calculated as the geometric mean between five slices at 1 and 5 km below the shallowest point of the isotherm.
intrusions near the temperature maximum reinforces (Figure 12a) and narrows this high-temperature region by about 6 km (Figure 12c). Note that the cooler regions below the active faults result from stronger background cooling of the brittle lithosphere (i.e., larger Nu\({}_{0}\)), which is adjusted to the extra heat input from the intrusions to reproduce the observed lithosphere thickness.
The effects of these temperature variations on the faulting mode can be best understood by translating the temperature field in the deep brittle lithosphere and below to a modified viscosity and thus strength structure. Reduced temperature in the deeper fault zone corresponds to a viscosity increase, making the fault zone less efficient after a period of slip and cooling. Magmatic intrusions on the other side cause increased temperatures in the footwall below the brittle lithosphere, serving as a weak spot to focus flexural deformation. This combination of reducing the active fault zone efficiency and providing a weak spot in a geometrically favorable position is what triggers the next detachment of opposite polarity. The repetition of this cycle leads to the flip-flop faulting sequence ([PERSON], 2018; [PERSON] et al., 2013).
### Model Assumptions
#### 4.2.1 Hydrothermal Cooling of Active Fault Zones
As a first step toward a hydro-thermo-mechanical model that resolves porous flow within a visco-elasto-plastic deforming lithosphere, we have parametrized the heat transport by hydrothermal fluids taking into account the deformation state of the rock. To relate the magnitude of hydrothermal cooling predicted by our model to natural systems, we convert the enhanced thermal conductivity and resulting temperature gradients to an equivalent hydrothermal power output at a hypothetical fault-related vent site. To facilitate a comparison between all model calculations shown in Figure 11, we aim for a relation that only depends on the factor \(F_{\text{max}}\), by which we enhance the cooling effect of fault zones. Doing so allows to place a second axis of hypothetical hydrothermal heat fluxes on the right side of Figure 11. From our simulations we evaluate representative values for a fault-related seafloor temperature gradient of 0.05\({}^{\circ}\)C m\({}^{-1}\), and a fault zone width, over which an enhanced heat flux from the lithosphere into the ocean occurs, of 2 km. As fault zone thermal conductivity we take the conductivity of serpent-tinized mantle at the seafloor reduced by the background cooling. Using Equations 21b and 22 we obtain a fault zone thermal conductivity of
\[\kappa_{FZ}=\kappa_{0,strip}(\text{Nu}_{0}-1)\exp\left(\beta\Big{(}1-\frac{P_{sf }}{P_{sf}}\Big{)}\right)\cdot\big{(}10^{F_{\text{max}}}-1\big{)}. \tag{25}\]
The value of Nu\({}_{0}\) for each value of \(F_{\text{max}}\) is taken from the simulation at \(M=0\). Seafloor hydrostatic pressure \(P_{sf}\) is evaluated in the axial valley. Multiplication of temperature gradient, fault zone width, and fault zone conductivity \(\kappa_{FZ}\) provides an estimate for the total power output of the hypothetical vent fields. Although the resulting estimates should be viewed with caution because of the uncertainties involved, they allow at least for an order-of-magnitude comparison with vent field observations. Fault related heat fluxes predicted by our model (axis on the right-hand-side of Figure 11) span a plausible range from the low-temperature Lost City Hydrothermal Field located on a core complex off-axis the Mid-Atlantic Ridge ([PERSON], 2017) to the high-temperature Longqi-1 Vent Field located on the hanging wall of a detachment fault in a magmatic section of the SWIR ([PERSON] et al., 2020).
The hydrothermal site that is most relevant for the flip-flop dominated section of the SWIR investigated here is the recently discovered Old City hydrothermal field ([PERSON], [PERSON], et al., 2019) located on the exposed fault surface of the currently active detachment in the amangantic segment. Total heat flux estimates or venting temperature data are still missing, however, the vent field has a larger spatial extent than Lost City ([PERSON], [PERSON], et al., 2019) and an estimated comparable venting temperature of <100\({}^{\circ}\)C ([PERSON] et al., 2021). We therefore suppose that values of \(F_{\text{max}}\) much larger than 1.5 seem unlikely, because they would correspond to heat fluxes of more than 20 times that of Lost City. However, venting temperatures of >335\({}^{\circ}\)C of the inactive Tianzuo hydrothermal field inferred from geochemical data ([PERSON] et al., 2021) could point toward higher heat fluxes. More data on those and other, presumably existing ([PERSON] et al., 2004) yet undiscovered vent fields in similar tectonic settings, is needed to constrain representative numerical models. Note that our model cannot account for the limited life time of individual vent fields ([PERSON], 2000) but parametrizes the time-averaged cooling effect of all hydrothermal activity.
An open question is, to which depth hydrothermal circulation can efficiently cool the lithosphere. The maximum depth of hydrothermal fluid flow is mainly controlled by the subsurface permeability structure, which is a difficult to assess quantity and suggested values for oceanic lithosphere span orders of magnitude (e.g., [PERSON] et al., 2015; [PERSON] et al., 2018; [PERSON] et al., 2014; [PERSON] et al., 2019). Models and data generally suggest a decrease of permeability with depth (e.g., [PERSON] & [PERSON], 2014, and references therein), which would inhibit hydrothermal heat extraction at depths greater than a few kilometers. At temperatures above 600-800\({}^{\circ}\)C, pore space is assumed to be thermally closed to vigorous fluid flow ([PERSON] et al., 1998). [PERSON] et al. (2021) argue that under certain circumstances thermal cracking can extend the reach of hydrothermal convection down to 10 km depth. [PERSON] et al. (2020) model fluid circulation in the brittle lithosphere over a thickness of 13 km if permeability increase in the fractured fault zone is sufficient. Observation of hydrothermally altered minerals at this and comparable tectonic settings indicate that at least a limited amount of fluids reaches down to the brittle-ductile transition, even in the presence of an extremely thick lithosphere ([PERSON] et al., 2023; [PERSON] et al., 2021; [PERSON] et al., 2020). However, these observations may represent the limit of maximum fluid penetration depth, while active hydrothermal convection and cooling may be efficient only at shallower depth. Our model accounts for the discussed effects by having a pressure-dependent scaling of thermal conductivity leading to a decrease with depth in agreement with previous studies (e.g., [PERSON] et al., 2009), however possibly underestimated compared to scaling lengths given by [PERSON] and [PERSON] (2014), a fading influence across the brittle-ductile transition and a significant increase of the hydrothermal cooling effect around actively deforming fault zones. Note that the cooling effect incorporated by the Nusselt number parametrization spatially integrates the effect of fluid flow and may thus reach deeper than active hydrothermal circulation. To answer more in-depth questions about the role of active fault zones on hydrothermal circulation pathways--including potential feedbacks with magmatism and faulting--will require to resolve porous flow of hydrothermal fluids in the model instead of parametrizing its cooling effect.
While certainly affected by our model limitations, including its 2-D nature (discussed below), our results nonetheless indicate that enhanced cooling of active fault zones is a key process controlling the tectonic mode of a magma-poor ridge section. Simulations in which the tectonic state has no influence on the parametrized hydrothermal cooling (\(F_{\text{max}}=0\)) produce only limited flip-flop faulting, while simulations with a too strong enhancement of fault zone cooling do not produce flip-flop faulting at all.
#### 4.2.2. **Magmatic Sill Intrusions--Model Versus Data**
In this study we have varied sill sizes as well as emplacement frequencies such that the magmatic input fraction corresponds to a reasonable range of \(M\)-values lower than 0.12. This can be considered almost magmatic, and limited amounts of melt are in agreement with observations ([PERSON] et al., 2016; [PERSON] et al., 2013). Intrusions in our model facilitate flip-flop faulting through direct (rheological) and indirect (thermal) weakening. We hypothesize that further mechanical aspects which we have not considered in our model, such as additional stresses resulting from volumetric effects of intrusion emplacement and cooling or melt migration along faults could increase the influence of intrusions and affect the faulting types summarized in Figure 11. Moreover, we cannot speculate on the dominant faulting modes at greater \(M\)-values, where volumetric effects become critical and diking is essential to explain the transition to the more magmatic faulting mode of corrugated detachments.
When designing our model our intention was to put as few constrains on the dynamic evolution as possible. We therefore decided to not prescribe the location of intrusions but to choose realistic criteria for where ascending melts might gather to form a sill. We assume that melts migrate up to the shallowest position of the basaltic solidus temperature, which most often is located in the footwall below the active fault. While variable emplacement depths could affect our results, our chosen method is consistent with the predictions of the numerical study by [PERSON] et al. (2022) on the thermal regime of magma-poor segments. After emplacement, cooling intrusions are transported upward where they are cut and sheared by subsequent faults. This cycle is in agreement with recent seismic data ([PERSON] et al., 2020): Stacked sills in the deep lithosphere can potentially explain a cluster of sub-horizontal seismic reflectors between 9.3 and 13 km, while sheared intrusions could intensify the seismic signature of the detachment faults, which are identified by a series of dipping reflectors.
#### 4.2.3 3-D Effects of the Ridge Axis
Both amagmatic corridors of the 62\({}^{\circ}\)-65\({}^{\circ}\)E segment of the SWIR are enclosed by more magmatic sections characterized by axial volcanism and symmetric normal faulting. This segmentation presumably results from strong along-axis focusing of melts ([PERSON] et al., 2003). The more magmatic sections do most likely serve as thermal and mechanical anchors for the evolution of their magma-poor neighbor-segments. We presume this to be the main factor missing in our 2-D model, which cannot account for along-ridge variations in magma supply or faulting patterns. Coupling between an amagmatic segment sandwiched between magmatic sections could prevent long-lived detachment faults from shifting tectonic activity several tens of kilometers from the initial position at the ridge axis. Fault life times would consequently be shorter and faulting patterns more stable.
However, being able to reproduce a stable flip-flop faulting mode in a dynamic thermo-mechanical 2-D model without prescribing the ridge axis position lets us speculate that the interplay of hydrothermal cooling (enhanced in fault zones) and the heat input plus weakening effect of sill intrusions are key mechanisms that facilitate flip-flop faulting.
### Tectonic Significance of Observed Faulting Modes
We performed a three-step analysis on each of the simulations. First, we picked the onset time of every fault zone and categorized it (Figure 11). In the second step, we identified fault sequences of at least 4 consecutive faults that fall in one of the two categories \"apparent flip-flop\" and \"true flip-flop\" (Figures 13a and 13b). As \"apparent flip-flop\" we categorize faults that produce off-axis dipping fault zones and relatively regular spaced ridges, since these are the main features used to identify flip-flop detachments from observational data. For the category \"true flip-flop\" we additionally evaluate if the faulting mechanism resembles the flip-flop mechanism described in the previous sections. Faulting sequences are mostly terminated by a long-lived detachment or a deep-cutting fault/ spider mode phase. As a last step of our analyses, we calculate the mean fault duration during the faulting sequences (Figure 13c).
#### 4.3.1 Fault Life Time
Before we discuss the relevance of the different fault sequences, we will first have a look at the observed fault life times during these sequences. Figure 13c shows that the mean fault duration of simulations with \(F_{\rm max}\leq 1.5\), including the presented flip-flop sequence from simulation 28, is about 1.6 Myr thus \(\sim\)0.5 Myr longer than estimated for the SWIR. This is presumably due to the missing 3-D effects of the ridge axis providing external triggers for the formation of new on-axis faults. Another potential reason is the chosen rheology with relatively high yield stress promoting well defined and stable fault zones.
Fault duration slightly increases with an increase of \(M\). Before fault zone cooling can significantly shift the temperature maximum and thus intrusion replacement into the footwall, intrusions are emplaced close to the root
Figure 13: Parameter space plot showing the analysis of faulting sequences. All three plots use the framework described for Figure 11. Trim angular outlined region marks the parameter range producing stable true flip-flop faulting. Gray hatched region at \(F_{\rm max}=2.0\) is excluded from further analyses, see Section 4.3.2. (a) Proportion of faults within identified fault sequences that reproduce bathymetric and subsurface features without displaying classical flip-flop mechanics. (b) Proportion of faults within identified fault sequences that, additionally to the conditions for a, reproduce the flip-flop mechanism. (c) Mean fault duration of faults within identified flip-flop sequences (apparent and true). The black hatched region gives mean general fault duration for simulations without SWIR/flip-flop resembling faulting sequences.
of the new fault zone, stabilizing and prolonging its initial phase. This mechanism is evident in Figure 12b, where in the first phase of D7 the temperature maximum is shifted toward the fault zone instead of into the footwall, if intrusions are considered (red and yellow lines).
Increasing \(F_{\text{max}}\) to 2.0 results in a clear drop in the mean flip-flop fault duration. Simulation 5 for example, displays sequences of rather uniform flip-flop faulting with a mean fault duration of 1.0 Myr (see Movie S8). However, we cannot verify the role of a footwall temperature maximum as a trigger for the new faults in these simulations, as it does not coincide as clearly with the evolving shear band that develops into the next detachment of opposite polarity. We rather believe that instead the feedback loop between rheology, deformation and cooling that allows for a more spontaneous fault initiation explains the increased fault frequency. These feedbacks, however, occur very localized in the fault zone and to be able to properly address it, we would require to resolve hydrothermal flow inside the fault zone and to include effects of fluid-rock-interaction on rheology. Consequently, we see \(F_{\text{max}}=2.0\) as the point, where the concept of our parametrization breaks down and we therefore hatched the corresponding region in the parameter space plots in Figure 13.
#### 4.3.2 True Flip-Flop Faulting
From Figure 13b it can be inferred that the activation of flip-flop faulting mechanism is not simply caused by the absence of melt input but seems to result from a sensitive interplay of thermal, tectonic and magmatic processes. The relevant parameter range that best reproduces the conditions necessary for a stable flip-flop faulting mode in line with the commonly accepted interpretation of SWIR observations is identified by the green band in Figure 13b.
A feature that we observe in many flip-flop producing simulations are antithetic faults in the hanging wall of the active detachment (Figures 7a, 7b, and 7d). These are highly consistent with microseismicity data ([PERSON] et al., 2023). In our simulations, they often help to focus the footwall deformation resulting in the next fault of opposite polarity (Figures 7b and 7c). This could indicate that new faults indeed form around the emergence of their predecessor as predicted by our simulations. While we know of no evidence for still ongoing deformation along the preceding fault zone, that is, D2 in Figure 2b, we could imagine that activity alternates between the two faults on a time scale not resolved by existing observations instead of both being continuously active.
Flip-flop faulting has originally been proposed for the magma-poor rifled west Iberia margin ([PERSON] and [PERSON], 2011) and is also observed at another segment of the SWIR (51.5-53.5\"E; [PERSON] et al., 2020). However, at virtually magmatic segments along other ultraslow-spreading ridges like the Gakkel or the Enjovovich Ridge this distinct faulting pattern has not been observed yet ([PERSON] et al., 2021; [PERSON] et al., 2003). If flip-flop faulting is indeed absent at these settings, this mode may represent a special case that depends on the specific regional conditions--for example, thermal structure, stress field or the characteristics of neighboring magmatic segments--rather than being the normal state for ridges at this spreading rate and melt supply. This is further supported by the high sensitivity of stable flip-flop faulting to the imposed temperature field and rheology that we observed in tests for the simulation presented in Section 3.1. It could explain, why smooth seafloor areas are not observed more frequently.
Note that the parameter range yielding realistic results possibly goes beyond the simulations displaying the longest and most uniform flip-flop sequences, which is supported by both models and data. [PERSON] and [PERSON] (2011) suggest alternating polarities to be dominant, but do not preclude successive detachments of the same polarity. Flip-flop sequences observed at mid-ocean ridges are of limited duration: eastern corridor of the 62\({}^{\circ}\)-65\({}^{\circ}\)E segment: 11 Myr ([PERSON] et al., 2013); 51.5\({}^{\circ}\)-53.5\"E segment: \(\sim\)7 Myr (Figure 7 in [PERSON] et al. (2020)). They also show considerable variability: The western magma-poor corridor of the 62\({}^{\circ}\)-65\({}^{\circ}\)E segment of the SWIR appears to have a lower magmatic budget and more symmetric ridges than the eastern corridor, indicating at least a variable periodicity of the faulting sequence ([PERSON] et al., 2013). More symmetrical ridges in our simulations often reflect host-like flip-flop detachments (especially in simulations with imposed thermal structure, Figure 3). Ridges with steeper outward- than inward-facing slopes as observed in the eastern corridor, are indicative of more intensive footwall rollback, or of another faulting mode (see Section 4.3.3). For a more in-depth analyses of the surface relief, surface processes such as erosion and mass wasting would need to be considered. Without, our experiments generally produce stronger relief than observed.
#### 4.3.3 \"Apparent Flip-Flop\" Modes
We now consider sequences featuring other modes besides true flip-flop faulting that are also compatible with some of the most important observations. These modes are antithetic accommodating faults in the wake of long-lived detachments (Figures (e)e and (f)f) and criss-cross faults succeeding a deep-cutting fault. The latter ones are only classified as apparent flip-flop if they offset the enclosed ridge only slightly before they separate at the surface and continue just as regular flip-flop detachments (e.g., Figures (g)g-(g)g-(g)). There are some arguments in favor of considering these modes as potential alternative interpretation of the SWIR observations, especially since they occur over a wide and realistic parameter range as Figure (a)a shows. Both modes produce a series of off-axis, outward dipping inactive faults and pronounced, more or less regularly spaced ridges. Furthermore, they are generally able to produce abnormal seafloor age pattern (see arrows indicating seafloor age in Figure 2): antithetic accommodating faults as they are passively transported toward their hanging wall side after becoming inactive, and deep-cutting faults like regular flip-flop faults, depending on where they finally cut their predecessors exhumed shear plane. However, this is mainly a conceptual notion, because seafloor age with distance from the SWIR axis is, to our knowledge, mostly inferred from sampling breakaway and fault emergence locations and interpreting these within the conceptual kinematics of flip-flop faulting.
Even though high-resolution magnetic profiles exist for this region ([PERSON] et al., 2014), only one magnetic anomaly can be confidently traced to the magmatic corridors (C5 in Figure (d)d) due to the extensive serpentinization and very low contribution of magmatic rocks. These data indicate long-term symmetric spreading compatible with flip-flop mode as well as antithetic accommodating (cf. a L-r-r-R-l-l sequence, where uppercase letters stand for long-lived detachments and lowercase letters for accommodating faults) and deep-cutting faulting modes. We are not aware of other data such as high-resolution petrological profiles that would rule out one or the other faulting mode. Moreover, some of the interpreted fault zones are still under debate. For example, D3' interpreted by [PERSON] et al. (2021) from seismic velocities has significantly smaller relief than the other detachments and could well be attributed to one of our alternative two modes. Also, both modes can produce asymmetric ridges in agreement with the bathymetry from the eastern magma-poor corridor of the 62\({}^{\circ}\)-65\({}^{\circ}\)E segment of the SWIR.
Including these possible alternative interpretations provides a much broader fit of our simulations to observations than constraining the results to perfectly uniform flip-flop detachment faulting. We thus hypothesize that while pure flip-flop mode may indeed represent a special case, a mix of the three modes discussed here provides a more robust explanation for magma-poor spreading in a very thick brittle lithosphere. This sheds new light on existing data and emphasizes the need for more densely sampled profile data, such as seafloor age measurements and hypocenter locations of microsecismicity, also at other settings potentially hosting flip-flop detachment faulting.
## 5 Conclusions
Numerical experiments with an imposed temperature structure have demonstrated the key role of a temperature maximum in the central footwall of a detachment for focusing strain to trigger a new on-axis fault of opposite polarity. Using a dynamic thermo-mechanical model that accounts for the key mechanisms grain size evolution, serpentinization, enhanced hydrothermal cooling of fault zones, and influence of periodic sill intrusions at the base of the lithosphere, we have further explored the evolving faulting modes. Results of experiments in which we systematically varied magnitudes of magmatic input and hydrothermal cooling show that:
* Fault zone cooling increases the temperature difference between the active fault and its surroundings. It thereby shifts the temperature maximum caused by the upwelling mantle material into the footwall.
* Intrusion emplacement reinforces this temperature maximum and assists strain focusing through thermal and rheological weakening.
* Stable flip-flop faulting that is controlled by the large-scale temperature field is limited to simulations with a fault-related long-term average heat flux about 20 times that of the Lost City Hydrothermal Field. Generally, flip-flop faulting is observed at reduced magnitudes of hydrothermal fault zone cooling and magmatic sill intrusions if both processes act together.
* Two other faulting modes, antithetic accommodating footwall faults and criss-cross faults, offer an alternative interpretation of the current data base.
Our results indicate that the combination of weak magmatism at the base of the lithosphere and fault zone related hydrothermal activity can explain the thermal structure of the lithosphere and consequently the faulting mode of magma-poor mid-ocean ridges like the 62 degE to 65 degE segment of the SWIR, which might be more diverse than previously thought.
## Data Availability Statement
The code of the numerical model M2 TRI_vep(Hasenclever & Glink, 2024) used to produce our results is available at [[http://doi.org/10.25592/uhhfdm.13585](http://doi.org/10.25592/uhhfdm.13585)]([http://doi.org/10.25592/uhhfdm.13585](http://doi.org/10.25592/uhhfdm.13585)). Figures 12a and 13c use the color map \"vik\" from the \"Scientific Colour Maps\" package by [PERSON] (2021). Animations of the simulations discussed in the paper can be found in Supporting Information S1 in the online version of this article.
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wiley/ffdcd525_85e5_4165_86dc_a6d1ff23b7c0.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
[PERSON]
1 National Engineering Research Center for Geographic Information System, China University of Geosciences (Wuhan), Wuhan, China, 2 School of Navigation, Wuhan University of Technology, Wuhan, China, 2 College of Resource Environment and Tourism, Capital Normal University, Beijing, China
[PERSON]
1 National Engineering Research Center for Geographic Information System, China University of Geosciences (Wuhan), Wuhan, China, 2 School of Navigation, Wuhan University of Technology, Wuhan, China, 2 College of Resource Environment and Tourism, Capital Normal University, Beijing, China
[PERSON]
1 National Engineering Research Center for Geographic Information System, China University of Geosciences (Wuhan), Wuhan, China, 2 School of Navigation, Wuhan University of Technology, Wuhan, China, 2 College of Resource Environment and Tourism, Capital Normal University, Beijing, China
[PERSON]
2 College of Resource Environment and Tourism, Capital Normal University, Beijing, China
[PERSON]
1 National Engineering Research Center for Geographic Information System, China University of Geosciences (Wuhan), Wuhan, China, 2 School of Navigation, Wuhan University of Technology, Wuhan, China, 2 College of Resource Environment and Tourism, Capital Normal University, Beijing, China
[PERSON]
337 and 245 global flush drought onset and termination events can be correctly predicted at 7 days lead time Machine learning improves global flash drought prediction over dynamic model
###### Abstract
Flash droughts are rapidly developing extreme weather events with sudden onset and quick intensification. Global prediction of flash droughts at sub-seasonal time scales remains a great challenge. Current state-of-the-art dynamic models subject to large errors and demonstrate low skills in global flash drought prediction. Here, we develop a machine learning-based framework that uses meteorological forecasts as inputs to predict global root-zone soil moisture and flash droughts from 1 day to 2 week lead times. The results indicate that 33% and 24% global flash drought onset and termination events can be correctly predicted by machine learning at 7 day lead time, versus 19% and 11% fractions by state-of-the-art dynamic model. The developed machine learning model demonstrates substantial improvements over dynamic model in global soil moisture prediction, and thus enhances global flash drought forecasting skills in space and time. The presented framework may benefit global flash drought prediction and early warning at sub-seasonal scales.
Suporting Information may be found in the online version of this article.
10.1029/2024 GL111134
1
## 1 Introduction
Drought is a complex climate phenomenon usually characterized by high evaporative demand, sustained precipitation deficits and low soil moisture, which can lead to severe agricultural, hydrological and socioeconomic impacts ([PERSON] et al., 2024; [PERSON] et al., 2021; [PERSON] et al., 2012; [PERSON] et al., 2019). Flash drought, unlike traditionally slowly evolving drought events, develops at sub-seasonal scales with sudden onset and rapid intensification ([PERSON] et al., 2019; [PERSON] et al., 2019). During a flash drought, the soil moisture quickly depletes due to anomaly high temperature and strong precipitation shortage within a few weeks, causing unexpected damage to crop yields, livestock production and ecosystem functions ([PERSON] et al., 2018, 2022; [PERSON] et al., 2019). In recent years, global flash drought is accelerated and the flash drought risk prevails in United States, China, Brazil and Australia ([PERSON] et al., 2021; [PERSON] et al., 2022). Therefore, effective global flash drought prediction can provide early warnings for agricultural preparations and water resources management.
Coupled models which simulate the Earth's climate through integrated modeling of atmosphere, oceans and land are usually used for flash drought prediction ([PERSON] et al., 1997; [PERSON] et al., 2018) (see Supplementary Text 1.1 in Supporting Information S1). Global flash drought prediction at sub-seasonal scales remains a great challenge due to limited ability to forecast flash drought-related variables in state-of-the-art coupled models ([PERSON] and [PERSON], 2016; [PERSON] et al., 2013; [PERSON] et al., 2003; [PERSON] et al., 2021; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2018; [PERSON] et al., 2017). Successful prediction of the timing of flash drought requires relatively accurate forecasts of precipitation, temperature, winds and other influential factors at least days to weeks in advance, which still faces difficulties in current weather models ([PERSON] et al., 2023; [PERSON] et al., 2022; [PERSON] et al., 2023; [PERSON] et al., 2024; [PERSON] et al., 2023). The subseasonal-to-seasonal (S2S) projectprovides global meteorological and land surface forecasts by a number of coupled models ([PERSON] et al., 2023; [PERSON] et al., 2017) (Table S1 in Supporting Information S1), demonstrating some predictive skills for temperature and precipitation over days to weeks ahead. However, large errors still exist in model forecasts due to uncertainties in initial conditions, imperfection in model structures and parameterization schemes and the chaotic nature of climate system, hindering skillful global flash drought prediction ([PERSON] et al., 2020; [PERSON] et al., 2024; [PERSON] & [PERSON], 2023; [PERSON] et al., 2023; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON], [PERSON], [PERSON], et al., 2021) (Supplementary Text 1.2 in Supporting Information S1).
Flash drought can be defined based on evaporative demand ([PERSON] et al., 2016), precipitation index ([PERSON] & [PERSON], 2015), evaporative stress ratio ([PERSON] et al., 2019), US Drought Monitor ([PERSON] et al., 2020) and soil moisture ([PERSON] et al., 2022; [PERSON] et al., 2019). Of which, soil moisture is a good indicator in detecting flash drought onset and the rapid decline of soil moisture can serve a precursor for agricultural drought ([PERSON] & [PERSON], 2022; [PERSON] et al., 2019, 2023). Here we use the root-zone soil moisture (RZSM) as the target variable to define flash drought and assess its forecasting skills by coupled models. Current flash drought prediction models demonstrate some skills locally ([PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] & [PERSON], 2023; [PERSON] & [PERSON], 2020; [PERSON] et al., 2022; [PERSON] et al., 2024; [PERSON] et al., 2020) (Supplementary Text 1.2 in Supporting Information S1), while the global flash drought prediction predictability remains unclear. The soil moisture-based flash drought onset hit rate by S2S is approximately 20% in China at 1 week lead time ([PERSON] & [PERSON], 2023), due to strong predictive biases in RZSM forecasts. How to effectively resolve the RZSM forecasting error to improve flash drought prediction skill is a critical concern ([PERSON] et al., 2024; [PERSON] et al., 2024; [PERSON] & [PERSON], 2024; [PERSON] et al., 2024; [PERSON] & [PERSON], 2023; [PERSON] et al., 2023; [PERSON] et al., 2022).
Given the limited understanding of global flash drought predictability, here we provide a global view of flash drought forecasting skills by machine learning (ML) and state-of-the-art dynamic models at 1 day to 2 week time scales. The model-based meteorological forecasts and the initial conditions from observations are jointly taken as inputs in a ML-based flash drought forecasting framework. We show that the data-driven machine learning approaches can alleviate the RZSM predictive errors substantially and improve flash drought forecasting skills. Multisource datasets and multi-model ensembles are used to validate the effectiveness of the developed ML model in global flash drought prediction. The flash drought forecasting skills from ML and dynamic S2S models are comprehensively compared over different lead times, continents, spatial locations and datasets. The presented ML-based predictive modeling may help gain a better understanding of global flash drought forecasting capability and shed light on skillful global flash drought early warning at sub-seasonal timescales.
## 2 Materials and Methods
### Datasets
Meteorological forecasts from the European Center for Medium-Range Weather Forecasts (ECMWF) sub-seasonal to seasonal (S2S) model are taken as inputs to machine learning ([PERSON] et al., 2017), including 2 m temperature (T), 2 m dewpoint temperature (DT), 10 m U wind component (UW), 10 m V wind component (VW), total precipitation (TP), surface pressure (SP), surface net thermal radiation (STR), surface net solar radiation (SSR) and snowfall (SF). The meteorological reforecasts from ECMWF S2S model are collected during 2000-2020 from 1 day to 2 weeks time scales at the archived 1.5\({}^{\circ}\) resolution in the S2S website. An ensemble of 11 ECMWF members is used to obtain root-zone soil moisture (RZSM) forecasts and thus the flash drought prediction for dynamic ECMWF model. The initial RZSM, T, DT, UW, VW, TP, SP, STR, SSR and SF control forecasts from ECMWF S2S are adopted as independent variables to predict RZSM by the machine learning model. Multiple reforecasts from different ECMWF S2S model versions are averaged to obtain daily mean values of predictors and predictands. The RZSM forecasts from 11 ECMWF S2S members are aggregated to pentads by average to estimate flash drought predictions and the predictive uncertainty is derived by 10,000 bootstrapped sampling.
Besides the dynamic predictors, six static features from the fifth generation ECMWF atmospheric reanalysis (ERA5) ([PERSON] et al., 2020) are collected to reflect the spatial heterogeneity of land surface, including high vegetation cover, low vegetation cover, type of high vegetation, type of low vegetation, land-sea mask and soil type. As for the predictand, the ERA5 reanalysis RZSM data demonstrated good accuracy by in-situ validation and have been used in flash drought monitoring and assessment ([PERSON] et al., 2020; [PERSON] & [PERSON], 2023; [PERSON], [PERSON], et al., 2021; [PERSON] et al., 2023). The RZSM variable is generated by a weighted average of soil moisture at 0-7, 7-28 and 28-100 cm soil layers according to their depths to represent the averaged soil water content during 0-100 cm ([PERSON] et al., 2024; [PERSON] et al., 2023; [PERSON] & [PERSON], 2023; [PERSON], [PERSON], [PERSON], et al., 2021) (Supplementary Text 2.1 in Supporting Information S1). As the flash drought classification is dependent on the choice of data sources, the GLEAM version 3.8a ([PERSON] et al., 2017) and MERRA2 ([PERSON] et al., 2017) RZSM datasets are also collected to understand the disparities in flash drought forecasting skill using different datasets.
### Flash Drought Definition and Calculation
Here we adopt the soil moisture-based flash drought definition ([PERSON] et al., 2022; [PERSON] et al., 2019, 2023): the 0-100 cm RZSM decreases from above the 40 th percentile to below the twentieth percentile during the growing season (April-September in the Northern Hemisphere, October-March in the Southern Hemisphere), with an averaged declining rate of no less than 5% for each pentad and the total flash drought duration should be no less than four pentads (20 days). The pentad soil moisture percentiles are calculated based on the RZSM climatology during 2000-2020 for observations and forecasts separately to alleviate the influence of predictive bias. The flash drought onset is defined as the time range in which the RZSM drops below 40 th percentile to the pentad below twentieth percentile first during a flash drought event. The flash drought is terminated when the RZSM percentile rises to twentieth percentile after onset. The consecutive pentads from flash drought onset to termination is regarded as flash drought duration. For RZSM forecasts less than one-pentad lead time, the observed and forecasted daily RZSM are concatenated to calculate the pentad-mean RZSM and percentiles to predict flash drought. For RZSM forecasts no less than one-pentad lead time, only the daily RZSM forecasts are used to calculate the forecasted percentiles and flash drought.
### Machine Learning Forecasting Model
The Light Gradient Boosting Machine (LightGBM) ([PERSON] et al., 2017) is used as the machine learning model to construct the flash drought forecasting framework, as it is widely used in hydrometeorological modeling with relatively high accuracy ([PERSON] et al., 2019; [PERSON] et al., 2023; [PERSON] et al., 2024). Here, the meteorological forecasts, historical observations and static features are concatenated as independent variables to predict RZSM using LightGBM (Figure S1 in Supporting Information S1). The static and dynamic features are jointly used to train a global machine learning forecasting model to predict RZSM from 1 day to 2 weeks time scales. All the predictors and predictands data are collected from year 2000-2020 and are resampled to 1.5\({}^{\circ}\)\(\times\) 1.5\({}^{\circ}\) resolution. An ensemble of three machine learning models is constructed by setting different number of leaf nodes (2,000, 3,000 and 4,000) in LightGBM models. The number of trees and the learning rate are set to 500 and 0.02, respectively, after a comparison of various parameters (Figure S2 in Supporting Information S1 and Supplementary Text 2.2 in Supporting Information S1). A five-fold cross-validation is conducted to predict RZSM during 2000-2020 and calculate flash drought over the past 20 years. The variable importances of the LightGBM models are demonstrated in Figure S3 in Supporting Information S1 and the interpretability is explored using the SHapley Additive exPlanations (SHAP) method (Figures S4-S5 in Supporting Information S1).
### Evaluation Metrics
The flash drought forecasting skill is evaluated by the contingency table method, including the hit rate (_HIT_), false alarm ratio (_FAR_) and equitable threat score (_ETS_) ([PERSON], 2011) (Supplementary Text 2.3 in Supporting Information S1). The _HIT_ metric indicates probability of detection, with a range of (0,1) and a value of one indicates the success of predicting all the flash drought events. _FAR_ represents the probability of false alarms and a perfect value is zero. _ETS_ is a balanced score that takes into misses and false alarms both into account, with the range of (\(\sim\)1/3,1) and a perfect score of one. _ETS_ measures the forecasting skill relative to chance and a _ETS_ value above zero could be considered as skillful relative to the chance forecast.
## 3 Results
### Flash Drought Forecasting Skill
The flash drought forecasting skill decreases with the increase of lead time, both for ML and ECMWF models (Figure 1). Approximately global 84% FDO events can be correctly forecasted at 1 day lead time by the ML model (Figure 1a), while this fraction reduces to 33% and 17% for 7 and 14 day lead times, respectively. However, only different lead times over most of global lands (Figures S7-S8 in Supporting Information S1), suggesting spatial superiority of ML over ECMWF. In addition, the ML-based flash drought forecasting skills exhibit significant superiority relative to the ECMWF model over all the six continents (Figures S9-S14 in Supporting Information S1).
### Forecasting Skill Analysis
As flash drought is defined based on soil moisture, we plotted the RZSM forecasting skills by ML and ECMWF to understand their differences. The anomaly correlation between forecasts and observations for ML is significantly higher than the ECMWF model (\(N\) = 6,646, \(p\) = 0.000) for RZSM prediction at 1-14 day lead times (Figure 4a). The global mean anomaly correlation coefficient (ACC) reaches up to 0.99 (0.79), 0.95 (0.76) and 0.87 (0.70) for RZSM prediction by ML (ECMWF) model at 1, 7 and 14 day lead times, with a relative 25% ACC improvement over ECMWF (Figure 4a). The ACC spatial patterns indicate that the ML-based RZSM prediction skill is superior to that of ECMWF at 7 day lead time over most of global lands (Figure 4b), suggesting spatial effectiveness for RZSM skill improvement by ML. Substantial ACC improvements are demonstrated over central Africa, central
Figure 1.— The flash drought forecasting skills over different lead times by ECMWF and ML models. The skills are calculated on a global average (except the Antarctica), weighted by the number of flash drought events and the area over each grid cell. The a HIT, b FAR and c ETS metrics are calculated based on predicted and observed flash drought events for ECMWF and ML models, respectively. The HIT indicator indicates the hit rate, FAR is the false alarm ratio, and ETS is the equitable threat score. The shaded areas represent the 95% confidence interval and are obtained by 10,000 bootstrapped sampling. The predictive skills for flash drought onset (PDO) and flash drought termination (FDT) are demonstrated. The confidence intervals for ML models may be too small to be visually distinguishable.
and eastern Asia, northern South America and western North America for ML versus ECMWF. The spatial RZSM skill improvement for ML over ECMWF is expected for different lead times (Figure S15 in Supporting Information S1), which accounts for enhanced flash drought forecasting skills spatiotemporally.
The ML-based flash drought predictions are also evaluated using GLEAM and MERRA2 datasets besides the ERA5 data. Approximately global 74% (75%), 28% (27%) and 14% (15%) FDO events can be correctly predicted by the ML model at 1, 7 and 14 day leads, based on the GLEAM (MERRA2) dataset (Figure S16 in Supporting Information S1), which is relatively lower compared to ML prediction with ERA5 data, but still higher than that of the ECMWF model. As for FDT, the ML models with GLEAM and MERRA2 datasets demonstrate higher HIT scores for 1-12 days leads over ECMWF with ERA5 data. For the FAR and ETS indicators, similar skill improvements are expected from ML versus ECMWF for most of the lead times. The spatial patterns also reveal the superiority of the ML model with different RZSM datasets versus the ECMWF model over large global lands in flash drought prediction (Figures S17-S21 in Supporting Information S1).
We calculated the flash drought prediction skills using only initial conditions from soil moisture, precipitation, temperature and other related factors. The results indicate that 83% (83%), 29% (14%) and 13% (5%) FDO (FDT) events are captured by the ML model using initial conditions at 1, 7 and 14 day leads (Figure S22 in Supporting Information S1), respectively, accounting for 98% (97%), 85% (56%) and 75% (59%) fractions of FDO (FDT)
Figure 2: The statistical distribution of flash drought forecasting skills. The HIT (a), (b), FAR (c), (d) and ETS (e), (f) metrics are demonstrated for FDO and FDT event predictions over 1–14 day leads. The boxes represent the distribution quartiles and the horizontal central line within the boxes indicates the mean value. The whiskers denote the 5–95% confidence interval of statistical metrics. The box plots are generated based on the ensemble mean predictions from ECMWF and ML models at a global 1.5” \(\times\) 1.5” spatial resolution.
skills by combined meteorological forecasts and initial conditions. Therefore, the initial conditions from atmospheric and hydrological components are critical for flash drought prediction within 2 week lead time ([PERSON] & [PERSON], 2023; [PERSON] & [PERSON], 2020; [PERSON] et al., 2020). Meanwhile, the meteorological forecasts also play an important role in modulating flash drought prediction skills in space (Figures S23-S24 in Supporting Information S1). The statistical distributions of RZSM forecasting skills indicate improved anomaly correlation for the ML model with combined meteorological forecasts and initial conditions versus that with only initial conditions (Figure S25 in Supporting Information S1).
The forecasting skills of nine flash drought relevant variables by ECMWF are evaluated using ACC. It is seen that temperature, dewpoint temperature and surface pressure are relatively more skillful versus winds, precipitation, snow and radiations (Figures S26-S27 in Supporting Information S1). The global averaged ACC for temperature (surface pressure) forecasting reaches up to 0.93 (0.84), 0.76 (0.72) and 0.34 (0.29) for 1, 7 and 14 day lead times respectively, while becomes 0.83 (0.70), 0.34 (0.49) and 0.07 (0.14) for precipitation (U wind). The skills of the nine influential factors account for RZSM and flash drought forecasting performances spatiotemporally and the limited FDO and FDT skills beyond 1 week are expected due to limited predictability in these factors ([PERSON] et al., 2024; [PERSON] et al., 2020).
## 4 Discussion and Conclusions
Here we use machine learning techniques to examine soil moisture and flash drought forecasting skills at 1 day to 2 week timescales and we show that the flash drought predictive skills can be further improved by data-driven modeling. The initial conditions from soil moisture, temperature, precipitation and other related factors provide important predictive information for flash drought ([PERSON] et al., 2020; [PERSON], 2023; [PERSON] et al., 2020), and the incorporation of these initial conditions improves flash drought prediction skills significantly relative to the ECMWF S2S model, especially when incorporating observations (Figure S28 in Supporting Information S1 and Supplementary Text 3 in Supporting Information S1). Incorporating observations in flash drought predictions at a lead time less than a pentad may cause slight overestimation of predictive skills by offline
Figure 3: Spatial patterns of flash drought onset prediction skills at different lead times. HIT and ETS indicators are demonstrated for 3 day (a), (b), 7 day (c), (d) and 10 day (c), (f) lead times. The HIT and ETS metrics are calculated over global lands (except the Antarctica) at \(1.5^{\circ}\times 1.5^{\circ}\) resolution.
experiment, when observations are not released for use in near-real-time. The relatively quicker decline of predictive skills with increasing lead times for ML versus ECMWF may be caused mainly by initial conditions (Figure S24 in Supporting Information S1 and Supplementary Text 3 in Supporting Information S1).
Current flash drought forecasting skills can be further enhanced from several aspects. First, atmospheric forecasting skills are precursors for flash drought prediction and the ongoing advances in atmospheric predictability will provide new chances for flash drought prediction ([PERSON] et al., 2023; [PERSON] et al., 2022; [PERSON] et al., 2023). An in-depth understanding of flash drought mechanisms over different regions, time scales and processes is urgently needed, such as the Madden-Julian Oscillation and land-atmospheric feedback ([PERSON] et al., 2024; [PERSON] and [PERSON], 2022; [PERSON] and [PERSON], 2023; [PERSON] and [PERSON], 2024; [PERSON] and [PERSON], 2023; [PERSON] et al., 2022). Second, more accurate representations of flash drought initial conditions and relevant factors would provide new insights on flash drought forecasting ([PERSON] et al., 2020; [PERSON] and [PERSON], 2022; [PERSON] et al., 2020). Finally, the flash drought responses to atmospheric forecasts can be further enhanced by sophisticated physical and deep learning methods ([PERSON] et al., 2023; [PERSON] et al., 2019; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2022).
This study has some limitations. The RZSM is used for flash drought definition and forecasting in this study, while the soil moisture at different depths (Figure S29 in Supporting Information S1) may be explored because vegetation root depths are spatially heterogeneous. The developed model can generate subseasonal flash drought predictions at 1-14 days at a relative coarse resolution (1.5\({}^{\circ}\)) due to limited computation capacity. The flash drought prediction skills may be different at different spatial resolutions because atmospheric predictability and land surface processes may have different driving mechanisms at various spatial scales. Future work should explore high-resolution (e.g., 0.25\({}^{\circ}\)) flash drought predictions using high-performance computers at a lead time up to 2 months. Currently, the reanalysis soil moisture datasets are used to define and predict flash drought, which may have some delays in operational flash drought predictions. For operational use, the near-real-time observed or assimilated soil moisture datasets should be used, such as the Soil Moisture Active Passive (SMAP) level 3 or level 4 product. The near-real-time flash drought predictions and evaluations would be examined in future work.
## Data Availability Statement
The S2S data ([PERSON] et al., 2017) are hosted by ECMWF and are available at [[https://www.ecmwf.int/en/research/projects/s2s](https://www.ecmwf.int/en/research/projects/s2s)]([https://www.ecmwf.int/en/research/projects/s2s](https://www.ecmwf.int/en/research/projects/s2s)). The ERA5 forcings and RZSM datasets ([PERSON] et al., 2020) are downloaded from the Copernicus Climate Data Store ([[https://cds.climate.copernicus.eu/cdsapp#/dataset/reanalysis-era5-single-levels](https://cds.climate.copernicus.eu/cdsapp#/dataset/reanalysis-era5-single-levels)]([https://cds.climate.copernicus.eu/cdsapp#/dataset/reanalysis-era5-single-levels](https://cds.climate.copernicus.eu/cdsapp#/dataset/reanalysis-era5-single-levels))). The GLEAM RZSM data ([PERSON] et al., 2017) is collected from Ghent University ([[https://www.gleam.eu/](https://www.gleam.eu/)]([https://www.gleam.eu/](https://www.gleam.eu/))) and the MERRA2 RZSM data ([PERSON] et al., 2017) is obtained from the Goddard Space Flight Center Distributed Active Archive Center, National Aeronautics and Space Administration ([[https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/](https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/)]([https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/](https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/))). The sample datasets and codes used to process data and generate the figures in this study are available online at [PERSON] et al. (2024).
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wiley/ffd4c007_fe7f_4e1f_90e1_af8da5bcac6e.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
###### Abstract
Arctic temperature is one of the most uncertain aspects of mid-Holocene (MH) climate change modeling, usually attributed to the different responses of different models to external forcing. However, in this study, we find that significant discrepancies (i.e., the noise is close to the signal in term of climate change) in the MH Arctic temperature changes can occur within the same model and for identical external forcing due to initial ocean condition perturbations. It is shown that initial ocean perturbations can affect the surface energy budget change through the uncertain cloud effect on shortwave radiation in boreal summer. The resulted uncertain change in summer surface heat flux alters the subsequent autumn and winter sea ice and contributes to significant differences in Arctic temperature via sea ice-albedo feedback. This study suggests that internal uncertainty of an individual model is a non-negligible source of overall uncertainty in simulating the MH Arctic temperature change.
[1][PERSON],
[1][PERSON],
[2]Schoolerable uncertainty of simulated Arctic temperature change in the mid-Holocene due to initial ocean perturbation.
[1]Kay Laboratory of Meteorological Dissster, Ministry of Education/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, China, [3]University of Bremen, Bremen, Germany
[4][PERSON]
conundrum\": proxies indicate a temperature maximum at early and middle Holocene and cooling afterward, while climate models suggested a continuous warming Holocene ([PERSON] et al., 2014).
Great efforts have been made to explain and reduce the gap between proxies and model results. The Holocene annual SST showed a warming trend by transforming the seasonal SST records to annual mean ([PERSON] et al., 2021), showing that the puzzle is partly due to the seasonal bias in the interpretation of proxies ([PERSON] et al., 2014). Holocene temperatures were cooling in the NH high latitudes and warming in the tropics, emphasizing a latitudinal dependent response ([PERSON] et al., 2020; [PERSON] et al., 2013). Assimiliating proxies to a climate model, the Holocene temperature was rising, and the MH was \(\sim\)0.1\({}^{\circ}\)C colder than PI ([PERSON] et al., 2021). It was concluded that uncertainty is due to the seasonal bias and poor spatial coverage of the data. The model-data inconsistency could also result from unrealistic responses of external forcing or lack of forcings in climate models. After removing the MH atmospheric dust load caused by enhanced monsoon and resulting vegetation cover, the global temperature increased by 0.3\({}^{\circ}\)C([PERSON] et al., 2018). [PERSON] et al. (2018, 2019) emphasize the role of the Arctic sea ice loss in MH and its feedback on NH temperature. If climate models can simulate the mid-latitude Arctic as warm as proxies suggest, they should indicate a warmer NH than PI. Recently, [PERSON] et al. (2022) applied expanded vegetation in the Sahara and NH mid-latitudes during the early and middle Holocene in their model, whereupon the global temperature increased by 0.8 and 0.7\({}^{\circ}\)C, respectively, especially over the Arctic, which is over 5\({}^{\circ}\)C warmer.
Though the conundrum remains puzzling ([PERSON] et al., 2021; [PERSON] et al., 2023; [PERSON] and [PERSON], 2023; [PERSON] et al., 2021), plenty of studies pointed out that the Arctic could be the key, where the polar amplification effect acts as a bridge between the external forcing and global temperature in various climate models (e.g., [PERSON] et al., 2020; [PERSON] et al., 2022; [PERSON] et al., 2018, 2019; [PERSON] et al., 2019; [PERSON] et al., 2022). Nevertheless, responses of MH Arctic temperature changes are largely inconsistent among different models ([PERSON] et al., 2020), highlighting the uncertainty of models in simulating physical processes over the Arctic and emphasizing the uncertainties regarding the Arctic.
The uncertainty of a multi-model ensemble can be due to the models' different responses to external forcing, linked to their dynamical cores and physical parameterizations. Meanwhile, the uncertainty within an individual model (hereafter as internal uncertainty), for example, resulting from different initial conditions, should also contribute. Since the equilibrium simulations in PMIP were generally integrated over hundreds to thousands of years and the last hundreds of years were used for the analysis, the influence of the initial condition was considered ignorable. Nevertheless, in this study, using a set of MH and PI experiments conducted with identical model setups and perturbing only the initial ocean condition, we show that the Arctic temperature changes in the MH exhibit considerable inconsistencies. This suggests a non-negligible influence of internal uncertainty on the modeling of Arctic temperature change in the MH.
## 2 Data and Methods
The simulations are performed with the third generation of climate model developed at the Alfred Wegener Institute (AWI-CM3), consisting of the atmosphere, ocean and sea ice components. The atmosphere model is the Integrated Forecast System in the version OpenIFS (version cy43r3v2; ECMWF, 2017a, 2017b, 2017c) developed at the European Center for Medium-Range Weather Forecast. The ocean model is the second version of the Alfred Wegener Institute's global ocean model, the Finite volume Sea ice-Ocean Model (FESOM2) with unstructured meshes, which contains the sea ice module ([PERSON] et al., 2017). For all the experiments, the OpenIFS has a TC96v2 horizontal resolution (\(\sim\)100 km) with 91 vertical layers, coupled with the FESOM2 using the CORE2 mesh (\(\sim\)0.13 million surface nodes, 47 vertical layers). The AWI-CM3 has a good reproduction of observed climate in many aspects ([PERSON] et al., 2023; [PERSON] et al., 2022). For more model details, we refer to [[https://awi-cm3-documentation.readthedocs.io/en/latest/index.html](https://awi-cm3-documentation.readthedocs.io/en/latest/index.html)]([https://awi-cm3-documentation.readthedocs.io/en/latest/index.html](https://awi-cm3-documentation.readthedocs.io/en/latest/index.html)).
First, a PI spin-up experiment is integrated for 700 years under PI boundary conditions. A MH spin-up experiment, which is restarted from the 500 th year of the PI spin-up ocean state is integrated for 200 years, forced by the MH boundary conditions (labeled as 501-700 th simulation year; Figure S1 in Supporting Information S1). After the PI and MH spin-up experiments, we run the PI and MH experiments for 100 years under respective forcings (labeled as 701-800 th simulation year), which are used for the analysis. For each period, we create 5 ensemble runs with initial perturbations based on restarts from the 690 th, 695 th, 698 th, 699 th, and 700 th year ocean states, respectively. The PI and MH boundary conditions are listed in Table S1 in Supporting Information S1, with differences in orbital parameters and greenhouse gas (GHG) concentrations. The global annual mean surface air temperature (GAST) evolution shows little trends for the last 100 years, implying that the simulations reach quasi-equilibrium (Figure S1 in Supporting Information S1).
All members of the AWI-CM3 ensemble are considered equally and independently, giving us 25 (\(5\times 5\)) differences between the MH and PI experiments. For convenience, these differences are named the \"difference ensemble (DE).\" Their arithmetic median is defined as the signal of the climate change caused by the external forcing, and their standard deviation is considered as the noise depending on the initial conditions. The (absolute) signal-to-noise-ratio (SNR) is used to measure the robustness of the modeled climate change. Since this ensemble is artificially generated, its members exhibit strong auto-correlation. To assess the significance level of our difference ensemble, we employed Monte Carlo simulation. Initially, we generated two MH-PI difference ensembles, each consisting of 25 values obtained by subtracting 5 random MH values from 5 random PI values. We then calculated the correlation coefficient between these two 25 values and repeated these steps 10,000 times. Subsequently, we determined the 95 th percentile of the 10,000 correlation coefficients, which served as the threshold for conducting a 95% significance test when performing correlation analyses within the ensemble.
## 3 Uncertainty in Modeling the Mid-Holocene Temperature
The GAST of the AWI-CM3 ensemble ranges from 12.86 to 12.93 degC for MH and 13.15-13.22 degC for PI, implying an average cooling of 0.29 degC in MH relative to PI (Figure S2 in Supporting Information S1). This value is close to the PMIP4 ensemble mean (\(-0.3\)degC; [PERSON] et al., 2022). The spatial pattern of surface temperature change exhibits a large-scale cooling over the tropical and NH mid-latitudes and a warming over NH high latitudes (Figure 1a), resembling the PMIP2, PMIP3, PMIP4 ensemble result ([PERSON] et al., 2020; [PERSON] et al., 2013). The general global cooling is mainly caused by the lower GHG concentrations in MH. The most significant cooling takes place over the North African and South Asian monsoon regions, which is mainly caused by the increased cloud induced by the enhanced monsoonal precipitation in response to stronger summer solar insolation (Figure S3 in Supporting Information S1). The mechanisms can be attributed to the insolation forcing in interglacials ([PERSON] and [PERSON], 2009). The warming over the Arctic is caused by sea ice loss due to increased summer insolation and its feedback to the atmosphere. Our seasonal temperature changes generally agree with the PMIP4 results (Figure S4 in Supporting Information S1), following the seasonal solar insolation, suggesting that AWI-CM3 largely reproduces the MH temperature responses similar to other models.
However, the GAST changes between the MH and PI differ notably for the AWI-CM3 initial ocean perturbation experiments, ranging from \(-0.37\) to \(-0.22\)degC among the DE (Figure S2 in Supporting Information S1). The GAST difference between the warmest and coldest member (0.15 degC) exceeds one standard deviation among the PMIP4 ensemble (0.12 degC; [PERSON] et al., 2020; [PERSON] et al., 2022). This suggests that MH climate change uncertainty also exists within a single model, which could lead to large uncertainty in a multi-model ensemble result because most models only provide one ensemble for the multi-model comparison.
Specifically, the noise of GAST changes in the DE is 0.04 degC and the corresponding SNR is 7.3, which implies that the global mean temperature response among AWI-CM3 simulations is less affected by the initial ocean perturbation. Nevertheless, this large global SNR is mainly dominated by the consistent strong cooling over the tropics, especially over the NH monsoon regions and tropical eastern Pacific, where the local SNR exceeds 20, indicating the robustness of AWI-CM3 in simulating the MH climate change over these regions (Figure 1). Meanwhile, the SNR reduces sharply from tropical to polar regions in both hemispheres, with SNR close to or even less than one over the Arctic/Antarctic, emphasizing the pronounced influence of the initial ocean on the simulated MH polar climate change. For the seasonal temperature change, the SNR shows similar spatial distributions (Figure S4 in Supporting Information S1). The smallest SNR over the Arctic (Antarctic) occurs in local winter, which implies that this large uncertainty of polar temperature response may be closely related to the seasonal sea ice variation. Although both the Arctic and Antarctic show widespread temperature changes in the DE, the global temperature change is dominated by the Arctic (Figures S1 and S2 in Supporting Information S1). The inter-DE Arctic temperature change is approximately 6 times of the global mean temperature change (Figure S5 in Supporting Information S1). This ratio is significantly larger than the well-known Arctic amplification effect, which is about twice as warm as the global average ([PERSON], 2006), indicating additional processes happening there other than the cooling effect due to reduced GHG concentrations ([PERSON] et al., 2020). In Antarctica, on the other hand, the warming/cooling rate is not significantly different from the global average. Its zonal mean is close to 0, contributing little to the global temperature difference in the DE.
## 4 Source of the Uncertainty
### Arctic Sea Ice Responses
To better illustrate the different temperature responses due to the initial perturbation, the five coldest and five warmest ensemble members, regarding GAST, of DE are chosen (Figure 2). Generally, the seasonal cycle of MH temperature changes directly follows the solar insolation because the GHG effect is more spatial- and seasonal
Figure 1: (a) Signal, (b) noise, and (c) signal-to-noise-ratio of annual mean surface air temperature changes in the DE. Units for (a) and (b) are \({}^{\circ}\)C. Right panel of each subplot is the corresponding zonal mean.
uniform (Figure S3 in Supporting Information S1). For the Arctic region, the largest warming occurs in boreal autumn, lagging the orbital-induced solar insolation change by 3 months. This is because the increased solar insolation will continuously cause an Arctic sea ice loss during boreal summer, hence less sea ice accumulation in autumn, then strongly warming the Arctic atmosphere (e.g., [PERSON] et al., 2019). For the coldest ensemble, the autumn warming lasts until December, and the winter is cooling again by the reduced solar insolation and accompanied sea ice increase (Figure 2b). However, the warmest ensemble exhibits a long-lasting warming from autumn to February, and the winter cooling is also less remarkable (Figure 2a). As a result, the warmest ensemble displays significantly warmer NH high latitudes throughout the year (Figure 2c).
Because changes in Arctic sea ice play an important role in altering the temperature response to solar insolation, we also show the Arctic sea ice concentration (SIC) in the DE (Figure 2d). The Arctic sea ice loss in MH shows a large spread, especially during boreal autumn. In the coldest ensemble, the Arctic SIC reduced by 7% in September, which is one-third less compared to a 10.5% SIC reduction in the warmest ensemble. This is directly reflected in their autumn temperature responses (Figure 2c). Moreover, in the coldest ensemble, the Arctic SIC stops reducing around December and turns to increasing from January to May. This sea ice growth in the latter period is responsible for the colder Arctic in winter and spring. The SIC in the warmest ensemble decreases throughout the year, which is distinct form that in the coldest ensemble. Particularly, the Arctic sea ice remains reduced in winter despite the solar insolation decreases, and decreases significantly in the sequent summer, warming the Arctic.
These differences in seasonal SIC changes are also obvious in the spatial distribution (Figure 3). Compared to the coldest ensemble, the warmest ensemble simulates a more pronounced sea ice loss in September, concentrating on the sea ice edge, where the sea ice is thinner and vulnerable to solar insolation change (Figures 3a-3c). In March, the climatological sea ice extends southward. The coldest ensemble indicates sea ice loss mainly over the Barents
Figure 2: Zonal mean surface temperature change in the (a) warmest ensemble and (b) coldest ensemble and (c) their difference (in °C) in the DE. (d) Regionally averaged (70°\(-\)90°N) sea ice concentration (SIC) changes (in %) in the warmest ensemble (red curve) and coldest ensemble (blue curve). The black contours in (a) and (b) represent zero contours. The black dashed curve in (d) represents the median SIC change and the gray shading represents one standard deviation uncertainty of SIC change in the DE.
Sea, which is insignificant in the warmest ensemble. The sea ice also loses remarkably over the Bering Sea in both coldest and warmest ensembles in response to the decreased solar radiation through winter (Figures 3d and 3e). However, along with the seasonal movement of sea ice, the increased loss of summer sea ice in the warmest ensemble is unfavorable for winter sea ice growth over the Bering Sea (Figure 3f). In summary, different sea ice loss responses to summer solar insolation change between MH and PI accounts for the uncertainty in simulating Arctic temperatures change.
### Surface Energy Budget
An unresolved question remains: why do MH changes in sea ice and temperature in the Arctic differ significantly between simulations using the same model and identical external forcing with different initial conditions? We analyze the surface energy budget over the Arctic, which is the direct controller of sea ice amount. In the individual PI and MH simulations, the climatological surface heat flux is quite consistent for each component (Figures 4a and 4b): the net shortwave radiation (NSR), net longwave radiation (NLR), sensible heat and latent heat at the surface (Equation 1).
\[\text{Heat Flux}_{\text{surface}}=\text{NSR}_{\text{surface}}+\text{ NLR}_{\text{surface}}+\text{Sensible Heat + Latent Heat} \tag{1}\]
\[\text{NSR}_{\text{surface}}=\text{DSR}_{\text{surface}}+\text{USR}_{\text{ surface}} \tag{2}\]
\[\text{DSR}_{\text{surface}}=\text{DSR}_{\text{TOA}}+E_{\text{surface}}+E_{ \text{cloud}} \tag{3}\]
Figure 3: September sea ice concentration (SIC) changes (in %) in (a) warmest ensemble, (b) coldest ensemble and (c) their difference in the DE. Panels (d–f) are the same as (a–c), respectively, but for March. The black contours represent the climatological sea ice edge (\(15\%\) SIC) for the corresponding months of the PI ensemble median.
Among these four items, the surface NSR dominates the annual cycle of heat flux. In the MH, the surface heat flux is more negative in summer and more positive in winter, indicating more surface energy gained and lost respectively relative to the PI (Figure 4c). Besides that, the DE exhibits considerable noise compared to the signal in the heat flux, particularly during summer and winter. The first noise is inherited from the NSR change while the second noise is mainly caused by the NLR and Sensible Heat changes. As analyzed above, since summer solar insolation is crucial to the simultaneous and delayed sea ice changes, we focus on the uncertainty in the summer surface NSR change. The surface NSR consists of two items: the downwelling shortwave radiation (DSR) and the upwelling shortwave radiation (USR) at the surface (Equation 2). The surface DSR and USR changes are anti-correlated since the USR is mainly the reflection of DSR by Arctic sea ice (Figure 4d). In late summer, this anti-correlation is disturbed because the NLR is less positive, implying that the atmosphere warms the surface and causes additional sea ice loss (Figure 4c). Generally, the surface NSR change is mostly triggered by the surface DSR change. However, the uncertainty of surface DSR change is smaller than the NSR change, which demonstrates that the sea ice-albedo positive feedback amplifies the uncertainty from DSR.
To connect the surface DSR with external forcing, we further decompose the surface DSR into three items: (a) the DSR at the top-of-atmosphere (TOA), which is the ultimate energy source of the whole climate system; (b) and (c): the effects of atmosphere (without clouds) and cloud on DSR before it reaches the Arctic surface, respectively (Equation 3; See Text S1 in Supporting Information S1 for the definition of \(E_{\text{atom}}\), and \(E_{\text{cloud}}\)). First, the changes in DSR at TOA are almost identical in the DE (Figure 4e). This is reasonable since this item is merely forced by the Earth's orbital changes, which are fixed in our experiments. The atmosphere effect items also show large consistency in the entire year. As a result, the uncertainty of surface DSR change is almost completely caused by noise from changes in cloud effect, particularly in summer. In short, the cloud effect is sensitive to the initial condition, which makes the solar insolation reaching the surface different in the ensemble members, although the changes in solar insolation at TOA are identical. These differences in incoming surface solar insolation are further amplified
Figure 4.— Arctic (70°-90°N) surface energy budget for (a) PI and (b) MH, and (c) their differences (MH minus PI); (d) Differences in surface downwelling (downwelling shortwave radiation (DSR)) and upwelling shortwave radiation; (e) Differences in DSR at the top of atmosphere, effect of atmosphere (\(E_{\text{atom}}\)) and cloud (\(E_{\text{cloud}}\)). Shadings represent one standard deviation uncertainty. Positive (negative) values in (a) and (b) represent upwelling (downwelling) radiation, sensible heat or latent heat.
by the sea ice-albedo feedback, leading to considerable uncertainty in the Arctic surface temperature changes in the MH.
To sum up, it is shown that even for the same climate model using identical external forcing for the MH and PI, the temperature responses in the Arctic can vary significantly due to different initial ocean conditions, which is attributed to the indeterminate cloud effect on the incoming solar insolation.
## 5 Discussion and Conclusions
The cloud effect is one of the most complex and uncertain parts of the climate system ([PERSON] and [PERSON], 2016; [PERSON] et al., 2021; [PERSON] et al., 2013; [PERSON] et al., 2020). In addition to the sea ice-albedo feedback, the cloud feedback is an important process over the Arctic, whose sign is determined by the balance of shortwave cooling and longwave heating. Although we do not analyze the detailed cloud feedback, the differential cloud effect on shortwave radiation in DE will further alter the sign or strength of the Arctic cloud feedback, which in turn will affect the Arctic climate. For instance, cloud liquid particles are smaller than cloud ice particles and more effective at diffusing and reflecting solar insolation ([PERSON] et al., 2018). Due to the increased solar insolation, the warmer MH summer may contain more mixed-phase clouds and the proportion of cloud liquid particles increases as well, which will increase the planetary albedo and cool the Arctic ([PERSON] et al., 2016; [PERSON] et al., 1989). These cloud feedbacks make their effects on Arctic temperature quite complicated and increase the uncertainty in the simulation.
The large uncertainty in Arctic temperature change in MH is a prominent feature in multi-model comparisons: For the PMIP4 MH experiments, the standard deviation between the models is about twice the median of the models regarding the Arctic surface temperature (Figure S6 and Table S2 in Supporting Information S1). This overall uncertainty could be due to the different model structures and internal uncertainty (e.g., dependence on initial conditions), although the latter receives less attention. The internal uncertainty is difficult to measure because most models did not have ensembles for the MH and PI. Here, we provide a rough estimate of its relative contribution. As shown in Figure S6 in Supporting Information S1, the internal uncertainty could account for up to 40% of the overall uncertainty for local annual temperature in the Arctic, which could be up to over 100% for boreal winter. This indicates that the internal noise can have a significant impact on multi-model results, highlighting the importance of detecting or reducing internal uncertainty.
In conclusion, we have shown that initial ocean condition could lead to considerable uncertainty in modeling the Holocene Arctic climate change. Previous studies also revealed that the cloud effect is sensitive to the initial response to the ocean perturbation ([PERSON] et al., 2012; [PERSON] et al., 2006; [PERSON] et al., 2013; [PERSON] et al., 2012), or model resolution ([PERSON] et al., 2021; [PERSON] et al., 2020), suggesting that the uncertainty in Arctic temperature responses is a common feature modeling climate change scenarios. As all the perturbation experiments run for 100 years, it is plausible that multi-centennial variability, as observed in reconstructions, may also contribute to the uncertainty in 100-year climatologies. In our simulations, we have not identified significant multi-centennial variability in Arctic temperature, suggesting that multi-centennial variability may not play a decisive role in our specific problem (Figure S7 in Supporting Information S1). However, it's worth noting that in some climate models (e.g., EC-Earth3-LR; Q. [PERSON] et al., 2021), multi-centennial variability is dominant in the climate system. The inability of our climate model to capture the multi-centennial variability recorded in reconstructions makes it challenging to investigate its origin and sensitivity to initial conditions. Furthermore, it is questionable whether a longer simulation is possible to reduce the influence of initial perturbation. We further show the time evolution of related shortwave radiation processes (Figure S8 in Supporting Information S1). The DSR change at TOA is almost constant for the entire simulation period, and the change in atmosphere effect on DSR also reaches quasi-equilibrium after approximately 20 years. In contrast, the change in cloud effects declines in the first 20 years and recovers to a relatively stable state after 50 years of the integration. However, its uncertainty does not show a reducing trend along with the integration length, which indicates that a longer simulation would not expect to reduce uncertainty in the MH Arctic temperature change. Since the ensemble result becomes stable after \(\sim\)50 years, we suggest that conducting an ensemble of relatively short runs with different initial ocean conditions instead of a long run for MH and PI could help qualitatively distinguish the internal uncertainty and provide a better understanding of the results between different models.
## Data Availability Statement
We thank PMIP4 for providing the MH and PI simulations which are available at [[https://esgf-node.llnl.gov/search/cmip6/](https://esgf-node.llnl.gov/search/cmip6/)]([https://esgf-node.llnl.gov/search/cmip6/](https://esgf-node.llnl.gov/search/cmip6/)) ([PERSON] et al., 2018; [PERSON], 2019; [PERSON], 2019; EC-Earth, 2020; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2020; NASA/GISS, 2019; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] & Dong, 2019; [PERSON] & [PERSON], 2019; [PERSON] et al., 2021). AWI-CM3 experiments output related to the present study is available online at Shi (2023). The ocean model FESOM2 source code is available at [[https://github.com/FESOM/tesom2/releases/AWI-CM3_v3.0](https://github.com/FESOM/tesom2/releases/AWI-CM3_v3.0)]([https://github.com/FESOM/tesom2/releases/AWI-CM3_v3.0](https://github.com/FESOM/tesom2/releases/AWI-CM3_v3.0)). OpenIFS is not publicly available but rather subject to licensing by ECMWF. Licenses are given free of charge to any academic or research institute. Please visit [[https://confluence.ecmwf.int/display/OIFS/Request+OpenIFS+license](https://confluence.ecmwf.int/display/OIFS/Request+OpenIFS+license)]([https://confluence.ecmwf.int/display/OIFS/Request+OpenIFS+license](https://confluence.ecmwf.int/display/OIFS/Request+OpenIFS+license)) for more information.
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* NASA Goddard Institute for Space Studies (NASASA/GISS), (2019), NASA-AISS GISS-E2.1G model output prepared for CMIP6 PMIP mid Holocene (version 20230720) [Dataset]. Earth System Grid Federation. [[https://doi.org/10.22033/ESGF/CMIP6.7225](https://doi.org/10.22033/ESGF/CMIP6.7225)]([https://doi.org/10.22033/ESGF/CMIP6.7225](https://doi.org/10.22033/ESGF/CMIP6.7225))
* [PERSON] et al. (2020) [PERSON], [PERSON], [PERSON], & [PERSON] (2020). AWI-ESM1.1 LR model output prepared for CMIP6 PMIP mid Holocene (version 20230720) [Dataset]. Earth System Grid Federation. [[https://doi.org/10.22033/ESGF/CMIP6.9332](https://doi.org/10.22033/ESGF/CMIP6.9332)]([https://doi.org/10.22033/ESGF/CMIP6.9332](https://doi.org/10.22033/ESGF/CMIP6.9332)) | wiley | Considerable Uncertainty of Simulated Arctic Temperature Change in the Mid‐Holocene Due To Initial Ocean Perturbation | Jian Shi, Gerrit Lohmann | https://doi.org/10.1029/2023gl106337 | 2,024 | CC-BY |
wiley/ffd08a09_4d50_4741_ac35_08ed72f89c0c.md | # Earth and Space Science
Research Article
10.1029/2021 EA001645
Themal and Physical Properties of Deccan Basalt and
Neoarchean Basement Cores From a Deep Scientific
Borehole in the Koyna\(-\)Warna Seismogenic Region,
Deccan Volcanic Province, Western India: Implications
on Thermal Modeling and Seismogenesis
[PERSON]\({}^{1}\)
1 CSIR-National Geophysical Research Institute, Hyderabad, India, 1 MIT-Indian School of Mines, Dhanbad, India, 1 Geological Survey of India, Hyderabad, India
[PERSON]\({}^{1,2}\)
1 CSIR-National Geophysical Research Institute, Hyderabad, India, 1 MIT-Indian School of Mines, Dhanbad, India, 1 Geological Survey of India, Hyderabad, India
[PERSON]\({}^{1}\)
1 CSIR-National Geophysical Research Institute, Hyderabad, India, 1 MIT-Indian School of Mines, Dhanbad, India, 1 Geological Survey of India, Hyderabad, India
[PERSON]\({}^{1}\)
1 CSIR-National Geophysical Research Institute, Hyderabad, India, 1 MIT-Indian School of Mines, Dhanbad, India, 1 Geological Survey of India, Hyderabad, India
[PERSON]\({}^{3}\)
1 CSIR-National Geophysical Research Institute, Hyderabad, India, 1 MIT-Indian School of Mines, Dhanbad, India, 1 Geological Survey of India, Hyderabad, India
###### Abstract
We have investigated 78 core samples of basaltic trap and Neoarchean basement in the laboratory from a 981 m deep scientific borehole KBH-05, in the Koyna\(-\)Warna seismic zone, in order to characterize their thermal and physical properties and present a probable crustal thermal model. The Koyna\(-\)Warna, located in the Deccan Volcanic Province (DVP), is globally one of the most prominent Reservoir Triggered Seismicity (RTS) regions. Thermal conductivity, density, and porosity vary widely (1.0-1.7 Wm\({}^{-}\)K\({}^{-}\), 2,400-3,000 kg m\({}^{-3}\), 0.2%-10%) for the basalt due to their lithological heterogeneities, i.e., massive/amygdala/vesicular. In comparison, the basement, which dominantly consists of gneiss/migmatic eneiss (grandoiorite to tonalite to quartz monozdorite in composition) and amphibolite, have shown a wider range in thermal conductivity (2.2-3.4 Wm\({}^{-1}\)K\({}^{-}\)) but constricted range in density and porosity (2,600-2,800 kg m\({}^{-3}\), 0.01%-0.15%). Based on gamma and sonic logs, as well as radioelements (Th, U, K), the 499 m thick basaltic trap can be divided into two thick layers (325, 174 m) and five sub-layers, which can be correlated with different basaltic formations. Similarly, the underlying basement can also be divided into two layers (93, 384 m). The upper basement layer has two times higher concentrations of Th and U than the lower layer, with heat production of 2.0, 0.8 \(\mu\)Wm\({}^{-3}\). Further, the study provides a robust temperature estimate of 165\({}^{\circ}\)C-250\({}^{\circ}\)C at 10 km depth, considerably higher than reported earlier for the DVP, and reveals that in addition to thermal parameters, RTS also plays an important role in the seismogenesis of the region.
SIS in an ocean across article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
15 JAN 2021
Accepted 28 JUL 2021
## 1 Introduction
Deccan Volcanic Province (DVP) was formed due to the volcanic eruption during ca. 68 to 60 Ma, with a major peak at around 66 Ma ([PERSON] et al., 2015; [PERSON] et al., 2019). It covers an area of about 500,000 sq km in the central and western parts of India (e.g., West, 1959). Thickness of the volcanic traps increasesfrom east to west; a few hundred meters in the east to about one and half thousand meters over the western escarpment and only a few hundred meters further west below the Konkan plains (e.g., [PERSON] et al., 1981). The northern part of the DVP is underlain by Mesozoic sediments and supracrustal rocks of Cambay Basin, Aravalli Craton, and Bundelkhand Craton, whereas the southern part of the DVP is underlain by metamorphic rocks of the Dharwar Craton.
Koyna-Warna seismogenic region, which is located in the southwestern part of this province, is experiencing continuous seismic activity since 1967. Earthquake at Koyna in 1967 (M 6.3) is the largest Reservoir Triggered Seismicity (RTS) event globally. RTS is an anthropogenic effect of filling artificial water reservoirs. The first scientifically accepted case of RTS was reported from Lake Mead in USA ([PERSON], 1945), and till now, over 120 sites have been reported globally ([PERSON], 2011; [PERSON] et al., 2002). At Koyna, earthquakes started soon after the impoundment of the Shivaji Sagar Lake in 1962. Filling of another reservoir Warna, just south of Koyna, in 1985, gave a further impulse to RTS in the region. Thus, the RTS has continued in the Koyna-Warna region for the last six decades. These include 22 earthquakes of magnitude \(\geq\)5.0 and several thousand smaller events (Figure 1). The earthquakes keep on occurring in a small area of 20 x 30 km\({}^{2}\), and have focal depths shallower than 10 km ([PERSON] & [PERSON], 2016).
Detail knowledge of the basement is considered important to characterize and access the seismicity of the region. Due to the inaccessibility of the basement below the Koyna-Warna region, several geophysical and geological investigations were carried out in the past, to characterize the nature of the concealed basement ([PERSON] et al., 1981; [PERSON] et al., 2005; [PERSON] et al., 2008) as well as the basaltic trap ([PERSON], 1988; [PERSON] et al., 1976; [PERSON] et al., 2006). In spite of such studies, the nature of subsurface geologic terrain remains a subject of considerable speculation, and in that context, attempts have been made to drill a scientific borehole. First, a set of four boreholes were drilled in the epicentral zone of the deadly 1993 Killari earthquake in Latur district, located 400 km NE of the Koyna-Warna region ([PERSON] et al., 2003). It was then followed further by the drilling of nine boreholes (906-1,022 m deep) in the Koyna-Warna- - as seismogenic region ([PERSON] et al., 2015), which penetrated the entire sequence of Deccan basalt flows and a large thickness of the underlying 2.7 Ga Neoarchean basement, made up largely of gneiss/migmatite gneiss of granodiorite, tonalite, quartz monzogramite composition and amphibolite, developed under amphibolite facies condition ([PERSON] et al., 2017; [PERSON] et al., 2017). Geophysical logging data, magnetic properties and geological studies on the borehole cores of the Koyna- Warna region ([PERSON] et al., 2019; [PERSON] et al., 2017; [PERSON] et al., 2017), indicate complex lithological variations within the basaltic column as well as the crystalline basement.
Detailed thermal studies carried out earlier in different geological provinces of the southern Indian shield, located south of DVP, that is, Dharwar Craton and Southern Granulite Province, have indicated systematic differences in thermal characteristics in the crust ([PERSON] et al., 2003, 2008; [PERSON] et al., 2003, 2008), which are concordant with geological, geochronological and tectonic variations. However, similar detailed studies have not been carried out for the DVP, which hinders in determining a precise crustal thermal model of this region, although previously there have been few attempts ([PERSON] et al., 2015; [PERSON] & [PERSON], 1999).
Due to the heterogeneous nature of the basaltic trap and basement column, considerable variation in the physical (density, porosity), as well as thermal (thermal conductivity, radioelemental abundances, heat production) properties, are anticipated. In view of this, core samples recovered from the deep borehole KBH-05, have provided a good opportunity to study in detail such properties in the laboratory. In the present study, we investigate in detail
Figure 1.— (a) Geological map showing Deccan Volcanic Province (DVP) and the surrounding geological units. Abbreviations are, AC: Aravalli Craton; BC: Bundelkhand Craton; BAC: Bastar Craton; EDC: Eastern Dharwar Craton; WDC: Western Dharwar Craton; (b) Shaded relief map with location of KBH-05 borehole in Phansavale, Koyna–Warna region, Deccan Volcanic Province (DVP), India.
the thermal, physical, geochemical, and petrological properties of 78 core samples from a 981 m deep KBH-05 borehole, which penetrated 499 m thick column of Deccan basalts, followed by a 5 m transition zone and a further 477 m thick crystalline basement. We also make an attempt to: (a) characterize the vertical variation of the thermal conductivity, radioelemental abundances, heat production, density, and porosity; (b) correlate the variations in the thermal and physical properties with chemical/mineralogical compositions and gamma-sonic logs; (c) provide an accurate upper crustal thermal model (up to 10 km depth) for this seismogenic region in particular and DVP in general; (d) throw light on the probable factors controlling seismogenesis of the region.
## 2 Study Area
Koyna\(-\)Wama seismic zone is located over the Western Ghats Escarpment in the western part of DVP. Nine boreholes (906-1,522 m deep), which have been drilled in the Koyna\(-\)Wama region, surrounding the earthquake cluster (Figure 1), reveal a large variation in the trap thickness from 412 to 1,251 m ([PERSON] et al., 2015), within the small areal extent of about 20 x 30 km\({}^{2}\). Deep drilling confirms that the flood basalt cover (usually referred to as the Deccan traps), is underlain by the granitoid rocks (TTG) below this seismic region ([PERSON] et al., 2017; [PERSON] et al., 2017). Uneven basement topography, as revealed by the borehole studies, may either be due to its original uneven nature or due to the fault systems that ought to have developed later ([PERSON] & [PERSON], 2017).
Presently studied KBH-05 borehole, at Phanasavale, is 981 m deep. It is located in the Konkan region, west of the Western Ghats Escarpment (Figure 1). It penetrated 499 m thick basaltic column, consisting of amygdala, locald, vesicular, and massive basalts, together with intervening layers of red boles. Underlying 477 m thick crystalline basement, is made up of metamorphic rocks of different grades. These two units are separated by about 5 m thick transition zone. Present investigations were done on 45 basalt and 33 basement core samples.
## 3 Methodology
### Sampling Scheme and Megascopic-Microscopic Studies
Megascopic study is carried out on core samples of both basalt as well as the basement, before laboratory analysis. Basement rocks are also studied microscopically to address major and accessory minerals in them. XRF analysis is carried out on 17 representative basement cores. Major oxide data, along with petrography, are used to characterize the basement rocks. Radioelemental (Th, U, K) concentrations, density, and porosity are measured in the laboratory on 45 basalt and 33 basement core samples, as mentioned before. Measurements are also done on 3 red bole cores within the basalt layer and 2 amphibole core samples from the basement in order to complete the succession of the borehole. Thermal conductivity is measured in the laboratory on the sub-set of the above samples, i.e., 18 basalt cores and 31 basement cores, which were found suitable for carrying out such measurements.
### Measurement of Major Oxides
Major oxide concentrations have been determined by Wavelength-Dispersive X-ray Fluorescence Spectrometry (PANalytical-WDXRF) using pressed pellets. The rock samples from basement cores are crushed and converted to fine powders using agate mortar. Two grams of the finely powdered sample is filled in the collapsible aluminum cups with boric acid. These cups were then pressed under hydraulic pressure (at 25-Ton) to make the pellet ([PERSON] et al., 2007).
### Measurement of Density and Porosity
For measuring density and porosity, cylindrical samples are used. It involves measurements of three weights: (a) weight in the air at dry condition (W\({}_{\text{air}}\)), (b) weight in water at dry condition (W\({}_{\text{water}}\)), and (c) weight in the air at saturated condition (W\({}_{\text{aval}}\)), using a high precision balance. First, samples are dried in an oven for 12 hours, and weights are taken in air and water. The samples are dried again and then placed in desicactors for 15 min to remove the air from the pores. In vacuum condition, it is saturated with tap water and kept for 24 h to allow water to enter into the pores ([PERSON] et al., 2018, 2020).
Density is then determined using Archimedes' principle by the equation given below using the weight of the sample in the air (W\({}_{\text{water}}\)) and weight of the sample in water (W\({}_{\text{water}}\)) and density of water (\(\rho_{\text{water}}\))
\[\rho_{\text{sample}}=\frac{W_{\text{air}}*\rho_{\text{water}}}{W_{\text{air}}-W_ {\text{water}}}. \tag{1}\]
Porosity (\(\phi\)) is the volume of the open space in a rock (V\({}_{\text{p}}\)) divided by the total volume of rock (V\({}_{\text{v}}\)) (solid + space or holes). It is calculated as
\[\phi=\frac{Wsat-Wdry}{\pi*R*R*H}*100, \tag{2}\]
where, R and H are radius and thickness of the sample, respectively.
### Measurement of Thermal Conductivity
Thermal conductivity of rock samples is measured at ambient condition, using a steady-state thermal conductivity meter (model QL-10\({}^{\text{m}}\), Anter Corporation). This apparatus is designed on the basic principle of a Guarded Heat Flow Meter (ASTM E1530). The setup consists of the hot brass plate at the top, the cold brass plate at the bottom, and the sample in between the two brass plates. The accuracy varies between \(\pm\)3% and \(\pm\)8% depending on sample size and thermal conductivity, and the precision of measurement with this setup is 0.03. Rock samples collected from the borehole cores are cored, cut, and polished into cylindrical discs of 2.54 cm diameter. Thickness of samples varied between 1.0 and 2.5 cm, depending on rock type and grain size. Cut surfaces of disc samples are grounded and polished until the thickness variation is less than 0.01 mm. Details about the apparatus and measurement procedure are described in [PERSON] et al. (2018, 2020).
### Measurement of Radioelements (Th, U, K) and Calculation of Heat Production
Abundances of radioelements (Th, U, and K) are measured in the laboratory by a low-level, spectrum-stabilized gamma ray spectrometer for the studied core samples. Sensor is NaI (Tl) crystal with 5 inches in diameter and 6 inches in height. Sample preparation, laboratory set-up, and measurement method are described in detail by [PERSON] et al. (2016). Before analyzing samples, background and standard counts are determined by using background and standard samples. Concentrations of Th, U, and K are calculated considering the counting statistics.
Heat production (A) in rocks is determined by using the expression given by [PERSON] (1954) as,
\[A\left(\mu\text{Wm}^{-3}\right)=\rho_{\text{sample}}*\left(0.026*\text{C}_{ \text{Th}}+0.097*\text{C}_{\text{U}}+0.035*\text{C}_{\text{K}}\right) \tag{3}\]
where, numerical constants 0.026, 0.097, and 0.035 refer to heat produced (in 10\({}^{-12}\) W) per 1 g of rock per ppm of Th, per ppm of U and per % of K, respectively; \(\rho_{\text{sample}}\) is density in g/cc; C\({}_{\text{Th}}\), C\({}_{\text{U}}\) and C\({}_{\text{K}}\) are the concentration of Th in ppm, U in ppm and K in % obtained from the gamma ray spectrometer.
## 4 Results
### Megascopic and Microscopic Study of Basement Rock and Radioactive Accessory Minerals
Megascopic study on the basaltic trap and the basement rocks, and microscopic study on the basement rocks are given in Data Set D1 and Table S1, respectively. Basement section in the borehole KBH-05 predominantly consists of medium to coarse-grained gneiss/migmatite gneiss and amphibolite composed
Figure 2: Photomicregraphs of basement rocks of the KBH-05 borehole, Køyna–Warma region, Deccan Volcanic Province, India, showing major minerals and processes like (a) bionization, (b) pepisosity, (c) saussuritization and seticitization, (d) recrystallization, (e) sutured quartz, (f) saussuritization and undulose quartz (g) (h) bitization and crude foliation. For abbreviations of mineralogy, see Table S1.
mainly of quartz, plagioclase feldspar, K-feldspar, hornblende, and biotite (Table S1, Figure 2). Petrographically, these rocks have been classified as granodiorite, tonalite, quartz monozodiorite and amphibolite. Rocks have undergone metasomatism and moderate to intense deformation, as revealed by sericitization, saussuritization, chloritization, and bio-tittization. Plagioclase and K-feldspar have been altered into saussurite and seric, respectively, in most of the samples. Sheared planar fabric is well preserved in the samples, and features like stretching, undulose extinction, and sutured grain boundaries of quartz grains, indicate ductile deformation due to shearing. Further, petrographic studies have recorded genesis texture, which is defined by biotite and hornblende with feldspar and quartz that are produced under amphibolite facies condition. Thus, the study reveals that the basement column in the borehole is made up of genesis/migmatite genesis, varying from granodiorite to tonalite to monozodiorite in composition, along with few amphibolites. This corroborates the results of [PERSON] et al. (2017) and [PERSON] et al. (2017). According to [PERSON] et al. (2017), overprinting and transposition by chlorite and recrystallized muscovite may suggest deformation under greneshist facies condition, which would indicate retrogression and exhumation of the basement. Accessory minerals such as titanite, apatite, zircon, muscovite, opaques, and secondary minerals such as chlorite, epidote are also present in almost all the samples (Table S1, Figure 3).
### Major Oxides
Major oxides were analyzed to characterize the basement rocks (Data Set D2). Total Alkali versus Silica (TAS) diagram (Figure 4a) indicates that basement rocks fall in the field of granodiorite, diorite, and gabbro. A/NK versus A/CNK diagram (Figure 4b) shows that basement rocks are of 1-type and metaluminous. Mineralogical compositions of the studied samples have been determined by CIPW NORM (Data Set D3), using major oxides. NORM data show that quartz, plagioclase feldspar, K-feldspar are major mineral phases, while hypersthene, ilmenite, apatite, hematite, titanite, rutile are accessory mineral phases. Major minerals obtained from the NORM are verified by the petrographic studies. NORM calculation suggests that rocks are rich in anorthite compared to albite and orthoclase. Ab-An-Or ternary diagram (Figure 4c) shows that the basement rocks are trendhyemite to to nonalite to grandodiorite, whereas, QAP diagram (Figure 4d) shows that basement rocks are grandodiorite to nonalite to quartz monozodiorite. Hence, from the above petrographical and geochemical study, it is inferred that that basement rocks are largely intermediate to mafic in composition.
### Density and Porosity
Density, porosity, Th, U, K, and A values for individual samples are given in Data Set D1 and plotted in Figure 5. Density and porosity of basalt vary in a wider range corresponding to their flow nature, that is, massive, amygdala1/vesicular, brecciated, or red bole (Table 1). Amygdaloidal/vesicular, brecciated basalts are mostly observed in two broad zones in the basaltic layer. Such zones are mainly located from 32 to 125 m and 355\(-\)499 m. Amygdaloidal/vesicular basalts have a distinctly lower density (2,400-2,870 kg m\({}^{-3}\)) and higher porosity (3.6%-9.7%), compared to the massive basalt (2,810-3,000 kg m\({}^{-3}\)) and 0.2%-2.0%, respectively). In comparison, the basement has a lower density (2,600-2,820 kg m\({}^{-3}\)) with very low porosity (0.01%-0.15%) compared to the massive basalt. Amphibolite bands found within the basement, show very high density (avg. 2,970 kg m\({}^{-3}\)), much higher than the basement, and as such have low porosity (<1%).
Figure 3: Photomicrographs of basement rocks of the KBH-05 borehole, Koyna–Warma region, Deccan Volcanic Province, India, showing accessory minerals. (a) Zircon and Titanite (PPL), (b) Apatite and Biotite (PPL), (c) Titanite, Apatite and Zircon (PPL), (d) Epidote and Apatite (XPL), (e) Epidote and Biotite (XPL), (f) K-feldspar and Biotite (XPL). PPL: Plane polarized light, XPL: Cross polarized light. For abbreviations of mineralogy, see Table S1.
### Thermal Conductivity
Thermal conductivity measurement is carried out on massive/hard basalt, amygdaloidal/vesicular basalt, and red hole at the saturated condition (Data Set D4, Figure 5). Massive/hard basalt has the highest thermal conductivity among these three varieties, followed by amygdaloidal/vesicular basalt and red bole (Table 1). Thermal conductivity shows a narrow range for each type, with average values for the above three types being 1.6, 1.3, and 1.1 \(\rm{Wm^{-1}K^{-1}}\), respectively. Similarly, the thermal conductivity of the basement rocks includes engiss/migmatitic gneiss of granodiorite to tonalite to quartz monozodiorite in composition, and amphibolite. Due to the wide compositional variations, the gneiss basement shows a wide variation from 2.2 to 3.4 \(\rm{Wm^{-1}K^{-1}}\) over a large borehole section (477 \(\rm{m}\)) with an average of 2.7 \(\rm{Wm^{-1}K^{-1}}\). Amphibolites, which occur as thin layers within the basement, are characterized by comparatively lower thermal conductivity (1.9-2.1 \(\rm{Wm^{-1}K^{-1}}\) with an average of 2.0 \(\rm{Wm^{-1}K^{-1}}\)) (Table 1).
### Radioelemental Concentrations and Radiogenic Heat Production
Radioelemental abundances and heat production for the individual samples of the basaltic trap and basement are shown in Figure 5 and given in Data Set D1. Based on the radiochemical data, the basaltic column can be broadly divided into two layers (Table 2). Two layers in basaltic trap (i.e., BT1 and BT2) have distinct variations in radiochemements and heat production. In the first basaltic layer BT1, average values of Th, U, K, A are slightly lower (1.8 ppm, 0.4 ppm, 0.3%, and 0.3 \(\rm{\mu Wm^{-3}}\)), compared to the second basaltic layer BT2 (2.6 ppm, 0.5 ppm, 0.7%, and 0.4 \(\rm{\mu Wm^{-3}}\)). First layer, BT1, extends up to 323 \(\rm{m}\) depth and consists of amygdaloidal, vesicular, breccitated intermixed layers (up to 125 \(\rm{m}\)), followed by two hard basalt layers, i.e., 125-175 and 175 \(\rm{m}\)-323 \(\rm{m}\). These are designated as BT1a, BT1b, BT1c. Second basaltic layer, BT2, extending from 323 to 499 \(\rm{m}\), consists of the amygdaloidal, vesicular, breccitated intermixed layer (323-355 \(\rm{m}\)), followed by the massive/hard basalt layer (355-499 \(\rm{m}\)). These are designated as BT2a,
Figure 4: Geochemical characterizations of the basement rocks of the KBH-05 borehole, Koyma–Warma region, Deccan Volcanic Province, India. (a) Total alkalis (K,O + Na,O) versus silica (SiO,) (TAS) diagram ([PERSON] et al., 1979), (b) A/NK versus A/CNK diagram ([PERSON], 1943), (c) Normative Ab-An-Or composition ([PERSON], 1979), (d) QAP diagram ([PERSON], 1974). The NORM derived mineralogy (Data Set D3) is used in (c) and (d).
BT2b (Table 3). There are thin red bole layers around 346 m, 406 m, and 454 m in the second basaltic layer. Within the first basaltic layer (BT1), the upper part BT1a (amygdaloidal, vesicular, brecciated intermixing layers) show a slight difference in radioelemental abundances and heat production (2.2 ppm, 0.3 ppm, 0.2%, 0.3 \(\mu\)Wm\({}^{-3}\)), compared to the two hard basalt sections, BT1b and BT1c (2.3 ppm, 0.6 ppm, 0.4%, 0.4 \(\mu\)Wm\({}^{-3}\), and 1.4 ppm, 0.3 ppm, 0.3%, 0.2 \(\mu\)Wm\({}^{-3}\), respectively) (Table 3). In the second basaltic layer (BT2), upper part BT2a (amygdaloidal, vesicular, brecciated intermixing layers), show similar radioelemental abundances (2.4 ppm, 0.4 ppm, 0.9%) as the lower part BT2b (2.8 ppm, 0.6 ppm, 0.6%), resulting in same heat production of 0.4 \(\mu\)Wm\({}^{-3}\). Red bole within the second basaltic layer has slightly higher Th and K and similar U than the basalt surrounding it, resulting in slightly higher A (0.5 \(\mu\)Wm\({}^{-3}\)) than the surrounding basalt (0.4 \(\mu\)Wm\({}^{-3}\)).
The basement genesis, which underlay the basalt, can also be broadly divided into two layers, BG1 and BG2 (Table 2). Upper basement layer BG1 is 93 m thick (from 504 to 597 m), and the lower basement layer BG2 is 384 m thick (from 597 to 981 m). Upper basement layer shows higher Th, U, K, and A (11.6 ppm, 3 ppm, 1.8%, and 2.0 \(\mu\)Wm\({}^{-3}\), respectively), compared to the lower part of the basement (4.6 ppm, 1.3 ppm, K 1.3%, and 0.8 \(\mu\)Wm\({}^{-3}\), respectively). Lower basement layer can be further divided into five layers of about 40-170 m thick with similar A values into alternative layers (0.7, 1.0, 0.6, 1.0, and 0.8 \(\mu\)Wm\({}^{-3}\)). Amphibolites are associated with very low Th: 0.4 ppm, U: 0.1 ppm, and K: 0.7%, with A of 0.1 \(\mu\)Wm\({}^{-3}\) (Table 3).
Radieemental ratios of basaltic trap and basement gneiss layers and sub-layers are summarized in Tables 2 and 3, respectively. For basalt, the Th/U ratio ranges from 3.8 to 7.3, and the K/U ratio from \(0.7\times 10^{-4}\) to \(2.3\times 10^{-4}\). The values of ratios for red bole also fall within the above range. Variations of these ratios for consecutive sub-layers within each layer have also been analyzed. Data indicate uneven radioelemental distribution between the layers. For basement gneiss, a similar study depicts narrower ranges of Th/U (3.2-4), whereas the wider range of K/U (\(0.4\times 10^{-4}\) to \(1.9\times 10^{-4}\)) indicates a uniform distribution of Th and U compared to K.
## 5 Discussion
### Thermal and Physical Properties of Deccan Trap Basalts
#### 5.1.1 Thermal Conductivity and Density
Basaltic trap sequence reveals thermal conductivity differences due to the variations in lithology; highest for massive/hard basalt, medium for the amygdaloidal/vesicular basalt, and lowest for red bole (Figure 5). Average thermal conductivity of massive basalts of this region (\(1.6\) Wm\({}^{-1}\)K\({}^{-1}\)) is marginally lower than that observed in the basaltic cores from the Killari borehole (\(1.7\) Wm\({}^{-1}\)K\({}^{-1}\)), drilled in the southeastern part of the DVP. Basalt samples measured from the fresh outcrops in different parts of the DVP for heat flow studies also yielded similar thermal conductivity values, ranging between 1.6 and 1.8 Wm\({}^{-1}\)K\({}^{-1}\)([PERSON] & [PERSON], 1999). This indicates that the massive basalt layers are homogenous in terms of thermal conductivity as it depends on the major mineralogy of the rock. Thermal conductivity of the amygdaloidal/vesicular basalt and red boles are comparatively very low (\(1.3\) & \(1.1\) Wm\({}^{-1}\)K\({}^{-1}\)) and have been reported first time in the present study.
In a similar manner, density shows large variations between different lithological units; highest for the massive basalt (\(2\),\(930\) kg m\({}^{-3}\)), followed by amygdaloidal/vesicular basalt (\(2\),\(650\) kg m\({}^{-3}\)), and the lowest for the red bole (\(2\),\(530\) kg m\({}^{-3}\)) (Table 1, Figure 6). Density of the massive/hard basalt and vesicular basalt of the present study shows almost similar values with the core samples from the Killari borehole ([PERSON] et al., 2018) and outcrop samples from the different parts of the DVP ([PERSON] et al., 2014). This show homogeneity in density values for the various types of basalts throughout the DVP. Density of the red bole is reported first time in the present study.
#### 5.1.2 Radioelemental Distribution
Radioelemental study on 499 m thick basaltic column, broadly shows two layers of basaltic trap, FT1 and BT2, having different radioelemental abundances and heat production (Figure 7, Table 2). The sublayers of the BT1 and BT2 show slight differences in radioelemental abundances as well as heat production (Table 3). The observed variations in radioelemental data can be correlated with lithological variations. Megascopic
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c} \hline & & & \multicolumn{3}{c}{Th (ppm)} & \multicolumn{3}{c}{U (ppm)} & \multicolumn{3}{c}{K (\%)} & \multicolumn{3}{c}{A (\(\mathrm{\mu Wm^{-1}}\))} & \\ \cline{3-14} Lithology & \multicolumn{2}{c}{Depths/Depth} & \multicolumn{3}{c}{} & \multicolumn{1}{c}{} & Range & Avg. & s.d. & Range & Avg. & s.d. & Range & Avg. & s.d. & Range & Avg. & s.d. & Th/U & K/U \\ \hline Basalt (BT1) & 32-323 & 33 & 1.1–2.5 & 1.8 & 0.5 & 0.2–0.8 & 0.4 & 0.2 & 0.1–0.5 & 0.3 & 0.1 & 0.1–0.4 & 0.3 & 0.1 & 4.5 & 0.8 \\ Basalt (BT2) & 323-499 & 9 & 1.9–3.7 & 2.6 & 0.6 & 0.2–0.8 & 0.5 & 0.2 & 0.2–2.7 & 0.7 & 0.7 & 0.3–0.6 & 0.4 & 0.1 & 5.2 & 1.4 \\ Red bole & 346, 406, 454 & 3 & 1.9–3.7 & 2.9 & 0.9 & 0.2–0.6 & 0.5 & 0.2 & 1.0–1.1 & 1.0 & 0.1 & 0.4–0.6 & 0.5 & 0.1 & 5.8 & 2.0 \\ Granodorite (BG1) & 504–610 & 9 & 10.4–13.6 & 11.6 & 1.0 & 1.9–5.1 & 3.1 & 0.8 & 1.2–2.7 & 1.8 & 0.5 & 1.5–2.7 & 2.0 & 0.3 & 3.7 & 0.6 \\ Granodorite \& 610–981 & 22 & 2.2–7.3 & 4.6 & 1.5 & 0.7–2.3 & 1.3 & 0.5 & 0.1–3.1 & 1.3 & 0.7 & 0.4–1.3 & 0.8 & 0.2 & 3.5 & 1.0 \\ Tonalite (BG2) & & & & & & & & & & & & & & & & \\ Amphibolite & 680–704 & 2 & 0.34, 0.37 & 0.36 & 0.01 & 0.08, 0.11 & 0.1 & 0.01 & 0.67, 0.7 & 0.69 & 0.01 & 0.12, 0.13 & 0.1 & 0.01 & 3.6 & 6.8 \\ \hline \end{tabular}
\end{table}
Table 2: Range, Average and s.d. of Th, U, K and Heat Production (A) for the Major Layers of the KBH-05 Borehole, Koyana–Warna Region, Deccan Volcanic Province, India
## References
* [1] [PERSON], [PERSON], and [PERSON], \"The Anderson-McMillan Model of the Anderson-McMillan Model,\" _Phys. Rev. Lett._**108**, 101801 (2011).
study showed that within three sub-layers of the BT1, amygdaloidal/vesicular basalt is underlain by two massive basalt layers. Similarly, within two sub-layers of the BT2, amygdaloidal/vesicular basalt layer, followed by a massive basalt layer.
Due to the lithological variations in these layers, distinct changes in the physical properties of these layers have been observed, which are well reflected by gamma and sonic logs (Figure 8, Table 4). Among the five sub-layers, the gamma log is not available for BT1a, and the sonic log is not available for BT1a and BT1b. Gamma counts are distinctly different in four sub-layers (BT1b, BT1c, BT2a, BT2b), and sonic velocities (V\({}_{p}\) and V\({}_{S}\)) are also different in the three sub-layers (BT1c, BT2a, BT2b) (Table 4). Consequently, the calculated Poisson's ratio is different for these layers. Amygdaloidal/vesicular samples (at the depths \(\sim\)200 and 270 m), as well as red bole samples (at the depths 346, 406, and 454 m), show a sharp peak in gamma log and-ve peak in V\({}_{p}\) and V\({}_{S}\) in sonic logs (Table S2). Thus, the variations in the radioelemental abundances in the sub-layers are reasonably explained by the gamma and sonic logs.
Basaltic trap of the DVP consists of as many as 46 lava flows ([PERSON] et al., 2017) that erupted in a short duration of \(<\)5 Ma around 66 Ma ([PERSON] et al., 2015; [PERSON] et al., 2019). These lava flows have been divided into three sub-groups and 12 major formations. These formations have different thicknesses at different places within the DVP. Reportedly, these formations can be differentiated on the basis of their trace elements (Sr, Rb, Ba, TiO\({}_{x}\)) and isotopic ratios (\({}^{87}\)Sr/\({}^{88}\)Sr) ([PERSON], 1985; [PERSON] et al., 1994). Based on surface geology, chemo- and magneto-stratigraphy, and the boreholes studies, out of the total 12 Deccan volcanic formations, five formations (Desur, Mahabaleshwar, Poladpur, Bushe, and Khandala), belonging to two sub-groups, Lonavala and Wai, are present in the Koyna\(-\)Warna region ([PERSON] & [PERSON], 2017). According to the present study, differences in radioelements and heat production within the two basaltic layers and their five sub-layers can be explained by the variations in the composition and the radioactive elements (Th, U).
### Thermal and Physical Properties of Basement
#### 5.2.1 Thermal Conductivity and Density
Thermal conductivity of the crystalline basement rocks shows a wide range (2.2-3.4 Wm\({}^{-1}\)K\({}^{-1}\)), which can be correlated well with their mineralogical/compositional changes, that is, change in the composition of the basementensis from granodiorite to tonalite to quartz monozlotrie. In this wide range, thermal conductivity is higher in granodiorite and lower in quartz monozlotrie (Data Set D4). Further, thin layers of amphibolites have shown very low thermal conductivity (2.0 Wm\({}^{-1}\)K\({}^{-1}\)). But since they occur as very thin layers within the basement, their effect on bulk thermal conductivity will be very less and thus can be ignored in thermal modeling. Therefore, an average thermal conductivity value of 2.7 Wm\({}^{-1}\)K\({}^{-1}\) can be
Figure 6: Bivariate plot showing thermal conductivity versus density along with 1-\(\sigma\) standard deviations, for the rocks in basaltic trap and basement of the KBH-05 borehole, Koyna\(-\)Warna region, Deccan Volcanic Province, India.
considered as the representative for the concealed Neoarchen basement rock. In comparison to the Koyna\(-\)Warna region, the thermal conductivity of the samples from the Killari borehole has shown relatively higher values, between 2.8 and 2.9 Wm\({}^{-1}\)K\({}^{-1}\)([PERSON] & [PERSON], 1999).
On a subset of the basement samples, thermal conductivity is determined from the modal mineralogy (Table S1) and NORM derived mineralogy (Data Set D3), using harmonic mean model. It is also determined from the oxide data using the expressions given by [PERSON] et al., 2019 (Table 5). Variation is generally less than 15% by modal mineralogy, but slightly more than by other two methods. The observed deviation is slightly more than the results of the previous studies on metamorphic ([PERSON] et al., 2015) and igneous rocks ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2021). Larger deviation between measured and calculated thermal conductivity from the previously published results on igneous and metamorphic rocks could be attributed to the alteration and deformation of the minerals, as observed in the petrographic study
Figure 7.— Bar diagram showing distribution of Th, U, K, and heat production (A) for the different layers of the basaltic trap and basement of the KBH-05 borehole, Koyna\(-\)Warna region, Deccan Volcanic Province, India. BT1 and BT2: two layers of basaltic trap, BG1 and BG2: two layers of basement genesis.
as sericitization, saussuritization and myelination, which may have affected thermal conductivity of the minerals which could not be considered while thermal conductivity determination.
Density of the basement rocks in the present study (range from 2,600 to 2,820 kg m\({}^{-3}\) with an average of 2,720 kg m\({}^{-3}\)) is significantly lower than the basement rocks of the Killari borehole (range from 2,690 to 3,060 kg m\({}^{-3}\), with an average of 2,819 kg m\({}^{-3}\)) ([PERSON] et al., 2012), but slightly higher than the range that is observed for the granite rocks of the Dharwar Caton (2,520-2,730 kg m\({}^{-3}\) with an average of 2,640 kg m\({}^{-3}\)) ([PERSON] et al., 1977), as well as upper crustal granitic/gnesis rocks from different regions of the Indian shield ([PERSON] et al., 2018, 2020; [PERSON] et al., 2017; [PERSON] et al., 2003). These studies yielded two important points: (a) the subsurface basement density is not the same in different parts of the DVP, which as corroborates the results of [PERSON] et al. (2001), and (b) the basement density is not of typically upper crustal granite type, but possibly represent mid crustal density. Petrological and geochemical results also indicate that the basement is greenchist to amphibolite facies granitidis, having intermediate to mafic composition (Figures 2 and 4). Previous studies reveal that the basement rocks beneath the Koyna\(-\)Warna region are
Figure 8: Gamma and sonic log (P-wave velocity and S-wave velocity) of the KBH-05 borehole, Koyna\(-\)Warna region, Dececan Volcanic Province, India. Gamma log is available for basaltic trap and sonic log is available for both basaltic trap and basement. BT1 and BT2: two layers of basaltic trap; BT1b and BT1c: two sub-layers within BT1 layer; BT2a and BT2b: two sub-layers within BT2 layer; BG1 and BG2: two layers of basement gneiss.
greenschist to amphibolite facies ([PERSON] et al., 2017), whereas Killari region are amphibolite to granululte facies ([PERSON] et al., 2012).
#### 5.2.2 Radioelemental Distribution
Radioelemental concentrations carried out on 477 m thick basement column containing greisses/migmatite gneiss (granodiorite to to quantize monzodiorite in composition) and amphibolites indicate that it can be divided into two distinct layers (BG1 and BG2). Upper-basement layer BG1, which is 93 m thick, shows two times higher Th, U, K, and A, compared to the underlying 384 m thick basement layer BG2 (Table 3). The above variations can be well correlated with sonic log data (Table 4, Figure 8), which indicate significant differences in P- and S-wave velocities and Poisson's ratio. The latter may indicate significant lithological changes between these two basement layers. Petrographic study also exhibits that there are differences in the abundances of radioactive accessory minerals in such layers, like K-feldspar, biotite, epidote, titanite, apatite, and muscovite.
\begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline \multicolumn{2}{c}{Radioelemental data} & \multicolumn{3}{c}{Gamma log counts (cps)} & \multicolumn{3}{c}{Sonic log (V\({}_{\text{y}}\)) (km/s)} & \multicolumn{3}{c}{Sonic log (V\({}_{\text{y}}\)) (km/s)} \\ \hline Depth (m) & Layer & Min. & Max. & Av. & Min. & Max. & Av. & Min. & Max. & Av. \\ \hline \multicolumn{2}{l}{Basaltic trap} & & & & & & & & & \\
125–175 & BT1b & 4.06 & 40.47 & 20.02 & \(\cdot\cdot\cdot\cdot\) & \(\cdot\cdot\cdot\) & \(\cdot\cdot\cdot\) & \(\cdot\cdot\cdot\) \\
175–323 & BT1c & 3.21 & 44.97 & 13.70 & 3.59 & 5.84 & 5.05 & 1.66 & 2.44 & 2.23 \\
**125–323** & **BT1** & **3.21** & **44.97** & **19.29** & **3.59** & **5.84** & **5.05** & **1.66** & **2.44** & **2.23** \\
323–406 & BT2a & 7.45 & 48.00 & 21.19 & 2.68 & 5.62 & 4.40 & 1.53 & 2.44 & 2.15 \\
406–497 & BT2b & 13.15 & 59.81 & 31.36 & 3.04 & 5.32 & 4.26 & 1.44 & 2.40 & 2.03 \\
**323–497** & **BT2** & **7.45** & **59.81** & **26.47** & **2.68** & **5.62** & **4.32** & **1.44** & **2.44** & **2.09** \\ \multicolumn{2}{l}{Basementa} & & & & & & & & & \\
504–610 & BG1 & – & – & – & 4.32 & 5.62 & **5.17** & 2.21 & 2.73 & **2.53** \\
610–930 & BG2 & – & – & – & - & 5.05 & 6.21 & **5.51** & 2.29 & 2.81 & **2.55** \\ \hline \multicolumn{2}{l}{\({}^{\ast}\)Geniss/migmatite gneiss (granodiorite to to qualite to quartz monzodiorite in composition) and amphibolite.} & & & & & & & & \\ \end{tabular}
\end{table}
Table 4: Gamma Counts, P-Wave and S-Wave Velocity From Gamma and Sonic Logs for Different Layers as Observed in the Radoicelemental Study of the KBH-05 Borohole, Deccan Volcanic Province, India
\begin{table}
\begin{tabular}{l l c c c c c c c} \hline \hline \multicolumn{2}{c}{_Measured and Calculated Thermal Conductivity of the Basement Rocks of the KBH-05 Borohole, Deccan Volcanic Province, India_} & & \multicolumn{3}{c}{Deviation (in \(\%\))} \\ \hline Sample & & From & From & Using Jennings & From & From & From & Using [PERSON] \\ no. & Rock type & \(\lambda_{\text{sr}}\) & modala & NORMa & et al., 2019b & et al., 2019b \\ \hline
**KBH-50** & Granodiorite & 3.05 & 2.94 & 3.01 & 2.84 & \(-\)3.6 & \(-\)1.3 & \(-\)6.9 \\
**KBH-54** & Granodiorite & 2.69 & 2.96 & 3.06 & 2.89 & 10.0 & 13.8 & 7.3 \\
**KBH-65** & Granodiorite & 3.29 & 2.9 & 2.84 & 2.75 & \(-\)11.9 & \(-\)13.7 & \(-\)16.4 \\
**KBH-73** & Granodiorite & 2.73 & 2.79 & 3.35 & 3.06 & 2.2 & 22.7 & 12.1 \\
**KBH-74** & Tonalite & 2.94 & 3.03 & 2.80 & 2.61 & 3.1 & \(-\)4.8 & \(-\)11.2 \\
**KBH-75** & Tonalite & 3.03 & 2.86 & 2.95 & 2.84 & \(-\)5.6 & \(-\)2.6 & \(-\)6.4 \\
**KBH-77** & Granodiorite & 2.4 & 2.76 & 2.85 & 2.57 & 15.0 & 18.8 & 7.1 \\ \hline \multicolumn{2}{l}{\({}^{\ast}\)Calculated Harmonic mean thermal conductivity, \({}^{\text{b}}\)\({}_{\text{sr}}^{\text{k}}=\text{exp}\left(1.72^{\text{TC}}\text{{}_{\text{s}}_{ \text{202}}}+1.018^{\text{TC}}\text{{}_{\text{ MgO}}}\right)\) - 3.652\({}^{\text{TC}}\)\({}_{\text{s}}_{\text{s}}_{\text{s}}_{\text{s}}_{\text{s}}_{\text{s}}_{\text{s}}_{\text{s}} _{\text{s}
Radioemental study on a large number of samples from the fresh outcrops of the TTG engisess in the Western Dharwar Caton (WDC), occurring south of this region, shows a consistent heat production of 1.0-1.1 \(\mu\)Wm\({}^{-3}\) from greenschist to amphibolite facies rocks. However, felsic volcanic of the Eastern Dharwar Caton (EDC), occurring south-east of this region, show a larger variation of 1.3-2.2 \(\mu\)Wm\({}^{-3}\) from greenschist to amphibolite facies rocks ([PERSON] & [PERSON], 2004). In comparison, we found a heat production of 0.8 \(\mu\)Wm\({}^{-3}\) for the lower part of the basement rocks (\(\sim\)400 m thick), which is similar to the greenschist facies grasses of the WDC (1.0 \(\mu\)Wm\({}^{-3}\)). It also corresponds very well with the globally average value for continental middle crust. Petrographic results from present and previous studies on borehole core samples from the Koyna\(-\)Warna region show evidence of greenschist to amphibolite facies condition. Such a low level of radioelemental concentration in the lower basement layer is not observed in the major lithologies of the EDC. Considerably higher heat production of 2.0 \(\mu\)Wm\({}^{-3}\) for the 100 m thick upper part of the basement rocks may be ascribed to the enrichment in the radioelements in the transition zone between the trap and the basement due to metasomatic alteration, which also observed in the petrographic study. Radioelemental data from the geochemical study of the basement rock ([PERSON] et al., 2017) from another deep borehole KBH-01 (Figure 1), yielded similar radioelements and heat production, as observed in two basement layers of borehole KBH-05, where the upper layer has comparatively higher radioactivity than the lower layer. To confirm such variations in radioelements in the basement, the other boreholes in the Koyna\(-\)Warna region need to be studied.
Previous radiochemical study of the basement rocks from the Killari borehole (Figure 9a, Table S3) showed that the upper part of the basement (\(\sim\)350-450 m) consists of thin alternating layers of low and high radioelements and heat production (Table S4). Average values for the low heat-producing layers (Th: 2.1 ppm, U: 0.5 ppm, K: 1.1%, and A: 0 \(\mu\)Wm\({}^{-3}\)) are few times lower in comparison to the high producing layers (Th: 24 ppm, U: 2.5 ppm, K: 1.8%, and A: 2.6 \(\mu\)Wm\({}^{-3}\)). Below this alternating band of layers, a thick column of the basement (\(\sim\)450-600 m) was found to have higher radioelemental concentrations as well as higher heat production (Th: 20 ppm, U: 3.2 ppm, K: 2.3%, and A: 2.5 \(\mu\)Wm\({}^{-3}\)), similar to that observed in the upper part of the basement layer in the KBH-05 borehole in Koyna\(-\)Warna region (Figure 9b; Table 3). However, at the bottom part of the Killari borehole, again thin layers of low radioelements are observed. In other words, by and large, Killari borehole consists of high as well as variable radioelemental rocks having average heat
Figure 9: Heat production variations of the basement rocks from two regions in the Deccan Volcanic Province, India. Detail lithology for the basement in (b), see Figure 5.
production between 2.5 and 2.6 \(\mu\)Wm\({}^{-3}\), with thin layers of low radioelemental rocks having average heat production between 0.3 and 0.6 \(\mu\)Wm\({}^{-3}\) (Figure 9a). Thin layers of low radioelements abundances are observed more in the upper 100 m of the basement and could be mismattie genesis (0.4 \(\mu\)Wm\({}^{-3}\)), whereas higher heat production correlates well with the greenschist to amphibolite facies grandoitorite genies (2.4 \(\mu\)Wm\({}^{-3}\)) of the EDC. Further, wide variations in radioelements and heat production is observed in Killari basement samples, whereas comparatively narrow variations observed in Koyna\(-\)Warna basement samples (Figure 9b). Thus, in the radioactivity point of view, the basement below Koyna\(-\)Warna region differs from the basement below the Killari region. This indicates that the different parts of the DVP may be underlain by a different type of basement rocks which produces the above differences. Differences also revealed by petrographic and geochemical studies ([PERSON] et al., 2017; [PERSON] et al., 2012). Moreover, geochronological studies indicate Koyna\(-\)Warna basement to be 2.7 Ga old ([PERSON] et al., 2017), compared to 2.5 Ga in Killari ([PERSON], 1998). Thus, the differences in radioactivity could be attributed to the differing nature of basement rocks between these two regions due to their spatial distributions. This is corroborated with the view of the heterogeneous crust beneath the region, as indicated by various geophysical and geological studies ([PERSON] et al., 2019; [PERSON] et al., 2020). These differences should be considered while doing thermal modeling in the different regions of the DVP. Thus, much more studies are needed to confirm the nature of the basement below different parts of DVP.
### 1-D Thermal Model Upto 10 km: Koyna\(-\)Warna Region
To construct a 1-D thermal model up to a depth of 10 km beneath the studied region, thermal, physical, and geochemical data of the present study, along with available information from geophysical and geological studies, are used. Seismic study ([PERSON] et al., 1981) indicates that the basement is made up of rocks similar to that of the Dharwarn Craton situated south of it. Geochemical study yielded that the genesis/migmating genesis basement is made up of grandoitorite to to onalite to quartz monoziodorite in composition (Figure 4d). Recent study on various types of granidiotis ([PERSON] et al., 2021) showed that the temperature coefficient of thermal conductivity for the granidoids varied in a wide range, depending upon their composition. For the alkali feldspar granite to monozgranite, it is 0.0015 K\({}^{-1}\), whereas, for granodiorite to tonalite to quartz diorite, it is 0.0007 K\({}^{-1}\). In case of the former, the temperature coefficient value is the same as generally being used for thermal modeling of the upper crust ([PERSON], 1986). However, in the temperature calculation of the present study, we use the latter value, which appears more appropriate to represent the underlying crustal rocks which is grandoitorite to tonalite in nature (Figure 4d).
Heat flow estimates in the Koyna\(-\)Warna region from a 1,500 m deep borehole yielded an average value of 45 mWm\({}^{-2}\)([PERSON] et al., 2015), which is slightly higher than the earlier reported value (41 mWm\({}^{-2}\)) from a \(\sim\)200 m deep boreholes ([PERSON] & [PERSON], 1984) and 617 m deep Killari borehole ([PERSON] & [PERSON], 1999). An increased heat flow is often recorded in deeper boreholes, which are adopted here as they are considered better representative of the regional heat flow field. Lower and upper bound for heat flow is considered as \(\pm\)10% of the representative heat flow, that is, 40 and 50 mWm\({}^{-2}\). Considering surface heat flow as a boundary condition, thermal conductivity variations and heat production play a controlling factor in estimating temperatures at the deeper depths ([PERSON] & [PERSON], 2020). 1-D steady-state thermal modeling is carried out for the study region by considering two plausible crustal models up to 10 km (Model 1 and Model 2), where heat flow is taken as 40 and 50 mWm\({}^{-2}\), respectively (Figure 10a). Temperature estimates for Model 1 and Model 2 are shown by blue and red solid lines (Figure 10b). Previous studies showed that thermal conductivity and heat production are the most important parameters to control temperature estimates ([PERSON] et al., 2016; [PERSON] et al., 1999; [PERSON] et al., 2021). Therefore, for each model, \(\pm\)10% uncertainty in thermal conductivity and heat production are used to estimate the temperatures, which are plotted by dashed lines in Figure 10b. 1-D thermal modeling indicates that at the 10 km depth, temperature could vary from 165 degC to 250 degC (Figure 10b).
### Thermal Model and Earthquake Nucleation
Brittle-ductile transition zone is the approximate depth below which the ductile transformation dominates. This depth corresponds to an isotherm, which is useful for the crustal rheological modeling. In the stable continental regions, the maximum focal depth of earthquakes, known as cut-off depth, generally matcheswith the brittle-ductile zone, usually associated with temperature \(\sim\)350\({}^{\circ}\)C, although it can vary between 260\({}^{\circ}\)C and 450\({}^{\circ}\)C, which depend on the tectono-thermal setting of the region and the nature of crustal lithologies ([PERSON], 1995). In any region, to determine the depth of these isotherms, robust thermal modeling is essential.
In the Koyna\(-\)Warna region, the focal depth of the earthquakes is generally less than 10 km. Robust thermal modeling shows that the brittle-ductile transition zone could reach at 12-18 km depth only. It would mean that the brittle-ductile transition may not be the sole factor responsible for the earthquake nucleation in this region. This region is well known for RTS for the last 6 decades ([PERSON], 2017), which increases the pore pressure to trigger the seismic activity ([PERSON] et al., 1997). Several deep fracture zones have been identified in the basement in this region by the seismic method ([PERSON] et al., 1981). Also, tectonically active NW-SE trending fractures in the basement have been identified by various studies, like geomorphic anomalies and fracture zone analysis ([PERSON] et al., 2017; [PERSON] et al., 2017), magnetic potential ([PERSON] et al., 2017), and LIDAR mapping ([PERSON] et al., 2018), etc. Global studies show that the presence of fluid in the fracture zone ([PERSON] et al., 2019) and deformation microstructures in rocks ([PERSON] et al., 2018) can control the seismogenesis. Thus, seismogenic depth below the Koyna\(-\)Warna region is controlled not only by the thermal condition of the region but also guided by factors discussed above, which produces seismicity at a few km shallower depth than that deduced by thermal modeling.
## 6 Conclusion
Thermal (radioelements, heat production, thermal conductivity) and physical (density, porosity) properties are studied in the laboratory on the drilled core samples from a 981 m deep scientific borehole in the Koyna\(-\)Warna region, located over the southwestern part of the DVP, western India. This has helped us to characterize the nature of Deccan basalts and the concealed basement rocks and further to arrive at a precise 1-D thermal model for the upper 10 km of the crust in the Koyna\(-\)Warna region, where most of the earthquakes are generated due to RTS from the last six decades. Present study provides the following significant outcomes:
1. In basaltic traps, thermal conductivity, density and porosity vary in distinct range for different lithological variants, that is, massive/hard basalt (1.5-1.7 Wm\({}^{-1}\)K\({}^{-1}\), 2,810-3,000 kg m\({}^{-3}\), 0.2%-2.0%), amygdaladalal/vesicular basalt (1.2-1.4 Wm\({}^{-1}\)K\({}^{-1}\), 2,400-2,870 kg m\({}^{-3}\), 3.6%-9.7%) and red lobe (1.0-1.1 Wm\({}^{-1}\)K\({}^{-1}\), 2,440-2,620 kg m\({}^{-3}\), 4.2%-5.4%). Similarly, in basement rocks, above properties are different for greisses/migmatite greisses (2.2-3.4 Wm\({}^{-1}\)K\({}^{-1}\), 2,600-2,820 kg m\({}^{-3}\), <0.2%), which is the main component of
Figure 10: (a) Crustal heat production/thermal conductivity model up to 10 km, (b) Temperature estimates up to 10 km of the Koyna\(-\)Warna region, Deccan Volcanic Province, India. A: heat production (with \(\pm\)10% uncertainty); \(\lambda\): initial thermal conductivity (with \(\pm\)10% uncertainty); b: 0.0007 K\({}^{-1}\); c: 0.0015 km\({}^{-1}\), where b and c are temperature and pressure coefficients of thermal conductivity, respectively.
basement and for the very thin mafic layer (1.9-2.1 Wm-1K-1, 2,960-2,980 kg m-3, <0.1%) within the main component.
2. Entire column can be divided into four broad layers on the basis of radioelemental abundances and heat production data. Two basalt layers in the top section of the borehole are about 323 and 175 m thick, which are followed by two genies/migmatic genies basement layers of the thickness 93 and 384 m. Both basement layers are I-type, metaluminous, and grandointe to tonalite to quartz monozidorite in composition. Lower basement layer consists of very thin bands of amphibolites.
3. Upper basaltic layer has slightly low radioelemental concentrations and heat production (1.8 ppm, 0.4 ppm, 0.3%, 0.3 \(\mu\)Wm-3), compared to the lower basaltic layer (2.6 ppm, 0.5 ppm, 0.7%, 0.4 \(\mu\)Wm-3). Red lobe within the lower layer have slightly higher Th, U, K, and heat production (2.9 ppm, 0.5 ppm, 1.0%, 0.5 \(\mu\)Wm-3) compared to the surrounding basalts. Two basaltic layers obtained from radioelemental study could be correlated with two major flood basaltic formations. In the basement, Th, and U abundances in the upper layer are approximately two times higher (11.6 ppm, 3.1 ppm) than the lower layer (4.6 ppm, 1.3 ppm), although both have similar K content (1.8% and 1.3%), resulting in heat production of 2.0 and 0.8 \(\mu\)Wm-3, respectively. The differences could be correlated with the variations in lithology from greenshastic to amphibolite and the abundances of the radioactive accessory minerals in them.
4. Lower basement layer has similar heat production as the TTG eigenses of the WDC, and thus WDC could form the basement in the southwest part of the DVP. The heat production also corresponds very well with the global average heat production values for the continental middle crust.
5. At 10 km depth, temperature estimates range between 165\({}^{\circ}\)C and 250\({}^{\circ}\)C, which is much higher than reported earlier for this region. This is for the first time that detailed temperature estimates are made for this region based on the thermal and physical properties of the rocks from drill core samples. The study further reveals that seismicity in the Koyna-Warna region is not entirely controlled by temperature, it is also reservoir induced, which yields seismicity at a few km shallower depth than that estimated by thermal modeling.
## Data Availability Statement
Data supporting the study are available CSIR-NGRI repository [[https://ngri.org.in/files/koyna_data/Data-set_Supporting_Tables_zip](https://ngri.org.in/files/koyna_data/Data-set_Supporting_Tables_zip)]([https://ngri.org.in/files/koyna_data/Data-set_Supporting_Tables_zip](https://ngri.org.in/files/koyna_data/Data-set_Supporting_Tables_zip)).
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wiley/ffc23f97_b278_4dd3_8af6_c75ce9e3a5db.md | Illuminating the Arctic: Unveiling seabird responses to artificial light during polar darkness through citizen science and remote sensing
[PERSON]
Department of Marine Ecology, Institute of Oceanology, Polish Academy of Sciences, Powstancow Warszawy 55, Sopot 81-712, Poland
[PERSON]
Department of Vertebrate Ecology and Zoology, Faculty of Biology, University of Gdansk, Gdansk 80-309, Poland
[PERSON]
Space Research Centre, Polish Academy of Sciences, Warsaw 00-716, Poland
& [PERSON]
Department of Marine Ecology, Institute of Oceanology, Polish Academy of Sciences, Powstancow Warszawy 55, Sopot 81-712, Poland
###### Abstract
Artificial light at night (ALAN) has global impacts on animals, often negative, yet its effects in polar regions remains largely underexplored. These regions experience prolonged darkness during the polar night, while human activity and artificial lighting are rapidly increasing. In this study, we analyzed a decade of citizen science data on light-sensitive seabird occurrences in Longyearbyen, a High-Arctic port settlement, to examine the impact of environmental factors including ALAN during polar night. Our investigation incorporated remote sensing data on nighttime lights levels, sea ice presence, and air temperature measurements from local meteorological station. Our findings reveal that artificial light may potentially impact seabird diversity in this region, with overall diversity decreasing alongside light intensity. However, the relationship between artificial light and seabird diversity was not uniformly negative; individual species exhibited varied responses. We also detected a correlation between artificial light and air temperature, emphasizing the complexity of environmental interactions. Notably, the piscivorous Black Guillemot (_Cepplus grylle_), the dominant species in Longyearbyen during the polar night, showed increased contribution in the local seabird assemblage with higher light levels. In contrast, the zooplankton's Little Auk (_Alle alle_) exhibited reduced contribution with higher light intensity and increased presence with higher air temperatures. We hypothesize that these differing responses are closely tied to the distinct dietary habits, varying sensitivity to artificial light due to individual adaptations, and overall ecological flexibility of these species, underscoring the need for further research. This study, which uniquely combines citizen science with remote sensing data, represents the first effort to systematically assess the effects of artificial lighting on seabirds during the polar night. The findings underscore the potential importance of this issue for seabird conservation in polar regions.
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## 1 Introduction
The nocturnal activities of pelagic organisms ([PERSON], 1999), long-distance bird migrations ([PERSON] et al., 2001), and prey-predator interactions ([PERSON] et al., 1991) are primarily driven by natural light sources such as moonlight and starlight, which play crucial roles in their functioning ([PERSON] et al., 2012). However, these natural light-dark patterns are constantly disrupted by artificial light at night (ALAN; [PERSON] et al., 2015; [PERSON] et al., 2020). The increase in ALAN intensity has been observed since the last century and is estimated to grow by 6% annually ([PERSON] et al., 2010), making understanding the potential impacts of this stressor on various organisms essential. Rapid environmental changes resulting from increased human activity (Human-Induced Rapid Environmental Change--HIREC; [PERSON] et al., 2011) can have serious consequences for ecosystem balance. ALAN can impact organisms in various ways, often negative. Persistent ALAN can disrupt the natural photoperiod, leading to significant effects on a variety of physiological traits ([PERSON] et al., 2013).
A more immediate effect of ALAN could be linked to foraging behavior, which may have both positive and negative outcomes ([PERSON] & [PERSON], 2006; [PERSON], 2006), depending on the species and context ([PERSON] & [PERSON], 2024). For example, interactions with fisheries or cargo vessels can vary significantly across different species ([PERSON] et al., 2021; [PERSON], 2023).
Increased visibility of prey due to ALAN may influence foraging success in different ways: while it can enhance the ability of predators to locate their prey, it also makes predators more detectable, potentially allowing prey to evade capture more effectively. Furthermore, artificial lighting may also result in direct, often fatal consequences, such as attracting animals to wrong locations or temporarily blinding them ([PERSON], [PERSON], et al., 2017; [PERSON] et al., 2018). The increase in artificial light levels has been identified as a threat during the breeding period for seabirds, including petrels ([PERSON] et al., 2019; [PERSON] et al., 2019), and the Mans Shearwater (_Puffinus puffinus_) ([PERSON] et al., 2021). Therefore, studying the impact of \"ecological light pollution\" ([PERSON] & [PERSON], 2004) on the behavior and community ecology of species is now a major challenge for wildlife conservationists ([PERSON] et al., 2017; [PERSON] et al., 2015; [PERSON], [PERSON], et al., 2017).
Different seabird species have previously been observed exploiting foraging grounds exposed to artificial light ([PERSON], 2006). However, the presence of artificial light in the Arctic during the polar night could be an especially intense stimulant due to the stark contrast against the completely dark environment ([PERSON] & [PERSON], 2016). It has been shown that attraction to artificial light sources is stronger during the night or at times of low cloud cover ([PERSON], 2006; [PERSON] et al., 1987). Studies on light-induced seabird strikes on vessels in Southwest Greenland during winter found the highest frequency of bird strikes during the darkest mid-winter period (Now-Jan), always during the night or twilight ([PERSON] & [PERSON], 2011). Birds can lose a significant amount of energy by following light sources, which can pose a serious threat to their winter survival ([PERSON], 2006). Artificial light may cause seabirds to mistakenly select poor-quality habitats over better alternatives, leading them into an \"ecological trap\" ([PERSON] et al., 2002; [PERSON] et al., 2017). It may also prevent individuals from migrating south to their wintering areas and result in higher energetic demands during the harsh Arctic polar night ([PERSON] et al., 2013; [PERSON] et al., 2011).
High latitudes above 78\({}^{\circ}\)N, experiencing apparent darkness during the Arctic polar night, are particularly vulnerable to global changes, especially due to the Arctic warming two to three times faster than any other place on Earth ([PERSON], [PERSON], et al., 2020), resulting in the drastic loss of its icy character ([PERSON] et al., 2019). With the projected loss of sea ice ([PERSON], 2017), increased human activity in the Arctic, such as open access to new fishing grounds, transport of oil/gas deposits, and touristim routes like the Northwest Passage and the Northern Sea Route along Russia's Arctic coast, is expected to bring more artificial light to this otherwise dark polar night environment. By mid-century, sea routes through the Arctic Ocean are anticipated to become shortcuts between Pacific and Atlantic ports ([PERSON] et al., 2016), potentially irreversibly altering the dark character of the winter time environment.
The impact of artificial light on polar ecosystems during the polar night remains understudied. Disruption of behavior in marine organisms, such as plankton or fish, has been reported ([PERSON] et al., 2020). However, little is known about the impact of artificial light on a particularly light-sensitive group of animals-seabirds. Recent reports of actively foraging pelagic seabirds under continuously dark conditions in Svalbard ([PERSON], [PERSON], et al., 2015) have shown that some, like the psychorous Black Guillemot (_Ceplus gylle_) or Bruninch's Guillemot (_Uria lomvia_), may opportunistically use artificial light sources to forage, while others, like zooplankton Little Auss (_Allle alle_), appear to avoid it ([PERSON] et al., 2017). Furthermore, research on seabird\(-\)fishery interactions, particularly with Northern Fulmars (_Fulmanus glacialis_) in the North-East Atlantic and Barents Sea during the non-breeding season, suggests that artificial lights can affect the activity of birds around fishing vessels ([PERSON] et al., 2021). Despite these insights, the scale and impact of artificial light on high-Arctic polar ecosystems remain insufficiently studied. While feeding in areas exposed to artificial nocturnal lighting is often considered favorable for seabirds in some regions, as it enhances food availability in surface waters where it can be easily caught ([PERSON] et al., 2005; [PERSON], 2006), for the vast majority of the zooplankton community during the polar night, artificial light should evoke a strong light-escape response ([PERSON] et al., 2018). However, as a particularly strong stimulant, artificial light can have various effects on organisms with different sensitivities to light, resulting in contrasting responses among different taxa ([PERSON] et al., 2020), which may, in turn, have different consequences for different seabird foraging guilds.
Here, we present a unique study of seabirds from a citizen science-based database spanning the last decade in the High-Arctic port settlement of Svalbard--Longyear-byen, and remote sensing data on light intensity, presence of sea ice, and air temperature from local meteorological station. This research aims to investigate the potential impact of environmental conditions, including artificial light, on seabird diversity during the Arctic polar night. Specifically, we seek to answer two important questions for the first time: (1) which environmental conditions shape the composition of seabird assemblages during the polar night in light-polluted Longyearbyen, and (2) for which species may the presence of artificial light be potentially beneficial or disadvantageous. This study is, to our knowledge, the first to investigate the impact of light pollution on seabirds during the Arctic polar night and may be particularly significant in the context of conserving one of the most globally threatened groups of birds.
## Material and Methods
### Study area
The west coast of Spitsbergen is influenced by two current systems: the cold and fresh coastal Spitsbergen Polar Current (SPC) and the warm and more saline West Spitsbergen Current (WSC) ([PERSON] et al., 2017; [PERSON] et al., 2022). The convergence of these two distinct water masses creates a frontal zone of varying extent in different seasons ([PERSON] & [PERSON], 2007). Sea ice is frequently present during winter along the western coast of Spitsbergen; however, its thickness and occurrence fluctuate significantly depending on prevailing conditions such as wind, ocean currents, and atmospheric conditions. Overall, there has been a decrease in sea ice concentration, with a trend of up to 10% per decade. This decline correlates with a warming of Atlantic Water entering the Arctic Ocean in this region, resulting in reduced sea ice cover and increased transfer of oceanic heat to the atmosphere, which contributes to atmospheric warming ([PERSON] et al., 2020; [PERSON] et al., 2014).
This study includes records of seabirds from Longyearbyen, the most populated and urbanized settlement of Spitsbergen, with approximately 1750 inhabitants. Longyearbyen is situated in Adventfjorden, a small body of water measuring around 7 km long and 4 km wide, located at the foot of Longyearbyen and serving as a northwest to southeast-directed side arm of Isfjorden, the largest fjord complex in west Spitsbergen. Numerous large breeding colonies of seabirds are situated on mountain slopes and islands within Isfjorden. Hydrological conditions within Isfjorden exhibit dynamic equilibrium between thermally contrasting large water masses, but due to climate change, they are increasingly influenced by \"Atlantication\", characterized by stronger advection of warmer, highly saline waters from lower latitudes (IPCC, 2022; [PERSON] et al., 2020). Surface water typically freezes in winter for several months, especially in the innermost parts of the fjords; however, in recent years, some winters have remained ice-free in this area ([PERSON] et al., 2008; [PERSON] et al., 2017).
Adventfjorden, where Longyearbyen is situated, experiences a unique high Arctic light climate. During winter, the sun stays below the horizon for nearly 4 months, while in summer, it remains above the horizon for an equal duration ([PERSON], [PERSON], et al., 2020). At latitudes above 78\({}^{\circ}\)N, including Longyearbyen, the period from November to February is often referred to as the \"dark season\" due to the apparent darkness. However, the most intense part of this dark season spans from mid-November to the end of January ([PERSON], [PERSON], et al., 2015). In our study, we focused specifically on observations from December and January, intentionally excluding the final 2 weeks of November. This decision was based on the fact that certain data, such as radiance, are reported as monthly averages; including the slightly brighter early November period could have affected the accuracy of our observations. The dark season in Longyearbyen, as an industrial settlement with coal mines and a port, stands out as the most prominent area for light pollution in the Svalbard archipelago. Numerous structures contribute to the coastal light pollution, including street and building lighting, as well as the continuous activity of the harbor, marina, airport, and lights from vessels anchored at the roadstead. This study site, encompassing both urbanized areas and wild, natural regions devoid of human interference, serves as a laboratory for observing seabird responses to various light and environmental conditions.
### Seabirds data
Records of seabirds in Spitsbergen originate from the citizen science-based database [[https://www.artsobservasjoner.no/](https://www.artsobservasjoner.no/)]([https://www.artsobservasjoner.no/](https://www.artsobservasjoner.no/)). Species observations are developed and maintained by the Norwegian Biodiversity Information Centre on behalf of the Norwegian Ministry of Climate and Environment. We assume a high quality of the bird observation data used in our study. This is supported by the extensive dataset available, the limited number of observers, and the detailed information provided about the birds, including age and sex. Such detailed identification, particularly under the challenging conditions of the Arctic polar night, can only be achieved by individuals with considerable expertise in ornithology. Furthermore, each observation is attributed to a specific observer, allowing for verification. The dataset includes names of scientists affiliated with academic institutions and active naturalists. Some observations were also conducted as part of specific projects, which are noted in the database. Seabird data from the Longyearbyen area during the darkest period of the polar night--December and January from 2012 to 2022--were extracted. Each period, consisting of December at the end and January at the beginning of the following year, is later referred to in the manuscript as a \"polar night\". Only specific observations of birds, categorized as foraging or staging, were considered, while data on individuals found dead were excluded. Observations from individual days were aggregated into monthly observations for each species to compare them with the monthly mean radiance values for the study area derived from remote sensing data, as described below in the methodology section under \"Light Intensity.\"
## Environmental parameters
For each month considered, average air temperature data in the Longyearbyen area (Longyearbyen Camping with 1 m elevation) were downloaded from the Norwegian Meteorological Institute website yr.no.
Data on the presence of sea ice in Adventfjorden were obtained from daily ice charts provided by the Norwegian Meteorological Institute on cryo.met. The ice charts available from the Norwegian Ice Service are high-resolution products created using a range of satellite data sources, with a focus on Synthetic Aperture Radar (SAR) and optical imagery. These charts offer detailed information on sea ice concentration and identify areas of fast ice. In this study, each daily ice chart from a given month (December, January) was scanned and categorized as \"O\" for open water or \"1\" for sea ice of various origins in the fjord. The type/origin of sea ice and its surface area were not considered; only its presence was taken into account as a significant factor altering foraging conditions within the fjord, providing access to different types of prey, such as ice-associated fauna. The number of DSI was then counted and divided by the total number of days with available ice charts in that month, resulting in the DSI index.
## Light intensity
The intensity of nighttime light in Longyearbyen is measured in radiances (nW-cm\({}^{-2}\)-sr\({}^{-1}\)) recorded by the Visible Infrared Imaging Radiometer Suite (VIIRS) instrument aboard the Suomi National Polar-orbiting Partnership (SNPP) satellite ([PERSON] et al., 2012). Specifically, a NASA-provided SNPP product codenamed 'VNP46A3' was utilized (Table S1). This product offers monthly cloud-free composites of nighttime lights (NTL) derived from daily NTL observations, and it mitigates atmospheric and lunar interference on NTL through a dedicated Bidirectional Reflectance Distribution Function (BDRF) correction ([PERSON] et al., 2018). The spatial resolution of VNP46A3 data is 15 arc seconds, equivalent to approximately 190 \(\times\) 460 m at the geographic latitude of Longyearbyen (resampled by the data provider from the original VIIRS spatial resolution of 750 m/pixel).
In the study, only VNP46A3 observation classified with the highest reliability (quality flag set to 'good') were considered. These observations were collected under snow-free conditions using all possible VIIRS scanning angles (near-nadir and off-nadir observations), specifically from the 'All Angle Composite Snow Free' variable within the VNP46A3 data files. The 'All Angle Composite Snow Free' variable provides composite images of snow-free areas observed from various angles, since our study area encompasses coastal waters along the shoreline.
The study area in Longyearbyen was limited to the coastal zone extending from the piers in the port to the airport, as this area is where seabirds are most frequently observed and forage (Fig. 1). Satellite light intensity data were extracted for pixels with centers located within this coastal zone (Fig. 1). The average monthly radiance for the entire designated area outlined in yellow in Figure 1 was then calculated and assessed for each month (January and December) within the time frame from 2012 to 2022. This data was then used to analyze temporal variability by comparing it with the other environmental parameters and seabird data under investigation.
## Statistical analyses
Our study is based on monthly bird observations, which were compared with average monthly environmental parameters (artificial light intensity, DSI, and air temperature). We included data starting from December 2012, as this is when the first radiance data for the region became available. We only considered months for which data were available for all the studied parameters, excluding any months where data for even one parameter were missing. As a result, out of the 20 months of January and December occurring between December 2012 and January 2022, we included 15 months in our analysis for which we had a complete dataset.
### Seabird assemblage composition during polar night in port settlement
To assess differences in seabirds assemblage composition between polar nights, we employed multivariate nonparametric permutational anova (PERMANOVA) ([PERSON] et al., 2008). Species monthly percentages (15 months) were used as response variables, with polar night (comprising December and January of the subsequent year) as the fixed effect (a total of 9 polar nights). Before conducting the PERMANOVA analyses, the data were arcsine square root transformed, as recommended for multivariate studies of percentages and proportions ([PERSON] & [PERSON], 2011). Pseudo-\(F\) and \(P\) values were calculated based on 9999 permutations of the residuals under a reduced model ([PERSON] & [PERSON], 2003).
### Variation in environmental conditions during polar night
To evaluate differences in environmental conditions (air temperature, sea ice presence and artificial light intensity), we used a multivariate nonparametric permutational anova (PERMANOVA) ([PERSON] et al., 2008). Prior to conducting the PERMANOVA, the data were normalized. Pseudo-\(F\) and \(P\) values were calculated based on 9999 permutations of the residuals under a reduced model ([PERSON] & [PERSON], 2003).
### The effect of artificial light on seabird diversity
As there was no consistent methodology for conducting seabird observation, we chose not to work with raw bird counts from the database. Instead, we converted the observations into percentages of individual species and calculated the Shannon diversity index. This index is influenced by species richness (the total number of species) and the presence or absence of rare species, which we believe is the most reliable way to present these data.
To examine the relationships between the Shannon diversity index ([PERSON], 1948) and environmental variables--air temperature, sea ice presence, and light intensity (considered as explanatory variables)--we employed a distance-based linear model (DistLM) as described by [PERSON] et al. (2008). Initially, the Shannon diversity index was computed using Primer v7 and Permanova software. Before conducting the DistLM analyses, the environmental parameters underwent normalization. A forward-selection procedure was employed to identify the optimal combination of predictor variables that accounted for variations in the Shannon diversity index. This procedure adds one variable at a time to the model, selecting the variable that results in the greatest improvement in the model's selection criterion at each step. Selection criteria were based on \(R^{2}\) values ([PERSON] et al., 2008). Using \(R^{2}\) as the selection criterion allows us to assess the cumulative effect of incorporating successive environmental parameters into the model. This approach provides a comprehensive view of the overall explanatory power of the model, as measures how well the model explains the variance in the response variable. By evaluating the incremental improvement in with the addition of each environmental factor, we can understand the combined effects of multiple variables and their interactions on the outcome. This method helps in identifying the most informative set of predictors, balancing model complexity with explanatory power ([PERSON] et al., 2008).
Figure 1: Location of the seabird records in Longevarben (Adventfjorden) marked by yellow star. The study area in Longevarben along the shoreline, where the Nighttime Lights (NTL) monthly mean radiance was provided for each pixel is represented by yellow dots. Location of the meteorological station operated by the Norwegian Meteorological Institute, from which the air temperature data were obtained, is marked with a pink star. The data on sea ice presence pertain to the entire Adventfjorden area. Photo of Longevarben during the polar night: [PERSON]. Maps created in Ocean Data View (ODV) software v.5.7.2 ([PERSON], 2015). Satellite images source: [[https://geodata.npolar.no](https://geodata.npolar.no)]([https://geodata.npolar.no](https://geodata.npolar.no)).
Calculation of the Pseudo-\(F\) and \(P\) values relied on 9999 permutations of the residuals under a reduced model ([PERSON], 2003). To explore the strength and direction of the relationship between the Shannon diversity index and light intensity, we computed the Pearson correlation coefficient using R software version 4.1.3 (R Core Team, 2023). The linear relationship was depicted in a scatter plot using Primer v7 and Permanova software.
To assess the relationship between the contribution of specific seabird species in the local assemblage and environmental variables, correlation coefficient were calculated. Prior to analysis, the dataset was evaluated for normal distribution using the Shapiro-Wilk test in PAST version 4.03 ([PERSON] et al., 2001). Based on the results of the normality test, the Pearson correlation coefficient was computed for the Black Guillemot, while the Spearman correlation coefficient was used for all other species studied. Correlations were calculated and visualized using R software version 4.1.3 (R Core Team, 2023).
A Canonical Analysis of Principal Coordinates (CAP) was employed to depict the variability of seabird species composition between distinct polar nights along the two axes that best discriminated among the sample groups defined by the polar night. Pearson correlation vectors of environmental indices with axes were superimposed on the CAP plot. These vectors illustrate how each environmental parameter relates to the CAP axes. They indicate the extent to which different environmental variables influence the distribution of samples in the CAP space.
PERMANOVA, DistLM, and CAP analyses were carried out using Primer v7 and Permanova software ([PERSON] et al., 2008; [PERSON] & Warwick, 2001).
## Results
### Seabird assemblage composition during polar night in port settlement
In total, six seabird species were documented in Longyearbyen during the studied period: the Black Guillemot, Brunnich's Guillemot (_U. lornvia_), Little Auk (_A. alle_), Glaucous Gull (_Larus hyperboreus_), Black-legged Kittiwake (_Rissa tridactyla_), and Iceland Gull (_Larus glaucoides_). Seabird species composition exhibited significant differences between the considered polar nights from 2012 to 2022 (PERMANOVA, MS = 0.13, Pseudo-\(F\) = 6.64, \(P\) = 0.01). The Black Guillemot dominated each year, representing between 43 and 100% of the seabird assemblage (Fig. 2) Less abundant but consistently recorded species included the Little Auk and Brunnich's Guillemot, contributing a maximum of 23 and 33% to the seabird population, respectively. The remaining species, the Black-legged Kittiwake and Iceland Gull, accounted for less than 10% of the population and were observed only sporadically, while the Glaucous Gull was sighted only once over the 10-year period.
### Variation in environmental conditions during polar night
Environmental parameters studied (average air temperature, light intensity and DSI) exhibited significant differences between the considered polar nights from 2012 to 2022 (PERMANOVA, MS = 3.99, Pseudo-\(F\) = 2.39, \(P\) = 0.02). The mean values of air temperature and light intensity exhibited fluctuations (Fig. 2) and were significantly negatively correlated with each other (Pearson correlation, \(R=-0.65\), \(P=0.008\), Fig. 4). The lowest temperatures were recorded during the polar nights of 2016/2017 and 2019/2020, with values of \(-10.3\) and \(-13.4^{\circ}\)C, respectively (Fig. 2). In contrast, notable spikes in the average monthly radiance were observed during the polar nights of 2012/2013, 2016/2017, 2019/2020, and 2020/2021, with values of 26.4 nWatts \(\cdot\) (cm\({}^{2}\) sr)\({}^{-1}\), 16.3 nWatts \(\cdot\) (cm\({}^{2}\) sr)\({}^{-1}\), 23.5 nWatts \(\cdot\) (cm\({}^{2}\) sr)\({}^{-1}\), and 28.8 nWatts \(\cdot\) (cm\({}^{2}\) sr)\({}^{-1}\), respectively. The highest percentage of DSI was recorded during the polar nights of 2014/2015 and throughout the period from 2017 to 2021 (Fig. 2). However, this parameter was not significantly correlated with the other environmental conditions under study (Fig. 4).
### The effect of artificial light on seabird diversity
Among all the environmental parameters considered (light intensity, air temperature, and DSI), only light intensity had a significant impact on seabird species composition (DistLM, SS = 0.62, Pseudo-\(F\) = 3.86, \(P\) = 0.04) and on the Shannon diversity index (DistLM, SS = 0.61, Pseudo-\(F\) = 5.72, \(P\) = 0.03), explaining 23 and 30% of their total variability, respectively (Table 1).
In Longyearbyen during the polar nights from 2012/2013 to 2021/2022, seabird diversity decreased with rising light intensity (Pearson correlation, \(R=-0.55\), \(P\) = 0.03) (Fig. 3). When light intensity was low (\(<\)20 nWatts\(\cdot\)[cm\({}^{2}\) sr]\({}^{-1}\)), all seabird species were observed, whereas at higher levels (\(>\)30 nWatts \(\cdot\)[cm\({}^{2}\) sr]\({}^{-1}\)), only the Black Guillemot was present.
A significant, positive relationship has been identified between the relative abundance of the piscivorous Black Guillemot and light intensity during the polar nights from 2012 to 2022 ([PERSON]'s correlation coefficient, \(r\) = 0.52, \(P\) = 0.04), indicating an increased share in the assemblage with rising light intensity (Fig. 4). Conversely, an inverse relationship was observed for the zooplanktonkitvorous Little Auk (Spearman rank correlation coefficient, \(r_{\mathrm{s}}=-0.58\), \(P=0.02\)). Additionally, the contribution of the Little Auk to the assemblage significantly increased with rising air temperature (Spearman rank correlation coefficient, \(r_{\mathrm{s}}=0.61\), \(P=0.02\)) (Fig. 4).
Canonical Analysis of Principal Coordinates (CAP) analyses revealed a clear separation of polar nights, with the dominance of the Black Guillemot and a significant contribution of the Little Auk to the seabird assemblage under different environmental conditions studied (Avg, air temperature, 96 DSI and radiation, see Fig. 5).
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline & \multicolumn{2}{l}{Marginal test} & \multicolumn{6}{l}{Sequential test} \\ \cline{2-10} & Variable & Pseudo-\(F\) & \(P\) & \% Var & Variable & \(R^{2}\) & Pseudo-\(F\) & \(P\) & Cum\% \\ \hline Seabird community & Avg. air temp. & 2.62 & 0.10 & 0.17 & Light intensity & 0.24 & 4.00 & **0.04** & 0.24 \\ & Light intensity & 4.00 & **0.04** & 0.24 & + Avg. air temp. & 0.29 & 0.89 & 0.40 & 0.29 \\ & DSI & 0.57 & 0.53 & 0.04 & + DSI & 0.29 & 0.09 & 0.91 & 0.29 \\ Seabird diversity & Avg. air temp. & 1.86 & 0.19 & 0.12 & Light intensity & 0.32 & 5.94 & **0.02** & 0.31 \\ & Light intensity & 5.94 & **0.02** & 0.31 & + Avg. air temp. & 0.33 & 0.34 & 0.58 & 0.02 \\ & DSI & 0.07 & 0.82 & 0.01 & + DSI & 0.34 & 0.13 & 0.75 & 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the DistLM analysis for fitting environmental variables (average air temperature, light intensity and days with sea ice) to the seabird community (with bird abundances arcsin square root transformed) and seabird diversity (Shannon diversity index). %Var—percentage of explained variance; Cum%—cumulative percentage explained by the added variable. Bolded values are significant (\(P<0.05\)).
Figure 2: Seabird species qualitative and quantitative composition during the polar nights of 2012/2013 through 2021/2022 in Longyearbyen (upper panel). The color scale represents the mean percentage composition, while the numbers in the boxes represents the total number of individuals observed. Variability of environmental parameters (air temperature, light intensity (radiance), and sea ice presence (DS) during studied polar nights (bottom panel).
Figure 4: Correlation coefficient (Pearson or Spearman--see details in the text) of the relationship between the contribution of specific seabird species and environmental indices. Boxed values are significant (\(P<0.05\)).
Figure 3: The relationship between the Shannon diversity index for seabirds and light intensity (radiation) in Longyearbypen during the polar nights from 2012/2013 to 2021/2022. The colored markers on the plot represent individual months of the polar nights.
## Discussion
### Seabird responses to various light conditions
Light is considered the primary regulatory factor for most ecological interactions during the polar night ([PERSON] et al., 2016; [PERSON] et al., 2018). Even slight differences in light levels, barely perceptible to the human eye, can significantly impact the functioning of organisms and ecological processes. While the effects of light, both natural and artificial, on various groups of organisms, particularly zooplankton, during the polar night have been increasingly well-documented ([PERSON] et al., 2020), our understanding of its impact on seabirds remains limited. This gap in knowledge is particularly intriguing given that most seabirds traditionally migrate away from high latitudes during the Arctic winter, heading southward. However, recent observations indicate that many seabirds are present in these regions, even during the darkest period of the polar night. This phenomenon is especially interesting because the majority of seabird species are visual predators, for whom both the quantity and quality of light are critical factors during foraging ([PERSON] et al., 2021). To gain a better understanding of the presence of seabirds in the seemingly inhospitable conditions of the harsh polar night, we analyzed their occurrence over the past 10 polar nights using publicly available database. We then compared these observations with environmental conditions, including artificial light, derived from remote sensing data.
In illuminated area in Longyearbyen, seabird diversity clearly decreases with increasing levels of artificial light. The only species that appears to be most adapted to or capable of utilizing artificial light sources is the piscivorous Black Guillemot ([PERSON] et al., 2016). It has been previously observed approaching various sources of artificial light during the polar night and initiating foraging when the water was illuminated ([PERSON] et al., 2017). Our research also indicates that not all seabirds exhibit such adaptable behavior regarding artificial light. We found a negative relationship between the relative abundance of the zooplankton's Little Auk ([PERSON] et al., 2016), suggesting that these birds actively avoid artificial light. This findings aligns with recent observations indicating that Little Auk's exhibit light avoidance behavior during the polar night ([PERSON] et al., 2017). Similarly, experimental studies on Cory's Shearwater chicks exposed to various artificial light stimuli have confirmed that ontogenetic exposure to light significantly influences seabird vulnerability to light pollution ([PERSON] et al., 2023). In contrast, studies on Northern Fulmars in the North-East Atlantic and Barents Sea reveal a different pattern. Fulmars frequently encounter fisheries at night during the non-breeding season, with encounter rates increasing in areas of intense fishing activity ([PERSON] et al., 2021). During these periods, fulmars demonstrate increased foraging activity and reduced resting, highlighting a more opportunistic response to artificial light. Furthermore, research on Little Penguins (_Eudyptula minor_) from South Australia shows that artificial lights from coastal developments can substantially alter penguin behavior ([PERSON] and [PERSON], 2024). However, these effects are context-dependent and vary according to the specific environmental and situational factors involved. Collectively, these observations and our findings under-score the considerable variability in seabird responses to artificial light. Birds' use of light sources is influenced not only by the availability of preferred prey but also by the specific location and context of the light exposure. This variability highlights the necessity for tailored, case-by-case assessments to effectively evaluate and mitigate the impacts of artificial light on different seabird species.
### Potential influence of diet on various seabird reactions
Considering that the efficiency of foraging in visual predators is heavily influenced by light levels (Jetz
Figure 5: Canonical Analysis of Principal Coordinates (CAP) ordinations show the groups of samples providing the best discrimination based on Bray-Curtis similarities of the percentage of seabird species after arcin square root transformation. Each bubble represents a particular polar night. Vectors indicate the Pearson correlation of environmental indices with the ordination coordinates, with vector length corresponding to the correlation value. The size of the bubble slices represents the percentages of Black Guillemot and Little Auk in the seabird assemblage (species whose contributions correlated significantly with environmental parameters—light intensity and/or temperature, see Fig. 4).
et al., 2003), the question arises: what enables seabirds to forage in conditions of limited light? Among potential explanations are a shift to different prey types, utilization of nocturnal light sources (moonlight, starlight; [PERSON] et al., 2001; [PERSON] et al., 2011), or reliance on bioluminescence ([PERSON], 1975) for foraging. Avian reliance on the vertical migration of prey and bioluminescence is assumed to operate under natural ambient light conditions. The heightened activity of zooplankton during periods of extremely low light intensifies the importance of natural light sources such as the moon, stars, and aurora borealis, which likely guide their behavior, including diel vertical migrations (DVM), persisting throughout the Arctic winter ([PERSON] et al., 2009; [PERSON] et al., 2018). However, issues arise when ambient light is disrupted by artificial sources.
Considering the proven role of ambient illumination as crucial cue for zooplankton, it is unsurprising that artificial light, as potent stimulus, can significantly disrupt many processes, including DVM ([PERSON] et al., 2020; [PERSON] et al., 2018). The extremely rapid light-escape reaction of zooplankton (within only 5 s) to the appearance of an artificial light source, such as normal working light from a ship, and its wide-ranging impact (extending even up to 200 m deep and across an area of \(>\)0.125 km\({}^{2}\) around the ship) demonstrate the severity of the problem ([PERSON] et al., 2020; [PERSON] et al., 2018). As a particularly potent stimulus, artificial light can have various effects on organisms with differing sensitivities to light, resulting in contrasting responses among different taxa ([PERSON] et al., 2020). While it may attract some organisms (e.g., the krill _Thyannessal_ spp.), it may deter others (e.g., northern shrimp _Pandalus borealis_; [PERSON] et al., 2020). However, for the vast majority of the zooplankton community during the polar night, artificial light is likely to trigger a strong light-escape response ([PERSON] et al., 2018).
When considering the role of diet in the occurrence of seabirds during the polar night, it is important to acknowledge the significant gaps in our understanding of their actual dietary composition during the Arctic winter. While there is extensive and detailed information about seabird diets during the Arctic summer, these diets can differ substantially during winter, not only due to variations in the availability of specific zooplankton or fish species but also because of the birds' differing nutritional needs ([PERSON] et al., 2010). In summer, during the breeding season, seabirds focus on providing optimal food for their offspring, which involves considerable energy expenditure ([PERSON] et al., 2014). For example, in Little Auls, the energy costs of foraging flights during the summer are considered among the highest of all birds ([PERSON] et al., 1991; [PERSON] et al., 1993). Moreover, the diet of Little Auls can vary even within the same summer period, depending on whether the food is intended for chicks or for self-maintenance ([PERSON] et al., 2020). This suggests that seabird diets during winter could differ dramatically from those in summer.
Some studies on the dietary composition of seabirds in this region during the Arctic polar night shed light on this issue. Observations of the contents of birds' stomachs during the darkest period of the polar night in Kongsforden revealed that krill was one of the most abundant food items ([PERSON], [PERSON], et al., 2015), showing a positive response to artificial light ([PERSON] et al., 2020). While krill has also been found to be a part of the Little Auls's diet during the polar night ([PERSON], [PERSON], et al., 2015) or winter ([PERSON] et al., 2013), this bird is known for its high selectivity towards _Calanus_ copepods during summer ([PERSON] et al., 2023; [PERSON] et al., 2018). Although _Calanus_ _fimranchicus_ has been observed forming surface aggregations during the polar night, Arctic copepods generally avoid ALAN ([PERSON] et al., 2018), which may significantly limit their availability. Therefore, the absence of Little Auls observed in our study under higher artificial light conditions might suggest that their dietary flexibility is insufficient to survive in a light-polluted environment during the polar night. However, this issue may be more complex, given the aforementioned limitations in our knowledge of seabird diets during the polar night and their energy requirements during this period.
## Limitations of the study
We acknowledge the limitations of our study and recognize that certain factors may have influenced our findings. In our research, among all the parameters investigated, light emerged as the most influential factor in regulating the diversity and occurrence of individual bird species. However, we must also consider the influence of other factors on the occurrence of seabirds during the polar night. We anticipated that the presence of sea ice, along with the associated fauna that serves as a food source for seabirds ([PERSON] et al., 2017; [PERSON] et al., 1999), would be a significant factor affecting their diversity. The lack of a significant correlation between the number of DSI and seabird assemblage may be attributed to limitations of satellite data of sea ice presence for this region, often affected by cloudiness ([PERSON] et al., 2014; [PERSON] et al., 2017; [PERSON] et al., 2020). On the other hand, we hypothesize that if the presence of sea ice exerted a notable impact on seabird assemblages, it would be evident in the correlation between seabird diversity and air temperature. This is because air temperature is closely associated with the presence of sea ice and serves as a crucial indicator for predicting fast ice extent in the Svalbard region ([PERSON] and [PERSON], 2022). However, this correlation was also insignificant for seabird diversity and was found to be significant only for the Little Auk. In turn we found statistically significant correlation between average air temperature and radiance (as confirmed by the Pearson correlation test) when analyzing species separately, but only the Little Auk was affected by both parameters. What is more the DistLM analysis which considered all environmental parameters individually and accounted for relations between them showed that only light intensity had a significant impact on the variation in species composition and diversity. All this leads us to conclude that light had potentially the most substantial influence on seabird presence in the study area during studied period.
Our inference could also have been influenced by the characteristics of observations from citizen science, which are associated with certain limitations, such as the lack of a consistent methodology for conducting observations (differing numbers of days and locations in a given month). Furthermore, we do not know the life histories of the individuals spending winter in Adventfjorden. Wintering areas of Little Auks (documented based on geolocator loggers data) are situated further south or east according to SEATRACK dataset ([[https://seapop.no/en/seatrack/](https://seapop.no/en/seatrack/)]([https://seapop.no/en/seatrack/](https://seapop.no/en/seatrack/)); [PERSON] et al., 2019). On the other hand, Birdlife International ([[https://datazone.birdlife.org/species/factsheet/](https://datazone.birdlife.org/species/factsheet/)]([https://datazone.birdlife.org/species/factsheet/](https://datazone.birdlife.org/species/factsheet/))) reports the presence of wintering grounds for the Little Auk in Isfjorden and for the Black Guillemot, located further south, in Bellsund. Thus, based on current knowledge, we cannot conclude if observed individuals represent a group of individuals in suboptimal condition and/or health status or if these individuals constantly visiting wintering grounds there.
Moreover, our study is based on monthly averaged observations, and while higher-resolution environmental measurements combined with simultaneous bird monitoring would yield more precise results, this limitation is inherent to research utilizing historical data. Despite these methodological constraints, such data provide a crucial foundation for future, more detailed studies and ongoing monitoring of this phenomenon in the region. Although not without imperfections, these historical datasets offer valuable insights that can inform and refine future research with greater accuracy and resolution. Despite some limitations, we consider this citizen science data to be particularly valuable, as it encompasses a decade of observations during the poorly studied polar night period. Conducting scientific research over such an extended timeframe would pose significant logistical and financial challenges, highlighting the importance of these long
Figure 6: This visualization illustrates the observed trend in the conducted research: seabird diversity decreases with increasing artificial light intensity in high-Arctic port settlement exposed to artificial light during polar night.
term, community-driven efforts combined with remote sensing.
## Conclusions
Given that seabirds navigate across marine, aerial, and terrestrial environments and are among the most globally threatened bird groups, they are particularly vulnerable to pollutants such as artificial light. The expansion of light-polluted coastal areas, especially in the increasingly ice-free Arctic, exacerbates this issue. By integrating remote sensing and citizen science data, our study offers pioneering insights into the effects of light pollution on seabirds in the Arctic polar night, highlighting an urgent need for further research and mitigation strategies. Various reactions of birds to light, encompassing both attraction and avoidance, underscore its potency as a stimulant capable of altering their feeding and behavioral patterns. While it can create favorable conditions by attracting prey, it also poses a significant threat, leading to collisions with illuminated structures or causing disorientation. We have demonstrated that the Black Guillemot appear to be tolerant to higher artificial light levels, whereas the Little Auk shows a decline in numbers as light intensity increases, suggesting a negative impact. The variation in species-specific responses points to the role of dietary preferences and overall flexibility in shaping their light-related behavior, an area that warrants further investigation. Despite these differences, ALAN is broadly recognized as a significant threat to seabird populations worldwide. This study provides the first comprehensive assessment of ALAN's impact on seabird communities during the Arctic polar night, revealing a general negative trend that reduces seabird diversity (Fig. 6).
## Acknowledgements
KB was financed by the Polish National Science Centre project (no. 2021/41/B/N28/03830). We would like to thank [PERSON] for providing the seabird photos, which were graphically processed and used in the figures. We also want to thank all birdwatchers participating in citizen science and providing the data used in this study.
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## Supporting Information
Additional supporting information may be found online in the Supporting Information section at the end of the article. | wiley | Illuminating the Arctic: Unveiling seabird responses to artificial light during polar darkness through citizen science and remote sensing | Kaja Balazy, Dariusz Jakubas, Andrzej Kotarba, Katarzyna Wojczulanis‐Jakubas | https://doi.org/10.1002/rse2.425 | 2,024 | CC-BY |
wiley/ffb975e5_3075_47f7_8fad_c899fab33107.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly.
radiative forcing and result in a weakening of the zonal SST gradient due to erroneous SST warming in the east ([PERSON] et al., 2019).
Apart from the local biases within the tropical Pacific, remote biases outside of the tropical Pacific could also affect the projections of the TPSW pattern via strong trans-basian climate interactions ([PERSON] et al., 2019; [PERSON] et al., 2021), yet they are not as well studied as have been the local biases. Of particular importance is the common cold SST bias in the tropical North Atlantic (TNA), which is comparable in the magnitude to the CT bias (Figure 1a). Previous studies have revealed that there are robust inter-basian interactions between the TNA and the tropical Pacific on decadal and longer time scales ([PERSON] and [PERSON], 2018; [PERSON] et al., 2010). As such, the TNA cold SST bias has been found to be partly responsible for the biases within the tropical Pacific, such as the underestimated Pacific trade wind trends in recent decades ([PERSON] et al., 2018; [PERSON] et al., 2018), the warm SST bias in the southeastern Pacific (SEP) ([PERSON] et al., 2014; [PERSON] et al., 2014) and the double inter-tropical convergence zone problem ([PERSON] and [PERSON], 2017). However, the effect of the TNA cold SST bias on projecting the TPSW pattern as well as the associated mechanism remains unclear.
In this study, we focus on the influence of the common TNA cold SST bias on CMIP6 projections of the TPSW pattern. A significant linkage is found between the simulated present-day TNA SSTs and the projected TPSW patterns across models, which allows the observed TNA SST to provide a useful constraint on the projected TPSW pattern. The rest of the paper is organized as follows. Section 2 briefly describes the data and methods. Section 3 presents the process-based analyses. Conclusions and discussion are in Section 4.
## 2 Data and Methods
### Data Sets
Monthly outputs from 30 CMIP6 models are used in this study ([PERSON] et al., 2016), and four observational SSTs are chosen to compare with the modeled ones. Details about the models and variables are available in Text S1 and Table S1 in Supporting Information S1. We average the four observational SST data sets as the observed SST. All the model data and observations are first interpolated into a common \(2.5^{\circ}\times 2.5^{\circ}\) grid before analyses.
### Definitions
The long-term mean of 1961-2000 in historical runs is chosen as the present-day climate, and that of 2061-2100 in SSP585 runs which with the strongest external forcing effect in this century, is chosen as the future climate. The main conclusions do not change if a different time period, say, 1995-2014 (2081-2100) in historical (SSP585) runs, is chosen. For each model, the change under global warming is defined as the difference between the future and the present-day climate, which is further normalized by the respective SST warming averaged from 60\({}^{\circ}\)S to 60\({}^{\circ}\)N to remove the effect of differences in the global-mean SST warming in response to the increasing GHGs. The TPSW pattern is defined by the SST change in the tropical Pacific region (\(30^{\circ}\)S-\(30^{\circ}\)N,\(120^{\circ}\)E\(-80^{\circ}\)W), and the present-day TNA SST is defined by averaging the region (\(0^{\circ}\)-\(25^{\circ}\)N, \(80^{\circ}\)W-\(30^{\circ}\)W) where there are common cold SST biases (Figure 1a). The zonal SST gradient in the tropical Pacific is defined as the difference between the WEP (\(5^{\circ}\)S-\(5^{\circ}\)N, \(120^{\circ}\)-\(160^{\circ}\)E) and the EEP (\(5^{\circ}\)S-\(5^{\circ}\)N, \(120^{\circ}\)-\(5^{\circ}\)N, \(30^{\circ}\)W), so that a negative change in the zonal SST gradient represents a weakening of the zonal gradient.
The surface downward shortwave cloud radiation (\(\Delta\)SW\({}_{\rm cloud}\)) is represented by the difference in the surface downward shortwave radiation between the all-sky and the clear-sky ([PERSON] et al., 2020). Then a cloud-shortwave-SST feedback index (CSFI) is defined by regressing the monthly \(\Delta\)SW\({}_{\rm cloud}\) anomalies onto the SST anomalies in historical period (1961-2000) to quantify the modeled cloud-shortwave-SST feedback. The monthly anomalies are obtained by first removing the annual cycle of the chosen period and then detrending the data. The estimation of cloud radiation-related feedback based on historically monthly anomalies has been widely used when studying their roles in long-term climate change ([PERSON] et al., 2017; [PERSON] et al., 2021; [PERSON] et al., 2015).
### Spatial Emergent Constraint
The emergent constraints (EC) approach aims to find a statistically relationship between the simulated present-day climate and the projected change across models, and then uses the observed present-day climatology to constrain the projected results so as to improve the model projections ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2019). In contrast to the traditional EC that constrains the projected one-dimensional variable changes such Figure 1: The MME biases of sea surface temperature (SST) (a) and velocity potential (VP) as well as divergent winds at 200 hPa (b). Contours in (a) and (b) denote the observed SST with the tropical-mean SST removed (with an interval of 1 K; zero contour thickened and negative dashed) and the observed VP at 200 hPa (with an interval of \(1\times 10^{6}\) m\({}^{2}\) s\({}^{-1}\)). The black and purple boxes in (a) and (b) denote the tropical North Atlantic (TNA) and SEP (\(15^{\circ}\)-\(2.5^{\circ}\)S, \(110^{\circ}\)-\(80^{\circ}\)W). Panels (c) and (d), the inter-model standard deviation of the tropical Pacific SST warming (TPSW) pattern (c) and the inter-model regression of the TPSW pattern and the horizontal wind at 1,000 hPa onto the present-day TNA SST (d), Contours in (c) and (d) are the MME TPSW patterns. (e) Scatter plot between the TNA SST and the zonal SST gradient change, with the inter-model correlation shown in the upper-right corner. The yellow shading is the range of the observed TNA SST from four observations and the orange line is their averaged result. Stippling in (a) and (b) denotes that more than 70% of the models have the same sign, whereas in (d) denotes that the regressions are significant at the 95% confidence level, based on the Student’s \(t\) test.
as the equilibrium climate sensitivity or snow albedo feedback ([PERSON] et al., 2018; [PERSON] & [PERSON], 2006), here we perform a spatial EC by constructing an inter-model relationship between the present-day TNA SSTs and the projected TPSW patterns, thus the observed TNA SST can be used as a constraint to calibrate the SST change spatially (Text S2 in Supporting Information S1).
## 3 Results
### Connecting the Simulated Present-Day TNA SST With the Projected TPSW Pattern
All the chosen models except for four suffer from a cold TNA SST bias with prominent differences in magnitude (Figure S1a in Supporting Information S1), leading to a common cold bias that covers the Western Hemisphere warm pool region (Figure 1a) where the local SSTs are always above the tropical-mean value ([PERSON] & [PERSON], 2001) and thus any local small biases can have a large impact on the convective activities locally ([PERSON] & [PERSON], 2010) and beyond through tropical trans-basin atmospheric circulations ([PERSON] et al., 2019; [PERSON] et al., 2010). The cold SST bias acts to suppress local deep convection, which induces an anomalous positive velocity potential (VP) center in the local upper troposphere including the region where there is a slight negative climatological VP center over the Caribbean and Central America (Figure 1b). Meanwhile, an anomalous negative VP center is present in the upper troposphere in the southeast Pacific, with parts of the anomalous divergent winds at upper-level 200 hPa flowing trans-basinity from the southeastern Pacific to the TNA (Figure 1b, vectors). Thus, the simulations of the TNA SST and those of the eastern Pacific climate are connected by the regional Hadley-type circulation with an anomalous sinking branch over the TNA and an anomalous rising branch over the SEP ([PERSON] et al., 2014; [PERSON] et al., 2014).
On the other hand, almost all models project an El Nino-like SST warming pattern with weakened zonal SST gradient (Figures S1b and S2 in Supporting Information S1), yet the magnitudes of the SST warming vary among models. The largest inter-model standard deviation (STD) of the equatorial SST warming is located in the EEP where there is the strongest multi-model ensemble mean (MME) SST warming along the equator (Figure 1c, shaded). The inter-model STD in the EEP SST warming exceeds 50% of the local MME SST warming, implying large inter-model uncertainties in the projected zonal SST gradient change.
The inter-model regression pattern of the TPSW onto the present-day TNA SST reveals a positive relationship between the two, with higher present-day TNA SSTs tending to have more SST warming in the central to EEP as well as stronger equatorial surface westerly wind anomalies (Figures 1c and 1d), leading to a significant negative correlation (\(-0.66\)) between the simulated TNA SST and the zonal SST gradient change across models (Figure 1e). The SST warming most strongly related to the simulated present-day TNA SST lies in the EEP where there is the largest inter-model STD of SST warming along the equatorial Pacific (Figure 1d), implying a potential important role of the TNA SST in modulating the diversified magnitudes of the TPSW pattern.
### Mechanism of the Impact of the TNA Cold SST Bias
As previous studies have revealed a significant relationship between the simulation of the TNA SST and that of the SEP SST in CMIP5 models--models with a higher TNA SST tend to have a lower SEP SST and vice versa ([PERSON] et al., 2014; [PERSON] et al., 2014), we consider whether the effect of simulated present-day TNA SST on the projected TPSW pattern could be reached by first altering the simulated SST in the SEP. It appears that the simulated TNA SSTs do not show a significant negative correlation to the simulated SEP SST among models (Figure S3 in Supporting Information S1) as the result based on CMIP5 models ([PERSON] et al., 2014; [PERSON] et al., 2014). Meanwhile, the simulated present-day SEP SSTs are not significantly correlated to the projected TPSW patterns among models (Figure S4 in Supporting Information S1), implying that the simulated present-day SST in the SEP is not an alternative to that in the TNA in affecting the projected TPSW patterns.
The impact of simulated present-day TNA SST on the projected TPSW pattern can be achieved by modulating the present-day atmospheric conditions over the tropical Pacific. As shown in Figure 2a, models with a higher TNA SST tend to produce a stronger upper-level divergence over the Caribbean and Central America where there is an observational divergent center, and an associated stronger convergence in the upper troposphere of the EEP and south, indicating a trans-basin connection through the regional Hadley-type circulation ([PERSON] et al., 2010, 2014). The stronger upper-level convergence over the EEP contributes to a stronger local subsidence (Figure 2b), which helps to make the marine boundary layer more stable. To confirm, we measure the low-level tropospheric stability by the estimated inversion strength (EIS), defined as the difference in the potential temperature between 700 hPa and the surface at 1,000 hPa ([PERSON], 2021; [PERSON], 1993). The result finds that models with a higher TNA SST correspond to a stronger EIS over the EEP (Figure 2c). The stronger atmospheric stability over the EEP further favors greater local low-level cloud cover (LCC). Indeed, models with a higher TNA SST tend to have more cloud cover over the EEP that is confined below to 700 hPa (Figure 2d, shaded). We further use the modeled \(cl\) variable to approximate the LCC as the maximum of cloud cover between the 1,000 and 680 hPa ([PERSON], 2014; [PERSON] et al., 2015):
\[\mathrm{LCC_{cl}}=\mathrm{max}\ (\mathrm{cl_{680-1000}}) \tag{1}\]
where the subscript \"cl\" denotes that the LCC is obtained from the \(cl\) variable. A significant positive correlation emerges between the TNA SST and the \(\mathrm{LCC_{cl}}\) over the EEP across models, with the correlation reaching up to 0.57 (Figure S5a in Supporting Information S1). Accordingly, the common TNA cold SST bias is associated with anomalous downward motions over the Caribbean and Central America and anomalous upward motions over the EEP (Figure S6a in Supporting Information S1), the bias of weak EIS over the EEP (Figure S6b in Supporting Information S1), and the bias of too few LCC over the EEP and south (Figure S6c in Supporting Information S1), suggesting a causal chain of the TNA cold SST bias on the simulated climate in the EEP.
Given the dominant role of the LCC in the total cloud cover (Figure 2d, contours), the simulations of the LCC over the EEP can further impact the behavior of the local cloud-shortwave-SST feedback. As the simulated CSFs over the EEP are diverse across models with both positive and negative values (Figure S7 in Supporting Information S1) and the MME one is very small (Figure 3a), models with more \(\mathrm{LCC_{cl}}\) over the EEP tend to have local positive cloud-shortwave-SST feedback and vice versa (Figure S5b in Supporting Information S1). Thus, the simulations of the TNA SST can impact cloud-shortwave-SST feedbacks over the EEP by affecting the
Figure 2.— The inter-model regression patterns of the velocity potential (VP) and divergent winds at 200 hPa (a), the equatorial (5\({}^{\circ}\)S–5\({}^{\circ}\)N) vertical pressure velocity (b), the estimated inversion strength (EIS) (c), and the equatorial \(cl\) (d) onto the tropical North Atlantic sea surface temperature. Contours in (a)–(d) are the MME VP (with an interval of \(1\times 10^{6}\) m\({}^{2}\) s\({}^{-1}\)), vertical pressure velocity (with an interval of 0.5 hPa s\({}^{-1}\)), EIS (K), and \(cl\) (%), respectively. Stippling denotes that the regressions are significant at the 95% confidence level, based on the student’s \(t\) test.
simulation of the local LCC\({}_{\rm cl}\), with higher TNA SSTs favoring positive cloud-shortwave-SST feedbacks over the EEP (Figure 3b).
The different regimes of cloud-shortwave-SST feedback have been suggested to be influential on the future SST change, with positive (negative) feedbacks favoring (suppressing) the local SST warming by absorbing more (less) incoming shortwave radiation ([PERSON] et al., 2016). The changes in \(\Delta\)SW\({}_{\rm cloud}\) measured by TPSW \(\times\) CSFI are found to be significantly correlated to the SST warming in the EEP, with larger TPSW \(\times\) CSFI in the EEP producing more local SST warming (Figure 3c).
For each model, the TPSW \(\times\) CSFI includes both the effect of cloud-shortwave-SST feedback acting on the SST warming and the SST warming in turn feeding back to the changes in \(\Delta\)SW\({}_{\rm cloud}\) by producing convections. Thus, we further separate them by linearizing the TPSW \(\times\) CSFI as follows:
Figure 3.— The spatial distribution of the MME CSFI (a) and the inter-model regression pattern of CSFI onto the tropical North Atlantic sea surface temperature (SST) (b). Contours in (b) denote the MME CSFI (with an interval of 4 W m\({}^{-2}\) K\({}^{-1}\)). Slipping in (a) denotes that more than 70% of models have the same sign, while that in (b) indicates that the regressions are significant at the 95% confidence level, based on the students’ \(t\)-test. (c)–(e) Inter-model scatterplots between the SST warming in the eastern equatorial Pacific (EEP) and (c) the TPSW \(\times\) CSFI, (d) the TPSW\({}_{\rm Mt}\)\(\times\) CSFI\({}^{\prime}\), and (e) the TPSW\({}^{\prime}\)\(\times\) CSFI\({}_{\rm Mt}\) averaged over the EEP, with the inter-model correlation shown in the upper-right corner of each plot. The black lines denote the linear regression.
\[\text{TPSW}\times\text{CSFI}=\text{TPSW}_{\text{M}}\times\text{CSFI}_{\text{M}}+ \text{TPSW}_{\text{M}}\times\text{CSFI}^{\prime}+\text{TPSW}^{\prime}\times \text{CSFI}_{\text{M}}+\text{TPSW}^{\prime}\times\text{CSFI}^{\prime}, \tag{2}\]
where the subscript \"M\" denotes the MME result and the prime denotes the deviation from the MME. The terms \(\text{TPSW}_{\text{M}}\times\text{CSFI}_{\text{M}}\), \(\text{TPSW}_{\text{M}}\times\text{CSFI}^{\prime}\), \(\text{TPSW}^{\prime}\times\text{CSFI}_{\text{M}}\), and \(\text{TPSW}^{\prime}\times\text{CSFI}^{\prime}\) represent the MME result of TPSW \(\times\) CSFI, the effect of difference in CSFI acting on the MME TPSW, the effect of difference in TPSW modulated by the MME CSFI, and the nonlinear term, respectively. The linearized results find a dominant role of \(\text{TPSW}_{\text{M}}\times\text{CSFI}^{\prime}\) in affecting the different EEP SST warming in the TPSW \(\times\) CSFI, with more \(\text{TPSW}_{\text{M}}\times\text{CSFI}^{\prime}\) in the EEP tending to have local more SST warming (Figure 3d), while the effects of \(\text{TPSW}^{\prime}\times\text{CSFI}_{\text{M}}\) (Figure 3e) and \(\text{TPSW}^{\prime}\times\text{CSFI}^{\prime}\) (not shown) are both secondary and small enough to be neglected. Thus, it is the differences in the cloud-shortwave-SST feedback over the EEP induced by different TNA SSTs that contribute to differences in the EEP SST warming. When the EEP SST warming difference emerges, it can further spread to the west through the already triggered ocean-atmosphere coupled Bjerknes feedback reflected in the MME El Nifo-like warming pattern to form the final warming pattern differences (Figures 1c and 1d).
### Spatial EC on the Projected TPSW Pattern
The significant relationship between the simulated present-day TNA SSTs and the projected TPSW patterns allows EC on the projections of the TPSW pattern (Text S1 in Supporting Information S1). When constrained by the observed TNA SSTs, the TPSW displays a more El Nifo-like warming pattern with enhanced SST warming especially in the EEP in most models as well as in the MME (Figures 4a and 4c; Figure S8 in Supporting Information S1). Meanwhile, there is also a reduction of the inter-model uncertainty in the corrected TPSW patterns (Figures 4b and 4d), with the largest reduction being more than 20% in the EEP (Figure 4d, contours). As a result, all the projected TPSW present a weakened zonal SST gradient after the correction (Figure S9 in Supporting Information S1). The weakening of the zonal SST gradient shown in the MME result is strengthened from the original \(-0.24\) to \(-0.34\), together with the inter-model STD decreased from \(0.13\) K K\({}^{-1}\) to \(0.1\) K K\({}^{1}\) (Figure 4e), indicating a better inter-model consensus.
The corrected TPSW patterns could be different when constrained by different observational TNA SSTs, thus observational uncertainty is accounted for by using four different observed SSTs. Given that the TNA SSTs range from \(26.5\) to \(26.7^{\circ}\)C in the four observational data sets (Figure 1e), the corresponding corrected MME zonal SST gradient changes range from \(-0.33\) to \(-0.35\) (Figure S10 in Supporting Information S1). Such a range is much smaller than that between the original and the corrected zonal SST gradient change by the mean observations (Figure 1e), implying that the corrected result of a more weakened zonal SST gradient is insensitive to different observations.
## 4 Conclusions and Discussion
Reliable projections of the future TPSW pattern by climate models are often hampered by the common biases in simulating the current climate. Here we focus on the role of common TNA cold SST bias and find that models with a higher present-day TNA SST tend to have more SST warming in the central to eastern Pacific under GHG forcing. Inter-model analyses reveal that the TNA cold SST bias acts to reduce the LCC over the EEP by suppressing the regional Hadley-type circulation, which weakens the local positive cloud-shortwave-SST feedbacks. An emergent constraint using the observed TNA SST yields a more El Nifo-like SST warming with more weakened zonal SST gradient compared with the original ones, together with a reduction of the inter-model uncertainty in the projected zonal SST gradient change by more than 20%. The constrained result is in sync with the recent point of view, which indicates that the mechanisms favoring an El Nifo-like warming pattern may dominate in the future ([PERSON] et al., 2024).
However, whether the future \"_real_\" TPSW pattern will be El Nifo-like or not may be still debatable. This is because, on the one hand, the simulated TNA SST explains only about 40% of the inter-model spread in the zonal SST gradient change (Figure 1e). Other simulated present-day SSTs with specific common biases may have different effects ([PERSON] et al., 2021). Revealing the joint effect of multiple common biases would be another step to have a more reliable projection of the TPSW pattern. In particular, given that there reveals a significant inter-model relationship between the TNA SSTs and the CT SSTs (Figure S11 in Supporting Information S1), and that between the CT SST and the projected TPSW patterns and the zonal SST gradient changes (Figure S12 in Supporting Information S1), it is potential that the well-known common excessive CT bias has an effect on the projected TPSW pattern by impacting the TNA cold SST bias, which deserves further study. On the other hand, as our constrained result of a more El Nino-like pattern takes the model projections further away from the observed strengthened zonal SST gradient ([PERSON] et al., 2022), we may not rule out that the model projections as a whole may be biased too El Nino-like owing to some deficient physical processes. Nevertheless, our result gives a process-based explanation of the effect of the TNA SST bias on the projected TPSW pattern, as well as a way to reduce the uncertainty in the projected TPSW pattern.
### Data Availability Statement
The CMIP6 model monthly outputs are archived at the Earth System Grid Federation server ([[https://esgf-node.llnl.gov/search/cmip6/](https://esgf-node.llnl.gov/search/cmip6/)]([https://esgf-node.llnl.gov/search/cmip6/](https://esgf-node.llnl.gov/search/cmip6/))). The HadISSTv1 data set can be obtained from [[https://www.metoffice.gov.uk/hadobs/](https://www.metoffice.gov.uk/hadobs/)]([https://www.metoffice.gov.uk/hadobs/](https://www.metoffice.gov.uk/hadobs/)). The ERSSTv5, COBE and COBE2 SST data sets are all available from [[https://www.esrl.noaa.gov/psd/data/gridded/](https://www.esrl.noaa.gov/psd/data/gridded/)]([https://www.esrl.noaa.gov/psd/data/gridded/](https://www.esrl.noaa.gov/psd/data/gridded/)). The ERA5 data set can be obtained from [[https://www.ecmwf.int/en/forecasts/dataset/ecmwf-](https://www.ecmwf.int/en/forecasts/dataset/ecmwf-)]([https://www.ecmwf.int/en/forecasts/dataset/ecmwf-](https://www.ecmwf.int/en/forecasts/dataset/ecmwf-))
Figure 4: The original MME tropical Pacific SST warming pattern (a) and the associated inter-model STDs (b). Panels (c)–(d), the same as (a)–(b), but for the corrected ones. Contours in (d) are the percentage changes of the inter-model STDs relative to the original one (with an interiod of \(5\%\), negative dashed). (e), the probability distribution function of uncorrected (light blue) and corrected (orange) zonal sea surface temperature gradient changes. Dots indicate the MME results, while the horizontal lines denote the one inter-model standard deviation. The blue and green boxes in (a)–(d) denote the western equatorial Pacific and eastern equatorial Pacific regions, respectively.
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* [PERSON] et al. (2003) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2003). Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. _Journal of Geophysical Research_, 108(D14), 4407. [[https://doi.org/10.1029/2002j.4002570](https://doi.org/10.1029/2002j.4002570)]([https://doi.org/10.1029/2002j.4002570](https://doi.org/10.1029/2002j.4002570)) | wiley | Constraints on the Projected Tropical Pacific Sea Surface Temperature Warming Pattern by the Tropical North Atlantic Cold SST Bias in CMIP6 Models | Jun Ying, Matthew Collins, Robin Chadwick, Jian Ma, Tao Lian | https://doi.org/10.1029/2024gl111233 | 2,024 | CC-BY |
wiley/ff9c0e3f_cc49_454c_b255_53e4c69833ec.md | # Earth and Space Science
Research Article
10.1029/2023 EA002909
Reonstructing and Nowcasting the Rainfall Field by a CML Network
[PERSON]
1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China, High Impact Weather Key Laboratory of CMA, Changsha, China, 1 River Management Division, Jiangyin, China 1
[PERSON]
1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China, High Impact Weather Key Laboratory of CMA, Changsha, China, 1 River Management Division, Jiangyin, China 1
[PERSON]
1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China, High Impact Weather Key Laboratory of CMA, Changsha, China, 1 River Management Division, Jiangyin, China 1
###### Abstract
Currently, the opportunistic method to estimate rainfall using commercial microwave links (CMLs) has been shown as an efficient way to complement traditional instruments in terms of spatial-temporal resolution and coverage. In this paper, we collected data from 26 CMLs in Jiangyin City, Jiangsu Province, and conducted experiments on rainfall field reconstruction and nowcasting. First, the raw CML data were processed to invert the path-averaged rainfall intensity. Second, the algorithms of inverse distance weighting (IDW) and ordinary kriging (OK) interpolation were employed to reconstruct the rainfall field. Then a 10-min prediction of the rainfall field was achieved using a nowcasting model based on the long short-term memory neural network and a setup window was introduced to improve the prediction performance of the first few minutes. The reconstruction results show that the average correlation coefficient (ACC) and the average root mean square error (ARMSE) between the IDW-based results and daily cumulative rainfall from rain gauges (RGs) are 0.89 and 8.69 mm, respectively, while the ACC and ARMSE between the OK-based results and RG data are 0.89 and 9.13 mm, respectively. The nowcasting results show that the ACC between the prediction results with a 5-min setup window and the IDW-retrieved rainfall fields can reach 0.91 at the first minute and gradually decrease to 0.20 within 10 min. Furthermore, the model has better nowcasting performance for stratiform precipitation and mixed precipitation compared to convective precipitation.
1
[PERSON], 1 [PERSON]SS]
2023
[PERSON], 1 [PERSON]@mud.
commercial microwave links (CMLs) ([PERSON] et al., 2006). Among these, CML is one of the most promising sources. CMLs provide line-of-sight wireless backhaul connectivity in cellular communication networks, with data exchange performed between the transmitter and receiver. When rainfall occurs along the CML path, additional microwave signal attenuation occurs due to wave absorption and scattering by raindrops. In this case, the measured attenuation [transmitted signal level (TSL) minus received signal level (RSL)] can be mainly divided into two categories: non-rain-induced attenuation (also known as attenuation baseline, caused by free-space loss, gas, etc.) and rain-induced attenuation (caused by the scattering and absorption of signals by raindrops) ([PERSON] & [PERSON], 2018). The heavier it rans, the more raindrops will obstruct the propagation path, hence the rain-induced attenuation increases with the rainfall intensity. Based on the assumption of uniform rainfall along the path, the rain-induced specific attenuation can be obtained by dividing the total rain-induced attenuation by the path length. Then according to the power-law relationship between rain-induced specific attenuation and rainfall intensity ([PERSON] et al., 1978), the path-averaged rainfall intensity can be calculated, which is usually considered as an estimate of the rainfall intensity at the midpoint of the path. Therefore, accurate extraction of rain-induced attenuation from measured attenuation is the core of CML rain measurement technology. Due to the complexity on the CML path during the wet period, it is difficult to extract rain-induced attenuation directly from the measured attenuation. In applications, based on the assumption that the baseline only changes slowly during rainfall events, the data samples are classified into the dry and wet periods with dry period attenuation used to estimate the baseline, which may be considered constant over the wet period ([PERSON], 2003), or may be determined by calculating the median value of dry period attenuation over a certain period prior to rainfall through a sliding window ([PERSON] et al., 2012; [PERSON] et al., 2008; [PERSON] et al., 2022). However, these methods require a large CML dataset or additional dedicated rain sensors for calibration, otherwise, they may not work effectively. Consequently, dynamic determination methods of the attenuation baseline without the need for dry and wet period classification have been proposed ([PERSON] et al., 2020; [PERSON] & [PERSON], 2018). Hence, rain-induced attenuation can be estimated by subtracting the baseline from the measured attenuation. In this way, most of the non-rain-induced attenuation is eliminated ([PERSON] et al., 2020). In addition, the wet antenna attenuation (WAA) produced by the water film covering the antenna can lead to an overestimation of rainfall ([PERSON] et al., 2013). Especially in the case of short CMLs and light rainfall, the compensation of WAA cannot be neglected. After obtaining the rainfall intensity, to reconstruct rainfall fields, spatial interpolation algorithms ([PERSON] et al., 2008), machine learning algorithms ([PERSON] et al., 2022), and tomographic methods ([PERSON] et al., 2016) are adopted. Finally, deep learning approaches are employed to nowcast the rainfall fields ([PERSON] et al., 2020; [PERSON] et al., 2020).
To date, the rainfall measuring technology by CMLs has been compared with conventional rain sensors in Germany ([PERSON] et al., 2012; [PERSON] et al., 2020), Czech Republic ([PERSON] et al., 2015), Israel ([PERSON] et al., 2006; [PERSON] et al., 2012), Italy ([PERSON] et al., 2022; [PERSON] et al., 2020), and the Netherlands ([PERSON] et al., 2019). However, in China, most of the existing research on measuring precipitation by CMLs remains theoretical or individual experiments ([PERSON] et al., 2019; [PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON]. [PERSON] et al., 2017), and research on the reconstruction and nowcasting of rainfall fields by CMLs has yet to be conducted. This study attempts to reconstruct and novasate rainfall fields by CMLs, to promote the application of CMLs in China. First, path-averaged rainfall intensity is retrieved using CML data from July to December 2021 in Jiangyin City. Second, the inverse distance weighting (IDW) and ordinary kriging (OK) interpolation algorithms are employed to reconstruct rainfall fields, with the results evaluated by radar and RG data. Then, a nowcasting model based on the long short-term memory (LSTM) neural network is proposed and a setup window (i.e., the time interval for optimizing the model parameters to fit the current rainfall event) is introduced to improve its prediction performance for the first few minutes. Finally, 10-min continuous predictions are conducted followed by the analysis of the results.
The rest of this article is organized as follows. The experimental data are introduced in Section 2. Then, the methods involved in this paper will be described in Section 3. Section 4 shows the results and discussions. Finally, we conclude in Section 5.
## 2 Experimental Data
### CML Data
For the period from July to December 2021, we obtained CML data from the CML precipitation monitoring network in Jiangyin City, China. The network is deployed in urban areas, covering 31 deg41'N to 31 deg56'N and 120\({}^{\rm{1}}\)4\({}^{\rm{\prime}}\)E to 120\({}^{\rm{\circ}}\)23\({}^{\rm{\prime}}\)E, with an area of about 380 km\({}^{\rm{2}}\), as shown in Figure 1a. The terrain is flat and the elevation angle of CML path can be negligible. The TSL of CMLs is constant at 27 dBm, while the RSL is quantized to 0.1 dBm. The frequency of the CMLs is 26 GHz, which ensures the relationship between rain-induced specific attenuation and rainfall intensity is close to linear. In addition, the polarization type of the CMLs is designated as vertical. Data acquisition is performed by a micro-receiver terminal, which records instantaneous RSL minutely and transmits it to a cloud server in real time. Additional information on CMLs is shown in Figures 1c and 1d. Due to equipment power outages, commissioning, and maintenance, some CML data are not available for a short period of time, which have been excluded through quality control. The available time of CML data is shown in Figure 2.
### Reference Data
As the additional equipment installed on the CML network, an OTT Parsivel disdrometer (OTT) and five RGs are used to evaluate the performance of rainfall intensity inversions and rainfall field reconstructions (Figure 1b), respectively. Since they were removed after the calibration and stability tests; we only obtained RG data from July 1 to August 27, 2021 and OTT data from July to November 2021. Note that RG3 was not available on July 2, 15, and August 10 due to power outages. Moreover, RGs record the cumulative rainfall every 5 min with the minimum detectable rainfall of 0.5 mm.
The OTT uses a parallel laser beam as the sampling space and a phototube array as the receiving sensor ([PERSON], 2000). When a raindrop crosses the sampling space, the width of the occlusion and the crossing time are automatically recorded to calculate the size and velocity of the raindrop. OTT records the number of raindrops in 32 size bins and 32 velocity bins every minute and converts them to rainfall intensity with the resolution of 0.01 mm/hr by software.
Data from an S-band dual-polarization radar located in Changzhou were compared with reconstructed rainfall fields. The radar carries out a full volume scan at nine elevation angles every 6 min, with a radial resolution of
Figure 1: Information on commercial microwave links (CMLs), OTT, and rain gauges (RGs). (a) Map of Jiangpin with the locations of 26 CMLs. (b) Map of Jiangpin with the locations of an OTT and five RGs. (c) The path lengths of CMLs. (d) The directions of CMLs.
250 m and a beam width of 1\({}^{\circ}\). Before conducting quantitative precipitation estimation (QPE) at the lowest elevation angle (0.5\({}^{\circ}\)), quality control algorithms are employed to reduce ground clutter. QPE is obtained by a method based on a specific attenuation and a specific differential phase ([PERSON] et al., 2019). Finally, the processed data are interpolated onto Cartesian grids with a horizontal resolution of 250 m using the nearest neighbor and vertical linear interpolation. However, because of lacking access to the radar database, we only acquired radar products from July 26 to 27, 2021.
## 3 Methods
### Rainfall Intensity Inversion Algorithm
In general, the CML-based rainfall inversion method in this paper mainly consists of the following steps (Figure 3):
1. Data processing: exclude missing data by quality control and convert RSL data to measured attenuation.
2. Classification of dry and wet periods: determine whether rainfall exists at the current time based on the characteristics in attenuation data.
3. Determination of attenuation baseline: estimate the attenuation baseline based on the dry and wet period classification results.
4. Calibration of the relationship between rain-induced specific attenuation and rainfall intensity: calibrate the power-law parameters using raindrop size distribution (DSD) data from OTT.
5. WAA correction: eliminate the effect of WAA on rainfall inversion using empirical models.
6. Inversion of path-averaged rainfall intensity: extract the rain-induced specific attenuation based on the attenuation baseline and WAA correction, and estimate the path-averaged rainfall intensity based on the power-law relationship.
#### 3.1.1 Classification of Dry and Wet Periods and Determination of Baseline
In microwave signal transmission, microwave attenuation varies with time. However, the stability of the atmospheric environment in the dry period and the high variability of the rainfall intensity in the wet period with time lead to different local variability of the attenuation sequences in the dry and wet periods. Hence, we employed the
Figure 2: The available time of commercial microwave links (CMLs) data.
rolling standard deviation (RSD) method ([PERSON] & Berne, 2010) to classify dry and wet periods. The standard deviation std\({}^{\omega}\) of attenuation sequence within the previous \(\omega\) minutes at time \(t_{0}\) can be calculated as follows:
\[\mathrm{std}^{\omega}=\sqrt{\frac{1}{\omega+1}\sum_{i=t_{0}-\omega}^{t_{0}}\left( \mathcal{A}^{v}-\overline{A}^{v_{0}}\right)}, \tag{1}\]
where \(\overline{A}^{v_{0}}\) is the average attenuation of the attenuation sequence within the previous \(\omega\) minutes at time \(t_{0}\), and \(A^{v_{0}}\) is the measured attenuation at time \(t_{v}\). Then, according to a pre-determined threshold thr, data can be labeled into dry and wet periods by the following principle:
\[\mathrm{label}^{f}=\begin{cases}\mathrm{dry}&\mathrm{if\,std}^{\prime}\leq \mathrm{thr}\\ \mathrm{wet}&\mathrm{if\,std}^{\prime}>\mathrm{thr}\end{cases}, \tag{2}\]
\[\mathrm{thr}=\omega_{f}\left\{\mathrm{std}^{\prime}|t\in D\right\}. \tag{3}\]
\(\omega_{f}\) represents the \(r\) quantile, and \(D\) is the data set for calculating thr. Because not every CML is deployed near a rain sensor and the similarity of the local climate, the OTT and two RGs deployed near CML6 were used to determine the window length \(\omega\) and the quantile parameter \(r\). CML data from August, September, and October were used to determine thr, with data from July to August used to validate the classification method. When the OTT detects rainfall intensity exceeding 0.1 mm/hr or at least one of the RGs produces tips, it is considered that rainfall is present along the path. To quantitatively assess the effect of combination of different \(\omega\) and \(r\) on the RSD classification performance, true positive rate (TPR) and true negative rate (TNR) is commonly used. TPR, also known as recall rate, indicates the rate of correctly classified wet period data. And TNR indicates the proportion of correctly classified dry period data. In this paper, in order to obtain high TPR and TNR simultaneously, geometric mean (G-mean) ([PERSON] et al., 1998), an indicator that integrates TPR and TNR, is used. They can be calculated as follows:
\[\mathrm{TPR}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}^{\ast}}. \tag{4}\]
Figure 3: Flow chart of rainfall inversion algorithm based on commercial microwave links (CMLs).
#### 3.1.2 Calibration of the Power-Law Relationship
In the field of wireless communications, the empirical power-law relationship in Recommendation P. 838-3 of the International Telecommunication Union (ITU-R) is often used to estimate rain-induced specific attenuation \(\gamma_{\rm rain}\) (dB/km) (ITU, 2005):
\[\gamma_{\rm rain}=aR^{b}, \tag{8}\]
where \(a\) and \(b\) are power-law parameters, which are related to frequency, DSD, raindrop temperature, etc. By referring to ITU-R, the parameters corresponding to frequencies from 1 to 1,000 GHz can be obtained directly or by interpolation. However, some local rain-induced attenuation results have shown large deviations from the ITU-R model ([PERSON] et al., 2019; [PERSON] et al., 2013), demonstrating that the model requires calibration by DSD data.
Based on the OTT measurement principle, the DSD can be calculated by Equation 9:
\[N(D_{i})=\sum_{j=1}^{32}\frac{n_{i,j}}{\
u_{j}\cdot T\cdot S\cdot d_{i}}, \tag{9}\]
where \(N(D_{i})\) (m\({}^{-3}\) mm\({}^{-1}\)) is the concentration of raindrops per unit volume in the interval from \(D_{i}\) to \((D_{i}+d_{j})\), \(D_{i}\) (mm) and \(d_{i}\) (mm) are the average value and the width of the \(i\)th size bin, respectively. \(n_{i,j}\) is the number of rain-drops in the \(i\)th size bin and the \(j\)th falling velocity bin recorded by the OTT during the sampling time \(T\) (60 s). \(V_{j}\) (m/s) is the average value of the \(j\)th falling velocity bin, and \(S\) (0.0054 m\({}^{2}\)) is the sampling area.
According to electromagnetic scattering theory, microwave signals can be attenuated by the absorption and scattering of raindrop particles along the path. The rain-induced specific attenuation can be expressed as (Eriksson et al., 2018):
\[\gamma_{\rm rain}=4.343\times 10^{3}\int_{0}^{\infty}Q_{\rm est}(D,f,T)\times N (D)d\,D, \tag{10}\]
where \(Q_{\rm est}(D,f,T)\) (m\({}^{2}\)) is the extinction cross-section of the raindrop particle, which is associated with microwave frequency \(f\)(GHz), raindrop size \(D\) (mm), and temperature \(T\)(C). The extinction cross-section is calculated based on T-matrix method for nonspherical raindrop particles ([PERSON] et al., 2004). And the raindrops are assumed to be oblate spheroids whose shape is mainly decided by the axis ratio ([PERSON], 1970):
\[{\rm ratio}=1.03-0.062D\,(0<D<6\,{\rm mm}). \tag{11}\]
Figure 4: The dry and wet period classification results of CML6 applying the combination of different \(\omega\) and \(r\). The combination of parameters with the highest G-mean has been marked. Notably, most of the results with \(r\) exceeding 95 lie outside the lower boundary of the color bar.
And the rainfall intensity \(R\) can be expressed as follows:
\[R=6\pi\times 10^{-4}\sum_{i=1}^{32}V(D_{i})N(D_{i})D_{i}^{3}d_{i}, \tag{12}\]
where \(V(D_{i})\) (m/s) is the fall velocity of the raindrop with diameter \(D_{i}\) (mm), which is recorded by the OTT. Since both \(\gamma_{\rm rain}\) and \(R\) are functions of \(N(D)\), the relationship between the two can be calculated from the measured DSD data. Notably, data with any raindrops larger than 6 mm, which are mainly caused by overlapping raindrops along the laser beam ([PERSON] et al., 2006; [PERSON] et al., 2022), are excluded. In addition, raindrops in DSDs with unmatched \(D\)-\(V\) (normal \(D\)/\(V\) vs. excessively large or small _V/D_) were also considered to be unreliable data, which could be produced under strong wind shear conditions or by raindrops splashing on the surface of the instrument. We compared the measured \(D\)-\(V\) of OTT data with the Atlas diameter-velocity empirical model ([PERSON] et al., 1973), and data with more than 50% deviation between theoretical and measured velocity were removed by quality control ([PERSON] et al., 2023):
\[V_{\rm radius}(D_{i})=9.65-10.3e^{-0.6D_{i}}. \tag{13}\]
In this experiment, the OTT data from July to November 2021 are used to calibrate the \(\gamma_{\rm rain}\)-\(R\) relationship. The fitted \(\gamma_{\rm rain}\)-\(R\) relationship and ITU-R model are shown in Figure 5. It can be noticed that the fitted curve deviates more from the ITU-R model at lower and higher rainfall intensity, with the smallest deviation at about 60 mm/hr. Compared with the ITU-R model, the fitted model is more consistent with the relationship between rain-induced specific attenuation and rainfall intensity, therefore, the calibrated power-law relationship is used to retrieve the rainfall intensity:
\[\gamma_{\rm rain}=0.105R^{1.057}. \tag{14}\]
#### 3.1.3 WAA Correction
When there is rain, fog, and dew, the water film generated on the antenna surface will cause additional attenuation of the signal. Inadequate correction for WAA may lead to large biases in rainfall inversions by CMLs ([PERSON] et al., 2019). Currently, WAA has been shown to be related to antenna efficiency, antenna directivity ([PERSON] et al., 2020), and rainfall intensity ([PERSON] et al., 2019). Since the CMLs in this experiment are all at the same frequency, we chose the power-law model based on the rain-induced specific attenuation proposed by [PERSON] ([PERSON] et al., 2022):
\[A_{\rm wa}=2p\gamma_{\rm rain}^{4}, \tag{15}\]
where \(p\) and \(q\) are frequency-dependent power-law parameters. For CMLs at a given frequency, the model requires only one CML for calibration and can be applied to that frequency band. Thus, to determine the parameters \(p\) and \(q\), we conducted simulation experiments using OTT and CML6 data from July to November 2021. Based on the assumption of uniform rainfall over the path (the path length of CML6 is only 1.5 km), the OTT data were used to pick the rainfall events and calculate the rain-induced specific attenuation, while the \(A_{\rm wa}\) was obtained by subtracting the rain-induced attenuation from the measured attenuation. The fitted results are shown in Figure 6, and the relationship can be given as:
\[A_{\rm wa}=3.22\gamma_{\rm rain}^{0.35}. \tag{16}\]
#### 3.1.4 Path-Averaged Rainfall Intensity Inversion
In the process of microwave signal transmission, the measured attenuation \(A\) can be expressed as:
\[A=\begin{cases}A_{\rm base}&\text{if dry}\\ A_{\rm base}+A_{\rm rain}+A_{\rm wa}&\text{if wet}\end{cases}, \tag{17}\]
Figure 5: Variation of the rain-induced specific attenuation with rainfall intensity.
where \(A_{\text{train}}\) is the integrated rain-induced attenuation. Then, based on the assumption of uniform rainfall distribution along the path and Equations 16 and 17, the rain-induced specific attenuation \(\gamma_{\text{train}}\) can be obtained by:
\[L\gamma_{\text{train}}+3.22\gamma_{\text{train}}^{0.35}=A-A_{\text{base}}, \tag{18}\]
where \(L\) (km) is the length of the CML path. Since the \(\gamma_{\text{train}}\)-\(R\) relationship is approximately linear for 26 GHz, according to Equation 14, the path-averaged rainfall intensity \(\overline{R}\) can be estimated:
\[\overline{R}=\left(\frac{\gamma_{\text{train}}}{0.105}\right)^{\frac{1}{1.057}}. \tag{19}\]
### Rainfall Field Reconstruction Algorithm
#### 3.2.1 Inverse Distance Weighting Interpolation Algorithm
The IDW interpolation algorithm is one of the simplest and most commonly used interpolation methods ([PERSON] et al., 1998) and has proven effective in reconstructing rainfall fields using CML data ([PERSON] et al., 2021, 2020). The IDW principle is concise: When estimating the rainfall intensity at a point in the rainfall field, the weight coefficient of the CML measurement is only a function of the reciprocal distance of that point from the midpoint of the CML path ([PERSON], 1968). The steps of IDW are shown below:
1. Calculate the distance \(h_{i}\) from each sample (\(X_{i}\), \(Y_{i}\)) to the interpolated point (\(X_{i}\), \(Y_{i}\)): \[h_{i}=\sqrt{\left(X-X_{i}\right)^{2}+\left(Y-Y_{i}\right)^{2}}.\] (20)
Figure 6: The fitted relationship between wet antenna attenuation (WAA) and \(\gamma_{\text{train}}\).
2. The weight coefficient \(W_{i}\) of each measurement point is calculated as: \[W_{i}=\begin{cases}\frac{h_{\text{tar}}^{i-n}}{\sum_{j=1}^{n}h_{j}^{i-n}}&\text{ if }h_{i}\leq h_{\text{tar}}\\ 0&\text{ if }h_{i}>h_{\text{tar}}\end{cases},\] (21) where \(n\) is the number of measurement points whose distance from the interpolation point is less than \(h_{\text{tar}}\), \(m\) (2) is the parameter for determining the influence degree, and \(h_{\text{tar}}\) (10 km) is the distance beyond which the measurement point has a negligible effect on the interpolated point (i.e., the radius of influence).
3. The rainfall intensity \(R\) at the interpolated point is given as a weighted sum according to the rainfall intensity \(R_{i}\) and the weight coefficient \(W_{i}\) at the measurement points: \[R=\sum_{i=1}^{n}W_{i}R_{i}.\] (22)
#### 3.2.2 OK Interpolation Algorithm
The OK algorithm was the first proposed kriging interpolation algorithm ([PERSON], 1989) for all intrinsically smooth random fields that satisfy isotropic assumptions. Similar to IDW, OK also uses a weighted sum of data from measurement points to estimate the unknown points. However, OK weights are a set of optimal coefficients based on the relationship between distance and semi-variance ([PERSON] et al., 1984). In addition, related studies have shown CML products interpolated by OK have excellent results in rainfall field reconstruction ([PERSON] et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2017; [PERSON] et al., 2022). The procedure of OK is as follows:
1. Calculate the distance \(h_{g}\) and the semi-variance \(\gamma_{g}\) between measurement points: \[h_{ij}=\sqrt{\left(X_{i}-X_{j}\right)^{2}+\left(Y_{i}-Y_{j}\right)^{2}},\] (23) \[\gamma_{ij}=\frac{1}{2}(R_{i}-R_{i})^{2},\] (24) where \(R_{i}\) is the rainfall intensity of the measurement point (\(X_{e}\), \(Y_{i}\)) and \(\gamma_{g}\) is the semi-variance between the \(i\)th and \(j\)th measurement points.
2. The spherical model is adopted to fit the relationship between distance and semi-variance to acquire the expression of the variance function \(\gamma\).
3. The semi-variance between each measurement and the interpolated point is calculated according to \(\gamma\), and the weight coefficient of measurement points can be solved by the weight matrix: \[\begin{bmatrix}\gamma_{11}&\gamma_{12}&\cdots&\gamma_{1n}&1\\ \gamma_{21}&\gamma_{22}&\cdots&\gamma_{2n}&1\\ \cdots&\cdots&\cdots&\cdots&\cdots&\cdots\\ \gamma_{41}&\gamma_{42}&\cdots&\gamma_{4m}&1&\lambda_{4n}\\ 1&1&\cdots&1&1&\mu\\ \end{bmatrix}=\begin{bmatrix}\gamma_{10}\\ \gamma_{20}\\ \cdots\\ \gamma_{40}\\ 1\\ \end{bmatrix},\] (25) where \(\lambda_{i}\) is the weight of the \(i\)th measurement point, \(\gamma_{\mu}\) is the semi-variance between the \(i\)th measurement point and the interpolated point, and \(\mu\) is the Lagrangian multiplier.
4. The rainfall intensity \(R\) at the interpolated points is calculated by weighted summing: \[R=\sum_{i=1}^{n}\lambda_{i}R_{i}.\] (26)
### Rainfall Field Nowcasting Algorithm
#### 3.3.1 LSTMemory Network
As an improved algorithm from recurrent neural networks, the LSTM network was proposed in 1997 ([PERSON] and [PERSON], 1997) to solve the long-term dependency problem ([PERSON] et al., 1998). LSTM introduces a self-loop to keep the gradient flowing, whose weight can be determined automatically according to the sequence instead of being fixed. There are three gate units imported into the LSTM: the historical information can be selectively retained by the forget gate; the input gate is employed to pick new input information; and the output of the hidden layer is determined by the output gate. Based on these features, LSTM has been used to classify dry and wet periods ([PERSON] and [PERSON], 2018), estimate attenuation ([PERSON] et al., 2022; [PERSON], [PERSON], & [PERSON], 2020), and nowcast rainfall fields ([PERSON] et al., 2020). In this paper, LSTM cells are used to learn the time dependence of spatial rainfall distribution characteristics.
#### 3.3.2 A Deep Learning Model for Rainfall Nowcasting
Based on the LSTM network, a deep learning model is proposed to nowcast rainfall fields using CML data. The model consists of a sequence input layer, a convolutional layer, a pooling layer, an LSTM layer, a fully connected layer, a regression layer, and an output layer (Figure 7a). To grasp spatial-temporal variation trends of the rainfall field in advance, a setup window is introduced. Prior to each rainfall event prediction, the window will input rainfall field data of the previous period into the model to optimize the parameters for the current event, as shown in Figure 7b.
The parameter \(n\) (min) is the length of the window. During model training, the rainfall field data in the train set are input into the sequence input layer and delivered to the next layer sequentially. In the convolutional layer, a \(3\times 3\) Laplace convolutional kernel is adopted to extract the spatial rainfall features, and the feature matrix \(C_{i}\) can be expressed as:
\[C_{i}(i,j)=\sum_{p=1}^{S}\sum_{i=1}^{S}A(p,q)R_{i}(i-p+1,j-q+1), \tag{27}\]
\[\begin{cases}1\leq i\leq W_{r}-S+1\\ 1\leq j\leq W_{c}-S+1\end{cases}, \tag{28}\]
where \(t\) denotes the rh rainfall field of the \(N\) samples in the train set, \(S\) equals \(3\) is the size of the convolutional kernel \(A\), \(R_{i}\) indicates the rainfall intensity matrix of the rainfall field, and \(W_{a}\) and \(W_{c}\) are the numbers of rows and columns of \(R_{r}\) respectively. Considering that excessive elements in \(C_{r}\) may lead to long training time and poor learning effects, a pooling layer is used to reduce elements while retaining the main information. The pooled feature matrix \(D_{i}\) is:
\[D_{i}(i,j)=\max(B*C_{i}(1-P+P\cdot i:P\cdot i,1-P+P\cdot j:P\cdot j)), \tag{29}\]
\[\begin{cases}1\leq i\leq H_{i}/P\\ 1\leq i\leq H_{c}/P\end{cases}, \tag{30}\]
where \(P\) equals \(3\) is the size of the sampling kernel \(B\), and \(H_{a}\) and \(H_{c}\) denote the number of rows and columns of \(C_{r}\) respectively. Then, \(D_{i}\) is reshaped into a one-dimensional feature vector and output to the LSTM layer. The LSTM cell is updated as shown below:
\[\hat{r}=\text{sigmoid}\big{(}W_{si}x^{i}+W_{ni}h^{(n-1)}+b_{i}\big{)}, \tag{31}\]
\[f^{i}=\tanh\big{(}W_{xf}x^{i}+W_{nf}h^{(n-1)}+b_{f}\big{)}, \tag{32}\]
\[\text{g}^{i}=\text{sigmoid}\big{(}W_{sg}x^{i}+W_{sg}h^{(n-1)}+b_{g}\big{)}, \tag{33}\]
connected layer are optimized by the regression layer to satisfy the terminal condition: loss \(<\) 0.01 or maximum iterations reached. The expression of loss is given by:
\[\text{loss}=\frac{1}{2N}\sum_{i=1}^{N}\sum_{j=1}^{W_{i}^{*}W_{c}}(R_{(0+1,\omega (j))}-R_{0+1,\omega(j)})^{2}, \tag{38}\]
where \(R_{(\omega+1,\omega(j))}\) and \(R_{(\omega+1,\omega(j)})\) are the rainfall intensity of the inverted rainfall field and the prediction, respectively. For model training, the Adam optimizer is used, and the maximum number of iterations is set to 1,000. To prevent gradient explosion, the gradient threshold is set to 1, and the initial learning rate is 0.002, which is halved after every 200 iterations.
After model training, we test the model using the test set. Prior to predicting each rainfall event, rainfall field data from the previous period are entered through the setup window to optimize the model parameters, followed by a step-by-step 10-min continuous nowcast. After the prediction, the parameters are reset to remove the influence of the previous rainfall event and prepared for nowcasting the next rainfall event. The flow chart of model training and testing is shown in Figure 6(c).
To eliminate seasonal differences, we select the rainfall field data reconstructed by IDW method in July, September, and November 2021 as the train set, which totals 3,714 min of data. The CML data from August, October, and December 2021 are used as the test set, which contains 17 rainfall events for a total of 1,346 min. To clarify, in this experiment, we treat the rainfall field reconstructed by IDW as the ground truth, ignoring the errors in the rainfall intensity inversion and rainfall field reconstruction sections. In addition, the selection of rainfall events follows two principles:
1. Long duration. Since the temporal resolution of CMLs is 1 min, the selected rainfall events are more than 40 min in duration to better reflect the temporal trends of the rainfall distribution and to facilitate extracting the setup window.
2. Constrained rainfall intensity. Due to the interference of clouds and fog, equipment status, and other factors, signal may fluctuate abnormally in rain-free weather, which causes false positives. Moreover, intense rainfall and rain showers generally have a short duration, leading to sharp variations in the magnitude and spatial distribution of rainfall intensity within tens of minutes, which is not conducive to model prediction. Therefore, the maximum rainfall intensity of the selected rainfall events ranged from 5 to 50 mm/hr.
### Performance Evaluation
To provide a quantitative evaluation of rainfall inversion, rainfall field reconstruction, and nowcasting, mean absolute error (MAE), root mean square error (RMSE), relative RMSE (RRMSE), and correlation coefficient (CC) are used as assessment metrics. For clarification, MAE is the mean of the absolute errors between the estimated and true values, RMSE is the square root of the mean of the squares of the errors between the estimated and true values, RRMSE is a statistical indicator used to evaluate a prediction model, which can reflect the prediction accuracy of the model, while CC is the statistical indicator that reflects the similarity degree. They can be calculated as:
\[\text{MAE}=\frac{1}{m}\bigg{|}\sum_{i=1}^{n}(R-R_{\text{max}})\bigg{|}, \tag{39}\]
\[\text{RMSE}=\sqrt{\frac{1}{m}\sum_{i=1}^{n}(R-R_{\text{max}})^{2}}, \tag{40}\]
\[\text{RRMSE}=\frac{\text{RMSE}}{\overline{R}_{\text{max}}}, \tag{41}\]
\[\text{CC}=\frac{\text{Cov}(X,Y)}{\sqrt{\text{Var}[X]\cdot\text{Var}[Y]}}, \tag{42}\]
where \(m\) is the number of samples, \(R\) is the reconstructed or predicted rainfall field, \(R_{\text{max}}\) is the reference measurements, \(\overline{R}_{\text{max}}\) is the average rainfall intensity of the measured rainfall field, \(X\) and \(Y\) are the rainfall intensity matrices, and \(\text{Var}[X]\) and \(\text{Var}[Y]\) are the variances of \(X\) and \(Y\), respectively.
## 4 Results and Discussion
### Rainfall Inversion by CMLs
Based on the above methods, the rainfall intensity inversion by CMLs was achieved and its performance was evaluated using CML6 and OTT data. The results of the rainfall inversions for two rainfall events from July 25 to 26, 2021 are given in Figure 8. When the OTT detects rain, the measured attenuation rises significantly compared to the baseline, and the deviation between the two increases with the rainfall intensity. The CC and MAE between the inverted rainfall intensity and OTT measurements are 0.76 and 0.76 mm/hr, respectively, while the CC and MAE of the accumulated rainfall results are 0.99 and 4.08 mm, respectively.
Then, to evaluate the long-term performance of the rainfall inversion method, the daily cumulative rainfall from CML6 inversions and OTT measurements from July to November 2021 were compared (Figure 9). Notably, data for which no rainfall is detected by either method have been excluded. It can be seen that there is a good agreement between the rainfall inversion results and the OTT measurements, with a CC of 0.93 and a MAE of 3.28 mm. Considering that precipitation might have complex and random distribution in time and space, the point measurement of OTT cannot represent the overall rainfall intensity along the path, which may result in spatial discrepancies between the inverted rainfall intensity and the measurements. However, the discrepancies can be offset by the temporal integration of accumulated rainfall, leading to a higher CC. Although the results show that accurate inversion of rainfall
Figure 8: Evaluation of rainfall inversion methods applied on CML6 from July 25 to 26, 2021. (a) \(A\) and \(A_{\text{base}}\) of CML6. (b) Rainfall intensity and (c) accumulated rainfall obtained from CML6 inversions and OTT measurements.
Figure 9: Comparison between daily cumulative rainfall from CML inversions and OTT measurements from July to November 2021. Notably, data for which no rainfall is detected by either method have been excluded.
intensity can be achieved using CML6 by the above method, considering that it would be unfair to use OTT data to validate rainfall inversion methods calibrated by OTT, further validation is performed in the comparison of CMLs with RGs in the next section.
### Reconstruction of Rainfall Field
Figure 10 shows the comparison between the radar QPE and the rainfall fields reconstructed by IDW and OK, and Table 1 provides quantitative assessment results. To clarify, since CMLs do not cover the entire rectangular region, it is of little significance to evaluate the interpolation effect at locations far from the CML. Therefore, the CC and RMSE are calculated to include only pixels within 5 km from the midpoint of the CML path. It can be seen, the
\begin{table}
\begin{tabular}{l c c c c} \hline \hline & \multicolumn{2}{c}{CC} & \multicolumn{2}{c}{RMSE (mm/hr)} \\ \cline{2-5} Time & IDW & OK & IDW & OK \\ \hline
08:42, July 26, 2021 & 0.82 & 0.71 & 2.07 & 3.47 \\
18:12, July 27, 2021 & 0.75 & 0.62 & 1.48 & 1.87 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation Coefficient (CC) and Root Mean Square Error (RMSE) Between Ordinary Kriging (OK)- and Inverse Distance Weighting (IDW)-Based Rainfall Field and Radar Quantitative Precipitation Estimation
Figure 10: Comparison of radar quantitative precipitation estimation and the reconstructed rainfall fields at 08:42, July 26, 2021 and 18:12, July 27, 2021. Red lines represent commercial microwave link (CML) paths.
overall rainfall distribution of the QPE and reconstructed rainfall fields are remarkably consistent, with the CC of reconstruction results exceeding 0.62. However, the reconstructed rainfall fields did not capture the rainfall features in the northwest, especially on July 27, resulting in lower CC and higher RMSE. Considering the spatial distribution of CMLs, we believe this is due to the absence of CMLs erected in the above areas, resulting in the rainfall intensity in areas without CMLs always being lower than CML measurements when interpolating. In addition, note the central part of the rainfall field on July 27, where the overestimation of rainfall by CMLs adversely affected the reconstruction of the rainfall field.
To quantitatively evaluate the long-term performance of the two methods, the daily cumulative rainfall measured by RGs from July to August 2021 are compared with the estimates at the location nearest to the RGs in the reconstructed rainfall field (Figure 11). The CC and RMSE of the results are shown in Table 2. The results of both methods are in high agreement with RG measurements, which demonstrates the good performance of the rainfall inversion method indirectly. However, it is worth noting that both interpolation methods tend to underestimate rainfall more, which may be due to the overcompensation of WAA. In addition, the small rainfall obtained on rainless days may be false positives caused by the high variability of attenuation in the dry period.
In the five groups of comparisons, the average CC (ACC) of IDW and OK is both 0.89, which was higher than the values documented in the literature ([PERSON] et al., 2021). And the average RMSE (ARMSE) of IDW and OK is 8.69 and 9.13 mm, respectively. It not only proves both methods can achieve accurate reconstruction of rainfall fields over long time, but also demonstrates the small advantage of IDW over OK. In addition, the performance of OK method decreases significantly mainly at RG1 and RG5, showing obviously higher RMSE than the IDW-based results. It is speculated to be associated with the location of the RGs: RG1 and RG5 are located in the northernmost and southernmost part of the CML network, respectively, which means, estimating the rainfall intensity at these locations is equivalent to using the sample data for extrapolation; meanwhile, the spatial correlation of OK, which is obtained using the distance-semi-variance relationship, may not be optimal for external data, while the simple assumption of IDW on the rainfall intensity distribution (only related to the reciprocal distance) may have produced better results. Therefore, we choose the rainfall field data reconstructed by IDW to train and test the nowcasting model.
### Nowcasting of Rainfall Field
Then the performance of the nowcasting model is assessed quantitatively. As shown in Figure 12, the model with the setup window performs remarkably better than that without the setup window in terms of both ACC and average RRMSE (ARRMSE). In addition, the best nowcasting performance was achieved with a window length of 5 min, while as the window length increased, the results showed a similar ACC but higher ARRMSE. The explanation for this phenomenon may be related to the area of the experimental region. The small area of the rainfall field in this experiment leads to the possibility that the rain cells may move outside the area within tens or even minutes, thus, data too long from the rainfall event may instead interfere with the optimization of the model parameters. In contrast, when the length is too short, the small amount of data is insufficient to reflect the spatial
Figure 11: Comparison of daily cumulative rainfall interpolated by inverse distance weighting (IDW) and ordinary kriging (OK) methods with the rain gauge (RG) data. The left column shows the results of IDW, while the right column shows the results of OK.
Figure 13 shows a nowcasting result from 00:07 to 00:16, October 8, 2021. The rain cell initially appears in the eastern region and begins to extend to the west within 10 min. The RRMSE and CC between the results and the measurements are shown in Table 3. It can be clearly seen that the prediction results are of good consistency with the measurement in the first 3 min, however, predictions get progressively worse over time. Although the prediction model is only able to achieve a few minutes of rainfall field nowcasting in this experiment, this is inseparable from the limited experimental area. When the rainfall field is large enough, the rain cell can stay in it for one or even several hours, which means the rainfall field data can contain more information to support longer forecasts. Then the temporal resolution of the rainfall field nowcasting can be reduced to 15 min or even longer to achieve longer prediction using the past rainfall field data by the setup window.
In addition, the performance of the nowcasting model was evaluated for different types of precipitation. Due to the lack of sufficient radar data, we used OTT data to classify rainfall events into different precipitation types. If the standard deviation of the rainfall intensity of five consecutive DSD samples is \(\leq\)1.5 mmr then it is considered stratiform precipitation, otherwise it is convective ([PERSON] et al., 2003). However, OTT only provides point measurements and cannot distinguish precipitation types when the rain area does not cover its location, therefore, this part of the samples is labeled as unknown. Furthermore, there are some rainfall events, which are not entirely and temporal trends of rainfall distribution. Therefore, the optimal length should be proportional to the area of the predicted region. For this experiment, a setup window of 5 min is sufficient to optimize the model parameters. Furthermore, the ARRMSE of the nowcasting results without a setup window reaches 8 in the first minute and plummets to 1.92 in the second minute. The reason for this phenomenon is speculated to be the mismatch between the initial parameters of the model and the rainfall event, while the effect of the prediction in the second minute is similar to the application of the 1-min setup window, resulting in a plunge in ARRMSE. In terms of the temporal variation of the nowcasting effects, the ACC with the 5-min setup window reaches 0.91 in the first minute and decreases to 0.20 within 10 min. On the other hand, the ARRMSE keeps increasing but is always lower than 1.86 within 10 min. This is mainly caused by the accumulation of errors in each prediction.
\begin{table}
\begin{tabular}{l c c c c} \hline & \multicolumn{2}{c}{CC} & \multicolumn{2}{c}{RMSE (mm)} \\ \cline{2-5} RG ID & IDW & OK & IDW & OK \\ \hline RG1 & 0.88 & 0.84 & 8.96 & 10.48 \\ RG2 & 0.77 & 0.84 & 11.40 & 10.12 \\ RG3 & 0.90 & 0.90 & 7.96 & 7.41 \\ RG4 & 0.95 & 0.93 & 8.64 & 8.50 \\ RG5 & 0.97 & 0.94 & 6.48 & 9.16 \\ \hline \end{tabular}
\end{table}
Table 2: The Correlation Coefficient (CC) and Root Mean Square Error (RMSE) Between Reconstructed Rainfall Fields and Rain Gauge (RG) Data
Figure 12: Average correlation coefficient (ACC) and average relative root mean square error (ARRMSE) of the test results from the model with no, 5-, 10-, 15-, 20-, 25-, and 30-min setup windows.
Figure 13. The nowcasting results from 00:07 to 00:16, October 8, 2021. Truth denotes the rainfall field reconstructed by inverse distance weighting (IDW). Prediction denotes the prediction results using a 5-min setup window.
convective or stratiform, that are classified as mixed precipitation. Figure 14 shows the classification results for the train and test sets. Excluding the unknown data, the train set contains a large amount of stratiform precipitation and mixed precipitation, which are about seven times and four times more than convective precipitation, respectively. In contrast, the majority of the test set is stratiform precipitation, followed by mixed precipitation, and the least convective precipitation.
Figure 15 shows the nowcasting performance of the model applied to different precipitation types. It can be seen that the prediction performance for stratiform and mixed precipitation does not differ much, while the prediction results for convective precipitation are significantly worse than the former. This phenomenon may be caused by two aspects: On the one hand, there are far more stratiform and mixed precipitation data than convective precipitation in the train set, thus, the model learns stratiform and mixed precipitation more adequately; on the other hand, the characteristics of uneven spatial distribution, short duration, and high spatial and temporal variability of convective precipitation also pose difficulties for prediction.
## 5 Conclusions
In this paper, we carry out the experiment of rainfall field reconstruction and nowcasting based on data from the CML precipitation monitoring network in Jiangxin City. First, the raw CML data are processed to retrieve the path-averaged rainfall intensity. Second, the IDW and OK algorithms are employed to interpolate the sparsely distributed rainfall intensity to reconstruct two-dimensional rainfall fields. Third, we propose an LSTM-based rainfall field nowcasting model and achieve a 10-min continuous prediction. Finally, the performance of rainfall field reconstruction is evaluated by RG and radar data, whereas the nowcasting effect is assessed by IDW-retrieved rainfall fields. The main conclusions of this paper are as follows:
1. The CML-based rainfall inversion method is calibrated using rain sensor data and CML data. The results show that the CC of daily cumulative rainfall between CMLs and both OTT and RGs is higher than 0.77, which achieves an accurate retrieval of rainfall.
2. The two-dimensional rainfall fields are accurately reconstructed using IDW and OK methods based on CML data. The reconstructed rainfall fields are in good agreement with the radar QPE products. And the ACC between the rainfall fields reconstructed by the two methods and RG data reaches 0.89, while the ARMSE
Figure 14: The proportion of different types of rainfall events in the train and test sets.
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline Metrics & 1 st & 2 nd & 3 rd & 4 th & 5 th & 6 th & 7 th & 8 th & 9 th & 10 th \\ \hline RRMSE & 0.37 & 0.43 & 0.47 & 0.53 & 0.57 & 0.69 & 0.73 & 0.78 & 0.81 & 0.87 \\ CC & 0.92 & 0.79 & 0.71 & 0.65 & 0.64 & 0.50 & 0.41 & 0.30 & 0.29 & 0.32 \\ \hline \end{tabular} _Note._ CC, correlation coefficient; RRMSE, relative root mean square error.
\end{table}
Table 3: Evaluation Metrics for Nowcasting of the Rainfall Field From 00:07 to 00:16, October 8, 2021 based on IDW and OK is 8.69 and 9.13 mm, respectively. Both methods are able to achieve accurate reconstruction of rainfall fields.
3. An LSTM-based rainfall field nowcasting model is proposed, and a setup window is used to make it possible to grasp the spatial and temporal trend of rainfall distribution in advance. The results show that a short window length is insufficient to support the model optimization parameters, while a too long length may introduce data unrelated to the current rainfall event, resulting in poor prediction performance. An appropriate setup window can significantly improve the performance of the first few minutes of the prediction model. The ACC of the predicted results with the 5-min setup window reaches 0.91 in the first minute and decreases to 0.20 in 10 min. In addition, rainfall types were classified using OTT data, and the prediction results for different types of rainfall events were analyzed. The results show that the model performs better in predicting stratiform precipitation and mixed precipitation than convective precipitation. It should be emphasized that considering the uncertainty of CMLs in measuring light rainfall and the drastic spatial and temporal variability of heavy rainfall, only rainfall events with rainfall intensity in the range of 5-50 mm/hr were selected for this experiment. In addition, due to the limited experimental area, only a 10-min extrapolation nowcasting of the rainfall field is implemented. However, we believe that it is possible to appropriately reduce the temporal resolution of the rainfall field data to achieve longer predictions when the area of the rainfall field is large enough.
In addition, there are some limitations to this study:
1. The calibration of the dry/wet period classification method and the \(\gamma_{min}\)-\(R\) relationship was performed under the assumption of uniform rainfall over the paths of the CMLs. Although this assumption is satisfied in most cases, some convective and extreme rainfall events may have higher spatial variability.
2. The OTT data used to calibrate the \(\gamma_{min}\)-\(R\) relationship is only available for 5 months, which may not be sufficient to reflect the rainfall characteristics of the experimental area.
3. The relatively small experimental area (29 km \(\times\) 13 km) and the uneven distribution of CMLs may pose a negative impact on the reconstruction and nowcasting of the rainfall field.
As a supplemental approach, CMLs do not replace traditional rainfall measurement methods but rather provide additional precipitation information. Their high spatial and temporal resolution, wide coverage and low maintenance cost can effectively compensate for the shortcomings of dedicated precipitation sensors. In the next studies, we will try to expand the CML network and address the above limitations. In addition, the fusion of high-quality CML data with operational meteorological observation networks using data assimilation methods for accurate rainfall monitoring and forecasting is also our future research focus.
Figure 15: Prediction performance of the nowcasting model applied to different types of rainfall events.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The data used in the paper are available for scientific purposes via [[https://doi.org/10.5281/zenodo.7646796](https://doi.org/10.5281/zenodo.7646796)]([https://doi.org/10.5281/zenodo.7646796](https://doi.org/10.5281/zenodo.7646796)) ([PERSON] et al., 2023).
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wiley/ffb6a6af_0845_4ca2_936e_60eaaf2aa7fd.md | ## 2 Methods
### Emulators and Simulators of Air Quality
We trained emulators to predict air quality across China from emission changes using simulation data. Simulations of air quality in China used WRFChem (Weather Research and Forecasting model online-coupled with Chemistry) version 3.7.1 ([PERSON] et al., 2005; [PERSON] et al., 2008). WRFChem was described and evaluated in our previous work ([PERSON], [PERSON], [PERSON], [PERSON], et al., 2021; [PERSON], [PERSON], [PERSON], [PERSON], et al., 2021; [PERSON]. [PERSON] et al., 2019; [PERSON], [PERSON], et al., 2020). The simulations were for 2015 at 30 km horizontal resolution. There were 50 simulations for the training data and 5 additional simulations for the test data. Each simulation only varied the fraction of anthropogenic emissions for these five sectors. The fractions were applied for each sector individually, determined using maxi\(-\)min Latin hypercube space-filling designs separately for both the training data and the test data. The scaling factors for each anthropogenic emission sector of the training and test simulators are provided in the Supplementary Tables of [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2022). This design produces efficient and accurate emulators, as demonstrated in our previous work ([PERSON] et al., 2020; [PERSON], [PERSON], [PERSON], [PERSON], et al., 2021; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al., 2022).
Anthropogenic emissions were from the MEIC (Multi-resolution Emission Inventory for China) emission inventory ([PERSON], [PERSON], et al., 2017; [PERSON], [PERSON], et al., 2017; MEIC Research Group & Tsinghua University, 2019; [PERSON] et al., 2018). Gas phase chemistry was from the extended MOZART (Model for Ozone and Related Chemical Tracers) scheme ([PERSON] et al., 2010; [PERSON] & [PERSON], 2011; [PERSON] et al., 2014). Aerosol physics and chemistry were from the updated MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) scheme with aqueous chemistry ([PERSON] & [PERSON], 2014; [PERSON] et al., 2008). Secondary organic aerosol formation was from an updated volatility basis set mechanism ([PERSON] et al., 2015).
The emulators were Gaussian process machine learning models, developed and evaluated in ([PERSON], [PERSON], [PERSON], [PERSON], et al., 2021; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al., 2022). The inputs to the emulators were fractional changes in anthropogenic emissions from the residential (RES), industrial (IND), land transport (TRA), agricultural (AGR), and power generation (ENE) sectors. The outputs of the emulators were the metrics used in the health impact assessment of annual\(-\)mean PM\({}_{2.5}\) concentrations and maximum 6\(-\)monthly\(-\)mean daily\(-\)maximum 8\(-\)hour (6 mDM8h) O\({}_{3}\) concentrations. The 6 mDM8h metric was calculated by quantifying 24 separate 8\(-\)hour rolling mean O\({}_{3}\) concentrations, finding the maximum of these each day, creating 12 separate 6\(-\)monthly means to account for seasonal variations, and finding the maximum of these over the year.
There was one emulator per output and grid cell in China, with 30,556 emulators in total. The emulators predicted air quality for all emission configurations within a 0-150% matrix of emission scaling factors at 20% increments, with 32,768 emission configurations in total. The emulators were specific to their training data, and predicted based on associational knowledge, rather than explanatory knowledge ([PERSON], 2012; [PERSON], 2019).
For the simulator evaluation (Figure 1 in Supporting Information S1), we independently assessed a control simulation against measurements across China ([PERSON] et al., 2020; [PERSON] et al., 2018). The control simulation underestimated PM\({}_{2.5}\) concentrations (normalized mean bias factor, NMBF = \(-\)0.05 and normalized mean absolute error factor, NMAEF = 0.18) and overestimated O\({}_{3}\) concentrations (NMBF = 0.39 and NMAEF = 0.40). In order to provide the closest match with observations, we scaled PM\({}_{2.5}\) and O\({}_{3}\) concentrations to measurements. We applied the scaling to the control model and applied identical scalings to the emulators. Scalings were applied by prefecture where observations were available, otherwise scalings were applied by province (administrative division). After this scaling was applied, the control simulation had low bias and error for both PM\({}_{2.5}\) concentrations (NMBF = 0.02 and NMAEF = 0.10) and O\({}_{3}\) concentrations (NMBF = 0.03 and NMAEF = 0.11). Our approach relies on the sensitivity of the WRFChem simulations to emissions change. Future work is needed to explore the sensitivity of concentrations simulated by WRFChem to uncertainty in the chemistry and physics of the model.
For the emulators evaluation (Figure 2 in Supporting Information S1), we independently assessed the (scaled) emulators on the unseen test simulations. The emulators accurately predicted the unseen test simulation data, with a coefficient of determination (R\({}^{2}\)) value for both PM\({}_{2.5}\) and O\({}_{3}\) concentrations of 0.999 and root mean squared errors (RMSE) of 0.5094 \(\mu\)g m\({}^{-3}\) for PM\({}_{2.5}\) and 0.1667 ppb for O\({}_{3}\) concentrations. These evaluations showed that the simulators accurately represented the spatial pattern and magnitude of measured PM\({}_{2.5}\) and O\({}_{3}\) concentrations across China, and that the emulators accurately predicted the simulator ([PERSON], [PERSON], [PERSON], [PERSON], et al., 2021; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al., 2022).
The emulators were designed to quickly predict air quality solely from fractional changes in the five key anthropogenic emission sectors. The emulators did not account for changes in other sectors and sources due to computational constraints ([PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al., 2022). The simulated training data for the emulators was based on meteorology from 2015 and did not account for the interannual variation in meteorology over 2010-2020. The recent impacts from interannual changes in meteorology on air quality at the annual scale in China have been found to be substantially smaller than the impacts from changes in emissions ([PERSON] et al., 2019; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2019). We note that variability in meteorology can have a very important impact on air quality at shorter (days\(-\)weeks) timescales ([PERSON] et al., 2020).
### Health Impact Assessment
The health impact assessment estimated the disease burden attributable to PM\({}_{2.5}\) and O\({}_{3}\) exposure using population attributable fractions (PAF) of relative risk (RR). Exposure variations were used to predict associated outcome variations.
The chronic PM\({}_{2.5}\) disease burden was estimated using the GEMM (Global Exposure Mortality Model, [PERSON] et al., 2018). The outcomes were non-accidental mortality (non-communicable disease, NCD, plus lower respiratory infections, LRI). The minimum exposure of no excess risk was 2.4 mg m\({}^{-3}\). The chronic O\({}_{3}\) disease burden was estimated using the methods of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) for 2017 (GBD 2017 Risk Factor Collaborators, 2018). The outcome was chronic obstructive pulmonary disease (COPD). The minimum exposure of no excess risk was 35.7 ppb ([PERSON] et al., 2016).
The measures used were the number of premature mortalities (MORT) per year. The population count for 2010, 2015, and 2020 was from the Gridded Population of the World, Version 4.11, at 15 arc\(-\)minute resolution (Center for International Earth Science Information Network & NASA Socioeconomic Data and Applications Center, 2018). The population count was interpolated between these three years for the remaining years within 2010-2020. The population age groupings for 2010-2019 for adults of 25-80 years of age in 5\(-\)year intervals and for 80 years plus were from the GBD2019 (GBD 2019 Risk Factors Collaborators, 2020). The baseline health rates for 2010-2019 for each outcome (NCD: group category B, LRI: specific category A.2.2, and COPD: specific category B.3.1), measure, and age grouping were from the GBD2019 (Institute for Health Metrics and Evaluation, 2020). The population age groupings and baseline health rates were extrapolated for 2020.
Sector\(-\)specific changes in the air pollution disease burden can either be calculated using the subtraction or attribution methods ([PERSON] et al., 2018; [PERSON] et al., 2016). The subtraction method estimates the change in the air pollution disease burden over time. The attribution method estimates the sector\(-\)specific contributions to the air pollution disease burden. In high\(-\)exposure regions, the sector\(-\)specific public health benefits from the subtraction method are smaller than those from the attribution method due to the non\(-\)linear exposure\(-\)outcome association for PM\({}_{2.5}\) concentrations ([PERSON] et al., 2018; [PERSON] et al., 2016). Both of these approaches were in the results for their different purposes and were identified when used.
Shapefiles were used to aggregate results at the country, province, and preference level ([PERSON] et al., 2020). Uncertainty intervals at the 95% confidence level were estimated using the uncertainty intervals from the exposure\(-\)outcome associations, baseline health rates, and population age groupings. Health impact assessments of the disease burden associated with air pollution exposure have many uncertainties ([PERSON] & [PERSON], 2019). These include uncertainties in the simulator (i.e., in WRFChem from input data, parameterisations, grid aggregations, etc.), exposure\(-\)outcome associations (e.g., confounding, induction, study variability), and population generalisations (e.g., non\(-\)representative cohorts, extrapolations). The uncertainties and limitations of the population count data are detailed in Center for International Earth Science Information Network & NASA Socioeconomic Data and Applications Center, (2018). Present day emissions in China are uncertain, especially for non\(-\)methane volatile organic compounds (VOC) emissions ([PERSON] et al., 2018; [PERSON]. [PERSON], [PERSON], et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2019).
### Measurement\(-\)Informed and Bottom\(-\)Up Emission Changes
We combined the emulators with measurements over the last 6 years to derive a \"measurement\(-\)informed\" estimate of the change in emissions that occurred over this period. The measured changes in annual\(-\)mean PM\({}_{2.5}\) and 6 mDM8h O\({}_{3}\) concentrations over 2015-2020 were calculated for each measurement station (1,633 in total). The year of 2015 was chosen as the start year, as this is when extensive measurements became available. Each measurement station was spatially paired to the nearest emulator. The emission configurations were taken at 20% increments, with the edges of the parameter space (0% and 140%) removed (7,776 emission configurations remaining). The predicted changes in air quality were calculated for the remaining emission configurations relative to the baseline. The measured and predicted changes in air quality were compared, and those that matched within 1% were retained. The emission configurations that corresponded to these retained predictions were then counted to find the most frequently occurring. The top 1,000 occurring emission configurations were analyzed for matching trends in PM\({}_{2.5}\) concentrations only, due to the emulators ability to accurately capture the trend in PM\({}_{2.5}\) concentrations. These most common emission configurations represented measurement\(-\)informed estimates of the changes in anthropogenic emissions that matched the measured trend in air quality. We do not account for the impacts of interannual variability in meteorology, though we expect that this has relatively small impacts at the annual scale.
The measurement\(-\)informed estimate was compared to the bottom\(-\)up estimate of the changes in anthropogenic emissions over 2010-2017 from [PERSON] et al. (2018) (Table 1 in Supporting Information S1). Mean emission changes were calculated over carbon monoxide, nitrogen oxides (NO\({}_{\text{X}}\)), sulfur dioxide, ammonia (NH\({}_{\text{J}}\)), black carbon, organic carbon, PM\({}_{2.5}\), coarse particulate matter, and VOC emissions. The results were similar when averaging over a few key species (i.e., NO\({}_{\text{X}}\), VOC, NH\({}_{\text{J}}\) and PM\({}_{2.5}\)) instead of averaging over all species. The results using the average over all species were presented here, as the emulator inputs were averaged over all species. The bottom\(-\)up emission change estimates from [PERSON] et al. (2018) used sector\(-\)specific MEIC emissions from 2010-2017. MEIC emissions cover 31 provinces in China and include approximately 700 anthropogenic sources.
## 3 Results and Discussion
In the results and discussion, PM\({}_{2.5}\) concentrations are ambient annual\(-\)means and O\({}_{3}\) concentrations are ambient 6 mDM8h. Exposures are population\(-\)weighted concentrations.
### Measurement\(-\)Informed and Bottom\(-\)Up Emission Estimates Over 2015\(-\)2017
The bottom\(-\)up emissions for 2015-2017 from [PERSON] et al. (2018) suggest large reductions in industrial (19%), residential (16%), and power generation (11%) emissions (Figure 1). Our measurement\(-\)informed estimate for 2015\(-\)2017 suggest larger reductions in power generation (29%) and residential (28%) emissions and smaller reductions in industrial (14%) emissions. The reductions in land transport (29%) and agricultural (26%) emissions from our estimate are larger than the bottom\(-\)up reductions (both 1%).
The measurement\(-\)informed estimate has large variability, where many possible emission configurations match the measured trends in air quality. We calculate different mean emission reductions if we match to PM\({}_{2.5}\) concentrations only, O\({}_{3}\) concentrations only, both PM\({}_{2.5}\) and O\({}_{3}\) concentrations, or either PM\({}_{2.5}\) or O\({}_{3}\) concentrations (Figures 3-5 in Supporting Information S1). We note that our approach well matches the observed trend in PM\({}_{2.5}\) concentrations, but does not well match the observed trend in O\({}_{3}\) concentrations (see Section 3.2), providing larger confidence in emission estimates based on PM\({}_{2.5}\) concentrations. If our estimate is matched to both PM\({}_{2.5}\) and O\({}_{3}\) concentrations, then there are larger reductions in industry of 21% (Figure 4 in Supporting Information S1). If our estimate is matched to O\({}_{3}\) concentrations only, then the reductions are larger in power generation (57%), agriculture (36%), and industry (24%), and smaller in residential (18%) emissions (Figure 5 in Supporting Information S1). The reductions in land transport emissions are similar for all matching methods.
### Trends in Emissions, Exposure, and Public Health Over 2010\(-\)2020
Figure 2 shows 2010\(-\)2020 changes in emissions, air quality, and health impacts over China. Bottom\(-\)up emissions are from [PERSON]. [PERSON] et al. (2018). These emissions are combined with our emulators to produce bottom\(-\)up concentrations, exposure, and disease burden. Our measurement\(-\)informed emission estimates are the mean emission configurations that when combined with the emulator match the trend in measured concentrations
Figure 1: Comparison of our estimates of anthropogenic emission changes in China over 2015\(-\)2017 with previous and bottom\(-\)up estimates ([PERSON] et al., 2018). Our estimates are for the top 1,000 occurring emission configurations that matched the measured trend in fine particulate matter (PM\({}_{2.5}\), annual\(-\)mean) concentrations only. Emissions are for the (a) residential (RES), (b) industrial (IND), (c) land transport (TRA), (d) agricultural (AGR), and (e) power generation (ENE) sectors. Boxplot percentiles are fifth, 25 th, 50 th, 75 th, and 95 th. Mean emission changes are over carbon monoxide, nitrogen oxides, sulfur dioxide, ammonia, black carbon, organic carbon, PM\({}_{2.5}\) coarse particulate matter, and non\(-\)methane volatile organic compounds.
(matched to PM\({}_{2.5}\) concentrations only). The concentrations from these simulations are used to calculate measurement--informed exposure and disease burden. Our measurement--informed emission estimates were compared with bottom--up estimates for 2015-2017 when both estimates were available.
Figure 2:
In the bottom\(-\)up estimate, power generation emissions steeply decline over 2011-2016, and slightly decrease further to 2020 in the measurement\(-\)informed estimate (Figure 2a). Industrial and residential emissions both decrease from 2013-2017 in the bottom\(-\)up estimate, and both further decrease in 2020 compared to 2017 in the measurement\(-\)informed estimate. Land transport and agricultural emissions remain relatively unchanged in the bottom\(-\)up estimate over 2010-2017, while decrease after 2015 in the measurement\(-\)informed estimate.
From 2015-2020, average observed PM\({}_{2.5}\) concentrations at measurement locations reduced by 12.7 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\) (Figure 2b), well reproduced by our estimates (\(-\)14.2 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)). Over 2015-2017, the observed change in PM\({}_{2.5}\) concentrations (\(-\)5.1 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)), is slightly underestimated by the bottom\(-\)up estimate (\(-\)4.3 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)) and slightly overestimated by the measurement\(-\)informed estimate (\(-\)6.0 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)). From 2017-2020, observed PM\({}_{2.5}\) concentrations reduce by 7.7 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\) (Figure 2b), similar to the reduction in the measurement\(-\)informed estimate (8.2 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)). The regional trends for PM\({}_{2.5}\) exposure are similar for all regions (Figure 6 in Supporting Information S1).
Average PM\({}_{2.5}\) exposure across China declined by 36% from a peak of 52.8 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\) (bottom\(-\)up estimate) in 2012 to 33.5 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\) (measurement\(-\)informed estimate) in 2020 (Figure 2c). However, we note this compares estimates from bottom\(-\)up and measurement\(-\)informed estimates. The reasonable agreement between these two approaches over 2015-2017 when both are available suggests this comparison is appropriate. In the bottom\(-\)up estimate, national PM\({}_{3}\) exposure increases from 2010 (51.9 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)) to 2012 (52.8 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\)), and then decreases by 5.6 \(\mathrm{\SIUnitSymbolMicro g}\) m\({}^{-3}\) over 2012-2015 (a reduction of 11%, Figure 2e). A similar reduction in national PM\({}_{2.5}\) exposure over 2013-2019 was seen in previous work ([PERSON] et al., 2021; Health Effects Institute, 2020; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] & Sarkar, 2020; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2019; [PERSON] et al., 2021).
From 2015-2017, observed \(\mathrm{O}_{3}\) concentrations increased by 6.9 ppb (Figure 2c) compared to small changes in both bottom\(-\)up (\(-\)0.3 ppb) and measurement\(-\)informed (\(-\)0.0 ppb) estimates. The inability of the model to simulate the observed trend means that simulated national \(\mathrm{O}_{3}\) exposure, which remains relatively constant over 2010-2015 at 44 ppb (Figure 2f), is unlikely to be realistic. From 2017-2020, observed \(\mathrm{O}_{3}\) concentrations increase by a further 1.6 ppb (Figure 2c), while the measurement\(-\)informed estimate slightly decreases by 1.7 ppb. The decrease in measurement\(-\)informed \(\mathrm{O}_{3}\) exposure over 2017-2020 is driven by reductions over South Central, South West, and North West China, while measurement\(-\)informed \(\mathrm{O}_{3}\) exposure increases in North China (Figure 6 in Supporting Information S1).
As the measurement\(-\)informed estimates of \(\mathrm{O}_{3}\) concentrations do not match the observed positive trend in \(\mathrm{O}_{3}\) concentrations (Figure 2c), we are likely to underestimate the increase in disease burden associated with \(\mathrm{O}_{3}\) exposure over 2010-2020. The bottom\(-\)up and measurement\(-\)informed estimates may not match the observed trend in \(\mathrm{O}_{3}\) concentrations in China because of emission uncertainties over China ([PERSON], [PERSON], et al., 2017; [PERSON] et al., 2017) or due to missing chemistry in the simulators ([PERSON] et al., 2020, 2021). Previous work found that meteorology variability had a substantially smaller impact on the \(\mathrm{O}_{3}\) concentration trend than either emissions or chemistry, and so is unlikely to explain the mismatch ([PERSON] et al., 2019, 2021). Some previous studies found a different trend in national \(\mathrm{O}_{3}\) exposure, where it increased from 2014 to 2017 (Health Effects Institute, 2020; [PERSON] & [PERSON], 2020; [PERSON] et al., 2021).
In our analysis, the PM\({}_{2.5}\) disease burden declines by 9% from a peak of 2,091,100 (95 UI: 1,925,000-2,252,000) premature deaths per year in 2012 (bottom\(-\)up estimate) to 1,903,300 (95 UI: 1,745,100\(-\)2,057,800) premature deaths per year in 2020 (measurement\(-\)informed estimate, Figure 2h). This is less than the concurrent 36% decline in PM\({}_{2.5}\) exposure (Figure 2e), due to the non\(-\)linear exposure\(-\)outcome association and population aging.
Figure 2.— Changes in emissions, air quality, and health impacts in China over 2010\(-\)2020. The bottom\(-\)up estimates use emissions from [PERSON] et al. (2018) for 2010\(-\)2017. The measurement\(-\)informed estimates are from the emulators for 2015-2020 using the mean of the top 1,000 occurring emission configurations that match the measured trend in fine particulate matter (PM\({}_{2.5}\) annual\(-\)mean) concentrations only. Results are for (a) mean emission changes relative to 2015 across all species, (b) mean PM\({}_{2.5}\) concentrations at observation locations, (c) mean ozone (\(\mathrm{O}_{3}\), maximum 6\(-\)monthly\(-\)mean daily\(-\)maximum 8\(-\)hour, 6 mDMbh) concentrations at observation locations, (d) sectoral contributions to PM\({}_{3.5}\) exposure, (e) national PM\({}_{3.5}\) exposure, (f) national \(\mathrm{O}_{3}\) exposure, (g) sector\(-\)specific premature mortalities (MORT) from PM\({}_{2.5}\) exposure using the attribution method, (h) annual MORT from PM\({}_{2.5}\) exposure, and (i) annual MORT from \(\mathrm{O}_{3}\) exposure. Factors are residential (RES), industrial (IND), land transport (TRA), agricultural (AGR), and power generation (ENE) emissions. Results are added from various previous studies ([PERSON] & [PERSON], 2019; [PERSON] et al., 2019; GBD 2019 Risk Factors Collaborators, 2020; [PERSON] et al., 2021; Health Effects Institute, 2020; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON], [PERSON], et al., 2020; [PERSON] & [PERSON], 2020; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2019; [PERSON] et al., 2021).
Most previous studies find a reduction in PM\({}_{2.5}\) disease burden due to reduced PM\({}_{2.5}\) exposure ([PERSON] et al., 2019; [PERSON] et al., 2021), with a larger trend in studies that did not account for population aging ([PERSON] and [PERSON], 2019; [PERSON] et al., 2020; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2019). We estimate that if population age, count, and baseline health were kept constant at 2012 rates, then the PM\({}_{2.5}\) disease burden in 2020 would have reduced by 22% relative to 2012. The population count in China grew by 5% over 2010-2020. If the population count did not increase beyond 2010 levels, then we estimate that the disease burden in 2020 would have been 7% smaller.
In contrast, some previous studies found that the impact on the disease burden from population aging outweighed that from exposure reductions. For example, the GBD 2019 Risk Factors Collaborators (2020) found that the PM\({}_{2.5}\) disease burden increased by 13% over 2012-2019 and [PERSON] et al. (2020) found that the PM\({}_{2.5}\) disease burden increased by 10% over 2012-2017. The increasing disease burden in these studies, in comparison to the reducing disease burden in this study, is primarily due to their smaller exposure reductions of 19% for GBD 2019 Risk Factors Collaborators, (2020) and 10% for [PERSON] et al. (2020).
Based on the bottom-up emissions, the national disease burden associated with O\({}_{3}\) exposure in 2010 is 53,200 (95 UI: 38,400\(-\)67,700) premature deaths per year (Figure 2i). This disease burden remains approximately the same in the bottom-up (until 2017) and measurement-informed (until 2020) estimates. Previous studies found the national disease burden from O\({}_{3}\) exposure increased over 2015-2017, primarily from increased exposure ([PERSON] and [PERSON], 2019; GBD 2019 Risk Factors Collaborators, 2020; [PERSON], [PERSON], et al., 2020). The health impact assessments in previous studies use a wide range of exposure estimation methods, exposure-outcome associations, and input data.
### Emission Sector Contributions to Exposure Over 2010\(-\)2020
At the PM\({}_{2.5}\) exposure peak in 2012 (bottom-up) of 52.8 ug m\({}^{-3}\), the sector contributions are 31% from industrial, 22% from residential, 4% from land transport, 3% from agriculture, and 2% from power generation emissions (Figure 3). Over 2012 (bottom-up) to 2020 (measurement-informed), when PM\({}_{2.5}\) exposure decreased by 36% to 33.5 ug m\({}^{-3}\), the contributions reduce in industry to 15% (\(-\)15% points) and in residential to 17% (\(-\)4% points), while remaining approximately the same in land transport, agriculture, and power generation emissions (Figure 3). The PM\({}_{2.5}\) exposure reductions are largest in East and North China. The substantial reduction in PM\({}_{2.5}\)
Figure 3: Sectoral contributions to ambient fine particulate matter (PM\({}_{2.5}\), annual–mean) concentrations and exposure in China for 2012, 2020, and 2020 minus 2012. The results for 2012 are the bottom–up estimate using emissions from [PERSON] et al. (2018). The results for 2020 are the measurement–informed estimate from the emulators using the mean of the top 1,000 occurring emission configurations that match the measured trend in PM\({}_{2.5}\) concentrations only. The rows are for the years of 2012, 2020, and 2020 minus 2012. The row annotations (far left) show the PM\({}_{2.5}\) exposure for these years, with the percentage change for 2020 minus 2012. The columns are for the PM\({}_{2.5}\) concentrations per sector of residential (RES), industrial (IND), land transport (TRA), agricultural (AGR), and power generation (ENE) emissions. The columns annotations (above each map) show the absolute and percentage attribution of PM\({}_{2.5}\) exposure to that sector for 2012 and 2020, and the percentage change between these for 2020 minus 2012.
concentrations from industrial sources over 2012-2020 (\(-\)11.3 \(\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro}\)g m\({}^{-3}\)) means that residential emissions make the largest contribution to PM\({}_{2.5}\) exposure in 2020, despite the 5.8 \(\mathrm{\SIUnitSymbolMicro\SIUnitSymbolMicro}\)g m\({}^{-3}\) reduction in this sector.
Industrial, residential, energy generation, land transport, and agriculture emissions together contributed 62% of PM\({}_{2.5}\) exposure in 2012 (bottom-up), declining to 40% in 2020 (measurement-informed). This means the contribution to PM\({}_{2.5}\) exposure from other sources increased from 38% to 60% over 2012-2020 (Figure 2d). These other sources include other anthropogenic sources inside China such as shipping, aviation, and agricultural fires, anthropogenic emissions outside China, and natural emission sources. Previous studies have estimated that dust contributes up to 10% of PM\({}_{2.5}\) concentrations in China ([PERSON] et al., 2021; [PERSON] et al., 2017; [PERSON] et al., 2011), waste combustion up to 9% ([PERSON] et al., 2021), fires up to 8% ([PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2017), biogenic secondary organic aerosol (SOA) up to 8% ([PERSON] et al., 2017; [PERSON] et al., 2017), anthropogenic emissions outside China up to 3% ([PERSON] et al., 2020), shipping up to 3% ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2019), aviation up to 1% ([PERSON] et al., 2019; [PERSON] et al., 2017), and sea salt up to 1% ([PERSON] et al., 2017). This would suggest the importance of other anthropogenic emission sources inside China (21% including fire as an anthropogenic source) and natural emissions (19%), with a smaller contribution from anthropogenic sources outside China (3%).
We estimate the reduction in PM\({}_{2.5}\) exposure over 2012-2020 results in 187,800 (95 UI: 179,900\(-\)194,200) fewer premature deaths per year in 2020 (subtraction method). Most of these public health benefits are from reductions in industrial emissions (58%), then residential emissions (29%), with smaller contributions from reductions in land transport (4%), agriculture (3%), and power generation (3%) emissions.
[PERSON], [PERSON], et al. (2020) found that the sector attributions to PM\({}_{2.5}\) concentrations over 2010-2015 reduced in industry from 38% to 35% and in power generation from 8% to 6%, increased in agriculture from 22% to 23%, and remained the same in residential emissions at 25% (Figure 2d). We find a similar decrease in the attribution to industry (from 31% to 28%), while the attribution to other sectors remained approximately the same (residential at 21%, land transport at 4%, agriculture at 3%, and power generation at 2%). The PM\({}_{2.5}\) disease burden from [PERSON], [PERSON], et al. (2020) was the total of the contributions from the power, industry, residential, transportation, and agriculture sectors, and did not include other sources. [PERSON], [PERSON], et al. (2020) found that most of the reduction in the PM\({}_{2.5}\) disease burden were attributed to reductions in industrial emissions with 63,700 (95 UI: 55,800\(-\)70,400) fewer premature deaths (attribution method), similar to our estimate of 110,100 (95 UI: 105,500\(-\)113,900) fewer premature deaths (Figure 2g).
We estimate that national PM\({}_{2.5}\) exposure could meet the World Health Organization (WHO) Interim Target 2 (25 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)) (World Health Organization, 2021) by reducing residential and industrial emissions by 80% below 2020 emissions (equivalent to a 88-92% reduction in 2015 emissions). Regional PM\({}_{2.5}\) exposure varies under this scenario, where it is lower in the Greater Bay Area (16.2 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)) and South West China (17.1 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)), and higher in North China (30.2 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)). These emissions reductions would reduce the 2020 national disease burden associated with PM\({}_{2.5}\) exposure by 23%, avoiding a further 440,800 (95 UI: 424,200\(-\)444,500) premature deaths each year. The WHO Interim Target 2 (25 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)) is the lowest attainable target from changes solely in these five emission sectors. Removing emissions from the five sectors in China does not enable the attainment of the WHO Annual Guideline (5 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\)) due to the remaining emissions from shipping, aviation, waste combustion, and agricultural fires, emissions from outside China, and emissions from natural sources including forest fires, mineral dust, and vegetation (biogenic SOA).
## 4 Conclusion
We used emulators to explore how different emission sectors have contributed to air quality and public health changes in China over 2010-2020. We show that national PM\({}_{2.5}\) exposure peaked in 2012 at 52.8 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\), then declined by 36% to 33.5 \(\mathrm{\SIUnitSymbolMicro}\)g m\({}^{-3}\) in 2020. The associated PM\({}_{2.5}\) disease burden declined from 2,091,100 (95 UI: 1,925,000\(-\)2,252,000) premature deaths in 2012 to 1,903,300 (95 UI: 1,745,100\(-\)2,057,800) premature deaths in 2020. This 9% reduction (187,800, 95 UI: 179,900\(-\)194,200, fewer premature deaths per year in 2020) would have been larger if it were not for an aging population. Most of these public health benefits are from reduced industrial (58%) and residential (29%) emissions. The contribution from other sources to PM\({}_{2.5}\) exposure increases from 38% to 60% over 2012-2020.
Our work highlights the challenges faced by China to further improve air quality and public health. Despite the National Air Quality Target (35 \(\mu\)g m\({}^{-3}\)) being met at the national level in 2020, the disease burden from PM\({}_{2.5}\) exposure remains substantial. Reducing national mean PM\({}_{2.5}\) exposure below the WHO Interim Target 2 (25 \(\mu\)g m\({}^{-3}\)) would require 80% reductions in both residential and industrial emissions, which would avoid 440,800 (95 UI: 424,200-444,500) premature deaths each year. China has implemented strategies to reduce emissions in the power generation, industrial, and land transportation sectors, achieving large reductions in PM\({}_{2.5}\) exposure. However, the recent strategy for tackling residential emissions has focused on North China ([PERSON] et al., 2020). The expansion of these strategies to South China could provide substantial health benefits ([PERSON], [PERSON], [PERSON], [PERSON], et al., 2021). For example, removing residential emissions could reduce PM\({}_{2.5}\) exposure by 22% in South West China, 19% in South Central China, and 8% in the Greater Bay Area (GBA). Our work emphasizes the importance of further reductions in industrial and residential emissions and the need for policy to address a broader range of pollution sources.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Code to setup and run WRFChem (using WRFotron version 2.0) is available through Conibear and Knote (2020). Emulator code and data is available through Conibear (2021). The trained emulators per grid cell in China that support the findings of this study are available in Conibear, [PERSON], [PERSON], [PERSON], [PERSON], et al. (2022).
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Code to setup and run WRFChem (using WRFotron version 2.0) is available through Conibear and Knote (2020). Emulator code and data is available through Conibear (2021). The trained emulators per grid cell in China that support the findings of this study are available in Conibear, [PERSON], [PERSON], [PERSON], [PERSON], et al. (2022).
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Code to setup and run WRFChem (using WRFotron version 2.0) is available through Conibear and Knote (2020). Emulator code and data is available through Conibear (2021). The trained emulators per grid cell in China that support the findings of this study are available in Conibear, Reddington, [PERSON], [PERSON], [PERSON], et al. (2022).
## Data Availability Statement
Code to setup and run WRFChem (using WRFotron version 2.0) is available through Conibear and Knote (2020). Emulator code and data is available through Conibear (2021). The trained emulators per grid cell in China that support the findings of this study are available in Conibear, Reddington, [PERSON], [PERSON], [PERSON], et al. (2022).
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## Erratum
In the originally published version of this article, the author neglected to include a second source of funding. The Natural Environment Research Council had been added to the acknowledgments. No other changes were made and this may be considered the version of record. | wiley | Emission Sector Impacts on Air Quality and Public Health in China From 2010 to 2020 | Luke Conibear, Carly L. Reddington, Ben J. Silver, Ying Chen, Stephen R. Arnold, Dominick V. Spracklen | https://doi.org/10.1029/2021gh000567 | 2,022 | CC-BY |
wiley/ff858e6f_ef61_47e3_a491_93a8e8b7e9b2.md | Parameterizing the Response of Vegetation Cover to Water Limitation in Africa Using Geostationary Satellites
[PERSON]
1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
[PERSON]
1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
[PERSON]
1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
[PERSON]
3 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
[PERSON]
1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
[PERSON]
1 Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, Jena, Germany, 2 Hydro-Climate Extremes Lab (H-CEL), Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium, 3 Departamento de Ciencias e Engenharia do Ambiente, CENSE, Faculdade de Ciencias e Tecnologia, Universidade NOVA de Lisboa, Caparica, Portugal
###### Abstract
Hydrological interactions between vegetation, soil, and topography are complex, and heterogeneous in semi-arid landscapes. This along with data scarcity poses challenges for large-scale modeling of vegetation-water interactions. Here, we exploit metrics derived from daily Meteostat data over Africa at ca. 5 km spatial resolution for ecohydrological analysis. Their spatial patterns are based on Fractional Vegetation Cover (FVC) time series and emphasize limiting conditions of the seasonal wet to dry transition: the minimum and maximum FVC of temporal record, the FVC decay rate and the FVC integral over the decay period. We investigate the relevance of these metrics for large scale ecohydrological studies by assessing their co-variation with soil moisture, and with topographic, soil, and vegetation factors. Consistent with our initial hypothesis, FVC minimum and maximum increase with soil moisture, while the FVC integral and decay rate peak at intermediate soil moisture. We find evidence for the relevance of topographic moisture variations in arid regions, which, counter-intuitively, is detectable in the maximum but not in the minimum FVC. We find no clear evidence for wide-spread occurrence of the \"inverse texture effect\" on FVC. The FVC integral over the decay period correlates with independent data sets of plant water storage capacity or routing depth while correlations increase with aridity. In arid regions, the FVC decay rate decreases with canopy height and tree cover fraction as expected for ecosystems with a more conservative water-use strategy. Thus, our observation-based products have large potential for better understanding complex vegetation-water interactions from regional to continental scales.
keywords: Modeling Earth Systems +
Footnote †: journal: Advances in Modeling Earth Systems
et al., 2005, 2008; [PERSON]. [PERSON] et al., 2019). Moreover, evidence suggests that ecosystem functioning--even in the wettest part of the continent, the central African tropical forest--responds to soil moisture fluctuations ([PERSON] et al., 2013; [PERSON] et al., 2013) along with co-limitations of other factors such as radiation ([PERSON] et al., 2019). Within the complex rainfall seasonality patterns having unimodal, bimodal or trimodal regimes, less than 5% of the continent is reported to be non-seasonally humid ([PERSON] and [PERSON], 2011).
Soil moisture is the critical variable that characterizes the water limitation of vegetation ([PERSON] et al., 2001), which, in turn, shapes land-atmosphere exchanges of carbon, water, and energy fluxes ([PERSON] et al., 2012), phenology ([PERSON] et al., 2004), and vegetation functional traits ([PERSON] et al., 2015; [PERSON]. [PERSON] et al., 2019), along with their species or biome distribution ([PERSON] et al., 2016). Rainfall is the primary source of moisture but plant available water in drylands is characterized by non-trivial and complex ecohydrological processes that control the availability of moisture from secondary sources ([PERSON] et al., 2019). Overall, comprehensive understanding on multiple ecohydrological processes is needed to understand land-atmosphere interactions under water limitation.
In order to address this problem in a systematic way, [PERSON] et al. (2017) conceptualized three critical ecohydrological junctures: (a) infiltration versus overland flow, (b) soil evaporation versus transpiration, and (c) root water uptake versus drainage, that are all centered around the hydrological response of the ecosystem. Beyond precipitation intensity, topography, and soil properties, the first juncture is affected by presence of vegetation patches that interact with overdland flow causing the typical runoff-runon dynamics at hillslope-scale ([PERSON] et al., 2005). The second juncture, partitioning of terrestrial evaporation, is critical as an interplay between biological activity and productivity, and physical water losses by direct evaporation. Vegetation transpiration generally dominates terrestrial evaporation ([PERSON] et al., 2017), and the partitioning is controlled more by vegetation and soil characteristics given the climate ([PERSON] et al., 2020), highlighting a pivotal role of vegetation. The third juncture within the root zone is largely controlled by below-ground vegetation properties, such as depth and distribution of roots, that control the soil-plant hydraulics continuum. Deep rooting facilitates access to a larger moisture reservoir, a frequently observed trait in savanna and woodland ecosystems ([PERSON], 2008; [PERSON] and [PERSON], 1998). In fact, the diversity and complementarity of ecohydrological plant traits by different species within ecosystems was shown to determine resilience to drought ([PERSON] et al., 2018) and to maximize plant water use ([PERSON] et al., 2009; [PERSON] et al., 2005).
There are further ecohydrological phenomena that should be considered when exploring vegetation-water interactions, emerging from non-monotonic ecosystem responses to episodic events, and ephemeral waterbodies occurring across spatial scales. Non-monotonic effects of soil properties on the interaction between climatological aridity and vegetation can lead to the frequently observed \"inverse texture effect\" in arid climates, whereby sandy soils appear to be associated with less water stress compared to clay soils, due to their higher infiltration capacity ([PERSON], 1973). Additionally, dryland ecosystems locally return nearly all rainfall back to atmosphere as terrestrial evaporation ([PERSON] et al., 2006) with very little water draining from the root zone to groundwater ([PERSON] et al., 2017), except extreme rainfall events that episodically recharge aquifers ([PERSON] et al., 2013; [PERSON] et al., 2016). Moreover, riparian processes such as river channel losses from ephemeral rivers can provide critical source of moisture ([PERSON] and [PERSON], 2013; [PERSON] and [PERSON], 2005; [PERSON], 2000; [PERSON] et al., 2018). Riparian corridors and groundwater-fed valleys, therefore, often appear as \"green islands\" ([PERSON] et al., 2015), where access to the shallow groundwater supports vegetation activities. In such ecosystems, the growing season may continue several months after the rain season has ceased while the trees appear to have access to groundwater via deep roots or recharge their trunks with water during these times ([PERSON], [PERSON], et al., 2014; [PERSON] et al., 2018).
Previous studies, therefore, provide clear evidence that vegetation functions are controlled by moisture availability in non-humid climate, with moisture availability, itself, emerging from the complex interplay among climate characteristics, vegetation traits, hillslope topography, soil properties, and presence of secondary moisture sources, for example, aquifers. In fact, incorporation of all these ecohydrological factors poses a challenge for land-surface modelers ([PERSON] et al., 2015; [PERSON] and [PERSON], 2020). Relatedly, models overestimate sensitivity between ecosystem productivity and precipitation in annual scales, which increases uncertainty in climate models against drought conditions ([PERSON] et al., 2021). Moreover, disagreements within models become larger with stronger water limitation, where parametrization of plant water stress is non-standard and often ignores soil texture properties ([PERSON] et al., 2020). Consequently, models fall short on capturing ecosystem exchange in annual and interannual time scales ([PERSON] et al., 2021), where authors suggest improvements in simulating vegetation responses to changes in water availability. Another main limitation for models is the specification of Rooting Depth (RD) ([PERSON] et al., 2019). Over recent years, several studies have put forward estimations of the rooting depth or Effective Rooting Depth (ERD) that represents the potential moisture access of the vegetation. A comparison of different estimates, though, reveals a large uncertainty with rooting depth varying from a few centimeters to tens of meters for a given location ([PERSON] et al., 2016). This, in part, is caused by the underlying assumptions in the estimation methods, whose effect on the prediction cannot be constrained by or validated against observations, especially in data scarce regions like Africa. Considering the particular difficulties associated with below-ground observation of ecosystem and land properties at large-scales, remotely sensed products of vegetation characteristics, indices, and responses provide opportunities to back infer the underlying environmental factors and land surface characteristics.
Remote sensing vegetation indices has been extensively used to capture phenological states of vegetation, such as detecting onset and length of growing season or peak greenness, as well as specific agricultural applications (reviewed in [PERSON] et al. (2020)). Moreover, the temporal dynamics of vegetation indices can be exploited to understand ecologically relevant concepts such as land cover effects on vegetation dynamics ([PERSON] et al., 2017), early green-up of woody vegetation in Africa ([PERSON] et al., 2019; [PERSON], [PERSON], et al., 2014; [PERSON] et al., 2020), effects of plant water storage ([PERSON] et al., 2018), and early diagnosis of climate-induced forest mortality ([PERSON] et al., 2019). The majority of vegetation remote sensing studies focusing on Africa are based on image acquisitions from polar orbiting satellites like MODIS ([PERSON] et al., 2016), while only a few studies are based on vegetation indices derived from the geostationary satellite Meteosat Second Generation (MSG; e.g., [PERSON], [PERSON], et al., 2014; [PERSON] et al., 2017). Geostationary satellite based vegetation indices are available in daily temporal resolution, which is their biggest advantage compared to polar orbiting satellites where such high resolution in time is not possible.
In this study, we analyze the daily Fraction of Vegetation Cover (FVC) time series from MSG to infer the coohydrological characteristics of ecosystems over Africa. We derive a set of coohydrological metrics from the vegetation decay period, and evaluate their spatial patterns. Our overarching hypothesis is that these metrics, derived from the vegetation dynamics over decay periods, contain valuable information on plant water access, presence of secondary moisture sources, and other coohydrological processes, which are modulated by climate, topography, soil properties, groundwater access, as well as vegetation traits and scales. The coohydrological metrics include (a) robust estimates of the minimum and maximum FVC, (b) FVC integral over the decay period, and (c) the exponential decay rate during dry-down. Using the metrics, we evaluate several hypotheses that encompass the coohydrological characteristics of moisture-limited ecosystems and the influence of environmental factors and land characteristics therein, such as:
1. In arid regions, minimum and maximum FVC are larger in sandy soil while this covariation is inverted in semi-arid and humid regions. This hypothesis follows the \"inverse texture effect\" ([PERSON], 1973) often reported in drylands.
2. Within similar climatic aridity, secondary moisture sources increase the minimum FVC and decrease seasonal FVC range. This hypothesis is derived from the classical approach of mapping groundwater-dependent ecosystems--with shallow water table or potentially larger runoff due to topography--as \"green islands\" of attenuated seasonality ([PERSON] et al., 2015).
3. The time integral of FVC over the decay period as a proxy for plant accessible water storage is larger in semi-arid regions where the water deficit (the difference between precipitation and potential transpiration) is marginally smaller at annual scales than at seasonal scales, compared to arid regions. This hypothesis follows the theory that vegetation expands root zone storage capacity to compensate water deficit during dry season ([PERSON] et al., 2016), parallel to the expected optimal RD of plants considering cost and benefit of developing root structure ([PERSON], 2010).
4. FVC decay rate driven by progressive water limitation becomes lower with increasing aridity, tree cover and canopy height. This hypothesis assumes FVC mimics the decay rate of land evaporation during decay period and follows previously reported increase in timescale of land evaporation decay with aridity, canopy height, and woody vegetation ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2006). Therefore, FVC decay rate would reflect adaptations of ecosystem water use strategies.
We approach the analysis first by looking at the continental scale variations of the metrics, together with climatic aridity as the first order driver. This covariation is further scrutinized with other environmental factors relevant to the hypotheses given above. As aridity metric we chose mean annual root-zone soil moisture from the Global Land Evaporation Amsterdam Model (GLEAM).
To derive the ecohydrological metrics for the African continent from high-resolution remote sensing data (Section 2), we developed a robust methodology (Section 3) to deal with noise, gaps, widely varying dynamics, and data size. The quality diagnostics along with the derived metrics and discussion of underlying mechanisms (Section 4), and open code for derivations, enables future advances in understanding and modeling ecohydrological processes and variability. Furthermore, initial analysis and corroboration with independent data illustrates the potential of applications of the ecohydrological metrics (Section 4). Finally, we close the manuscript with a summary of the study and potential outlook (Section 5).
## 2 Data
### Fraction of Vegetation Cover
The FVC, derived from a spectral mixture analysis of the satellite retrievals, is a vegetation index summarizing the two-dimensional coverage ratio of vegetation per unit land area ([PERSON] et al., 2011). With a range of [0, 1, 1], FVC is often used to derive fundamental vegetation indices such as the Leaf Area Index. The FVC product used in this study, officially labeled as LSA-421 (MDFVC), was obtained from the Satellite Application Facility for Land Surface Analysis (LSA-SAF) of the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT). The product is based on the retrievals of the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor on board the MSG satellite ([PERSON] et al., 2011). As a geostationary satellite, the MSG has a circular spatial coverage of Earth centered at 0' longitude, and it covers Europe and Africa entirely (see an example of the original FVC data for a day in Figure A1). The SEVIRI is a multispectral optical sensor with 12 spectral bands, and a temporal resolution of 15 min. Under the sub-satellite point (nadir), it has 3.1 km spatial resolution in the normal bands, and a high-resolution band with 1 km spatial resolution. The spatial resolution of the retrieval decreases with increasing distance from nadir.
The FVC data product is available at daily temporal resolution spanning the time period from early 2004 to present. FVC is estimated using parameters of a bidirectional reflectance distribution function on the cloud-corrected top of canopy reflectance values of three spectral channels namely red, near-infrared, and middle-infrared ([PERSON] et al., 2019; LSA-SAF, 2016). Thanks to the very high temporal resolution of the SEVIRI sensor, spatial consistency of cloud-free data is ensured by the data providers ([PERSON] et al., 2011), which is also confirmed by studies comparing enhanced vegetation index products of SEVIRI and MODIS across the Congo Basin ([PERSON] et al., 2016). Further details of the product, and access to downloading data are available at [[https://landsaf.ipma.pt/en/products/vegotation/fvc/](https://landsaf.ipma.pt/en/products/vegotation/fvc/)]([https://landsaf.ipma.pt/en/products/vegotation/fvc/](https://landsaf.ipma.pt/en/products/vegotation/fvc/)).
For this study, we selected the spatial domain as the African continent. In order to convert the product into equal width grids to facilitate analyses with other products, we resampled the original data to a spatial resolution of 0.0417\({}^{\circ}\) (ca. 5 km) via nearest neighbor (using gdalwarp function in GDAL, GDAL/OGR contributors, 2020). In terms of temporal domain, we used nearly 16 years of data, from the beginning of the records in 2004, to the end of 2019.
### Ancillary Data
#### 2.2.1 Soil Moisture
We used the third version of GLEAM estimates of root-zone soil moisture ([PERSON] et al., 2017; [PERSON] et al., 2011). GLEAM consists a set of modules to estimate different components of land evaporation simultaneously. Therefore, the model estimates multiple products including root-zone soil moisture (hereafter referred to as soil moisture). Among the input data of the model, precipitation may have relatively low quality over Africa due to lower density of rain gauges across the continent. However, the model assimilates satellite based soil moisture, which is known to be of the best quality in semi-arid regions with sparse vegetation. GLEAM data is available at 0.25\({}^{\circ}\) space and at daily resolution in time from 2003 up to date with a small latency. We used mean value of daily estimates from 2004 to 2019 (parallel to the temporal domain of FVC data used) as a diagnostic for average climatological aridity in Section 4. Additionally, we used daily values to compute temporal correlation between soil moisture and FVC, after aggregating original FVC data into 0.25\({}^{\circ}\) by simple averaging (see Appendix D for spatial variation of correlation values).
#### 2.2.2 Sand Content of Soil
In order to quantify effects of soil texture, we used gridded sand percentage of soil data from SoilGrids data set ([PERSON] et al., 2017), which is a machine learning based interpolation of soil profiles at 250 m resolution. SoilGrids data set is available globally and provides information from different layers, ranging from surface to 2 m depth. Though in this study, for interpretability, we used the average of the top five layers that are not deeper than 1 m for interpretability, and used the data at 0.0417\({}^{\circ}\) after aggregating by simple averaging.
#### 2.2.3 Height Above Nearest Drainage
To relate the variation of the metrics to meso-scale heterogeneity and convergence of moisture caused by topography, we used the Height Above Nearest Drainage (HAND) data from [PERSON] et al. (2019). Quantifying the vertical distance of a given point to the nearest drainage, HAND is closely related to drainage topology and hillslope-scale convergence of soil moisture and groundwater ([PERSON] et al., 2011). The HAND data used here is based on the MERIT digital elevation model at a spatial resolution of 3-arc second (ca. 90 m). We used the original high-resolution data after aggregating (simple average) to the resolution of the ecohydrological metrics presented in this study (0.0417\({}^{\circ}\)).
#### 2.2.4 Topographic Wetness Index
In order to understand the runoff related effects of topography, we used Topographic Wetness Index (TWI), also known as compound topographic index. Being a function of both slope and the upstream area that potentially contribute to runoff of a given point, TWI is a metric to diagnose topography-induced effects on water cycle at hillslope scales. Even though HAND and TWI are both topography related metrics, TWI, being a function of upstream area and slope of a given point, is a proxy for runoff, while HAND is a proxy for water table depth. We used TWI data from [PERSON] et al. (2020), which is computed by using the MERIT digital elevation model at 3-arc seconds, as in the case of HAND. In order to account for the high variability of TWI at hillslope scales while aggregating the data into 0.041 7\({}^{\circ}\), we first calculated median TWI value of the domain (0.069). Then, we aggregated the TWI values by calculating percentage of sub-grid cells having larger TWI values than the median value computed in the first step. Eventually, similar to TWI itself, larger values in the normalized TWI means larger potential runoff due to topographic complexity.
#### 2.2.5 Accessible Water Storage Capacity and Rooting Depth
We used multiple proxies of plant accessible water to understand their effects on vegetation dynamics. Effective RD (ERD, [PERSON] et al., 2016) is one of those products, which is natively at 0.5\({}^{\circ}\) spatial resolution. ERD comes from a global parametrization of a process-based, analytical model of carbon costs and benefits of deeper rooting in plants, proposed by [PERSON] (2008). In this model, the cost of deeper roots is estimated considering the physical structure of roots like density and length together with root respiration, while the benefit is estimated considering water use efficiency, growing season length and mean transpiration rate per rooting depth. In order to parametrize the model, root and soil properties were obtained from the literature, water use efficiency from an ensemble of process based models while climatological information from a long-term mean of remote sensing based products.
In addition, the RD product from [PERSON] et al. (2017) is also used in this study. RD is estimated with inverse modeling of root water uptake profiles in three steps, where first soil water profile, as the supply, is estimated using climate, soil properties and topography. Thanks to the availability of high-resolution information on soil and topography, RD has a much higher spatial resolution (0.0083\({}^{\circ}\), ca. 1 km) than the other products. After estimation of plant water demand using atmospheric conditions and leaf area index, the supply is allocated as root water uptake using Ohm's law at different soil depths, where amount of infiltration, groundwater recharge, and subsequent uptake were effected ([PERSON] et al., 2017). Note that the model includes multiple forcing data, with a temporal coverage from 1979 to the time of the study.
Apart from the rooting depth products, we also used estimates of plant water storage capacity. Accessible Water Storage Capacity (AWSC, [PERSON] et al., 2019) is derived at 0.25\({}^{\circ}\) by assimilating an ecohydrological model (World-Wide Water, [PERSON] et al., 2013) with different remote sensing based water observations, namely surface water extent, near-surface soil moisture and variations of terrestrial water storage. World-Wide Water is a process based model using atmospheric conditions, containing three soil layers to simulate vegetation access to soil moisture, which also accounts for recharge and discharge from groundwater. Due to the temporal availability of the forcing data, AWSC product is derived using 6 years of data starting from 2010.
The forth and last product used to analyze plant AWSC is the Root Zone Storage capacity (\(RZS_{CR2}\), [PERSON] et al., 2016) product derived by contrasting water fluxes observed by remote sensing, precipitation and irrigation as influx, and evaporation as outflux. Owing the assumption that plants develop their roots to optimize their root zone storage capacity, and using a simple approach on water fluxes, [PERSON] et al. (2016) did not use any external information on vegetation or soil properties. While different precipitation data are used as forcing data with different drought return periods, we used the final product forced by Climate Research Unit precipitation data (CRU TS3.22, [PERSON] et al., 2014) with the shortest return period, 2 years. \(RZS_{CR2}\), which is derived using data from 2003 to 2013, is available at 0.5\({}^{\circ}\) spatial resolution.
For a consistent comparison across data at different resolutions, we aggregated all data to a common spatial resolution of 0.5\({}^{\circ}\) by simple averaging. Note that the spatial aggregation may result in loss of the spatial variability prevalent locally and potentially captured at a high resolution. Moreover, we only used the grid cells that all products have an estimate.
#### 2.2.6 Canopy Height
Since canopy height is an important indicator of ecosystem functions and is associated mostly with water limitation ([PERSON] et al., 2016), we analyzed the effects of canopy height on the decay rate of vegetation cover through their covariation in space. We used the lidar-derived canopy height data from the retrievals of the ICESAT satellite at a spatial resolution of 1 km ([PERSON] et al., 2011). We used the data after aggregating (simple average) to 0.0417\({}^{\circ}\).
#### 2.2.7 Tree Cover
We used tree cover data in order to analyze the sensitivity between the relationship of decay rate of FVC and climatological aridity. We used the tree percent component of the MOD44B Version 6 Vegetation Continuous Fields from MODIS ([PERSON] et al., 2015), which is available globally in 250 m spatial and annual temporal resolution. We aggregated the product in space to the target resolution of this study by taking the mean of higher resolution grid cells. Finally, we used the median tree cover value over the years covering the temporal domain of FVC data to obtain a time invariant metric, same approach taken for the annual estimates of the metrics derived from FVC (see Section 3).
## 3 Methodology
The derivation of the ecohydrological metrics is based exclusively on the daily FVC time series. The method can be divided into four main steps: (a) masking and retrieval of minimum and maximum FVC (\(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\)), (b) detection of start and end of the decay periods, (c) estimation of the decay period FVC integral (\(I_{\text{J,b}}\)), and (d) estimation of the FVC decay rate during dry-down (\(\lambda\)). Each methodological step is described in detail in the following subsections together with the final products, and their quality diagnostics when needed.
### Masking and Retrieval of FVC Extrema
To remove the effect of outliers within a time series, we selected the 2 nd and 98 th percentiles of the entire records of the FVC data as the minimum (\(\text{FVC}_{\text{min}}\)) and the maximum asymptotic values (\(\text{FVC}_{\text{max}}\)). To maintain a reliable signal-to-noise ratio before taking further steps, we filtered out any grid cell if \(\text{FVC}_{\text{max}}<0.1\) or more than one-third of the time series were missing. Due to the simplicity of the derivation of \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) metrics, quality diagnostics were deemed unnecessary, and not derived in this set of metrics.
### Detection of Decay Periods
The detection of the decay period was based on a procedure using the first derivative of the smoothed FVC (\(V\)) (see Algorithm 1). We smoothed daily time series of the FVC with a 31-day moving average (\(V_{\text{min}}\)). Then each day in the time series was marked as decay, growth or stable. To do so, we set two thresholds for decay and growth periods as \(H_{\text{decay}}\) and \(H_{\text{growth}}\), respectively. After rigorous investigation of time series of individual grid cells, we used the 75 th and 70 th percentiles of the negative derivative (\(V\)) as thresholds \(H_{\text{decay}}\) and \(-H_{\text{growth}}\) for each grid cell. The magnitude \(H_{\text{decay}}\) is, thus, bigger than \(H_{\text{growth}}\), in accordance with the larger gradient in the beginning of the period than the end. Only the magnitude of \(H_{\text{growth}}\) was taken as a positive threshold to detect the increase in FVC.
An observation was considered as decay if \(V<H_{\text{decay}}\) growth if \(V>H_{\text{growth}}\) and stable if \(H_{\text{decay}}\leq V\leq H_{\text{growth}}\). The resulting time series of classes (decay, growth, or recovery) were then smoothed by retaining the majority of decay and stable against recovery within a 5-day moving window. Complete decay period, which is considered as the initial decay period followed by a stable, non-increasing period, was then identified as the period from the beginning of a decay to the end of a stable period. In order to ensure robustness of the end of the stable period, especially in hyper-arid regions with poor signal-to-noise ratio, we extended the detected decay periods until the next significant increase in \(V_{\text{sim}}\) (>5% of the corresponding seasonal amplitude of FVC). Note that selection of the thresholds and the moving window sizes were based on extensive exploration and visual inspection of the FVC time series. This was a necessary step to ensure the robustness against noise in the data, as well to address the diversity of FVC dynamics across African ecosystems. To highlight the complexity, some representative time series of FVC in selected grid cells across different climatological arity are included in Appendix B, together with soil moisture and precipitation time series.
After detection of all decay periods in the time series, we only selected the longest one per calendar year. This is necessary for regions where vegetation may potentially have two growing (and decaying) seasons within a year. The longest decay period within a year is likely to be the most indicative of the largest water limitation, and the underlying ecohydrological mechanisms. When the detected decay period spanned over two calendar years, it was assigned as the decay period of the starting year. In total, the decay period detection algorithm (Algorithm 1) yielded 16,423,339 decay periods in 1,029,847 grid cells.
### Estimation of the Integral Over FVC Decay
We calculated the integral of FVC during decay period (\(I_{\text{up}}\)) as the total area under the FVC time series from the start to end of the decay period, with the area under \(\text{FVC}_{\text{min}}\) removed. This can be expressed as,
\[I_{\text{up}}=\sum_{i=1}^{deepvid}(FVC(t)-FVC_{\text{min}}) \tag{1}\]
Removal of the baseline FVC value (\(\text{FVC}_{\text{min}}\)) enhances the signal of seasonal decay of vegetation with respect to baseline vegetation activity. Note that, upon necessity, the full integral (total area under the curve) can be calculated as the sum of \(I_{\text{up}}\) and multiplication of decay period duration with minimum FVC (\(D\times\text{FVC}_{\text{min}}\)).
From the yearly dry season detection, 16 (the number of years) values of \(I_{\phi}\) were computed for each grid cell. We selected the median of the 16 values as the representative inference to be used for spatial analyses. The median was preferred over the mean to make the estimation robust against annual variations, for instance, by intermittent rain events in the dry season or issues related to FVC derivation. In addition, we also calculate and report the normalized robust Standard Error (SE) as an indicator of variability. The SE is calculated as,
\[\mathrm{SE}=\frac{\mathrm{SD}_{s}}{\sqrt{n}} \tag{2}\]
where \(\mathrm{SD}_{s}\) is the robust standard error, calculated from the Median Absolute Deviation across years (with the assumption of a normal distribution, [PERSON], 1993), and corrected for the low number of samples (\(n=16\)) as:
\[\mathrm{SD}_{s}=MAD\times 1.4826\times\frac{n}{n-1} \tag{3}\]
The robust standard error reflects variability of the metrics among years as well as methodological uncertainty, and is therefore suitable for customized filtering in the context of spatial analysis.
### Estimation of FVC Decay Rate
Temporal decay of the FVC can be characterized using an exponential function as,
\[FVC(t)=(FVC_{dt}-FVC_{\mathrm{min}})\times e^{-t/\lambda}+FVC_{\mathrm{min}} \tag{4}\]
where \(\mathrm{FVC}_{dt}\) is the initial FVC value in the beginning of a dry-down, and \(\lambda\) is the \(e\)-folding time with the same unit of the time scale (days in our case)--see Figure 1 for a graphical explanation. Note that \(\lambda\) is merely an inverse of the exponential decay rate. The formulation in Equation 4 uses \(\lambda\) as it is easier to interpret. In simple terms, \(\lambda\) denotes the number of days needed to have a decrease in the seasonal amplitude of FVC (\(\mathrm{FVC}_{dt}-\mathrm{FVC}_{\mathrm{min}}\)) to \(1/e\) of its original value during a dry-down event. Note that the selected exponential decay function explicitly takes an asymptotic minimum value of the FVC, as \(\mathrm{FVC}_{\mathrm{min}}\), into account while estimating the decay rate (see Section 3.1) since \(\mathrm{FVC}_{\mathrm{min}}\) is included in the formulation (Equation 4).
Due to the S-shaped character of temporal vegetation dynamics, functions allowing different convexity, for example, logistic functions, have been used to characterize these dynamics ([PERSON] et al., 2006). As exponential decay functions are strictly convex, the concave part of the decay, which is mostly observed in the beginning of the
Figure 1: Conceptual plot of the coohydrological metrics derived from time series using synthetic data. Points represent observations for growing period, early decay period and decay period with dry-down in light gray, gray and black, respectively. Decay and growth periods are defined by presence of decay, that is, first derivative of the time series, while dry-down period is defined by the convexity of the decay, that is, using both first and second derivatives (see Section 3.4 for details). The shaded area shows the integral of FVC during decay period. The red curve shows the fitted line on the FVC time series during dry-down using the asymptotic exponential decay function. All metrics presented in this study are shown in bold characters.
decay period, is not considered for this metric. The latter part of the decay period, with convex curvature (i.e., the first derivative is negative while the second is positive), is labeled as \"dry-down\" during the decay period. To define the dry-down period, we first discarded the time steps with concave observations (negative first and negative second derivative). Afterward, we filtered out the convex observations before the inflection point of the FVC, that mostly associated with low signal-to-noise ratio at the beginning of the dry-down. Once daily observations are marked as convex or concave, we searched for local minimum of \(V^{\prime}\) in the first third of the dry season, and identified the inflection point as the start of the dry-down. Note that, in the above process, second derivative of the FVC (\(V^{\prime}\)) was also smoothed with a 31-day moving window.
This procedure effectively removes observations with concave shape in the dry season, especially at the beginning of an event. For each event, if more than half of the data points showed convexity, we estimated \(\lambda\), together with \(\text{FVC}_{\alpha\beta}\) based on an asymptotic regression model that minimizes least squares error with the Levenberg-Marquardt algorithm ([PERSON] et al., 2016; [PERSON], 1978). We used both the Nash-Sutcliffe modeling efficiency (NSE; [PERSON] & Sutcliffe, 1970) and the standard error of the model (\(\text{SE}_{\alpha\beta}\)) to assess the estimates of the model fitting. From the multiple \(\lambda\) estimates, only those with successful convergence of the Levenberg-Marquardt algorithm with NSE \(>\)0.5 and \(\text{SE}_{\alpha\beta}(\lambda)<0.5\times\lambda\) were accepted, the median of which was taken as the representative final \(\lambda\) for a grid cell.
After defining the final \(\lambda\), we estimated the variation as done in Section 3.3. Unlike in Section 3.3, the sample size per grid cell (\(n\)) may change, as \(\lambda\) estimation may not converge in cases with high noise. We, therefore, also report the number of successful convergences of the Algorithm 2 as an additional quality diagnostic that can be used for filtering \(\lambda\) (mapped in Figure 11).
## 4 Results and Discussion
In this section, we present and discuss the coohydrorological metrics derived in this study. For each metric we show the spatial variation in continental scale by maps along with zoomed inset plots (see Appendix E for further information and visual impression by corresponding Google Earth cut-outs) to visualize regional variability. Box plots of metrics per mean annual root-zone soil moisture show first order variations while heatmaps show sensitivity of these first order variations to different parameters addressing the hypotheses given in Section 1 (see Section 2.2 for the details of the data). Here we present the metrics independently, but we summarize their cross-comparison with a density plot in Figure 11.
### FVC Extremes
Spatial distributions of \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\), histograms of the distribution over the full domain, and six zoomed insets focusing on selected regions are shown in Figures 1(a) and 1(b), respectively (see Figure 11 for the seasonal dynamics expressed as \(\text{FVC}_{\text{max}}-\text{FVC}_{\text{min}}\)). At the continental scale, both \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) follow the moisture gradient with the highest and the lowest values in humid and arid regions, respectively. Saturation in the increase of \(\mathrm{FVC_{max}}\) (Figure 2c) in semi-arid regions suggests that water does not severely limit the vegetation cover at the peak of the wet season in regions with intermediate to high mean annual soil moisture values (see Figure E1 for map of mean annual root-zone soil moisture as an indicator of climatological acidity together with Google Earth views of the insets). On the contrary, \(\mathrm{FVC_{min}}\) stays low up to intermediate mean annual soil moisture and increases only slightly with it suggesting that water limits FVC severely at the peak of the dry season. Understandably, the largest seasonal ranges in FVC are observed in regions with semi-arid climate systems.
In addition to the climate-associated large-scale gradients, the metrics also exhibit a substantial meso-scale heterogeneity. In arid regions, \(\mathrm{FVC_{min}}\) is higher in areas closer to perennial water sources, as can be seen near the Senegal and Gambaix rivers (Box-A in Figure 2a). \(\mathrm{FVC_{min}}\) is also elevated near large inland deltas and wetlands, that is, the Okavango Delta ([PERSON], 2006) and the Sudd swamp ([PERSON] et al., 2019), Box-D and Box-F in Figure 2a, respectively, presumably indicating groundwater access by the vegetation in the dry season. Interestingly, the meso-scale spatial patterns differ remarkably between \(\mathrm{FVC_{min}}\) and \(\mathrm{FVC_{max}}\) with a tendency of \(\mathrm{FVC_{max}}\) showing more spatial structure than \(\mathrm{FVC_{min}}\). This is likely because there is too little water input in the dry season to cause big topographic moisture effects for \(\mathrm{FVC_{min}}\) except for the perennial secondary water sources. Thus, such meso-scale heterogeneity suggests the importance of secondary water sources in moisture-limited systems, especially on top of the large climate-driven spatial variations, and highlights the value of \(\mathrm{FVC_{min}}\) and \(\mathrm{FVC_{max}}\) for ecohydrological studies.
#### 4.1.1 Inverse Texture Effect
Here, we tested if an \"inverse texture effect\" ([PERSON], 1973) could be observed from 5 km spatial resolution remote sensing FVC data over continental Africa on the variations of \(\mathrm{FVC_{min}}\) and \(\mathrm{FVC_{max}}\) conditioned on mean annual soil moisture and sand content of soil. In humid regions coarse textured soil is less favorable for vegetation than fine textured soil while in arid regions this pattern is inverted. This inverse texture effect has been documented by several site-scale studies ([PERSON] et al., 2001; [PERSON] et al., 2001; [PERSON] et al., 2012;
Figure 2.— (a) Minimum asymptotic values of \(\mathrm{FVC}\), \(\mathrm{FVC_{min}}\) (b) maximum asymptotic values of \(\mathrm{FVC}\), \(\mathrm{FVC_{max}}\), and (c) box plot showing the variation of \(\mathrm{FVC_{min}}\) and \(\mathrm{FVC_{max}}\) with mean annual soil moisture. In the maps, histogram of the metrics mapped can be seen inside the main panel, with a dashed line indicating the mean values of the domain, as well as six insets to show local variability (See Appendix E for details of the insets). In all of the following box plots, binning of soil moisture is done automatically to equalize frequency of observations among the bins while median values per each bin are shown in the intermediate line of the boxes, with their 95% confidence intervals notched. Upper and lower edges of the boxes show the interquartile range (75 th and 25 th percentiles, respectively) while the error bars show 1.5 times the interquartile range.
[PERSON] et al., 1988). [PERSON] (1973) suggested this inversion to occur with precipitation values of 300-500 mm/ year, although it has also been reported for higher precipitation values ([PERSON] et al., 1997). The inversion of the texture effect in arid climates is likely due to enhanced infiltration and hydraulic conductivity which reduced soil evaporation losses ([PERSON], 1973) and/or due to reduced water stress thanks to lower matrix potentials of sandy soils ([PERSON] et al., 2005).
We binned soil moisture and sand percentage values to have equal number of observations in each bin of a given variable. We than calculated the mean of \(\text{FVC}_{\text{min}}\) or \(\text{FVC}_{\text{max}}\) per soil moisture bin, and mapped the deviation from these values with changing sand percentage in Figure 3 (see Figure F1 for the heatmaps of raw \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) values). Our analysis did not show clear patterns of an inverse texture effect where FVC would be expected to increase with sand content. In the driest regions with the lowest mean annual soil moisture level, \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) are slightly elevated for low sand content, consistent with the \"normal\" texture effect. For intermediate aridity levels, no clear and systematic pattern with sand content can be observed. The temporal scale of the metrics might have hindered observing the inverted texture effect, as [PERSON] (1973) considered this effect in the context of rain pulses, which remain effective over days to weeks. Furthermore, spatial resolution and quality of the large-scale data used in this analysis may not be high enough to observe such localized effects. Despite the sound motivation, it remains for further studies to clarify the extent to which the \"inverse texture effect\" is significant and can be observed from remote sensing products across large domains.
#### 4.1.2 Green Islands
Another phenomenon we investigated are the \"green islands\" patterns where localized moisture availability supports vegetation activity in otherwise dried down conditions by analyzing variations in \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) conditioned with soil moisture, HAND and TWI. This approach has been used to detect groundwater dependent ecosystems ([PERSON] et al., 2014; [PERSON] & [PERSON], 2010; [PERSON] et al., 2011; [PERSON] et al., 2013; [PERSON] & [PERSON], 2007) or riparian corridors ([PERSON] et al., 2008; [PERSON] & [PERSON], 1990; [PERSON] et al., 1996; [PERSON], 1997) based on high spatial resolution remote sensing within relatively small regions. Here we analyze if such patterns due to secondary moisture sources are still evident at 5 km resolution and at continental scale by looking at the covariation of \(\text{FVC}_{\text{min}}\) and \(\text{FVC}_{\text{max}}\) with HAND and TWI, conditioned on mean aridity (Figure 3). HAND is a hillslope scale proxy for groundwater accessibility ([PERSON] et al., 2019) while TWI, a metric considering local slope together with upstream area, is a strong proxy for topographic soil moisture variations ([PERSON] et al., 2018). Contrary to our expectations, we did not observe a positive effect of these secondary moisture resources in arid regions on \(\text{FVC}_{\text{min}}\) (Figure 3a) but instead for \(\text{FVC}_{\text{max}}\) at high aridity levels (Figure 3b). This implies that shallow water table support vegetation with additional moisture during the growing period as also shown in [PERSON] et al. (2017) but this effect largely disappears in the dry season since most of the secondary moisture resource is also depleted or not available. This suggests that the effect of secondary moisture sources goes much beyond the frequently studied perennial \"green islands\" phenomenon and is likely more important in the wet rather than the dry season.
Figure 3: Deviation of asymptote-related metrics from their mean per root-zone soil moisture bins with changing sand percentage, HAND, and TWI. Note that binning of the continuous variables in \(x\)- and \(y\)-axes are done automatically to equalize frequency of observations among the bins of a given variable.
### Integral of FVC Decay
The integral of FVC time series during the decay period, \(I_{\phi}\), is smallest in arid regions, followed by humid regions. The largest \(I_{\phi}\) values are observed in regions with intermediate to low aridity (Figure 4a). Median values, as well as variations of \(I_{\phi}\) within similar climatology is larger when subject to intermediate aridity (Figure 4c). Uncertainties, which may also be driven by interannual variability to some degree (see Section 3.3 for details), are larger in some of the hyper-arid regions with low FVC and rare, episodic rainfall (Figure 4b).
At local scales, variations in \(I_{\phi}\) emerge as a combined effect of climate and other ecohydrological factors change over hillslope scales, such as proximity to the nearest drainage or occurrences of shallow water table depth. While a sharp aridity gradient in Sahel is clearly seen at Box-A and Box-B of Figure 4a, local scale increases in \(I_{\phi}\) are also present at riparian zones like Senegal River (Box-A in Figure 4a). Within similar aridity, \(I_{\phi}\) is smaller in seasonally flooding regions like the Sudd swamp ([PERSON] et al., 2019), Box-F in Figure 4a. The highest values of \(I_{\phi}\) in the Lower Zambezi bear strong similarity with the rooting depth product presented in [PERSON] et al. (2016), and the previously reported seasonal hydrologic buffer ([PERSON] et al., 2017) in these regions. This motivates further analysis of \(I_{\phi}\) with a plant accessible water storage perspective.
#### 4.2.1 Plant Accessible Water Storage
Here, we tested the third hypothesis of the study by analyzing the agreement between \(I_{\phi}\) and other plant accessible water storage products, and presenting the conceptual reasoning behind. Conceptually, plant accessible water storage is related to the vertical distribution of roots, and the water holding capacity of the soil that is determined largely by texture and organic carbon content. The root profile of water-limited ecosystems appears to adapt to the prevailing hydrologic and soil conditions while being constrained by other ecosystem properties and traits ([PERSON] et al., 2017; [PERSON], 2008; [PERSON] et al., 2006; [PERSON], 2008; [PERSON] & [PERSON], 2002; [PERSON], 2011). Plant accessible water storage controls the propensity and sensitivity of ecosystems to drought stress in dry periods. Various modeling approaches to infer rooting depth or plant water storage capacity have been proposed (explained in detail in [PERSON] et al. (2016)), as it cannot be observed directly but still contains a critical information for global-scale models ([PERSON] & [PERSON], 1998).
Figure 4: (a) Integral of FVC time series in the decay period, \(I_{\phi}\), (b) variation of \(I_{\phi}\) and (c) distribution of \(I_{\phi}\) within mean annual soil moisture. See Figure 2 for plotting details.
The integral of FVC during the dry season should be positively correlated with plant accessible water storage of the soil, as larger water storage would facilitate vegetation activity for longer period against water-limited conditions. The continental-scale patterns of \(I_{dp}\) (Figure 4a) with the largest values in strongly seasonal semi-arid savanna systems of both hemispheres are qualitatively consistent with the previous observation-based analysis (e.g., [PERSON], 2002) as well as the optimality-based models (e.g., [PERSON] & [PERSON], 1998). \(I_{dp}\) declines in hyper-arid regions like the Sahel, the Somalian desert, Southern Africa, as well as the Congo rainforest. A similar pattern would be expected for optimal rooting depth, which increases in regions with small differences between rainfall and potential evaporation in annual scales but large differences in seasonal scales ([PERSON] et al., 2006; [PERSON], 2011). The inset plots in Figure 4a clearly reveal the landscape scale patterns of \(I_{dp}\) presumably, due to topography-driven large variations of moisture. This may reflect enhanced and continued moisture supply due to topographic moisture convergence or shallow water tables along with possible adaptations of rooting depth to these local hydrological conditions ([PERSON] et al., 2017).
We compared \(I_{dp}\) with 4 products related to plant accessible water storage, namely two storage capacity products from [PERSON] et al. (2016) and [PERSON] et al. (2019), and two rooting depth products from [PERSON] et al. (2016) and [PERSON] et al. (2017) at 0.5\({}^{\circ}\) across Africa (see Section 2.2 for product details). As shown in Figure 11, there is qualitative agreement of large values of \(I_{dp}\) with AWSC and \(RZSC_{ext2}\) in the Miombo woodlands and also, to a lesser extent, in the northern savannas. All three also agree on low values in hyper-arid regions like the Sahel, the Somalian desert and in Southern Africa. In order to quantify the extent of agreement among the five estimates, we made a pairwise comparison of Spearman's correlation coefficient per climatological aritdio via soil moisture (Figure 6a). While the overall low-to-moderate correlation values among the products available in the literature demonstrate the scale of the challenge in estimating plant water storage capacity or rooting depth, highest correlation was observed between \(I_{dp}\) and \(RZSC_{ext2}\). Regardless of the product pairs, correlations decrease with increasing humidity, which is presumably related with other limiting factors than water, such as radiation or nutrients.
All four independent products utilized meteorological input data for water balance estimation, and also use remotely sensed vegetation products in some way. While \(RZSC_{ext2}\) and AWSC are constrained by hydrological Earth observations, the rooting depth products \(RD\) and \(ERD\) originate largely from different assumptions of optimality and plant adaptation. Our comparison suggests that estimating plant accessible water storage based on Earth observation data may be more suitable than the presently used optimality principles over the given resolution and domain of this study, despite the uncertainties of remote sensing data. Using \(I_{dp}\) as an indicator of plant accessible water storage has the advantage that it is derived from dense time series of a geostationary satellite alone, requiring no additional meteorological inputs or modeling assumptions that introduce their inherent uncertainties. Furthermore, \(I_{dp}\) features higher spatial resolution than most other storage capacity data, which provides insights on subsurface moisture variations at meso-scales.
### Decay Rate of FVC
Similar to \(I_{dp}\), the \(e\)-folding time (\(\lambda\)), presented in Figure 5a, also has a hump-shaped covariation with climatological aritdio at continental scales. We find the lowest \(\lambda\) values throughout humid regions and partially in arid regions, such as edges of the Sahara desert or the Somalian desert, while the highest \(\lambda\) values are found in regions with high to intermediate aridity. Though variation of \(\lambda\) (Figure 5b) suggests that the low values of \(\lambda\) in some hyper-arid regions are associated with higher uncertainty due to low signal-to-noise ratio.
Besides the coherent continental-scale spatial patterns, \(\lambda\) also has strong variations over meso-scales. Stronger lateral moisture convergence positively affects the \(\lambda\) in arid regions, as seen in the Senegal (Box-A, Figure 5a) and the Niger (partially in Box-B, Figure 5a) rivers' riparian zones in the arid climate. However, lateral moisture convergence does not always affect \(\lambda\) positively, as seen in the riparian zones of the Upper Zamezi and the Okavango rivers and their tributaries. Shown in Box-D in Figure 5a, \(\lambda\) is high around the Cuando river, the Okavango Delta and the Linyanti swamp, but low in the Barotse Floodplain (see [PERSON] et al. (1995) and [PERSON] et al. (2018) for general information about the region). Such non-trivial patterns suggest the role of complex interactions between the vegetation traits and local moisture conditions ([PERSON] et al., 2019), which also affect \(\lambda\).
#### 4.3.1 \(\lambda\) and Ecosystem Water Use
We tested the last hypothesis of this study by analyzing the variations in \(\lambda\) conditioned against soil moisture, canopy height and tree cover, and grounded this to similar studies on ecosystem scale decay rates. \(\lambda\) can corroborate the rate of decrease of plant available water, ecosystem scale water use efficiency, and the propensity to senescence. Ecosystems differ widely in their water use strategies, from being water conservative--typically associated with strong down-regulation of stomatal conductance with water deficiency--to aggressive exploitation of water resources ([PERSON] et al., 2001). Herbaceous plants are typically aggressive water users and cease with the depletion of surface soil moisture. Woody plants risk cavitation and death under severe water stress, and such, trees in places with frequent dry periods benefit from a water saving strategy or senescence for prolonged periods. [PERSON] and [PERSON] (2017) inferred ecosystem water-use strategies globally based on diurnal variations of vegetation optical depth assuming that those reflect stomatal regulation to maintain leaf-water potential. They found an increase in isobridcity, that is, the degree of stomatal regulation and subsequent water savings, with increase in vegetation height, consistent with the need of tall trees to prevent hydraulic failure during drought. [PERSON] et al. (2006) characterized decay rate in land evaporation (soil evaporation and transpiration) under water limitation using flux tower measurements and found that sites with stronger seasonality and larger woody coverage have slower decays. This association is supported by similar studies, for seasonality and canopy height ([PERSON] et al., 2019), and for differences in the responses of trees and grasses ([PERSON] et al., 2019). Stower decay of land evaporation of taller/woody canopy despite the faster decay of soil moisture with stronger acidity ([PERSON] et al., 2017) suggests reduced transpiration or other plant adaptation mechanisms.
If the rate of FVC decay was also related to ecosystems' water use strategy in a similar manner, we would expect slower FVC decay (higher \(\lambda\)) with increasing canopy height. In regions with strong to intermediate airdi-, we indeed find a tendency of increasing \(\lambda\) with canopy height except very tall canopy (Figure 6b), suggesting that \(\lambda\) incorporates ecosystem water use strategy traits as well as direct or indirect effects of soil moisture therein. However, as the climate gets better \(\lambda\) tends to decrease with canopy height. Possible explanations are that (a) changes in ecosystem scale drought coping strategies such as deep rooting ([PERSON] et al., 2020), (b) water consumption, that is, transpiration, increases with canopy height resulting in a faster depletion of moisture storage ([PERSON] et al., 2017), or (c) increasing ecosystem water use efficiency with aridity.
Figure 5.— (a) \(e\)-folding time of FVC time series during dry-down (in days), \(\lambda\), (b) variation of \(\lambda\), and (c) distribution of \(\lambda\) within soil moisture. See Figure 2 for plotting details.
Sensitivity of the nonlinear relationship between \(\lambda\) and climatological acidity to tree cover (see Figure 6b) shows that \(\lambda\) systematically increases with larger tree cover values in regions with high to intermediate acidity, where it peaks in regions with intermediate acidity and with 26%-43% of tree cover. This trend agrees with the reported interval for the transition from highly water-stressed forest to savanna ([PERSON] et al., 2020). However this pattern is inverted moving toward regions with weaker water-stress, hence denser tree cover, which agrees with [PERSON] et al. (2020) as moderately or lowly water-stressed forests do not develop strong adaptation against water limitation, nor change canopy structure. The agreement among these two studies having different methodologies shows the value of the observation-driven metric \(\lambda\) to gain ecohydrological insights and have a better understand in vegetation-water dynamics.
## 5 Summary and Perspectives
Using retrievals of the SEVIRI sensor of the geostationary satellite MSG, we derived ecohydrological metrics for continental Africa entirely from the temporal dynamics of the daily Fraction of Vegetation Cover (FVC) time series from 2004 to 2019 at ca. 5 km (0.0417\({}^{\circ}\)) spatial resolution. Our metrics captures both continental scale gradients and covariations with climate as well as structured regional variations, for example, due to topographic factors. This provides an unprecedented opportunity to improve our understanding of ecohydrological processes across spatial scales over Africa.
We tested whether \(\text{FVC}_{\text{min}}\) or \(\text{FVC}_{\text{max}}\) are elevated in sandy soils due to the \"inverse texture effect\" and we found no evidence for this hypothesis, which, however could be also due to scale issues or uncertainty of the soil product. We further tested it access to secondary moisture sources such as groundwater generates \"green islands\" by increased \(\text{FVC}_{\text{min}}\) for topographic moisture indices. Also this hypothesis was not supported at continental scale, although riparian corridors, seasonal wetlands and floodplains are visually evident in \(\text{FVC}_{\text{min}}\) regionally. In contrast, and somewhat surprisingly, we found evidence for elevated \(\text{FVC}_{\text{max}}\) with increased topographic moisture conditions in dry regions. It suggests that in dry regions, the vegetation benefits from topographically induced secondary moisture input during the rainy season, while in the dry season water limitation is too severe for the vegetation to benefit from this secondary input. Our results imply that the patterns of \(\text{FVC}_{\text{max}}\) help diagnosing effects of secondary water resources in water limited regions. We analyzed to what extent the integral of FVC time series in decay period (\(l_{\phi\phi}\)) reflects expected variations of the plant storage capacity or rooting depth. We found broad consistency between \(l_{\phi\phi}\) variations and aridity that are in agreement with theoretical considerations of rooting depth, and reasonable correlations with independent products of inferred plant water storage capacity. While the large uncertainty of independent evidence for variations of plant storage capacity precludes a more precise evaluation, our analysis suggests that \(l_{\phi\phi}\) is useful to diagnose variations in the buffering capacity of
Figure 6: (a) [PERSON]’s correlation coefficients between pairs of products related to plant accessible water content, namely Effective Rooting Depth from [PERSON] et al. (2016), Rooting Depth from [PERSON] et al. (2017), Accessible Water Storage Capacity (AWSC) from [PERSON]. [PERSON] et al. (2019), Root Zone Storage Capacity (\(RZS_{\text{CM2}}\)) from [PERSON] et al. (2016), and integral of FVC during decay period (\(l_{\phi\phi}\)) presented in this study. Black dots indicate significant correlation with \(\rho>0.05\). (b) Covariation of \(\dot{\lambda}\) and root-zone soil moisture with canopy height, and tree cover. Note that binning of soil moisture, canopy height and tree cover are done automatically to equalize frequency of observations among the bins of the given variable.
vegetation driven by moisture limitation. Finally, we analyzed whether the FVC decay rate during dry-down (\(\lambda\)) follows patterns expected for soil moisture or decay time scale of terrestrial evaporation. Generally, the continental scale patterns against aridity and its sensitivity to canopy height and tree cover of \(\lambda\) agrees broadly with the plant adaptation strategies proposed in the literature. It seems \(\lambda\) indeed contains signatures of the complex ecohydrological interactions between moisture availability and vegetation. Clearly structured variations of \(\lambda\) at meso-scales motivate in-depth analyses of the metric to better understand ecohydrological interactions at finer scales, yet over a continental gradient.
Overall, given the the large amount of information stored in spatial variations of the metrics reflecting different driving mechanisms across spatial scales, the metrics have great potential to improve our understanding on vegetation dynamics on: (a) testing hypotheses on understanding relevance of local-scale ecohydrological processes over large domains like continental Africa, (b) better understanding basic ecosystem properties like water usage in ecosystem scale and diagnosing their driving factors, and (c) extracting information and reducing uncertainty on concepts like plant water storage capacity.
Our ecohydrological metrics can help improving simulations of vegetation-water cycle interactions by providing an observational basis for model evaluation and parameterizations. Since land surface models simulate vegetation cover fraction, the same ecohydrological metrics derived from simulated FVC can be computed using the code we provide. This has the advantage that multiple processes affecting FVC at different temporal scales--such as leaf shedding, adjustments in leaf area and canopy height, and differential responses of trees and grasses--are accounted for. A consistent and parallel assessment between observed and modeled variations of the ecohydrological metrics with relevant factors, such as those presented in this paper, can uncover model deficiencies and provide indications which processes or model parameters require attention. In a step further, these patterns of model data mismatch can be included in model calibration exercises to improve land surface models. As the spatialization of vegetation related parameters remains to be a major challenge ([PERSON] and [PERSON], 2020) our ecohydrological metrics can also facilitate exploring alternatives to the plant functional type paradigm. For example, one could test if a linear scaling of the spatial \(I_{dp}\) field to spatialiae parameters controlling vegetation water storage capacity is sufficient, or better than plant functional type specific parameters (see e.g., [PERSON] et al., 2021). Similarly, one could test if model parameters controlling drydown rates (see e.g., [PERSON] et al., 2021) can be better spatialized using our \(\lambda\) map than by using plant functional types. Our initial analyses points the importance of topographic effects against moisture limitation, emerging from lateral convergence and spatial heterogeneity that are mostly not represented in the models ([PERSON] et al., 2015). This motivates for in-depth analysis of the spatial variation of the metrics presented here to resolve and quantify importance of nontrivial components of water cycle against water limitation.
There remain multiple opportunities for further synergistic exploitation with retrievals of surface temperature from geostationary satellites which could provide complementary indicators on variations of moisture states inferred from an energy balance perspective. The suggested algorithms for deriving the metrics and the provision of the code facilitates parallel assessments and helps overcome the technical difficulties of dealing with large volumes of data and the particularities of vegetation cover retrievals from the geostationary satellites.
Figure 11: Continuation of Figure 12 with samples having larger mean annual soil moisture.
## Appendix C Density Plots of the Ecohydrological Metrics
Figure 11. Density plots of the ecohydrological metrics presented in this study.
## Appendix D Temporal Correlation Between FVC and Soil Moisture Figure D1.
## Appendix E Map of Climatological Aridity and Google Earth View of Insets
Figure E1 shows the continental map of mean annual root-zone soil moisture (%) from GLEAM and the Google Earth views of the insets. Note that soil moisture values are binned to have equal number of observations in each class. Box-A: the Gamba and large portion of the Senegal rivers; Box-B: a small area of the Niger river mostly showing the transition from the Sahara desert to Sahel; Box-C: more on the transition from Sahel to tropical regions; Box-D: located in one of the most complex regions of Africa in terms of topography and lateral flow of water with lower sections of the Okavango and the Cuando rivers and upper section of the Zambezi river, together with multiple seasonally flooding areas like the Okavango delta, the Baroste Floodplain, and the Linyanti swamp. These seasonal wetlands are vital for the ecosystem and also provides great support against water limitation and heat for not only plants but also animals; Box-E: Lower Zambezi Basin together with the drainage of Lake Malawi to Zambezi. It also covers the Inyanga mountains located between Mozambique and Zimbabwe where a climatic shift happens over the mountain range. Last but not least, Box-F: largely covered by tropical savanna, is divided by the White Nile from South to North, covers the Sudd swamp.
## Appendix G Summary of Seasonal Dynamics of FVC, \(\text{FVC}_{\text{range}}\)
Figure G1. Variations in \(\text{FVC}_{\text{range}}\) (as \(\text{FVC}_{\text{max}}-\text{FVC}_{\text{max}}\)) (a) in space (b) with climatological arstitty (c) similar to Figure 3a but for \(\text{FVC}_{\text{range}}\) (d) similar to Figure F1a but for \(\text{FVC}_{\text{range}}\).
## Appendix I Map of Number of Convergences of Algorithm 2
Figure 11: Number of decay periods in which the Algorithm 2 successfully converged.
## Data Availability Statement
All cohydrodrological metrics presented in this study are available in standardized netCDF data format in [[https://doi.org/10.6084/m9.figshare.14987211.v1](https://doi.org/10.6084/m9.figshare.14987211.v1)]([https://doi.org/10.6084/m9.figshare.14987211.v1](https://doi.org/10.6084/m9.figshare.14987211.v1)), together with their quality diagnostics. The R scripts developed for the implementation of the methodology are available for research uses. They can be accessed through [[https://github.com/caglarkucuk/EcohydroMetrics_Africa.git](https://github.com/caglarkucuk/EcohydroMetrics_Africa.git)]([https://github.com/caglarkucuk/EcohydroMetrics_Africa.git](https://github.com/caglarkucuk/EcohydroMetrics_Africa.git)). All the data used in this study are available in the cited literature (see Section 2), except the AWSC data from [PERSON] et al. (2019) which was obtained from the corresponding author.
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wiley/ff7de045_93ca_472c_8498_3ca2fc6710b8.md | # Earth and Space Science
Modeling Coastal Water Clarity Using Landsat-8 and Sentinel-2
[PERSON]
1 Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA, 2 Graduate School of Oceanography, University of Rhode Island, Narraganset, RI, USA, 2 School for the Environment, University of Massachusetts Boston, Boston, MA, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
[PERSON]
1 Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA, 2 Graduate School of Oceanography, University of Rhode Island, Narraganset, RI, USA, 2 School for the Environment, University of Massachusetts Boston, Boston, MA, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
[PERSON]
1 Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA, 2 Graduate School of Oceanography, University of Rhode Island, Narraganset, RI, USA, 2 School for the Environment, University of Massachusetts Boston, Boston, MA, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
[PERSON]
1 Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA, 2 Graduate School of Oceanography, University of Rhode Island, Narraganset, RI, USA, 2 School for the Environment, University of Massachusetts Boston, Boston, MA, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
[PERSON]
1 Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA, 2 Graduate School of Oceanography, University of Rhode Island, Narraganset, RI, USA, 2 School for the Environment, University of Massachusetts Boston, Boston, MA, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
###### Abstract
Understanding and attributing changes to water quality is essential to the study and management of coastal ecosystems and the ecological functions they sustain (e.g., primary productivity, predation, and submerged aquatic vegetation growth). However, describing patterns of water clarity--a key aspect of water quality--over meaningful scales in space and time is challenged by high spatial and temporal variability due to natural and anthropogenic processes. Regionally tuned satellite algorithms can provide a more complete understanding of coastal water clarity changes and drivers. In this study, we used open-access satellite data and low-cost in situ methods to improve estimates of water clarity in an optically complex coastal water body. Specifically, we created a remote sensing water clarity product by compiling Landsat-8 and Sentinel-2 reflectance data with long-term Secchi depth measurements at 12 sites over 8 years in a shallow turbid coastal lagoon system in Virginia, USA. Our satellite-based model explained \(\sim\)33% of the variation in in situ water clarity. Our approach increases the spatiotemporal coverage of in situ water clarity data and improves estimates from bio-optical algorithms that overpredicted water clarity. This could lead to a better understanding of water clarity changes and drivers to better predict how water quality will change in the future.
Key Words.:
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## 2 Methods
### Study System and In Situ Data Collection
We focused our investigation on a coastal lagoon system studied by the Virginia Coast Reserve (VCR) Long Term Ecological Research Project (VCR-LTER) located on the Eastern Shore of Virginia, USA, near the southern tip of the Delmarva Peninsula (Figure 1). The VCR is the largest expanse of undeveloped coastline along the U.S. Atlantic seaboard. Low nitrogen inputs and frequent exchange with the Atlantic Ocean via inlets between barrier islands (Figure 1) results in relatively good water quality in comparison with most temperate coastal boys and estuaries in the United States and worldwide ([PERSON] et al., 2001). Due to low human impacts, the VCR serves as a model system for studying the long-term impacts of climate on temperate coastal logoons. The VCR also serves as the site of a successful large-scale edelgrams restoration project, after a massive die-off in the early 1930s due to storms and disease ([PERSON] et al., 2016). Water quality monitoring in the bay has informed restoration efforts and helped quantify positive environmental effects of restoration ([PERSON] et al., 2020). Since 1992, VCR-LTER researchers have collected \(Z_{\text{SD}}\) and other water quality parameters at 17 sites that include tidal flats (0-2 m depth), deep flats (2-4 m depth), and deeper oceanic inlets and channels (>4 m depth) ([PERSON] & [PERSON], 2020; [PERSON] et al., 2015). Sampling was carried out monthly from 1998 to 2008, and quarterly from 2008 to 2021 ([PERSON] & [PERSON], 2020). Temperature, salinity, and dissolved oxygen (converted to apparent oxygen utilization) were measured with a YSI Datasonde (6600 V2). Total suspended solids were estimatedvia dry weight difference after filtering water samples with Whatman GF/F filters (0.7 \(\mathrm{\SIUnitSymbolMicro m}\) nominal pore size), chlorophyll-a and phaeopignments were determined spectrophotometrically, and 500 mL water samples were analyzed for nutrient concentrations on a Lachat Quick-Chem 8500 flow-through analyzer.
### Satellite Data Processing and Algorithm Evaluation
To retrieve remote sensing reflectances (\(R_{n}\)) for the calculation of satellite-derived \(Z_{\mathrm{SD}}\), Landsat-8 and Sentinel-2 Level-1 images were collected. The Sentinel-2A and -2B satellites have a combined 5-day repeat orbit, while Landsat-8 has a 16-day repeat orbit. The OLI on Landsat-8 collects data at a 30 m spatial resolution in four spectral bands centered on wavelengths 443, 482, 561, and 655 nm. The MSI on Sentinel-2 collects data at 60 m spatial resolution with a band centered on 443 nm and at 10 m resolution for bands centered on 490, 560, and 665 nm. USGS Earth Explorer was used (U.S. Geological Survey, 2022; [[https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)]([https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)), accessed June 2019 through July 2022) to collect Level-1 Collection-1 Landsat-8 images ([[https://doi.org/10.5066/F7183556](https://doi.org/10.5066/F7183556)]([https://doi.org/10.5066/F7183556](https://doi.org/10.5066/F7183556))) and the Copernicus Open Access Hub (European Space Agency, 2022; [[https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)]([https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)), accessed June 2020 through July 2022) to collect Level-1 Collection-1 Sentinel-2 images. The Landsat-8 and Sentinel-2 satellite images used in this study are listed as Tables S1 and S2 in Supporting Information S1, respectively.
\(R_{n}\) were generated with two atmospheric correction processors: NASA's standard Level-2 generator atmospheric correction algorithm (I2 gen) in NASA SeaDAS 8.2 ([PERSON] et al., 2001) and ACOLITE from the Royal Belgian Institute of Natural Sciences (Version 2020-2222.0) (Vanhellemont, 2019, 2020; [PERSON], 2018). In 12 gen, the NASA standard NIR-SWIR algorithm with bands 5 and 7 (865 and 2,201 nm) were selected for atmospheric correction of coastal waters ([PERSON] et al., 2018). The following default Level-2 quality flags were used: CLDICE (probable cloud or ice contamination), HILT (very high or saturated radiance), and STRAY-LIGHT (straylight contamination). LAND (pixel is over land) was deselected due to the default land mask being too coarse for this area and the following reflectance thresholds were used to flag and remove land pixels: \(R_{n}(655)<0.01\), \(R_{n}\) (561) \(<0.012\), \(R_{n}\) (482) \(<0.001\), and \(R_{n}\) (443) \(<0.001\). The bidirectional reflectance distribution function of [PERSON] et al. (2002) was implemented. In ACOLITE, the default Dark Spectrum Fitting algorithm was implemented (Vanhellemont, 2019, 2020; [PERSON] & Ruddick, 2018) with default masks for
Figure 1: Map of the 17 tested sites with in situ \(Z_{\mathrm{SD}}\) data. Numbers identify each site. Green markers indicate that satellite data could be collected at the site using the appropriate quality flags, while red markers indicate sites without valid satellite data.
land, negative reflectances, cirrus clouds, and high reflectance. Valid \(R_{\rm n}\) from I2 gen and ACOLITE were recovered at 12 of 17 in situ sampling sites (five sites were too close to land): six ocean inlet sites, two lagoon sites, and three mainland tidal crack sites (Figure 1).
\(Z_{\rm SD}\) was computed by deriving inherent and apparent optical properties from \(R_{\rm n}\). The Quasi-Analytical Algorithm (QAA, version 6) was used to derive total absorption (\(a\)) and backscattering (\(b_{\rm n}\)) coefficients from \(R_{\rm n}\) with the QAA ([PERSON] et al., 2002), and these inherent optical property (IOP) coefficients were used to calculate the diffuse attenuation coefficient (\(K_{d}\)) with [PERSON] et al., 2013. \(K_{d}\)(530) was determined empirically by the methods of [PERSON] et al. (2016) to fill the large spectral gap between 482 and 561 nm. The minimum \(K_{d}\) value, the spectral band with the lowest attenuation, and the \(R_{\rm n}\) value at the corresponding wavelength (\(R_{\rm vis}^{\rm cr}\)), were then used to compute the satellite derived Secchi depth (\(Z_{\rm SD,ant}\), m) (Equation 1) ([PERSON] et al., 2015, 2016).
\[Z_{\rm SD,ant}=\frac{1}{2.5{\rm Min}\left(K_{d}^{\rm cr}\right)}\ln\left(\frac {0.14-R_{\rm vis}^{\rm cr}}{0.013}\right) \tag{1}\]
Satellite imagery within \(\pm 0\)-1 day of in situ sampling were used (2 OLI images, 6 MSI images) and \(Z_{\rm SD,ant}\) was found by averaging pixels in a 3 x 3 box (\(90\times 90\) m for Canthel-2) centered around the corresponding in situ site coordinate (Figure 11 in Supporting Information S1). The impact of anomalous data points on the spatial averaging within the 3 x 3 box was evaluated by also calculating the median of the 3 x 3 box. The mean and medians were not statistically different (Landsat-8: \(P=0.5\); Sentinel-2: \(P=0.9\)). We did not filter for large variance due to limited match-ups, as is done in some studies using a coefficient of variation threshold ([PERSON] et al., 2011; [PERSON], 2022). L2 gen yielded 11 matchups from OLI and 41 matchups from MSI. ACOLITE yielded 3 OLI and 44 MSI matchups. The number of observations varied by site and date due to varying cloud cover and choice of quality flags. We removed matchups with recorded water depths within 0.5 m of the recorded in situ Secchi depths. The workflow is synthesized in Figure 2.
### Cross Sensor Comparison
Landsat-8 and Sentinel-2 Secchi depths from I2 gen and the [PERSON] et al. (2016) algorithm (\(Z_{\rm SD,ant}\)) (Equation 1) from the same day at the same location were compared. This approach yielded 5 clear-sky same-day images from 2021, from which we sampled 150 random coordinates using QGIS 3.14 (QGIS.org, 2020). We compared Landsat-8 \(Z_{\rm SD,ant}\) and Sentinel-2 \(Z_{\rm SD,ant}\) using a Type II ordinary least squares linear regression.
### Modeling for Algorithm Adjustment
We used Type II ordinary least squares linear regression to predict in situ Secchi depths (\(Z_{\rm SD,int}\)) from satellite Secchi depth estimates (\(Z_{\rm SD,int}\)) from I2 gen and ACOLITE to determine which atmospheric correction software was most suitable. We also fit two individual linear models for Landsat-8 and Sentinel-2 data to determine whether Landsat-8 and Sentinel-2 differed in their predictions of in situ \(Z_{\rm SD}\) and to determine the proportion of variance of in situ \(Z_{\rm SD}\) explained by each satellite separately.
Models were fit in R 4.2.1 (R Core Team, 2022). We assessed the significance of model terms using \(F\) tests to determine if the model better fit the data than the \(Z_{\rm SD}\) algorithm. We checked for homogeneity of variance by plotting normalized model residuals against model predictions and individual predictors. We ensured normality of residuals using histograms and quantile-quantile plots. We tested for temporal autocorrelation using autocorrelation function analysis; no significant autocorrelation was detected.
### Model Assessment
We evaluated model skill by comparing modeled Secchi depths (\(Z_{\rm SD,int}\)) to in situ Secchi depths (\(Z_{\rm SD,int}\)) using the root mean square error (RMSE) and the mean absolute percent difference (MAPD) in R using the package _Metrics_ 0.1.4 (Hammer & Frasco, 2018).
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{m=1}^{n}\left(x_{\rm model,\it{i}}-x_{\rm init,\it{i}}\right)^{2}} \tag{2}\]\[\mathrm{MAPD}=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{x_{\mathrm{model},i}-x_{\mathrm{ noise,i},i}}{x_{\mathrm{in},\mathrm{data},i}}\right|\times 100\% \tag{3}\]
Due to the lack of a sufficient number of observations for an out-of-sample validation, we assessed the uncertainty in the model coefficients by calculating the standard errors and confidence intervals with bootstrapping (\(n=\) 10,000) (R package _boot_ 1.3-28; [PERSON] & Ripley, 2021; Davison & Hinkley, 1997).
Figure 2.— Workflow for obtaining \(Z_{\mathrm{BD}}\) with I2 gen in NASA SeaDAS, bio-optical algorithms, and empirical adjustments. I2 gen ultimately chosen over ACOLITE for processing (Section 3.1).
### Spatiotemporal Analysis
We compared spatial trends of water clarity maps generated from clear sky Landsat-8 and Sentinel-2 images taken on the same day (30 January 2021). We also generated monthly water clarity maps from clear sky Landsat-8 images to demonstrate changing spatial patterns with time. To determine the benefit of increased temporal coverage, we visually compared temporal patterns in time series of combined satellite model estimates (\(n=396\) observations; 2013-2021) and all in situ data (\(n=306\) observations; 1992-2021) at three water quality sites in a lagoon (site 2), mainland creek (site 6), and ocean inlet (site 16). Specifically, generalized additive models (GAMs; [PERSON], 1986) were used to estimate nonlinear trends as a function of date (intemannal variation), year-day (seasonal variation), and their interaction (tensor product) in R using the package mgcv 1.8-35 ([PERSON], 2017). By checking \(k\)-indices and \(P\) values, the following number of basis functions were selected: (a) 15 for date, (b) 15 for year day, and (c) 10 for the interaction/tensor product. Thin plate regression splines, computationally-efficient splines used to estimate smooth functions of multiple predictors, were used to model interannual variation and the interaction. We used cyclic cubic splines to model seasonal variation to avoid a discontinuity between the end and beginning of the year ([PERSON], 2017). To investigate seasonal trends in in situ water quality data, we used locally weighted scatterplot smoothing fits.
## 3 Results
### Algorithm Evaluation
Satellite estimates overpredicted \(Z_{\text{SD}}\) relative to their corresponding in situ values by an average factor of about 2.4 for l2 gen and 1.8 for ACOLITE. l2 gen and ACOLITE \(Z_{\text{SD}}\) both predicted in situ \(Z_{\text{SD}}\) (l2 gen: \(R^{2}_{\text{adj}}=32.5\%\), \(F_{\text{L,0}}=25.05\), \(P<0.001\); ACOLITE: \(R^{2}_{\text{adj}}=22.0\%\), \(F_{\text{L,0}}=13.38\), \(P<0.001\); Figure 3) and NASA l2 gen yielded larger \(Z_{\text{SD}}\) from the [PERSON] et al. (2016) algorithm (mean, \(\overline{x}=1.75\) m, standard deviation, \(s=0.46\) m) than ACOLITE (\(\overline{x}=1.30\) m, \(s=0.24\) m). However, ACOLITE still overpredicted \(Z_{\text{SD}}\) relative to the corresponding in situ values (\(\overline{x}=0.77\) m, \(s=0.26\) m).
Figure 3: \(Z_{\text{SD}}\) predictions from l2 gen (a) were generally greater than those from ACOLITE (b), although both were positively correlated with in situ measurements. Dotted line shows 1:1 relationship.
### Cross-Sensor Comparisons
\(Z_{\text{SD}}\) estimates from the three satellites were highly correlated with a linear relationship (\(R^{2}_{\text{adj}}\) = 85.3%, \(F_{1,545}\) = 3,170, \(P<0.001\)). Sentinel-2 generally yielded higher \(Z_{\text{SD,nat}}\) than Landsat-8 (note that most points are below the 1:1 line in Figure 4).
### Model Statistics and Assessment
Spectral shapes were similar for both atmospheric correction processors, but ACOLITE systematically yielded larger \(R_{n}\) than l2 gen (Figure S2 in Supporting Information S1). Although ACOLITE yielded \(Z_{\text{SD,nat}}\) that were closer to the 1:1 line (\(Z_{\text{SD,nat}}\) = 0.56 \(Z_{\text{SD,nat}}\) + 0.04; Figure 3a) than l2 gen \(Z_{\text{SD,nat}}\) (\(Z_{\text{SD,nat}}\) = 0.33 \(Z_{\text{SD,nat}}\) + 0.19; Figure 3b), \(R^{2}_{\text{adj}}\) model skill metrics, and standard errors were better for the l2 gen-based model (Table 1).
Due to differences in Landsat-8 and Sentinel-2 \(Z_{\text{SD,nat}}\) estimates (Figure 4), the final algorithm adjustment involved separate satellite models (Equations 4 and 5). We also used l2 gen atmospheric correction due to improved results over ACOLITE (Table 1).
\[\text{Landsat-8}:\,Z_{\text{SD,nat}}=0.25\,Z_{\text{SD,nat}}+0.36 \tag{4}\]
\[\text{Sentinel-2}:\,Z_{\text{SD,model}}=0.37\,Z_{\text{SD,nat}}+0.10 \tag{5}\]
The final model (Equations 4 and 5; Figure 5) improved estimates (Landsat-8: RMSE = 0.16 m, MAPD = 19%; Sentinel-2: RMSE = 0.22 m, MAPD = 26%; Table 2) relative to the [PERSON] et al. (2016) model (Landsat-8: RMSE = 1.04 m, MAPD = 121%; Sentinel-2: RMSE = 1.05 m, MAPD = 148%).
Model skill was similar among lagoon, mainland creek, and ocean inlet sites (Figure 6). There were no clear trends between water depth and model performance (Figure S3 and Table S3 in Supporting Information S1). Ocean inlet sites are most well-represented in the model, although the MSI model tends to underestimate high \(Z_{\text{SD}}\) at ocean inlet sites and overestimate low \(Z_{\text{SD}}\) (orange in Figure 6c).
### Spatiotemporal Analysis
Spatial trends within the system were similar in Landsat-8 and Sentinel-2 water clarity maps taken on the same day, providing confidence that the remote sensing data is capturing robust geophysical and ecological patterns. Flows from the inlets through the deeper channels have higher \(Z_{\text{SD}}\) (ca. \(>\)0.8 m) than the surrounding water (ca. 0.4-0.7 m), and plumes off-shore of inlets have shallower \(Z_{\text{SD}}\) (0.6-0.8 m) than further offshore (\(>\)1 m). Sentinel-2 MSI had a larger \(Z_{\text{SD}}\) range (ca. 0.3-1 m) than Landsat-8 OLI (ca. 0.4-0.9 m) and captured finer scale spatial variability (Figure 7). Satellite images from individual dates highlight that Secchi depths in this system are highly variable in both time and space (Figure 8).
Season cycles were significant at all three sites (Site 2: \(P<0.001\), Site 6: \(P=0.002\), Site 16: \(P<0.001\)), as well as the tensor product explaining the interaction between interannual and seasonal variability (Site 2: \(P=0.006\), Site 6: \(P=0.009\), Site 16: \(P=0.01\); Figures 9a, 9c, and 9e). Sites 2 and 16 experienced the strongest seasonality and water clarity dips around July, corresponding to a dip in in situ \(Z_{\rm SD}\) and peaks in in situ particulate inorganic matter, total suspended solids, apparent oxygen utilization, chlorophyll-a, phaeopigments, PO\({}_{\rm Ar}\) and NH\({}_{4}\) (Figure 10). Interannual trends were not significant at any of the 3 sites (Site 2: \(P=0.20\), Site 6: \(P=0.66\), Site 16: \(P=0.26\); Figures 9b, 9d, and 9f).
## 4 Discussion
Landsat-8 and Sentinel-2 models were developed to increase and improve water clarity observations in the VCR-LTER. Our results demonstrate that high-resolution satellite observations can enable the estimation of water clarity in estuaries and coastal seas across a range of spatiotemporal scales, but require sensor-specific calibration and validation with in situ measurements. We anticipate that our approach can be adapted to coastal waters broadly where environmental monitoring organizations are limited to in situ data and potentially biased satellite estimates. The potential for high frequency water clarity estimation is further enhanced because we found that Landsat-8 and Sentinel-2 reflectances and Secchi depths are highly comparable.
\begin{table}
\begin{tabular}{l c c} \hline & Landsat-8 OLI (12 gen) & Sentinel-2 MSI (12 gen) \\ \hline RMSE & 0.16 m & 0.22 m \\ MAPD & 19\% & 26\% \\ Mean, standard error, and 95\% CIs of the slope & \(0.25\pm 0.092\) [0.10, 0.48] & \(0.37\pm 0.094\) [0.21, 0.58] \\ \(F\), \(P\) value of the slope & \(F=7.30\), \(P=0.024\) & \(F=19.22\), \(P<0.001\) \\ Mean, standard error, and 95\% CIs of the intercept & \(0.36\pm 0.16\) [0.005, 0.64] & \(0.10\pm 0.16\) [\(-0.25\), 0.38] \\ \(F\), \(P\) value of the intercept & \(F=4.74\), \(P=0.06\) & \(F=0.44\), \(P=0.51\) \\ Mean and standard error of \(R^{2}_{\rm std}\) & \(38.6\%\pm 22\%\) & \(31.8\%\pm 14.5\%\) \\ \hline \end{tabular}
\end{table}
Table 2: Model Still Metrics, Model Uncertainties, and Fixed-Effects Results for Satellite Models
Figure 5: \(Z_{\rm SD,min}\) from Landsat-8 (a) and Sentinel-2 (b) plotted against \(Z_{\rm SD,min}\). The single-satellite regression models (Equations 4 and 5) are plotted as solid lines with 95% confidence intervals plotted in gray.
### Satellite Oversation of \(Z_{\rm{SD}}\)
Biases introduced during atmospheric correction could have led to satellite \(Z_{\rm{SD}}\) overestimation. The atmospheric correction methods implemented by I2 gen explained more variation in in situ \(Z_{\rm{SD}}\) than ACOLITE (Figure 3, Table 1). This result complements previous work showing that I2 gen performs better than ACOLITE for turbid waters and complex, optically shallow coastal environments ([PERSON] et al., 2019; [PERSON], 2019, 2020; [PERSON] et al., 2018). We also found that ACOLITE consistently yielded higher reflectance values than I2 gen at all four
Figure 6.— \(Z_{\rm{SD,tra}}\) from Landsat-8 (green) and Sentinel-2 (orange) plotted against \(Z_{\rm{SD,limit}}\) for each site type. Sites no. 8 and 16 are lagoons, sites no. 2, 13, and 14 are mainland creeks, and sites no. 3, 5, 6, 12, 15, and 17 are ocean inlets. Landsat-8 (green) and Sentinel-2 (orange) prediction lines are plotted. Mean absolute percent difference (MAPD) and root mean square error (RMSE) are reported for each region. Sample size is not equal between site types.
Figure 7.— Maps of model-corrected Landsat-8 derived \(Z_{\rm{SD}}\) (a) and Sentinel-2 derived \(Z_{\rm{SD}}\) (b) from 30 January 2021.
wavelength bands (Figure S2 in Supporting Information S1). These results are consistent with the findings of [PERSON] et al. (2019) who compared different atmospheric correction methods over optically complex coastal waters using in situ radiometric measurements from the Aerosol Robotic Network--Ocean Color (AERONET-OC). Future work could investigate other atmospheric correction algorithms such as Case 2 Regional CoastColour (C2 RCC) and POLYnomial-based algorithm applied to Medium Resolution Imaging Spectrometer (POLYMER) in this water body as was done in the Chesapeake Bay ([PERSON] et al., 2022).
Validation of remote sensing products with in situ radiometric observations would be useful in regionally adjusting the algorithm. However, using an existing long-term data set for regional adjustment, as demonstrated in this paper, has its own advantages compared to this approach. Long term datasets have repeated seasonal sampling, so statistical models are less biased by the timing of in situ sampling. Capturing a wide range of variability in in situ sampling is especially important in systems that experience dynamic change across seasons. Using existing datasets is also cost effective compared to radiometric calibration. Another source of bias could have
Figure 8: Maps of model-corrected Landsat-8 derived Secchi depths from monthly clear sky images (2019–2021).
been introduced during the derivation of IOPs. It has been found that the QAA can lead to underestimation of IOPs in turbid waters ([PERSON] et al., 2014), which ultimately leads to an overestimation of \(Z_{\text{SD}}\). Alternative \(R_{n}\) to IOP algorithms, such as the \"QAA turbid\" ([PERSON] et al., 2014), or alternative \(Z_{\text{SD}}\) algorithms could possibly yield more accurate \(Z_{\text{SD}}\) values.
### Using Sentinel-2 Data in Conjunction With Landsat-8 Data
The strong relationship between Landsat-8 and Sentinel-2 measurements (Figure 4) and similarities in spatial water clarity patterns (Figure 7) demonstrate the compatibility of their data products for estimating water clarity. We found that Sentinel-2 consistently yields larger \(Z_{\text{SD}}\) values (corresponding to lower \(R_{n}\) values) than Landsat-8, suggesting that differences are most likely due to inherent satellite product differences rather than environmental factors (e.g., tidal differences occurring in the temporal window between satellite overpasses).
We decided to fit two separate models for each satellite due to differences in satellite estimates and to preserve the highest spatial resolution of Sentinel-2 MSI. However, care must be taken when comparing water clarity maps with different spatial resolutions. Down-sampling Sentinel-2 MSI to the spatial resolution of Landsat-8 OLI may be necessary for certain spatial analyses. Although down-sampling did not affect match-ups used in modeling (Figure S1 in Supporting Information S1), differences are significant when models are applied to entire satellite images (Figure 7).
Another consideration regarding merging Landsat and Sentinel data is parametrizing NASA's HLS products, surface reflectances with 30 m spatial resolutions and 5 days temporal resolutions ([PERSON] et al., 2018). Although developed primarily for terrestrial applications, HLS data have been used in water quality modeling to increase temporal resolution while minimizing errors associated with satellite product differences ([PERSON] et al., 2020). The workflow for harmonizing products includes common atmospheric correction, spatial co-registration, normalization of the solar and view angles, and adjustment for differences in wave
Figure 9: \(Z_{\text{SD,min}}\) values (blue) and \(Z_{\text{SD,model}}\) values (green: Operational Land Imager (OLL) and orange: MultiSpectral Instrument (MSI)) plotted against time (top; a, c, and e) and day of the year (bottom; b, d, and f) in a mainland creek (site 2; a-b), lagoon (site 6; c-d), and ocean inlet (site 16; e–f). Black lines show thin-plate regression splines and cyclic cubic splines for interannual (top) and seasonal (bottom) patterns from the generalized additive model, respectively. The splines were calculated from in situ, OLI, and MSI data. The 95% confidence intervals are plotted in gray.
length bands ([PERSON] et al., 2018). This procedure corrects for Landsat-8/Sentinel-2 differences that could have contributed to the mismatch between Landsat-8 and Sentinel-2 reflectances and Secchi depths in our study.
Figure 10.— Seasonal trends in water quality parameters at 17 sites as shown by locally weighted scatterplot smoothing (LOWESS) fits. All parameters except Secchi depth and water temperature have been standardized. Panel A shows a peak in temperature (blue) corresponding to a dip in Secchi depth (black) mid-summer. Water temperature data are shown in light blue and Secchi depth data are shown in gray. Panels B–D show the seasonal variations of water quality parameters as modeled by LOWESS. Particulate organic matter denoted by POM, particulate inorganic matter denoted by PIM, total suspended solids denoted by TSS, and total dissolved nitrogen denoted by TDN. Secchi depths are plotted as well, as shown by the gray data points and black smooth. Data from 1992 to 2020 water quality sampling ([PERSON] and [PERSON], 2020).
### Data Collection and Model Limitations
Our work highlights the need for in situ bio-optical and water quality measurements to fully leverage satellite imagery as an effective and reliable water quality monitoring tool, especially in dynamic waters. Increasing the number of in situ match-ups, especially to cover a large dynamic range, will strengthen the predictive power of statistical water clarity models. In this study, in situ sites were limited to the area shown in Figure 1. Application of the satellite model (adjustment to standard water clarity algorithm) outside of the VCR-LTER region and conditions introduces potential uncertainties. This could be addressed in future work by expanding the spread of in situ evaluation sites to quantify the accuracy of the model outside this region.
Although both satellites capture similar spatial patterns (Figure 7), the Sentinel-2 model captures higher Secchi depth values than the Landsat-8 model. We had limited in situ data for Landsat-8 adjustment due to its infrequent overpass relative to Sentinel-2. The discrepancy could be due to the inclusion of high (>1 m) in situ Secchi depths in the Sentinel-2 model. Although we captured a sufficient range of Secchi depths for a statistical fit, the Landsat-8 model would be strengthened by adding higher in situ Secchi depth values (>1 m). Coordinating field surveys with satellite overpasses would strengthen future remote sensing studies and provide more matchups for empirical algorithm adjustments.
Additionally, further investigation into the diurnal variability introduced by tidal forcing is important for interpreting water clarity ([PERSON] et al., 2013). Future work could expand on our model to include tidal effects, which are different at each site. The residence times in this system range from weeks near the mainland to hours near the inlets ([PERSON] et al., 2015), so tides more significantly affect inlet match-ups. We recommend that the current model be used to map spatiotemporal patterns and changes in water clarity across Landsat and Sentinel sensors.
### Coupled In Situ/Satellite Spatiotemporal Analysis
Spatial variation in water clarity as captured by MSI and OLI (Figures 7 and 8) is affected by aquatic vegetation, salt marshes, tides, winds, bathymetry, and other factors. Submerged aquatic vegetation decreases turbidity by enhancing sediment deposition, and salt marshes (masked in white) slow down exchange with the ocean ([PERSON] et al., 2018). Strong winds can lead to increased mixing in the lagoon and decreased lagoon/ocean exchange ([PERSON] et al., 2015). Patterns in water clarity can be paired with other data (e.g., bathymetry, weather data, hydrology) to better understand drivers of water clarity.
Satellite \(Z_{\text{SD}}\) maps (Figure 8) and in situ water quality data (Figure 10) demonstrate strong temporal variability in Secchi depth. As a highly seasonal system, we expect water clarity to change over the course of the year, but trends shown by in situ or satellite data alone may be affected by unique biases introduced by each approach. Field measurements are rarely taken during stormy winter weather when the water is more mixed and turbid, so in situ winter values may be biased toward higher measurements. In situ \(Z_{\text{SD}}\) depth measurements can also be biased by reduced visibility from waves, cloud cover, and sun position, as well as observer error ([PERSON], 2020). Satellite measurements are also imperfect, being affected by adjacency effects, proximity to land, seafloor backscatter, cloud cover, and aliasing due to whitecaps. There are also spatial limitations in satellite data retrievals, as shown by the inability to obtain satellite data too close to land (ca. <100 m away) or in areas affected by sunlight.
Coupling in situ \(Z_{\text{SD}}\) with satellite \(Z_{\text{SD}}\) can help alleviate these biases. For example, satellite data in our temporal analysis of three representative water quality sites may have alleviated the wintertime bias in in situ measurements. Additionally, the timing of field sampling within a season changed among years, which may have led to seasonal trends being confounded with interannual variability. Satellite data from 2013 to 2021 helped fill these gaps and create a more even spread of data across the year (Figures 8(b), 8(d), and 8(f)). An area for future work would be to conduct a rigorous analysis of Secchi depth seasonality using paired in situ and satellite observations. Interannual in situ \(Z_{\text{SD}}\) were also scarce at all three sites from 2013 to 2021 before satellite data was added. The combined time series showed no evidence of interannual changes, although relative constancy in water clarity may soon be changing ([PERSON] and [PERSON], 2011). This provides opportunities to further evaluate the model's predictive power with future in situ matchups. Rapid, accelerating sea level rise ([PERSON] et al., 2012) and storm intensification ([PERSON] and [PERSON], 2007; [PERSON] et al., 1991) may increase coastal erosion and increase turbidity ([PERSON] et al., 2021). Likewise, increasing frequency, duration, and intensity of marine heatwaves threaten recently restored seagrass meadows, which have stabilized sediments and reduced local turbidity and chlorophyll concentrations ([PERSON] et al., 2020; [PERSON] et al., 2012; [PERSON] and [PERSON], 2017). Rising water temperatures could alsoaffect numerous parameters relevant to water clarity such as phytoplankton concentrations ([PERSON] et al., 2018; [PERSON] et al., 2019). It is vital to couple in situ observations with satellite observations over the long term to understand and derive changes in water clarity and separate directional trends from natural variability.
## 5 Conclusion
We developed a Landsat-8/Sentinel-2 remote sensing model to estimate water clarity in an optically complex coastal water body. The application of this model increases the spatiotemporal resolution of water clarity estimation, addresses algorithm overestimates of water clarity for specific localities, and decreases errors associated with Landsat-8/Sentinel-2. We believe our approach can be implemented in dynamic coastal water bodies with limited in situ measurements; for example, as part of routine water quality monitoring. Coupling accurate satellite estimates with in situ observations over the long term is crucial to understanding coastal water clarity variability and its underlying physical and biological drivers. This understanding could help improve water clarity predictions and lead to the better management of coastal ecosystems.
## Data Availability Statement
Datasets and software used for the analysis of in situ and satellite data were archived with the Environmental Data Portal (EDI) via [[https://doi.org/10.6073/pasta/fe66683665a0133b2d831e552](https://doi.org/10.6073/pasta/fe66683665a0133b2d831e552) echae10]([https://doi.org/10.6073/pasta/fe66683665a0133b2d831e552](https://doi.org/10.6073/pasta/fe66683665a0133b2d831e552) echae10) under a CC-BY Attribution license and are available in this in-text citation reference: [PERSON] et al. (2022). Satellite data was processed by NASA SeaDAS 8.2 ([PERSON] et al., 2001; National Aeronatics and Space Administration and Ocean Biology Processing Group, 2022), available for download at [[https://seadas.gsfc.nasa.gov/downloads/](https://seadas.gsfc.nasa.gov/downloads/)]([https://seadas.gsfc.nasa.gov/downloads/](https://seadas.gsfc.nasa.gov/downloads/)) under the GNU General Public License (GPL), and ACOLITE from the Royal Belgian Institute of Natural Sciences (Version 20220222.0) (Royal Belgian Institute of Natural Sciences and The Remote Sensing and Ecosystem Modelling Team, 2022; Vanhellemont, 2019, 2020; Vanhellemont & Ruddick, 2018), available for download at [[https://donature.naturalsciences.be/remsem/software-and-data/acolite](https://donature.naturalsciences.be/remsem/software-and-data/acolite)]([https://donature.naturalsciences.be/remsem/software-and-data/acolite](https://donature.naturalsciences.be/remsem/software-and-data/acolite)) under the GNU General Public License v2. Level-1 Collection 1 Landsat-8 were downloaded from USGS Earth Explorer, available here: [[https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov)]([https://earthexplorer.usgs.gov](https://earthexplorer.usgs.gov)) (U.S. Geological Survey, 2022) in compliance with U.S. Public Domain. Level-1 images used in this study can be downloaded using the bounding box [37.6501, \(-\)75.7864], [37.6077, \(-\)75.4582], [37.0596, \(-\)75.7809], [37.1570, \(-\)76.0776], date range 1 January 2013 to 30 July 2022, and Landsat Level-1 Collection-1 under Data Sets. Level-1 Collection-1 Sentinel-2 images are available to download from the Copernicus Open Access Hub (European Space Agency, 2022), available here: [[https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)]([https://scihub.copernicus.eu/](https://scihub.copernicus.eu/)) and subject to the Legal Notice on the use of Copernicus Sentinel Data and Service Information: [[https://sentinels.copernicus.eu/documents/247904/690755/Sentinel_Data_Legal_Notice](https://sentinels.copernicus.eu/documents/247904/690755/Sentinel_Data_Legal_Notice)]([https://sentinels.copernicus.eu/documents/247904/690755/Sentinel_Data_Legal_Notice](https://sentinels.copernicus.eu/documents/247904/690755/Sentinel_Data_Legal_Notice)). Level-1 data used in this study can be downloaded by selecting the appropriate bounding box around the VCR peninsula (see above coordinates), selecting Sentinel-2 mission, and selecting SZANSIC as the Product Type. Processed Level-2 imagery available at [PERSON] et al., 2022 data set described above. In situ water quality data is available at this in-text citation reference: [PERSON] and [PERSON] (2020) and at [[http://www.vcrlter.virginia.edu/cgi-bin/showDataset.cgi?docid=knb-Iter-vcr.247](http://www.vcrlter.virginia.edu/cgi-bin/showDataset.cgi?docid=knb-Iter-vcr.247)]([http://www.vcrlter.virginia.edu/cgi-bin/showDataset.cgi?docid=knb-Iter-vcr.247](http://www.vcrlter.virginia.edu/cgi-bin/showDataset.cgi?docid=knb-Iter-vcr.247)) under a CC-BY Attribution license. Random sampling of coordinate points was done in QGIS 3.14 (QGIS.org, 2020) at [[https://www.qgis.org/en/site/forusers/download.html](https://www.qgis.org/en/site/forusers/download.html)]([https://www.qgis.org/en/site/forusers/download.html](https://www.qgis.org/en/site/forusers/download.html)) and under the GNU General Public License (GPL). Figures and statistics were done in R 4.2.1 (R Core Team, 2022) at [[https://www.qgis.org/en/site/forusers/download.html](https://www.qgis.org/en/site/forusers/download.html)]([https://www.qgis.org/en/site/forusers/download.html](https://www.qgis.org/en/site/forusers/download.html)) and under the GNU General Public License v2. Satellite algorithms were applied in MATLAB (The MathWorks, Inc., 2022) at [[https://www.mathworks.com/products/matlab.html](https://www.mathworks.com/products/matlab.html)]([https://www.mathworks.com/products/matlab.html](https://www.mathworks.com/products/matlab.html)).
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* Sullivan et al. (2021) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (20 | wiley | Modeling Coastal Water Clarity Using Landsat‐8 and Sentinel‐2 | Sarah E. Lang, Kelly M. A. Luis, Scott C. Doney, Olivia Cronin‐Golomb, Max C. N. Castorani | https://doi.org/10.1029/2022ea002579 | 2,023 | CC-BY |
wiley/ff81dcbd_0432_4672_8b06_6acfea95656b.md | the route to our results, we demonstrate that each of those conclusions is invalid. We use our expressions to examine thermal gradients along and beneath plate interfaces in active subduction zones.
### The Plate Interface
We refer to the portion of a subduction zone that is bounded above and below by rigid plates as the \"plate interface\" (Figure 1). Here, the thermal regime is dominated by diffusion of heat perpendicular to the interface and advection of heat by the relative motion of the plates parallel to the interface (e.g., [PERSON], 1969; [PERSON] & [PERSON], 1990; [PERSON] & [PERSON], 1973). The plate interface extends from the trench to at least the maximum depth of thrust-faulting earthquakes on it, which varies between \(\sim\)30 and 60 km ([PERSON] et al., 2012), but the presence of tremor and silent-slip events (e.g., [PERSON], 2011; [PERSON], 2012), implies that the plate interface may extend 10-20 km deeper than this.
We begin by determining a representative shape for plate interfaces by fitting the surfaces of descending plates, as determined by [PERSON] et al. (2018), to a parabolic form
\[z_{f}=ax^{2}, \tag{1}\]
where \(z_{f}\) is the depth of the interface at horizontal distance \(x\) measured perpendicularly from the trench. The profiles used are those of SubMap 4.3 ([PERSON], 2005; [PERSON] et al., 2017), excluding profiles for which convergence velocities are uncertain (principally those involving small plates in the southwest Pacific), or for which the age of ocean floor is unavailable. The profiles of [PERSON] et al. (2018) are fit to a depth of 60 km. We later make use of a subset of profiles, for which England (2018, Appendix C and Supporting Information) could obtain a reliable maximum depth of thrust faulting, \(z_{f}\); each of those profiles is fit from the surface to that depth.
As Figure 2a shows, 130 out of 154 of the larger set of profiles, and all 80 of the subset, have an RMS misfit to a parabola of 5 km or less. Those profiles with larger misfit are concentrated in Mexico, and in regions of low slab dip in northern South America. Because uncertainties in depth of slab given by [PERSON] et al. (2018) comfortably exceed 5 km in the depth range of interest, we do not need to seek a more complex form. Of the 154 profiles in the full set, 138 have curvature in the range \(5\times 10^{-4}<a<3.5\times 10^{-3}\) km\({}^{-1}\), and all but 6 of the profiles in the subset have curvature in that range (Figure 2b). The cosine of the dip appears in the analytical approximations for temperature; the distribution of its minimum value, at \(z_{f}\), is shown in Figure 2c, for the subset of profiles on which \(z_{f}\) has been determined (England, 2018).
Figure 1: Definition sketch of the subduction interface. This study addresses the distribution of temperatures on the plate interface, which separates two plates, each of which transfer heat by diffusion. Temperatures on the wedge-slab interface, which are influenced by advection of heat in the wedge, are not considered here.
## 2 Analytical Approximations to Temperatures at, Above, and Below the Plate Interface
We consider two plates that transfer heat by conduction, and which are separated by an interface on which dissipation may occur (Figures 1 and A1). [PERSON] and [PERSON] (1990) gave approximate expressions for temperatures near planar interfaces which were elaborated, for different conductivities of upper and lower
Figure 2: (a) Distribution of misfits to a parabolic shape (Equation 1) of the depth to top of the slab for 154 profiles of [PERSON] and [PERSON] (2005); the parabola is fit to slab depths of [PERSON] et al. (2018) between the trench and 60 km (full set, open bars) and the maximum depth of thrust faulting (subset of 80, see text, gray bars). (b) Distribution of \(a\) (Equation 1) with distances measured in kilometers; open bars show full set, gray bars show subset. (c) Distribution of cosine of maximum dip of the interface for the parabolic fits to the subset of 80 slab profiles for which maximum depth of thrust faulting \(z_{\tau}\) has been obtained. (d) Distribution of Pe (Equation 5) for the subset of 80 profiles, evaluated at \(z_{\tau}\).
plates, by [PERSON] and [PERSON] (1993) and, for the case in which young ocean floor approaches a trench, by [PERSON] and England (1995). Our development follows [PERSON] and England (1990) (Appendix B) and [PERSON] and England (1995), with the exception that we allow for curved plate interfaces.
Let the speed of convergence between the two plates be \(V\), and the angle between the convergence vector and the normal to the trench be \(\phi\). Depending upon the application, one may wish to express \(u\) either in terms of horizontal distance from a point on the profile to the nearest point on the trench (\(x\), Equation 2), or in terms of the horizontal distance along a profile from its origin at the trench (\(X\), Equation 3), or in terms of the depth of a point on the profile (\(z_{f}\), Equation 4):
\[u(x) = \frac{x}{2}\sqrt{4a^{2}x^{2}+\sec^{2}\left(\phi\right)}+\frac{\sinh^{ -1}\left(2 ax\cos\left(\phi\right)\right)}{4a\cos^{2}\left(\phi\right)}, \tag{2}\]
\[u(X) = \frac{X}{2}\sqrt{4a^{2}x^{2}\cos^{4}\left(\phi\right)+1}+\frac{ \sinh^{-1}\left(2 aX\cos^{2}\left(\phi\right)\right)}{4a\cos^{2}\left(\phi \right)}, \tag{3}\] \[u(z_{f}) = z_{f}\sqrt{1+\frac{\sec^{2}\left(\phi\right)}{4 az_{f}}+\frac{ \sinh^{-1}\left(2\sqrt{az_{f}}\cos\left(\phi\right)\right)}{4a\cos^{2}\left( \phi\right)}}. \tag{4}\]
Temperatures on the plate interface depend on the Peclet number (Pe), a dimensionless combination of parameters which is the ratio of the time scale for diffusion of heat through the thickness \(z_{f}\) of the upper plate, \(t_{2}=z_{f}^{2}\) / \(\kappa\), to the time \(t_{1}\), equal to \(u\) / \(V\), taken for the lower plate to travel the distance \(u\) down the interface:
\[\mathrm{Pe}=\frac{t_{2}}{t_{1}}=\frac{V_{f}^{2}}{\kappa u}. \tag{5}\]
The distribution of Pe for active subduction segments, evaluated at \(z_{f}\), is shown in Figure 2d.
[PERSON] and [PERSON] (1990) showed that, provided a time \(t>(t_{1}+t_{2}\) / \(\pi^{2})\) elapses following the onset of subduction (or a major change in its rate), then steady-state conditions are obtained in which, while the temperatures of material points in the lower plate vary with time as they pass beneath the upper plate, the temperature field in a coordinate system fixed to the upper plate is independent of time. For the range of \(t_{1}\) and \(t_{2}\) relevant to modern subduction zones, that elapsed time is between 10 and 20 Myr, which is smaller, and usually substantially so, than the age of most volcanic arcs at subduction zones ([PERSON], 1986). We therefore concentrate on steady-state solutions. [PERSON] and [PERSON] (1990) give expressions that may be used to estimate temperatures on plate interfaces of subduction zones that are younger than \((t_{1}+t_{2}\) / \(\pi^{2})\).
### Temperatures on the Plate Interface in the Absence of Heat Sources
We neglect radiogenic heat production, which is generally unimportant in the subduction setting but may, if necessary, be treated with the expressions of England (2018). With negligible radiogenic heat production, temperature gradients within the upper plate are independent of depth, and
\[T(z)=T_{f}\frac{z}{z_{f}}, \tag{6}\]
where \(T(z)\) is temperature at depth \(z\) and \(T_{f}\) is the temperature on the plate interface. Here, as in the rest of the study, we use the Centigrade scale, and approximate temperature at Earth's surface to 0\({}^{\circ}\)C.
The top of the lower plate heats as it passes beneath the upper plate. Provided that diffusion of heat parallel to the plate interface may be neglected, temperatures in the lower plate are equivalent to those within a half-space whose surface temperature varies with time. In such cases, a temperature perturbation arises at the top of the half-space over a distance, perpendicular to the interface, that scales as \(\sqrt{\kappa t}\) where \(t\) is the time scale over which the surface is heated ([PERSON], 1959; Section 2.5).
One class of temperature variation is particularly useful for the problem under consideration: if the upper surface of a half-space \(y>0\) is maintained at \(T=Ct^{n/2}\) for \(t>0\), where \(C\) is constant and \(m\) is a positive integer, then the temperature at a distance \(y\) below the surface of the half-space is
\[T(y,t)=C\Gamma(m\;/\;2+1)\big{(}4t\big{)}^{(m/2)}\mathrm{i}^{n}\mathrm{erfc} \Bigg{(}\frac{y}{2\sqrt{\kappa t}}\Bigg{)} \tag{7}\]
where \(\Gamma\) is the gamma function and \(\mathrm{i}^{n}\mathrm{erfc}\) is the repeated integral of the error function ([PERSON], 1959, p 63 and Appendix II). With temperature at Earth's surface being \(\sim\)\(0^{n}\mathrm{C}\), we may set \(T(0,0)=0\) and \(T(0,t)=T_{f}(t)\). The heat flux at the surface of the half-space is
\[K_{2}\frac{\partial T}{\partial y}\Bigg{|}_{y=0} = -b_{m}\frac{K_{2}T_{f}}{\sqrt{\kappa t}}, \tag{8}\]
\[\mathrm{where}\qquad b_{m} = \frac{\Gamma(m/2+1)}{\Gamma(m/2+1/2)} \tag{9}\]
and \(K_{2}\) is the thermal conductivity of the half-space. The analytical expressions for temperatures around the plate interface are obtained by finding \(T_{f}\) such that the difference between the heat flux out of the lower plate and the heat flux into the base of the upper plate is equal to whatever heat flux is generated on the plate interface ([PERSON] & [PERSON], 1990).
We consider first the case in which there is no generation of heat on the plate interface, and denote the heat flux that would have been flowing through the top of the lower plate, had it not been subducted, as \(Q\). We concentrate below on oceanic lithosphere, for which \(Q\) depends on its age, but the derivation is general ([PERSON], 1990) and we do not yet specify a form for \(Q\). Equation 8 gives the diminution of heat flux from the top of the lower plate as a result of its having been heated. Equating the vertical heat fluxes either side of the interface gives
\[\frac{K_{1}T_{f}}{z_{f}}\mathrm{cos}(\delta) = Q-b_{Q}\frac{K_{2}T_{f}}{\sqrt{\kappa u\;/\;V}}, \tag{10}\]
\[T_{f} = \frac{Qz_{f}}{K_{i}\mathrm{cos}(\delta)+b_{Q}K_{2}z_{f}\sqrt{ \kappa u\;/\;V}}=\frac{Qz_{f}}{K_{1}S_{Q}}, \tag{11}\]
\[S_{Q} = \mathrm{cos}(\delta)+b_{Q}\frac{K_{2}}{K_{1}}\sqrt{\frac{Vz_{f}^{2 }}{\kappa u}} \tag{12}\]
\[= \mathrm{cos}(\delta)+b_{Q}\frac{K_{2}}{K_{1}}\sqrt{\mathrm{Pe}}\;, \tag{13}\]
where \(\delta\) is the local dip of the interface and we have substituted \(t\;=u/V\).
For the rest of this study, we consider the lower plate to be oceanic lithosphere of age \(t_{0}\) when it enters the trench and of age (\(t_{0}\;+\;t_{1}\)) when its top is a distance \(u\;(=Vt_{1})\) from the trench. The heat flux, \(Q\), is calculated from the age of the ocean floor using the cooling half-space plate model
\[Q=\frac{KT_{1}}{\sqrt{\kappa u(t_{0}+t_{1})}}, \tag{14}\]where \(T_{i}\) is the temperature of the mantle at the oceanic ridges. Differences between heat fluxes calculated from this expression and from plate models are negligible in the present context (e.g., [PERSON], 1977). However, an important but uncertain adjustment is needed to account for removal of heat from the upper levels of young oceanic lithosphere by hydrothermal circulation (e.g., [PERSON], 1972; [PERSON] et al., 1995; [PERSON] & Stein, 1994; [PERSON], 1976). This process may be allowed for by multiplying the conductive heat flux (Equation 14) by a factor
\[f=0.5+(t_{0}+t_{1})/134\;{\rm Myr}\qquad t_{0}\lesssim 67\;\;{\rm Myr}, \tag{15}\]
([PERSON] & Stein, 1994, Figure 4).
### Temperatures on the Plate Interface in the Presence of Dissipative Heating
We now address the temperatures resulting from dissipative heating on the interface, without any other source of heat. This heating takes place at a rate \(\tau V\), where \(\tau^{\prime}\) is the average shear stress during relative motion across the interface; if that motion takes place primarily in earthquakes, then \(\tau^{\prime}\) may be much lower than the static shear stress (e.g., [PERSON], 2006). As with Equations 6-13, we equate vertical heat fluxes across the interface, but now--in the absence of other heat sources--the heat flux generated at the interface is the sum of the heat fluxes away from the interface
\[\tau V = \frac{K_{i}T_{f}}{z_{f}}{\rm cos}(\delta)+b_{r}\frac{K_{z}T_{f}} {\sqrt{\kappa u\;/\;V}}, \tag{16}\]
\[T_{f} = \frac{\tau Vz_{f}}{K_{i}S_{r}}, \tag{17}\]
\[S_{r} = {\rm cos}(\delta)+b_{r}\frac{K_{z}}{K_{1}}\sqrt{\frac{Vz_{f}^{2} }{\kappa u}} \tag{18}\] \[= {\rm cos}(\delta)+b_{r}\frac{K_{z}}{K_{1}}\sqrt{\rm Pe}. \tag{19}\]
### Appropriate Values for \(b_{0}\) and \(b_{r}\)
Following [PERSON] and [PERSON] (1990), we note that the calculated temperatures on the interface in the case of no dissipation increase approximately linearly with time
\[T_{f}\propto u, \tag{20}\]
which suggests that, when employing Equations 13 and 19, we should use \(m=2\) and \(b=2/\sqrt{\pi}\).
In considering dissipative heating, we shall assume that the effective shear stress, \(\tau^{\prime}\), during slip on plate interfaces is proportional to depth
\[\tau^{\prime}=\mu^{\prime}g\rho z_{f} \tag{21}\]
where \(g\) is the acceleration due to gravity, \(\rho\) is the average density of the plate above \(z_{f}\) and \(\mu^{\prime}\) is an effective coefficient of friction. In this case, Equations 16-19 imply that, for small Pe (\(S\sim{\rm cos}(\delta)\))
\[T_{f}\propto z_{f}^{2}\propto t^{4}, \tag{22}\]
equivalent to \(b=384\;/\;105\sqrt{\pi}\sim 2.06\), and for large Pe
\[T_{f}\propto z_{f}\sqrt{u}\propto t^{3/2}, \tag{23}\]equivalent to \(b=15\sqrt{\pi}\) / \(16\sim 1.66\). For depth-dependent heating on a planar interface, as considered by [PERSON] and [PERSON] (1990),
\[T_{f}\propto z_{f}\sqrt{u_{t}}\propto t^{3/2}, \tag{24}\]
so the appropriate value of \(b\) for that case is \(3\sqrt{\pi}\) / \(4\sim 1.33\) (Table 1).
### Comparison With Previous Analytical Approximations
The essential aspect of the analytical approximations is that temperatures on the interface are reduced, by a divisor \(S\), from those that would be calculated for the same sources of heat (\(Q\) and/or \(\tau V\)), but in the absence of advection. In general,
\[S = \cos(\delta)+b\frac{K_{1}}{K_{2}}\sqrt{\mathrm{Pe}}, \tag{25}\]\[\text{Pe} = \frac{z_{f}^{2}}{\kappa t}, \tag{26}\]
where \(t\) is the time taken for the lower plate to travel from the trench to depth \(z_{f}\)([PERSON], 1990). The relation between distance-squared and time, expressed in Pe, is fundamental to the diffusion of heat, whereas \(b\) and \(\cos(\delta)\) arise from the shape of the plate interface, reflecting respectively the time evolution of temperature rise along the interface, and its local dip.
[PERSON] (2018) and [PERSON] (1993) dealt with curvature of the interface by using the expressions for planar interface with the sine of the dip given by \(z_{f}/\mu\); the influence of this approximation is negligible, as can be seen from Equation 2, recalling that \(\sinh^{-1}(x)\sim x\) for small \(x\). Early applications of the analytical expressions (e.g., [PERSON], 1990, 1995; [PERSON] & [PERSON], 1993) approximated \(\cos(\delta)\sim\)1, recognizing that this simplification is minor in comparison with variation in Pe along, and between, interfaces (Equation 5 and Figure 2).
#### 2.4.1 Errors in the Analysis of [PERSON] et al. (2019)
[PERSON] et al. (2019) revisited the analysis of [PERSON] and [PERSON] (1990) in its entirety, and concluded that neither the original expressions given by [PERSON] and [PERSON] (1990) nor their own modifications to those expressions could \"model the thermal structure for slabs with low thermal parameter due to a fundamental assumption in the derivation of the equations.\" They also concluded that the analytical expressions \"cannot be used for models with significant variation in dip.\" Those conclusions are incorrect.
Although a fundamental error is indeed associated with the first conclusion of [PERSON] et al. (2019), it lies not in the derivation of the original equations but in [PERSON] and coworkers' use of the age of the oceanic lithosphere at the trench to calculate its contribution to the heat flux at depth on the plate interface. As described above (Equation 14), and initially by [PERSON] and [PERSON] (1995, Equation 6), one should use the age of the lithosphere as it passes below the point of interest. In consequence [PERSON] et al. (2019), overestimate temperatures on interfaces above young subducting oceanic lithosphere by up to hundreds of \"C. The correct analytical expressions agree with numerical calculations to within a few percent, even for ocean floor as young as 3 Myr (see [PERSON], 1995, Figures 3 and 4). [PERSON] et al. (2020, Equation 7) appear to have noticed the error of [PERSON] et al. (2019) but, in attempting to correct it, gave the wrong sign in the denominator of the right-hand side of Equation 6 of [PERSON] (1995).
In discussing dissipation on the interface, [PERSON] et al. (2019) found poorer agreement than we do between numerical solutions and analytical approximations, because they used the incorrect value of \(b_{r}\) (1, rather than \(3\sqrt{\pi}\ \text{/}\ 4\), Equation 24) when evaluating [PERSON] and [PERSON]'s (1990) expressions; this can be verified by comparing Figure 10 of [PERSON] and England (1990) with Figure S2.4 of [PERSON] et al. (2019).
[PERSON] and coworkers' conclusion that analytical expressions cannot be applied to plate interfaces whose dip varies with depth is disproved in the subsection that follows. We differ from [PERSON] et al. (2019) on other mathematical points that are of secondary importance to the arguments we develop here; we do not discuss those issues, but our silence should not be interpreted as acquiescence.
### Accuracy of the Analytical Expressions
To determine the accuracy of the analytical expressions of Equations 10-19, we compare them against numerical solutions to the full equations; the means of numerical solution are described in Appendix A. We use \(a=0.001,0.002\), and \(0.004\ \text{km}^{-1}\), which span most of the range observed in modern plate interfaces (Figure 2b), and consider depths up to 80 km, at which the dip of the interface is \(9^{\circ}\), \(18^{\circ}\), and \(33^{\circ}\), respectively.
Figures 3a, 3c and 3e compare the analytical approximation for heating from below (Equations 10-13) using \(b_{\text{Q}}=2/\sqrt{\pi}\ \left(m=2\right)\) with the numerical solutions. For ocean floor of age 100 Myr, the differences between numerical and approximate calculations are smaller than \(15^{\circ}\)C, with the exception of a maximum difference of \(18^{\circ}\)C for a rate of 10 mm/yr, with \(a=0.0004\). For ocean floor of age 9 Myr, the differences rise to 20-\(30^{\circ}\)C but remain smaller than 10% of the actual temperature.
For the case in which there is dissipation on the interface but no heat supplied from below (Equations 16-19 and Figures 3b, 3d and 3f), we use \(b_{r}=15\sqrt{\pi}16\) (\(m=5\)). Temperatures, and hence differences between analytical and numerical solutions, are proportional to \(\mu^{\prime}\); those illustrated are for \(\mu^{\prime}=0.06\). The maximum differences between numerical and approximate calculations are, again, less than \(15^{\circ}\)C, except for a maximum difference of \(22^{\circ}\)C for a rate of \(100\) mm/yr, with \(a=0.004\).
## 3 Range of Temperatures at and Near Plate Interfaces
Our aim has been to provide simple and accurate expressions that may be used for quantitative analysis of a wide range of questions concerning thermal regimes on plate interfaces. We illustrate their use by applying them to the global range of subduction zones to determine the influence of their parameters on the thermal gradients along, and perpendicular to, their plate interfaces. The profiles we use are those of the 80 subduction segments for which England (2018) could reliably determine maximum depths of thrust faulting on the plate interface (the subset illustrated in Figure 2), and temperatures are calculated from the trench to those depths. Convergence rate, \(V\), and the angle, \(\phi\), between the trench and the convergence vector at the origin of the profile, are determined from NNR-MORVEL65 ([PERSON] et al., 2011), the slab configuration is given by its best-fitting parabola (Section 1.1) and the heat flux, \(Q\), is calculated from the age of the ocean floor entering the trench, using Equations 14 and 15.
### Temperature Profiles in the Absence of Dissipation on the Interface
If shear stress on the interface is sufficiently low that dissipation may be neglected in comparison with heat flux out of the lower plate, then the temperature on the interface is
\[T_{f}\sim\frac{Q}{K_{1}}\sqrt{\frac{\kappa u}{V}}-\frac{Q}{K_{1}}\sqrt{\frac{ \kappa z_{f}}{V\sin(\mathcal{N})}}, \tag{27}\]
where the approximation consists in taking \(S_{0}\gg 1\), and we have defined an average plunge, \(\mathcal{N}\), of the interface in the direction of motion by \(u=z_{f}\)\(/\sin(\mathcal{N})\). Equation 27 gives a scale, \(\Theta\), for the temperature gradient
\[\Theta=\frac{T_{f}}{z_{f}}\sim\frac{Q}{K_{1}}\sqrt{\frac{\kappa}{V\sin( \mathcal{N})z_{f}}}. \tag{28}\]
Figure 4a shows profiles of temperature along plate interfaces, calculated under the assumption of no dissipative heating using Equation 11; the parameter \(\Theta\) encapsulates well the variation in temperature profiles. Making the simplification that \(Q\) is inversely proportional to the square root of the age, \(A\), of the ocean floor (Equation 14) the determining parameter, \(\Theta\), may be written
\[\Theta\propto 1\ \sqrt{\frac{AV\sin(\mathcal{N})z_{f}}{f}}, \tag{29}\]
from which it may be seen that descent speed is of equal importance to the age of the slab in determining the thermal gradient along the interface. Furthermore, the temperature gradient along the top of the slab decreases with depth, as can be seen in Figure 4a.
Although the quantity \(AV\sin(\mathcal{N})\) in Equation 29 resembles the \"slab thermal parameter,\" often given the symbol \(\Phi\)([PERSON] et al., 1991), its physical significance is different. \(\Phi\) relates to temperatures in the interior of the slab; in particular, the maximum distance that a given isotherm is advected down-dip increases with \(\Phi\)(e.g., [PERSON], 1969; [PERSON] et al., 1979). In the present context, \(AV\sin\mathcal{N}\) determines temperatures only near the top of the slab, and only when dissipative heating on the interface is negligible.
### Temperature Profiles With Dissipative Heating on the Interface
It is unlikely, however, that shear stresses on the interface are negligible: estimates of shear stresses on plate boundaries from heat flux (e.g., [PERSON] & [PERSON], 2014; [PERSON] et al., 2008; Molnar & England, 1990; [PERSON] et al., 2001; [PERSON] et al., 2013) and the support of topography (e.g., [PERSON] et al., 1997; [PERSON] et al., 2013; [PERSON], 1990; [PERSON] et al., 1983; [PERSON], 2017; [PERSON], 2006; [PERSON], 2007) lie in the range of Figure 4:
tens to a few hundred MPa. With the same approximations that lead to Equation 28, we obtain a scale temperature gradient associated with dissipative heating
\[\Psi=\frac{T_{f}}{z_{f}}\sim\frac{\mu/\rho g}{K_{1}}\sqrt{\frac{\kappa\
abla z_{f }}{\sin(\beta^{\prime})}}. \tag{30}\]
Whereas 6 decreases with convergence rate, \(\Psi\) increases, so the simple dependence of temperature gradient on slab age and descent speed is now lost. The ratio of the two scale temperature gradients is
\[\frac{\Psi}{\Theta}=\frac{\
u r^{\prime}}{Q}. \tag{31}\]
With \(\
u\) varying between 10 and 150 mm/yr, and \(Q\) being 100-200 mW/m\({}^{2}\) for some zones with young ocean floor, and \(\sim\)40 mW/m\({}^{2}\) for old ocean floor, it is evident that the balance between basal heat flux, \(Q\), and dissipation, \(\tau^{\prime}V\) must vary from zone to zone. Figures 4b and 4c, which show calculations with dissipation added on the interface, confirms that there is no simple dependence of thermal gradient along the interface on \(\Psi\). Nevertheless, there is some simplicity: with the exception of a small number of profiles involving young ocean floor, temperature gradients along the interface lie in the range \(6.5\pm 2.5^{\circ}\)C/km for \(\mu^{\prime}=0.03\) and \(11\pm 4^{\circ}\)C/km for \(\mu^{\prime}=0.06\).
### Temperature Gradients at the Top of the Lower Plate
We may also determine scale temperature gradients beneath the interface. In what follows, we assume that the conductivity is uniform, setting \(K_{1}=K_{2}=K\), for which we assume a value of 3 W m\({}^{-1}\) K\({}^{-1}\). In the absence of dissipative heating, the thermal gradient beneath the interface is
\[\frac{\partial T}{\partial\gamma}\bigg{|}_{\gamma=0}=\frac{Q}{K}\bigg{[}1- \frac{b_{Q}\sqrt{\mathrm{Pe}}}{1+b_{Q}\sqrt{\mathrm{Pe}}}\bigg{]}; \tag{32}\]
\(y\) is positive downwards into the plate, so negative gradients correspond to temperatures decreasing with distance into the lower plate. The first term inside the brackets in Equation 32 arises from the thermal gradient near the top of the lower plate had it not been subducted, and the second term from the perturbation due to subduction (Section 2.1). At small and large Pe, the thermal gradient becomes
\[\Gamma_{Q}=\frac{\partial T}{\partial\gamma}\bigg{|}_{\gamma=0} \sim \frac{Q}{K}\bigg{(}1-b_{Q}\sqrt{\mathrm{Pe}}\bigg{)}\qquad\mathrm{ Pe}\ll 1 \tag{33}\] \[\sim 0\qquad\qquad\qquad\qquad\mathrm{Pe}\gg 1 \tag{34}\]
The expressions for dissipative heating alone give perturbations to the thermal gradient of
\[\Gamma_{r} \sim -\frac{\tau Vh_{r}\sqrt{\mathrm{Pe}}}{K}\qquad\mathrm{Pe}\ll 1 \tag{35}\] \[\sim -\frac{\tau^{\prime}V}{K}\qquad\qquad\mathrm{Pe}\gg 1, \tag{36}\]
We define a dimensionless temperature gradient below the interface
Figure 4.— Profiles of temperature along the plate interface, and of inverted temperature gradient beneath the interface. (a) Temperature profiles on the plate interfaces of the 80 subduction zones considered here, using Equation 11 alone (no dissipation on the interface), with the value of \(Q\) appropriate to the age of the ocean floor adjacent to the beginning of the profile adjusted for hydrothermal circulation (Equation 15). Colors of line correspond to (Equation 28), evaluated at \(z_{T}\). Dashed profiles are for ocean floor younger than 20 Myr, with temperatures calculated without hydrothermal adjustment (Equation 14); influence of that adjustment is negligible for greater ages. (b) As for (a), with the addition of temperatures due to dissipative heating on the interface, with \(\mu^{\prime}=0.03\) (Equation 17); (c) as for (a), with \(\mu^{\prime}=0.06\). Colors of line correspond to \(\Psi\) (Equation 30), evaluated at \(z_{T}\). The end of each profile is at the maximum depth of thrust-fluthing earthquakes for that interface (England, 2018), and is marked by a dot. Gray lines are labeled with their slopes in \({}^{\circ}\)C/km. (d) Dimensionless temperature gradient (Equation 37) immediately beneath the 80 interfaces considered here, with conditions corresponding to those in (a). (e) Scale inverted gradient for dissipative heating on the interface (\(\tau^{\prime}V\) / \(K\), Equation 36), contours in \({}^{\circ}\)C/km. (f) As for (d), but with dissipative heating on the interface, and \(\mu^{\prime}=0.03,0.06\); curves from the two values of \(\mu^{\prime}\) overlap.
\[\Gamma^{\tau}=\frac{K\Gamma_{0}}{Q}+\frac{K\Gamma_{\tau}}{\tau V}. \tag{37}\]
The scale gradient when there is no dissipative heating is \(Q\) / \(K\); for example, using the expressions of [PERSON] and [PERSON] (1977), it is \(\sim\)50\({}^{\circ}\)C/km for ocean floor of age 10 Myr, and (30, 20, 15)\({}^{\circ}\)C/km for ages of (25, 60, 120) Myr. The thermal gradient drops from this scale value when it enters the trench to 20% of that value when \(\sqrt{\text{Pe}}\sim 3\) and to 10% of that value when \(\sqrt{\text{Pe}}\sim 6\) (Figure 4d).
The scale gradients in the case of dissipative heating on the interface are shown in Figure 4e for shear stress up to 100 MPa, and convergence rates up to 150 mm/yr. Figure 4f shows dimensionless gradients for the 80 subduction zones when both heating from below and on the interface are included; the curves for \(\mu^{\prime}=0.03\) and \(\mu^{\prime}=0.06\) overlap one another. In all cases, the influence of dissipation on the interface exceeds that of heating from below (gradients become negative) when \(\sqrt{\text{Pe}}\gtrsim 1\); the negative gradients reach about half of their final value when \(\sqrt{\text{Pe}}\sim 2\) and 80% of that value when \(\sqrt{\text{Pe}}\sim 6\).
### \"Hot,\" \"Cool,\" and \"Young\" Plate Interfaces
Many discussions of the distribution of temperatures along plate interfaces posit end-member \"hot\" and \"cool\" subduction zones, and often associate the former with subduction of young ocean floor--the Nankai and Cascadia margins are common exemplars--and associate the latter with subduction of old ocean floor, such as beneath Japan and the Marianas (e.g., [PERSON] and [PERSON], 1999; [PERSON] and [PERSON], 2013; [PERSON] et al., 2018). The discussion of Section 3.1 shows that the age of the ocean floor does not, alone, determine the temperature profile along the interface, even in the absence of dissipation. When dissipation does occur on the interface, then its influence generally outweighs that of slab age, so differences between \"hot\" and \"cold\" subduction zones reflect variation in the product of shear stress and convergence rate on the interface (Section 3.2 and Figure 4).
The notion of hot and cool subduction zones often arises in the interpretation of rocks from high-pressure-low-temperature (HPLT) terrains; here an additional problem arises because the stratigraphic position, within the interface, of the rocks is usually unknown. The temperature differences across a depth range of a kilometer near the interface are tens to about 100\({}^{\circ}\)C (Figures 4d-4f), which is comparable to the range of temperatures at given depths and \(\mu^{\prime}\) across all the subduction segments shown in Figures 4a-4c. P-T measurements from HPLT terrains are therefore unreliable indicators of parameters of subduction such as convergence rate or the age of the descending plate.
Another tenet sometimes applied to the discussion of HPLT terrains is that temperatures in young subduction zones are hotter, at a given depth, than they are in mature subduction zones (e.g., [PERSON] et al., 2018; [PERSON] et al., 2008; [PERSON], 2020; [PERSON] et al., 2018). Expressions for the evolution of temperature on the plate interface during the initiation of subduction show that in the absence of dissipation temperatures do, indeed, drop ([PERSON] and [PERSON], 1990, Equations 3-9, Figure 4), but the steady-state temperatures are less than 100-200\({}^{\circ}\)C unless the age of the subduction ocean floor is also very young (Figure 4a) (see also numerical calculations for three individual subduction zones ([PERSON] et al., 2018, Figure 15)).
In contrast, if there is dissipative heating on the interface--which is required if temperatures on plate interfaces are to approach those of rocks from HPLT terrains that record equivalent pressures (\(\lesssim 1.5\) GPa) ([PERSON] et al., 2018; [PERSON] et al., 2015)--temperatures rise on the interface during the early phase of subduction ([PERSON] and [PERSON], 1990, Equations 11 and 12, Figure 5). It therefore seems that the plate interfaces of young subduction zones are likely to be cooler, not hotter, than in their final states.
Our calculations do not address the interface between the mantle wedge and the slab, but we note that the aforementioned calculations of [PERSON] et al. (2018) show temperature drops of \(\lesssim 100\)\({}^{\circ}\)C on the wedge-slab interface during the first few Myr; those drops are small in comparison with the range of temperatures calculated for mature wedge-slab interfaces (e.g., [PERSON] et al., 2010, as corrected and reported by [PERSON] et al., 2011, Supporting Information). In contrast, [PERSON] et al. (2002) show temperatures in the mantle wedge increasing as the subduction zone ages. That evolution is consistent with scaling arguments (e.g.,[PERSON] & [PERSON], 2004; [PERSON] & [PERSON], 2010): temperatures in the mantle wedge are dominated by the advection of heat toward the wedge corner, which is driven by the downward motion of the descending slab. We should therefore expect temperatures within the wedge and on the wedge-slab interface to increase as the subduction zone ages, the slab lengthens, and the intensity of flow in the wedge increases.
## 4 Conclusions
The shapes of most modern plate interfaces are well described by parabolas, with curvature in the range 0.0005-0.004 km\({}^{-1}\) (Figure 2). We give analytical expressions for temperatures on parabolic plate interfaces (Equations 10-19) and discuss, in Section 2.4, the differences between these and previous expressions, some of which ([PERSON] et al., 2019) are erroneous. The analytical expressions differ from numerical solutions to the full equations by a few percent (Figure 3). Such differences are negligible in comparison with the epistemic uncertainty attached to the idealization of plate interfaces by a simple mathematical model, and with uncertainties in the physical parameters. For instance, uncertainties in the relevant thermal conductivity and diffusivity are at least 20% (e.g., England, 2018, Appendix A) and uncertainties in shear stresses during motion on the interface are surely some tens of percent (Section 3.2). There is therefore no way of telling, for a given case of interest, whether a numerical model lies closer to reality than do the analytical expressions. The latter are to be preferred because they provide a simple and transparent means of evaluating temperatures, and their uncertainties, on plate boundaries.
Temperatures calculated for plate interfaces depend critically upon assumptions about the level of shear heating there (e.g., [PERSON] et al., 2018; Molnar & England, 1990; [PERSON], 1996; [PERSON] et al., 2015). The global range of temperatures at 30-60 km is \(\sim\)\(50-200^{\circ}\)C without shear heating (Figure 4a), \(\sim 250-350^{\circ}\)C if the effective coefficient of friction during slip, \(\mu^{\prime}\), is 0.003 (Figure 4b), and \(\sim 250-600^{\circ}\)C if \(\mu^{\prime}\), is 0.006 (Figure 4c). For the range of shear stresses likely to operate during slip on plate interfaces (e.g., England, 2018; [PERSON] & [PERSON], 2014; [PERSON] et al., 2008; [PERSON] & England, 1990; [PERSON] et al., 2001; [PERSON] et al., 2013), inverted temperature gradients at the plate interface are likely to be several tens of, to about \(100^{\circ}\)C/km (Figure 4e).
The use of pressure-temperature conditions recorded by HPLT rocks to infer parameters of ancient subduction zones, such as convergence rate, ages of ocean floor, or maturity, should be approached with caution (Section 3.4).
## Appendix A Numerical Calculations
The numerical calculations employed in this work share many similarities with previous kinematically driven models of subduction zones (e.g., [PERSON] et al., 2004; [PERSON] et al., 2010; [PERSON] et al., 2002, 2008). In such models, the flow in the wedge is driven by a subducting plate that is prescribed in terms of a time-independent geometry and of a convergence rate \(V\). The geometry of the calculations is defined by four non-overlapping domains, shown in Figure A1: the mantle wedge \(\Omega_{\pm}\); the subducting plate \(\Omega_{z}\); the over-riding plate \(\Omega_{\varphi}\) and a thin dissipation layer charged on top of the plate interface \(\Omega_{\mathrm{r}}\). The geometry of \(\Gamma_{\mathrm{interface}}\) is given by Equation 1. The line \(\Gamma_{\mathrm{c}}\) is obtained by locally projecting \(\Gamma_{\mathrm{interface}}\) a distance \(\delta_{\mathrm{s}}\) (the subducting plate thickness) in the direction normal to the interface. The tip of the dissipation layer, which connects to \(\Omega_{\varphi}\) is defined by a straight line segment and constructed such that it intersects the plate interface at \(30^{\circ}\). We describe the full calculation scheme here, although for the present application we solve for deformation only in the slab.
The origin on the coordinate system is located at the trench (indicated by the solid gray circle in Figure A1). The overall width of the calculation domain, \(L\), is set to 1,200 km to accommodate the full range of interface geometry we consider, and the thickness \(\delta_{\mathrm{s}}\) is set to 100 km. These lengths are comfortably large enough that the positions of the associated boundaries do not influence our calculations. For the shallowest interfaces \(a=0.001\), at the smallest convergence rates, we consider (10 mm/yr), the top of the lower plate reaches 80 km (the maximum depth over which we analyze solutions) in \(\sim 30\) Myr; the diffusion length (\(\sim\sqrt{\mu\pi\pi}\) ) associated with this time is \(\sim\)15 km.
The numerical simulations utilize a continuous Galerkin finite element (FE) method employing an unstructured mesh comprised of triangles. An inf-sup stable mixed formulation ([PERSON], 1991) was used to discretize the flow problem in Equation 1 employing \(\mathbf{P}_{2}\) (quadratic) \(\times P_{1}\) (linear) function space for velocity \(\mathbf{r}\) and pressure \(p\) respectively. The energy equation (Equation 2) was also solved using continuous Galerkin finite element, with temperature \(T\) discretized by a \(P_{2}\) function space. The use of an analytic description of the subduction interface is particularly useful in the context of FE modeling as it provides an analytic description of the normal and tangent vectors along the slab. This is particularly useful when describing the boundary conditions for the flow problem in the slab. Additionally, since the subduction interface used here is quadratic, we can exactly represent this geometry with the quadratic function space used for velocity and temperature. Hence, in the calculations here, the finite elements along the subduction interface are actually curved and conform exactly to Equation 1. Constraints on the normal and tangential components of the velocity field along this interface are imposed by locally rotating the coordinate system associated with each FE basis function to be aligned with the geometry of the subduction interface. The numerical solution of the steady-state energy equation did not require any numerical stabilization techniques (e.g., SUPG, entropy viscosity) due to the magnitude of the Peclet numbers under consideration and the numerical spatial resolution used. Denoting the area of each finite element as \(\Delta_{e}\), in the calculations shown here the meshes were constructed such that within the dissipation layer \(\Delta_{e}\leq 0.0025\) km\({}^{2}\), while in all other regions (\(\Omega_{w,s,p}\)), we used \(\Delta_{e}\leq 5.0\) km\({}^{2}\). This results in a spatial resolution of \(\approx 0.7\) km inside \(\Omega_{1}\) and \(\approx 3\) km elsewhere. The underlying finite element software was developed using PETSc ([PERSON] et al., 2017).
## Data Availability Statement
Data used in this study are from the published sources cited.
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* [PERSON] (2007) [PERSON] (2007). Absolute heat and crustal strength from wake slopes. _Geology_, 35, 1127-1130. [[https://doi.org/10.1130/ja20053a.1](https://doi.org/10.1130/ja20053a.1)]([https://doi.org/10.1130/ja20053a.1](https://doi.org/10.1130/ja20053a.1))
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wiley/ff83f961_3088_4758_97b2_0803ce1ee2bb.md | # Earth and Space Science
###### Abstract
Over arid areas, observations of brightness temperatures by passive microwave radiometers are affected by the variation of the emitting depth with wavelengths. When this variation is unaccounted for, it limits the assimilation of passive microwaves over deserts in Numerical Weather Prediction models and it causes large errors in passive microwave retrievals of land surface temperatures. The emitting depths, along with the corresponding emissivities, are estimated from 10 to 89 GHz, using the non-Sun-synchronous observations of the Global Precipitation Mission Microwave Imager to reconstruct the monthly diurnal cycle of brightness temperature. The soil temperature profile is modeled using a two-term Fourier decomposition based on the ERA5 surface temperature. The combination of the observation and the modeled temperature allows for an estimation of the microwave effective emitting depth. The emitting depth is estimated to be up to 25 cm at 36 GHz, resulting in large differences between the surface temperature and the effective emitting temperature. The variation of emitting depth with frequency is parameterized, and a companion data set provides the necessary parameters to calculate the emitting depth for arid areas between 10 and 89 GHz, globally. The benefit of this parameterization is quantified, with an application to the modeling of observations from the Special Sensor Microwave Imager Sounder over arid areas.
10.1029/2022 EA002756
EARTHAND
**Global Mapping of Microwave Emissivity and Emitting Depth**
**in Arid Areas Using GMI Observations**
**[PERSON]\({}^{1,2}\)\({}^{\copyright}\), [PERSON]\({}^{1,2}\)\({}^{\copyright}\), [PERSON]\({}^{1,2}\), and [PERSON]\({}^{\copyright}\)\({}^{1}\)**
\({}^{1}\)Observatoire de Paris, Sorbonne Universite, CNRS, LERMA, PSL University, Paris, France, \({}^{2}\)Estellus, Paris, France, \({}^{3}\)Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, \({}^{4}\)Department of Environmental Sciences, University of Basel, Basel, Switzerland
**Clication:**
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON], [PERSON] (2023). Global mapping of microwave emissivity and emitting depth in arid areas using GMI observations
**10**, 2022 EA002756. [[http://doi.org/10.2022](http://doi.org/10.2022) EA002756]([http://doi.org/10.2022](http://doi.org/10.2022) EA002756)
Received 19 DEC 2022
Accepted 17 JUN 2023
**Author Contributions:**
**Conceptualization:** [PERSON], [PERSON], [PERSON],
**Data extraction:** [PERSON], [PERSON]
**Formal analysis:** [PERSON]
**Funding acquisition:** [PERSON]
**Investigation:** [PERSON],
**Contribute:**
**Methodology:** [PERSON]
**Project Administration:** [PERSON], [PERSON]**
**Resources:** [PERSON]
**Solver:** [PERSON]
**Supervision:** [PERSON], [PERSON],
**Funding acquisition:** [PERSON]
**Visualization:** [PERSON]
**Writing- original draft:** [PERSON]**
**Global Mapping of Microwave Emissivity and Emitting Depth**
**in Arid Areas Using GMI Observations**
**[PERSON]\({}^{1,2}\)\({}^{\copyright}\), [PERSON]\({}^{1,2}\)\({}^{\copyright}\), [PERSON]\({}^{1,2}\), and [PERSON]\({}^{\copyright}\)\({}^{1}\)**
\({}^{1}\)Observatoire de Paris, Sorbonne Universite, CNRS, LERMA, PSL University, Paris, France, \({}^{2}\)Estellus, Paris, France, \({}^{3}\)Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, \({}^{4}\)Department of Environmental Sciences, University of Basel, Basel, Switzerland
## 1 Introduction
Passive microwave satellite observations are extensively contributing to the monitoring of the Earth atmosphere and surface, through the direct retrieval of geophysical parameters or through data assimilation within Numerical Weather Prediction (NWP) schemes. Compared to the ocean, microwave assimilation and surface parameter retrievals are complicated over land by the large spatial and temporal variability of the surface contribution. Deserts have been identified as a particularly challenging land surface type for microwaves, where the surface emission is not always directly related to the surface temperature. The diurnal variations of the microwave brightness temperatures \(T_{b}\) can be small relative to the surface temperature changes and the difference is larger in sand deserts, where the radiation is likely to come from deeper layers in the sub-surface.
For instance, the assimilation of the 50 GHz microwave temperature sounding observations is significantly limited over deserts by the inability to accurately model the surface emission, resulting in the rejection of many satellite measurements ([PERSON] et al., 2017). Similarly, \"all weather\" surface temperatures are derived from passive microwaves over snow-free land, but over deserts the accuracy of the retrievals is hampered by the lack of direct link between the microwave signal and the surface temperature ([PERSON] et al., 2017; [PERSON] et al., 2017).
The atypical microwave responses over arid regions have been mentioned early, at 19.35 and 37 GHz with the Electrically Scanning Microwave Radiometer on board the Nimbus 5 and 6 satellites ([PERSON], 1976). The attribution of the observed signal to emission from the sub-surface was described by [PERSON] et al. (1981): the dryerthe soil the deeper the emitting layer, and the emitting depth increases with wavelength increase. The surface emissivities and emitting depths in arid regions were estimated by [PERSON] et al. (1999) from 19 to 85 GHz. The diurnal cycles of Special Sensor Microwave/Imager (SSM/I) observations and satellite-derived infrared surface temperature were jointly analyzed with a simple thermal conduction model, to extract these parameters. [PERSON] et al. (2011) applied a similar method to both SSM/I and Advanced Microwave Scanning Radiometer-E (AMSR-E) observations, along with the Moderate Resolution Imaging Spectroradiometer surface temperatures, to estimate emissivity and emission depth index (encompassing emitting depth and a thermal parameter) at a global scale.
To understand the microwave emissions from arid areas, theoretical models and experiments have also been designed. Measurements of the dielectric properties of mineral and soil samples were conducted, from which the emitting depth can be calculated ([PERSON] et al., 1985; [PERSON], 1998; [PERSON], 2004; [PERSON] et al., 1990; [PERSON] et al., 2012; [PERSON] et al., 2005). Parametric models have been derived from these experiments, as a function of multiple parameters such as soil texture, porosity, moisture content, temperature, and frequency.
At a global scale, the estimation of the emitting depth from satellites has been hampered so far by the lack of \(T_{b}\) observations at multiple local times with Sun-synchronous imagers such as SSM/I and AMSR-E. Here, we propose to revisit the calculation of the emitting depth in the microwaves from 10 to 89 GHz, with the Global Precipitation Measurement (GPM) Microwave Imager (GMI) that is on a non-Sun-synchronous orbit and can therefore observe a given location under the full diurnal cycle ([PERSON] et al., 2014). The methodology follows the procedure proposed by [PERSON] et al. (1999). Hourly atmospheric and surface reanalyses from the European Center for Medium range Weather Forecast (ECMWF) ERA5 are used to provide the atmospheric vertical profile and surface parameters, especially Land Surface Temperature (LST). Both emissivities and emitting depths are simultaneously estimated for all arid areas. The dielectric properties of the arid soils are derived from the estimated emitting depths, and a parameterization of the penetrating depth is proposed, as a function of frequencies between 10 and 89 GHz. A companion data set is generated, providing the community with the emissivities and necessary parameters to derive the penetration depths estimated using the aforementioned input datasets.
Section 2 lists the data used in the estimations and their evaluation. Section 3 describes the methodology, including the radiative transfer, the thermal diffusion model, and the retrieval procedure. The resulting maps of emissivities and emitting depths are presented and evaluated, along with the estimated soil temperature profiles (Section 4). After a discussion on the soil moisture effect, Section 5 proposes a parameterization of the dielectric properties and penetration depth in arid areas. Finally, the utility of the emitting depth estimation for an assimilation application is tested. Section 6 concludes this study.
## 2 Data
To estimate the microwave emitting depths and effective emissivities over arid areas, several datasets are collected, including microwave observations from GMI, ERA5 reanalyzes, and necessary ancillary information.
### Gmi
The GPM mission was launched in 2014, on a non-Sun-synchronous orbit that provides data between 68\({}^{\circ}\)S and 68\({}^{\circ}\)N over the full diurnal cycle. GPM carries a multichannel passive Microwave Imager (GMI) observing at 52.8\({}^{\circ}\) incidence angle, in addition to a dual frequency precipitation radar. Thirteen microwave channels are available on board GMI, but only the window channels at 10.65, 18.7, 36.5, and 89.0 GHz (both in vertical [V] and horizontal [H] polarizations) are used in this study for their sensitivity to the surface properties, the other channels being mainly designed for atmospheric analysis. In the following, the channel denomination is rounded to the lowest integer. The spatial resolution varies from 25 km at 10 GHz to 6 km at 89 GHz.
The GMI brightness temperature (\(T_{b}\)) products are extracted, from January 2015 to December 2020. Time and space averaging is necessary to have enough observations of a given location, at a given local time. For a robust analysis of the diurnal variability of the microwave \(T_{b}\), an hourly sampling of the diurnal cycle was decided. Several tests have been conducted and \(T_{b}\) data are averaged over a 0.25\({}^{\circ}\times\) 0.25\({}^{\circ}\) regular grid, averaged per hour, per month, and over the 6 years (2015-2020). A statistical cloud filtering is further applied to avoid cloud contamination ([PERSON] et al., 2019). Note that the hourly temporal sampling and the 0.25\({}^{\circ}\) grid are compatible with the surface temperature reanalyzes also used in this study (see Section 2.2). Figure 1 presents the resulting amplitude of the \(T_{b}\) diurnal cycles, for January, at 10 and 85 GHz, over the Sahara and the Arabian Peninsula.
### Era5
The ECMWF and Copernicus produce a reanalysis, ERA5, that provides estimates of a large range of atmospheric and surface variables at a global scale with a 1-hr temporal resolution and a 0.25\({}^{\circ}\) spatial resolution ([PERSON] et al., 2020). The reanalysis uses models developed for weather forecast and assimilates multiple sources of measurement, including in situ stations and satellite observations. For the soil thermal conduction model developed in this study, the ERA5 surface \"skin\" temperature (_skt_ variable) is adopted. It is considered equal to the temperature at a 0 cm depth in the soil \(T_{\text{c}=\text{min}}\). The ERA5 soil moisture in the first soil layer is also used, for further analysis. To compute the atmospheric contribution to the \(T_{b}\), the ERA5 atmospheric temperature, humidity, and pressure profiles are extracted. For all these variables, the monthly diurnal cycles are calculated, averaged over the 6 years, as for the GMI data. Figure 1 shows the mean diurnal amplitude of the surface skin temperature for January, over 2015-2020, for comparison with the GMI \(T_{b}\) amplitudes. The diurnal amplitudes of the ERA5 skin temperatures and the \(T_{b}\) at 85 GHz share similar spatial patterns, but they strongly differ with the patterns observed on the corresponding 10 GHz maps. The \(T_{b}\) amplitudes at 10 GHz show areas with almost no diurnal \(T_{b}\) variation, despite large surface temperature amplitudes with ERA5 and large \(T_{b}\) amplitudes at 89 GHz, contrasting with regions where \(T_{b}\) amplitudes at 10 GHz are of similar amplitudes than at 89 GHz.
### Ancillary Data
To delineate the arid regions, the land cover map from [PERSON] et al. (2002) is adopted and the barren and open shrubland types are selected.
Soil properties such as sand fraction and soil density are derived from the Global Soil Data set for Earth System Modeling (GSDE) ([PERSON] et al., 2014). This data set combines geological surveys and machine learning to create global maps of soil parameters. Data are available on multiple soil layers, but the variability with depth is low in arid regions and the uppermost layer value (between 0 and 4.5 cm) is used in the analysis. Figure 1 shows the soil density (g.cm\({}^{-3}\)) over the Sahara and the Arabian Peninsula, regridded on the 0.25\({}^{\circ}\times\) 0.25\({}^{\circ}\) grid. The maps can show non-natural features such as the block-like patterns around 20\({}^{\circ}\)N 10\({}^{\circ}\)E, likely due to a lack of information.
For the evaluation of the thermal conduction model, very limited in situ soil temperature measurements are available in arid regions, at different depths. The Gobabeb station (\(-\)23.56\({}^{\circ}\)N 15.04\({}^{\circ}\)E at 409 m altitude) in the Namib Desert provides such a data set, combining infrared radiometer for skin temperature measurements with soil temperature probes from 5 to 100 cm depths in 2017 and 2018 ([PERSON], 2021).
Figure 1: Maps over North Africa and the Arabic Peninsula of the amplitude of the brightness temperature diurnal cycle in January for the H polarization, at 10 GHz (a) and at 89 GHz (b), along with the amplitude of the average monthly skin temperature diurnal cycle from ERA5 for the same month (c), and the soil density (d) provided by the Global Soil Data set for Earth System Modeling data set, for the top soil layer (0–4.5 cm depth).
The microwave emissivity maps from the Tool to Estimate Land Surface Emissivities from Microwave to Millimeter waves (TELSEM\({}^{\rm 2}\)) ([PERSON] et al., 2011; [PERSON] et al., 2017) is used for comparison of the estimated emissivities. TELSEM\({}^{\rm 2}\) is derived from a collection of passive microwave satellite observations, and provides global monthly mean emissivities over a large range of frequencies, and incidence angles, for both orthogonal polarizations.
For an evaluation of the method on independent microwave satellite observations, the Special Sensor Microwave Imager Sounder (SSMIS) brightness temperature observations are used. The observations are collected from a Sun synchronous orbit at 19.35 and 37.00 GHz in V and H polarizations with an observing incidence angle of 53.1\({}^{\circ}\), close to the GMI one ([PERSON] et al., 2008). Observations provided in the Satellite Application Facility for Climate Monitoring archive ([PERSON] et al., 2020) are aggregated by day of year over the same years (2015-2020) and a sample of those is used to evaluate the methodology.
## 3 Methodology
### A Simplified Radiative Transfer Equation
The radiative transfer equation links the \(T_{b}\) measured at the satellite level to the different signal sources, including atmospheric and surface contributions. Here, it is assumed that in the arid regions, the soil can be described by a single effective layer at depth \(d_{\rm eff}\)(called the effective emitting depth) with its associated effective temperature \(T_{\rm eff}\) and effective emissivity \(e_{\rm eff}\) from which all soil microwave radiation emanates. All these parameters depend upon the observation frequency \(\
u\), with \(d_{\rm eff,a}\) expected to increase with increasing wavelength in the dry soils. Specular reflection can only occur at the air-soil interface, and all reflection and scattering within the soil are neglected. The \(e_{\rm eff,b}\) will also depend upon the polarization, while it is assumed that \(d_{\rm eff}\) will not ([PERSON] et al., 1999). At a frequency \(\
u\) and polarization \(p\) (with \(p=V\) or \(p=H\)), the measured brightness temperature \(T_{b,\rm eff,a}\) can be written as ([PERSON] et al., 1999; [PERSON] et al., 2013):
\[T_{b,\rm eff,a}=T_{b,\rm i,\
u}\,\big{[}e_{eff/\
u,a}T_{eff/\
u}+(1-e_{eff/\
u, a})T_{b,\rm i,\
u}\big{]}. \tag{1}\]
with \(T_{b,\rm i,\
u}\) and \(T_{b,\rm i,\
u}\) representing the ascending and descending atmospheric brightness temperature contributions, and \(\tau_{\rm e}\) the atmospheric transmission, with due consideration to the observation incidence angle.
The atmospheric contributions \(\tau_{\rm e}\), \(T_{b,\rm i,\
u}\), and \(T_{b,\rm i,\
u}\) and \(e_{\rm eff,a,\
u}\) are calculated at each wavelength, to minimize the mean square differences between the monthly mean simulated and measured \(T_{b,\rm a,\
u}\) and \(T_{b,\rm a,\mu}\) over the diurnal cycle (24 samples) for the given month. This requires the calculation of the sub-surface temperature profile with a one-dimensional heat conduction model (described in the following section), using the monthly mean ERA5 skin temperature as a boundary condition.
### Estimating the Sub-Surface Temperature Profile Over the Diurnal Cycle
The temperature evolution at any depth in the soil can be computed using the [PERSON]'s law of thermal conduction:
\[k\frac{\partial^{2}T}{\partial z^{2}}=\rho C\frac{\partial T}{\partial t} \tag{2}\]
This equation describes the rate of change of temperature \(T\) with time \(t\) in the vertical direction \(z\). The thermal conductivity \(k\) (W - m\({}^{-1}\). K\({}^{-1}\)) is a measure of the ability of the material to conduct heat. The product between the density \(\rho\) (kg - m\({}^{-3}\)) and the specific heat capacity \(C\) (J - kg\({}^{-1}\)) represents the amount of heat stored per soil unit volume. To simplify the equation, a single parameter called thermal diffusivity, \(\alpha=\frac{k}{\rho c}\), can be adopted. Here, it is assumed that the heat exchange only happens in the vertical direction, without any exothermic process in the soil. In addition, within a given 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) grid cell, the soil properties are assumed constant with depth and time. In these arid regions, the soil moisture content is small, and therefore the heat changes caused by water displacement or state change (evaporation, freezing) are neglected. In [PERSON] et al. (1999), \(\alpha=2\times 10^{-7}\) m\({}^{2}\)/s was adopted as representative of the average value of thermal parameters in arid areas. The same value is used here as it is a good approximation of the dry soil thermal properties and the exact values (depending on soil moisture, soil thermal properties) remain difficult to compute. The effect of changing this parameter will be discussed in Sections 4.1 and 5.1. The boundary condition at the surface is provided by the monthly mean ERA5 skin temperature over the diurnal cycle, and the temperature stays constant with time, past a certain depth (\(\geq\)1 m). Numericalor analytical methods can be adopted to compute the solution to Equation 2, but with periodic surface boundary conditions, the analytical solution is faster to compute.
With the surface temperature \(T\) following daily periodic variations with a pulsation \(\omega=\frac{2\pi}{86,400}\) (rad.s\({}^{-1}\)), the temperature \(T(z,t)\) at a depth \(z\) and time \(t\) can be expressed as the sum of sinusoidal functions:
\[T(z,t)=\overline{T}+\sum_{n}\exp\left(-z\sqrt{\frac{n\omega}{2\alpha}}\right) A_{n}\text{cos}\left(n\text{{\it m}}+\phi_{n}-z\sqrt{\frac{n\omega}{2 \alpha}}\right) \tag{3}\]
\(\overline{T}\) is the average temperature over a diurnal cycle. \(A_{n}\) and \(\phi_{n}\) are the amplitude and phase of the cyclic components. The parameters to be found in this equation depend upon the number of components in the summation. With \(n=2\), satisfactory accuracy can be reached and there are only four parameters to be fitted to the surface temperature diurnal cycle, expressed as:
\[T(z=0,t)=\overline{T}+A_{1}\text{cos}(\text{{\it or}}+\phi_{1})+A_{2}\text{ cos}(2\text{{\it or}}+\phi_{2}) \tag{4}\]
The four parameters (\(A_{1},A_{2},\phi_{1}\), and \(\phi_{2}\)) are estimated with a least square fit to the monthly mean surface skin temperatures from the ERA5 reanalysis. This provides an estimation of the parameters describing the surface diurnal cycle for every for each month and location. Note that ERA5 also provides sub-surface temperature profiles, averaged over rather thick layers (from 0 to 7 cm, 7-28 cm, 28-100 cm and 100-289 cm). This possibility was tested, but it was not offering the vertical resolution needed for this application.
### Minimization Procedure at Each Location for Each Frequency
A least square minimization is applied between the modeled and observed brightness temperatures in order to calculate simultaneously \(e_{\phi_{th},n}\) or \(e_{\phi_{d},v}\) and the emitting depth \(d_{\phi_{d}}\) such that \(T_{\phi_{d},v}(t)=T(z=d_{\phi_{d}},t)\).
The following cost function between the modeled \(T_{b}^{*}\) and observed \(T_{b}^{\text{{\it G}}MI}\) (with a standard deviation \(\sigma_{T_{b}^{\text{{\it G}}MI}}\)) is minimized:
\[CF=\sum_{h=0}^{23}\left(\frac{T_{h,V}^{*}-T_{h,V}^{\text{{\it G}}MI}}{\sigma_{ T_{h,V}^{\text{{\it G}}MI}}}\right)^{2}+\sum_{h=0}^{23}\left(\frac{T_{h,H}^{*}-T_{h,H}^{ \text{{\it G}}MI}}{\sigma_{T_{h,V}^{\text{{\it G}}MI}}}\right)^{2} \tag{5}\]
This operation is repeated for all arid pixels, for each month and each frequency, providing global effective emissivity maps over arid areas (\(e_{\phi_{th},n}\) and \(e_{\phi_{d},v}\)), along with corresponding emitting depth maps (\(d_{\phi_{d},v}\)). For all retrievals, the uncertainty corresponding to the square root of the variance of the estimated parameters are reported. They give an indication of the goodness of fit of the parameter optimization procedure.
## 4 Results
First, the soil temperature profile results are presented, with an evaluation from one in situ data set, followed by an illustration of the sensitivity of the temperature profile to the thermal parameters. Then, the emissivity maps are displayed, and compared to previous emissivity estimates. Finally, the emitting depth maps are shown.
### The Soil Temperature Diurnal Cycle at Different Depths
Figure 2 shows the mean diurnal cycles of the surface skin temperatures \(T(z=0\) cm) from ERA5, in May at two locations in the Sahara, along with the corresponding GMI \(T_{b}\) at different frequencies and polarizations. The mean surface temperature diurnal cycle is propagated below the sub-surface following the [PERSON]'s equation (Section 3.2). For both locations, the analytical temperature fit at the surface (\(z=0\) cm) shows as expected a good agreement with the ERA5 temperature (black crosses), with limited differences, mostly noticeable around 06:00 and 18:00. The resulting sub-surface temperature diurnal cycle is shown for different depths at 5, 10, and 30 cm. With increasing depth, the diurnal amplitude of the temperature cycle decreases, and the maximum temperature is reached later in the day. For a depth over 30 cm, the amplitude of the diurnal cycle is very limited.
The two locations show very contrasted \(T_{b}\) behaviors. Over a sandy desert (Bilma Erg, 25\({}^{\circ}\)N 12.5\({}^{\circ}\)E, on the left), the amplitudes of the \(T_{b}\) diurnal cycles are limited, compared to the amplitude of the surface temperature, and the \(T_{b}\) amplitudes tend to increase with increasing frequency. Over rocky areas (around the Haruj volcanic field, 28\({}^{\circ}\)N 17\({}^{\circ}\)E, on the right), all \(T_{b,v}\) have similar diurnal variations, regardless of the frequencies, and the amplitude of the \(T_{b,v}\) cycles is similar to the amplitude of the ERA5 skin temperature cycle. For both sites, at a given frequency,\(T_{b,H}\) are lower than \(T_{b,v}\), as expected from weaker emissivities in the horizontal polarization compared to the vertical polarization, for off-nadir observations.
To further evaluate the ability of the analytical model to represent the temperature cycle in the ground, data from 2017 at an in situ station in Gobabeb (\(-\)23.56\({}^{\circ}\)N 15.04\({}^{\circ}\)E) are analyzed. The diurnal cycle of soil temperatures is estimated at different depths, and compared to the corresponding in situ measurements. On Figure 3, the monthly averaged diurnal cycles from the GMI \(T_{b}\) observations are computed for the month of December. The description of the diurnal variations by the simplified Fourier model matches reasonably well the actual in situ variations. The in situ skin temperature shows some noise around 06:00 possibly caused by instrumental issues. The effect of the thermal model parameter is tested, and also shown on Figure 3 using different \(\alpha\) values in the calculation. The variation of the thermal diffusivity can be partially driven by changes in the soil moisture content or local soil thermal properties. In arid areas with very low soil moisture content, the \(\alpha\) variations are limited between 1 and 3 m\({}^{2}\)/s, leading to small differences in the soil temperature cycles. Evaluation of the thermal parameters is very challenging, given the very limited information on the soil properties.
The calculated and observed amplitudes of the temperature diurnal cycles have also been systematically compared over the year at 0, 5, and 10 cm and 30 cm (results not shown here). The change in amplitude with depth is significant, especially over the first centimeters, with a division of the amplitude by \(\sim\)2 between 0 and 5 cm depth, for both observation and model values. For the Gobabeb site and for the selected thermal parameter (\(\alpha=2\times 10^{-7}\) m\({}^{2}\)/s), the model provides similar diurnal amplitudes at 5 cm, but tends to under-estimate the amplitudes around 10 cm depth. The agreement between the model and the measurements at this single in situ station is encouraging. Unfortunately, evaluation of the model at other sites and at larger scales is limited by the available in situ datasets.
### Emissivity Maps
Monthly effective emissivity maps are produced, for each frequency and polarization. For North Africa and the Arabic Peninsula, the results at 36 GHz are shown for September, for V and V-H polarizations, along with
Figure 3: Average soil temperature diurnal cycles (K) in December at Gobabeb at 0, 5, 10, and 30 cm depths. In situ measurements from the station in continuous lines, the discontinuous lines from the analytical model with different values for the \(a\) parameter.
Figure 2: Average temperature diurnal cycles modeled at different depths (full line no marker) and brightness temperatures cycles from GMI for the month of May, over a sandy area (25\({}^{\circ}\)N 12.5\({}^{\circ}\)E, left) and over a rocky area (28\({}^{\circ}\)N 17\({}^{\circ}\)E, right). The ERA5 skin temperatures are shown with black cross, and the temperatures modeled by the analytical solution of the Fourier equation at 0, 5, 10, and 30 cm depths in full lines. GMI \(T_{a}\) are given for the vertical (triangle) and horizontal (square) polarizations at 10, 18, 36, and 89 GHz with one standard deviation around the mean brightness temperature indicated with shades.
the retrieval uncertainty (Figure 4). The corresponding TELSEM\({}^{2}\) estimates are also indicated. The emissivity maps are in good agreement with TELSEM\({}^{2}\) results, with similar emissivity ranges and spatial structures, although the penetration depth is not taken into account in the TELSEM\({}^{2}\) methodology. The difference between the two datasets does not exhibit systematic differences, and the maximum root mean squared deviation between the two datasets for each month is less than 0.02 at 18 and 36 GHz. This is reasonable, considering that different instruments, hypotheses, and ancillary parameters (LST especially) are used to estimate these two emissivity datasets. In the hot arid areas considered here, the annual variability of the emissivity parameters stays below 0.005 for all frequencies below 36 GHz and below 0.01 at 89 GHz.
The obtained emissivity spatial structures match known topographic and geological features. For instance, the contrast between flat (ergs, and desert) and mountainous areas (e.g., Hoggar, Atlas) are evidenced on the V-H emissivity maps, with decreasing polarization difference with increasing topographic roughness ([PERSON] et al., 1997). At 36 GHz in V polarization, lower emissivities are calculated in Oman, or in Egypt, as already described by [PERSON] et al. (2010). These low emissivity structures are related to the presence of tertiary carbonate sedimentary platforms. Carbonate dielectric properties have been measured and showed high permittivities compared to other materials (such as silicates also widely spread in deserts), resulting in much lower emissivity observed over carbonate outcrops ([PERSON] et al., 2005).
### Maps of the Emitting Depth
The emitting depth and the associated retrieval uncertainty is estimated for each month and frequency, and it is assumed to be the same for both orthogonal polarizations. Figure 5 shows the estimate emitting depth at 18 GHz for the month of September. The area with noticeable emitting depths are mostly located in the Sahara and Arabian deserts, but the effect can also be detected in the Taklamakan and other arid and semi arid areas in Namibia and Australia.
Figure 4: Maps of emissivities at 36 GHz for V polarization (a) and for the difference V-H polarization (b) over the Sahara and Arabian deserts obtained with our method (top), and with Tool to Estimate Land Surface Emissivities from Microwave to Millimeter waves (TELSEM\({}^{2}\)) (bottom) for the month of September. The middle row shows the retrieval uncertainty for the V (left) and H (right) polarizations for the same month.
of the deserts, with dryer and more stable arid conditions. In the sub-Saharan transition zone (around 15\({}^{\circ}\)N), the sandy regions are likely to experience more soil moisture variations along the year, and as a consequence show also smaller emitting depths, compared to dryer regions. Figure 7b shows the normalized standard deviation of the emitting depth at 10 GHz over 12 months. It is computed as the standard deviation of emitting depth for each pixel divided by the mean value of that pixel. The penetration depth standard deviation is high in areas surrounding regions of large emitting depth possibly caused by large annual variability in regions with a lower absolute emitting depth value, and in transition zone around the arid regions (e.g., coastal areas). This large variability of the emitting depth can be caused by different factors. First, with higher values of the emitting depth, the standard deviation is bound to increase. Second, soil moisture changes can be responsible for part of the variations, and this effect is explored in Section 5.1.
## 5 Discussion and Application
First, the emitting depth variations are further analyzed, as a function of soil moisture. Then we investigate the possibility to estimate the dielectric properties of arid soil, from the estimated emitting depths. Finally, an application of the emitting depth estimation is presented.
### Effects of the Soil Moisture on the Emitting Depth
In the previous section, we compared different retrievals and found some variability in the month to month emitting depths. This variability could be related to seasonal changes in soil moisture content, as observed over the course of a year.
Water has a large effect on the dielectric properties of a soil mixture ([PERSON] et al., 1985), and as a consequence, the presence of water is expected to significantly reduce the emitting depth. In addition, soil moisture also affects the thermal diffusivity of the sub-surface and therefore the temperature estimate at a certain depth within the sub-surface. In most soils, an increase in soil moisture leads to an increase of the thermal conductivity (and also of the thermal capacity), leading to an increase of the thermal diffusivity (\(a\)). As illustrated in Figure 3, with higher \(a\) values, the daily temperature variations are reduced at a lower soil depth, which would cause the estimated emitting depth to be smaller. Both phenomena can contribute to the same observed reduction of the estimation of the emitting depth.
To investigate the soil moisture effect, the annual variation of the estimated emitting depth is displayed as a function of the soil moisture obtained for the first layer in ERA5 data (0-7 cm). Figure 8 presents the monthly emitting
Figure 7: Maps over the Sahara and Arabic deserts. (a) The intersection and union of the high sand fraction (\(\geq\)75%) from Global Soil Data set for Earth System Modeling and the emitting depth above 10 cm at 10 GHz. Areas with emitting depth \(\geq\)10 cm at 10 GHz and sand fraction \(\geq\)75% are in green (A), the areas with only a sand fraction \(\geq\)75% in blue (B), with only the emitting depth \(\geq\)10 cm at 10 GHz in orange (C), and in gray the other arid areas (D). (b) The normalized standard deviation at 10 GHz over 12 months is shown in the lower panel.
depth averaged over 1\({}^{\circ}\) areas at 10 and 36 GHz, as a function of the ERA5 soil moisture in the top soil layer, for several locations in the Sahara and Arabian deserts.
For most locations, the emitting depths tend to decrease with increasing soil moisture, at both frequencies. Even with very small moisture contents, the emitting depth decreases until it reaches a plateau with very low emitting depth (soil moisture \(\geq\)3%). On the other hand, the large emitting depth values saturate due to the lack of diurnal temperature variations in the soil below a certain depth, making the method unable to detect emitting depth variations larger than \(\sim\)40 cm.
Figure 8 (bottom row) shows the annual variations of the emitting depth and of the soil moisture. The annual variations are consistent with the weather cycles in these distinct regions: in the rocky area (yellow) there is no influence of the soil moisture on the penetration depth, that remains negligible. In northern Arabia (29\"N 40\"E, blue) the driest month occur during the Northern Hemisphere summer (July-September) where an increase in emitting depth can be noticed at 10 GHz. The penetration remains low and is not detected in the measurements at 36 GHz. In the southern part of the Sahara (17\"N 17.5\"E, red) an increase in the soil moisture in August coincides with a decrease of the estimated emitting depths at 10 and 36 GHz. The Murzuq desert (green) shows a weaker annual cycle, and the monthly variations are not easily associated to corresponding changes in the related emitting depth. Comparing the variation of emitting depths at 10
Figure 8.— Monthly average values of emitting depth at 10 GHz (left) and 36 GHz (right) versus the soil top layer soil moisture (top) and along the year (bottom) in a rocky area (28”N 17\"E, yellow), and sandy areas in the Murzuq desert (25”N 12.5”E, green), the Bodele region (17”N 17.5”E, red), and in the Al Nafud desert in the Arabian Peninsula (29”N 40”E, blue). The month of observation is overlaid with each data point on the top panels, and the soil moisture along the year in the bottom panel (dashed lines).
and 36 GHz shows some differences in the annual cycle. These can be caused by a noisier retrieval at 36 GHz, and less overall penetration depth resulting in less sensitivity to top-layer variations of soil moisture from the reanalysis. Furthermore, saturation of penetration at 10 GHz eliminates sensitivity to penetration greater than 40 cm, potentially causing discrepancies in observed annual cycles (such as between May and June in the Bodele region).
Considering the expected uncertainties in the soil moisture estimates from ERA5 and from dedicated satellite estimates (expected \(\sim\)4% error for retrievals from Soil Moisture and Ocean Salinity or Soil Moisture Active Passive instruments) ([PERSON] et al., 2018; [PERSON] et al., 2012), in further applications of these emitting depth calculations, it is reasonable to neglect the annual variations of the emitting depth and to use a yearly value, along with its yearly standard deviation.
### Global Parameterization of the Dielectric Properties and Emitting Depth of Arid Surfaces
The dielectric properties of the soil largely condition the interaction between the microwave radiation and the soil surface and sub-surface ([PERSON] et al., 1985; [PERSON] et al., 1990), and as a consequence, are key information for many surface remote sensing applications. These dielectric properties are written as a complex value \(\epsilon_{v}=\epsilon_{v}^{\prime}+\epsilon_{v}^{\prime\prime}\) dependent on several parameters, the most important one being soil moisture ([PERSON] et al., 1985; [PERSON] et al., 2004). However, linking soil property maps to dielectric properties at large scale is still challenging. Here, we propose to derive the dielectric properties of the arid soil from the estimated emitting depths, between 10 and 90 GHz.
Under arid conditions with low losses within the soil (i.e., \(e^{*}\ll\epsilon^{*}\)), the soil penetration depth (at which the signal power is reduced by a factor \(e^{-1}\)) can be written as a function of frequency \(\
u\)([PERSON] et al., 2013):
\[p_{eff,\
u}=\frac{c\sqrt{\epsilon_{v}^{\prime}}}{2\
u\pi e_{v}^{\prime\prime}}. \tag{6}\]
The penetrating and emitting depths are related, applying the [PERSON]'s law with an incidence angle of 52.8\({}^{\circ}\) for GMI ([PERSON] et al., 1986; [PERSON], 2005).
In arid areas, the real part of the dielectric properties is expected to be only dependent on the soil density (\(\rho\)) and is stable for the whole frequency range. It can be expressed as \(\epsilon^{\prime}=(1+0.44\rho)^{2}\), with \(\rho\) the soil bulk density ([PERSON] et al., 1985). Other models ([PERSON] et al., 1990) provide similar results for dry soils. The soil density (\(\rho\)) from the GSDE ([PERSON] et al., 2014) (Section 2) is used here to calculate \(\epsilon^{\prime}\). Knowing \(d_{eff,\
u}\) and with this estimate of \(e^{*}\), the previous equation can provide an estimate of \(\epsilon_{v}^{\prime\prime}\) globally, for the observed frequencies.
For North Africa and the Arabian Peninsula, Figure 9a shows the resulting \(\epsilon^{\prime}\) (independent on frequency and time), directly related to the soil density variations. Figure 9b presents the yearly mean \(\epsilon_{v}^{\prime\prime}\) at 10 GHz, showing low values in highly penetrating areas.
To extend the applicability of the derived dielectric properties to frequencies between 10 and 89 GHz, a simple parameterization of the imaginary part of the permittivity is proposed. \(\epsilon_{v}^{\prime\prime}\) has been described as an inverse function of the frequency for dry rocks ([PERSON] et al., 1990), or with a Debye-type model dependent on multiple parameters such as the sand fraction ([PERSON] et al., 1985; [PERSON], 2011; [PERSON] et al., 1995), and soil moisture contents above 5%. For very dry soil, we suggest an empirical approach, only retaining the inverse relationship of \(\epsilon_{v}^{\prime\prime}\) with frequency:
\[\epsilon_{v}^{\prime\prime}=a+\frac{b}{\
u}, \tag{7}\]
with \(a\) and \(b\) coefficients to represent the spatial variation of the dielectric properties. These spatial variations may be caused by changes in the mineral or structural properties of the soil at each location.
Figure 9: Maps of (a) dielectric coefficients \(\epsilon^{\prime}\) (independent of the frequency) and (b) mean annual \(\epsilon^{*}\) value at 10 GHz.
For each arid location, \(a\) and \(b\) are estimated with a least square fitting of the yearly mean \(\epsilon_{\
u}^{*}\) estimated from the monthly GMI observations at 10, 18, 36, and 89 GHz. Knowing \(a\) and \(b\) makes it possible to calculate \(\epsilon_{\
u}^{*}\) and the related \(d_{effx}\) and \(p_{effx}\) (using Equations 6 and 7), for all microwave frequencies between 10 and 89 GHz.
The resulting penetration depths are computed from \(e\) at two locations (a high penetration sand desert 25\"N 12.5\"E, and a low penetration rocky area 28\"N 17\"E). Similar to Figure 2 from [PERSON] and [PERSON] (2008), they are compared to the penetration depths obtained in other studies (Figure 10). Some of these studies estimate \(\epsilon\) from soil samples ([PERSON] et al., 1972; [PERSON] et al., 1990), and have been converted to penetration depth (see Equation 6). From [PERSON] et al. (1990), the values obtained for two rocky types are used, for carbonates (\(e^{*}=0.02\)) and volcanic silicates (\(\epsilon^{*}=0.08\)) that have the largest difference in dielectric properties. Others estimate the penetration depths from observations ([PERSON] et al., 1999), or model the penetration depth as a soil type dependent parameter ([PERSON] et al., 2012) with local experiments. The shaded areas represent the interquartile range, containing half of the possible monthly penetration depth values for the specific location. For the other studies, we used the maximum of the estimated values for the penetrating depth at 19, 37, and 89 GHz from [PERSON] et al. (1999) and the sand soil model with a soil moisture of 5% for [PERSON] et al. (2012). The different estimations provide a similar range of values.
For a practical use by the community, digital maps of the \(a\) and \(b\) coefficients are made available, on a \(0.25^{\circ}\times 0.25^{\circ}\) grid, along with \(\epsilon^{*}\). With the above equations, the dielectric properties and the emitting depth can be estimated from this data set, for all arid areas, globally, between 10 and 89 GHz. The extension to higher frequencies is possible, with a decreasing penetration depth. However, extrapolation toward the lower frequencies is questionable, with the soil temperature quite stable past a certain depth, and the vertical properties likely more heterogeneous, deeper in the soil.
Note that the created maps of dielectric properties in arid regions present interesting spatial structures, as compared to the existing available soil maps (GSDE for instance), and could be further explored to improve the soil mapping as complementary information.
The companion data set also includes the emissivities (V and H) computed for the four GMI frequencies, with the possibility to interpolate the estimated emissivities to all frequencies in the 10-89 GHz range.
### Application to the Assimilation of Microwave Observations Over Deserts
A preliminary step in the assimilation of satellite data in a NWP model is to calculate the departure between the satellite observations and its counterparts derived from a short-range forecast. Over deserts, many microwave observations in surface-sensitive channels are discarded, because of too large departures from the first guess estimate ([PERSON] et al., 2017): the calculated emission from the surface (mostly related to the product between the surface emissivity and the first guess surface temperature) is too far from the measured quantities. Including the information of emitting depths into the radiative transfer simulations in NWP models could be a way to improve the assimilation of these measurements.
To evaluate the utility of the emitting depth estimation for this practical application, we compare simulated \(T_{b}\) to SSMIS observations (with local over-passing times around 06:00 and 18:00). Sixty days sampled along the year are selected from the SSMIS \(T_{b}\) archive. For each observation, the corresponding ERA5 monthly average data atmospheric vertical profile and surface temperature is selected. For every pixel in regions with large emitting depth values (larger than 5 cm at 18 GHz), the radiative transfer equation is computed using the procedure described in Section 3.1. For the surface temperature and the emissivities two different combinations are used: first, using the skin temperature from ERA5 (\(T_{i-0}\)) along with the TELSEM\({}^{2}\) emissivities; second, using the soil
Figure 10: Penetration depths in different studies: in full lines, the mean annual value obtained by the simple model in this study on a 1° region around 25”N 12.5”E (pink) and 28”N 17”E (red), the shaded areas contain 50% of the monthly values for a given year. The dotted lines with gray squares (triangles) are the values from [PERSON] et al. (1990) for carbonate rocks (vocanic silicates), the yellow dashed line is from [PERSON] et al. (2012) model for sandy soils, the dashed lines are the values obtained at different frequencies by [PERSON] et al. (1972) in blue crosses, and by [PERSON] et al. (1999) with green squares.
temperature at the emitting depth, estimated by the coefficients described in Section 5.2 (\(T_{z\to d_{eff}}\)) and the emissivities estimated in this study.
Figure 11 shows the distribution of the departure between the observations and the modeled \(T_{b}\), for V polarization at 18 and 36 GHz. All observations regardless of the time of the day are overlaid. The distribution of the \(T_{b}\) departure when using the initial surface temperature and TELSEM\({}^{2}\) emissivities (orange) shows two distinct peaks, with \(T_{b}\) respectively under and overestimated. These peaks correspond to the evening (resp. morning) overpasses as already observed by various studies. To further emphasize the ability to increase the number of assimilated observations using the calculated emitting depth and corresponding emissivities, Figure 11 also estimates the cumulative fraction of observations whose departure fall below a threshold for both frequency and polarizations. The number of observations available is \(\sim\)4 times higher when using the emitting depth correction for a threshold at 1 K.
Using the emitting depth correction removes a large part of the error between observations and simulations. The magnitude of the correction is similar at 18 and 36 GHz at these times of the day close to dusk and dawn. Larger corrections are expected at 18 GHz than at 36 GHz, closer to the peak of the diurnal temperature given the larger penetration of lower frequencies (as observed by the AMSR2 instrument at noon, for instance). The large standard deviation in the retrievals can be attributed to multiple factors, the most important one being the natural variability of daily surface temperature and atmospheric profiles compared to the monthly means used for the simulation.
Figure 11: Distribution of the difference between observed Special Sensor Microwave Imager Sounder (SSMIS) \(T_{b}\) over the regions with penetration depth (\(\geq\)5 cm) and the one estimated by a radiative transfer model using the surface temperature (\(T_{z}\) = 0)) and Tool to Estimate Land Surface Emissivities from Microwave to Millimeter waves emissivity as input (orange) or the soil temperature at the emitting depth (\(T_{(z}\) = \(d_{eff}\))) and the estimated emissivities at 18 GHz (a) and 36 GHz (b), the second line (c, d) shows the cumulative fraction of the observed differences below the threshold on the \(x\)-axis.
## 6 Conclusion
Over arid surfaces at global scale, the microwave surface emissivities and emitting depths are estimated between 10 and 89 GHz, using GMI satellite observations and ERA5 reanalysis, at a 0.25\({}^{\circ}\) spatial resolution. The method is based on the analysis of diurnal times series of \(T_{b}\) from GMI and surface skin temperatures from ERA5, with the GMI non-Sun-synchronous orbit providing unique microwave measurements of the full diurnal cycle. A simplified thermal conduction model is developed to derive the sub-surface temperature profile, with the diurnal cycle of the ERA5 surface skin temperatures as a boundary condition. The emissivities and emitting depths are estimated from a minimization procedure, using radiative transfer calculations.
The calculated emissivities and emitting depths are evaluated with published results. It confirms that the large emitting depths are associated to the regions of very dry sands in deserts. Their seasonal variations are examined in the light of the soil moisture variations. A parameterization of the dielectric properties of the arid surfaces is proposed. These results open up some interesting future developments: first, the precise evaluation of the complex effect of the very small soil moisture variations in arid areas could be further explored. Second, the signal observed by other radiometers at lower frequency could be used to validate the model applicability outside the 10-89 GHz range. For practical use of the results in the community, a companion data set is prepared, to provide emissivities and necessary information to produce the emitting depths between 10 and 89 GHz, for all arid areas, based on the ERA5 skin temperature, on a \(0.25^{\circ}\times 0.25^{\circ}\) regular grid.
For application to the assimilation of passive microwave observations in NWP models, the use of the emitting depth and corresponding emissivity is tested with SSMIS data. Using the calculated emissivities and emitting depths can increase the usage of the microwave satellite observations by a factor of \(\sim\)4 in the arid penetrating regions. This can help improve the assimilation of the microwave satellite data over the deserts in NWP forecast systems, especially for atmospheric temperature profiling with channels around 50 GHz ([PERSON] et al., 2017).
For the \"all weather\" estimation of the LST from passive microwave observations over deserts, corrections have been developed, to account for the depth of the emitting soil layer ([PERSON], 2003; [PERSON] et al., 2017). Long time series of microwave-derived land surface temperatures are currently produced within the European Space Agency Climate Change Initiative (CCI LST, [[https://climate.esa.int/en/odp/#/project/land-surface-temperature](https://climate.esa.int/en/odp/#/project/land-surface-temperature)]([https://climate.esa.int/en/odp/#/project/land-surface-temperature](https://climate.esa.int/en/odp/#/project/land-surface-temperature))): the emissivities and emitting depths calculated in the present study will be exploited to improve the results over arid areas.
## Data Availability Statement
Open source software used to conduct this analysis are listed below:
* For the data preprocessing, the python packages pyresample [Software] and xarray [Software] ([PERSON] et al., 2021; [PERSON] and [PERSON], 2017) are used.
* For model fitting and data analysis, packages numpy [Software] ([PERSON] et al., 2020) and scikit-learn [Software] ([PERSON] et al., 2011) are used.
* The packages Matplotlib [Software] ([PERSON], 2007), Adjust Text [Software] ([PERSON] et al., 2023) are used for the figures.
All the data used in this study is available from the original data providers:
* The Global Precipitation Measurement mission microwave imager ([PERSON] et al., 2014) from [Dataset] 10.5067/GPM/GMI/GPM/1C/07.
* The ECMWF reanalysis archive ([PERSON] et al., 2020) from the Copernicus Climate Change Service (C3S) Climate Data Store (CDS) (Accessed on 1 September 2021), [Dataset] 10.24381/cds.adbb2d47.
* The global soil data set for Earth System modeling [Dataset] from [PERSON] et al. (2014).
* The data from the field station in Gobabeb Vogt (2021) [Dataset], the soil temperature data used in this study is available at [[https://doi.org/10.5281/zenodo.7882451](https://doi.org/10.5281/zenodo.7882451)]([https://doi.org/10.5281/zenodo.7882451](https://doi.org/10.5281/zenodo.7882451)). The station is partially funded by University of Basel (GobaBas--Measurement of the Surface Energy Balance in the Namib Desert, Project-ID 101714).
* The Special Sensor Microwave Imager Sounder (SSMIS) brightness temperatures are obtained from the Satellite Application Facility on Climate Monitoring (CMSAF) [Dataset] ([PERSON] et al., 2022).
The data produced in this study ([PERSON] et al., 2022) is available at: [[https://doi.org/10.5281/zenodo.7325716](https://doi.org/10.5281/zenodo.7325716)]([https://doi.org/10.5281/zenodo.7325716](https://doi.org/10.5281/zenodo.7325716)).
## References
* [PERSON] et al. (2011) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2011). A tool to estimate land-surface emissivities at microwave frequencies (TELSEM) for use in numerical weather prediction. _Quarterly Journal of the Royal Meteorological Society_, _137_(656), 690-699. [[https://doi.org/10.1002/qja.803](https://doi.org/10.1002/qja.803)]([https://doi.org/10.1002/qja.803](https://doi.org/10.1002/qja.803))
* [PERSON] (1976) [PERSON] (1976). Geological applications of Nimbus radiation data in Middle East. No. NASA-TM-X-71207.
* [PERSON] et al. (1972) [PERSON], [PERSON], & [PERSON] (1972). Microwave emission from geological materials: Observations of interference effects. _Journal of Geophysical Research_, _77_(23), 4366-4378. [[https://doi.org/10.1293/09707203466](https://doi.org/10.1293/09707203466)]([https://doi.org/10.1293/09707203466](https://doi.org/10.1293/09707203466))
* [PERSON] et al. (2017) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2017). Assessment of the forecast impact of surface-sensitive microwave radiances over land and sea-ice. ECMV Technical Memoranda (October), Retrieved from [[https://www.ecmvr.int/node/17674](https://www.ecmvr.int/node/17674)]([https://www.ecmvr.int/node/17674](https://www.ecmvr.int/node/17674))
* [PERSON] et al. (2018) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2018). Development and assessment of the SMART enhanced passive soil moisture product. _Remar Sensing of Environment_, _201_, 931-941. [[https://doi.org/10.1016/j.res.2017.08.025](https://doi.org/10.1016/j.res.2017.08.025)]([https://doi.org/10.1016/j.res.2017.08.025](https://doi.org/10.1016/j.res.2017.08.025))
* [PERSON] et al. (1951) [PERSON], [PERSON], [PERSON] | wiley | Global Mapping of Microwave Emissivity and Emitting Depth in Arid Areas Using GMI Observations | Samuel Favrichon, Catherine Prigent, Carlos Jimenez, Roland Vogt | https://doi.org/10.1029/2022ea002756 | 2,023 | CC-BY |
wiley/ff47de8f_0f4b_43a2_a193_f1bf6d73342a.md | # Earth's Future
Humen Activity Coupled With Climate Change Strengthens
the Role of Lakes as an Active Pipe of Dissolved Organic Matter
[PERSON]
[PERSON] and [PERSON], [EMAIL_ADDRESS]; [EMAIL_ADDRESS]
[PERSON] [PERSON] [PERSON]
## Earth's Future
### Methodology
[PERSON], [PERSON]
**Resources:** [PERSON], [PERSON]
**Superposition:** [PERSON], [PERSON]
**Visualization:** [PERSON]
**Writing - original draft:** [PERSON]
**Writing - review & editing:** [PERSON], [PERSON], [PERSON]
and reservoirs are approximately equivalent to 20% of global fossil fuel emissions ([PERSON] et al., 2018). Furthermore, the amount of carbon buried in the sediments of lakes and reservoirs is comparable to the amount buried by the entire ocean over the same time period ([PERSON] et al., 2006; [PERSON] et al., 2017). As lakes undergo widespread eutrophication, both the emissions of carbon gases from lakes and the carbon burial in lake sediments are expected to increase ([PERSON] et al., 2018; [PERSON] et al., 2017). DOM represents about 70% of the organic carbon pool in global lake ecosystems ([PERSON] et al., 2015; [PERSON] et al., 2020) and plays important environmental and ecological roles, such as serving as a light attenuator, providing metabolic substrates for heterotrophic bacteria, acting as a transport vector for trace metals, and influencing carbon fluxes between terrestrial, aquatic and atmospheric reservoirs ([PERSON] et al., 2013; [PERSON] et al., 2018; [PERSON] et al., 2021). The quantity and quality of DOM determine its liability to photochemical and microbial alterations ([PERSON] et al., 2013), as well as its potential to be buried through association with metal-containing minerals ([PERSON] et al., 2022), and thus are crucial factors in mediating the role of lakes in the global carbon cycle.
DOM in lakes is influenced by allochthonous inputs from the surrounding watershed and autochthonous production and transformation within the lake. Climate, land cover, human activity, and retention time have been found as significant environmental drivers in controlling the quantity and quality of DOM in inland waters ([PERSON], 2012; [PERSON] et al., 2014; [PERSON] et al., 2019; [PERSON] et al., 2014). These environmental drivers can influence lake DOM quantity and quality through multiple, interactive pathways (Figure 1). The effects of climate can operate directly, that is, through influencing in-lake generation and processing of DOM ([PERSON] et al., 2021), or indirectly, for example, through altering land cover and thus allochthonous inputs ([PERSON] et al., 2018; [PERSON] et al., 2017; [PERSON] et al., 2014; [PERSON] et al., 2010). Land cover can influence allochthonous DOM in lakes directly via mediating soil OM production, storage, and decomposition ([PERSON] et al., 2014; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2019), as well as indirectly via altering autochthonous DOM production and decomposition through changing nutrient inputs ([PERSON] & [PERSON], 2019). Human activities can also operate directly through altering the source, composition, and reactivity of DOM in various water bodies by changing soil OM characters and flow paths and exporting anthropogenic organic substances ([PERSON] et al., 2021; [PERSON] et al., 2013; [PERSON] et al., 2020; [PERSON] et al., 2016), and operate indirectly through stimulating autochthonous productivity ([PERSON] et al., 2013; [PERSON] et al., 2015; [PERSON] et al., 2021). Hydrological factors influence DOM processing (a direct pathway) and autochthonous DOM production (an indirect pathway) through controlling water residence time, such as lake volume and the connectivity to land ([PERSON] et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2014; [PERSON] et al., 2019).
Previous studies have been conducted predominantly on local or regional scales, examining sites with specific hydroclimatic and economic characteristics. As a result, the identified primary environmental drivers vary across regional characters and spatial scales ([PERSON] et al., 2014; [PERSON] et al., 2019; [PERSON] et al., 2019). While valuable in their respective regional contexts, translating and upscaling these findings to a large spatial scale is challenging. Until now, quantifying the relative importance of major environmental drivers in modulating lake DOM has not been undertaken on a continental scale. The goals of the present study are to quantify the magnitude of environmental drivers and unravel their individual and interactive effects on modulating lacustrine DOM quantity and quality at a continental scale. Additionally, we aim to identify specific pathways that connect different environmental drivers, including climate, land cover, human activity, and water retention time. Our approaches included the following steps, as outlined in Figure 1. First, we constructed a structural equation model framework that incorporated both direct and indirect pathways. Second, we collected a continental-scale data set of lake DOM quantity and quality, along with the corresponding environmental driver variables from a group of carefully selected lakes (\(n=182\)). These lakes were chosen to represent a wide range of climatic conditions, land cover types, levels of human activity, and water retention times. Using this extensive data set, we applied the structure equation models to analyze DOM quantity and quality variations as a function of the four environmental drivers. By solving these models, we estimated the relative magnitude of the effect of each environmental driver through different pathways and discussed the corresponding mechanisms. Lastly, we proposed several CDOM proxies that can serve as indicators for assessing the magnitude of environmental drivers regulating lake DOM across different eecclimatic zones. This study represents the first attempt to quantify the impacts of major environmental drivers on lacustrine DOM quantity and quality at a continental scale. Our findings contribute to a better understanding and improved prediction regarding the changing role of lakes within the carbon cycle across diverse geographic regions, particularly in response to climate change and rapid societal development.
## 2 Methods
### Structural Equation Model Framework
Structure equation modeling has been extensively used to elucidate the underlying cause-effect dynamics between multiple explanatory variables and the response variables. The construction of the structure equation model (Figure S1 in Supporting Information S1) was based on literature-reported mechanisms through which each environmental driver modulates allochthonous inputs and autochthonous generation, and in-lake processing of DOM. Climatic characters (e.g., temperature, precipitation, and irradiation) can directly influence in-lake processing as a warm and wet climate can promote in-lake processing of DOM ([PERSON], [PERSON], et al., 2021) and strong solar irradiation would enhance photochemical alterations of DOM ([PERSON] et al., 2013). The effect of climate is also associated with multiple indirect pathways: (a) indirectly altering allochthonous DOM inputs via shaping land cover ([PERSON] et al., 2018; [PERSON] et al., 2017; [PERSON] et al., 2014; [PERSON] et al., 2010), (b) modifying autochthonous DOM generation through impacting nutrient input (e.g., precipitation increases total phosphorus and total nitrogen fluxes) ([PERSON] et al., 2015), and (c) mediating lake hydrology via the change of precipitation (e.g., the retention time decreases due to high precipitation) ([PERSON] et al., 2019). Land cover performs via (a) a direct pathway, that is, altering allochthonous DOM inputs by mediating soil OM production, storage, and composition ([PERSON] et al., 2014; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2019), and (b) an indirect pathway, that is, impacting autochthonous DOM generation through changing nutrient inputs (e.g., the degradation of pasture into hardland leads to a decrease in soil total phosphorus and total nitrogen) ([PERSON] et al., 2018). Societal development alters DOM composition mainly by exporting anthropogenic organic substances ([PERSON] et al., 2014; [PERSON] et al., 2016) and stimulating autochthonous productivity ([PERSON] et al., 2013; [PERSON] et al., 2015; [PERSON] et al., 2021). The hydrological characters focused on in this study are those associated with water retention time, such as lake morphometry ([PERSON] et al., 2021) and precipitation ([PERSON] et al., 2019), which influence the extent of in-lake DOM transformations, as well as nutrient availability that can affect autochthonous DOM production ([PERSON], [PERSON], et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2014). Lastly, all environmental drivers can influence the trophic state of lakes, which regulates autochthonous DOM variation. Hence, trophic state was added as a mediator for lacustrine DOM.
Testing and resolving this model took three steps (Figure 1). First, we selected a large number of lakes (\(n=182\)) associated with a diverse range of hydroclimatic patterns and economic development levels. We analyzed the
Figure 1: Conceptual sketch of direct and indirect influencing pathways by which environmental drivers regulate lake DOM quantity and quality. DOM in lakes is influenced by allochthonous inputs, autochthonous production, and in-lake transformation. These processes are mediated by multiple and interactive environment drivers, including climate, land cover, societal development, retention time, and trophic state. In this study, we established a structure equation model to quantify the relative importance of these drivers and their direct and indirect pathways. The model used a large-scale database collected from lakes with strong climatic and economic gradients. The solid lines indicate the direct influencing pathways of the environmental drivers on DOM quantity or quality (yellow lines denote the effect on allochthonous input/autochthonous input and orange lines denote the effect on in-lake transformation); dash lines indicate the indirect influencing pathways.
quantity and quality of CDOM using absorption spectroscopy and excitation-emission matrix fluorescence coupled with parallel factor analysis (EEM-PARAFAC). Second, we collected or calculated the indicators for climate, societal development, land cover, retention time, and trophic state (Table 1). Finally, we employed the partial lease squares method to solve the model. The obtained pathway coefficients were used to quantify the relative magnitude of the climate, land cover, societal development, and retention time on controlling lake CDOM quantity or CDOM quality.
### Study Sites and Sample Collection
The 182 lakes we sampled were distributed across a vast area of China (Figure 2). Previous studies have classified lakes in China based on five geographical zones ([PERSON] and [PERSON], 1998): the eastern plain lake zone (EPL), the Inner Mongolia-Xinjiang (northwestern) lake zone (IMXL), the northeastern plain and mountain lake zone (NPML), the Tibetan Plateau lake zone (TPL), and the Yunnan-Guizhou (southwestern) plateau lake zone (YGPL). The elevation decreased rapidly from the southwest (TPL, IMXL, and YGPL) to the northeast of China (NPML, EPL). The median elevation of the study lakes was 4,535, 2,695, 1,100, 136, and 13 m in TPL, YGPL, IMXL, NPML, and EPL, respectively (Table S1 in Supporting Information S1). The majority of lakes had a surface area greater than 1.0 km\({}^{2}\). The median surface area of the lakes was 43.9 km\({}^{2}\) in TPL, 2.74 km\({}^{2}\) in YGPL, 11.02 km\({}^{2}\) in IMXL, 31.17 km\({}^{2}\) in NPML, and 26.37 km\({}^{2}\) in EPL.
During the summer (July and August) of 2012, lakes in EPL (\(n=69\)), IMXL (\(n=13\)), NPML (\(n=9\)), and YGPL (\(n=25\)) were sampled. Sample collection was done on a caone. Samples were taken at a depth of ca. 0.5 m. Due to limited resources to conduct such a large-scale survey in the same year, the lakes in TPL were sampled in later years. During the summer of 2015 (\(n=37\)) and 2018 (\(n=42\)), lakes in TPL were sampled. Lakes sampled in 2015 were mostly in the eastern and central Tibetan Plateau while lakes sampled in 2018 were mostly in the western Tibetan Plateau. In order to determine the effect of sampling-associated temporal variability on our data interpretation, 13 of the lakes in the eastern and central Tibetan Plateau were sampled in both surveys. No significant difference in absorbance coefficients and fluorescent intensity between the two surveys was found (Figure S2 in Supporting Information S1).
### Water Chemistry and DOM Measurement
The method for measuring the proxies of trophic state, that is, the concentrations of total nitrogen (TN) and total phosphorus (TP), were shown Text S1 in Supporting Information S1. We analyzed the quantity and quality of CDOM using absorption spectroscopy and excitation-emission matrix fluorescence coupled with parallel factor analysis (EEM-PARAFAC). Detailed procedures for these analyses, as well as the establishment of PARAFAC model, can be found Text S2 in Supporting Information S1. The model identified five components, C1-C5 (Figure S3 in Supporting Information S1), and generated the fluorescent intensity (R.U.) of each component. Component 1 (C1) (two excitation maxima at \(<\)250 and 305 nm and an emission maximum at 400 nm) represents humic substances and/or compounds that have been altered by microbial reprocessing. Component 2 (C2) (excitation) emission maximum = \(<\)250, 350/470 nm) represents humic materials produced from terrestrial sources. Component 3 (C3, excitation/emission = 270/308 nm) is identified as proteinaceous, tyrosine-like DOM, and component 4 (C4, excitation/emission = \(<\)250, 290/340 nm) is proteinaceous, tryptophan-like DOM. Component 5 (C5) (excitation/emission maximum = 260/434 nm) is assigned as photo/bio-degradation products of terrestrarily derived DOM. The total fluorescent intensity (\(F_{\text{total}}\)) is calculated as the sum of the fluorescent intensity of C1 to C5.
The absorption coefficients of \(a_{\text{250}}\)\(a_{\text{280}}\)\(a_{\text{320}}\) and \(a_{\text{350}}\), as well as the fluorescent intensity of C1-C5 and \(F_{\text{total}}\) were used to describe the amount of lacustrine chromophoric/fluorescent DOM (CDOM/FDOM) ([PERSON] et al., 2011; [PERSON] et al., 2011). A series of optical indices were calculated to evaluate the quality of DOM, including the ratio of \(a_{\text{250}}\) to \(a_{\text{365}}\)(\(E_{\text{/}}\)\(E_{\text{/}}\)\(E_{\text{/}}\)), spectral slope (\(S_{\text{275-290}}\)), fluorescent index (FI), humification index (HIX), autotrophic productivity (BIX), and the relative abundance of PARAFAC components. The associated calculation and interpretation are provided in Table S2 in Supporting Information S1. Table S3 in Supporting Information S1 lists the summary of the reflective indicators for CDOM quantity and quality in lakes from the five zones across China.
### Requirement of Climatic Characteristics, Land Cover, Human Activity, and Hydrology
Watershed delineation for each sampling lake was done using spatial analyst and hydrology toolboxes in ArcGIS and digital elevation models. The lake surface area and the catchment area were calculated based on the delineatedwatersheds. The percentage of land cover, population density (persons/km\({}^{2}\)), and gross domestic product (GDP, 10\({}^{4}\)RMB/km\({}^{2}\)) of the delineated watershed of each lake were calculated. The land cover data were obtained from Finer Resolution Observation and Monitoring of Global Land Cover (FROM-GLC) data with a 30-m resolution ([[http://data.ess.tsinghua.edu.cn/](http://data.ess.tsinghua.edu.cn/)]([http://data.ess.tsinghua.edu.cn/](http://data.ess.tsinghua.edu.cn/))), which contained the land cover types of forest, grassland, wetland, shrubland, cropland, impervious surface, bareland, snow/ice, and tundra. The data on population density and GDP were acquired from Resource and Environment Science and Data Center, China (www.resdc.cn). The 182 study lakes represent a broad range in depetiers of climate, landcover, human activity, and hydrology (Table S1 in Supporting Information S1). MAT and MAP varied in the range of \(-\)3.0-2.0-7.0\({}^{\circ}\)C and 3.7-2.181.8 mm, respectively. The percentage contributions of the land cover varied in the range of 0%-95.94% for forest, 0%-88.66% for cropland, 0%-45.22% for impervious surface, 0.32%-98.26% for grassland, and 0%-95.1% for bareland. The population density and GDP ranged from 0 to 5,525 person/km\({}^{2}\) and 0 to 10,150 RMB/km\({}^{2}\), respectively. The mean depth and surface area of lakes ranged from 0.3 to 146 m and 0.01 to 3,192 km\({}^{2}\), respectively.
Reflective indicators for climate included mean annual precipitation, mean annual temperature, and mean annual irradiation period. They were calculated via interpolation through the data from weather stations (China Meteorological Data Service Center ([[http://data.cma.cn/en](http://data.cma.cn/en)]([http://data.cma.cn/en](http://data.cma.cn/en)))). Reflective indicators for societal development included population density (persons/km\({}^{2}\)) and GDP. For land cover, reflective indicators included the percentage of cropland, impervious surface, forest, grassland, water, shrubland, bareland, and snow/ice. The percentages of tundra and wetland were not included due to their extremely low contributions, that is, less than 0.5% and 2.8%, respectively. Reflective indicators for hydrology used retention time parameters, including the mean depth of the lakes, lake surface area (LA), and precipitation. The mean depths for lakes were collected from the literature ([PERSON] et al., 2015; NIGLAS, 1982; [PERSON] and [PERSON], 1998). When mean depths were unavailable, they were calculated from the depth at the sampling site depth, using a geostatistical model that determines the lake depth based on lake geometry relations, surrounding landscape characteristics, and lake bathymetry ([PERSON] et al., 2016; [PERSON] et al., 2013). Table S1 in Supporting Information S1 lists the summary of all reflective indicators for the environmental drivers in the five zones across China.
### Solving the Model Based on the Continental-Scale Database
Based on our collected database of the reflective indicators (Table 1) for CDOM composition, path coefficients of climate, land cover, societal development, retention time and trophic state in the structure equation model were quantified via the method of partial least square-path modeling (PLS-PM). This method allows for resolving complex cause-effect relationship models with latent variables and hence is particularly suitable for multivariate data ([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2021; [PERSON] et al., 2016). The PLS-PM analysis was completed using the R package \"plspm\" ([PERSON], 2013). All the parameters in the model were square-root transformed prior to the analysis to improve the fitting of the model.
To satisfy the PLS-PM criterion that the indicators' loading on the latent variables needs to be positive, some indicators were transformed when solving the model so that the indicators were all positively correlated to corresponding environmental drivers or CDOM composition ([PERSON], 2013). MAI was transformed into its negative values. %bareland, %snow/ice, and %grassland were transformed to (100%-%bareland), (100%-%snow/ice), (100%-%grassland), respectively. _E_/_E_\({}_{3}\) and _S_\({}_{275-289}\) were transformed to their multiplicative inverse, while %C3 and %C5 were transformed to (100%-%C3) and (100%-%C5), respectively. FI was transformed to 5.0-FI, since 4.6 was the maximum FI value observed for the study lakes. After the transformation of reflective indicators, land cover was positively associated with a higher contribution of well-vegetated watersheds (i.e., higher %forest, %shrubland, %wetland), and CDOM quality was positively associated with a larger contribution of high-molecular-weight, high-humification, allochthonous CDOM.
### Generalized Additive Models of CDOM Proxies
To further illustrate the relationships between some environmental variables and CDOM proxies, generalized additive models that allow flexibility in data distribution and variances were used. The models were performed in the package of \"mgcv.\" The associated equations took the following format:
\[\text{DOM\,indices}\sim\text{s(P1)}+\text{s(P2)}+\text{te(P1,P2)} \tag{1}\]where P1 and P2 represent environmental predictors; the term s() indicates a one-dimensional nonlinear function based on thin plate regression spline, and te() indicates a two-dimensional effect based on tensor product spline. All other parameters were kept constant.
## 3 Results
### Loading of Reflective Indicators Onto Environmental Drivers and CDOM
The loadings of reflective indicators to environmental or CDOM latent variables in the established models reveal specific environmental conditions or CDOM properties represented by each latent variable. The latent variable representing CDOM quantity is positively influenced by all parameters, indicating a positive association with increased CDOM quantities in lakes (Figure 3). CDOM quality exhibits high loadings (\(\geq\)0.5) from 100-%C5, 1/ (\(E_{s}\)/\(E_{3}\)), 1/\(S_{275-299}\), %C2, 5.0-FI, and %C1, indicating a positive association between CDOM quality and higher contributions of high-molecular-weight, humic, terrestrtially derived DOM (Figure 4).
The loadings of reflective indicators onto environmental drivers are similar between the CDOM quantity and quality models (Figures 3 and 4). Climate is positively loaded by MAT, MAP, and -MAI at comparable weights, and as such, has a positive association with warmer and wetter regions characterized by elevated precipitation and temperature but reduced irradiation duration. Societal development is positively influenced by population density and GDP at similar loadings and hence has a positive association with economically more developed areas. Land cover is influenced positively by %cropland, %impervious surface, 100-%bareland, and %forest at higher loadings (\(\geq\)0.5). This pattern suggests that land cover is positively associated with larger contributions of agricultural and urban lands and well-vegetated lands (forest). Retention time, positively loaded by mean lake depth, lake surface area, and the inverse of MAP, has a positive association with large lakes with longer retention times. Tropic state, positively loaded by TP and TN, is higher for more eutrophic lakes.
of retention time (\(-0.46\)) is negative. Among all environmental drivers, land cover and retention time display the strongest effects.
The total effect of climate is weak (0.07) but it represents a balance between two strong effects of opposite directions-- a negative direct effect (\(-0.52\)) and a positive indirect effect (\(0.59\)). The negative direct effect of climate on DOM quantity (\(-0.52\)) indicates that in wetter and warmer regions, there is a tendency for lower CDOM quantity in lakes. The indirect effect of climate (\(0.59\)) is operated via three pathways--(a) a strong one (\(0.42=0.9\times 0.47\)), resulting from a positive effect of climate on land cover (\(0.90\)) and a positive total effect of land cover on DOM quantity (\(0.47\), Table 2), (b) a moderate one (\(0.24\)) through the effect of climate on lake retention time (\(-0.52\)) and a moderate, negative total effect of retention time on CDOM quantity (\(-0.46\)), and (c) a negligible one (\(-0.07\)) that includes a positive effect of climate on lake trophic state (\(-0.24\)) and a positive total effect of trophic state on DOM quantity (\(0.31\)).
Land cover has a positive direct effect (\(0.43\)) and a weak, positive indirect effect (\(0.04\)) on CDOM quantity, resulting in a strong, positive total effect (\(0.47\)). Land cover with more %cropland, %impervious surface, %forest but less %bareland (Figure 3b) corresponds to higher quantities of CDOM and FDOM. This positive direct effect indicates that human-modified and well-vegetated land covers usually export more terrestrial CDOM to lakes.
Societal development influences CDOM quantity mostly through a moderate positive direct effect (\(0.32\)). The associated indirect effect is weak (\(0.03\)), combining a positive effect of human activity on trophic state (\(0.11\)) and a positive effect of trophic state on autochthonous DOM production (\(0.30\)).
Retention time influences CDOM quantity mainly through a direct effect (\(-0.40\)). The associated indirect effect is weak (\(-0.06\)), combining a negative effect of retention time on trophic state (\(-0.20\)) and a positive effect of trophic state on DOM quantity (\(0.30\)). The strong negative effect of retention time highlights the importance of in-lake transformation and removal in mediating lake CDOM quantity at a continental scale.
### Model Results for CDOM Quality
For CDOM quality model (\(R^{2}\) = \(0.76\)), the total effect is strongest from climate (\(0.89\)), followed by land cover (\(0.72\)), retention time (\(-0.45\)), societal development (\(-0.18\)), and trophic state (\(-0.11\)) (Figure 4, Table 2). The effect of climate (\(0.89\)) is the sum of a minor negative direct effect (\(-0.12\)) and a more important positive indirect effect (\(1.01\)). The latter is operated via three pathways--(a) a strong one (\(0.65\)) resulting from the effect of climate on land cover (\(0.91\)) and the total effect of land cover on CDOM quality (\(0.72\)), (b) a moderate one (\(0.36\)) from the effect of climate on retention time (\(-0.80\)) and the total effect of retention time on CDOM quality (\(-0.45\)), and (c) a negligible one (\(-0.01\)) that includes the effect of climate on trophic state (\(0.07\)) and the total effect of trophic state on CDOM quality (\(-0.11\)). These results suggest that the effect of climate on DOM quality occurs mostly through an indirect effect via altering land cover. The direct climatic effect due to changes in temperature, precipitation, and irradiation is less important (Figure 4b and Table 2).
The total effect of societal development on DOM quality is moderate (\(-0.18\)), combining a negative direct effect (\(-0.16\)) and an indirect negative effect through influencing topic state (\(-0.02\)). The negative direct effect indicates
\begin{table}
\begin{tabular}{l r r r} \hline Relationships & Direct & Indirect & Total \\ \hline DOM quantity & & & \\ Climate\(\rightarrow\)CDOM quantity & \(-0.52\) & \(0.59\) & \(0.07\) \\ Societal development\(\rightarrow\)CDOM quantity & \(0.32\) & \(0.03\) & \(0.35\) \\ Land cover\(\rightarrow\)CDOM quantity & \(0.43\) & \(0.04\) & \(0.47\) \\ Retention time\(\rightarrow\)CDOM quantity & \(-0.40\) & \(-0.06\) & \(-0.46\) \\ Trophic state\(\rightarrow\)CDOM quantity & \(0.30\) & \(0.00\) & \(0.30\) \\ DOM quality & & & \\ Climate\(\rightarrow\)CDOM quality & \(-0.12\) & \(1.00\) & \(0.88\) \\ Societal development\(\rightarrow\)CDOM quality & \(-0.16\) & \(-0.02\) & \(-0.18\) \\ Land cover\(\rightarrow\)CDOM quality & \(0.70\) & \(0.02\) & \(0.72\) \\ Retention time\(\rightarrow\)CDOM quality & \(-0.46\) & \(0.01\) & \(-0.45\) \\ Trophic state\(\rightarrow\)CDOM quality & \(-0.11\) & \(0.00\) & \(-0.11\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Direct and Indirect Effects of Climate, Human Activity, Land Cover, Retention Time on Lake CDOM Quantity and Quality_
Figure 3: Results of the PLS-PM models for lake DOM quantity. (a) Arrows mark linear effects of predictors on dependent variables; the numbers on arrows are standardized partial regression coefficients. The solid line indicates that the path coefficients are significant, and the dotted lines indicate that the associated effects are insignificant. Blue lines denote positive effects and orange lines denote negative effects. (b) Loadings of reflective indicators for the latent variables; the numbers on arrows are the loadings. The goodness of fit for the whole model is \(0.50\), and \(R^{2}\) values for the block of DOM quantity is \(0.58\).
that the input of anthropogenic DOM weakens the signature of allochthonous, humic-like compounds in lakes. The weak indirect effect indicates that lake eutrophication due to societal development has little influence on altering lake DOM quality at the continental scale.
The effect of land cover (0.72) is the sum of a strong direct effect (0.70) and a weak indirect effect (0.02). The latter occurs through the effect of land cover on trophic state (\(-0.16\)) and the effect of trophic state (\(-0.11\)) on DOM quality. This observation suggests that well-vegetated and human-modified lands, relative to barren lands, have a strong, positive contribution to the signature of allochthonous, humic-like compounds.
The effect of retention time arises mainly from a direct effect (\(-0.46\)), and the associated indirect effect is negligible (0.01). The total negative effect of retention time (\(-0.45\)) indicates that within-like processing weakens the signatures of allochthonous, humic-like compounds but strengthens those from autochthonous, protein-like compounds.
### CDOM Proxies for Societal Development and DOM Processing
The relationship of the optical proxies with selected environmental predictors was further evaluated by generalized additive models, as shown in Equations 2-4. Three DOM proxies were selected, because of their strong associations with the corresponding predictors based on the correlation and RDA analyses (Text S3 and Figure S4 in Supporting Information S1), as well as their biogeochemical interpretations (see the discussion Section 4.4). The term describing interactive effects was not included in the model for %C3 since the two predictors were not expected to have interactive pathways.
\[F_{\rm{total}}/{\rm{DOC}} \sim \rm{s(GDP)}+\rm{s(population\,density)} \tag{2}\] \[+\rm{te(GDP,population\,density)}\] \[\%{\rm{C5}}\sim \rm{s(MAI)}+\rm{s(\%bareland)}+\rm{te(MAI,\%bareland)}\] (3) \[\%{\rm{C3}}\sim \rm{s(\%water)}+\rm{s(mean\,depth)} \tag{4}\]
The results of the three generalized additive models are shown in Figure 5 and Table 3. All three models are significant. The model for \(F_{\rm{total}}/{\rm{DOC}}\) has an \(R^{2}\) of 0.56. The two terms s(GDP) and te(GDP, population density) are significant, but the term (population density) is insignificant (Figure 3, Table 3). The model for %C5 has an \(R^{2}\) of 0.75, with the effect of MAI and the interactive effect of MAI and %bareland being significant but the effect of %bareland alone being insignificant. The model for %C3 has relatively low explanatory power with an \(R^{2}\) of 0.20, and both terms of %water and lake water depth are significant.
## 4 Discussion
### Environmental Drivers and the Effect of Spatial Scale
Our model resolves the relative importance of four environmental drivers in mediating lake CDOM variability on a continental scale and identifies their associated influencing pathways. Climate exerts the most significant indirect effect on both CDOM quantity and quality. Societal development, land cover, retention time, and trophic state all display important direct effects on CDOM quality, and land cover and retention time demonstrate strong direct effects on CDOM quantity. When it comes to the total effect, land cover is the most significant driver for CDOM quantity and climate is the most significant for CDOM quality. The unexplained variances for CDOM quantity (42%) and quality (24%) may arise from temporal variations and dynamic lake processes that this study design cannot capture, as well as data limitations of some environmental parameters (e.g., the mean lake depth data acquired from the literature were measured using different methods and carried different levels of accuracy).
Figure 4: Results of the PLS-PM models for DOM quality. (a) Arrows mark linear effects of predictors on dependent variables; the numbers on arrows are standardized partial regression coefficients. The solid line indicates that the path coefficients are significant, and the dotted lines indicate that the associated effects are insignificant. Blue lines denote positive effects and orange lines denote negative effects. (b) Loadings of reflective indicators for the latent variables; the numbers on arrows are the loadings. The goodness of fit for the whole model is 0.52, and \(R^{2}\) values for the block of DOM quantity is 0.76.
\begin{table}
\begin{tabular}{l l c c c c c} \hline \hline & & cdf & Ref.df & \(F\) & \(p\)-value & \(R^{2}\) \\ \hline \(F_{\text{test}}\)/DOC & s(GDP) & 1.00 & 1 & 34.26 & \textless{}0.001******* & 0.56 \\ & s(population density) & 1.00 & 1 & 2.53 & 0.11 & \\ & t(GDP, population density) & 5.91 & 20 & 1.72 & \textless{}0.001******* & \\ \(\%\)C5 & s(MAI) & 1.00 & 1 & 34.83 & \textless{}0.001******* & 0.75 \\ & s(\(\%\)barcland) & 4.25 & 5.25 & 1.68 & 0.12 & \\ & t(MAI, \(\%\)barcland) & 5.38 & 5.80 & 7.31 & \textless{}0.001******* & \\ \(\%\)C3 & s(\(\%\)water) & 3.08 & 3.83 & 3.16 & 0.014* & 0.20 \\ & s(mean depth) & 2.27 & 2.82 & 8.63 & \textless{}0.001*** & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of Generalized Additive Model for \(F_{\text{test}}\)/DOC, \(\%\)C5, and \(\%\)C3
Figure 5: Partial effects of environmental predictors on lake DOM proxies. (a) GDP and population density on \(F_{\text{test}}\)/ DOC, (b) MAI and \(\%\)bare land on \(\%\)C5, and (c)\(\%\)water and depth on \(\%\)C3. The solid lines in scatter plots are generated by combining forecasts, and the shaded areas represent the 95% confidence intervals.
In addition, some relevant parameters that could serve as reflective indicators are not available, such as the content of soil organic carbon for land cover.
Our data sets capture a larger variability of DOM characteristics compared to previous studies conducted at a smaller spatial scale. The DOC concentration in this study (only available for freshwater lakes) and CDOM quantity represent a substantial range spanning two to four orders of magnitude, that is, 0.36-78.55 mg/L (DOC), 0.01-229.05 m\({}^{-1}\) (\(a_{254}\)), 0.03-79.68 m\({}^{-1}\) (\(a_{250}\)), and 0.06-23.87 R.U. (\(F_{\text{total}}\)). By comparison, the DOM characteristics reported in previous studies vary in the range of one to two orders of magnitude. [PERSON] et al. (2014) reported DOC ranging from 2.4 to 32.4 mg/L and CDOM absorbance at 420 nm ranging from 0.00 to 0.14 m\({}^{-1}\) from 560 boreal lakes across Sweden. [PERSON] et al. (2019) found that DOC from 34 Estonian lakes varied from 3.2 to 53.0 mg/L. [PERSON] et al. (2019) observed that DOC concentrations fluctuated in the range of 0.267-4.140 mg L\({}^{-1}\) and \(a_{350}\) in the range of 0.096-7.134 m\({}^{-1}\) in their study of 13 temperate lakes at the leeward side of the southern Andes. The lower variability of DOM observed in those studies can be tied to the smaller spatial scale at which they were conducted. A smaller scale is typically linked to reduced variations and gradients of specific relevant environmental drivers. Consequently, different conclusions have been drawn regarding the primary environmental driver of lake DOM variability, highlighting the importance of considering the spatial scale when identifying relevant drivers. The study on 34 Estonian lakes by [PERSON] et al. (2019) was conducted at a scale of \(\sim\)250 km \(\times\) 250 km. Although the study covered a wide land cover range (i.e., forest, bog, and agriculture areas with percentages of 0%-85.6%, 12.5%-98.5%, and 0%-65.6%, respectively), the climate indicators varied in a relatively small range (MAT: 5.3-7.0\({}^{\circ}\)C, MAP: 591-780 mm). Their results showed that land cover and water retention time, rather than climate or human activity, controlled DOM quantity and quality ([PERSON] et al., 2019). The investigation of 13 temperate lakes of the southern Andes covered sharp gradients in climatic variables (MAT: 2.0-8.0\({}^{\circ}\)C, MAP: 700-3,500 mm), land cover (from forest to steppe), and lake morphometry (lake area: 0.004-114.3 km\({}^{2}\); maximal depth: 5-236 m), but the range of the climatic and land cover gradients are small compared to the range captured in the present study. The authors concluded that terrestrial input (mediated via precipitation and vegetation, rather than land cover) and water retention time (controlled by precipitation and lake morphometry) collectively determined DOM quantity and quality ([PERSON] et al., 2019). The boreal lake study in Sweden ([PERSON] et al., 2014) surveyed a large number of lakes (560), but the associated climatic gradients are also relatively narrow (MAT: \(-\)6.2-7.5\({}^{\circ}\)C; MAP: 450-1,250 mm) in comparison to our study. Their results showed that %water was the primary predictor and MAT was the secondary predictor for DOM quality. These findings, along with ours, demonstrate that the effects and relative importance of environmental drivers vary as a function of the spatial scale, because those drivers with a narrow range and gradient are less likely to be a significant player in driving lake DOM variability. Our study includes lakes spanning across a vast area of approximately \(\sim\)3,500 km \(\times\) 3,000 km exhibiting a wide range and strong gradients of the four environmental drivers of concern (Table S1 in Supporting Information S1). Specifically, MAT and MAP in this study ranged \(-\)3.0-20.7\({}^{\circ}\)C and 3.7-2,181.8 mm, respectively. Additionally, population density ranged from 0 to 5,525 persons/km\({}^{2}\), while GDP ranged from 0 to 10,150 RMB/km\({}^{2}\). The extensive variability in these environmental drivers allows for the first identification and quantification of their impacts on a continental scale.
### Land Cover Versus Societal Development on Lake CDOM
According to our model, the influence of land cover on CDOM quantity is slightly stronger compared to societal development (0.47 vs. 0.35) (Table 2). Land cover is positively reflected by well-vegetated lands (forest and shrubland) and human-modified lands (cropland and impervious surface). Well-vegetated lands correspond to soils with high organic carbon contents and hence a significant supply of terrestrial CDOM to the aquatic environment. The positive influences of forests and shrublands on DOM concentrations have been reported for streams and rivers at the continental scale ([PERSON] et al., 2017). However, observations of this relationship for lakes have predominantly been made at regional scales ([PERSON] et al., 2019; [PERSON] et al., 2020), and our results indicate this relationship also holds at the continental scale. The positive influences of human-modified lands on lake CDOM quantity may occur through two possible pathways, direct export of CDOM or the stimulation of autochthonous CDOM generation. Our model results show that land cover has an insignificant influence on the trophic state of lakes, suggesting that the first pathway, involving direct CDOM export, is more significant. Previous studies examining the link between agricultural and urban lands and the quantities of DOM in waterways have yielded mixed results. Some studies have reported increased DOM quantities, while others have reported reduced quantities or no detectable changes (e.g., [PERSON] et al., 2014; [PERSON] et al., 2011; [PERSON] et al., 2018; [PERSON] et al., 2017), highlighting the spatial heterogeneity of anthropogenic influences on the coupled carbon cycling between terrestrial and aquatic ecosystems. Positive influences of agricultural lands have been attributed to enhanced export of soil organics through aggravated soil erosion or flow paths shifting to upper organic-rich soil horizons ([PERSON] et al., 2021; [PERSON] et al., 2012; [PERSON] et al., 2018). Positive influences of urban lands have been tied to the export of organic-rich wastewater and effluents or the destabilization of legacy soil carbon ([PERSON] et al., 2011). However, it is important to acknowledge that previous studies often compare agricultural/urban lands against natural-vegetated lands such as forests. In contrast, our model compares these lands against grassland, snow/ice, and bareland (Table 1). Therefore, it is not surprising that human-modified lands also serve as significant sources of terrestrial CDOM when compared to land covers associated with soils with lower organic content. The higher loading of %cropland than %forest onto land cover (0.87 vs. 0.54, Figure 3b), however, implies that the export of terrestrial DOM from agricultural lands plays a more substantial role in lake CDOM quantities compared to forests at the continental scale. This finding aligns with results from certain observation studies. For instance, a recent study by [PERSON] et al. (2021) found that converting forested areas to agricultural lands in a large watershed (8,542 km\({}^{2}\)) resulted in an increase in the amount of CDOM entering the aquatic continuum.
Similar to land cover, societal development has a strong direct effect (0.32) on CDOM quantity. A more developed society, as measured by higher GDP or population density, is associated with a larger CDOM quantity in lakes. Societal development can augment the influx of CDOM into the aquatic environment through direct discharge from industrial and residential sources in densely populated, economically developed regions ([PERSON] et al., 2011; [PERSON] et al., 2015), as well as through the indirect pathway of stimulating the production of autochthonous DOM via nutrient enrichment ([PERSON] et al., 2021; [PERSON] et al., 2014). Our results clarify that at the continental scale, societal development primarily contributes to an increase in lake CDOM quantity through the direct export pathway (0.32), while the indirect effect pathway has a minor impact (0.03) (Table 2).
Moreover, the comparison of the relative importance of land cover versus societal development versus trophic state (0.47 vs. 0.35 vs. 0.30) in relation to lacustrine CDOM quantity indicates the effect of allochthonous input (0.47 + 0.35) is about 2.7 times greater than that of autochthonous generation (0.30) in increasing lacustrine DOM quantity. This analysis emphasizes the importance of lakes in receiving and processing terrestrial organic carbon at the continental scale.
As for CDOM quality, the effects of land cover and societal development exhibit opposite directions (0.72 vs. \(-\)0.18, Table 2). This can be explained by varied chemical compositions of DOM of different origins. DOM leached from well-vegetated and organic-rich soils, compared to that from bareland, grassland, and snow/ice, is characterized by a higher presence of high-molecular-weight, high-aromaticity, and humic compounds ([PERSON] et al., 2015; [PERSON] et al., 2015). Anthropogenic DOM related to societal development, however, exhibits a more diverse range of source-composition characteristics (e.g., [PERSON], [PERSON], et al., 2021; [PERSON] et al., 2011; [PERSON] et al., 2015). The effluent of municipal wastewater treatment plants can be chemically heterogeneous, containing microbially-derived humic-like substances, tryptophan-like substances, and tyrosine-like substances ([PERSON] et al., 2011), and treated industrial wastewater is dominated by protein-like substances ([PERSON] et al., 2015). As a result, DOM derived from societal development activities can lead to divergent directions in shifting lake DOM composition, resulting in the observed overall weak effect on lake DOM quality. The negative coefficient, however, suggests that the society development overall reduces the aromaticity and molecular weights of lake DOM and weakens the allochthonous signatures at the continental scale.
### The Effect of Climate on Lake CDOM Quantity and Quality
Although the total effect of climate on CDOM quantity is relatively weak (0.07), it does not imply that the effect of climate on CDOM biogeochemical process is minor. Rather, it underlines the diverse roles that climate plays in exporting terrestrial DOM and mediating in-lake DOM transformations. Both the direct (\(-\)0.52) and indirect effects of climate (0.59) on CDOM quantity are strong (Table 2), but they shift CDOM quantity in opposite directions (negative vs. positive). In our model, climate is positively correlated with high temperature and precipitation and low solar irradiation. Thus, the strong negative direct effect of climate indicates that the great effect of a warmer and wetter climate on accelerating in-lake CDOM removal, implying that lakes will become more active in processing DOM under the projected scenario of a warmer future climate. The negative direct effect can be attributed to the increased intensity of processes such as biodegradation, photodegradation, and flocculation of CDOM under higher temperatures ([PERSON] et al., 2004; [PERSON] and [PERSON], 1995; [PERSON] et al., 2015), as well as DOM dilution under higher precipitation ([PERSON] et al., 2020). Our model also shows MAI (-MAI had a loading of 0.95 on the Climate latent variable, Figure 2(b)) has a positive effect on CDOM quantity. Considering the numerous observations indicating the effective degradation of DOM by sunlight ([PERSON] et al., 2016; [PERSON] et al., 2013), this modeled relationship may simply reflect regions with low-precipitation and low-temperature tend to have higher MAI. This is supported by that MAI is negatively correlated with MAT and MAP (Pearson correlation \(P<0.001\)). As for the positive indirect effect (0.59) of climate on CDOM quantity, it indicates that a warmer and wetter climate promotes the accumulation of CDOM in lakes. For the indirect effect associated with the pathway of climate influencing land cover, earlier studies have similarly reported that a warmer, wetter climate favors the land cover type holding and exporting greater amounts of allochthonous CDOM to inland waters ([PERSON] et al., 2016; [PERSON] et al., 2014; [PERSON] et al., 2005). For the indirect effect associated with the pathway of climate influencing water retention time, a wetter climate could reduce the lake water retention time and thus DOM processing time, which, in turn, results in a large quantity of CDOM accumulating within lakes ([PERSON] et al., 2018; [PERSON] et al., 2019). As such, the weak total effect of climate on CDOM quantity observed in this study reflects the balance between the direct versus indirect effects.
In contrast to the weak total effect on CDOM quantity, climate has a strong total effect on CDOM quality, exhibiting the most pronounced influence among the four environment drivers (Table 2). This finding aligns with a previous study conducted in Wisconsin, USA, which performed trend analysis and synchrony analysis of long-term monitoring data on lacustrine DOM quantity and quality. They similarly concluded that DOM quality was highly sensitive to climate ([PERSON] et al., 2017). Our results demonstrate that climate regulates lake DOM quality mainly through the indirect effect of altering land cover (0.65) and lake hydrology (0.36), whereas the direct effect of climate is minor (\(-0.12\)). High levels of precipitation and temperature can promote the land cover type with soils rich in plant-derived polyphenols. Simultaneously, they can reduce lake water retention time, and in turn, DOM processing time. Both of these factors contribute to strengthening allochthonous DOM signatures in inland waters ([PERSON] et al., 2017; [PERSON] et al., 2021). The negative direct effect of climate on CDOM quality (\(-0.12\)), however, suggests that high temperatures could also enhance the in-lake transformation of CDOM, which can weaken the allochthonous signatures but strengthen the autochthonous signature of CDOM ([PERSON] et al., 2018; [PERSON] et al., 2014). Collectively, the high positive total effect of climate on DOM quality suggests that under a scenario of climate change with high temperature and high precipitation, CDOM quality in lakes would be increasingly influenced by land plant/soil-derived, structurally complex, humic-like compounds. This shift in DOM composition can result in a number of changes in lake biogeochemistry, such as shifts in light penetration and associated changes in primary productivity ([PERSON] and [PERSON], 2019; [PERSON] et al., 2009), modifications in nutrient regeneration and trophic status of lakes ([PERSON] et al., 2021), as well as inducing restructuring of chemical diversity-microbial diversity networks ([PERSON] et al., 2022; [PERSON] et al., 2021).
### CDOM Proxies for Continental-Scale Environmental Drivers
#### 4.4.1 A Tracer for Economic Activity: \(F_{\text{total}}\)/DOC
Our results show that societal development leads to increased levels of \(F_{\text{total}}\)/DOC in lakes across regions of various levels of economic activities. The generalized additive models show that the effect of GDP is significant, whereas the effect of population density is insignificant (Figure 5, Table 3). This suggests that \(F_{\text{total}}\)/DOC may serve as an indicator for societal development, particularly in relation to economic activity. A higher \(F_{\text{total}}\)/DOC value corresponds to a greater level of economic activity. Similar observations have been reported previously but on a smaller spatial scale. A higher ratio of FDOM to DOC in lakes was found to increase with human population density in the Great Lakes region ([PERSON] et al., 2016). Results from highly impacted lakes in central and eastern China showed that FDOM was enriched with anthropogenic sources, including aquaculture and sewage ([PERSON] et al., 2021). Our results here affirm the applicability of \(F_{\text{total}}\)/DOC as a tracer for societal development but further reveal that it can be applied to the continental scale across a large economic and ecoclimatic gradient as a source-tracking tracer to monitor and assess human impacts on lakes.
#### 4.4.2 A Tracer for Photo-Transformation: %C5
The importance of photochemical degradation in altering aquatic DOM composition has been widely recognized through laboratory or in situ incubation studies ([PERSON] et al., 2014; [PERSON] et al., 2016; [PERSON] et al., 2013; [PERSON] et al., 2017). Our study, however, is the first to establish the relationship between solar irradiation (measuredby MAI) and lacustrine DOM composition at the continental scale encompassing various ecoclimatic regions. Longer irradiation leads to increases in %C5 (Figure 5 and Table 3), and the quantitative relationship between MAI and %C5 indicates that C5 may serve as a tracer for the degree of photochemical processing of DOM in lakes. Fluorescence components similar to C5 have been found as a product of in situ photodegradation of DOM from a sub-alpine lake ([PERSON] et al., 2016) and the Baltic Sea ([PERSON] et al., 2007). Although the exact molecular structure of C5 remains unknown, literature data based on Fourier transform in cyclotron resonance mass spectrometry have shown that light can reduce aromatics and increase aliphatics, transforming aromatic compounds into much more saturated molecules with higher H/C and lower O/C ratios ([PERSON] et al., 2009; [PERSON] et al., 2015; [PERSON] et al., 2010; [PERSON], 2016). As such, the C5 fluorescence component likely represents compounds with relatively high H/C and low O/C ratios. Our results here demonstrate the significant potential of utilizing the abundance of this fluorescence signature as an effective tracer for assessing the level of photo-alteration of lacustrine DOM on a continental scale.
#### 4.4.3 A Tracer for DOM Processing Time
Both %water and lake depth exhibit positive correlations with the relative abundance of C3 representing tyrosine-like DOM (Figure 5, Table 3). This suggests that the relative abundance of the tyrosine-like component in lakes may be used as a tracer measuring DOM processing time across different eecoclimatic conditions. The percentage of water in the surrounding catchment (%water) has been previously suggested to be a good indicator for the duration of DOM exposure to processing within the catchment, with higher %water corresponding to a longer processing time ([PERSON] et al., 2014). Moreover, lake depth is usually positively associated with water retention time. A longer DOM processing time, both within the catchment and lake itself, corresponds to a greater extent of photodegradation, biodegradation, and/or sedimentation. Similar observations have been made on a smaller spatial scale. [PERSON] et al. (2014) found that %water positively covary with the relative abundance of tyrosine-like component in Sweden's boreal lakes. Tyrosine-like DOM, commonly considered a biodegradated product, exhibits low photoreactivity ([PERSON] et al., 2011) and high recalcitance to flocculation ([PERSON] et al., 2019). These characteristics contribute to its accumulation over processing time. Molecular data have revealed that aliphatics and N-containing compounds can increase with longer water retention time of lakes ([PERSON] et al., 2014, 2015). Furthermore, long-term microbially mediated transformations lead to the generation of source-independent common structural features, such as the accumulation of carboxylic-rich alicyclic moieties derived from linear terpenids ([PERSON] et al., 2006; [PERSON] et al., 2007; [PERSON] & [PERSON], 2018). Considering these findings, it is likely that the tyrosine-like fluorescence component includes aliphatic, nitrogen- and carboxyl-containing molecules. The relative abundance of these molecules captured by the parameter of %C3 can serve as a tracer for the extent to which lake DOM has been processed within the catchment and lake.
### Conclusions and Environmental Implication
Through analyzing an extensive data set of the quantity and quality of DOM from lakes situated in diverse eecoclimatic conditions in China, we resolve the relative importance of environmental drivers and elucidate the direct and indirect pathways through which they impact on lake DOM. Our analysis led to three main conclusions. First, both well-vegetated lands and society development play significant roles in exporting terrestrial DOM to lakes at a continental scale. The former source predominantly contributes humic, aromatic compounds, while the latter source introduces compounds with diverse source-composition characteristics. Second, climate exerts its influence on lake DOM directly and indirectly by modulating land covers. Higher temperatures stimulate the rates of DOM processing within lakes and lead to lower quantities of lake DOM. On the other hand, elevated temperatures and precipitation promote the presence of organic-rich soils, which enhance the export of allochthonous CDOM to lakes, consequently increasing the total amount of CDOM and allochthonous signatures in lakes. Third, we identified three fluorescence-derived parameters, \(F_{total}\)/DOC, %C3, and %C5, as effective tracers for the magnitude of continental-scale environmental drivers. They are relatively easy to measure and can be widely adopted in lake DOM monitoring programs.
Our results have important implications on future changes in how lakes store and transform organic carbon under the dual stressors of climate change and human activity. Based on our results, lake DOM quantity would increase, and allochthonous, high-molecular-weight, humic compounds would become more dominant in lakes under higher temperature and more intensive precipitation. Climate change is manifested differently across various eecoclimatic regions. Previous projection under the scenario of Representative Concentration Pathway(RCP) 4.5 indicated that a widespread increase of 1.5-2.5\({}^{\circ}\)C in MAT by the 2080s in China. Specifically, the Tibetan Plateau (TPL) and northern China (IMPL and NPML) were projected to experience the most substantial temperature rise. For MAP, the projection indicated that by the 2080s, the Tibetan Plateau (TPL) and the Yangtze River basin (where EPL is located) would undergo a large increase of 50-150 mm/year, IMPL, and NPML experiencing no significant change, and southwestern China (YGPL) would undergo a decrease of over 75 mm/year ([PERSON] & [PERSON], 2014; [PERSON] et al., 2019). As such, lake CDOM quantity in Chinese lakes (with the exception of southwest China) is likely to increase, accompanied by a greater dominance of allochthonous DOM. Another significant finding of this study is the strong influence of human activity on DOM quantity in lakes. Given the expected continued increase in human activity across all regions of China, there would be an amplified export of anthropogenic organic substances to lakes. This process could also contribute to the \"browning trend\" (increases in DOC) ([PERSON] & [PERSON], 2006) that has been observed in streams and lakes of the Northern Hemisphere. This mechanism adds to the previously suggested mechanism linking to changes in temperature and precipitation ([PERSON] et al., 2015).
Under the dual stress of climate change and more intensive human activity, we suggest that the loading of allochthonous DOM into the lake ecosystem would increase, further strengthening the role of lakes as conduits for organic carbon transferred across the terrestrial-aquatic boundary. Furthermore, a warmer climate amplifies the already-high decomposition rates of DOM within lakes, strengthening the role of lakes as hotspots for organic carbon transformation. This change, in conjunction with the substantial increase in allochthonous DOM loadings across different eco-climatic regions, will render lakes more active in transporting and transforming organic carbon. In essence, lakes will become a more dynamic active pipe for organic carbon.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The data on which this article is based are available in [PERSON] et al. (2023).
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wiley/ff2e6d9e_e591_4ad4_876c_e3de688e0af4.md | ## 1 Introduction
Typhoon Faxai (2019) occurred in early September 2019 and made landfall over the Kanto District, Japan. In early October, a month later, Typhoon Hagibis (2019) approached Japan along a track similar to Faxai's track, crossing the same ocean region around the southeastern Japanese Archipelago (Figure 1). According to the best track data of the Regional Specialised Meteorological Centres Tokyo-Typhoon Centre, Japan, the maximum wind speed (\(Vm\)) of Faxai reached 43.7 m\(\cdot\)s\({}^{-1}\) and the \(Vm\) of Hagibis was 54.0 m\(\cdot\)s\({}^{-1}\). The horizontal size of Faxai, that is, the radius of sustained wind of 15 m\(\cdot\)s\({}^{-1}\) (\(R15\)), was 330 km and that of Hagibis was 750 km. Faxai had an average speed of movement over the ocean south of the eastern Japanese main island of 8.1 m\(\cdot\)s\({}^{-1}\), similar to that of Hagibis (6.8 m\(\cdot\)s\({}^{-1}\)). Therefore, Hagibis was stronger and larger than Faxai, and the two typhoons had similar tracks and speeds over the ocean.
High-resolution satellite observations from Himawari-8 showed that sea surface temperature (SST) decreased with the passage of both typhoons (Figure 1a,c). Typhoon-induced SST cooling is caused by the effects of the strong winds associated with typhoons ([PERSON], 1995; [PERSON], 1981). A typhoon develops more efficiently over the ocean at higher SST as a result of ocean heat flux and water vapour inflow (e.g., [PERSON], 1986), but typhoon-induced SST cooling can directly suppress typhoon intensity via oceanic feedback (e.g., [PERSON], 2007; [PERSON] et al., 2010). Therefore, it is important to understand typhoon-induced SST cooling to predict typhoon intensity, that is, maximum wind speed.
SST cools as seawater is mixed by strong typhoon winds, which is a one-dimensional response, and a three-dimensional response also occurs due to the influence of currents in the ocean surface layer or upwelling ([PERSON], 1981; [PERSON] et al., 2011; [PERSON] & [PERSON], 2009). Quantitatively, rainfall contributes less to SST cooling than other factors ([PERSON] & [PERSON], 2017). In addition, the magnitude of typhoon-induced SST cooling is related not only to the ocean conditions beneath a typhoon but also to the characteristics of the typhoon, such as \(Vm\), horizontal size, and speed of movement. The impacts of ocean conditions on typhoon intensity are indicated by the ocean heat content (OHC) and the tropical cyclone heat potential (TCHP) ([PERSON] & [PERSON], 1972). These indicators represent ocean conditions but do not consider the magnitude of the impact on SST cooling of typhoon characteristics.
The cooling parameter (Co) is a non-dimensional number that theoretically indicates the magnitude of SST cooling during the passage of a typhoon, as proposed by [PERSON] et al. (2017). We used Co because it reflects not only ocean conditions but also typhoon characteristics. Co allows for a quantitative assessment of the relationship between ocean conditions and typhoon characteristics.
In this study, we utilise Co in a high-resolution ocean model for targeted analysis of typhoons Faxai and Hagibis, as [PERSON] et al. (2017) did not report an application of Co to real typhoons or ocean data in detail. The purpose of this study was to evaluate typhoon-induced SST cooling quantitatively, separating the impacts of typhoon characteristics from the impacts of ocean conditions using Co. The rest of the paper is organised as follows: Section 2 briefly describes the ocean model and the equations of Co;
Figure 1: Differences in SST over the 4-day periods of (a, b) 6–10 September 2019 during the passage of Typhoon Faxai and (c, d) 8–12 October 2019 during the passage of Typhoon Hagibis. (a, c) SST according to Himawari-8 and 6-hourly typhoon centre locations derived from the best track. (b, d) SST simulated based on the ocean model and hourly typhoon centres from the MSM. Grey areas indicate a lack of satellite data.
Section 3 validates the SST cooling caused by Faxai and Hagibis using Co; and Section 4 summarises the main findings of the study and future study.
## 2 Methods
This study used a submesoscale-permitting ocean general circulation model to investigate the distribution of seawater temperature at fine resolution according to the impacts of moving typhoons. The model, named ICTKSMW, is based on MRLCOM ver. 4.7 ([PERSON] et al., 2017) and covers the Pacific side of Eastern Japan (26.00-37.99\({}^{\circ}\) N, 135.32-142.54\({}^{\circ}\) E). The horizontal resolution is 1/60\({}^{\circ}\). It has 35 vertical layers (0.25-5825.00 m). Other settings are basically the same as those in [PERSON] et al. (2018). The bulk equation is [PERSON] and [PERSON] (2004), ([PERSON], 2009). The mixed layer model follows [PERSON] and [PERSON] (1999). The tidal forcing of the eight main constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) was considered through the tidal model of [PERSON] et al. (2013). The lateral boundary conditions for physical variables were derived from the daily analysis of the western North Pacific by the Japan Meteorological Agency ([PERSON] et al., 2006), and those for tidal sea surface height and barotropic velocity were from NAO.99 Jb ([PERSON] et al., 2000).
The model was driven by the hourly wind vectors, u and v, at 10-m height; sea level pressure; atmospheric temperature and specific humidity at 1.5-m height; downward shortwave radiation; precipitation rate from the mesoscale model (MSM; Japan Meteorological Agency, 2013); and 3-hourly downward longwave radiation from the Japanese 55-year Reanalysis Project (JRA55; [PERSON] et al., 2015). The numerical calculation was performed from 00 UTC on April 1, 2019 to 00 UTC on November 1, 2019. The seawater temperature from ICTKSMW was interpolated vertically at 1-m intervals to calculate Co.
[PERSON] et al. (2017) proposed Co as a non-dimensional indicator for evaluating the typhoon-induced SST cooling effect caused by ocean mixing, to improve the accuracy of the maximum potential intensity framework developed by [PERSON] (1986). Co is estimated from the ratio of typhoon characteristics and ocean conditions as follows:
\[\mathrm{Co}=\frac{2F_{\mathrm{mst}}^{2}(\lambda/\mathrm{wt})^{2}}{\rho^{2} \alpha\mathrm{g}\Gamma h_{0}^{4}} \tag{1}\]
\[F_{m\mathrm{st}}=\rho_{a}\times C_{d}\times V_{m}^{2} \tag{2}\]
where \(F_{m\mathrm{st}}\) (kg\(\cdot\)m\({}^{-1}\)s\({}^{-2}\)) is the surface momentum flux, \(\lambda\) (m) is the length scale of the vortex, \(\upsilon\) (m\(\cdot\)s\({}^{-1}\)) is the speed of movement, \(\alpha\) (K\({}^{-1}\)) is the thermal expansion coefficient, \(\rho\) (kg\(\cdot\)m\({}^{-3}\)) is water density, \(g\) (m\(\cdot\)s\({}^{-2}\))is gravitational acceleration, \(h_{0}\) (m) is the mixed layer depth (MLD), and \(\Gamma\) (K\(\cdot\)m\({}^{-1}\)) is the temperature lapse rate below the mixed layer. Note that MLD is defined only by ocean temperature. \(\rho_{a}\) (kg m\({}^{-3}\)) is air density and \(C_{d}\) is the surface exchange coefficient for momentum.
Co includes the following parameters for typhoon characteristics: _R15_ (nm), the radius of maximum wind (m) (RMW) (Equations 1 and 2), _Vm_ (m\(\cdot\)s\({}^{-1}\)), and _vt_ (m\(\cdot\)s\({}^{-1}\)). _R15_ and RMW are included in \(\lambda\), which represents the size of the typhoon, and \(\lambda\) is effective for the square. For the typhoon characters in this study, _R15_, RMW, and _Vm_ at 1-h intervals were detected from the MSM hourly data, instead of the best-track data with lower temporal resolution. Using the 10-m height winds in MSM, the centre of the typhoon, _R15_, and RMW were detected by the maximum axisymmetric mean tangential wind.
The ocean conditions considered in Co include \(h_{0}\) and \(\Gamma\). The ocean conditions for Co were standardised at 24 h before the time of each typhoon's passage. MLD works to the fourth power. The ocean conditions were derived from the ocean model results averaged over a 2\({}^{\circ}\times\) 2 box relative to the typhoon centre at each time point. Co was calculated for all 25 hourly positions of both typhoons from latitude 29\({}^{\circ}\) N to 34\({}^{\circ}\) N every 1 h. The Co of Faxai was estimated for 12 UTC September 7 to 12 UTC September 8, 2019, whereas the Co of Hagibis was estimated from 06 UTC October 11 to 06 UTC October 12, 2019. Note that Co values greater than 10 were excluded because the speed of movement was slow in such cases (\(<\)3 m\(\cdot\)s\({}^{-1}\)).
The magnitude of SST cooling (\(\Delta\)SST) was defined as the difference in SST from the reference time to the time of passage [0] (e.g., the time of passage [0] is 14 UTC September 7 for Faxai and 06 UTC October for Hagibis at 29\({}^{\circ}\) N) as well as to 3, 6, 9, 12, 24, 36 h after passage, and 4 days before and after passage. Except for the assessment at 4 days, the reference time is 24 h before the typhoon's closest approach to each location. This study used several time intervals for \(\Delta\)SST because long- and short-term intervals are affected differently by typhoon impacts and the recovery of ocean conditions.
## 3 Results
Figure 1 shows \(\Delta\)SST for the 4 days around the passages of Faxai and Hagibis derived from satellite observations, and the outputs of the ocean model. \(\Delta\)SST was negative; that is, SST decreased during the passage of the typhoon along the track, as cooling can be caused by the strong winds associated with typhoons. The negative \(\Delta\)SST
values distributed around the tracks of Faxai and Hagibis were generally in good agreement with the numerical results. Most of the SST decreases <2\({}^{\circ}\)C were associated with the passage of Faxai, while SST decreases >2\({}^{\circ}\)C accounted for about 40% of the total, including about 10% exceeding 3\({}^{\circ}\)C, and occurred in the negative \(\Delta\)SST region during the passage of Hagibis. The numerical results demonstrate that SST decreases more due to cooling during the passage of Hagibis than Faxai. Asymmetry in the distribution of the SST decrease appeared along the path of the typhoon according to both the satellite observations and numerical results, as noted by [PERSON] (1981).
Figure 2 shows vertical-latitudinal cross-sections at 29\({}^{\circ}\) N of ocean temperature changes based on the numeric results. The variations of ocean temperature at 0, 6, 12, and 24 h after the passages of Faxai and Hagibis are shown for the specific latitude of 29\({}^{\circ}\) N relative to the reference times of 14 UTC on September 6 for Faxai and 06 UTC on October 10 for Hagibis. Faxai cooled the shallow ocean layers above the 50 m depth over a horizontal width of <2\({}^{\circ}\), while Hagibis cooled the ocean at depths below 50 m across an area wider than 2\({}^{\circ}\). Hagibis produced a region showing an SST decrease of 2\({}^{\circ}\)C during its passage, which was broader than the equivalent region for Faxai and had local decreases >3\({}^{\circ}\)C. These results suggest that Hagibis cooled the ocean more widely and deeply than Faxai. Local ocean cooling started at the time of passage for both typhoons, proceeded further after 6 h, and then diminished at 12 h after the passage of Faxai, while the region associated with Hagibis showed a longer period of more extensive cooling. At 24 h after the passage, there was a slight recovery of ocean temperature in the case of Faxai.
The daily averages and standard deviations of \(\Delta\)SST, Co, and the typhoon characteristic and ocean condition statistics around Faxai and Hagibis are listed in Tables 1 and 2. The average Co values for Faxai and Hagibis were 1.6 and 3.6, respectively. Co for Hagibis was about twice that of Faxai, indicating that SST cooled more easily with the passage Hagibis than Faxai, consistent with the observations and results of the ocean model.
Figure 3 shows the distribution of the effect of ocean conditions on Co estimated from the ocean model data at an interval of 0.5\({}^{\circ}\) when both typhoons were located at 26.5-34.0\({}^{\circ}\) N. Most of the ocean conditions were less than 5 for Faxai and greater than 5 for Hagibis. The ocean conditions were high (greater than 15) during the passage of Hagibis in the area north of 31\({}^{\circ}\) N. In this case, the Kuroshio Current followed a different path (not shown), explaining the difference observed around 33\({}^{\circ}\) N. The average ocean condition values were 4.5 during Faxai and
Figure 2: Vertical cross-sections of ocean temperature changes at 29\({}^{\circ}\) N down to a depth of 225 m for the passage of typhoons (a) Faxai and (b) Hagibis. The intervals of the ocean temperature changes are 0, 6, 12, and 24 h after the passage of the typhoon at (a) 14 UTC on September 7, 2019, and (b) 06 UTC on October 11, 2019, relative to the reference time. The reference times are 14 UTC on September 6 for Faxai and 06 UTC on October 10 for Hagibis. The red dot represents the typhoon position at that time.
11.5 during Hagibis when the ocean before their passages is compared in ocean stability (Tables 1 and 2). A higher this value indicates that the ocean is more stable and less tends to mix and cool. As a result, oceanic condition values were approximately 2.6 times greater for Hagibis (11.5) than Faxai (4.5), indicating that the ocean before Hagibis passes is less hard to cool ocean than Faxai when only the ocean before the typhoon passages is compared. On average, MLD was about 10 m deeper during Hagibis (46.7 m) than Faxai (36.2 m). Meanwhile, the lapse rates under the mixed layer were 0.07 K\(\cdot\)m\({}^{-1}\) for Hagibis and 0.06 K\(\cdot\)m\({}^{-1}\) for Faxai. This finding indicates that the ocean was more difficult to cool before the passage of Hagibis compared to Faxai due to the significant impact of MLD. However, Hagibis actually cooled the ocean more than Faxai shown in Figure 2, suggesting that typhoon characteristics are important for ocean cooling.
The average impact of typhoon characteristics was 4.8 times larger for Hagibis (31.5) compared to Faxai (6.5). Among the typhoon characteristics listed in Tables 1 and 2, Hagibis had a three-times larger _R15_ (421.6 km vs. 150.2 km) and two-times larger RMW (59.6 km vs. 35.0 km) than Faxai. The 24-h average _Vm_ was almost equal between Faxai (36.7 m\(\cdot\)s\({}^{-1}\)) and Hagibis (33.2 m\(\cdot\)s\({}^{-1}\)), even though Hagibis had a larger life-time maximum _Vm_ value (54.0 m\(\cdot\)s\({}^{-1}\)) than Faxai (43.7 m\(\cdot\)s\({}^{-1}\)), as seen in the best track data of the Japan Meteorological Agency. The average speed of movement of Faxai (8.1 m\(\cdot\)s\({}^{-1}\)) was comparable to that of Hagibis (6.8 m\(\cdot\)s\({}^{-1}\)). Thus, in terms of the impact of typhoon characteristics,
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline & & **Co. typhoon** & **Co. ocean** & _R15_ & **RMW** & **Maximum** & **Speed of** & & \\
**Faxai** & **Co** & **(Rg\({}^{-2}\)m\({}^{-2}\)s\({}^{-2}\))** & **(Rg\({}^{-2}\)m\({}^{-2}\)s\({}^{-2}\))** & **(km)** & **(km)** & **wind (m\(\cdot\)s\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **(m)** & **(K\(\cdot\)m\({}^{-1}\))** \\ \hline \hline Average & 1.6 & 6.5 & 4.5 & 150.2 & 35.0 & 36.7 & 8.1 & 36.2 & 0.07 \\ Standard & **0.7** & **3.0** & **1.7** & 16.2 & 3.2 & 2.0 & 1.5 & 3.5 & 0.01 \\ deviation & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 1 Average and standard deviation of Co, Co separated by typhoon characteristics and ocean conditions, _R15_, RMW, maximum wind, speed of movement, MLD, and \(\Gamma\) for Typhoon Faxai.
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline & & **Co. typhoon** & **Co. ocean** & _R15_ & **RMW** & **Maximum** & **Speed of** & & \\
**Hagibis** & **Co** & **(Rg\({}^{-2}\)m\({}^{-2}\)s\({}^{-2}\))** & **(Rg\({}^{-2}\)m\({}^{-2}\)s\({}^{-2}\))** & **(km)** & **(km)** & **wind (m\(\cdot\)s\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **(m)** & **(K\(\cdot\)m\({}^{-1}\))** \\ \hline Average & 3.6 & 31.5 & 11.5 & 421.6 & 59.6 & 33.2 & 6.8 & 46.7 & 0.06 \\ Standard & 2.7 & 17.0 & 5.8 & 60.7 & 9.1 & 1.5 & 2.1 & 2.3 & 0.01 \\ deviation & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 2 As in Table 1, but for Typhoon Hagibis.
the Hagibis had more potential to cool the ocean than Faxai, attributable mainly to its larger size.
Figure 4 shows the relationships between Co and \(\Delta\)SST for Faxai and Hagibis. Larger Co values are explained by the greater \(\Delta\)SST values. The correlation coefficients are listed in Table 3; the correlation coefficients are from 24 h before passage to the time of passage (0) and to 3, 6, 9, 12, 24, and 36 h after passage. The correlation coefficients were 0.3-0.7 for Faxai and 0.7 for Hagibis. Therefore, Co is a practical indicator of SST cooling. Additionally, the increase rates of Faxai and Hagibis were similar (both within 0.11-0.16, as shown in Figure 4). The correlation coefficients between Co and \(\Delta\)SST decreased with time for Faxai but remained almost constant for Hagibis (Table 3). This result is consistent with the ocean temperature changes (Figure 2). The correlation for Faxai was 0.68 at the time of passage, which worsened after 6 h, decreased to 0.40
Figure 4: Correlation between hourly Co and \(\Delta\)SST. The periods are from 12 UTC September 7–12 UTC September 8 for Typhoon Faxai (red) and from 06 UTC October 11 to 06 UTC October 12 for Typhoon Hagibis (blue). SST cooling was determined from 24 h before passage to the time of passage (\(\Delta\)SST\(\_\)0) and to 6 h (\(\Delta\)SST\(\_\)6), 12 h (\(\Delta\)SST\(\_\)12), and 24 h (\(\Delta\)SST\(\_\)24) after passage.
after 12 h, and subsequently remained relatively constant (Table 3).
## 4 Conclusion
This study quantitatively evaluated the factors of typhoon-induced SST cooling caused by typhoons Faxai and Hagibis. The average observed \(\Delta\)SST differed substantially between the two typhoons. From the high-resolution ocean model results, the average Co was 1.6 for Faxai and 3.6 for Hagibis. The Co can separately estimate the impacts of ocean conditions and typhoon characteristics, such as \(Vm\), the size in the horizontal direction, and the speed of movement. The impact of ocean conditions on the typhoon-induced SST cooling by Hagibis was 2.6 times larger than the impact by Faxai; that is, SST is hard to cool in the case of the ocean before Hagibis passes. In short, it is important for ocean cooling not only ocean conditions but also typhoon characteristics because in fact, Hagibis cooled the ocean more than Faxai. In addition, the impact of Hagibis's characteristics on the typhoon-induced SST cooling was 4.8 times larger than the impact of Faxai's characteristics. Thus, SST was more likely to cool by typhoon characteristics in the case of Hagibis. Among Hagibis's characteristics, typhoon size had the greatest impact on ocean cooling. From the above, as indicated by the Co values, Hagibis cooled the ocean well due to the large impact of the typhoon, even though the ocean was less easily cooled than in the case of Faxai. The difference in ocean cooling between typhoons Faxai and Hagibis was clarified through the use of Co.
Although typhoon-induced SST cooling is mainly related to ocean conditions, such as OHC and TCHP, or to ocean structures such as MLD. Typhoon characteristics are also important factors in the ocean cooling associated with typhoon passage and can be assessed using Co. Therefore, we suggest that Co is a practical indicator for estimating the magnitude of SST cooling caused by strong typhoon winds, and comparing factors of typhoon-induced SST cooling in multiple cases even though it does not include the effects of ocean water advection. Future studies should apply Co to other cases to gain a better understanding of this parameter and clarify the domain within which the ocean is affected by typhoons.
In our future study, we will do a composite analysis of typhoon-induced SST cooling the dependence of typhoon characteristics and ocean conditions involved in physical processes including typhoons passed over the ocean around Japan region from April to October in 2019 to provide important findings to typhoon-ocean interactions.
## Author Contributions
**[PERSON]:** Conceptualization; data curation; formal analysis; investigation; methodology; software; visualization; writing - original draft; writing - review and editing. **[PERSON]:** Conceptualization; funding acquisition; project administration; supervision; validation; writing - review and editing. **[PERSON]:** Data curation; funding acquisition; project administration; resources; software; writing - review and editing. **[PERSON]:** Validation; writing - review and editing. **[PERSON]:** Methodology; software; writing - review and editing.
## Acknowledgements
This researchbegan during the first author's study at Yokohama National University as a Master's Program, which was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) KAKENHI Grants 19K24677, 21K03658, JP19H05696, 19H05697, 20H00289 and JST, CREST Grant, JPMJCR1681, Japan. Research product of Figure 1a,c. (produced from Himawari-8) that was used in this paper' was supplied by the P-Tree System, Japan Aerospace Exploration Agency (JAXA).
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wiley/ff2e87e4_9ef0_4c54_8964_71974f514aff.md | # Earth and Space Science
Future Climate Under CMIP6 Solar Activity Scenarios
[PERSON]\({}^{1}\)
\({}^{2}\), [PERSON]\({}^{1,2}\), [PERSON]\({}^{1}\), [PERSON]\({}^{1,3}\), and [PERSON]\({}^{1,2,3}\)
\({}^{1}\)Physikalisch-Meteorologisches Observatorium Dawos and World Radiation Center, Dawos, Switzerland, \({}^{2}\)St. Petersburg State University, St. Petersburg, Russia, \({}^{3}\)Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
###### Abstract
Predictions of solar activity in the future are difficult to make due to the chaotic state of solar dynamo and the high nonlinearity of physical processes on the Sun. Therefore, the Climate Intercomparison Project Phase 6 (CMIP6) used a statistical approach and recommended two different solar forcing scenarios for the simulations. The reference scenario was developed as the standard forcing, whereas the alternative forcing has lower solar activity (EXT CMIP6). In this study, we use both forcings in a set of experiments to explore the importance of the alternative CMIP6 solar forcing for future climate and ozone layer variability. In general, the difference in solar forcing scenarios is small, and thus most changes at the surface and at high altitudes are not significant. In addition, only the active phases of the Sun, which have the largest difference in amplitude of the forcing, are investigated. In this case, some statistically significant patterns emerge, mostly in the stratosphere, but still, the magnitude of the changes is not very large and a noticeable surface climate response to these changes is not expected and also not found. Our results indicate that low amplitude solar forcings such as the EXT CMIP6 or similar are not worthwhile considering during the next CMIP type of activities. The proposed solar irradiance decline does not represent any danger to the ozone layer.
Footnote †: c) 2023 The Authors. Earth and Space Science published by Willey Periodicals. Calc. on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
## 1 Introduction
Solar radiation, which reaches the Earth, is susceptible to different changes due to the dynamical characteristics of the Sun. There are long-term changes in solar irradiance which have time periods of several years to decades or even longer. Superimposed on these changes are the short-term white-noise signals such as the daily and monthly changes. Other changes are more periodic, like the 11-year solar cycle. At present time, the total solar irradiance (TSI) amplitude change between the maximum and minimum value in such a cycle is about 1 Wm\({}^{-2}\)([PERSON], 2006, 2013; [PERSON], 2016). The resulting forcing at the Earth's surface is around 0.17 Wm\({}^{-2}\)([PERSON] et al., 2010). A back-on-the-envelope calculation using typical values leads to a change of 0.08-0.16 K of mean surface warming (e.g., [PERSON] et al., 2016). However, a change in TSI goes in hand with a different distribution of the solar energy spectra. The changes in the ultraviolet (UV) part of the solar spectrum will particularly affect stratospheric ozone ([PERSON] et al., 2018), potentially leading to a non-linear response of the surface climate ([PERSON], 1994; [PERSON] et al., 2015).
For the far past, direct observations are not available and solar forcing models must rely entirely on proxy data, leading to highly uncertain long-term reconstructions (e.g., [PERSON] et al., 2018). Yet, for the recent past, the solar forcing is sufficiently established from direct satellite observations ([PERSON] et al., 2017; [PERSON], 2016). These data are suitable to verify the empirical and semi-empirical models ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2014), whose output is exploited in climate models. The future behavior of solar activity, however, is very uncertain and is mostly based on statistical extrapolations. Thus, different approaches are adopted to incorporate solar forcing in the Climate Model Intercomparison Project (CMIP). For example, in CMIP5, the TSI recommendation for future scenarios was to repeat the solar cycle 23, which lasted roughly from April 1996
model for carbon cycle HAMOCC, and the land surface model JSBACH. The MPI-ESM1.2 is coupled to the chemical module MEZON ([PERSON] et al., 2003; [PERSON] et al., 1999) and the size-resolving (40 bins) sulfate aerosol microphysics module AER ([PERSON] et al., 2019; [PERSON] et al., 2015; [PERSON] et al., 1997). The coupling occurs through the exchange of greenhouse gas concentrations, sulfate aerosol properties, and three-dimensional meteorological data such as relative humidity, clouds, and temperature. The SOCOLv4 is formulated on a Gaussian grid with a horizontal resolution of T63 spectral truncation (\(\sim\)1.9\({}^{\circ}\)\(\times\) 1.9\({}^{\circ}\)) as well as 47 vertical levels up to 0.01 hPa in a hybrid sigma-pressure coordinate system. The MEZON includes 99 chemical compounds, determined by 216 gas-phases, 72 photolysis, and 16 heterogeneous reactions. To compute dynamic processes, the SOCOLv4 uses a 15-min time step and a 2-hr time step to perform chemistry and radiation simulations. A lookup-table approach ([PERSON] et al., 1999) is used to calculate photolysis rates, including the solar irradiance variability effect. The actual solar forcing in the model is divided into 14 wavelength bands used in the solar radiation module ([PERSON] et al., 2014) and 78 bands for the photolysis and extra solar heating calculations ([PERSON] et al., 2016). Further details of the model and an in-depth validation are described in [PERSON] et al. (2021).
### The Experiment Design and Solar Forcing Description
The model is run using historical boundary conditions until 2015 and the \"middle-of-the-road\" SSP2-4.5 scenario afterward (see [PERSON] et al. (2017) for a description of the SSP (Shared Socio-economic Pathway) scenarios). The solar forcing is branched into two different scenarios starting in 2020 and for each forcing we performed ensemble runs with three ensemble members each. Two additional shorter ensemble runs starting in 2050 were performed for the two solar forcing scenarios to better assess the variability of the climate response during the second half of the 21 st century. For the analysis, all five ensemble members are used. The solar radiation scenarios used in our study are the REF and EXT described in [PERSON] et al. (2017). The corresponding TSI evolution is shown in Figure 1. Solar activity-related forcings such as the ionization by energetic particle precipitation (EPP) and NO\({}_{3}\) influx from the thermosphere also follow the recommendation by [PERSON] et al. (2017). No explicit eruptive volcanic forcing is used, however, the SSP scenarios include a background volcanic degassing forcing, as well as other surface emissions of sulfur compounds.
In the following, we analyze the result for two samples: the whole 20-year period between 2080 and 2099 and only periods where the Sun was in a high activity state. During the high activity phase, the difference between the REF and EXT forcings is the largest. These periods were defined as 5- to 6-year wide windows around the year where the REF solar cycle reached its maximum value. The following periods are selected: 2066-2071, 2079-2083, and 2090-2094 (gray bands in Figure 1). The mean differences in TSI during these periods are 0.46, 0.43, and 0.52 Wm\({}^{2}\). The TSI differences between the two scenarios are remarkably similar to the amplitude of
Figure 1: Time evolution of the total solar irradiance used in the simulations. The blue line denotes the REF forcing and the orange line the EXT forcing. The lighter colors are the monthly values, and the darker lines are the 13-month running averages. The gray bars indicate the three periods used to study the climate response during the solar active phase.
period, is 0.05 K (see Figure 2). Compared to the increase in warming between 2020 and the end of the century, which is around 2 K, the impact of the CMIP6-suggested solar forcing scenario is negligible and not significant. Similarly, the precipitation does not show any notable change until 2099 (not shown).
However, regionally there are some significant, although rare, temperature changes on the Earth's surface (see Figure 3). Most of the significant changes are present only for a specific season or month in a certain region as for example, the negative anomalies in summer and autumn in the Ross Sea. Previous studies which show the REF scenario itself. Thus, the results from the highly active periods could also be interpreted as a future change between active and quiet periods during an 11-year solar cycle.
The significance is computed as in the IPCC AR6 report (see [PERSON] et al., 2021, Cross-Chapter Box Atlas.1 (Approach C)). The variability threshold is computed as the standard deviation of the reference run (in our case REF) multiplied by the square root of two, a constant factor and divided by the square root of the period length. The square root of 2 accounts for the Gaussian propagation error as the variability of the two means could be different. The constant factor is in our case 1.645 and corresponds to a 90% confidence level. Thus, if the signal (in our case from EXT) exceeds 90% of the variability taking into account the propagation error and period length the signal is significant.
## 3 Results
### Changes at the End of the 21 st Century
The difference between the two forcings in the global mean values, such as temperature or precipitation, is marginal. For instance, the annual mean temperature difference during the period 2080-2099, a typical IPCC report period, is 0.05 K (see Figure 2). Compared to the increase in warming between 2020 and the end of the century, which is around 2 K, the impact of the CMIP6-suggested solar forcing scenario is negligible and not significant. Similarly, the precipitation does not show any notable change until 2099 (not shown).
However, regionally there are some significant, although rare, temperature changes on the Earth's surface (see Figure 3). Most of the significant changes are present only for a specific season or month in a certain region as for example, the negative anomalies in summer and autumn in the Ross Sea. Previous studies which show
Figure 3: The seasonal surface temperature difference between EXT minus REF ensemble, averaged for the period 2080 and 2099. The stippling denotes areas where the signal is not significant.
Figure 2: Yearly mean temperature evolution relative to the mean over the period 2020–2029. The blue line denotes the temperature change under the REF scenario and the orange line is the change due to the EXT forcing. The lighter colors denote the ensemble spread of one standard deviation.
substantial changes at the Earth's surface usually apply much stronger forcing (e.g., [PERSON] and [PERSON], 2020). As described in the introduction, the forcing difference at the surface is on the order of a few 1/10 th of a \(\mathrm{Wm^{-2}}\), which is small compared to other forcings. In order for small changes in TSI to have a significant effect on the surface temperature, there must be a mechanism that amplifies the response. Two such mechanisms are proposed in the literature, for example, the visible-driven \"bottom-up\" (i.e., [PERSON] et al., 2008; [PERSON] et al., 2009) and the UV-driven \"top-down\" (i.e., [PERSON] and [PERSON] (2002)) mechanisms (see [PERSON] and [PERSON] (2015) for an overview).
The \"bottom-up\" mechanism initiates with a temperature change at the surface, which will subsequently be modified through cloud and precipitation interactions (e.g., [PERSON] et al., 2008, 2009). In our case, the forcing is too small to produce a significant impact on surface climate, related to the \"bottom-up\" mechanism. The only regions with consistently significant temperature changes are the Ross and Amundsen Sea close to Antarctica. These changes are probably indirectly induced by sea-ice cover changes.
The \"top-down\" mechanism is a sequence of changes induced by stratospheric warming in the tropics due to enhanced ozone production at the maximum of solar activity (see Figures A1 and A2 in Appendix A). The warming causes changes in the zonal mean temperature field and subsequently in the strength and location of the polar vortex due to the impact on the planetary wave propagation (i.e., see [PERSON] et al. (2010) for an overview). Indeed, the zonal mean temperature changes show a large significant stratospheric cooling which travels from one polar region to the opposite polar region during their respective summer seasons (see Figure A2). This is expected as there is less incoming UV, less ozone production, and hence less warming in the sunlit stratosphere. Interestingly, these significant temperature anomalies are not changing the zonal wind and thus the vortex significantly (Figure A3). Even though the changes in zonal wind seem quite large, the signal is still smaller than the variability. In autumn and spring, there are only a few patches spread in the stratosphere which show a statistically significant change in temperature.
As mentioned above, during the considered period only traces of the \"top-down\" nor the \"bottom-up\" mechanisms are visible, which agrees with [PERSON] et al. (2016), who also used a weak future solar forcing scenario. The typical averaging period from 2080 to 2099 ranges roughly over two solar cycles. As the solar irradiances during the quiet phases are similar in the REF and EXT scenarios, the most extensive changes are expected due to a larger difference in the amplitude of the solar cycle. The mean TSI change at the end of the century is about 0.35 \(\mathrm{Wm^{-2}}\). This value is very small and lies within possible inter-monthly variability. Thus, in the second step, we investigate only the last three solar active phases of the 21 st century. The results are described in the next section.
### Changes During the Active Periods of Solar Irradiance
Narrowing the analysis only to the solar active phases does reveal some statistically significant features. The zonal mean ozone field shown in Figure 4 has a typical pattern of changes in the response to UV radiation decline (e.g., [PERSON] et al., 2018; [PERSON] et al., 2018). In the mesosphere, the reduced UV radiation produces less HO\({}_{x}\) from H\({}_{x}\)O photolysis suppressing the HO\({}_{x}\)-catalytic cycle of ozone destruction. In the stratosphere, there is less production of ozone due to abated O\({}_{x}\)-photolysis by reduced UV radiation below 242 nm, leading to 1%-3% lower ozone concentrations under the EXT solar forcing scenario. The decrease of ozone is present in every month and spans over the whole stratosphere. The largest significant patch in the mid-stratosphere is located in the southern high latitudes during the southern summer months and displaces to the northern high latitudes during the northern hemispheric summer. Additionally, there is a quasi-stable region in the troposphere south of 50\({}^{\circ}\)S with increased ozone concentrations. [PERSON] et al. (2011) reported a similar finding in the unpolluted Southern Hemisphere, mainly through the interplay of galactic cosmic rays (GCR), NO\({}_{x}\) and ozone called the NO\({}_{x}\)-limited regime, that is, the ozone production becomes more sensitive to changes in NO\({}_{x}\). In the Northern Hemisphere, the GCR-induced ozone changes in the troposphere are not present due to the atmosphere being more polluted with NO\({}_{x}\). In addition, ozone in this region is strongly affected by the transport of ozone-rich air from the stratosphere (e.g., [PERSON] et al., 2015). However, it is difficult to attribute this increased ozone signal to only one mechanism. Most likely it is caused by the interplay of all the above-mentioned factors.
Nevertheless, these variations in the ozone and reduction in irradiance available to be absorbed cause various changes in the temperature and wind fields (Figure A3). The zonal mean temperature changes during the active phase show large significant responses in the mid-stratosphere (see Figure 5). Likewise, with the ozone changes described above, the significant changes in temperature follow the seasonal variation of the solar zenith angle and are therefore statistically significant only in the sunlit regions of the stratosphere (the summer hemisphere), where the dynamical variability is also much smaller than in the winter hemisphere. This pattern is also similar to the pattern observed during the period 2080-2099. Most of the statistically robust changes show a temperature decrease with a few exceptions. The positive ozone changes in the mesosphere due to the slow-down of the HO\({}_{x}\)-cycle (see Figure 4) do not strongly impact the mesospheric temperature signal, because ozone absorbs very little above 70 km. The upper mesosphere is dominated by the absorption of molecular oxygen in the Lyman-\(\alpha\) line and the Schuman-Runge bands, which also get reduced due to less irradiance. However, the temperature changes due to dynamical variability are much larger in that region and therefore the solar signal is indistinguishable. This is consistent with results from high-top models which include O\({}_{z}\) absorption (e.g., [PERSON] et al., 2009).
In the northern latitudes, there is an effect that might be related to the \"top-down\" mechanism described by [PERSON] and [PERSON] (2002). In addition, there is a non-significant warming close to the surface in the Arctic during February due to changes in solar forcing, similar to that reported by [PERSON] et al. (2022). However, most temperature differences are non-significant. The zonal wind fields again show relatively large changes, but they all are also non-significant (Figure A3). Similar to the climatology between 2080 and 2099, the variability is larger than the signal itself.
Even in the active phase, there are no large significant changes in temperature visible at the Earth's surface. There are only two main spots with substantial changes (see Figure 6a). One is located close to Antarctica and the other is in the North Pacific. During the austr winter and spring, the region with significant temperature change emerges near Antarctica in the Weddell and Ross Seas. A similar dipole structure in temperature response is often
Figure 4: Zonal mean monthly ozone changes of EXT relative to REF averaged for the periods where the sun is highly active. The stippling denotes areas where the signal is not significant.
observed in the Southern Ocean sea ice and is correlated to the Southern Annular Mode (SAM) through pressure and advection changes ([PERSON], 2005). This is also the reason why the signal is more pronounced during the Southern Hemisphere winter- and springtime, as the sea ice in those regions melts to a large part during the summer.
A second significant temperature anomaly is located in the northern Pacific Ocean with positive values and the adjacent region of Alaska and the Rocky Mountains showing a negative anomaly, a typical picture of the Pacific Decadal Oscillation. Several studies (e.g., [PERSON] et al., 2021; [PERSON] et al., 2021) have found a similar relationship between changes in TSI and the Pacific Decadal Oscillation through changes in temperature gradients induced by different UV values. [PERSON] et al. (2016) found a similar change in temperature over the Pacific Ocean using idealized model experiments. They attributed the change mainly to the alteration of the visible part of the solar irradiance spectrum.
However, as shown in Figures (b)b-(d)d, the variability is quite large among the three active periods considered. The anomaly in the North Pacific is visible in two periods (see Figures (b)b and (c)c). Also, the anomaly close to Antarctica is not always pronounced. Additionally, one period shows a stronger, statistically significant cooling over Siberia, which is not as pronounced in the mean over the three considered periods (Figure (b)b). [PERSON] et al. (2014) and [PERSON] et al. (2018) report a link between Arctic warming and colder temperatures in Siberia. Depending on the baroclinicity over the Arctic and on the resolution of the stratosphere, a response over Siberia appears.
As seen above, each period by itself includes phenomena reported already in other studies. In the mean temperature, however, these signals are weakened and some of them become non-significant. Now, the question arises as to how these response patterns emerge. On the one hand, it could be that since the forcing difference is small, random long-term internal variability might emerge from other components, such as the ocean. On the other
Figure 5: Zonal mean monthly temperature changes averaged for the periods where the Sun is highly active. The stippling denotes areas where the signal is not significant.
hand, it may happen that there is a locking or interplay of the variability for various components, and this is mostly driven by dynamics. Since the solar forcing difference is relatively weak, it is difficult to assess the cause of the variations, and this is beyond the scope of this study.
## 4 Discussion and Summary
We have performed two sets of transient ensemble simulations, using the ESM SOCOLv4 for the period 2020-2099, applying the SSP2-4.5 future socio-economic scenario and two different solar forcing scenarios as proposed in [PERSON] et al. (2017) for CMIP6. One forcing is proposed as the best assumption resulting from statistical methods using the past solar cycles, while the other forcing represents a long-term low activity scenario so-called grand minimum. The amplitude of the TSI variations under the future grand minimum scenario is, however, rather small, and basically mostly just the reduction of the 11-year cycle amplitude with only slight (\(<\)0.2 Wm\({}^{-2}\)) reductions of the minima periods.
Figure 6: (a) The SH JJA and NH DIF mean temperature change averaged over the three highly active periods. (b)–(d) The single periods. The stippling denotes areas where the signal is not significant. The remaining seasons are shown in Appendix A (Figure A4).
The TSI difference in the used forcings is largest during the active phase of the 11-year solar cycle. During the low activity phases, the TSI values of the two forcings are very similar. Thus, averaging over several solar cycles results in a very small forcing difference which is even smaller than the intra-monthly variations. As a consequence, the analysis of the mean climate state change at the end of the 21 st century reveals very small and noisy responses. All major solar-related processes described in the literature such as the \"bottom-up\" (e.g., [PERSON] et al., 2008, 2009, 2013) and \"top-down\" mechanisms ([PERSON] and [PERSON], 2002; [PERSON] et al., 2015) involving downward signal propagation in high latitudes are visible, but the signals are only marginally significant. Generally, the mechanisms described in the literature are found using very large solar forcing and are often not transient (e.g., [PERSON] and [PERSON], 2020).
The changes observed during the active phases are qualitatively very compatible to those observed over the period 2080-2099 but are more pronounced in amplitude and therefore, more statistically significant. This suggests that the mechanisms and patterns are generally the same for the long-term TSI reduction and the 11-year cycle effects. However, this influence is too weak to induce a substantial change in the near-surface climate.
In this study only simple statistical methodologies on ensemble averages are used. It might well be the case that a more thorough analysis using more sophisticated methods would provide different results. But the first order impact of a low TSI change remains small. Although this study is conducted with several ensemble runs to improve statistical interpretability it is only conducted with one state-of-the-art model. Including a variety of models would solidify the results. However, the main message would likely be similar.
An intriguing question arises if, for a certain TSI difference, the climate response depends on the average background state of the climate. For example, is the response to a difference of 1 Wm\({}^{-2}\) in solar forcing different if the CO\({}_{2}\) concentration is closer to preindustrial times as compared to future CO\({}_{2}\) levels? A second interesting question is if the response to the 11-year solar cycle is different with a different background climate and which role the amplitude of the cycle plays in a warmer or colder climate.
These questions can be addressed in future studies. The current work demonstrates that the use of EXT CMIP6 or similar scenarios for future solar activity will not lead to new insights and should therefore not be recommended for any following CMIP activities. Given that all our future projections are always based on what we know from the past, instead of the low-forcing future runs, we would suggest having a closer look again on the past centennial changes, but using latest fully interactive models, climate proxy reconstructions, and a variety of available solar forcing estimates.
Figure 12: Zonal mean monthly temperature changes averaged over the period 2080–2099. The stippling denotes areas where the signal is not significant.
Figure 16: Zonal mean monthly zonal wind changes averaged for the highly active periods. The stippling denotes areas where the signal is not significant.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The data is published as open access under [[https://doi.org/10.5281/zenodo.7371147](https://doi.org/10.5281/zenodo.7371147)]([https://doi.org/10.5281/zenodo.7371147](https://doi.org/10.5281/zenodo.7371147)) ([PERSON] et al., 2022).
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wiley/ff2910cf_738b_470f_aa5c_039f9a7cc743.md | A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution
[PERSON]
1 Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA, 1 Now at Atmospheric Oceanic Sciences, Princeton University, Princeton, NJ, USA, 1 Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA, 1 Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, TN, USA, 1 Applied Physics Laboratory, Polar Science Center, University of Washington, Seattle, WA, USA
[PERSON]
1 Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA, 1 Now at Atmospheric Oceanic Sciences, Princeton University, Princeton, NJ, USA, 1 Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA, 1 Department of Earth and Environmental Sciences, Vanderbilt
rumples. Any loss of this resistance, or buttressing, results in an increased flux of grounded ice flow into the ocean, thereby contributing to sea level rise (Dupont & Alley, 2005).
On decade to century timescales, the magnitude of ice shelf buttressing is controlled by ice front evolution (i.e., fluctuations in contact with bay walls/pinning points), fracture or thermomechanical weakening (e.g., [PERSON] et al., 2013; [PERSON] et al., 2017), changes in ice thickness such as thinning from ocean-driven basal melt ([PERSON] et al., 2016; [PERSON] et al., 2012), and response of the upstream grounded ice that feeds the shelf. Ideally, these four processes should be represented in a fully coupled manner that accounts for the complex feedbacks between them. For example, ice shelf thinning from basal melt has been associated with increased fracture ([PERSON] et al., 2015; [PERSON] et al., 2003), and fracture determines the ice front position through tabular calving. Calved icebergs can then alter local ocean properties and circulation within the ice shelf cavity and wherever they drift, which in turn, may affect basal melting rates (e.g., [PERSON] et al., 2017; [PERSON] et al., 2010; [PERSON] et al., 2015, 2016). Further, a more general motivation for developing an integrated representation of these processes stems from the lack of basal friction in ice shelves, which causes a highly nonlocal stress regime where altering stress in one part of the shelf can affect stresses throughout the shelf ([PERSON] & [PERSON], 2010). Therefore, it is important that we develop advanced numerical models and methods to enable realistic simulation of these processes controlling large-scale ice shelf evolution, and thus gain a better understanding of Antarctic Ice Sheet dynamics and improve projections of sea level rise.
Current large-scale ice flow models have difficulty in capturing the simultaneous processes of front evolution, fracture, and thinning owing to the differences in the modeling frameworks that are effective at describing each process separately. Because large-scale ice flow is associated with extreme deformations, it is typically modeled within an Eulerian framework, where velocity is calculated as the ice flows through a fixed region in space. Typically, Eulerian models calculate flow velocity on a fixed mesh over time. However, some processes such as ice mass transport or fracture (represented by damage), are not well-suited to the Eulerian approach due to the artificial diffusion or dispersion inherent to Eulerian advection schemes. For example, this artificial or numerical diffusion smears sharp edges and therefore compromises the accuracy of damage advection and evolution. Furthermore, Eulerian approaches require separate schemes to approximate ice front evolution, such as level-set ([PERSON] et al., 2016) or volume of fluid methods ([PERSON] et al., 2011; [PERSON] et al., 2008). In contrast, a Lagrangian approach, where the position of mesh nodes update with flow, avoids numerical diffusion and naturally tracks ice front evolution. However, Lagrangian or updated Lagrangian methods are only well-suited for small deformation ice flow, such as within 2-D flow-band models for the propagation of individual crevasses over short timescales ([PERSON] & [PERSON], 2013; [PERSON] et al., 2013, 2020; [PERSON] et al., 2017; [PERSON] et al., 2021). Use of Lagrangian methods to model entire ice shelf-sheet systems could result in mesh degradation or tangling owing to the large deformations. Simple remeshing schemes are not ideal because they also introduce artificial diffusion.
These limitations of traditional Eulerian and Lagrangian schemes may be overcome using material point methods, which are formulated in a hybrid Eulerian-Lagrangian framework that simultaneously allows large deformation flow, error-free advection of history variables, and boundary tracking. The material point method (MPM) was originally introduced by [PERSON] et al. (1994, 1995) for solid mechanics, as an adaptation of the particle-in-cell (PIC; [PERSON], 1957) and fluid-implicit-particle (FLIP; [PERSON] et al., 1988) methods. Henceforth, we will refer to this original version as the standard MPM (SMPM). In the sMPM, the material domain is discretized into a set of material points, or particles, that provide a Lagrangian description. Each material point has a mass, volume, position, velocity, stress, and any history variables or other material properties of the constitutive model. A background Eulerian mesh/grid is also defined, which extends beyond the initial domain defined by the material points, and typically remains fixed throughout the simulation. Grid cells containing material points constitute the \"active\" mesh on which the equations of motion are solved in a similar manner as the finite element method (FEM), but with material points serving as moving integration points. The mesh solution is then used to update material point variables and positions.
Many variants of the sMPM have been formulated that retain the basic procedure, but exhibit higher accuracy. These variants are largely motivated by the need to mitigate the well-known \"cell-crossing error\" in sMPM. This error arises from mapping between the material point and the background grid using linear shape functions, which have discontinuous gradients between grid cells so that abrupt transfers of stiffness occur as material points cross cell boundaries or become unevenly distributed between neighboring cells. The first sMPM variant to mitigate this error was the generalized interpolation material point method (GIMPM) developed by [PERSON] and [PERSON] (2004), which convolves the linear nodal shape functions with characteristic functions associated with each material point to result in continuous gradients between grid cells (see Figure S1). Other common variants of sMPM that modify the shape functions to have continuous gradients include the convected particle domain interpolation (CPDI) methods ([PERSON] et al., 2011, 2013) and dual-domain material point (DDMP) methods ([PERSON] et al., 2011). These variants of the sMPM have found diverse applications for modeling impact, fracture, and granular media behavior; for a more detailed literature review we refer the reader to [PERSON] and [PERSON] (2015) and [PERSON] et al. (2020). Material point methods have also been used to model certain components of the cryosphere, including sea ice dynamics ([PERSON] et al., 2007), snow ([PERSON] et al., 2013), and avalanches ([PERSON] et al., 2018).
Here, we develop an implementation of the GIMPM for simulating shallow-shelf ice flow. To our knowledge, this is the first ever implementation of MPMs for shallow ice flow. Our GIMPM formulation solves the momentum and mass balance equations for ice flow and thickness evolution, and enables natural tracking of the ice front and grounding line. In Part II ([PERSON] et al., 2021), we incorporate an anisotropic nonlocal creep damage model ([PERSON] and [PERSON], 2012; [PERSON] and [PERSON], 2005) for fracture propagation. This paper solely focuses on the description and verification of the GIMPM in simulating shallow ice flow, ice thickness evolution, and ice-ocean boundary treatment. We solve for ice flow velocities using the Shallow Shelf Approximation, or Shelly-Stream Approximation (SSA), a 2-D vertically integrated flow model that is appropriate for large-scale ice shelf and ice stream flow, where horizontal velocities can be considered vertically invariant ([PERSON], 1989). The SSA constitutes the only equations solved using the background Eulerian mesh/grid, while history variables such as ice thickness and damage are updated explicitly and efficiently on each material point directly. The primary advantage of our GIMPM formulation is that advection of all variables only involves updating the material point positions, thus our Lagrangian advection scheme is computationally inexpensive and avoids the artificial diffusion errors associated with Eulerian schemes. Furthermore, the positions of the material points allow us to establish and track the ice front and grounding line at sub-grid scales. We implemented our model within the open-source finite element ice flow model Elmer/Ice ([PERSON] et al., 2013), by modifying the Elmer SSA solver to implement GIMPM integration schemes and by introducing several modules for tracking and evolving the set of material points.
In the following sections, we will detail the derivation of our method and quantify its accuracy and stability for 1-D and 2-D ice flow simulations, including front advection. We will illustrate that the GIMPM-SSA formulation is effective for: advecting history or internal state variables without diffusion, maintaining the steady-state grounding lines of marine ice sheets, and tracking ice front evolution on century timescales. To ensure numerical accuracy, we formulate novel schemes for enforcing the conditions at the ice front and outflow boundaries, as well as for determining ice thickness at material points due to particle splitting. This paper is organized as follows: in Section 2 we review the SSA equations and their numerical discretization using the FEM and the GIMPM; in Section 3 we provide the details of our numerical implementation related to grid and particle variable updates; in Section 4 we present schemes for boundary treatment and error control; in Section 5 we provide examples that test the accuracy and numerical performance of the GIMPM-SSA formulation; in Section 6 we provide a brief discussion on the pros and cons of the GIMPM, and finally, in Section 7 we make a few concluding remarks.
## 2 Governing Equations
In this section, we will briefly describe the governing equations of ice flow based on the Shallow Shelf Approximation (SSA), followed by the numerical discretization using the finite element and generalized material point methods. We will use indicial notation for vectors and tensors to describe the strong and weak forms of the governing equations and use matrix notation to present the corresponding discretized linear system. We will use [PERSON]'s summation convention only for spatial indices, where repeated indices imply summation. For brevity, we occasionally avoid indicial notation, and use bold face letters to denote vectors, tensors and matrices.
### Shallow Shelf Approximation
Ice shelves and ice streams can be modeled under the assumption of plug flow, where horizontal velocities and strain rates are constant over depth. Consequently, the incompressible Stokes equations are modified to exclude vertical shear and vertically integrated to derive the SSA that describes the horizontal force or momentum balance as
\[\frac{\partial T_{\hat{u}}}{\partial x_{j}}+\left(r_{\hat{u}}\right)_{i}=\rho gH \frac{\partial s}{\partial x_{i}}, \tag{1}\]
where spatial indices \(i,j\in\left\{1,2\right\}\) correspond to the horizontal plane, \(\mathbf{x}=x_{i}\hat{e}_{i}\) denotes the in-plane spatial coordinates, \(\hat{e}_{i}\) are the basis vectors for the Cartesian coordinate system, \(\rho\) is the ice density, \(g\) is the acceleration due to gravity, \(H\) is the ice thickness, \(s\) is the top surface elevation, \(\overline{\eta}\) is the depth-averaged effective viscosity, and \(r_{\hat{u}}\) is the basal traction described by a friction law. For simplicity, here we assume the friction law as
\[\left(r_{\hat{u}}\right)_{i}=\hat{\rho}v_{i}\,, \tag{2}\]
where \(\hat{\rho}\) is a friction parameter and \(v_{i}\) are the horizontal velocities for which the SSA is solved. Note that the above equation can used to specify several friction laws currently available in Elmer/Ice ([PERSON] et al., 2013) by defining \(\hat{\rho}\) to be dependent on velocity, and in some cases, pressure. In Equation 1, the two-dimensional vertically integrated stress tensor \(\mathbf{\Gamma}\) is defined as (Bueler & Brown, 2009; [PERSON], 1987):
\[\mathbf{\Gamma}=2\overline{\eta}H\begin{bmatrix}2\frac{\partial v_{1}}{\partial x _{1}}+\frac{\partial v_{2}}{\partial x_{2}}&\frac{1}{2}\left(\frac{\partial v _{1}}{\partial x_{2}}+\frac{\partial v_{2}}{\partial x_{1}}\right)\\ \frac{1}{2}\left(\frac{\partial v_{1}}{\partial x_{2}}+\frac{\partial v_{2}}{ \partial x_{1}}\right)&\frac{\partial v_{1}}{\partial x_{1}}+2\frac{\partial v _{2}}{\partial x_{2}}\end{bmatrix}, \tag{3}\]
which may alternatively be expressed in terms of strain rate \(\dot{\delta}_{ij}=1/2\left(\hat{\sigma}v_{i}\,/\,\,\hat{\sigma}x_{j}+\hat{ \sigma}v_{j}\,/\,\,\hat{\sigma}x_{i}\right)\) as
\[\mathbf{\Gamma}=2\overline{\eta}H\begin{bmatrix}2\hat{\epsilon}_{11}+\hat{ \epsilon}_{22}&\dot{\epsilon}_{12}\\ \dot{\epsilon}_{21}&\dot{\epsilon}_{11}+2\dot{\epsilon}_{22}\end{bmatrix}. \tag{4}\]
The constitutive relation for ice flow relates deviatoric stress, \(\sigma_{\hat{u}}^{\rm D}\), to strain rate as
\[\sigma_{\hat{u}}^{\rm D}=2\eta\dot{\epsilon}_{\hat{g}}, \tag{5}\]
where the effective viscosity, \(\eta\), follows the Norton-Hoff flow law ([PERSON], 1955; [PERSON], 1957):
\[\eta=\frac{1}{2}\,g\dot{\epsilon}_{\hat{e}}^{(-\hat{u})/\hat{u}}\,. \tag{6}\]
In the above equation, \(n\) is the flow law exponent, \(\dot{\epsilon}_{\hat{e}}\) is the scalar second invariant or effective strain rate \(\dot{\dot{\epsilon}}_{\hat{e}}=\sqrt{\dot{\dot{\epsilon}}_{\hat{g}}\dot{\dot{ \epsilon}}_{\hat{g}}\,/\,\,2}\), and \(B\) is a flow rate factor dependent on temperature and ice fabric. The depth-averaged effective viscosity used in the SSA takes the same form as (Equation 6), but uses only in-plane strain components to determine \(\dot{\epsilon}_{\hat{e}}\) and a depth-averaged rate factor, \(\overline{B}=1/\,\,H\left[\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ }}}}}}}}}}}}}}} \right]\) where \(\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{\dot{\dot{\dot{\dot{}}}}}}}}}}}}}}}}}}}\) is the vertical coordinate of the ice basal surface. We take \(z\) as positive in the upward direction, where \(z=0\) corresponds to sea level.
A boundary condition at the ice front is set according to the seawater pressure at the ice terminus opposing ice flow
\[\sigma_{\hat{g}}\,\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ }}}}}}}}}}}}}}}}}}=\begin{cases}\rho_{ \hat{u}}g\,\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{ \dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dot{\dotdot{\dotdotdot{\dotdotdotdotdotdotdotdotdotdotdotdotdot }}}}}}}}}}}}}}}}}}} }
### Weak Form and Discretization Using the FEM
The procedure for deriving the weak form of the SSA and discretization using the SMPM or the GIMPM is similar to that using the FEM, so we briefly review the procedure using the FEM first for clarity. Full details of this procedure can be found in the literature (e.g., [PERSON] and [PERSON], 2009; [PERSON] et al., 2019; [PERSON], 2001). The weak form of the SSA is derived using the Bubnov-Galerkin method of weighted residuals by multiplying Equation 1 by an arbitrary smooth test function \(\mathbf{w}\big{(}\mathbf{x}\big{)}\) and integrating over the domain. After applying the divergence theorem and introducing the boundary conditions, we obtain:
\[\begin{split}&\int\limits_{\Omega}\frac{\partial w_{i}}{\partial x _{j}}d\Omega+\begin{bmatrix}w_{i}\rho_{i}\rho_{B}H\frac{\partial s}{\partial x _{i}}d\Omega-\begin{bmatrix}w_{i}\big{(}\tau_{i}\big{)}_{i}d\Omega\\ \tau_{i}\big{)}_{i}d\Omega\\ -\int w_{i}\tau_{i}\partial t\tau-\int\limits_{\Gamma_{d}}\frac{1}{2}w_{i} \Big{(}\rho_{B}H^{2}-\rho_{w}gb^{2}\Big{)}\hat{n}_{i}d\Gamma=0\,,\end{split} \tag{9}\]
where \(\Omega\) and \(\Gamma_{\text{cf}}\) represent the area of the ice domain and calving front boundary, respectively. Dirichlet conditions for velocity are applied along the final boundary, represented by \(\Gamma_{k}\). Here, \(w_{i}\) is set to zero in accordance with the fixed velocities, and the integral over \(\Gamma_{k}\) is eliminated ([PERSON], 1989).
All variables in Equation 9, including the test function \(\mathbf{w}\), are represented continuously on the mesh/grid using nodal shape functions. For example, velocity at a spatial location \(\mathbf{x}\) and time \(t\) is defined as
\[\mathbf{v}\big{(}\mathbf{x},t\big{)}=\sum\limits_{t=1}^{N_{n}}\mathbf{v}_{i}\big{(}t\big{)} \phi_{t}\big{(}\mathbf{x}\big{)}, \tag{10}\]
where the nodes of the mesh are \(\mathbf{x}_{i},I=1,\dots,N_{n}\), \(\phi_{t}\big{(}\mathbf{x}\big{)}\) is the nodal shape function associated with node \(I\), and \(N_{n}\) is the number of nodes of the chosen finite element (here we use 4-noded quadrilateral elements, so \(N_{n}=4\)). Substituting the continuous representations for \(\mathbf{v}\) and \(\mathbf{w}\) from Equation 10 into Equation 9, and noting that the test functions are arbitrary, a linear system can be assembled and solved for horizontal velocities \(\mathbf{v}\). The element tangent stiffness matrix \(\mathbf{K}\) and residual force vector \(\mathbf{f}\) can be split into components and expressed as follows:
\[\begin{bmatrix}\mathbf{K}_{11}&\mathbf{K}_{12}\Bigg{\rvert}\begin{matrix}\bm {v}_{1}\\ \mathbf{K}_{21}&\mathbf{K}_{22}\end{matrix}\Bigg{\rvert}\begin{matrix}\mathbf{v}_{ 1}\\ \mathbf{v}_{2}\end{matrix}\Bigg{\rvert}\begin{matrix}\mathbf{f}_{1}\\ \mathbf{f}_{2}\end{matrix}\Bigg{\rvert}, \tag{11}\]
where \(\mathbf{v}_{i}\) and \(\mathbf{v}_{2}\) are the vectors of nodal velocity components, the vectors \(\mathbf{f}_{i}\) and \(\mathbf{f}_{2}\) contain the gravitational forcing, and the element submatrices of the tangent matrix are given by
\[\begin{split}\mathbf{K}_{11U}&\coloneqq\int\limits_{ \Omega^{E}}2\frac{\partial\phi_{t}\big{(}\mathbf{x}\big{)}}{\partial x_{1}}\frac{ \partial\phi_{t}\big{(}\mathbf{x}\big{)}}{\partial x_{1}}+\frac{1}{2}\frac{ \partial\phi_{t}\big{(}\mathbf{x}\big{)}}{\partial x_{2}}\frac{\partial\phi_{t} \big{(}\mathbf{x}\big{)}}{\partial x_{2}}\Bigg{\rvert}d\Omega\\
\[f_{1t} \coloneqq\begin{bmatrix}\phi_{t}\left(\mathbf{x}\right)\rho gH\frac{ \partial s}{\partial x_{1}}d\Omega,\\ \alpha^{R}\\ f_{2t} \coloneqq\begin{bmatrix}\phi_{t}\left(\mathbf{x}\right)\rho gH\frac{ \partial s}{\partial x_{2}}d\Omega.\end{bmatrix} \tag{13}\]
At boundary elements for the calving front,
\[f_{1t} =\int\limits_{\Gamma_{\rho}^{\rho}}\frac{1}{2}\phi_{t}\left(\mathbf{x} \right)\left(\rho gH^{2}-\rho_{w}gb^{2}\right)\hat{n}_{t}d\Gamma=0\,. \tag{14}\]
Following standard finite element procedure, the integrals in Equations 12-14 are evaluated using Gaussian quadrature. Variables \(H\), \(\rho\), \(b\), \(B\), and \(\
abla\mathbf{v}\) must be mapped to the Gauss points from the nodes, where \(B\) and \(\
abla\mathbf{v}\) are used to calculate the depth-averaged effective viscosity \(\overline{\eta}\).
### Weak Form and Discretization Using the GIMPM
The original formulation of the GIMPM ([PERSON], 2004) was derived using the Petrov-Galerkin method, wherein the test function \(\mathbf{w}\) and the trial function \(\mathbf{v}\) belong to different function spaces. In the GIMPM, each material point or particle is assigned with a particle characteristic function, \(\mathcal{X}_{p}\), that must satisfy partition of unity in the reference or undeformed configuration
\[\sum_{p}\mathcal{X}_{p}\left(\mathbf{x},t=0\right)=1\,\forall\,\mathbf{x}, \tag{15}\]
Note that partition of unity is also a requirement for the element shape functions. We choose \(\mathcal{X}_{p}\) to be the commonly used \"hat\" function with value one within the material point domain \(\Omega_{p}\) and zero outside as
\[\mathcal{X}_{p}\left(\mathbf{x}\right)=\begin{cases}1,&\text{if }\mathbf{x}\in\Omega_{p},\\ 0,&\text{otherwise}.\end{cases} \tag{16}\]
Note that if \(\mathcal{X}_{p}\left(\mathbf{x}\right)\) is chosen as a Dirac delta function, then the sMPM is retrieved. We assign a rectangular domain to each material point over which \(\mathcal{X}_{p}\) is defined, which we will refer to as the GIMPM domain of a material point. To satisfy Equations 15 and 16, the initial material domain must be discretized into material points so that no gaps or overlapping with neighboring GIMPM domains occurs. The GIMPM requires using a regular background grid of rectangular elements. We perform the initial discretization by evenly subdividing the domain \(\Omega\) into GIMPM domains \(\Omega_{p}\) by introducing a specified number of material points for each active background grid cell. In this formulation, we will update the lengths of the GIMPM domains due to deformation (see Section 3), with the goal of maintaining partition of unity over time precisely, to the extent possible. The area associated with a material point, \(A_{p}\) is then defined as
\[A_{p} =\int\limits_{\Omega_{p}}\mathcal{X}_{p}(\mathbf{x})d\Omega, \tag{17}\]
where \(\Omega_{p}\) is the support area of the particle characteristic function and \(\Omega\) is the area of the overall ice domain. Most literature on material point methods generalizes the formulation to 3-D by using volume (\(V_{p}\)) rather than area (\(A_{p}\)), but we use \(A_{p}\) here because the SSA is inherently 2-D.
The values of material point variables may be initialized by integrating properties of the continuum body against the particle characteristic functions. For example, the initial value of material point property, \(h_{p}^{0}\), may be expressed as an area-averaged form of the initial continuum field \(h^{0}(\mathbf{x})\) as
\[h_{p}^{0}=\frac{1}{A_{p}^{0}\,\int\limits_{\Omega^{0}}\mathcal{X}_{p}(\mathbf{x} )d\Omega^{0}}, \tag{18}\]
where superscript '0' indicates the initial time step. The validity of Equation 18 is a consequence of the partition of unity. Consistently, at any future time step \(m\), the particle characteristic functions may be used as a basis to represent the material property throughout the computational domain
For to a certain extent, but ultimately, an alternative material point weighting is required to more evenly distribute material point weights between elements and maintain accuracy ([PERSON] et al., 2017). The new weight, \(W_{p^{\prime}}\), is a function of both the element area, \(A_{\text{E}}\), and material point areas, \(A_{p^{\prime}}\) as given by
\[W_{p}=\frac{A_{\text{E}}}{\sum_{p^{\prime}=}^{n_{p}}A_{p}}\,. \tag{26}\]
Thus, in the reweighted sMPM, \(W_{p}\) replaces \(A_{p}\) as the integration weights in Equations 24 and 25. This reweighting can also be used with the GIMPM, where \(A_{p}\) becomes the area of overlap between a GIMPM domain and the element. However, reweighted GIMPM is mostly unnecessary because material point weight is already smoothly distributed between neighboring elements unless severe overlaps or gaps develop between neighboring GIMPM domains. We largely avoid these errors in our simulation studies, and therefore do not apply the reweighting to our GIMPM simulations here.
## 3 Numerical Implementation
At time \(t=0\), the ice domain is discretized into a specified number of material points per grid cell as described in Section 2.2. The unknown variables, namely ice flow velocity and ice thickness, are defined directly on the material points; whereas, the external parameters such as bedrock elevation, the basal friction parameter, and accumulation/ablation rates are defined on the background fixed mesh. For simplicity, each simulation presented here uses a constant flow rate factor \(B\) and density \(\rho\) for all material points. However, these quantities can be treated as spatially varying and history-dependent. In this section, we detail the numerical procedure for a typical computational cycle, according to the simplified representation given in Figure 1. The cycle begins with a series of parameter mappings between the material points and the grid (Figures 1a and 1b), which are needed in preparation for solving the SSA. The mappings are used to initialize the SSA grid velocity and to determine all parameters at the material point level needed to compute Equations 24 and 25. The SSA is solved using an iterative routine (Figure 1c), where material point viscosity is updated alongside grid velocity until convergence. Subsequently, the grid solution is used to update material point positions, velocities, and geometric parameters (Figure 1d). Finally, material point history variables are updated (Figure 1e), which only includes ice thickness in this study. To improve readability, we will use matrix notation for vectors and tensors to avoid showing spatial indices and show only node and particles indices to explain the mapping between nodes and particles.
Figure 1: Material point method-Shallow Shelf Approximation (MPM-SSA) numerical procedure. The orange dots are material points and blue circles are grid nodes. Grid processes (Eulerian) are highlighted in red and material point processes (Lagrangian) are highlighted in blue.
### SSA Initialization: Grid Parameters
To allow a solution of the SSA, the velocity field and thickness are initialized on the grid by mapping from the material points (Figure 0(a)), where the thickness on the grid is subsequently converted to surface elevation. The gradients of surface elevation and velocity are mapped to material points for the SSA matrix assembly. The initialized grid velocity is further required as part of the update routine for material point velocity (Section 3.4). The velocity mapping from particles to nodes is performed using a formula that enforces momentum conservation:
\[\mathbf{v}_{t}=\frac{\sum_{p}^{N_{p}}\!\!m_{p}\mathbf{v}_{p}S_{lp}}{\sum_{p}^{N_{p}}\! \!m_{p}S_{lp}}, \tag{27}\]
where \(m_{p}\) is the material point mass
\[m_{p}=\rho_{p}H_{p}A_{p}\,. \tag{28}\]
Ice thickness is mapped to the grid from material points as
\[H_{t}=\frac{\sum_{p}^{N_{p}}\!\!H_{p}S_{lp}A_{p}}{\sum_{p}^{N_{p}}\!\!S_{lp}A_{ p}}, \tag{29}\]
where the denominator is necessary to normalize the interpolation. After each mapping, nodal values of velocity or thickness at Dirichlet boundaries are overwritten with the values specified by the essential boundary condition. Nodal surface elevations are calculated from the nodal ice thicknesses as
\[s_{t}=b_{t}+H_{t}\,, \tag{30}\]
where the nodal elevation of the ice base, \(b_{t}\), is computed as the maximum value of the bedrock elevation (\(z_{\text{{b}el}}\)) or the ice base elevation according to hydrostatic equilibrium as
\[b_{t}=\max\left\{\left(z_{\text{{b}el}}\right)_{t},z_{\text{{e}ea}}-H_{t} \left(\frac{\rho}{\rho_{w}}\right)\right\}, \tag{31}\]
and \(z_{\text{{e}ea}}=0\) is the sea level.
### SSA Initialization: Material Point Parameters
The second half of the SSA initialization procedure is focused on updating material point variables (Figure 0(b)). Surface height and velocity gradients are determined at any material point \(p\) by mapping from the nodes. The friction parameter \(\left(\hat{\rho}_{p}\right)\) bedrock elevation \(\left(z_{\text{{b}el},p}\right)\), and rate factor (\(B_{p}\)) must also be defined at the material point level, which may require mapping from the nodes as well. Any scalar grid property, \(h_{t}\), may be interpolated to the material points as
\[h_{p}=\frac{N_{p}}{l}hS_{lp}. \tag{32}\]
Similarly, for gradients, the mapping is
\[\
abla h_{p}=\frac{N_{p}}{l}h\
abla S_{lp}. \tag{33}\]
Lastly, material points are marked as grounded or floating. Defining grounding status at material points (or at Gauss points in the FEM) rather than at nodes during the SSA solution has been shown to provide a more accurate estimate of grounding line dynamics during the SSA solution ([PERSON] et al., 2014). However, to be consistent with Elmer/Ice conventions, we also define grounding status at the nodal level as part of the procedure to define the sub-element scale grounding line. If node \(l\) has \(b_{t}=\left(z_{\text{{b}el}}\right)_{t}\), it is marked as grounded; otherwise, it is floating. If a material point belongs to an element whose surrounding elements have a mix of grounded and floating nodes, then that it is clear that material point is near the grounding line, andits grounding status is determined using the same procedure used for the nodes. Otherwise, it inherits the grounding status of its surrounding nodes.
### SSA Solution
The SSA is solved implicitly using an \"iteration on viscosity\" scheme where we update material point viscosity, \(\vec{\eta}_{p}\), each iteration until convergence ([PERSON], 1989; Figure 0(c)). This is done by mapping the gradients of nodal velocity solution from the previous iteration to material points using Equation 33, which are converted to strain-rates to calculate \(\vec{\eta}_{p}\) using Equation 6. We achieve quick convergence of the SSA solution using the Biconjugate Gradient Stabilized (BiCGSTAB) method, Incomplete LU preconditioning, and a combination of Picard and Newton iterations.
### Material Point Updates
Upon completion of the SSA, grid velocities are used to update material point velocities, position, and geometric properties (Figure 0(d)).
_Velocities and position:_ To update velocity and position, material point methods typically adopt the approach of the FLIP method. For velocity, this update is given as
\[r_{p}^{m+1}=r_{p}^{m}+\Delta\sum_{I}^{N_{p}}\vec{a}_{I}^{n}S_{dp}=r_{p}^{m}+ \sum_{I}^{N_{p}}\left(\vec{v}_{I}^{m+1}-\vec{v}_{I}^{m}\right)S_{dp}, \tag{34}\]
where \(\vec{a}_{I}^{m}\) is the acceleration at time step \(m\) at node \(I\), and \(\vec{v}_{I}^{m}\) is the nodal velocity previously interpolated to the grid from the material points before the SSA solution in Equation 27. This material point position update is
\[x_{p}^{m+1}=x_{p}^{m}+\Delta\sum_{I}^{N_{p}}\vec{v}^{m+1}S_{dp}\,. \tag{35}\]
In practice, the FLIP update scheme can introduce noise that results from the mismatch between the number of material points and grid nodes, so our code also includes the update scheme \(\text{XPIC}\left(k\right)\), an algorithm that can remove FLIP noise using a set of \(k\) additional projections ([PERSON] & [PERSON], 2017). Lower orders of \(k\) may introduce undesired damping, while higher orders of \(k\) are computationally expensive. Note that the additional projections required for \(\text{XPIC}(k)\) can accumulate a small amount of error in conjunction with our boundary treatment at the ice front (Section 4.1), but this error can be avoided by always using FLIP updates within \(k\) elements of the ice front. While the simulations in this paper are relatively insensitive to the update scheme chosen, [PERSON] et al. (2017) demonstrated that \(\text{XPIC}(5)\) yields sharp and stable crack propagation in damage simulations.
_Geometric properties:_ All updates to material point geometric properties, which include area and the lengths defining the GIMPM domain, depend on the deformation gradient, a fundamental kinematic quantity that characterizes the deformation at a material point based on its current (deformed) and reference (undeformed) spatial coordinates. The material point deformation gradients (\(\vec{F}_{p}\)) are tracked over time, and are updated as
\[\vec{F}_{p}^{m+1}=\left(\vec{I}+\Delta\
abla\vec{r}_{p}^{m+1}\right)\vec{F}_{ p}^{m}\,. \tag{36}\]
where \(\vec{I}\) is the second-order identity tensor. In the sMPM, the determinant of \(\vec{F}_{p}\) is used to update the material point area as
\[A_{p}^{m+1}=\det\left(\vec{F}_{p}^{m+1}\right)A_{p}^{0}\,. \tag{37}\]
In the GIMPM, material point area is calculated as the product of the lengths defining the rectangular GIMPM domain.
Our implementation currently includes two schemes to update GIMPM domain lengths. The lengths should be updated carefully in order to minimize overlap or separation of GIMPM domains over time, and thus maintain partition of unity as precisely as possible throughout the domain. The first scheme updates the lengths of a GIMPM domain such that the resulting rectangular domain approximates the quadrilateral domain that would be obtained if the position of each corner of the GIMPM domain was updated individually ([PERSON] et al., 2020). In practice, this \"corner-tracking\" update scheme may be simplified to tracking the midpoints \(\hat{\mathbf{x}}_{p}\) of the GIMPM domain edges as
\[\hat{\mathbf{x}}_{p}=\hat{\mathbf{x}}_{p}^{m}+\Delta t\sum_{l}\hat{\mathbf{r}}_{p}^{m+1} \phi_{l}\left(\hat{\mathbf{x}}_{p}^{m}\right). \tag{38}\]
The GIMPM domain lengths can be obtained using the maximum and minimum extents of \(\hat{\mathbf{x}}_{p}\) as
\[\left(\hat{r}_{p}^{m+1}\right)_{i}=\frac{1}{2}\Big{[}\max\left(\hat{\mathbf{x}}_{p }\right)_{i}-\min\left(\hat{\mathbf{x}}_{p}\right)_{i}\Big{]}, \tag{39}\]
followed by a correction that guarantees proper volume (area in 2-D) as
\[\left(\hat{r}_{p}^{m+1}\right)_{i}=\left(\hat{r}_{p}^{m+1}\right)_{i}\Bigg{[} \frac{\det\left(F_{i}^{m+1}\right)\prod_{j=1}^{n_{D}}\left(\hat{r}_{p}^{0} \right)_{j}}{\prod_{j=1}^{n_{D}}\left(\hat{r}_{p}^{0}\right)_{j}}\Bigg{]}^{ \
icefrac{{1}{1}}{{n_{D}}}}. \tag{40}\]
where \(n_{D}\) is the dimension of the problem (\(n_{D}=2\) in our case). More detailed derivations of the above scheme can be found in [PERSON] et al. (2020). This corner-tracking scheme performs well in minimizing overlap or separation of GIMPM domains over time in any flow regime, but cannot be used at outflow boundaries where a GIMPM domain may only partially overlap the active background grid, assuming velocities beyond the active grid are unknown (see Section 4.1). For these material points, we instead use the second update scheme, given by
\[\left(\hat{r}_{p}^{m+1}\right)_{i}=\left(\hat{r}_{p}^{0}\right)_{i}U_{i}^{m+1 }\ \left(\text{no implied sum on }i\right), \tag{41}\]
where \(\left(\hat{r}_{p}^{0}\right)_{i}\) are the original domain lengths and \(U_{ij}=\sqrt{F_{i}^{\top}F_{ij}}\) is the symmetric material stretch tensor, which is equivalent to the deformation gradient rotated into the original Cartesian reference frame ([PERSON] et al., 2017). Although the \"stretch-tensor\" update scheme can be used instead of the \"corner-tracking\" scheme in the entire domain, we caution that it is less capable of minimizing overlap or separation of GIMPM domains under large shearing deformation. Because the \"stretch-tensor\" scheme is sufficiently accurate under stretching and rotation and is computationally more efficient than the \"corner-tracking\" scheme, the former scheme is suitable for simulations without large shearing deformations. Here, we only use the stretch-tensor scheme for the 1-D flow-band simulations, noting that the corner-tracking scheme gives identical results. In all the 2-D simulations, we employ the corner-tracking scheme.
### History Variable Updates
The computational cycle finishes by updating the history variables on the material points (Figure 0(e)). Here, we only consider ice thickness (\(H_{p}\)), which is updated explicitly according to the Lagrangian description of surface mass conservation for a column of ice at time step \(m+1\) as
\[H_{p}^{m+1}=H_{p}^{m}+\left(\hat{a}_{p}^{m}-\
abla\cdot\
u_{p}^{m}H_{p}^{m} \right)\Delta t\,, \tag{42}\]
where \(\hat{u}_{p}^{m}\) (m a-1) is the sum of the basal and surface accumulation rates. We add damage as a history variable in Part II ([PERSON] et al., 2021).
## 4 Boundary Treatment and Splitting
Boundary conditions in MPMs may be applied at the edges of the active computational grid as in the FEM. However, special treatment is required at inflow boundaries to properly introduce new material points to the domain, and at outflow boundaries where material points must be eliminated or GIMPM domains may partially overlap the boundary. Further treatment is also needed at the moving ice front boundary to avoid integration errors, as this boundary may not align with element edges. We detail our boundary treatment in this section. In addition, we detail our material point splitting scheme, which mitigates additional integration errors that may arise under tension, where the resolution of material points per grid cell decreases over time as the area of the material points grows.
### Boundary Treatment
_Inflow boundaries_: Since material points at inflow boundaries advect downstream, a scheme is needed to ensure that that they are replaced by inflow of new material points. For the simple simulations in this paper, we incorporate inflow boundaries by seeding additional material points on a domain that extends beyond the boundaries. Velocities on the extra domain and inflow boundary are set so that the additional material points flow smoothly into the primary domain at the velocity specified by the boundary condition. This scheme is illustrated in Figure 2a, where the material point GIMPM domains are dotted gray, the inflow boundary is indicated by the dotted red line, and elements belonging to the additional inflow domain are highlighted in blue. We note that a more efficient, but complicated, scheme may be implemented, where in the \"inflow elements\" refill with material points automatically as they become empty ([PERSON] et al., 2019).
_Outflow boundaries_: At outflow boundaries, material points exit the domain and are removed from the simulation. In the GIMPM, material points with GIMPM domains that overlap an outflow boundary will not receive a full interpolation during grid to material point mappings by default, assuming parameter values are unknown beyond the active portion of the background grid. In Figure 2b (left side), a material point GIMPM domain is shown overlapping an outflow boundary (red). For each active element that the GIMPM domain overlaps, our treatment is to temporarily introduce a sub-particle with a GIMPM domain matching the area of overlap between the original material point domain and the element (Figure 2b, right side). The sub-particles receive the interpolation, with the original material point then receiving the average of sub-particle values weighted by the area of their subdomains.
Figure 2: Material point method-Shallow Shelf Approximation (MPM-SSA) boundary treatment. (a) At inflow boundaries (dotted red), an additional domain (shaded blue) is specified upstream and seeded with extra material points (black dots). Each material point is associated with a generalized interpolation material point method (GIMPM) domain (dashed gray rectangles). Velocities are specified throughout the additional domain so that the extra material points advect into the primary domain at the correct velocity. (b) A material point with a GIMPM domain overlapping an outflow boundary (red) is split into sub-particles during grid-to-material point mappings. The sub-particles separately receive the interpolation, which is subsequently consolidated back to the original material point. (c) At the ice front, grid cells partially full with material points domains (yellow) are integrated using the finite element method (FEM), where the boundary condition is assigned at the element edges (dashed red) that mark the transition between active and inactive (gray-striped) grid cells.
### Material Point Splitting
The highly tensile regime of ice shelves tends to cause material points to elongate or grow over time. Material points can be split as necessary to maintain a desired resolution of material points per grid cell. For the GIMPM, we initiate splitting when the domain length \(l_{p}\) exceeds a given threshold. We implement a similar procedure for the sMPM, where a pseudo-domain length is tracked using the accumulated strain of a material point in Cartesian directions ([PERSON] et al., 2009). The splitting threshold cannot exceed the length of a grid cell, and can vary across the domain if, for example, greater material point resolution is desired near the grounding line. For splitting in direction \(i\), the two split material point coordinates, \(\sfrac{1}{2}\left(x_{p}\right)_{i}\) and \(\sfrac{2}{2}\left(x_{p}\right)_{i}\) are set to
\[\sfrac{1}{2}\left(x_{p}\right)_{i} =\left(x_{p}\right)_{i}+\frac{1}{4}\left(l_{p}\right)_{i}, \tag{43}\] \[\sfrac{2}{2}\left(x_{p}\right)_{i} =\left(x_{p}\right)_{i}-\frac{1}{4}\left(l_{p}\right)_{i}.\]
Each new material point is then assigned half the current \(\left(l_{p}^{m+1}\right)_{i}\) and initial \(\left(l_{p}^{\theta}\right)_{i}\) domain length corresponding to the splitting direction \(i\), from the parent material point being split. For a unidirectional split, the non-split current and initial domain lengths are inherited from the parent material point without modification. The deformation gradient and velocities of the parent material point are transferred directly to the new material points, but direct transfer of thickness may cause visible thickness oscillations in areas of steep thickness gradients. We propose to mitigate these oscillations by instead reassigning thickness to each split material point as
\[\sfrac{1}{2}\left(x_{p}\right)_{i}^{2}-\left(x_{p}\right)_{i}. \tag{44}\]
where the thickness gradient, \(\hat{v}H_{p}/\hat{c}x_{i}\), must be interpolated from the grid. Figure 3 gives the thicknesses for a subset of material points at the end of the steady state flow-band test described in Section 5 (GIMPM at 5 km grid resolution and 4 material points per cell), both with and without adjusting thickness according to Equation 44. By using Equation 44, the thickness oscillations from splitting are almost fully eliminated.
Figure 3: Thickness for a subset of material points at the end of the steady state flow-band test with and without adjusting thickness according to its gradient during splitting. This simulation used the generalized interpolation material point method (GIMPM) at 5 km grid resolution and 4 material points per cell.
## 5 Examples
In this section, we consider several examples using the GIMPM and sMPM for SSA simulations to validate and test the methods. We quantify error in modeled stress and front propagation versus analytical solutions in 1-D, and further demonstrate front propagation in 2-D. We then test the methods on an idealized marine ice sheet to show that they can maintain steady state grounding line positions over time and can advect passive scalar fields without artificial diffusion.
### Flow-Band Test Case: Steady State
We test our GIMPM-SSA framework against a flow-band model that gives the analytical steady state for a longitudinally unconfined ice shelf with a constant flux at the upstream inflow boundary. The flow-band model is formulated under the assumption of unidirectional flow, and is therefore inherently 1-D. In practice, we model the flow-band in 2-D, where the domain is one element wide, but unidirectional flow is still enforced (i.e., \(\left(v_{2}\right)_{p}=0\)). This experiment was previously used to verify a finite-difference front-tracking scheme ([PERSON] et al., 2011), and we use the same values for ice density (\(\rho=910\) kg m\({}^{-3}\)), seawater density (\(\rho_{w}=1028\) kg m\({}^{-3}\)), and the flow rate factor (\(B=1.9\times 10^{8}\) Pa s\({}^{1/2}\)). The flux at the upstream boundary is given as \(Q_{0}=v_{0}H_{0}\) where we take the velocity, \(v_{0}=300\) m a\({}^{-1}\) and the thickness, \(H_{0}=600\) m. The solution for the spreading rate is given as
\[\frac{\partial v_{1}}{\partial x_{1}}=\left(\frac{\rho g}{4B}\Big{[}1-\frac{ \rho}{\rho_{w}}\Big{]}H\right)^{3}=CH^{3}\,, \tag{45}\]
where all flow is along the \(x_{1}\)-axis ([PERSON], 1957). The analytical deviatoric stress can be calculated using Equations 5 and 6. The thickness and velocity profiles are obtained from conservation of mass and momentum are given by \(H\left(x_{1}\right)=\left(4C\ /\ Q_{w}x_{1}+1\ /\ H_{0}^{4}\right)^{1/4}\) and \(v_{1}\left(x_{1}\right)=Q_{0}\ /\ H\left(x_{1}\right)\), respectively ([PERSON], 2013).
We first test the ability of the GIMPM-SSA model to maintain the given steady state. We consider a domain that spans from the inflow boundary at \(x_{1}=0\) to a fixed ice front at \(x_{1}=250\) km. The steady-state thickness corresponding to this configuration is shown in Figure 4. The initial material point locations fully cover this domain, as well an additional domain beyond the inflow boundary that must be included to enforce the inflow boundary condition. The initial velocity, \(v_{0}\), and thickness, \(H_{0}\), is always enforced on all nodes of the inflow domain. The first element of the primary domain, immediately adjacent to the inflow domain, is also given special treatment. We always enforce the analytical velocity and thickness on all nodes of this element, and we set the material point ice thicknesses within this element to the analytical solution. This inflow thickness and velocity correction scheme alleviates any error in material point ice thicknesses that would otherwise occur from the jump in velocity gradient between the inflow and primary domains.
Note that the analytical solution does not include an ice front, as \(H\left(x_{1}\right)=0\), but including an ice front at any location on the domain will not change the steady-state upstream provided the ice front boundary conditions (Equation 8) are assigned. Setting the ice front at \(x_{1}=250\) km gives a realistic thickness at the ice front of \(\sim\)219 m. We test the sMPM and the GIMPM at varying material point resolutions, and with and without the reweighting given by Equation 26. We use a 2.5 km resolution grid. Each trial is initialized with the analytical solutions for thickness and velocity, and run forward for 300 years using one-month time steps. The threshold material point length at which splitting is initiated is set to 1.5 times the original length. The length after splitting is then 0.75 times the original length, which due to the purely tensile flow regime, therefore constitutes the lower bound on potential lengths that will develop throughout the simulation.
Figure 5 shows the deviatoric stress and velocities for the material point initially located closest to \(x_{1}=0\) km as it advects to its final location of \(\sim\)177 km over 300 years. Unless otherwise indicated, these figures are initialized with 9 material points per cell (\(3\times 3\) in 2-D). Figure 5a compares the result that does not use the reweighting scheme from Equation 26 with the analytical result. Stresses fluctuate widely due to uneven
Figure 4: Analytical steady state ice thickness for the flow-band test and the generalized interpolation material point method (GIMPM) solution at 300 years using a 2.5 km resolution grid and 9 material points per cell.
material point weighting between elements, which results in inaccurate velocities, positions, and thicknesses. Figure 5b gives the velocities from the sMPM when using 9 and 16 material points per cell and the reweighted sMPM when using 4 material points per cell. It is evident that increasing the material point resolution in the sMPM may slightly mitigate the weighting error, but it increases the computational expense and is not nearly as accurate as reweighted sMPM. The reweighted sMPM ensures a smoother transition of the stiffness matrix between elements, and even with just 4 material points per cell, yields results that almost exactly match the analytical solution. The severity of the error without the reweighting scheme is not common to all MPM simulations, and is likely due to the highly nonlocal stress regime of the SSA. As there appears to be very little tolerance for this type of error, the reweighting scheme from Equation 26 appears to be essential for accurate SSA simulations using the sMPM.
The stress response using the reweighted sMPM and the GIMPM are given in Figure 5c, and show significant improvement over the sMPM in Figure 5a. Note that the reweighting scheme has no effect when implemented with the GIMPM, as no gaps or overlaps of the GIMPM domains develop in the test case. The fit with the analytical solution is less accurate where \(x_{1}<\sim\)40 km, as ice shelf surface slopes are high and therefore finer mesh resolution is needed for improved accuracy. In general, the GIMPM is more accurate
Figure 5: Results from the steady state flow-band test for the material point initially located closest to 0 km, where 9 material points are initialized per 2.5 km grid cell. (a) Deviatoric stress using the unweighted standard material point method (sMPM). (b) Velocities corresponding to (a) compared to the velocities obtained using 16 material points per cell, as well as the velocities using the reweighted sMPM with only 4 material points per cell. (c) Deviatoric stress using the reweighted sMPM and the generalized interpolation material point method (GIMPM), which closely match the analytical result. (d) Detail of the boxed region in (c). The discontinuities for the reweighted sMPM are caused by the grid-crossing error, and are largely alleviated using the GIMPM.
than the reweighted sMPM, as the latter still does not alleviate cell crossing errors as fully. This is evident in Figure 5d, which shows the zoom of the region within the gray box from Figure 5c. The GIMPM alleviates, but still cannot entirely eliminate the sharp stress discontinuities or oscillations as the material crosses cell boundaries.
We further investigate the performance of our methods by conducting a mesh convergence study. We run the steady-state flow-band model again using the GIMPM, sMPM, and reweighted sMPM, but now we test each method using four different grid resolutions: 5, 2.5, 1.25, and 0.625 km. We use a time step increment of 5 days and run each simulation for 150 years. For consistency between all grid resolutions, we also extend the inflow thickness and velocity correction scheme, applied previously to the first element of the primary domain, to include all elements in the primary domain with a downstream nodal coordinate of \(\left(x_{t_{1}}\right)\leq 5\) km. For each grid and method, three material point resolutions are tested: 4, 9, and 16 material points per cell. Each time step, we compute the normalized errors ([PERSON] et al., 2020)
\[e_{\sigma_{11}^{\text{D}}}=\frac{\left[\sum_{m=1}^{m}\sum_{p=1}^{N_{p}}A_{p}^ {n}\right]\left[\sigma_{11}^{\text{D}}\left(x_{p}^{m}\right)^{a}-\sigma_{11}^ {\text{D}}\left(x_{p}^{m}\right)^{a}\right]^{2}}{\sum_{m=1}^{m}\sum_{p=1}^{N_{ p}}\sum_{p=1}^{N_{p}}\left[\sigma_{11}^{\text{D}}\left(x_{p}^{m}\right)^{a} \right]^{2}},\]
\[e_{\sigma_{11}}=\sqrt{\frac{\sum_{m=1}^{m}\sum_{p=1}^{N_{p}}A_{p}^{n}\left[v_{ 1}\left(x_{p}^{m}\right)^{a}-v_{1}\left(x_{p}^{m}\right)^{a}\right]^{2}}{\sum_ {m=1}^{m}\sum_{p=1}^{N_{p}}A_{p}^{n}\left[v_{1}\left(x_{p}^{m}\right)^{a} \right]^{2}}} \tag{46}\]
for horizontal deviatoric stress and velocity, respectively. In these equations, superscripts \(n\) and \(a\) indicate the numerical and analytical values, respectively, \(m_{j}\) is the total number of time steps, and \(N_{p}\) is the number of material points with \(\left(x_{p}\right)_{j}\geq 5\) km. Figure 6 gives the error for the steady state flow-band test for all combinations of methods, material point resolutions, and grid resolutions. The corresponding convergence rates averaged over all material point resolutions are given in Tables 1 and 2 for deviatoric stress and velocity, respectively.
In Figure 6, only unweighted sMPM shows a significant decrease in error for both velocity and deviatoric stress when the number of material points are increased, because this alleviates grid-crossing and improves the accuracy of integration to a limited extent. For reweighted sMPM and GIMPM, grid resolution has a much larger influence on accuracy than the number of material point used to integrate each grid cell, although both methods do show a slight decrease in velocity error as the number of material points is increased. For reweighted sMPM, there is also a slight decrease in deviatoric stress error with increased material point resolution, whereas the opposite trend is observed for the GIMPM for deviatoric stress error, due to greater smoothing of the stress discontinuity between grid cells ([PERSON] and [PERSON], 2004).
### Flow-Band Test Case: Front Propagation
We also use the flow-band model to test the ability of our scheme to track the calving front. The analytical position of the ice front, \(x_{c}\), at time \(t\) can be found from the relation \(Q_{d}=\int_{0}^{x_{c}}H\left(x^{\prime}\right)dx^{\prime}\)([PERSON] et al., 2011), and is given by
\[x_{c}\left(t\right)=\frac{Q_{0}}{4C}\Bigg{[}3 Ct+\frac{1}{H_{0}^{3}}\Bigg{]}^{ \frac{4}{3}}-\frac{1}{H_{0}^{4}}\Bigg{]}. \tag{47}\]
For all grid and material point resolutions from the mesh convergence exercise, and using the GIMPM and reweighted sMPM, we track the ice front over 300 years using one month time steps, where the initial position of the ice front is set to \(x_{1}=0\,\mathrm{km}\). The modeled front position over time using the GIMPM with a 2.5 km grid and 9 material points per grid cell is shown in Figure 7 versus the analytical solution. This nearly perfect fit is reflected for all grid and material point resolutions tested, for both the GIMPM and reweighted sMPM. After 300 years of front propagation, none of the simulations deviate from the analytical front position of \(x_{1}\approx 177\,\mathrm{km}\) by more than 300 m (\(\sim\)0.17% error). Thus, this study demonstrates that the GIMPM can accurately simulate the stresses, geometry, and ice front position of an evolving ice shelf.
### Front Advection in 2-D
To test our front propagation scheme in 2-D, we simulate the radial spread of an unconstrained floating ice tongue. This benchmark example was considered under steady-state conditions in previous studies (e.g., [PERSON] and [PERSON], 1987; [PERSON] and [PERSON], 2012, 2013; [PERSON] et al., 2020). Our aim here is to achieve only qualitatively consistent results, because there is no analytical solution for 2-D diverging ice flow. The setup of this the simulation follows Example 1 in [PERSON] et al. (2020). The grid is shown in Figure 8a, and is comprised of non-uniform, linear, quadrilateral elements with straight edges. We use the reweighted sMPM,
\begin{table}
\begin{tabular}{l c c c} Cell size (km) & sMPM & Reweighted sMPM & GIMPM \\ \hline
2.5 km & 0.11 & 1.77 & 2.45 \\
1.25 km & 0.03 & 1.58 & 2.05 \\
0.625 km & 0.01 & 1.61 & 2.25 \\ Overall & 0.05 & 1.65 & 2.23 \\ \hline \end{tabular} Abbreviations: GIMPM, generalized interpolation material point method; sMPM, standard material point method.
\end{table}
Table 2: Velocity Convergence Rates at Each Cell Size, and Over all Cell Sizes
Figure 7: Ice front position using the generalized interpolation material point method (GIMPM) plotted against the analytical solution using 9 material points per 2.5 km grid cell. This nearly perfect fit is reflected for all grid and material point resolutions tested, for both the GIMPM and reweighted standard material point method (sMPM).
because the grid elements are not perfect rectilinear elements owing to the ice shelf geometry; whereas, the GIMPM using the hat function \(\chi_{p}\) for the particle characteristic function requires the use of perfect rectilinear elements. However, the reweighted sMPM can be classified as a special case of the GIMPM that uses the Dirac delta function instead of the hat function for the particle characteristic function. The upstream boundary (red) corresponds to an arc extracted from a circle with 70 km radius with a central angle of 10\({}^{\circ}\). Flow is axisymmetric with respect to the vertical axis defined at the center of the circle, and we set free slip conditions at the lateral boundaries by enforcing that the normal component of velocity is zero. At the upstream boundary, a constant thickness of 400 m and an inflow velocity of 500 m a\({}^{-1}\) is enforced. We evenly initialize 9 material points per cell on an inflow domain beyond the upstream boundary (not shown), and allow the system to evolve until the ice front reaches the downstream edge of the computational grid, which occurs after 86.6 years.
The corresponding final thicknesses and positions of all material points are plotted in Figure 8b. The thicknesses of all material points at any radial distance match very closely regardless of their azimuthal position, reflecting that the simulation has achieved the expected axisymmetric flow regime. Also plotted is the steady-state thickness profile as calculated using the FEM under the assumption that the calving front is fixed at the downstream edge. While it is encouraging that the two thickness profiles show similar trends, we emphasize that unlike in the 1-D case, we do not expect a simulation with a moving ice front to replicate the steady state flow exactly. Some mismatch is expected because an unconstrained ice tongue experiences buttressing that increases proportionately with ice tongue length ([PERSON] et al., 2020). This buttressing is related to \"hoop\" stresses that must be overcome for flow to diverge laterally. In Figure 8b, the material points toward the ice front are relatively thin compared to the steady state because they endured larger rates of spreading earlier in the simulation when the ice tongue was short and buttressing was lesser. This example demonstrates that material point methods can be used for 2-D ice front tracking in a physically consistent manner.
### Marine Ice Sheet Model Intercomparison Project (MISIMP+)
Our final experiment tests the ability of our model to maintain the steady state from the idealized, but more realistic, geometry detailed in the marine ice sheet model intercomparison project (MISIMP+; [PERSON] et al., 2016). This geometry is a 640 km \(\times\) 80 km marine ice sheet, spanning an ice divide at \(x_{\mathrm{i}}=0\) km to a calving front at 640 km. At steady state, the grounding line is centered at \(x_{\mathrm{i}}\sim 450\) km and \(x_{\mathrm{2}}=40\) km. At the lateral boundaries, \(v_{\mathrm{2}}=0\). The steady state grounding configuration where \(x_{\mathrm{i}}>350\) km is shown in Figure 9a. The grounding line lies on a retrograde slope, and is therefore very sensitive to perturbations or error, so that the configuration is ideal for testing the accuracy of the GIMPM. Furthermore, this is a
Figure 8: (a) Background grid used to simulate the unconstrained 2-D spreading of an ice tongue from an upstream boundary (red) with a 70 km radius of curvature. (b) The ice thicknesses of all material points after growing the ice tongue from the upstream boundary for 86.6 years, and the steady-state thickness profile calculated from the finite element method (FEM) using the same ice front position. Material point thicknesses are slightly lesser toward the ice front due to the increased rate of spreading these material points experienced earlier in the simulation, when the ice tongue was shorter and buttressing was lesser.
very high shear regime, which is often problematic for the MPMs. Therefore, we update GIMPM domains with the corner-tracking scheme from Equations 38-40.
For all MISMIP + simulations, we use a grid resolution of 0.5 km and time step size of one month. We initially determine the steady state using the FEM according to the recommended values for the friction parameter, the viscosity parameter, the rate factor, densities, and surface accumulation given for the MISMIP+. Afterward, we continue the simulation using both the GIMPM and the reweighted sMPM. We initialize these simulations with 9 material points per cell. After 100 years, both the GIMPM (Figure 9b) and the reweighted sMPM (Figure 9c) are able to maintain the sensitive initial grounding line position (Figure 9a). The reweighted sMPM grounding line region, however, is slightly noisier than GIMPM. This noise is especially evident in a close-up view of the image in Figure 9c (zoom not shown).
During the simulation, we also advect a passive scalar field to demonstrate how when using the GIMPM, this field can be advected without artificial diffusion. This field is initially assigned a value of unity along a series of across-flow strips and a value of zero elsewhere (Figure 10a). Each strip is separated by 50 km in the \(x_{\text{i}}\)-direction. Though the scalar is passive and does not affect flow, we loosely associate the scalar field with damage. We therefore chose the width of the strips to be 0.5 km to roughly correspond to the width of an ice shelf rift, which can range from zero to several kilometers wide. The field was initially assigned on the grid, and interpolated to the material points before the simulation. For comparison, we ran the same simulation using a Discontinuous Galerkin (DG) method ([PERSON] et al., 2004), the least-diffusive Eulerian advection method already available in Elmer/ Ice. During the DG advection solution, we limit the value of the scalar to be non-negative and no greater than 1, because we associate the scalar field with damage. This constraint is automatically satisfied with the GIMPM because the value of the scalar for a material point is never changed over time. However, in the DG
Figure 10.— Marine ice sheet model intercomparison project (MISIMP+) advection of a passive scalar. Results shown for same area as Figure 9 around the grounding line for the generalized interpolation material point method (GIMPM) versus Discontinuous Galerkin (DG). The initial state is given in (a). The field at 5 years is shown for (b) the GIMPM and (d) DG. The field at 100 years is shown for (c) the GIMPM and (e) DG.
Figure 9.— (a) Grounding line at 0 years after initiating the generalized interpolation material point method (GIMPM)/standard material point method (sMPM), where blue material points are grounded and red are floating. The configuration after 100 years is shown for (b) the GIMPM and (c) the reweighted sMPM.
method, these constraints must be enforced on the domain in Elmer using a scheme where they are applied and released iteratively according to a criterion based on residuals ([PERSON] et al., 2013). Whether or not we bound the scalar values using the constraint scheme, we notice that the same broad patterns of artificial diffusion are obtained with the DG method.
The advected profiles of the scalar field obtained from the GIMPM are shown in Figure 10b after 5 years and Figure 10c after 100 years. The scalar field does not experience artificial diffusion, and takes an arcuate shape over time that reflects the high shear experienced from the lateral grounded margins. The results from the DG method are shown in Figure 10d after 5 years and in Figure 10e after 100 years. Although the DG method produces a similar arcuate profile for the scalar field as the GIMPM, the value of the scalar field is diminished due to numerical diffusion over time. With the DG method, the furthest downstream, non-zero values of the scalar near the centerline of the \(y\)-domain (\(y=40\) km) quickly diminish from 1.0 to \(\sim\)0.8 over 5 years. By 100 years, the diffusion increases in severity, and these furthest-downstream, non-zero values diminish to \(\sim\)0.5. Consistently, the results from the DG method show the spatial spread of the damage region to be about twice that observed from the GIMPM results (Figure 10c). Thus, this simulation study illustrates the superior performance of the GIMPM, based on a hybrid Lagrangian-Eulerian framework, in alleviating numerical diffusion issues persistent with the DG method in a purely Eulerian framework.
Figure 11 shows the maximum principal deviatoric stress, \(\sigma_{\rm max}^{\rm D}\), for the MISMIP + test obtained using the GIMPM and the reweighted sMPM after \(t=100\) years. The initial \(\sigma_{\rm max}^{\rm D}\) is given in Figure 11a, where the largest stresses are concentrated near the lateral grounding line. The GIMPM field after 50 years (Figure 11b) is almost identical to the initial field. The reweighted sMPM field at 50 years (Figure 11d) while mostly identical to the initial field, however, is characterized by oscillations due to grid-crossing error, which also cause the noise in the grounding line configuration in Figure 9c. By 100 years, both the GIMPM (Figure 11c) and the reweighted sMPM (Figure 11e) stress fields develop some artifacts in the stress field near the grounding line, as material points tend to become poorly distributed under extreme shear (Figure 12). This type of error is a limitation of our current GIMPM implementation; we discuss potential approaches to alleviate it in Section 6.
Figure 11: Marine ice sheet model intercomparison project (MISMIP+): Maximum principal deviatoric stresses (MPa) for the (a) initial state, (b) generalized interpolation material point method (GIMPM) at 50 years, (c) GIMPM at 100 years, (d) reweighted standard material point method (sMPM) at 50 years, (e) reweighted sMPM at 100 years. The arrow in (c) indicates where continual heavy shear eventually causes poorly distributed material points, as shown in detail in Figure 12.
## 6 Discussion
Our current GIMPM or reweighted sMPM formulations should be sufficiently accurate for many applications in which it is essential to accurately track the ice front or history variables, such as damage ([PERSON] et al., 2021). However, additional developments are needed to mitigate the artifacts introduced due to intense distortion of material point domains in high shear regimes over long timescales (Section 5.4). One approach is to reinitialize the material points periodically, which in the simplest case would involve interpolating all material point properties to a new set of material points. Although this approach risks some artificial diffusion, it may be negligible if reinitialization is infrequent. However, more sophisticated schemes are also available that reinitialize material points locally as needed, while minimizing artificial diffusion (e.g., [PERSON] et al., 2015).
Further development of our method will likely include implementing more robust shape functions. For example, Convected Particle Domain Interpolation (CPDI) methods assemble shape functions according to the shapes of the material point domains, and alleviate cell-crossing error. Unlike the GIMPM, CPDI methods are not restricted to tracking rectangular domains, and instead may track parallelograms (CPDI1; [PERSON] et al., 2011) or the corners of the domains individually (CPDI2; [PERSON] et al., 2013). The CDPI1 method has been shown to perform especially well under intense shearing ([PERSON] et al., 2019), and may be appropriate for avoiding the errors related to high-shear observed in our GIMPM simulations over long timescales. However, we note that our current GIMPM formulation is computationally less expensive and easier to implement into existing finite element codes. Implementing CPDI methods will require substantial modifications to our current discretization scheme and boundary treatment.
As an alternative to using material point domain-tracking shape functions, it may also be advantageous to consider techniques that eliminate cell-crossing error through other means, such as the dual domain material point (DBMP) method ([PERSON] et al., 2011) or the use of spline-based shape functions (e.g., [PERSON] et al., 2013). All of these techniques, including CPDI, share an additional advantage over the GIMPM in that they may be employed using non-uniform meshes of varying element types, such as triangular meshes commonly used in major ice flow codes (e.g., ISSM and Elmer/Ice). Analyzing the error, convergence qualities, and speed of these methods in the context of ice shelf flow and fracture will constitute future research.
Although not illustrated in this paper, an additional advantage of our GIMPM-SSA model is that complex 3-D multiphysics can be represented while still being efficient enough to couple with Earth system models. Because horizontal velocities are vertically invariant within the SSA framework, 3-D processes can be approximated locally with each material point using a series of vertical layers, and subsequently vertically integrated if needed for implementation into the next SSA solution. While the same can be applied to mesh-based Eulerian methods, the associated advection schemes are not only dissipative, but involve solving a matrix equation for each 3-D field that scales in computational expense with the number of layers used. However, as for 2-D fields, horizontal advection of 3-D fields using the MPM-SSA framework avoids artificial diffusion and only requires explicitly updating 2-D material point locations, rather than solving a matrix equation as in Eulerian schemes. We employ this 3-D approach to model orthotropic damage evolution in ice shelves in Part II ([PERSON] et al., 2021). Given the simplicity and efficiency of 3-D advection in the MPM-SSA framework, it may prove useful even for modeling coupled processes that do not necessarily demand error-free advection as well, such as temperature evolution, firn compaction, fabric anisotropy, and marine ice formation. We also note that a full 3-D implementation of material point methods for full-Stokes models is also possible for studying individual glaciers, but it would be prohibitively expensive for continental-scale ice sheets.
Figure 12: Marine ice sheet model intercomparison project (MISMIP+): Poorly distributed material points develop in the generalized interpolation material point method (GIMPM) simulation after 100 years of heavy shear, where indicated by the arrow in Figure 11c. Underlying grid resolution is 0.5 km.
## 7 Conclusion
We presented the generalized interpolation material point method for shallow shelf ice flow, and verified that this formulation can reproduce and maintain analytical solutions for steady state ice flow and ice front advection. The advantages of this formulation include:
1. Error-free Lagrangian advection or transport without numerical diffusion or dispersion
2. Computationally inexpensive, explicit time updates that do not require solving a matrix equation for ice thickness and history variables, such as damage. History variables may be tracked in 3-D on a series of vertical layers associated with each material point. Horizontal advection of 3-D fields is naturally accounted for during the 2-D material point position update, because horizontal velocities are vertically invariant.
3. Natural tracking of the ice front and grounding line at sub-element scale
4. Accurate schemes for boundary treatment and redistribution of thickness during particle splitting that facilitate simulations over long timescales.
5. A framework consistent with the well-established conventions of the finite element method for shallow shelf ice flow
By choosing the particle characteristic functions to be either the Dirac delta or the \"hat\" functions, the present formulation can reproduce the existing implementations of sMPM and the GIMPM. We demonstrated that the sMPM shape functions are very sensitive to cell-crossing errors and uneven distributions of material points, likely due to the quasi-static and highly nonlocal stress regime of the SSA. By simply modifying the shape functions with a reweighting scheme in the sMPM, we can significantly decrease this sensitivity to cell-crossing errors. This numerical error is almost entirely alleviated using the GIMPM without the reweighting scheme, so it is more appropriate for many applications on timescales of decades to centuries. However, a major advantage of the reweighted sMPM over the GIMPM is that it is applicable with adaptive and non-uniform quadrilateral and triangular mesh discretization, which is ideal for accurately resolving grounding line dynamics. Future work is necessary to mitigate errors in the GIMPM associated with the intense distortion and gaps in the material point distribution observed in high shear regimes over long timescales. Potential solutions for this error involve developing material point reinitialization schemes, improving GIMPM domain updating schemes, and/or implementing different shape functions. In addition, future developments should focus on implementing additional physics to fully take advantage of the GIMPM-SSA treatment of history variables; this could be particularly beneficial when parameterizing complex 3-D processes using a series of vertical layers assigned to each material point. Thus, the GIMPM-SSA model can potentially develop into a powerful tool for studying large-scale, coupled ice sheet processes simultaneously, thus enabling the accurate prediction of ice sheet response to climate change and eventually global sea level rise.
## Data Availability Statement
The simulations in this paper can be reproduced using the experimental setups and model source code available at [[https://doi.org/10.5281/zenodo.4657848](https://doi.org/10.5281/zenodo.4657848)]([https://doi.org/10.5281/zenodo.4657848](https://doi.org/10.5281/zenodo.4657848)).
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wiley/ff2d6c61_d78e_46ea_bf2c_b49c86dc40dc.md | ## 2 Stakeholder Workshops for Research Planning
In a series of six research planning workshops, HEI Energy convened stakeholders representing various sectors (academia, consulting companies and law firms, foundations, government agencies [federal, state, and local], nongovernment organizations [including those connected to communities affected by UOGD], and the oil and natural gas industry) to ensure that HEI Energy funded research that is credible and widely useful for their decision-making. The workshops provided an opportunity for stakeholders to come together and share their perspectives on the UOGD exposure and health literature, important knowledge gaps, corresponding research priorities about potential community exposures and health effects associated with UOGD, and criteria that HEI Energy should use to prioritize and fund research.
### Participants
HEI Energy's stakeholder mapping involved several methods to identify stakeholder groups that would benefit from and contribute to the research program, as well as to define methods of engagement. Stakeholder groups can have both overlapping and competing priorities; therefore, HEI Energy encouraged balanced stakeholder group participation by directly contacting members of each stakeholder group and, for some community-based non-governmental organizations (NGOs) that could not otherwise be represented, covered expenses to allow for their participation in workshops (see Table S1 in Supporting Information S1 for list of workshop participants and Table S2 in Supporting Information S1 for participant distribution among stakeholder groups).
Figure 1: Stakeholder engagement process for research planning and implementation in the context of Health Effects Institute Energy’s broader model for providing impartial, policy-relevant science.
### Format
Each workshop included presentations on topics relevant to HEI Energy's scope of research, coupled with facilitated open discussion and breakout group exercises centered around a set of charge questions (Table S3 in Supporting Information S1). Two of the workshops included poster sessions where stakeholders could discuss ongoing and past research directly with the investigators.
The presentations provided technical context for each workshop, while the group exercises fostered an environment where individuals from stakeholder groups that do not typically interact (e.g., industry representatives and community-based NGOs) could come together and discuss their concerns and research. HEI Energy developed breakout group assignments ahead of each workshop to ensure a representative cross-section of stakeholder groups. Committee members and HEI Energy staff were assigned to each group to facilitate discussion.
A single representative from each group, selected by the group, reported on highlights from their group's discussion to all workshop participants. The report-back process elucidated shared priorities and highlighted where priorities diverged. The small group format allowed individuals who may feel uncomfortable speaking in large groups a more intimate setting for sharing their ideas. Participants (and anyone unable to attend the workshop) were also encouraged to share their perspectives on the charge questions in writing, providing a mechanism to share recommendations anonymously.
### Major Insights
Stakeholders provided important insights that shaped the Committee's approach to assessing UOGD scientific literature and to selecting HEI Energy's inaugural program of research. The major insights identified in the workshops and literature reviews are found in Table 1.
#### 2.3.1 Reviewing the Literature
The Committee reviewed the literature to assess the state-of-the science about potential community exposures and health effects associated with UOGD (HEI-Energy Research Committee, 2019a, 2019b). The workshops
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline Criterion & Description \\ \hline Brings value to and informs decision-making & Is useful to communities in study areas, government officials, industry, and other stakeholders. Ideal study designs will be informed by successful engagement with the communities in study areas and other stakeholders \\ Broadly generalizable & Designed to be broadly generalizable across geographic regions, UOGD operating conditions, or communities over time, including periods of low and high UOGD activity, without sacrificing validity \\ Determines whether an exposure pathway links a UOGD process with a community & Links one or more chemical or non-chemical agents directly released to the environment from a UOGD process to a potentially exposed community. The research allows for the detection of possible causal links between one or more UOGD processes (e.g., specific equipment, activity, or phase of development) and resulting human exposures. The study is designed to distinguish between agents released from UOGD and non-UOGD sources \\ Provides understanding of temporal and spatial variability of exposure & Selected study locations and designs will substantially fill important gaps in understanding of variability in exposure conditions over temporal and spatial scales relevant for decision-making by communities, regulators, industry, and other stakeholders \\ Optimizes use of the research budget by maximizing efficiency & Ensenses that the research budget is spent on gathering data and information that is not already available (e.g., by incorporating or complementing existing data and information) and that prioritization and sequencing of data collection maintains a focus on exposures of possible concern \\ Useful for assessing health risk & Collects data or analyzes existing data (or establishes practical exposure assessment methodologies) that is useful for assessing the potential for human health effects at resolutions relevant for application in an epidemiology study or risk assessment \\ \hline \hline \end{tabular}
\end{table}
Table 1: Criteria for Exposure Study Design and Implementation Identified by Health Effects Institute Energy Research Committee (in Alphabetical Order)shaped the objectives of the Committee's reviews of the epidemiology and exposure literature, ensuring that they were relevant and useful to various sectors. They also shaped the criteria that the Committee used to evaluate study quality and utility for assessing potential links between UOGD and community exposure and health. For example, workshop participants noted that much of the literature was not designed to identify complete exposure pathway(s), should one exist, between UOGD process(es) and a community(ies); the literature lacked statistical source apportionment, tracer release experiments, or other methods for understanding any connections between specific UOGD processes and community exposures. They also noted the lack of epidemiology studies quantifying exposure to specific chemicals or other possible health stressors. The Committee included these points as evaluative criteria in its reviews of the exposure and health literature.
To make the literature reviews accessible to various audiences, HEI Energy, and the Committee developed a video describing the epidemiology literature review and a fact sheet describing the content and potential applications of the epidemiology and exposure literature reviews.
#### 2.3.2 Selecting Research for Funding
Participants agreed that UOGD exposure and health research should consider industry trends and other factors that affect the magnitude and temporal and spatial variability of UOGD chemical releases; distinguish potential UOGD exposures from other sources of exposure including conventional OGD; design studies so that results are broadly applicable across major oil- and natural gas-producing regions of the United States, and, where feasible, use existing data instead of funding collection of new data. They sought research that provides a scientific basis for decision-making (e.g., setback distances separating UOGD from residences, schools, and other sensitive land uses) and expressed an urgent need for research involving multisector partnerships that can bring about actionable results to protect public health. The stakeholders also noted the importance of including community perception of risk as a valid consideration in identifying research priorities. At the same time, some expressed frustration with continued research and sought immediate action to limit exposures.
#### 2.3.3 Continuing Engagement With Stakeholders
At the workshops, stakeholders made clear that they wanted to stay involved with HEI Energy's research planning and the research itself such as frequent updates on research planning and progress, mechanisms to provide feedback on the research, and practical tools for them to put the research to use.
## 3 HEI Energy's Research Solicitation
The Committee alone is responsible for defining the direction of HEI Energy's research program. It considered all input received at the workshops and findings from its review of the literature to develop HEI Energy's solicitation for research in the form of two Requests for Applications (RFAs).
The Committee noted knowledge gaps about community exposures across oil and gas regions and, from its review of the epidemiology literature, the need for detailed exposure measures. Representatives of all stakeholder groups requested research that not only quantified exposure but identified its specific source so that action could be taken to protect health. For these reasons and others specified in the RFAs, the Committee prioritized funding for research on exposures related to UOGD impacts on air quality, water quality, and noise levels. The Committee apportioned more funding to air quality and noise research because air emissions and noise routinely occur as part of UOGD operations while water releases usually arise under accidental conditions that can be more challenging to study.
The RFA was based on major themes identified in the workshops and literature reviews (Table 1). While the Committee viewed all themes as important, they concluded that research selected for funding must be designed to quantify any links between specific UOGD processes and community exposures, maximize the applicability of results to different regions and conditions, and inform future health studies or risk assessments.
In 2021, HEI Energy awarded $5 million in funding to five research teams who are conducting research to understand the specific UOGD processes that might lead to community exposures through air and water.
## 4 Stakeholder Engagement During Research Implementation
### Guiding Principles for Stakeholder Engagement
In response to stakeholder recommendations for effective ongoing engagement, HEI Energy developed \"Guiding Principles for Research and Stakeholder Engagement\" (\"Guiding Principles\") to foster constructive engagement with stakeholders throughout implementation of HEI Energy-funded research.
Community members may face challenges that take precedence over their participation in workshops and other events. For this reason, the Guiding Principles recommends specific practices to promote equity and access for community members. With the Guiding Principles, investigators are well positioned to:
1. Keep stakeholders abreast of research plans and developments. The Guiding Principles includes a \"Stakeholder Engagement Roadmap,\" which details a set of practical steps to engage people living in communities where research is occurring, including members of traditionally underrepresented populations and environmental justice communities as defined in the Guiding Principles.
2. Hear and address any stakeholder concerns or questions.
3. Integrate stakeholder and community input into the research plans where appropriate.
### Research Team Stakeholder Engagement Plans
Workshop participants expressed a need for research translation and stakeholder involvement throughout this research. Toward this end, the RFA required successful research projects to include stakeholder engagement plans that foster \"effective multi-directional communication with communities living in the areas proposed for study as well as other stakeholders that have an interest in the proposed research.\" Successful research teams developed stakeholder engagement plans that feature:
1. Communication strategies to optimize constructive stakeholder engagement and to foster relationships among the research team, community members, industry representatives, government officials, and other local stakeholders;
2. Approaches ensuring that research translation and communication of study designs and results occur through culturally appropriate means;
3. Plans for effective engagement at key intervals during the research program; and
4. Expected outcomes from implementation of the Stakeholder Engagement Plan.
### HEI Energy and Research Team Collaboration on Stakeholder Engagement
The Committee recognized the importance of not only ensuring that research is of the highest quality, but also engaging with stakeholders across regions consistently and equitably. For this reason, the Committee recommended that HEI Energy partner with the research teams to confirm that individual research teams follow their proposed plans, coordinate engagement across research teams and study locations to ensure equity and consistency, participate in research team-led stakeholder engagement events, and work with investigators to ensure that interim and final findings are communicated clearly and consistently for a general audience. Early HEI Energy support has included organizing a peer learning session, hosting initial Open Houses in study locations, and developing a centralized research webpage on its website. In addition, HEI Energy is facilitating engagement by connecting research teams with their own network of stakeholders and providing a centralized mechanism for stakeholders to learn about the funded research.
#### 4.3.1 Peer Learning Session
HEI Energy and the Consensus Building Institute (CBI), a consulting company that specializes in facilitating stakeholder engagement, hosted a peer learning session. The session was facilitated by CBI and provided an opportunity for the research teams to learn from each other based on their variable levels of experience with community-engaged research. The session helped HEI Energy and the research teams to optimize and coordinate stakeholder engagement plans and identify potential challenges and approaches to address them.
#### 4.3.2 Open Houses
HEI Energy hosted initial in-person and virtual Open Houses in study locations in May and June 2022. The Open Houses provided an opportunity for research teams, community members, and other stakeholders to discuss theresearch and its objectives, ask questions and express concerns, and to open and encourage lines of communication throughout the research study. In accordance with the Guiding Principles, HEI Energy and its investigators employed several strategies to lower barriers to participation, including translation of educational materials into Spanish (based on knowledge of predominant languages spoken in the study location), an on-site interpreter, coverage of childcare expenses, a handicap accessible venue, free parking and, where available, public transportation. HEI Energy promoted the Open Houses through local news outlets, radio programs, email blasts, and personalized phone calls and emails. Both in-person and virtual Open Houses were attended by community members, NGOs with related work, local and regional policymakers and regulators, industry operating in the study area, and academics. The research teams' Principal Investigators continue to engage the local community through in-person and virtual presentations and meetings.
#### 4.3.3 HEI Energy Website
HEI Energy has developed a centralized website for stakeholders to learn about the research, upcoming and past events, and research progress. It includes fact sheets, live-streaming, slides from past events, links to future events, and quarterly research updates written for a general audience.
#### 4.3.4 Webinars
HEI Energy hosts educational webinars on emerging topics related to UOGD exposure and health to keep its funded investigators and other stakeholders apprized of research developments, opportunities for research synergy, and methods for successful stakeholder engagement (e.g., managing research fatigue among community participants).
## 5 Conclusions
Funding organizations play a key role in advancing, incentivizing, and providing mechanisms to promote community-engaged, actionable research. Here we describe HEI Energy's research planning and implementation process centered around multisectoral stakeholder engagement, with the goal of producing research that is likely to be used to inform key decisions. Having followed the process, the Committee could be confident that its research funding recommendations addressed both important knowledge gaps in the literature and the priorities of multisector stakeholders, including communities living in study locations.
The stakeholder workshops fostered open and collegial discussion among people representing all sectors and illuminated the priorities on which they agree. The process helped strengthen existing relationships and forged new ones, allowing for continued engagement during research implementation. The process also led to the production of HEI Energy's \"Guiding Principles for Research and Stakeholder Engagement,\" and its roadmap for building trust and facilitating constructive uptake of research data and results.
At the same time, HEI Energy and the Committee confronted several challenges. As highlighted in previous literature ([PERSON] et al., 2020), the process requires substantial effort from those planning the research and from stakeholders. In the context of community Open Houses in specific study locations, building connections with community members and organizations was more challenging than with government officials, NGOs, and other local stakeholders. Going forward, we will strive to meet these populations where they are, both literally and figuratively, share resources that may be useful to them (e.g., webinar invitations and fact sheets), develop an understanding of their priorities, needs, and time constraints, and take this knowledge into account before asking them to participate in research-related activities. We will continue to provide opportunities for learning and stakeholder engagement and measure progress to improve the utility of HEI Energy's work. We hope that the process and lessons described here provide building blocks for other funding organizations and investigators to involve stakeholders in research planning and implementation and enhance the utility and acceptance of their research.
## Conflict of Interest
The authors of this manuscript are solely employed by HEI Energy, which is supported with joint funding from the U. S. Environmental Protection Agency, ConocoPhillips, ExxonMobil, Halliburton Energy Services, Inc., and the Hillman Foundation. All research funded by HEI Energy is selected, overseen, and reviewed independently of HEI Energy's sponsors.
## Data Availability Statement
Summaries of the workshops described here are available on the HEI Energy website at the following links:
1. Unconventional Oil & Natural Gas--First Public Workshop, June 2014, Pittsburgh, PA (HEI Energy, 2014a).
2. Unconventional Oil & Natural Gas--Second Public Workshop, December 2014, Wheeling, WV (HEI Energy, 2014b).
3. Unconventional Oil & Natural Gas--Third Public Workshop, July 2015, Pittsburgh, PA (HEI Energy, 2015).
4. Scoping Meeting for Human Health Study Critique, January 2018, Boston, MA (HEI Energy, 2018a).
5. HEI Research Planning Workshop #1: Understanding Population-Level Exposures Related to the Development of Oil and Natural Gas from Unconventional Resources, July 2018, Denver, CO (HEI Energy, 2018b).
6. HEI Research Planning Workshop #2: Understanding Population-Level Exposures Related to the Development of Oil and Natural Gas from Unconventional Resources, September 2018, Austin, TX (HEI Energy, 2018c).
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* [13] HEI Energy. (2014a). Unconventional Oil & Natural Gas--First Public Workshop, June 2014, Pittsburgh, PA. [[https://www.heienergy.org/event/conventional-oil-natural-gas-first-public-workshop-2014-pitch-pa](https://www.heienergy.org/event/conventional-oil-natural-gas-first-public-workshop-2014-pitch-pa)]([https://www.heienergy.org/event/conventional-oil-natural-gas-first-public-workshop-2014-pitch-pa](https://www.heienergy.org/event/conventional-oil-natural-gas-first-public-workshop-2014-pitch-pa))
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* [15] HEI Energy. (2015). Unconventional Oil & Natural Gas--Third Public Workshop, July 2015, Pittsburgh, PA. [[https://www.heienergy.org/event/unc](https://www.heienergy.org/event/unc)]([https://www.heienergy.org/event/unc](https://www.heienergy.org/event/unc)) | wiley | Bringing Multisectoral and Multidisciplinary Stakeholders Together to Optimize Environmental Health Research | A. S. Rosofsky, D. J. Vorhees | https://doi.org/10.1029/2022gh000746 | 2,023 | CC-BY |
wiley/ff26a9ee_3cea_4dd7_9508_2a825ce80f32.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Bare Patches Created by Plateau Pikas Contribute to Warming Permafrost on the Tibet Plateau
[PERSON]\({}^{1}\)
[PERSON]\({}^{1,2}\)
[PERSON]\({}^{1}\)
###### Abstract
Plateau pikas, small mammals native to the Qinghai-Tibet Plateau (QTP), create bare patches through burrowing. No previous assessment exists on their impact on permafrost. This study fills this gap by simulating hypothetical scenarios in the Three Rivers Headwaters Region of the QTP using the Noah-MP model for the plant growing seasons during 2015-2018. Our findings reveal a significant increase in soil temperature in the active layer due to pikas-induced bare patches, particularly during July-August. The average temperature rise at 2.5 cm depth equals 0.36\({}^{\circ}\)C in permafrost regions and 0.29\({}^{\circ}\)C in seasonally frozen ground regions during August. Minimal impact on unfrozen water content was observed, with a slight increase in deep soil layers in permafrost regions, and negligible in seasonally frozen areas. These findings underscore the previously unexplored influence of pika burrowing on permafrost temperature, suggesting a potential risk of accelerating permafrost degradation, especially in permafrost-dominated regions.
Bare patches created by Plateau Pikas Contribute to Warming Permafrost on the Tibet Plateau
2024 GL108976
2
[PERSON], [PERSON] (2020). Bare patches created by plateau pikas contribute to warning permafrost to the Tibet Plateau. _Geophysical Research Letters, 51_, 2024 GL108976. [[https://doi.org/10.1029/2024](https://doi.org/10.1029/2024) GL108976]([https://doi.org/10.1029/2024](https://doi.org/10.1029/2024) GL108976)
2
## 1 Introduction
Permafrost, defined as ground continuously frozen for two or more years ([PERSON] et al., 2010), forms a significant portion of the Qinghai-Tibet Plateau (QTP), accounting for approximately 67% of its total area ([PERSON] et al., 2023). As the dominant vegetation type in the QTP, alpine grassland plays crucial roles in providing ecological functions such as biodiversity conservations, carbon storage, and permafrost preservation ([PERSON] et al., 2020; [PERSON] et al., 2013). Unfortunately, climate warming and human activities have contributed to the degradation of approximately 90% of alpine grassland, with 26% classified as extremely degraded ([PERSON], 2010; [PERSON] & [PERSON], 2007).
While climate change and overgrazing have significantly contributed to grassland degradation, recent studies highlight the role of rodent activities, particularly those of the plateau pika (_Ochotona curzoniae_), in grassland degradation ([PERSON] et al., 2021; [PERSON] et al., 2020). As a keystone species in the Tibetan grassland, plateau pikas play a crucial role in enhancing plant species diversity and stabilizing vegetational communities ([PERSON] & [PERSON], 1999). Notably, the population of plateau pikas has increased in recent decades ([PERSON] et al., 2013; [PERSON], 2010). Their subterranean lifestyle involves foraging and digging, bringing deep soil matters to the surface and creating distinct bare patches ([PERSON] & [PERSON], 2003; [PERSON] & [PERSON], 1999). These bare patches alter radiation partitioning and ground heat conduction, affecting both thermal and hydrological conditions of the underlying permafrost ([PERSON] et al., 2019; [PERSON] et al., 2017). Previous plot-based studies indicate that pika-induced bare patches, with a positive correlation with pika burrow density, can elevate soil temperatures ([PERSON] et al., 2018; [PERSON] et al., 2021). These findings suggest a potential contribution to permafrost degradation, although our understanding of this complex process remains limited.
Investigating the impact of pika-induced bare soil on permafrost hydrological-thermal processes at a regional scale requires accurate spatial distribution of these patches. However, their small size and spectral similarity to natural bare lands on satellite imagery pose challenges. To address this, we utilize a stochastic model to simulate pika burrow density, which informs the estimation of pika-induced bare patches based on statistical relationships derived from unmanned aerial vehicles (UAV) data. The Noah-MP land surface model (LSM) is then used to investigate the impacts of these bare patches on permafrost by configuring various scenarios in the Three Rivers Headwater Region (TRHR) of the QTP. This region is renowned for its unique role in China as an ecological shelter, extensive permafrost coverage, and widespread pika distribution ([PERSON] et al., 2022).
## 2 Materials and Methods
### Study Area and Data
The TRHR sits within the QTP hinterland, encompassing approximately 3.95 \(\times\) 10\({}^{5}\) km\({}^{2}\) and bounded by longitude 89\({}^{\circ}\)24\({}^{\prime}\)-102\({}^{\circ}\)27\({}^{\prime}\)E and latitude 31\({}^{\circ}\)39\({}^{\prime}\)-36\({}^{\circ}\)10\({}^{\prime}\)E (Figure 1). Its elevation gradually declines from northwest to southeast, with an average of 4,000 m above sea level (a.s.l.) (Figure 1a). The mean annual air temperatures in the TRHR range from \(-\)5.6\({}^{\circ}\)C to \(-\)3.8\({}^{\circ}\)C, with a south-to-northwest decreasing trend ([PERSON] et al., 2012). Spatially, annual precipitation varies significantly, with the southeast receiving 772 nm compared to 262 nm in the northwest. The majority of precipitation falls between June and September, influenced by warm and humid air currents emanating from the southern Bay of Bengal ([PERSON] et al., 2017). The TRHR primarily consists of alpine steppe and meadow, although other cover types like bare land, wetland, shrub, and forest are also present (Figure 1b) ([PERSON] et al., 2014). Permafrost distribution shows widespread coverage in the upper reaches of the Yangtze-River, whereas the eastern portion exhibits sporadic permafrost alongside seasonally frozen ground at lower elevations ([PERSON] et al., 2023) (Figure 1c). The average active layer thickness in this region measured approximately 2.57 m between 1980 and 2010 ([PERSON] & [PERSON], 2021). The growing season is relatively short, typically starting in early to late May and concluding in mid to late October ([PERSON] et al., 2022).
The gridded Chinese Meteorological Forcing Data set (ITP-forcing) (0.1\({}^{\circ}\) in space and 3 hr in time) were used to drive the Noah-MP model ([PERSON] et al., 2020). This data set includes seven meteorological elements including 2 m air temperature, 10 m wind speed, air pressure, specific humidity, precipitation rate, downward shortwave radiation, and longwave radiation. Vegetation type distribution was extracted from the 1:1 million scale Vegetation
Figure 1: Maps showing the location, topography (a), land cover types (b), and frozen ground types (c) in the Three River Headwaters Region on the Qinghai-Tibet Plateau. Labels 1, 2 and 3 in (a) indicate the headwaters of the Yangtze River, Lancang River, and Yellow River, respectively. Pika presence locations were recorded based on previous studies spanning 2011–2018. The land cover map is adapted from [PERSON] et al. (2014), and the frozen ground map from [PERSON] et al. (2023).
Atlas of China ([PERSON], 2019). Monthly leaf area index (LAI) data came from the level-4 Moderate Resolution Imaging Spectroradiometer (MODIS) 500 m global LAI and Fraction of Photosynthetically Active Radiation product (MCD15A2H). Stem area index (SAI) values, which are not directly obtainable from remote sensing, were sourced from the Noah-MP lookup table, considering 27 distinct vegetation types. Vegetation fractions were calculated from the normalized difference vegetation indices from the 1 km Terra MODIS vegetation indices data set (MOD13A3) ([PERSON] et al., 2023), and bare land fractions were subsequently derived by subtracting vegetation fractions from 100%. A QTP soil data set with a 1-km resolution and 18 layers, encompassing the entire TRHR, was used ([PERSON] & [PERSON], 2016).
Soil temperature and moisture data (measured at depths of 5-210 cm, daily) for model calibration and validation were collected from four TRHR permafrost sites (QT01, QT03, QT05, and QT08), representing major soil types ([PERSON], [PERSON], et al., 2021). Continuous soil temperature data covers 2010-2013 for all sites, while soil moisture data varies: 2010-2013 for QT01 and QT03, 2007-2008 for QT05, and 2012-2013 for QT08. Pika burrow density and bare patch fraction were derived from UAV data (2015-2018) acquired by [PERSON] et al. (2021) for four TRHR study plots (Phantom 3 drone, 1 cm resolution). These plots represent diverse bare patch levels, that is, no bare patches (NBP, \(<\)5%), low bare patches (LBP, 5%-20%), moderate bare patches (MBP, 20%-60%), and high bare patches (HBP, \(>\)60%), and minimized external disturbances.
### Estimation of Pika-Induced Bare Patch Fractions
To estimate the fraction of pika-induced bare patches within each modeling cell, we first utilized a stochastic model to simulate pika burrow density across the study region. This model leverages information from a Bayesian additive regression trees (BART)-based species distribution model ([PERSON] et al., 2012; [PERSON], 2020) that predicts pika habitat suitability. The habitat suitability map is categorized into four levels, unsuitable (0-0.2), low suitability (0.2-0.4), moderate suitability (0.4-0.6) and high suitability (0.6-1), based on predefined thresholds ([PERSON] et al., 2014; [PERSON] & [PERSON], 2018). Three Gaussian distributions representing these suitability levels (low, moderate, high) were fitted based on observed burrow density data ([PERSON] et al., 2015; [PERSON] & [PERSON], 2015). Unsuitable areas were considered to have no pika surface entrances. This stochastic model then generates pika burrow density for each grid cell. A more detailed introduction to this stochastic model can be found in Text S1 of Supporting Information S1.
Next, statistical relationships between pika burrow density and bare patch fraction were derived from UAV data ([PERSON] et al., 2021). Three linear equations were fitted for LBP, MBP and HBP levels (Figure S1 in Supporting Information S1). Each grid cell was categorized into LBP, MBP, or HBP based on satellite-derived bare land fractions from 2015 to 2018. Areas with NBP were merged into the LBP category in wake of satellite data's accuracy. By applying the corresponding UAV-based relationships to each grid cell based on its category, we estimated the pika-induced bare patch fraction.
### The Noah-MP LSM
The Noah-MP model is distinguished by its incorporation of the latest parameterization schemes ([PERSON] et al., 2011). It uses the Clapp-Hornberger water retention equation to solve vertical soil moisture distribution ([PERSON], 1978). To represent land surface heterogeneity, it adopts a \"semitile\" subgrid scheme with separate energy budgets for vegetated and bare ground areas (\(F_{avg}\) and 1-\(F_{vag}\) respectively). Equations S1-S3 in Supporting Information S1 detail these energy budgets. The model calculates net longwave radiation (\(L_{ab}\)), latent heat (\(LE\)), sensible heat (\(H\)), and ground heat (\(G\)) fluxes (Equation S4 in Supporting Information S1) and enforces overall energy balance (\(S_{av}+S_{sg}=L_{u}+LE+H+G\)). Vegetation canopy temperature (\(T_{v}\)), ground surface temperature in the vegetated fraction (\(T_{g,v}\)), and bare ground surface (\(T_{g,b}\)) are solved iteratively (Equations S1-S3 in Supporting Information S1). Noah-MP LSM allows users to choose among various parameterization options for individual processes, enabling customization based on research needs. The specific physical options used in this study are presented in Table S1 of Supporting Information S1.
### Experiment Design
The presence of pika-induced bare patches affects three land surface parameters in Noah-MP: vegetation coverage, LAI, and SAI. Two scenarios were designed to assess the impact of bare patches on soil temperature and moisture dynamics. The first scenario (undisturbed vegetation) represents pre-disturbance conditions characterized by maximum vegetation coverage, LAI, and SAI. The process to determine maximum vegetation coverage includes selecting various environmental factors affecting vegetation growth, clustering grid cells based on these factors, and using the maximum vegetation fraction value within each cluster as a representative of the undisturbed state. LAI and SAI were then determined proportionally in relation to vegetation coverage, following the approach applied in Noah-MP. We considered 31 environmental factors, including terrain, temperature, and precipitation-related variables (details in Table S2 of Supporting Information S1) and applied principal component analysis (PCA) to these factors before clustering, utilizing the resulting PCA components for the clustering process. The Gaussian Mixture Model (GMM) clustering algorithm, known for its flexibility and ability to model various data distributions, was selected for spatial clustering ([PERSON], 2009). Cluster number was determined based on the automatic cluster detection feature of the GMM algorithm.
The second scenario (pika-induced bare patches) accounts for the impact of pika activity on vegetation cover. These pika-induced bare patch fractions were modeled based on statistical relationships and then subtracted from the pre-disturbance vegetation coverage to derive the post-disturbance state. Adjustments were made to both LAI and SAI in proportion to the vegetation fraction. To ensure realistic bare land proportions, the modeled pika-induced bare patches were constrained by satellite-derived bare land fractions. However, due to data limitations (Figure S1 in Supporting Information S1), the modeled pika-induced fractional bare patches only represent the average state for July-August from 2015 to 2018. To extend these values to the entire growing season (June through September), we linearly extrapolated the patch fractions for June and September using the ratio of the maximum vegetation fraction in that month relative to the mean vegetation fraction of July and August. The impacts were only considered during the plant growing seasons, as indicated by satellite-derived vegetation fraction analysis in the TRHR, which showed sharply reduced vegetation coverage outside these months. Consequently, during non-growing seasons, the exposed surfaces created by plateau pikas resemble unvegetated areas elsewhere, likely minimizing their influence on the underlying permafrost.
### Model Settings, Calibration and Validation
The Noah-MP model was forced with the same ITP-forcing (0.1\({}^{\circ}\)) for both scenarios over the period of January 1984-December 2018. The model outputs during 2015-2018 were chosen for analysis, aligning with the time-frame of the UAV and in situ data. Prior to the start of the model run, a 300-year spin-up using the repeat forcing from 1979 to 1984 was conducted to mitigate the effects of initial values ([PERSON] et al., 2022). The model was calibrated and validated using in situ soil temperature and moisture records from four permafrost monitoring sites (Figure 1b). Data from all years except the last served for calibration, with the final year reserved for validation. Six sensitive parameters ([PERSON] et al., 2016; [PERSON] et al., 2023): the exponent in Brooks-Corey relation (B parameter), soil porosity, saturated hydraulic conductivity, momentum roughness length, thermal conductivity of very fluffy snow, and albedo of fresh snow, were calibrated. All model parameters except for vegetation coverage, LAI and SAI, were held constant in both the undisturbed and pika-induced bare patch scenarios. The model's performance was evaluated using widely-used Nash-Sutcliffe efficiency coefficient (NSE) and Pearson's correlation (\(R\)).
## 3 Results
### Assessment of Model Performance
Noah-MP simulations of soil temperature and unfrozen water content were validated with independent in situ data from four permafrost sites (Figures S2 and S3 in Supporting Information S1). Overall, high \(R\) and NSE values for most depths and sites were observed, indicating the calibrated Noah-MP LSM successfully reproduced observed soil temperature and unfrozen water content. During the validation periods, soil temperature simulations exhibited high agreement with observations across all depths and sites, with \(R\) values exceeding 0.9 for all depth profiles. NSE values generally surpassed 0.68, except for deeper soil layers (>200 m) at certain sites (Figure S21 in Supporting Information S1).
The Noah-MP LSM effectively captured the temporal variations of unfrozen water content at all four sites and across different depths during the validation period. At the QT01 site, simulations demonstrated excellent agreement with observations across all depths, with \(R\) values ranging from 0.84 to 0.94 and NSE values ranging from 0.64 to 0.80 (Figures S3a-S3d in Supporting Information S1). While other sites displayed some discrepancies, the model still effectively captured the temporal trends. An outlier was observed at the QT08 site, 40 cm depth (Figure S3n in Supporting Information S1), where measured unfrozen water content remained consistently at 0. This potentially indicates a malfunction in the instrument, and therefore, \(R\) and NSE values were not calculated for this depth at the QTP08 site.
### Spatial Distributions of Pika Burrows and Induced Bare Patches
Pika burrow density simulations revealed a distinct spatial pattern, with higher concentrations observed in the Yellow and Lancang River headwaters compared to the Yangtze River headwater (Figure 2a). Interestingly, the spatial distribution of pika-induced bare patches exhibited an inverse trend, with higher fractional bare patches concentrated in the Yangtze River headwater (Figures 2c and 2d). This contrasting pattern likely results from differences in climate conditions influencing vegetation recovery dynamics. The milder climate and abundant precipitation in the Yellow and Lancang River headwaters, while conducive to pika presence, also facilitate faster recovery of vegetation disturbed by burrow construction, leading to lower observed bare patch fractions. Conversely, the harsher climate and pre-existing bare lands in the Yangtze River headwater create conditions where even minor pika disturbances can readily expand bare land areas, impeding vegetation recovery and resulting in higher observed bare patch fractions. Figure 2c depicts the 1-km resolution distribution of pika-induced bare patches, subsequently aggregated to 10 km to match Noah-MP simulations (Figure 2d).
Clustering analysis based on 31 environmental factors related to vegetation growth yielded five distinct clusters within the study region (Figure 2b). The attached table in Figure 2 presents the maximum vegetation coverage within each clsuters, which were late used to construct the undisturbed scenario. Clusters R1 and R2 displayed the highest vegetation cover, exceeding 0.94 in both July-August. Cluster R3 exhibited moderate cover, reaching 0.71-0.73 during peak vegetation months. Moving westward, clusters R4 and R5 showed lower vegetation cover during peak months, ranging 0.27-0.50, with cluster R4 exhibiting slightly better conditions than cluster R5.
Figure 2: Modeled pika burrow density distribution and induced bare patch fractions in the Three Rivers Headwaters Region (TRHR). (a) Spatial distribution of pika burrows across the TRHR, (b) five clusters based on environmental factors used to derive undisturbed vegetation fractions, (c) modeled pika-induced fractional bare patches at 1-km resolution, and (d) Pika-induced fractional bare patches aggregated to 10 km from the 1-km map (c). “No data” areas in (c) and (d) indicate unsuitable regions for pika habitat and were excluded from simulations of pika-induced bare patches. The accompanying table represents the maximum vegetation fractions for each cluster (b) during the growing season (June–September). These values were used to construct the undisturbed scenario.
### Impact of Pika-Induced Bare Patches on Soil Temperature and Moisture
Pika-induced bare patches significantly warmed shallow soil layers (2.5 and 66 cm), as shown in Figures 3a-3h and. Warming intensity varied spatially and temporally, with the most pronounced increases occurring in July-August. September also showed a stronger impact compared to June. Spatially, among the five vegetation clusters (Figure 2), cluster R4, with the most extensive pika-made bare patches, experienced the greatest warming, followed by R3. Conversely, cluster R5, naturally dominated by bare land, exhibited minimal change. In clusters R1 and R2 (except R2 north), pika bare patches had a weaker influence. At the regional scale, significant warming (>1\({}^{\circ}\)C) was concentrated in the south and southeastern Y Yangtze River headwater and the western Yellow River headwater, while minimal impact (<0.2\({}^{\circ}\)C) occurred in the western Yangtze River headwater and the southern Yellow River headwater.
These spatial patterns likely reflect the underlying permafrost and seasonally frozen ground distribution. Within permafrost zones, significant temperature increases were observed, with a maximum difference of 2.37\({}^{\circ}\)C between the contrasting scenarios and an average warming of 0.36\({}^{\circ}\)C at 2.5 cm depth in August (Figure 3c). In areas with seasonally frozen ground, notable differences were also observed in the northern Yellow River headwater, where the maximum difference reached 2.31\({}^{\circ}\)C and the average warming was 0.29\({}^{\circ}\)C, again at the shallow depth of 2.5 cm in August (Figure 3c). Notably, deeper layers (184 cm) showed minimal temperature changes, indicating limited impacts on the base of the active layer (Figures 3i-3j).
Plateau pika-induced bare patches had minimal impact on shallow soil moisture content (2.5 and 66 cm) (Figures 4a-4h). A slight increase in moisture content was observed at deeper layers (184 cm), nearing the bottom
Figure 3: Maps illustrating changes in soil temperature during the plant growing seasons induced by the presence of pika-induced bare patches. Each row represents a specifc soil depth. Values were computed by subtracting soil temperatures simulated under pika-induced bare patch scenario from those simulated under undisturbed vegetation scenarios. Positive values indicate areas where pika-induced bare patches led to increase in soil temperature, while negative values represent areas where they caused decreases.
of the active layer (Figures 4j-4l). In space, the subtle changes were primarily concentrated in the southern Yangtze River headwater and the northern Yellow River headwater. The maximum observed increase was 0.06 m\({}^{3}\)m\({}^{-3}\) (Figure 4k), with an average increase 0.007 m\({}^{3}\)m\({}^{-3}\) in permafrost regions and 0.003 m\({}^{3}\)m\({}^{-3}\) in seasonally frozen ground regions at 184 cm in August. These changes are considered negligible compared to overall soil moisture content.
## 4 Conclusions and Discussion
This study provides a new perspective for understanding permafrost responses to the bare patches caused by plateau pikas over the QTP through hypothetical numerical experiments. The following conclusions have been drawn.
1. While plateau pikas prefer warmer and wetter headwater regions of the Yellow and Lancang Rivers, pikas-induced bare patches are more extensive in the drier and colder Yangtze River headwater. This inversely related pattern reflects the complex interplay between various environmental conditions and vegetation recovery across these regions.
2. The pika-created bare patches led to a substantial soil temperature rise, especially in shallow soil layers (2.5 and 66 cm). The impact was greater in permafrost zones compared to seasonally frozen ground. In August, the average temperature rise at 2.5 cm in the permafrost zone was 0.36\({}^{\circ}\)C (2015-2018), compared to 0.29\({}^{\circ}\)C in the seasonally frozen ground zone.
Figure 4: Maps illustrating differences in soil liquid water content (SWC) during the plant growing seasons induced by the presence of pika-induced bare patches. Each row represents a specific soil depth. Values were computed by subtracting SWC simulated under pika-induced bare patch scenario from those simulated under undisturbed vegetation scenarios. Positive values indicate areas where pika-induced bare patches led to increase in SWC, while negative values represent areas where they caused decreases.
3. The influence of pika-induced bare patches on soil unfrozen water was relatively minor. A slight increase in moisture content was observed near the active layer base, averaging 0.007 m\({}^{3}\) m\({}^{-3}\) at 184 cm in August simulations.
Uncertainties exists in estimating pika burrow density using the stochastic model. More field surveys could improve these estimates. Uncertainties are also associated with estimating pika-induced bare patch fractions and determining undistributed vegetation conditions. Rising permafrost temperature due to pika bare patches, combined with climate warming, would further amplify the risk of permafrost degradation. Pika burrow systems, averaging 55.2 cm deep ([PERSON] and [PERSON], 2018), act as macroopores in the active layer, facilitating deeper water infiltration. These macroopores potentially create pathways for convective heat transfer, allowing warm precipitation to reach deep soil layers and accelerate permafrost degradation ([PERSON] et al., 2020; [PERSON] et al., 2019; [PERSON] and [PERSON], 2015).
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The ITP-forcing used to drive the Noah-MP model can be accessed from [PERSON] et al. (2019). The measured temperature and moisture data of the active layer at QT01, QT03, QT05 and QT08 sites are accessible from [PERSON]. [PERSON], [PERSON], et al. (2021). The results and associated data are available at [PERSON] et al. (2024). The Noah-MP v1.1 was developed openly at the Research and Application Laboratory at National Center for Atmospheric Research (2012).
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* [PERSON] et al. (2021) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2021). A synthesis dataset of permafrost thermal state for the Qinghai-Tibet (Xizang) Plateau, China. _Earth System Science Data_, 138(3), 4207-4218. [[https://doi.org/10.5194/sssd-13-4207-20](https://doi.org/10.5194/sssd-13-4207-20)]([https://doi.org/10.5194/sssd-13-4207-20](https://doi.org/10.5194/sssd-13-4207-20)) | wiley | Bare Patches Created by Plateau Pikas Contribute to Warming Permafrost on the Tibet Plateau | Yuhong Chen, Zhuotong Nan, Shuping Zhao | https://doi.org/10.1029/2024gl108976 | 2,024 | CC-BY |
wiley/ff03fc95_1524_480e_a067_dcae29d26f89.md | # IGR Oceans
Research Article
10.1029/2020 JC016585
1
Local and Remote Influences on the Heat Content of Southern Ocean Mode Water Formation Regions
[PERSON]
1 British Antarctic Survey, Cambridge, UK, 1 Massachusetts Institute of Technology, Cambridge, MA, USA, 1 National Academy of Sciences, Southampton, UK
[PERSON]
1 British Antarctic Survey, Cambridge, UK, 1 Massachusetts Institute of Technology, Cambridge, MA, USA, 1 National Academy of Sciences, Southampton, UK
[PERSON]
1 British Antarctic Survey, Cambridge, UK, 1 Massachusetts Institute of Technology, Cambridge, MA, USA, 1 National Academy of Sciences, Southampton, UK
[PERSON]
2 British Antarctic Survey, Cambridge, UK, 1 Massachusetts Institute of Technology, Cambridge, MA, USA, 1 National Academy of Sciences, Southampton, UK
[PERSON]
3 British Antarctic Survey, Cambridge, UK, 1 Massachusetts Institute of Technology, Cambridge, MA, USA, 1 National Academy of Sciences, Southampton, UK
###### Abstract
The Southern Ocean (SO) is a crucial region for the global ocean uptake of heat and carbon. There are large uncertainties in the observations of fluxes of heat and carbon between the atmosphere and the ocean mixed layer, which lead to large uncertainties in the amount entering into the global overturning circulation. In order to better understand where and when fluxes of heat and momentum have the largest impact on near-surface heat content, we use an adjoint model to calculate the linear sensitivities of heat content in SO mode water formation regions (MWFRs) to surface fluxes. We find that the heat content of these regions is, in all three basins, most sensitive to same-winter, local heat fluxes, and to local and remote wind one to eight years (the maximum lead-time of our simulations) previously. This is supported by sensitivities to potential temperature changes, which reveal the sources of the MWFRs as well as dynamic links with boundary current regions and the Antarctic Circumpolar Current. We use the adjoint sensitivity fields to design a set of targeted perturbation experiments, allowing us to examine the linear and non-linear responses of the heat content to changes in surface forcing. In these targeted experiments, the heat content is sensitive to both temperature changes and mixed layer volume changes in roughly equal magnitude.
24 MAR 2021
14 JUL 2020
24 MAR 2021
## 1 Background
The Southern Ocean (SO) is home to the world's longest and strongest ocean current, the Antarctic Circumpolar Current (ACC), which encircles the globe free of continental barriers. Driven by strong wind and buoyancy forcing, the ACC transports climatically important tracers such as heat, salinity, and carbon between the three major ocean basins. These forcings also create sloping density surfaces (isopycnals) that tilt upwards from north to south, which connect deep waters from around the globe to the surface. At the surface, air-sea interactions modify the properties of water masses. These modified waters then return to depth and into the other ocean basins as dense waters near the Antarctic continental shelf, or as lighter mode and intermediate waters north of the ACC ([PERSON] & [PERSON], 2007; [PERSON] & [PERSON], 2012).
The SO is of critical importance to the global oceanic uptake of heat and carbon, due in part to this overturning circulation. It may be responsible for as much as 75% of the global ocean heat uptake and \(\sim\)50% of the carbon uptake ([PERSON] et al., 2015; [PERSON] et al., 2006). Roughly 30% of anthropogenic CO\({}_{2}\) emissions ends up in the ocean ([PERSON] et al., 2013), and around 93% of the excess heat added to the earth system since 1955 has been estimated to be stored in the ocean ([PERSON] et al., 2012), predominantly in the SO ([PERSON] et al., 2015).
Understanding what determines the time scales of SO overturning and the properties of the waters transported is of crucial importance to future climate predictions, including the continued efficiency of the carbon sink ([PERSON] et al., 2015; [PERSON] et al., 2018). The properties of the overturning circulation are affected by a range of processes, including variations in surface forcings, variations in the interactions of these forcings with ocean mixed layer properties, and variations in the draw-down of mixed layer properties into the ocean interior as mode, intermediate, and deep waters. Unfortunately, direct air-sea flux observations are scarce in the SO, especially in the winter when sea ice hinders access to the region ([PERSON] et al., 2015).
This work focuses on understanding how variations in surface forcings impact mixed layers in SO mode water formation regions (MWFRs), using a data-constrained estimate of these processes (ECCOv4, [PERSON], [PERSON], et al., 2015). This will provide insights into the influence of uncertainties in observations of surface forcings on estimates of mode water properties, as well as allowing for estimates of the impact of future changes in these forcings.
To this end, we follow the same approach as in [PERSON] et al. (2018), using an adjoint model, but here we target the SO mixed layer. The adjoint experiments designed in Section 2 derive the linear sensitivities of MWFRs in the Atlantic, Pacific, and Indian sectors of the SO to surface heat and winds (Section 3). We then decompose the potential temperature sensitivities of these regions into kinematic and dynamic sensitivities (Section 4). The linear sensitivities from the adjoint are then used to design targeted perturbation experiments using the non-linear forward model (Section 5). We finish with a summary of our results, discussion and perspectives (Section 6).
## 2 Experiment Design
### The ECCOv4 Global State Estimate and Its Adjoint
For this study we used the ECCOv4 (release 2) ocean state estimate framework ([PERSON], [PERSON], et al., 2015). This is a global \(\sim\)1\({}^{\circ}\) ocean and sea ice setup of the MITgcm ([PERSON] et al., 2004) that spans 20 years from 1992 to 2011, with surface forcings and initial conditions that have been optimized to reduce shifts to observations. Details of the 4D-Var optimization process and the residual model-data misfit can be found in [PERSON], [PERSON], et al. (2015). This set-up provides a recent, well-constrained estimate of the SO, which is also easily modified to carry out adjoint sensitivity experiments. We selected ECCOv4 in order to allow for possible dynamical connections with the global ocean, and to work with a two-decade time period. It would be instructive to repeat our experiments in the higher-resolution Southern Ocean State Estimate (SOSE, [PERSON] et al., 2010) although SOSE covers a shorter time period and has a boundary in the subtropics.
Mixed layer depths in ECCOv4, used to define mode water formation regions, closely match observations in terms of geography and magnitude (see Figure 6, [PERSON], [PERSON], & [PERSON], 2015). Figure S1 in [PERSON] et al. (2019) additionally shows a comparison of the sea level anomaly and sea surface temperatures in ECCOv4 with observations in the Indian and Pacific mixed layer regions also used in this study, showing that absolute values and variability are well captured. ARGO data is used to produce ECCOv4, and ECCOv4 temperature and salinity compare well with ARGO-derived values in the Pacific, Atlantic, and Indian mode water formation regions (Figure 1, S1, and S2). To allow for direct comparison with the monthly ECCOv4 solution, the ARGO profiles in the region from that month, and the months either side, were linearly interpolated to standard depths. The ECCOv4 solution was then subsampled identically (via linear interpolation) to produce a complementary set of profiles for the same three month period, which was then averaged to produce the red lines in Figure 1. The black lines were calculated by taking the sum of the ECCOv4 profile means (red lines) and the median model-data misfit for each three-month period. The model solution shows good general agreement with ARGO for both quantities at all depths, although note the differences near 400 m depth appear larger due to the smaller \(y\)-axis range.
An adjoint model, in this context, is one that starts from a quantity of interest (henceforth referred to as an \"objective function\")--such as the integrated temperature over a certain region (e.g., [PERSON] et al., 2018, 2019, 2020), the heat or volume transport of a particular current (e.g., [PERSON], et al, 2010, 2012; [PERSON] et al., 2011; [PERSON], et al, 2019; [PERSON], et al, 2016; [PERSON], 2019)--and steps backwards through a linearized version of the model, propagating the sensitivities of the objective function.
More detailed descriptions of how sensitivity information propagates backwards through an adjoint model can be found in [PERSON] et al. (2011); [PERSON] et al. (1999). The adjoint model produces the linear sensitivity of the objective function to a range of specified model variables, such as surface fluxes or interior properties (e.g., potential temperature, mixing parameters). In a more traditional model study, one might start by choosing a model variable or variables theorized to impact one's objective function, and then carry out a suite of perturbation experiments changing these variables by a range of magnitudes, locations, and/ or times. In contrast, an adjoint model can produce in one single model the linear sensitivity of one's objective function to a range of model variables, at all points in the model domain, at multiple time lags, allowing for a fully comprehensive experiment.
### Defining the Objective Function: Locating Mode Water Formation Regions
For this study, our objective function was the heat content of the mixed layer in SO mode water formation regions. Mode water is formed seasonally in the deep winter mixed layers to the north of the ACC, before subduction into the interior across the base of the mixed layer ([PERSON], et al., 2010; [PERSON], 1999). By definition, such water is characterized by low stratification (i.e., low potential vorticity [PV] values) (see e.g., [PERSON] & [PERSON], 2001). Figure 2 shows a latitude-depth plot along 90\({}^{\circ}\)E (in the Indian sector of the SO) of the minimum PV values for a representative year (1999) from the ECC0v4 r2 state estimate (notice the logarithmic color scale). There is a sharp lateral gradient in the minimum PV values just inside the winter mixed layer extent, and as such the winter mixed layer extent captures the mode water formation pools of interest.
#### 2.2.1 Atlantic, Pacific, and Indian Mode Water Pools
Three distinct mode water formation pools can be identified in the three main basins--Atlantic, Pacific, and Indian (Figure 3a). The winter mixed layer encloses the mode water formation pools (see also Figure 2). We used a combination of annual minimum potential vorticity (PV) values and winter (ASO) mixed layer depths to form the horizontal mask for the \"objective function\" volume for the suite of adjoint experiments we carried out, whilst ensuring that nothing too close to land or too far north was included. Specifically, we defined the objective function as anywhere between 30\({}^{\circ}\)S and 65\({}^{\circ}\)S with a minimum PV value of less than 10\({}^{-13}\) and an ASO mean mixed-layer depth (MLD) (for that given year) of greater than 300 m depth, then manually removed regions in the North of the basins (we removed regions north of 40\({}^{\circ}\)S in the Pacific and East Indian Ocean [60\({}^{\circ}\)W to 110\({}^{\circ}\)E], north of 35\({}^{\circ}\)S in the West Indian Ocean [110\({}^{\circ}\)E to 60\({}^{\circ}\)E] and north of
Figure 1: Comparison of direct measurements from ARGO floats (black line, see www.argo.ucsd.edu for more info) and the ECC0v4r2 solution, sub-sampled identically (red lines) with, for potential temperature (left) and salinity (right), in the median Pacific mode water formation region (yellow-shaded area bottom right, see text for how this region is defined). See text for details on the calculation. Note the different y-axis scales make the differences near 400 m appear larger, although they are of similar magnitude to the shallower depths.
45\({}^{\rm{\circ}}\)S close to South America [49.5\({}^{\rm{\circ}}\)W to 75\({}^{\rm{\circ}}\)W]), as we wished to concentrate on the main mode water pools. This mask as calculated for 1999 is shown by the black dotted line in Figure 3a. The objective function regions, referred to throughout as MWFRs, show a clear seasonal cycle in heat content (Figure A1).
Figure 3: (a) The winter mixed layer encloses mode water formation pools laterally: Blue colors are the absolute value (on a log\({}_{18}\) scale) of the 1999 minimum FV at the annual mean mixed-layer depth (the green dash-dotted line in Figure 2). Also shown are the 300 m August–October (ASO) mean mixed-layer depth contour (pink dotted line) and the extent of the mode water mask (black dashed line), as described further in the text. The domain is also divided into three basins by the three longitudinal black dotted lines shown, into the Atlantic, Indian, and Pacific basins referenced throughout. (b) An example sensitivity field: Colors indicate the adjoint sensitivity of the 1999 Indian mode water formation region (MWFR) heat content to zonal wind stress at \(\sim\)3 years lag. The gray contours indicate the \(-17,0\), and 30 Sv mean barotropic streamlines, for the entirety of ECCOv4 r2, chosen to highlight the boundary between the ACC and the sub-tropical gyre structure.
Figure 2: An example mode water formation region, characterized by low potential vorticity (PV) values, contained within the winter mixed layer: Latitude-depth plot of the absolute value of the 1999 minimum FV along 90\({}^{\rm{\circ}}\)E in ECCOv4 r2, on a log scale (color). Also shown are the August–October (ASO) mean mixed-layer depth (MLD) for 1999 (pink line) and 1995–2011 mean and variations by one standard deviation (pink dashed and dash-dotted lines) and the annual mean MLD for 1999 (green line) and 1995–2011 mean and standard deviations (green dashed and dash-dotted lines).
We split the SO into three basins using the three latitudinal black dashed lines shown in Figure 3a, and calculate a separate objective function for each basin:
\[J_{\text{SO}}^{Y}=J_{\text{AA}}^{Y}+J_{\text{Psc}}^{Y}+J_{\text{Int}}^{Y}, \tag{1}\]
where \(J_{b}^{Y}\) is the objective function in the given basin \(b\) in year \(Y\). The Indian and Pacific basins are divided at 180\({}^{\circ}\)W, the Pacific and Atlantic at 49.5\({}^{\circ}\)W and the Atlantic and Indian at 30.5\({}^{\circ}\)E. Because the adjoint model calculates linear sensitivities, the total SO sensitivity to a given model variable will be the sum of the sensitivities for each basin, that is,
\[\frac{\partial J_{\text{SO}}^{Y}}{\partial X}\big{(}\underline{r},t\big{)}= \frac{\partial J_{\text{M}}^{Y}}{\partial X}+\frac{\partial J_{\text{Psc}}^{Y }}{\partial X}+\frac{\partial J_{\text{Int}}^{Y}}{\partial X}, \tag{2}\]
where \(\partial J_{b}^{Y}\)\(/\)\(\partial X(\underline{r},t)\) is the linear adjoint sensitivity of the objective function \(J_{b}^{Y}\) to model variable \(X\) at point \(\underline{r}=(x,y,z)\) and time \(t\).
#### 2.2.2 Objective Function Definition
We re-calculated the objective function based on the same MLD and minimum PV criteria for each of the 20 years in ECC0v4 r2. We chose the annual maximum winter mixed layer depth as the vertical extent of our objective function [denoted max(MLD\({}_{\text{ASO}}\))]. To capture the peak of mode water formation, we chose our objective function to extend to the two months on either side of the peak heat contents of the three basin volumes, that is, from July to November (see Figure A1). Thus, our full objective function for a given year and basin is defined as the following volume averaged heat content:
\[J_{b}^{Y}=\frac{1}{V_{b}^{Y}\Delta t}\big{|}_{\text{JM}}^{\text{Nov}}\big{|}_{ \text{JM}}^{\text{Jan}(\text{MLD\({}_{\text{ASO}}\)})}\rho_{0}c_{p}\theta( \underline{r},t)dtdvdydz, \tag{3}\]
where \(\overset{Y}{b}=\iint^{B_{b}(x,y)}\rho_{0}\text{max(MLD\({}_{\text{ASO}}))}\)\(dvdydz\) is the control volume in year \(Y\) and basin \(b\), \(\Delta t\) is the averaging time interval, \(f_{b}(x,y)\) is the horizontal mask in basin \(b\); \(\rho_{0}\) a reference density; \(c_{p}\) the heat capacity of sea water; and \(\theta\), the potential temperature. Note that the extent of the objective function region is calculated offline and so is a fixed volume. The effect of choosing our objective function as defined above, with the lateral extent limited using our mask, rather than just looking at the entire SO mixed layer, is briefly investigated in Section A2.
An example sensitivity field, the sensitivity of the 1999 Indian MWFR heat content to zonal wind stress at \(\sim\)3 years lag, can be seen in Figure 3b. Thus, red (blue) colors indicate where an increase (decrease) in zonal wind stress in 1996 would result in an increase in the Indian MWFR heat content in 1999. The sensitivity has been scaled by \(1/\rho c_{p}\), and thus units indicate the number of degrees \(C\) the similarly scaled MWFR heat content would rise if the zonal wind stress changed by 1 N/m\({}^{2}\).
To assess inter-annual variability in objective function sensitivity, we carried out an ensemble of 13 eight-year adjoint runs, with objective functions defined in each winter from 1999 to 2011. For each ensemble member, sensitivities were output at two week intervals as averages over those two weeks. The sensitivities shown in Figure 4 are ensemble averages of winter (July-September) averages, which are then multiplied by a representative scalar standard deviation for the surface property \(\sigma_{0}\) (these values can be found in Table 1) and scaled by \(1/\rho_{0}c_{p}\). This makes the units of sensitivity the amount by which a unit perturbation of the given surface property at the relevant point in space and time would raise the objective function \(J_{b}^{Y}\) in \({}^{\circ}C\).
have close to zero standard deviation. Ensemble averaging therefore highlights the consistent structures in the sensitivity fields, and the year-to-year variability in magnitudes is investigated in Section 3.4. We do not show the fresh water flux sensitivities as they are an order of magnitude smaller than those shown here.
### Sensitivities to Net Heat Flux
\(Q_{\mathrm{net}}\) is defined as the net heat flux from the ocean to the atmosphere. Thus _negative_ sensitivities indicate that a _reduction_ in \(Q_{\mathrm{net}}\), that is, _less_ heat from ocean to atmosphere, results in an increase in the objective function, that is, MWFR heat content, and _positive_ sensitivities indicate instead that an _increase_ in \(Q_{\mathrm{net}}\) will result in an increase in the objective function. The largely negative sign of the \(Q_{\mathrm{net}}\) sensitivities (Figure 4, upper row) is thus not unexpected, showing that a cooling of the ocean surface in these regions results in a cooling of the MWFR. The location of the peak sensitivity is largely on top of, or at previous lags \"upstream\" of the location of the median objective function, inferred by the expansion of the sensitivities along ACC pathways with increased lag. Again, this is not unexpected and indicates that simply heating/cooling the source waters for the MWFR results in heating/cooling of the MWFR itself. These features are common across sensitivities to \(Q_{\mathrm{net}}\) for all lags and in each of the three basins (the Pacific and Atlantic can be seen in Figure S4 in the supporting information), and can be used to identify possible source regions of the MWFR waters.
### Sensitivities to Wind Stress
The wind stress sensitivities (Figure 4, middle and lower rows) have a very different structure to the \(Q_{\mathrm{net}}\) sensitivities, notably there are significant sensitivities of both signs. Dipole-type structures are common across all such wind stress sensitivities (not just those shown here), with features centered on the boundaries of the objective functions and over source water regions upstream. These types of features we associate with convergence/divergence and thus vertical Ekman pumping/suction of water ([PERSON] et al., 2012; [PERSON] et al., 2018; [PERSON] et al., 2020).
Additionally, the sensitivities to zonal wind stress stretch both north into the sub-tropical gyres and south across the ACC for all basins. This indicates a direct connection with the strength of the wind-driven sub-tropical gyres and possible links with ACC transport--an increase/decrease in zonal wind stress could imply an increase/decrease in meridional Ekman
Figure 4: Example sensitivity fields showing the range and general properties of adjoint model simulations: Ensemble mean winter (July–September) sensitivities for surface properties at lags of 5, 3, and 1 years (left, middle, and right columns respectively). The upper row shows sensitivities of the Indian mode water formation region (MWFR) (median location indicated by black contour) to surface net heat flux \(Q_{\mathrm{net}}\). The middle row shows sensitivities of the Pacific MWFR (median location indicated by black contour) to zonal wind stress \(\tau_{\mathrm{D}}\). The lower row shows sensitivities of the Atlantic MWFR (median location indicated by black contour) to meridional wind stress \(\tau_{\mathrm{D}}\). The gray contours indicate the \(-17\), \(0\), and \(30\)\(S\) mean barotropic streamlines. The associated ensemble standard deviations and sensitivities for the basins not shown here can be found in the supporting information.
transport across the ACC, or a change in the tilt of the isopycnals resulting in a change in zonal ACC transport. Other common features are what appear to be dynamical links with boundary current regions--dynamic because the sensitivities are not in source regions and because the sensitivities often propagate through space over time either along or away from boundaries in patterns similar to topographic, Kelvin, and Rossby waves. This can be seen more easily in the animations provided in the supporting information and is discussed further in Section 4.2.
Figure 5: Wind stress largely dominates basin-integrated absolute sensitivities: Integrated absolute sensitivities to surface for forcings by objective function basin (top to bottom, as labeled), scaled by a representative standard deviation \(\sigma_{\rm e}\) and normalized, dimensionless, plotted against lag relative to the start of the objective function. Colors indicate surface net heat flux (\(Q_{\rm enc}\) red), and zonal/meridional wind stress (\(\tau_{\rm Eos}\) purple/green). The shaded area indicates the ensemble envelope (spanning the ensemble max and min values, _not_ a standard deviation or similar) and thick lines the ensemble mean.
The negative sensitivity of the Pacific MWFR to zonal wind stress on 1-3 years lags in the region of 120\({}^{\rm o}\)W to 90\({}^{\rm o}\)W and South of 60\({}^{\rm o}\)S (the Amundsen Sea, see Figure 4) is consistent with the results of [PERSON] et al. (2013), who find a link between an increased Amundsen Sea Low (ASL, resulting in weaker zonal wind stress) and warmer Sub-Antarctic Mode Water (SAMW). However, this sensitivity is relatively weak compared with zonal and meridional (see Figure S10 in the supporting information) wind stress sensitivities over, to the north of, and upstream of the MWFR, whilst [PERSON] et al. (2013) believe the ASL is significant in determining SAMW properties. This may be because although the region shows low sensitivity relative to other regions, the actual wind-stress changes in the region are significantly larger than those in other regions, although this does not appear to be the case for climatological anomalies, see Figure S7.
### Time Evolution of Domain-Integrated Sensitivities
To compare sensitivities over time, we first calculated scaled domain-integrated absolute sensitivities over time for each basin's objective function, that is, the absolute value of the sensitivity is taken before integration over the global domain, meaning positive and negative sensitivities _do not_ cancel out. Thus, the integrated absolute sensitivity is the maximum possible impact on the objective function if perturbations are applied with the same sign and magnitude as the sensitivities themselves, demonstrating when the model has the most potential to alter the objective function. In each basin, sensitivity to \(Q_{\rm net}\) is highest at lag 0 and then decays with a strong seasonal cycle as the lag increases, peaking each winter (Figure 5). Here, lag 0 is defined as the beginning of the objective function integral, that is, at the start of July--see Equation 3--and so non-zero sensitivities are possible at positive lags between July and the end of the integral in November. Sensitivity to wind stress decays more slowly and has a very slight seasonal cycle, relative to the heat flux sensitivity, which it also appears to be out of phase with.
This study focuses on highlighting possible oceanic mechanisms, but if instead we wished to highlight the origins of forced variability, we could convolve the sensitivities with the contemporaneous anomalies of the surface fluxes from the climatological mean. We have included versions of Figures 4 and 5 weighted by such anomalies in the supporting information Figures S7, and S8.
With our chosen scalings, sensitivity to \(Q_{\rm net}\) initially dominates in the Pacific basin, with wind stress sensitivity dominating after around 1-year lag. Wind stress sensitivity dominates in the Atlantic basin, and largely dominates in the Indian basin apart from during the objective function integration period (positive lags), where the \(Q_{\rm net}\) ensemble mean sensitivity just dominates. However, the sensitivity that dominates at any given time is dependent on the scaling applied. Scaling the sensitivities instead by the climatological anomaly results in a relative increase in the \(Q_{\rm net}\) sensitivity, see supporting information Figure S8, although the overall pattern of \(Q_{\rm net}\) sensitivities dominating at short lags (0-1 year) and wind stress dominating at longer lags still holds.
These results indicate that the surface heat flux has the largest impact during winter on mode water formed during that same winter, and thereafter seasonally affects subsequent winters, but to a lesser and lesser degree. The large magnitude of the seasonal cycle means that heat fluxes in past winters have a much stronger influence on MWFRs than intervening summers, even years apart. Wind stress, however, can produce a similar or larger impact than heat flux for years to come, with relatively less seasonal variation, perhaps linked to the dynamical, longer-range nature of the connection with the MWFRs. More explicitly, dynamic processes such as changes in the Ekman pumping over source regions; changes in the ACC or other currents' strengths, the generation of Rossby/Kevin waves, could influence the MWFRs for many years, regardless of the local mixed layer depth in the MWFR itself. These findings are similar to the results of [PERSON] et al. (2019), who find the heat content of water that subducts from the MWFR is strongly controlled by the sub-tropical gyre strength and structure, which is in turn strongly related to wind-stress over the gyre for the previous 3-4 years.
The integrated sensitivities show remarkable similarity between the basins, despite the different locations and relative sizes of the MWFRs in each basin. The Atlantic MWFR is relatively far north, where it is strongly influenced by the wind-driven Atlantic sub-tropical gyre, which may be why wind stress influences are relatively strongest here. The Pacific and Indian MWFRs are both further south within the ACC, and have relatively lower sensitivity to wind stress compared with heat flux. In the following section, we investigate the influence of the varying MWFR volumes on the magnitude of the sensitivities.
### Analysis of Links Between Sensitivities and Mixed Layer Depths
The time dependence of the sensitivity to heat fluxes suggests a process very much dominated by mixed layer depths--the sensitivity is largest in the winter when mixed layers are deepest, and the relative importance of past years decreases in time as information from previous winters is lost, with sensitivities at two years lag around half of that at zero years. This is consistent with the fields in Figures 4 (upper row) and S4 that show \(Q_{\text{net}}\) sensitivities confined to the objective function region (where the mixed layers are deepest) and upstream. The slower decay and relatively weaker seasonal cycle in the wind stress sensitivities also point to the influence of remote processes which are not strongly correlated to local mixed layer depths, and have stronger influences at larger lags.
The link between heat flux sensitivities and mixed-layer depths is further explained by correlations between peak sensitivities and objective function volumes. In each adjoint simulation, the peak in basin-mean absolute \(dJ/dQ_{\text{net}}\) occurs in July in the lag zero year (see Figure 5), that is, at the beginning of the objective function integration time period (see Equation 3). The magnitude of the peak in each ensemble member is strongly anti-correlated with the objective function volume \(V_{g}^{F}\), with \(R^{2}\) values given in Table 2. Years with relatively low objective function volumes show relatively large peaks in basin-mean absolute \(Q_{\text{net}}\) sensitivity, and vice-versa. These anti-correlations are significant at the 99% level, with \(R^{2}=0.92\)-0.96 across the three basins (see Table 2). This implies that interannual variability in peak sensitivities is almost entirely determined by the volume of the objective function, with larger volumes showing a weaker sensitivity to surface heat fluxes, and vice versa. Given that, at their peak, \(Q_{\text{net}}\) sensitivities are located directly over the objective function regions (see Figures 4 and S4), this is not surprising for a given perturbation in surface heat flux, the amount by which a given well-mixed pool will warm will be inversely proportional to the volume of that pool.
There are weaker correlations between peak wind stress sensitivities and objective function volumes, as implied by the weaker seasonal cycles in basin-mean sensitivities. This correlation varies between the three basins--the correlations are strong in the Indian basin, weaker in the Pacific, and only statistically significant when involving meridional wind stress in the Atlantic (Table 2). All correlations are strongest in the Indian basin, with \(R^{2}=0.86\) for correlations between objective function volume and peak basin-mean absolute zonal wind stress sensitivity, and \(R^{2}=0.69\) for meridional wind stress sensitivity. Each of the peak sensitivities to the Indian MWFR heat content are also strongly correlated with each other (not shown), showing that the objective function volume is a strong control on the magnitude of all three absolute sensitivities to the Indian MWFR. This could be because the Indian basin has the largest volume of the three MWFRs, with a peak climatological heat content over twice that of the Atlantic or Pacific, see Figure A1.
These correlations imply that \(Q_{\text{net}}\) sensitivities are strongly controlled by changes in objective function volume, which is largely controlled by changing mixed layer depths. The controls on the magnitude of the wind stress sensitivities are not as clear, with the objective function volume a strong control on the absolute magnitude in the Indian basin, but weaker or not significantly correlated in the Pacific and Atlantic. This implies that there are other factors, such as the local density structure, that may be playing an important role in setting the magnitude of the wind stress sensitivities in these basins.
## 4 Sensitivities to Kinematic and Dynamic Potential Temperature Changes
### Defining Kinematic and Dynamic Sensitivities
As in [PERSON] et al. (1999) and [PERSON] et al. (2018), we analyzed the sensitivities of the objective function to potential temperature by splitting it into sensitivities due to changes in temperature along isopycnals (referred to as kinematic changes) and changes in temperature that result in density changes (referred to as dynamic changes). As discussed in [PERSON] et al. (1999), this is similar to the decomposition of temperature changes over time into \"spice\" and \"heave\" components ([PERSON] & [PERSON], 1994).
The dynamic sensitivity can be written:[PERSON] & [PERSON], 2011). Note that, unlike the sensitivities to surface fields, each dynamic/kinematic sensitivity snapshot is a three-dimensional field that also depends on depth.
### Kinematic and Dynamic Sensitivity Results
We calculated ensemble mean dynamic and kinematic sensitivities for the same experiments as previously discussed, where the objective function is the heat content of MWFRs. The sensitivities were scaled by \(1/\rho\omega_{P}\) and so are unitless, that is, the amount by which the objective function would increase in \({}^{\circ}C\) for a dynamic/kinematic rise in potential temperature of 1\({}^{\circ}C\). The kinematic sensitivities peak at an average depth of 410 m, and the dynamic sensitivities peak at an average depth of 3 km (not shown), indicating the effectiveness of density changes on the ocean floor for altering pressure gradients (ECCov4 has a mean depth of 3.8 km in the SO). We choose to plot both quantities at 410 m (Figure 6) as both sensitivities peak close to this depth when scaled by the relevant potential temperature anomalies from climatology (not shown).
Dynamic sensitivities at all depths within the upper \(\sim\)500 m show a similar structure, with the features seen in Figure 6a (from 410 m depth) moving further away/towards the MWFR regions at longer/shorter lags. Positive dynamic sensitivity indicates that decreasing the density (deepening the density surfaces) at this point would result in an increase in the MWFR heat content, and conversely negative dynamic sensitivity indicates increasing the density (raising the density surfaces) would result in an increase in the MWFR heat content. Within the objective function volume (indicated by the black contours) the sensitivity is largely positive, implying downwelling will produce an increase in the MWFR heat content.
As can be seen with comparison with Figure 6b, much of the strong dynamic sensitivity is placed along the same location as source waters, indicated by strong kinematic sensitivities, but they also stretch further south across the ACC. In the Indian sector, as in the Pacific sector, there are dynamic sensitivities of both signs, both over source regions and extended around these regions. These can be interpreted as highlighting that changes in the strength and structure of the ACC and sub-typical gyres can draw more or less heat into the mixed layer, although, as previously discussed, any such link would need to be confirmed in a forward run.
In general, dynamic sensitivities for all three sectors are a mix of positive and negative regions, with strong links to continental boundaries. Viewed as animations, one can see that there are many dynamical features that are generated at continental boundaries and then propagate along or away from these boundaries. This can be seen clearly in the Movies S2, S4, and S6, with the main features being:
1. **Atlantic**: A strong dipole directly over the objective function region pattern (as seen in Figure 6a), which rotates in place over time in an anti-clockwise or cyclonic direction, consistent with the westward motion of sensitivity peaks centered at \(\sim\)30\({}^{\circ}\)S and the eastward motion of sensitivity peaks at \(\sim\)40\({}^{\circ}\)S
2. **Pacific**: A strong dipole that is initially centered to the east of New Zealand for 0-1 year lag, which then moves to be centered on for New Zealand at 1-5 years lag (as seen in Figure 6a). A patch of negative
\begin{table}
\begin{tabular}{l c c c} \hline \multicolumn{4}{c}{Sensitivity} \\ \cline{2-4} Basin & \(d\)/\(d\omega_{\text{sat}}\) & \(d\)/\(d\omega_{x}\) & \(d\)/\(d\omega_{x}\) \\ \hline Atlantic & **0.92 (0.75-0.98)** & 0.15 (0.00–0.60) & **0.65 (0.21–0.88)** \\ Pacific & **0.94 (0.80-0.98)** & **0.30 (0.00–0.71)** & **0.52 (0.08–0.83)** \\ Indian & **0.96 (0.87-0.99)** & **0.86 (0.58–0.96)** & **0.69 (0.27–0.90)** \\ Global & **0.94 (0.81–0.98)** & **0.52 (0.08–0.83)** & **0.33 (0.00–0.73)** \\ \hline \end{tabular} _Note:_ Values shown are \(R^{2}\) (squared Pearson correlation coefficient) with 95% bounds, bold if significant.
\end{table}
Table 2: _Strength of Anti-correlations Between Peak Basin-Mean Absolute Sensitivities (\(\langle d\lambda t/d\lambda t\rangle\)) and Objective Function Volume (\(V_{p}^{T}\))._sensitivity sits upstream along barotropic streamlines. Relatively weaker wave trains are seen to the south of the ACC traveling eastwards, and from the south-west coast of South America traveling westwards
3. **Indian**: For 0-2 years lag, sensitivities are strongest in positive patches along the north of the objective function boundary, in negative patches along the east of South Africa and Australia, and in a wave train traveling eastwards that propagates from below South Africa and then continues just south of the objective function's southern boundary. At longer lags, this wave train can be seen to originate from the eastern boundary of South America, and other westward traveling wave trains can be seen in the Indian and Eastern Pacific oceans at \(\sim\)20\({}^{\circ}\)S to 30\({}^{\circ}\)S
The mean kinematic sensitivities at 4 years lag and 410 m depth, by contrast, are largely single signed (Figure 6b), and sensitivities at shallower depths and at longer/shorter lags are very similar but extend further/ less far upstream (see Movies S1, S3, and S5). The Indian and Pacific pools, being close to the northern ACC boundary, are affected by kinematic temperature changes upstream in the ACC, stretching around half its path at 4 years lag. The Indian MWFR is most strongly linked with the Agulhas and Agulhas Return Current regions, as well as more weakly with the East Australian Current region. The Pacific MWFR also shows the strongest links with New Zealand boundary current region. Conversely, the Atlantic pool is shallower (the maximum depth of the median Atlantic MWFR is 480 m, compared with 810 and 910 m for the Pacific and Indian MWFRs, respectively) and further north, more firmly in the sub-tropical gyre, and as such is highly sensitive to local gyre kinematic temperature changes rather than changes in the ACC.
As kinematic temperature changes take place on isopycnals, the sensitivities strongly resemble a passive tracer sensitivity and so reflect the influences of direct heat fluxes or irreversible mixing. In fact, one can directly calculate passive tracer sensitivities in the adjoint model, and they are highly correlated with the kinematic sensitivities at the depths of the objective function (see Figure S10 in supporting information). Thus, kinematic sensitivities reveal approximate source water pathways, and as we consider longer timescales, kinematic sensitivities weaken and are found further away.
Figure 6.— Example dynamic and kinematic sensitivities highlight their different properties: Sensitivities to (a) dynamic and (b) kinematic potential temperature changes at a fixed depth of 410 m, fixed lag of 4 years, in all three basins (top to bottom). The black contour indicates the median location of the objective function at each depth, and as previously, the contours indicate the \(-17\), 0, and 30 y mean barotropic streamlines. The associated ensemble standard deviations can be found in the supporting information. Sensitivities are scaled by \(1/\rho\kappa_{\rm p}\) and are untless.
### Time Evolution of Domain-Integrated Kinematic and Dynamic Sensitivities
Similarly to Section 3.3, we calculated the domain-integrated absolute dynamic (\(\langle\langle\left|Dy\right|\rangle\)) and kinematic (\(\langle\langle\left|KI\right|\rangle\)) sensitivities for each basin. We split the integrals into the upper 1000 and 1000 m+ (depths below 1000 m). The summed values are scaled by the maximum \(J_{s}^{y}\) for the basin, as well as the total thickness of the integral, to allow for comparison. As with Figure 5, this demonstrates when and where potential temperature changes are most likely to result in changes in the objective function. All three basins show very similar structures, see Figure 7, with the differences being mainly in the timing of the peaks of the various integrals and the degree of variability between ensemble members.
There is relatively more inter-ensemble variability in the Atlantic sensitivities than for the other basins, with several ensemble members showing peaks in upper 1000 m \(\langle\left|Dy\right|\rangle\) at \(\sim\)1 year's lag, as seen by the shaded ensemble envelope, whereas the ensemble mean peaks at \(\sim\)3 years's lag (Figure 7). This increased variability implies a relatively greater state dependence in the Atlantic than the other basins.
The summed absolute dynamic sensitivities are generally an order of magnitude higher than the summed absolute kinematic sensitivities, largely due to the dynamic sensitivities spreading further in space (see Figure 6a and Movies S2, S4, and S6). The magnitude of the thickness-scaled \(\langle\left|Dy\right|\rangle\) is similar in the upper and lower depth ranges, indicating dynamic pathways within the regions of strongest currents (in the upper 1000 m), are as strong as those at the depths of bottom topography (at 1000 m+). These topographic-depth dynamic pathways with the Pacific and Indian MWFRs are still growing in magnitude at 8 years lag.
The upper 1000 m \(\langle\left|KI\right|\rangle\) dominate over the 1000 m+ at all lags, peaking at 0 years and decaying with increased lag, with a slight seasonal cycle apparent. The faster decay in the first few years coincides with the peak sensitivities moving out of the MWFRs and upstream (see Figure 6 and Movies S1, S3, and S5), consistent with passive-tracer-like behavior (see Figure S10).
## 5 Perturbation Experiments
As discussed in Section 1, we consider adjoint sensitivities to be a useful tool for discovering which regions and timescales are of interest, which can then be explored using fully non-linear perturbation experiments. In this section, we describe how we used the adjoint sensitivities from Section 3 in order to choose the locations for a series of surface forcing perturbation experiments. These perturbation experiments allowed us to directly investigate the full response of our objective functions, including assessing the degree of linearity in the responses, that is, the impact of both the dynamics not captured in the adjoint model and its inherent degree of inexactness.
In the results below, we followed ([PERSON] et al., 2014) and used the combination of oppositely signed perturbation experiments to calculate the linear and non-linear responses. This allowed for qualitative and quantitative analysis of the two different types of effect, and allowed us to test our assumption that the non-linear component of our objective function is small compared with the linear. Further details of the derivation of the linear and non-linear responses can be found in A3. We applied perturbations in the surface heat flux and the zonal wind stress fields in regions where sensitivities to at least one field were relatively high.
We calculated the integrated heat content of the objective function regions for all perturbation experiments over the fixed maximum winter MLD, following the definition of the objective function \(J_{b}^{Y}\):
\[\mathrm{fix}H_{b}^{Y}(\theta,\mathrm{MLD},t)=[\int_{t_{0}}^{t_{ \mathrm{g}}(x,y)}\int_{z=0}^{\mathrm{max(MLD_{\mathrm{ASO}})}}\rho_{b}c_{p} \theta(r,t)dxdy\;dz, \tag{6}\]
and thus, the change in heat content with respect to the control simulation (the standard ECCOv4 r2 solution)
\[\Delta\mathrm{fix}H_{b}^{Y}(t)=\mathrm{fix}H_{b}^{Y}(\theta- \theta,\mathrm{max(MLD_{\mathrm{ASO}})},t), \tag{7}\]where \(\theta^{\prime}\) is the perturbed simulation potential temperature field and \(\theta\) is that from the control simulation. The MLD was taken from the control simulation and was therefore the same depth as used in the objective function for the adjoint sensitivity experiments. We also calculated the heat content of the mode water formation regions using the objective function mask for that year, \(f_{b}(x,y)\), but the time-varying _instantaneous_ mixed layer depth in each of the simulations:
\[\mathrm{var}H_{b}^{Y}(\theta,\mathrm{MLD},t)=\left[\hat{I}^{B_{b}(x,y)}\right] _{z=0}^{\mathrm{MLD}(t)}\rho_{b}c_{p}\theta(t,t)dudydz, \tag{8}\]
and thus the change in the varying-volume heat content
\[\Delta\mathrm{var}H_{b}^{Y}(t)=\mathrm{var}H_{b}^{Y}(\theta^{\prime},\mathrm{ MLD}^{\prime},t)-\mathrm{var}H_{b}^{Y}(\theta,\mathrm{MLD},t), \tag{9}\]
Figure 7: Domain-integrated absolute dynamic sensitivities dominate over domain-integrated absolute kinematic sensitivities, which both grow with time at depth: Domain-integrated absolute dynamic \(\theta\) sensitivities (left), and domain-integrated kinematic \(\theta\) sensitivities (right) split by basin (top to bottom, as labeled). Colors indicate the contributions from the upper 1000 m (blue lines), and the depths below 1000 m (red lines). The shaded region indicates the envelope of individual ensembles, and thick lines the ensemble mean. All sensitivities have been scaled by the maximum \(J_{k}^{y}\) for that basin and the overall depth of the integral in km, so have a dimension of \({}^{e}\)C\({}^{-1}\)\(km^{-1}\).
where the MLDs were taken instantaneously from the perturbed or control simulations as appropriate. To differentiate between the two volumes, the fixed-volume of the objective function and the instantaneously calculated, varying volume mode water formation region, we refer to them henceforth as the fix-MWFR and var-MWFR, respectively.
### Qnet Pacific Perturbation
For our first perturbation experiment, we chose a region in the South-East Pacific identified in other studies as important for downstream SAMW properties ([PERSON] et al., 2009), and additionally which shows an interesting pattern of heat flux sensitivity. At two years lag, the Atlantic MWFR heat content has a region of positive sensitivity in this region of the South-East Pacific, just upstream of Drake Passage (see Figure 8a upper panel). This implies that positive heat flux perturbations in this region, that is, increasing heat loss to the atmosphere, will result in a warmer MWFR in the Atlantic in two years time (as previously stated, Qnet is defined as positive out of the ocean). Notably there is negative sensitivity over the region of the objective function, so increasing heat loss directly over the Atlantic MWFR would result in a _cooler_ MWFR in two years time.
We designed a set of four perturbation experiments to test the sensitivity of the forward nonlinear model to changes in net heat flux in this key region. The black dashed contours in Figure 8a show the region over which the Qnet perturbations were applied, in four separate step changes with magnitudes of \(\pm 100\) Wm\({}^{-2}\) and \(\pm 100\) Wm\({}^{-2}\), constant over the box indicated. These perturbations were applied to the forward non-linear ECCOV4 r2 model at the beginning of the model run. Additionally to the changes in Qnet, there were results-ant changes in the fresh water flux E-P-R, which we do not show because, as demonstrated in Section 3, the sensitivities to this flux are extremely low. Thus the resultant experiment is close to being a test of the influence of Qnet independent of other surface fluxes. The perturbation region has a mean Qnet of 20 W/m\({}^{2}\) and a seasonal cycle of amplitude 120 W/m\({}^{2}\) in ECCOV4 r2, and so the \(\pm 10\) Wm\({}^{-2}\) perturbations are of similar magnitude to the mean, whereas the \(\pm 100\) Wm\({}^{-2}\) perturbations completely alter the entire seasonal cycle, shifting the region to entirely positive values year-round, or else largely negative.
The perturbation region sits over the Pacific MWFR (see Figure 8a, middle panel), where the sensitivity of the Pacific MWFR heat content is large and negative at all lead times investigated, showing that increasing the heat flux from ocean to atmosphere is an efficient way of cooling this region. At five years lag, the Indian MWFR heat content shows weak positive sensitivity to Qnet in the perturbation region (Figure 8a, lower panel). Thus, for a positively signed Qnet perturbation in the region indicated, we expect the Atlantic objective function to show an increase in heat content after roughly two years, we expect a decrease in heat content in the Pacific objective function within the first year, and after roughly five years we expect an increase in heat content in the Indian objective function. We expect all these changes to scale linearly with forcing magnitude. The exact adjoint predictions for each year up to 1999 can be calculated by convolving the ensemble mean net heat flux sensitivities with the perturbation, then integrating over time:
\[J_{b}^{r^{\prime}}=\int_{Y}^{2000}\int|\Delta X,\frac{\partial J_{b}^{r}}{ \partial X}dudy\,dt, \tag{10}\]
where \(J_{b}^{r^{\prime}}\) is the adjoint prediction of \(J_{b}^{r}\), \(\Delta X\) is the applied time-constant perturbation in the surface forcing field \(X\), and \(\partial J_{b}^{r}\)\(/\)\(\partial X\) can either be the individual ensemble member sensitivity from a given year Y, or the ensemble mean sensitivity at a given lag (in which case the time integral limits become relative to the beginning of each member simulation, rather than a specific year). The ensemble mean predictions for each of the first eight years (the length of our ensembles) and their standard deviations for each basin can be seen in the thick light blue solid and dashed lines in Figure 8, where the lines span July-November, the objective function period. The prediction for 1999, calculated only using the 1999 ensemble member, is shown similarly in green.
We combined the results of the positively and negatively signed experiments to produce the linear and non-linear impacts for the \(\pm 10\) Wm\({}^{-2}\) and \(\pm 100\) Wm\({}^{-2}\) perturbations. We chose the combinations such that the sign of the linear/non-linear changes indicate the changes for the positively signed \(Q_{\rm net}\) perturbations. Note that the heat content changes are discontinuous at the year boundaries due to the changing objective function definition for each year, as the objective function is based on the PV and MLD properties for each individual year, as discussed in Section 2. The magnitude of the changes can be significantly larger for the varying-volume heat contents than the fixed-volumes as the changes in the volume (dependent on the temperature scale used) because changes in the instantaneous MLD result in much larger heat content changes than potential temperature changes alone (see Figures 8b and 8c, noting the different \(y\)-axis scales.)
One would expect the normalized linear response to be identical for both magnitudes, by definition, and this is largely true, especially for the fixed-volume heat content (see Figure 8b, thick lines, which lie mostly on top of each other). There are small differences at the peaks of the varying-volume responses, likely due to the fact that the bulk formula will have introduced some non-linear changes to the perturbations that will have resulted in the positive- and negative-signed experiments not being exactly symmetric. The non-linear effects (Figures 8b and 8c, thin lines) are smaller in general than the linear effects, but increase in the \(\pm 100\) Wm\({}^{-2}\) case (red lines), as would be expected, becoming almost as large as the linear changes, especially in the Atlantic.
A positive response is seen in the Atlantic (Figures 8b and 8c, upper panels), with both the fix-MWFR and var-MWFR showing linear increases in heat content, starting after roughly two years. The fix-MWFR response lies within one standard deviation of the ensemble mean prediction for five years out of the first eight (light blue lines), and the exact prediction for 1999 lies very close to the measured response (green line). The heat content of the var-MWFR (Figure 8c) shows large spikes every winter as
Figure 8.— The adjoint sensitivities accurately predict the scaled linear response of the fix-MWFRs heat content: (a) Ensemble mean sensitivities of mode water heat content to \(Q_{\rm net}\) in various basins at lags as labeled. Thick gray contours indicated median location of objective functions, black dashed contour indicates location of \(Q_{\rm net}\) perturbation (see text for details), gray contours, as before, indicate \(-17\), \(0\), and \(30\) Sv mean SSH contours. (b and c) Results of Pacific \(Q_{\rm net}\) perturbation experiment, normalized linear (thick lines) and non-linear (thin lines) heat content changes divided by the perturbation magnitude, for either the fix-MWFR (b) or the var-MWFR (c), and for the \(\pm 10^{\rm o}\)W m\({}^{-2}\) (dark blue) or \(\pm 100^{\rm o}\)W m\({}^{-2}\) (red) experiments. Adjoint predictions for the objective function time periods are shown by thick lines in green (1999 only) and solid and dotted light blue (ensemble mean and standard deviations).
the mixed layer deepens, but largely agrees with the sign of the heat content change of the fix-MWFR (Figure 7(b)).
In the Pacific, at all lags a negative response was expected (Figure 7(b) middle panel light blue lines), and this is borne out in the fix-MWFR heat content changes (thick red and dark blue lines), which lie within one standard deviation of the ensemble mean prediction for three of the first eight years. However, the sign of the linear change in the var-MWFR (Figure 7(c) middle panel, bold lines) is opposite to that of the fix-MWFR: when the heat flux to the atmosphere increases, as in the +10 and +100 Wm\({}^{-2}\) experiments, the temperature in the fix-MWFR decreases and so does the heat content, but the heat content of the var-MWFR _increases_. This is because the cooler mixed layer deepens, resulting in more net heat content, as can be seen in Figure 9.
The responses in the Indian region (Figure 7(b) lower panel) are consistent with simple advection downstream--it takes over three years for the effect of the perturbation to reach the Indian region, and it remains much lower magnitude than the Pacific impact. After this, the impact grows year on year, and similarly to the Pacific basin has an opposite-signed linear effect on the fix-MWFR and the var-MWFR. The linear fix-MWFR changes (thick red and dark blue lines) lie within one standard deviation of the ensemble mean predictions (light blue lines) for three of the first eight years. Like the Atlantic, an increase in heat loss to the atmosphere results in an overall warming of the fix-MWFR, and vice-versa. The opposite sign of the response of the fixed and varying volume heat contents is for the same reason as in the Pacific, namely that a warming mixed layer shallows and so decreases its overall heat content when the volume considered is allowed to evolve.
The adjoint predictions lie within one standard deviation from the ensemble mean prediction for just less than half of the winter MWFRs, fewer than would be expected if the ensembles follow a normal distribution. There are a number of possible explanations, including the fact that the years 1992-1998 are not included in our ensemble mean sensitivities, and so can be expected to have slightly different variance. It could also be that the ensemble members do not follow a normal distribution. Whilst the ensemble mean sensitivities did not always predict the correct magnitude, the fix-MWFRs did indeed warm or cool as expected. However, this led to changes in MLD that acted counter to the temperature change and resulted in a larger mixed layer heat content when the mixed layer cooled and a lower mixed layer heat content when the mixed layer warmer (Figure 9). Whilst the temperature change was very linear, the change in MLD had a significant non-linear component, although the linear component is still largest in all but the Atlantic response to the \(\pm 100\) Wm\({}^{-2}\) perturbations (Figure 7(c)). This is not surprising as the temperature response is strongly linked with the imposed linear \(Q_{\rm net}\) changes, whereas the mixed layer response is, as the name suggests, mediated by mixing, which can be non-linear in the case of convective mixing.
### \(\tau_{\rm F}\) Pacific Perturbation
We now consider a regional experiment perturbing the zonal wind stress, \(\tau_{\rm F}\). In winter and at three years lag, a clear dipole in the ensemble mean sensitivity of the Pacific MWFR heat content to \(\tau_{\rm F}\) can be seen stretching east from New Zealand well into the Pacific (Figure 9(a), middle panel). This indicates that a zonal wind stress dipole of this sort, implying downwelling along the dipole center, would produce an increase in the heat content of the objective function region (median location indicated by the solid black contours). A perturbation closely matching this dipole was chosen to test this sensitivity (Figure 9(a), dashed black contours) which was applied either imitating the Pacific MWFR heat content sensitivity, with two oppositely signed regions of magnitudes \(\pm 0.1\) Nm\({}^{-2}\), or with the signs of the two regions reversed. These two perturbations were applied separately as step changes to the forward non-linear ECC0v4 z model at the beginning of the model run (the start of 1992). The mean dipole amplitude in ECC0v4 is \(-0.04\) Nm\({}^{-2}\) with a standard deviation of \(0.03\) Nm\({}^{-2}\) in the control run.
Additional to the changes in \(\tau_{\rm F}\), there were resultant changes in the net heat flux \(Q_{\rm net}\) due to the bulk formula (not shown). Thus, these experiments are not an exact test of the linear response to the wind-stress perturbations applied, but can nonetheless provide interesting insights into how the linear and non-linear responses compare.
Consistent with the adjoint sensitivity, the linear fix-MWFR heat content in the Pacific sector responded with an increase (decrease) in heat content over time for the positively (negatively) signed perturbation experiment (Figure 10b, thick lines, middle row). The response lies within one standard deviation of the ensemble mean prediction (calculated as in Section 5.1) for six out of the first eight years (very thick and dotted lines). The Indian and Atlantic fix-MWFR heat contents responses are more non-linear than the Pacific, with an especially asymmetric response in the Indian sector, although it becomes more symmetric after 1998.
Note the Atlantic responses are two orders of magnitude lower than climatology (see Figure A1), reflecting its low sensitivity to the perturbation region (Figure 10a, upper row). The Atlantic fix-MWFR responses are of the opposite sign to that predicted by the ensemble mean sensitivities (very thick and dotted lines), demonstrating that the adjoint sensitivities are not appropriate when applying such relatively large perturbations to regions of low sensitivity, when the linear approximation may well be inaccurate.
The \(\Delta\)var\(H\) response (Figure 10b, thin lines), calculated as before from the lateral extent of the objective functions but integrated in depth to the instantaneous MLD, are largely of the same sign as the \(\Delta\)fix\(H\) responses in all basins. This is due to large non-linear changes in mixed layer depths in the Pacific and Indian MWFRs (not shown), perhaps related to non-linear \(Q_{\text{net}}\) forcings via the bulk formula or indicative of
Figure 9: Linear changes in mixed layer depth act counter to linear changes in temperature, leading to opposite changes in heat content of the fix- and var- mode water formation regions (MWFRs): Latitude-depth snapshots of potential temperature changes (color) in the Pacific basin from the Pacific \(Q_{\text{net}}\) perturbation experiment in June 1996. \(Q_{\text{net}}\) is, as before, defined as positive from ocean to atmosphere. As labeled, the different panels show the difference from the control run for both positive and negative perturbations, and the combination of these to produce the linear and non-linear changes. The black solid lines show the control run instantaneous mixed layer depth (MLD) and the magenta lines show the 1996 objective function volume (the same in every panel). The black dashed lines show the instantaneous MLD for the perturbation experiments as labeled.
dynamic processes playing a part in setting the mixed layer depths. In both experiments, there is a seasonal decrease in the Pacific var-MWFR heat content during winter, largely due to non-uniform temperature changes and MLD decreases in the Western lobe of the MWFR.
The results in the Atlantic confirm that perturbing regions with low adjoint sensitivity produces weak linear responses in the forward non-linear model (when compared with regions of significant sensitivity). The relatively poor match to the ensemble mean adjoint predictions is likely due to the inexactness of the adjoint (discussed in Section 6.3), exacerbated by the relatively large perturbation, becoming more apparent when the predicted response is so low, that is, the signal is the same size as the noise.
The results in the Pacific and Indian show that, again, the adjoint sensitivities can accurately predict the linear response of the fix-MWFRs, with a relatively low non-linear response, especially at longer timescales. However, the response of the var-MWFR is highly non-linear, and, in the Pacific, varies spatially within the MWFR. This is consistent with [PERSON] et al., (2019) who find the East and West Pacific SAMW pools respond differently to forcings.
## 6 Summary of Results
We have identified locations with properties of winter mode water formation pools within the mixed layer of an observationally constrained model of the SO ([PERSON], [PERSON], et al., 2015). Using an adjoint model, we have determined the sensitivity of the fixed-volume heat contents of these mode water formation re
Figure 10: (a) Ensemble mean sensitivities of mode water heat content to \(\tau_{\rm z}\) in various basins in winter at 3 years lag as labeled. Black contours indicated median location of objective functions, black dashed contour indicates location of \(\tau_{\rm z}\) perturbation (with the positive-signed perturbation matching the sign of the Pacific basin sensitivity shown here), gray contours, as before, indicate \(-17.0\), and \(30\) Sv mean SSH contours. (b) Results of Pacific \(\tau_{\rm z}\) perturbation experiment. Heat content changes from positively (blue lines) and negatively (red lines)/signed perturbation experiments, for either the fix-MWFR (thick lines) or the var-MWFR (thin lines). Adjoint predictions for the objective function time periods are shown by very thick lines either dashed (1999 only), or solid and dotted (ensemble mean and standard deviations).
gions (MWFRs) to surface forcings, changes of potential temperature at constant density, and changes of potential temperature that lead to changes in density, in an ensemble of 13 eight year simulations. These determine the sensitivity of the winter heat content of the MWFRs in the years 1999-2011 to the properties mentioned in previous years. We have highlighted the key aspects of the sensitivities here.
### Summary: Sensitivities to Surface Net Heat Flux and Wind Stress
Analysis of the sensitivity fields revealed that, on the eight year time scale investigated using the ECCO adjoint model, the heat content of the MWFRs is significantly affected by surface net heat fluxes and wind stress, but much less by fresh water fluxes (discussed further on). The heat content of the MWFRs in all three basins was found to be most sensitive to local (within the MWFR), same winter changes to surface heat fluxes, and to both local and remote wind stress changes, which were found to be of comparable integrated magnitude and significant at all lead times.
Heat flux sensitivities have a strong seasonal cycle, with the largest sensitivities occurring during previous winters, with peak values strongly controlled by the objective function volume. This implies that surface heat fluxes are most effective at changing the heat content of MWFRs during winter, when the heat content throughout the deepened mixed layers can be influenced, but that smaller MWFRs allow for greater changes in heat content for a given change in surface heat flux. The mixed layer has a \"memory\" that allows for changes in one year to affect heat content the next year, indicated by the significant sensitivities in previous winters, although there is a clear decay with time that indicates the influence drops year by year, with the winter peaks in summed absolute sensitivity falling to 10%-15% of the maximum by 8 years lag. The decay of \(Q_{\text{max}}\) sensitivity with time is likely linked to the location of peak sensitivity moving upstream with increased lag (see Figure 4), where the influence is diluted. This, when combined with local rates of transformation, subduction, and advection results in an overall weakening in integrated sensitivity. These findings extends the role of SAMW formation preconditioning discussed in [PERSON] et al. (2010) beyond a single season to over several years. It also aligns well with recent results looking at SAMW variability in the Pacific ([PERSON] et al., 2019; [PERSON] et al., 2019) who find that while inter-annual variability in SAMW properties is largely the result of local forcing, preconditioning from upstream waters also influences properties on lags of 1-2 years (not unlike in [PERSON] et al., 2016).
Wind stress sensitivities revealed dipole patterns, and showed a less pronounced decay in magnitude with time and a less pronounced seasonal dependence, as compared with the heat flux sensitivities. Zonal wind stress sensitivities extend significantly farther south than for other properties, indicating a possible link with ACC dynamics. This is consistent with the findings of [PERSON] and England (2002), who find that Ekman transport across the South Antarctic Front (SAF) south of Australia (at roughly 50\(\lx@math@degree\)5) can drive the variability in \(T\) and \(S\) properties of SAMW in this region, rather than the variation of surface fluxes. Whilst the volume of the MWFRs shows some influence on the inter-annual variation in peak absolute sensitivities (especially in the Indian basin), the lack of a stronger link is consistent with the fact that wind stresses can influence the heat content of MWFRs through a range of dynamical mechanisms (such as horizontal advection, Ekman pumping/suction, heave of isopycnals) which are not clearly controlled by the volume of the MWFR alone.
### Summary: Sensitivities to Dynamic and Kinematic Potential Temperature Changes
The analysis of sensitivities to surface forcings was supplemented by analysis of the sensitivity of the heat content of MWFRs to potential temperature changes, split into kinematic (at constant density) and dynamic (involving changes in density) components. A summary of the results is provided in Figure 11. Kinematic sensitivities were, for the most part, single-signed and resemble passive tracer sensitivities and thus were largest in direct source regions for the MWFRs, with boundary currents mostly dominating over ACC sources. Dynamic sensitivities showed both signs and indicated the effects of raising/lowering density surfaces.
The largest sensitivities in both cases were over source regions as well as in boundary current regions, across the Southern ACC, and in the sub-tropical gyres. Our results suggest a rich range of possible dynamic pathways can influence the heat content of the MWFRs, which extends widely the regions where accurate observations may be required to faithfully model mode water formation regions beyond the local in space and time. When summed over the entire domain and over depth, then scaled by depth range, the dynamic pathways at topographic depths (1000 m+) were of the same magnitude as those at the depths of strongest currents (upper 1000 m). Whilst the sensitivities at the ocean floor are unlikely to be important for observations, due to the relatively weak changes in density at these depths, they may be of relevance for models, showing that small errors in bottom properties could have as much as an impact on the properties of mode water as discrepancies in source regions.
### Summary: Perturbation Experiment Results
Guided by the sensitivity fields, and by previous studies that highlighted regions of relevance for mode water properties, we designed two perturbation experiments using the full forward non-linear model.
These results confirmed that the adjoint sensitivities can successfully predict where and when changes in surface forcings will produce a linear impact on the objective function. In some regions, the sensitivities predicted the overall impact, even for relatively large perturbations, because the non-linear impacts were relatively small. The adjoint sensitivities were accurate at locating regions of high and low linear sensitivity. Additionally, low adjoint sensitivities resulted in low non-linear sensitivities. However, it should be noted that whilst the linearity of the responses were verified, and we compared the responses with the ensemble mean predictions, we did not explicitly verify the exactness of the predictions for each year (see, for example appendix A of [PERSON] et al., 2020). Inexactness can arrive from the approximation to linearity in the adjoint model and the differences between the forward and adjoint models, for example, increasing viscosity in the latter for stability ([PERSON], [PERSON], & [PERSON], 2015).
As well as calculating the impact of the perturbations on the fixed-volume MWFRs (fix-MWFRs), we recalculated the volume of the MWFRs in the forward experiments. This allowed us to assess the role played by mixed layer depth variability on the MWFRs through time. These results showed, in some cases, that the varying-volume MWFRs (var-MWFRs) had opposite signed linear heat content changes to the fix-MWFRs. The sometimes significant differences between the fix- and var-MWFRs highlight an important limitation when interpreting the adjoint sensitivities here, computed for fixed volumes, not a water mass or layer which may dynamically alter its thickness in response to forcing.
The zonal wind stress perturbation experiment highlighted the influence of the bulk formula on the surface properties in the model. Whilst linear, opposite-signed perturbations in zonal wind stress were applied in the two experiments, these resulted in significant _non-linear_ anomalies in the surface heat flux, due to the
Figure 11: Schematic illustrating the main kinematic and dynamic sensitivities up to \(\sim\)5 years lag for all three basins: Indian (yellow), Pacific (cyan), and Atlantic (pink). As before, thick black contours show the median location of the mode water formation regions (MWFRs) and gray contours the \(-17,0,\) and \(30\) Sv mean barotropic streamlines. Arrows indicate paths of kinematic sensitivities, with thinner lines indicating paths only found at depth and dashed lines showing relatively weaker paths. The circles connected by lines indicate where dynamic sensitivities resemble dipoles, where a change in isopycnal gradient will affect the MWFRs (the exact location of the symbols is not meaningful). Groups of curves indicate where wave-like patterns are found.
reactions of the bulk formula. In particular, in perturbation experiments of both signs, there was a similar, large decrease in the ocean to atmosphere net heat flux.
### Discussion and Perspectives
It might be surprising to observationalists that there is a lack of strong sensitivities to wind stress or net heat flux south of the ACC (see, e.g., [PERSON] et al., 2013). There are a number of reasons why this might be, including that the ECCOv4 model fails to accurately represent the processes responsible for these links in observations, with, for example, too weak off-shelf transport rates ([PERSON] et al., 2019). Additionally, the influence of fresh water fluxes on mode waters has been observed in, for example, [PERSON] et al. (2019); [PERSON] et al. (2013), which is not reflected in our results. Salinity changes are likely to have a strong influence on the density and therefore volume of mode waters, but not directly on the temperature of our fixed volume MWFRs.
The adjoint model does not calculate entirely independent sensitivities of the surface forcings considered here (net ocean-to-atmosphere heat flux, wind stress and fresh water flux). The bulk formula couple these quantities together, such that the sensitivities of the net heat flux fields are not entirely independent of wind-driven mechanisms, which can significantly alter the magnitude and spatial patterns of the sensitivity fields ([PERSON] et al., 2019). The adjoint sensitivities in this study are thus only entirely independent of _non-linear_ feedbacks. This makes it harder to compare the results of the perturbation experiments with the adjoint sensitivities, although we expect the non-linear forward model to behave differently than the adjoint linear model. A related issue with ocean-only models is that the bulk formula do not always represent ocean-atmosphere feedbacks correctly (e.g., [PERSON] et al., 2018), but again the exact magnitude and time scales of this effect is beyond the scope of this work.
An additional way to understand the sensitivities is to convolve them with the contemporaneous anomalies of the surface fluxes from the climatological mean. Rather than showing when the model is most sensitive to changes in in the surface fluxes, this elucidates when and where linear changes to the objective function took place. We have included repeats of Figures 4 and 5 in the supporting information, both of which show similarities with the original figures and do not alter any of our findings.
Combining sensitivity fields with anomaly fields can additionally allow reconstructions of the objective function, in order to attribute the influences of various properties (see, e.g., [PERSON] et al., 2016). For example, if a particular year had an unusually large MWFR heat content compared with the climatological mean, one could attribute the linear contributions to this difference using the time varying adjoint sensitivities of surface properties convolved with the time varying anomalies of these properties.
The richness of the information contained within the adjoint sensitivities leads to a number of possible uses, many of which we are actively pursuing with collaborators. Most of these possibilities involve combining the adjoint sensitivities with other spatially varying fields. For example, convolving adjoint sensitivities to surface properties with two-dimensional, spatially varying, standard deviation fields highlights where variability is amplified by increased sensitivity. Some regions may instead show high adjoint sensitivity that is offset by low variability. Thus, these analyses highlight where observational campaigns could focus in order to accurately characterize the variability in a given surface forcing. Similarly, predicted changes in surface forcing under climate change scenarios may be expected to have greater impact if they occur over areas of high sensitivity, and the areas of high sensitivity themselves could change as the ocean state changes.
Although care must be taken when interpreting adjoint experiments, specifically considering which timescales and regions that can be expected to have relatively important non-linear effects, the results as presented here indicate the usefulness of adjoint models in producing a rich array of information about regions of interest. Of particular interest to the SO research community are the findings that mode water formation regions appear to be as sensitive to non-local, dynamically linked, wind stress changes on multi-year timescales as to local, kinematically linked, heat flux changes in the same winter. With regards to modeling, it is noteworthy that the adjoint sensitivities can accurately predict the linear behavior of perturbations to the heat content of fixed-volumes in the forward, non-linear model. The exciting range of uses of adjoint sensitivities such as these are just starting to be realized by the community.
## Appendix A Further Details and Derivations
### ECCO Mode Water Formation Region Climatology
Figure 11 shows the climatology of the Mode Water Formation Region heat content from all 20 years of ECCOv4r2 (1992-2011), as defined in Section 2. The Indian MWFR heat content is the largest, peaking at 2.0 \(\pm\) 0.2 \(\times\) 10\({}^{23}\) J in September, with the Pacific and Atlantic peaking at 0.9 \(\pm\) 0.1 \(\times\) 10\({}^{23}\) J and 0.8 \(\pm\) 0.1 \(\times\) 10\({}^{23}\) J, respectively.
### Mask Comparison
Figure 12 shows the domain-integrated absolute sensitivities to surface properties for 1999, comparing the total sensitivity of the 1999 MWFR heat contents as described in Section 2 (red lines) with the sensitivity of the July-November, 1999 maximum mixed layer depth for the whole of the SO (south of 30\({}^{\circ}\)S). Thus the difference between the two objective functions is the horizontal extent--the MWFRs are restricted to the areas determined by low PV values and deep mixed layers, whereas the whole SO mixed layer stretches across the domain in the horizontal.
The differences are most striking for the sensitivities to E-P-R, with the mixed layer sensitivities not showing the growth with increased lag that the MWFRs do, however both sensitivities remain extremely small relative to the others calculated. In general, for the net heat flux and wind stress sensitivities, the mixed layer sensitivities peak at a similar or higher value at zero lag, and then decay faster with lag than the MWFR heat content sensitivities. This is not surprising as the SO mixed layer in general has a large surface area and is only on the order of \(\sim\)100 m depth outside the MWFRs (see, e.g., Figure 2), and so it is expected that it will be most sensitive to recent forcings and quickly lose memory of the past. The absolute wind stress sensitivities in particular show far longer reaching behavior for the MWFRs, likely due to the presence of dipoles along the boundaries of the MWFRs.
This demonstrates that the choice to restrict our objective functions to just the MWFRs themselves produces sensitivities with a richer range of behavior and avoids over-focus on recent surface interactions.
### Linear and Non-linear Component Derivation
Given a function _f(x)_ that is infinitely differentiable at a point \(a\), the Taylor series is defined as:
\[f(x)=f(a)+(x-a)\frac{f^{*}(a)}{1!}+(x-a)^{2}\frac{f^{*}(a)}{2!}+(x-a)^{3}\frac{f ^{*\prime\prime}(a)}{3!}+ , \tag{10}\]
If we assume that a given objective function value \(J\) is a function of the model surface forcings, defined by a state vector \(\chi\), that is, \(J\equiv J(\chi)\), and we consider perturbations to this state vector as \(\Delta\chi\), then we can approximate the perturbed objective function as an expansion about the point \(\chi\) using 10, that is,
\[J(\chi+\Delta\chi)=J(\chi)+\Delta\chi J^{\prime}(\chi)+(\Delta\chi)^{2}\frac{ f^{*}(\chi)}{2}+ , \tag{11}\]where we can identify \(J^{\prime}(\chi)\) with the linear component (which is estimated by the adjoint sensitivities \(\partial J/\zeta\chi\)) and \(J^{\prime\prime}(\chi)\) with the non-linear component of \(J(\chi)\). Using A1 to similarly define \(J(\chi-\Delta\chi)\), we can combine this with A2 to find:
\[\frac{J(\chi+\Delta\chi)}{2}-\frac{J(\chi-\Delta\chi)}{2}\approx\Delta\chi J^{ \prime}(\chi),\] (A3)
\[\frac{J(\chi+\Delta\chi)}{2}+\frac{J(\chi-\Delta\chi)}{2}-J(\chi)\approx(\Delta \chi)^{2}\frac{J^{\prime\prime}(\chi)}{2},\] (A4)
assuming that \(J^{\prime\prime\prime}(\chi)\) and higher order terms \(\ll J(\chi),J^{\prime}(\chi)\). Thus, by carrying out the perturbation experiments with state vectors \(\chi\pm\Delta\chi\), we can estimate the linear and non-linear behavior of the objective function and test this assumption. We can similarly identify any model variable as a function of the model surface forcings, and use the same method to combine results from the control and perturbation experiments to approximate the linear and non-linear behavior of those model variables.
## Data Availability Statement
The ECC0v4-r2 model setup used in this work is available from [[http://doi.org/10.5281/zenodo.1211363](http://doi.org/10.5281/zenodo.1211363)]([http://doi.org/10.5281/zenodo.1211363](http://doi.org/10.5281/zenodo.1211363)) ([PERSON], 2018) as an instance of the MIT general circulation model (MITgcm, [[http://mitgcm.org/](http://mitgcm.org/)]([http://mitgcm.org/](http://mitgcm.org/))). Numerical model runs were carried out on ARCHER, the UK national HPC facility ([[http://archer.ac.uk/](http://archer.ac.uk/)]([http://archer.ac.uk/](http://archer.ac.uk/))). Adjoint code was generated using the TAF software tool, created and maintained by FastOpt GmbH ([[http://www.fastopt.com/](http://www.fastopt.com/)]([http://www.fastopt.com/](http://www.fastopt.com/))).
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wiley/ff005d4e_98e0_4de2_9bcc_6b64d492efb8.md | # IGR Solid Earth
Research Article
10.1029/2024 JB030290
Short-Period Mass Variations and the Next Generation Gravity Mission
[PERSON]
1 JILA, University of Colorado Boulder and NIST, Boulder, CO, USA, 2 University of Florida, Gainesville, FL, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA 3
[PERSON]
2 JILA, University of Colorado Boulder and NIST, Boulder, CO, USA, 2 University of Florida, Gainesville, FL, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA 3
[PERSON]
2 JILA, University of Colorado Boulder and NIST, Boulder, CO, USA, 2 University of Florida, Gainesville, FL, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA 3
###### Abstract
At the time that the 2017-2027 Decadal Survey for Earth Science and Applications from Space was released, there was a strong emphasis on reducing the possibility of a substantial gap between the GRACE Follow-On mission and a successor mission. This has led to the subsequent rapid development of a successor mission in partnership between NASA and DLR, GRACE-Continuity (GRACE-C), expected to launch in 2028, to continue the timeseries of Earth system mass change established by GRACE and GRACE-FO. In parallel, ESA continues development of a pair of satellites called Next Generation Gravity Mission (NGGM), targeted for an inclination between 65\({}^{\circ}\) and 75\({}^{\circ}\) to complement GRACE-C, launching in the early 2030s. NGGM offers the possibility for reduced noise in measuring short-period variations in the satellite separation using an improved accelerometer relative to what is flying on GRACE-C. One pathway for this is by using a simplified version of the Gravitational Reference Sensors demonstrated on the LISA Pathfinder Mission in 2016. And, if the measurement accuracy is much improved, it appears desirable to fly NGGM with a fixed ground track and an approximately 5-day orbit repeat period.
The GRACE Follow-On mission has been flying since 2018 and monitoring time variations in the Earth's mass distribution due to hydrological, atmospheric, and oceanographic processes. It consists of two satellites in a circular polar orbit, with about 200 km separation. When the satellites fly over a local peak in the mass distribution, their separation changes. Short-period changes in the distance between them are monitored with a laser interferometer to about 0.01 m/Hz\({}^{1/2}\) accuracy. But the overall measurement accuracy is much worse because of noise in the satellite accelerometers. However, this noise source can be very much reduced with a simplified gravitational sensor that is now nearly fully space qualified. Adding these sensors on the next Earth gravity mission will permit considerably more accurate monitoring of quite local mass variations. This should permit 5-day resolution for such variations, which will be particularly important for hydrological studies.
2025 1
## 2 Future Gravity Missions
The 2017-2027 Decadal Survey for Earth Science and Applications from Space (National Academies, 2018) classified mass change as a \"Designated Observable,\" highlighting the importance of having continuous observations of Earth system mass change beyond the end of life of GRACE Follow-On (GRACE-FO). NASA responded to this designation by studying possible observing system architectures for observing Earth system mass change. The study found the option which had the highest probability of achieving continuity in the data record was to design a heritage mission closely resembling GRACE-FO ([PERSON] et al., 2022), keeping key requirements for the laser interferometry and accelerometer measurement accuracy about the same as for GRACE-FO. Such a mission is now being realized jointly by NASA and DLR, scheduled to launch in 2028, and is called GRACE-Continuity (GRACE-C). Concurrently, ESA is in the early stages of development of a pair of satellites called Next Generation Gravity Mission (NGGM), envisioned to fly in a lower inclination (65\({}^{\circ}\)-75\({}^{\circ}\)) to complement GRACE-C ([PERSON] et al., 2024; [PERSON] et al., 2020) with a launch date in the early 2030s.
Because of the extremely high accuracy of the scientific information that could be obtained from an improved measurement system, it has been suggested quite early that the measurement uncertainty relative to GRACE-FO should be sharply reduced. This could be done by replacing the accelerometers on the GRACE missions by a simplified version of what are called Gravitational Reference Sensors ([PERSON] et al., 2009). The ability of such sensors to detect even extremely low levels of acceleration disturbances to test masses was demonstrated on the LISA Pathfinder Mission in 2016 ([PERSON] et al., 2016, 2018, 2019).
Because of the planning and preparations for future missions, it was recognized quite early that a simplified Gravitational Reference Sensor could be used instead of accelerometers on future Earth gravity missions ([PERSON], 2021; [PERSON], 2015; [PERSON] et al., 2020; [PERSON] et al., 2022). Research and laboratory demonstrations have now been carried out by a group of institutions in order to design, test, and flight qualify highly Simplified Gravitational Reference Sensors (S-GRS) for possible use on a satellite gravimetry mission. Those efforts are expected to demonstrate a Technology Readiness Level 6 (TRL 6) in 2025 ([PERSON] et al., 2022). The Gravitational Reference Advanced Technology Test In Space (GRATTIS) mission, planned for launch in 2027, will demonstrate a pair of S-GRS on a microsatellite in Earth orbit ([PERSON] et al., 2024).
Even if it is not possible to reduce the uncertainty in measuring the satellite separation in GRACE-C relative to GRACE-FO, it is still possible to reduce the uncertainty in short-period mass variations in future missions, such as the Next Generation Gravity Mission (NGGM) currently in early stages of development by ESA. NGGM is targeting flying advanced accelerometers, and the S-GRS could be an option for this instrumentation. Further, NGGM could target a short-period repeat ground track for the mission, as discussed in [PERSON] et al. (2020) and [PERSON] et al. (2024). By adopting a short-period ground-track repeat orbit for the mission, valuable new information on short-period changes in the geopotential could still be obtained.
With only 28-day average results, it is not possible to obtain information about geopotential variations with periods substantially less than this. But, for a mission with a short-period ground-track repeat period, accurate information about such variations at considerably shorter periods would be obtained. For a 5-day repeat ground track, estimates indicate that useful geopotential variation information can be obtained for frequencies of about 60-90 cycles/rev.
Knowing when a mass change occurred at a particular location will be important because the times of changes need to be cross-correlated with the best information available on atmospheric variations in that area. This is necessary in order to increase our understanding of the connections between atmospheric variations and hydrological processes. Understanding that connection at different locations over the whole globe would help in improving our understanding of basic hydrological processes, which would lead to better modeling of changes in the surface and subsurface water variations even at remote locations.
In thinking about the scientific benefits of such a mission, it is desirable to consider the benefits for rapid mass changes at quite short wavelengths separately. The possible results have been reviewed recently ([PERSON] & [PERSON], 2021). In Figures 1(a), 1(b), 1(a), and 1(b), estimates of the present uncertainties in the geopotential variations as a function of frequency are given for four particular 180\({}^{\circ}\) orbital arcs. Possible total measurement uncertainty curves are given for two different cases. The black curve is based on assuming an accelerometer noise level similar to that for the GRACE missions, and the dashed curve is based on the projected noise level curve for the S-GRS. Both assumed a laser interferometer noise level similar to that achieved for GRACE-FO.
In each of the four figures, the black curve is above the estimated a priori uncertainty for the geophysical variations at frequencies above about 60 cycles/rev. Thus, little new information about the geopotential variations would be obtained at higher frequencies. However, the dashed curves stay below or at the level of the expected geopotential variations at frequencies up to about 90 cycles/rev. Thus changing to the use of simplified GRSs appears likely to be quite valuable for determining the geopotential variations at the higher frequencies. The geopotential variation uncertainties shown in the figures were based on the knowledge of these uncertainties in about 2016 and may be reduced by the time NGGM flies. However, that would just extend the main benefits of reduced measurement uncertainty down to somewhat lower frequencies.
If these simplified Gravitational Reference Sensors replace the accelerometers on the Next Generation Gravity Mission, the strongly increased accuracy for measuring short-period and short-wavelength variations in the geopotential suggests that an orbit for the pair of satellites having a fixed ground track and a quite short orbit-repeat period would be desirable. This would sharply reduce the effect of temporal aliasing for medium- and high-frequency mass variations. For this reason, orbits with between 3- and 7-day repeat ground tracks appear to be desirable. The particular case of a mission design with 76 orbital revolutions in 5 days will be discussed in the rest of this article. Since NGGM is targeting an orbital inclination between 65\({}^{\circ}\) and 75\({}^{\circ}\) to complement the information content obtained from GRACE-C ([PERSON] et al., 2008; [PERSON] et al., 2012), we restrict our analysis to a particular orbit with an inclination at 75\({}^{\circ}\).
## 3 Possible Mission Design With a 5-Day Repeat Period
If the satellite altitude for NGGM is above about 450 km, it appears that the mission can be flown drag free and with a fixed ground track pattern with a relatively small quantity of additional thruster fuel. In addition, if the repeat period for the ground track is quite short, and fixed-period analyses are used, the effect of temporal aliasing due to geopotential changes during the analysis period can be reduced. There also is an advantage for a short repeat period if an along track analysis approach ([PERSON] et al., 2022) is used. An attractive option appears to be an orbit at 463 km altitude with a fixed ground track and 76 orbital revolutions in 5 days. The geometry of the ground tracks over 5 days for such a mission is shown in Figure 1.
For this mission design, and for a 5-day analysis period, the coverage of the whole globe will be quite uniform when combined with GRACE-C information. The separation between adjacent northward and southward ground tracks at the equator (and maximum for all latitudes) for NGGM will be 2.36\({}^{\circ}\) (262 km), which is just 0.57 of the satellite altitude. A useful quantity for estimating the value of information obtainable about a rapid and local mass change from individual satellite arcs is the maximum difference in along track acceleration for the two satellites caused by that mass change.
Figure 1: The 5-day ground tracks are shown for a near-polar orbiting pair (red) and lower inclined pair (blue).
If there is a sudden and quite local mass change at the equator, and it is nearly under a particular satellite arc, the data from that arc will contribute strongly to determining the magnitude of the mass change and its north-south location. But the main information on the east-west location will come from the four satellite arcs that are 262 and 524 km to the east and west. Because there will be five of them in 5 days, the accuracy of determining both the magnitude and the location of the mass change will be quite good. This indicates that the results for determining the magnitude and location of a local mass change from a 5-day analysis will be valuable for all latitudes <75\({}^{\circ}\).
The suggestions above are grounded within the framework of examining local mass change features directly underneath an orbital track. A more traditional approach to data processing involves forming normal equations that relate the satellite observations to the gravity field parameters and combining those normal equations over some amount of time to estimate the mean global mass change that occurred during that time. To further demonstrate the utility of our suggested approach, we perform a numerical simulation and combine normal equations in a manner that is consistent with the standard (traditional) way of currently processing GRACE and GRACE-FO data. Figure 2 shows degree variance error for monthly solutions obtained from a single polar pair, and the combination of both pairs of satellites, and includes a 5-day solution for the combination of the two pairs of satellites. The polar pair is at an altitude of 488 km. Both pairs are assumed to carry a laser interferometer with commensurate performance as GRACE-FO and provide attitude observations and GNSS (Global Navigation Satellite System) observations with commensurate performance as GRACE-FO. The polar pair has an accelerometer consistent with what is expected to fly on GRACE-C, and the S-GRS with performance described in [PERSON] et al. (2022) is used in lieu of an electrostatic accelerometer for the lower inclined pair. The simulation includes both temporal aliasing error and measurement system error (LRI error, accelerometer error, attitude error, GNSS error). The simulation definition hydro force model definition and processing approach is fully consistent with what is described in [PERSON] et al. (2022).
Figure 2 shows the superior performance that the combination of the two pairs provides over the single polar pair, as has been documented by several studies ([PERSON] et al., 2020; [PERSON] et al., 2011). Further, it demonstrates the strength in a 5-day gravity solution, where errors at long wavelengths are slightly larger than a monthly gravity solution from a polar pair only, but errors in short wavelengths are reduced considerably. This analysis is presented here to reinforce that the community can rely on traditional data processing approaches to provide high-quality 5-day gravity solutions with the suggested mission design, while still collecting observations that would allow for examining the local mass change features directly underneath the orbital track, as suggested in this manuscript.
## 4 Conclusions
If a strong reduction on the acceleration noise is made in the Next Generation Gravity Mission with two satellites roughly 200 km apart, it appears that a substantial improvement in the scientific results can be made by going to an orbit with a fixed ground track and a short repeat period. A good candidate for this is an orbit at 463 km altitude with 76 orbital revolutions in five sidereal days. In this case, 5-day solutions would be quite accurate globally when combined with a polar pair in a free-drifting orbit. And the scientific results would benefit strongly if highly simplified gravitational reference sensors replace the accelerometers used in the GRACE and GRACE Follow-On missions, and future GRACE-C mission.
One of the benefits of such a mission would be the improved accuracy that would result for checking on present estimates of the short-period variations in the atmospheric mass density based on other types of geophysical information. Except for rare events, some of the highest frequency variations in the Earth's mass distribution come from atmospheric processes. Being able to determine them better globally would help to make up for the low density of local monitoring observations in a number of parts of the globe, including over the oceans.
However, the most important scientific benefits probably would be for hydrology. This is because of the difficulty of understanding all of the steps involved in hydrological processes. Even if the amount of local rainfall is known,
Figure 2: Degree variance error in units of geoid height for monthly gravity fields obtained from a polar pair only (magenta), a polar pair + lower inclined pair (blue), and a 5-day gravity field solution from the polar + inclined pair (green), compared against the power of the signal being estimated (black).
the steps involved in understanding the overall hydrological processes include understanding the following: evapotranspiration, runoff, storage near the surface, feeding into aquifers, and later withdrawal. More accurate measurements of short-period and quite-local mass changes would help to test and improve our understanding of all of these processes.
## Data Availability Statement
Data generated in the manuscript are based on output from model simulations. Configuration information for the simulation runs are available at [PERSON] et al. (2022). Software packages used to generate the synthetic data are restricted from being shared to due Export Administration Regulations from the U.S. government.
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wiley/fee33f44_1f81_4e4f_9412_efe0af42f998.md | signals observed in space are significantly stronger during the night than during the day ([PERSON] and [PERSON], 2012; [PERSON] et al., 2019).
Another effect to consider in the analysis of wave propagation toward or from the ground is the sudden change of the refractive index from values of a few tens in the ionized ionosphere to essentially unity in the neutral atmosphere. According to [PERSON]'s law, this limits possible transmitted waves to those with wave normals close to the vertical direction ([PERSON], 1965). Along with the magnetospheric reflection of downward-propagating whistler-mode waves near the lower hybrid frequency ([PERSON] and [PERSON], 1970), this considerably complicates the wave propagation to the ground. Consequently, the waves often seem to require at least partially ducted propagation to reach the ground ([PERSON] et al., 2023; [PERSON] et al., 2020).
In order to experimentally reveal characteristic spatial scales of the waves of interest, multipoint observations (either spacecraft-spacecraft, spacecraft-ground station, or ground station-ground station) can be used to study respective wave phenomena ([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2018; [PERSON], [PERSON], et al., 2018; [PERSON] et al., 2007; [PERSON] et al., 2019). Additionally, these multipoint observations can aid in investigating wave propagation between observation points ([PERSON] et al., 2023; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2016; [PERSON] et al., 2014). One possible approach involves identifying conjugate events that exhibit one-to-one correspondence in wave spectra between observation points, ensuring that the same wave phenomenon is indeed observed ([PERSON] et al., 2020; [PERSON] et al., 2021, 2023). Alternatively, wave intensities can be directly correlated, without the need to manually evaluate specific frequency-time structures ([PERSON] et al., 2018; [PERSON] et al., 2020).
We systematically investigate the correlations of wave intensities, as measured simultaneously by the Kannus-lehto station in Finland and the low-altitude DEMETER spacecraft, with respect to their L-shell and geomagnetic longitude separations. The primary aim is to identify distinctive spatial scales of these waves and to discuss their propagation to the ground, better characterizing the ducting conditions and penetration through the ionosphere. Prior work has not yet accounted for the effects of longitudinal separation between multipoint observations on such a global scale under this configuration. This is important for models of magnetospheric wave intensities, which should eventually aim to incorporate information about correlation lengths and times rather than simply predicting single-point wave intensities. Moreover, the highlighted issues with wave propagation to the ground during nighttime geomagnetically active periods are crucial for the proper interpretation and monitoring of ground-based measurements of magnetospheric plasma waves. The data set used is described in Section 2. The results obtained are presented in Section 3 and discussed in Section 4. Finally, Section 5 contains a brief summary.
## 2 Data Set
The Kannuslehto station is operated by the Sodankyla Geophysical Observatory (SGO) in Finland. It is located at 67.74\({}^{\circ}\) N and 26.27\({}^{\circ}\) E. The corresponding geomagnetic longitude is about 120\({}^{\circ}\), and the L-shell, estimated using the International Geomagnetic Reference Field (IGRF) model, is about 5.38. It operates in several months-long campaigns, primarily during the local winter. These have become progressively longer and nearly continuous measurements are achieved nowadays. The wave magnetic field is measured by two orthogonal vertical magnetic loop antennas oriented in the east-west and north-south directions. The signal is sampled at 78.125 kHz, and full waveforms are available ([PERSON], 2005). This work uses corresponding frequency-time spectrograms of total power spectral density of magnetic field fluctuations with a frequency resolution of about 10 Hz and a time resolution of about 1.5 s, across frequencies up to 16 kHz.
DEMETER was a French microsatellite that operated between the years 2004 and 2010 at an altitude of about 660 km. Its orbit was nearly Sun-synchronous with the corresponding local times of about 10:30 (\"daytime\") and 22:30 (\"nighttime\") hours, respectively. The measurements were performed continuously at geomagnetic latitudes lower than about 65\({}^{\circ}\). The wave instrumentation on board consisted of an electric field instrument and a search coil magnetometer. Only the electric field data are used in this study due to the large number of interferences in the magnetic field data. These provide us with onboard calculated frequency-time spectrograms of a single electric field component with a time resolution of about 2 s and a frequency resolution of about 20 Hz ([PERSON] et al., 2006).
The Kannuslehto data, which are continuous in time, are interpolated to match the individual measurement times of the DEMETER data set (with data gaps above the poles). This enables a direct comparison between the two data sets. Given the low altitude of the DEMETER spacecraft and the time resolution of the wave measurements, the time delay due to the wave propagation between the spacecraft and the ground can be neglected. Another possible issue is related to the wave magnetic field data (Kannuselheto) being compared with the wave electric field data (DEMETER). However, in an environment with a refractive index close to one (on the ground, in the atmosphere), the electric and magnetic wave intensities are directly proportional through a constant factor and can be converted from one to another at will. In a dispersive plasma environment (at DEMETER altitudes, in the ionosphere), the electric and magnetic wave intensities are still proportional, but the respective factor depends on the refractive index and wave normal angle (see, e.g., Equations 16-18 in Albert (2012)). Considering that the present study aims to evaluate correlations rather than compare the absolute values of wave intensities, this issue thus does not represent a problem.
The overlap between the two data sets (November 2006 to March 2008) corresponds to more than 500 DEMETER half-orbits (about 35 min each). Note that, due to the lack of Kannuselheto measurements during the northern summer, the seasonal distribution of the data is not uniform but rather concentrated in the northern winter months.
## 3 Results
Figure 1 shows the average wave intensities measured by the DEMETER spacecraft and the Kannuselheto station during the analyzed period of their overlap. The DEMETER measurements are confined to two distinct local time intervals while sampling a considerable L-shell interval. The average daytime and nighttime intensities measured by DEMETER are thus, respectively, plotted in color scale in Figures 0(a) and 0(b) as a function of frequency and L-shell. The vertical black lines in these figures mark the L-shell of the Kannuselheto. On the other hand, the Kannuselheto measurements are performed at a fixed L-shell and cover all local times. The respective wave intensities are thus plotted in color scale in Figure 0(c) as a function of frequency and local time (LT). The local time is calculated from the universal time (UT) by a simple shift corresponding to the longitude of the Kannuselheto station (about 1.5 hr). The two local time intervals approximately corresponding to the DEMETER daytime and nighttime half-orbits (9-12 and 21-24 hr, respectively) are denoted by the horizontal black lines.
It is observed that wave intensities measured by DEMETER at higher frequencies (above approximately 2 kHz) are generally higher during the nighttime than during the daytime across the entire range of L-shells, especially at higher L-shells. Analogously, the wave intensities measured by Kannuselheto are larger during the local airy, particularly at higher frequencies. These can be attributed to lightning-generated whistlers, dominant at frequencies above the Earth-ionosphere waveguide cut-off frequency, about 1.7 kHz ([PERSON] et al., 2012). On the other hand, the significant wave intensities at lower frequencies, especially at larger L-shells, can be attributed to hiss emissions ([PERSON], [PERSON], et al., 2006; [PERSON], 1999), coming from larger radial distances ([PERSON] et al., 2017; [PERSON], [PERSON], et al., 2006) and possibly ionospherically reflected ([PERSON] et al., 2017).
Whether or not the DEMETER spacecraft and the Kannuselheto station observe the same wave phenomenon depends, apart from the ionospheric conditions and the wave propagation direction, primarily on the spatial extent of a given phenomenon and the spatial separation between the two observation points. This separation can be either in longitude (azimuthal) or L-shell (latitudinal, within a given meridian). The correlations between wave intensities measured by DEMETER and Kannuselheto are thus, hereinafter, evaluated as a function of their longitudinal (\(\Delta mlon=mlonlonMETER-mlon_{Kannuselheto}\)) and L-shell (\(\Delta L=L_{DEMETER}-L_{Kannuselheto}\)) separations. Note that the L-shell separation can be negative when DEMETER is at lower L-shells than Kannuselheto. Moreover, the situations of the spacecraft located in the northern hemisphere (i.e., the hemisphere of the Kannuselheto station) and in the southern hemisphere are considered separately.
The amount of available data as a function of the L-shell and longitudinal separations is plotted in color scale in Figure 2. The size of the bins is 0.4 in \(\Delta L\) and 10\({}^{\circ}\) in \(\Delta mlon\). Given the rather fine time resolution of the DEMETER wave data (about 2 s), the amount of data is characterized both by the number of individual data points and by the number of DEMETER half-orbits. The total numbers of available data points in the northern and southern hemispheres are depicted in Figures 1(a) and 1(b), respectively. The total numbers of available DEMETER half-orbits in the northern and southern hemispheres are depicted in Figures 1(c) and 1(d). Note that these figures correspond to the total amount of available data, irrespective of the daytime/nighttime. However, the daytime and nighttime coverages are quite similar (not shown). Given its circular orbit that covers all latitudes nearly uniformly, DEMETER spends more time at lower L-shells. Consequently, the amount of data gradually decreasestoward larger \(\Delta L\). The measurements become relatively sparse at \(\Delta L\)\(>\) - 1, limited only to specific longitudinal ranges. This shows that DEMETER measurements are mostly confined to L-shells lower than the L-shell of Kannuslehto.
Two different approaches are used to evaluate the correlation of wave intensities measured by DEMETER and Kannuslehto as a function of their spatial separation. The first approach relies on calculating the Spearman's rank
Figure 1: (a–b) Average power spectral density of electric field fluctuations measured by the DEMETER spacecraft during daytime and nighttime half-orbits, respectively, is plotted in color scale as a function of frequency and time. The vertical black lines mark the L-shell of the Kannuslehto station. (c) Average power spectral density of magnetic field fluctuations measured by Kannuslehto is plotted in color scale as a function of frequency and local time. The horizontal black lines denote the local time intervals approximately corresponding to the local times of DEMETER daytime and nighttime half-orbits.
correlation coefficient ([PERSON] et al., 1992) of wave intensities measured by the two instruments at the same times and frequencies, addressing whether the wave intensity at one point increases along with the intensity at the other point. The second approach instead correlates frequency-time intervals simultaneously measured by the two instruments, addressing whether the two instruments observe identical frequency-time wave signatures.
The results obtained using the first approach for two different frequency ranges (1-1.5 kHz and 2-2.5 kHz) are depicted in Figures 3 and 4, respectively. These frequency ranges are chosen to be safely below/above the Earth-ionosphere waveguide cut-off frequency. The format of both figures is the same. The correlations of wave intensities obtained for the daytime DEMETER measurements in the northern and southern hemispheres are shown in panels (a) and (b), respectively. The results obtained for the two frequency ranges are very similar, at least qualitatively. The daytime correlation values are high at low longitudinal separations, as might be expected. The daytime peak correlations (indicated by the horizontal red line) exhibit, nevertheless, a slight shift toward negative \(\Delta\)_mlon_ values, and the correlations become negative for large longitudinal separations. The correlations obtained for DEMETER located in the northern/southern hemispheres are similar, indicating the symmetricity of the situation between the hemispheres. Moreover, the correlations are virtually independent of the L-shell separation. The situation remains similar also for other analyzed frequency ranges above 1 kHz; at lower frequencies, the correlation between DEMETER and Kannuselho wave intensities tends to disappear. The correlations of wave intensities obtained for the nighttime DEMETER measurements in the northern and southern hemispheres are shown in panels (c) and (d), respectively. The results obtained for the two frequency ranges are again very similar. However, this time the peak correlations are not observed at \(\Delta\)_mlon_\(\approx\) 0, but instead at \(\Delta\)_mlon_\(\approx\) 120\({}^{\circ}\) (indicated by the horizontal red line). Moreover, at low longitudinal separations, the correlations are not only low but even negative.
The negative correlations at low longitudinal separations and high positive correlations at significant longitudinal separations may seem counterintuitive. However, we believe they can be explained as follows. Recall that the local time of DEMETER during the daytime half-orbits is about 10:30. The maximum daytime correlations observed for DEMETER located slightly westward from Kannuselho (\(\Delta\)_mlon_ negative) thus correspond to the situation of the Kannuselho station located around local noon. Analogously, the local time of DEMETER during the nighttime half-orbits is about 22:30. The maximum nighttime correlations are observed when DEMETER is significantly eastward from Kannuselho. This positioning again corresponds to Kannuselho being around local
Figure 2.— Number of available data points and number of DEMETER half-orbits are plotted in color scale according to the color scale on the right-hand side as a function of the L-shell separation between the DEMETER spacecraft and the Kannuselho station (ordinate) and their geomagnetic longitude separation (abscissa). (a) Number of data points in the northern hemisphere. (b) Number of data points in the southern hemisphere. (c) Number of DEMETER half-orbits in the northern hemisphere. (d) Number of DEMETER half-orbits in the southern hemisphere.
noon. Consequently, we obtain a picture of the correlations being high when Kannuslehto is close to local noon, while they are negative when Kannuslehto is close to local midnight. Considering the global nature of the calculated correlations, evaluated over a wide range of geomagnetic activity levels, we can interpret this in terms of how DEMETER-measured and Kannuslehto-measured wave intensities respond to geomagnetic activity. Although they may exhibit similar behavior during Kannuslehto daytime, their responses could be opposite during Kannuslehto nighttime.
Figure 4.— The same as Figure 3, but for the frequency range 2-2.5 kHz.
Figure 3.— Global correlations of power spectral densities measured by the Kannuslehto station and the DEMETER spacecraft in the frequency range 1–1.5 kHz as a function of their L-shell and geomagnetic longitude separations. The horizontal red lines indicate the longitudinal separations with the highest correlations. (a) Daytime DEMETER measurements in the northern hemisphere. (b) Daytime DEMETER measurements in the southern hemisphere. (c) Nighttime DEMETER measurements in the northern hemisphere. (d) Nighttime DEMETER measurements in the southern hemisphere.
The aforementioned hypothesis is verified in Figures 5 and 6 using a direct correlation of the wave intensities measured at individual times with the geomagnetic activity at those times, as characterized by the \(K_{p}\) index. Figure 5a shows the number of DEMETER wave measurements as a function of L-shell. The amount of data is nearly the same for both daytime and nighttime, gradually decreasing with increasing L-shell. The correlations of wave intensities measured by the DEMETER spacecraft at individual L-shells and frequencies and \(K_{p}\) indices are shown in Figures 5b and 5c. They are plotted in color scale as a function of the wave frequency and L-shell, separately for daytime and nighttime DEMETER half-orbits. Vertical black lines mark the L-shell of the
Figure 5: Correlations between the DEMETER-measured wave intensities and \(K_{p}\) index are plotted in color scale as a function of the wave frequency and L-shell. (a) Daytime half-orbits. (b) Nighttime half-orbits. Vertical black lines denote the L-shell of the Kannuslehto station.
Kannuslehto station. It can be seen that the DEMETER-measured wave intensities are well correlated with the geomagnetic activity over a wide range of frequencies, in particular at higher L-shells.
The correlations of wave intensities measured by the Kannuslehto station and \(K_{p}\) indices are shown in Figure 6. The red and blue curves correspond, respectively, to the daytime and nighttime local time intervals (9-12 and 21-24 hr, including 50,889 and 44,125 data points, respectively). During the day, Kannuslehto-measured wave intensities are positively correlated with the geomagnetic activity at frequencies up to about 4 kHz, and they are close to zero at higher frequencies, dominated by lightning-generated whisters. On the other hand, during the night, Kannuslehto-measured wave intensities are negatively correlated with geomagnetic activity essentially all over the analyzed frequency range. Note that the sudden jumps in the correlation values at distinct higher frequencies, marked by the horizontal dotted lines, correspond to the signals from the Alpha navigation transmitters (11.905, 12.649, and 14.881 kHz).
Instead of calculating global correlations of wave intensities, the second approach checks whether the two instruments observe identical frequency-time wave signatures. For this purpose, correlations between the wave intensities measured simultaneously by DEMETER and Kannuslehto are evaluated in frequency-time windows of 750 Hz by 3 min. For each pair of these frequency-time windows, a single correlation value is obtained. The windows are then gradually shifted in frequency and time, and the average correlations obtained are evaluated as a function of \(\Delta L\) and \(\Delta mlon\). The results obtained for the frequency range 750-1,500 Hz and 2,000-2,750 Hz, that is, just below/above the Earth-ionosphere waveguide cut-off frequency, are depicted in Figures 7 and 8, respectively. The results obtained for DEMETER in the northern and southern hemispheres, as well as for daytime and nighttime DEMETER half-orbits, are separately plotted in individual panels, using the same format as in Figures 3 and 4. It can be seen that, this time, the correlations peak
Figure 6.— Frequency-dependence of the correlation between the Kannuslehto-measured wave intensities and \(K_{p}\) index. The results obtained for the daytime and nighttime local time intervals are plotted by the red and blue curves, respectively. Horizontal dotted black lines denote the frequencies of the Alpha navigation transmitters.
Figure 7.— Average correlations between frequency-time intervals measured simultaneously by the DEMETER spacecraft and the Kannuslehto station in the frequency range 0.75-1.5 kHz as a function of their L-shell and geomagnetic longitude separations. The horizontal red lines indicate the longitudinal separations with the highest correlations, corresponding to the estimated characteristic longitudinal scales. (a) Daytime DEMETER-half-orbits in the northern hemisphere. (b) Daytime DEMETER half-orbits in the southern hemisphere. (c) Nighttime DEMETER half-orbits in the northern hemisphere. (d) Nighttime DEMETER half-orbits in the southern hemisphere.
at zero longitudinal differences during both daytime and nighttime DEMETER half-orbits. The difference in L-shell appears to be of little importance, and the negative correlations are almost nonexistent. The correlations are somewhat higher when DEMETER is in the northern hemisphere, that is, in the same hemisphere as the station. However, the difference is rather small, suggesting a roughly symmetric situation between geomagnetically conjugated regions. Characteristic longitudinal correlation lengths are slightly higher for the lower frequency range analyzed. Overall, however, the longitudinal scales, determined as the longitudinal separations where the correlation value decreases to half of the peak value, range between about 60\({}^{\circ}\) and 90\({}^{\circ}\) (equivalent to 4-6 hr in local time).
## 4 Discussion
Although the data set used includes all available data from the intersection of the DEMETER spacecraft mission and the Kannuselheto station campaigns, it amounts to only about 500 DEMETER half-orbits. Given the Sun-synchronous nature of the DEMETER orbit, its measurements are limited to two distinct local time intervals, shortly before noon and shortly before midnight. Moreover, due to the lack of data measured by DEMETER at high geomagnetic latitudes and the comparatively large L-shell of the Kannuselheto station (\(L\approx 5.38\)), the vast majority of DEMETER data is measured at L-shells lower than that of Kannuselheto. Nevertheless, the available data is sufficient to reliably evaluate the correlations between DEMETER and Kannuselheto wave intensities. This is demonstrated by the smooth and relatively monotonic trends in Figures 3, 4, 7, and 8, considering that the data points in individual bins (and north vs. south plots) are virtually independent.
The correlation results obtained appear to be largely independent of the hemisphere in which the DEMETER measurements are taken, with correlations only marginally higher when DEMETER is in the hemisphere of Kannuselheto. In the case of whistler-mode chorus waves, which are generated by plasma instabilities at the geomagnetic equator at larger radial distances, their symmetrical propagation toward both the north and south can be naturally understood. This maintains the general symmetry of the situation. In the case of lightning-generated whistler-mode waves, this suggests that the waves can propagate smoothly between the hemispheres, potentially bouncing back and forth. This observation aligns with formerly reported symmetry of lightning-related whistler-mode wave intensities observed at low altitudes ([PERSON] et al., 2010). Additionally, the obtained correlations are virtually independent of \(\Delta L\). This is possibly due to a combination of ionospheric reflections ([PERSON] et al., 2017; [PERSON] et al., 2017) and wave propagation in the Earth-ionosphere waveguide, effectively spreading the wave power over a significant area at DEMETER altitudes and even more so on the ground. The longitudinal scales
Figure 8: The same as Figure 7, but for the frequency range 2–2.75 kHz.
between about 60\({}^{\circ}\) to 90\({}^{\circ}\) indicated by the present study appear to be in agreement with the longitudinal scales of about 76\({}^{\circ}\) estimated by [PERSON] et al. (2019) using ground-based PWING stations. However, they employed a somewhat different method, which relied on the identification and subsequent analysis of wave occurrence rates across individual ground-based stations. Moreover, using exclusively northern hemisphere ground-based stations located in a rather narrow range of latitudes (L-shells), they could neither investigate the effect of L-shell separation and different hemispheres, nor capture the issues related to the varying efficiency of wave penetration through the ionosphere.
Global correlations between coincident wave intensities measured by DEMETER and Kannuslehto revealed a puzzling phenomenon: the highest correlations occur around the Kannuslehto local noon, largely independent of the actual DEMETER longitude. This can be understood in terms of geomagnetic activity being the primary factor affecting the respective wave intensities. While DEMETER intensities and daytime intensities at Kannuslehto increase during geomagnetically active periods, nighttime intensities at Kannuslehto, somewhat surprisingly, decrease during such periods. This suggests potential issues with wave accessibility to the ground during geomagnetically disturbed periods, the reasons for which remain an open question. One possibility could be increased ionospheric attenuation during the periods of enhanced geomagnetic activity, which may result from enhanced electron precipitation and increased electron densities in the lower ionospheric layers ([PERSON] et al., 2023; [PERSON] et al., 2022). This is expected to primarily affect the nightside, as dayside electron densities are mainly controlled by incoming solar radiation. Another possibility could be that the ducted propagation, typically needed for waves to reach the ground ([PERSON] et al., 2023; [PERSON] et al., 2020), might become less likely during disturbed periods. Among other factors, a global change in the magnetic field configuration ([PERSON], 1989) could play a role and result in differences between day and night. However, at least for very low frequency transmitter signals at lower L-shells, this does not seem to be the case ([PERSON] et al., 2021; [PERSON], [PERSON], [PERSON], & [PERSON], 2022; [PERSON] et al., 1997).
## 5 Conclusions
We analyzed simultaneous wave measurements from the low-altitude DEMETER spacecraft and the ground-based Kannuslehto station. Both global correlations of measured wave intensities and correlations within corresponding frequency-time windows were analyzed. We found that the characteristic longitudinal scales of observed waves are between about 60\({}^{\circ}\) to 90\({}^{\circ}\). These correlation lengths should be reflected in models of magnetospheric wave intensities. Additionally, the wave intensities measured by Kannuslehto during nighttime were found to decrease with increasing geomagnetic activity. This contrasts with the DEMETER wave measurements and suggests potential issues with the nighttime wave propagation to the ground at the L-shells of Kannuslehto (\(\approx\) 5.38). Understanding this newly reported effect is crucial for the proper interpretation of ground-based measurements of magnetospheric plasma waves.
## Data Availability Statement
Kannuslehto quicklook plots are accessible from [[https://www.sgo.fi/Data/VLF/VLFData.php](https://www.sgo.fi/Data/VLF/VLFData.php)]([https://www.sgo.fi/Data/VLF/VLFData.php](https://www.sgo.fi/Data/VLF/VLFData.php)). DEMETER data are accessible upon registration from the [[https://sipad-cdpp.cnes.fr](https://sipad-cdpp.cnes.fr)]([https://sipad-cdpp.cnes.fr](https://sipad-cdpp.cnes.fr)) website.
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wiley/febcf729_380f_4e26_838a_32e03bf96312.md | An Online-Learned Neural Network Chemical Solver for Stable Long-Term Global Simulations of Atmospheric Chemistry
[PERSON]\({}^{\ddagger}\)
\({}^{1}\)Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA, \({}^{2}\)School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
[PERSON]\({}^{\ddagger}\)
\({}^{1}\)Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA, \({}^{2}\)School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
[PERSON]\({}^{\ddagger}\)
\({}^{1}\)Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA, \({}^{2}\)School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
and [PERSON]\({}^{\ddagger}\)
\({}^{1}\)Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA, \({}^{2}\)School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
###### Abstract
A major computational barrier in global modeling of atmospheric chemistry is the numerical integration of the coupled kinetic equations describing the chemical mechanism. Machine-learned (ML) solvers can offer order of magnitude speedup relative to conventional implicit solvers but past implementations have suffered from fast error growth and only run for short simulation times (<1 month). A successful ML solver for global models must avoid error growth over yearlong simulations and allow for reinitialization of the chemical trajectory by transport at every time step. Here, we explore the capability of a neural network solver equipped with an autoencoder to achieve stable full-year simulations of tropospheric oxidant chemistry in the global 3-D Goddard Earth Observing System (GEOS)-Chem model, replacing its standard mechanism (228 species) by the Super-Fast mechanism (12 species) to avoid the curse of dimensionality. We find that online training of the ML solver within GEOS-Chem is important for accuracy, whereas offline training from archived GEOS-Chem inputs/outputs produces large errors. After online training, we achieve stable I-year simulations with five-fold speedup compared to the standard implicit Rosenbrock solver with global tropospheric normalized mean biases of \(-0.3\%\) for ozone, \(1\%\) for hydrogen oxide radicals, and \(-5\%\) for nitrogen oxides. The ML solver captures the diurnal and synoptic variability of surface ozone at polluted and clean sites. There are however large regional biases for ozone and NO\({}_{x}\) under remote conditions where chemical aging leads to error accumulation. These regional biases remain a major limitation for practical application, and ML emulation would be more difficult in a more complex mechanism.
14 MAY 2022
## 1 Introduction
Global modeling of atmospheric chemistry is a grand computational challenge due to the large number of coupled chemical species, the nonlinearity and numerical stiffness of chemical mechanisms, and the interactions with transport on all scales. The U.S. National Research Council's National Strategy for Advancing Climate Modeling identifies atmospheric chemistry as a priority frontier for Earth System Model (ESM) development (National Research Council, 2012). Current atmospheric chemistry models integrate the coupled chemical kinetic equations for the mechanism species over model time steps by using high-order implicit numerical solvers, but these solvers are expensive ([PERSON] et al., 1997) and often dominate the cost of an atmospheric simulation ([PERSON] et al., 2018). Here, we explore the potential of machine learning (ML) neural network algorithms to dramatically reduce the computational intensity of atmospheric chemistry in global simulations.
Chemical solvers in atmospheric models compute the local evolution of species concentrations over a chemical time step that may range from minutes to hours depending on the model ([PERSON] & [PERSON], 2017). The chemical mechanism typically includes \(\sim\)100 coupled species with lifetimes ranging from less than a second to much larger than the chemical time step. Rosenbrock and Gear high-order implicit solvers can integrate this system of stiff coupled differential equations with high accuracy, and fast implementations of these schemes are available for example, through the Kinetic Pre-Processor (KPP) ([PERSON] & [PERSON], 2006) and SMVGER ([PERSON] & [PERSON], 1994). They are still extremely costly for atmospheric models. Models combat that cost by decreasing the size of the chemical mechanism ([PERSON] & [PERSON], 2000), breaking down the stiffness of the problem ([PERSON] & [PERSON], 1977), or using lower-order approximations, as reviewed by [PERSON] and [PERSON] (2017). But these methods rarely achieve a speedup of more than a factor of two ([PERSON] et al., 2020). ML methods could be transformative for reducing the cost.
ML methods would seem well-suited to chemical solvers in atmospheric models because the chemical computation is very repetitive, involving integration of similar conditions in neighboring grid cells and successive time steps. However, the large number of coupled species brings a curse of dimensionality to the problem. ML methods also have no check on error growth, unlike in standard chemical solvers where errors are dampened by the negative response to perturbations ([PERSON]'s principle). [PERSON] and [PERSON] (2019) created a prototype random forest integrator for the Goddard Earth Observing System (GEOS)-Chem global 3-D chemical transport model (CTM) driven by archived meteorological data. They achieved successful short-term simulations but found large error growth after a few weeks. [PERSON] et al. (2020) trained a neural network integrator in a chemical box model, including an encoder/decoder ([PERSON] et al., 2018) to decrease dimensionality, and a recursive feedback loop over 24-hr integration time to control error growth. They found that they could compress the 101-species dimension of their mechanism into fewer than 20 features without significant error penalty and that they could avoid error growth over a 1-week integration time. [PERSON] et al. (2021) developed a gas-phase neural network solver for the CMAQ regional CTM over China, combining a standard implicit solver for radicals and oxidants with an ML solver for volatile organic compounds (VOCs). They achieved an order of magnitude speedup over a 1-month simulation but with error growth over remote ocean grid cells.
Error growth in a ML chemical solver may be tolerable for short-term simulations such as in chemical forecasts or in small-scale air quality applications. But global simulations of atmospheric chemistry need stability over long-term horizons. For example, a global simulation of tropospheric oxidants (ozone and hydroxyl radical OH) with fixed concentration of methane has chemical modes of several months ([PERSON], 2016; [PERSON], 2000) and must typically be integrated over a year. Moreover, stability of the solution is required over the full range of tropospheric conditions from polluted to remote and from the surface to the upper troposphere. Operator splitting between chemistry and transport resets initial conditions after each transport time step, meaning that one cannot easily project the solution along long-term chemical trajectories as with dedicated ML time series algorithms such as Recurrent Neural Networks (RNNs) ([PERSON] et al., 1986) and Long-Short-Term Memory networks (LSTMs) ([PERSON], 1997) without introducing additional complexity ([PERSON] et al., 2022). Success in applying ML solvers to box models, such as in [PERSON] et al. (2020), may not translate to a global CTM.
One possible cause of error growth in the above applications is the use of offline training. In offline training, the ML solver learns the chemical tendencies from an archived data set of CTM inputs and outputs over chemical time steps. Training an ML solver offline is expedient, straightforward, and allows for easy manipulation of training data. However, offline training can overfit to the training data as the entire data set is typically cycled multiple times to improve learning. This may be alleviated by adding stochastic model regularizations such as dropout ([PERSON] et al., 2014), stopping the training process when the performance does not improve ([PERSON] et al., 2019), or employing custom loss functions. Offline training is also highly sensitive to the ML model architecture and may not properly represent the ensemble of conditions encountered by the CTM simulation in their temporal sequence ([PERSON], 2020).
An alternative is online training, in which the ML solver learns the chemical tendencies from the CTM simulation as it evolves with time. Online training creates ML models using data that become available sequentially in time and updates the trained model parameters when each new set of data is generated. Learning online from a dynamic input data stream is a method to forestall \"concept drift\" (the problem of ML predictions becoming less accurate as time advances), which plagues many offline training methods. Online training is more expensive and difficult as it requires running the CTM and ML training in tandem at every chemical time step. It may suffer from catastrophic forgetting where information from earlier training data is lost ([PERSON] & [PERSON], 1989) as each datapoint is used only once. It may also still overfit to the training data. However, it allows the ML solver to actually sample the conditions in the CTM as they evolve forward in time and learn from these chemical tendencies ([PERSON] et al., 2019; [PERSON], 2020). To our knowledge, online training has not been used previously for atmospheric chemistry applications.
Here, we demonstrate the capability of a neural network ML solver with online training to provide a stable representation of tropospheric chemistry in a global 3-D model environment over full-year simulations. We do so by emulating the 12-species \"Super-Fast\" chemical mechanism ([PERSON] et al., 2018; [PERSON] et al., 2006) in the GEOS-Chem CTM. The Super-Fast mechanism is a reduced representation of tropospheric chemistry used in climate models ([PERSON] et al., 2013). Although oversimplified in relation to the mechanisms used for atmospheric chemistry research, it is a useful prototype for our purpose because the limitation to 12 chemical variables alleviates the curse of dimensionality. This allows us to investigate other challenges in achieving stable and accurate ML solutions, thus providing a foundation for the application of ML methods to more complicated mechanisms.
## 2 Materials and Methods
### GEOS-Chem Model and Super-Fast Mechanism
We use the GEOS-Chem CTM version 12.0.0 ([[https://doi.org/10.5281/zenodo.1343547](https://doi.org/10.5281/zenodo.1343547)]([https://doi.org/10.5281/zenodo.1343547](https://doi.org/10.5281/zenodo.1343547))) driven by assimilated meteorological data from the NASA Global Modeling and Assimilation Office (GMAO) GEOS. GEOS-Chem computes the evolution of atmospheric composition by a successive application over model time steps of the operators simulating emissions, transport, chemistry, and deposition ([PERSON] et al., 2001). The chemical operator computes the changes in concentrations over the time step by integrating the coupled system of ordinary differential equations describing chemical production and loss for the ensemble of species in the mechanism ([PERSON] & [PERSON], 2017). Here, we conduct global simulations at \(4^{\circ}\times 5^{\circ}\) degrees resolution and 47 vertical levels (25-37 in the troposphere) using the GEOS Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2) meteorological data set with 3-hr temporal resolution (1-hr for surface variables). Time steps are 30 min for transport and 60 min for chemistry ([PERSON] et al., 2016). Photolysis frequencies are calculated with the Fast-JX scheme ([PERSON], 2002), as implemented in GEOS-Chem by [PERSON] et al. (2010).
The standard GEOS-Chem model includes a detailed oxidant-aerosol chemical mechanism for the troposphere and stratosphere with 228 species and 724 reactions ([PERSON] et al., 2014; [PERSON] et al., 2021), integrated with a fourth-order Rosenbrock Rodas3 chemical solver through KPP ([PERSON] et al., 1997). Here, we replace the chemical mechanism in the troposphere with the Super-Fast mechanism for oxidant chemistry ([PERSON] et al., 2018), including 12 chemical species coupled through 21 thermal reactions and 6 photolysis reactions. We replace the chemical mechanism in the stratosphere with a simple linear relaxation to chemical equilibrium intended to provide reasonable flux boundary conditions at the tropopause ([PERSON] et al., 2000; [PERSON] et al., 2012).
We integrate the Super-Fast mechanism with the KPP Rosenbrock solver in the same way as the standard mechanism and this defines the reference Super-Fast simulation to which our ML solver will be compared. The 12 coupled species in the Super-Fast mechanism include methane oxidation products (CH\({}_{\text{H}}\)O\({}_{\text{2}}\) CH\({}_{\text{3}}\)OOH, CH\({}_{\text{2}}\)O, and CO), oxidants and related radical chemistry (OH, HO\({}_{\text{2}}\) H\({}_{\text{2}}\)O\({}_{\text{2}}\) O\({}_{\text{3}}\) NO, NO\({}_{\text{2}}\) and HNO\({}_{\text{3}}\)), and biogenic isoprene (C\({}_{\text{3}}\)H\({}_{\text{3}}\)) that produces CH\({}_{\text{3}}\)O\({}_{\text{2}}\) upon oxidation. The mechanism also includes CH\({}_{\text{4}}\) and O\({}_{\text{2}}\) with fixed concentrations and H\({}_{\text{2}}\)O with concentration specified by the meteorological data. The nitrogen oxide radicals (NO\({}_{\text{2}}\) \(\equiv\) NO + NO\({}_{\text{2}}\)) are oxidized to HNO\({}_{\text{3}}\) solely by OH, and HNO\({}_{\text{3}}\) is chemically inert and removed by deposition.
We use standard GEOS-Chem emission inventories for the years 2016 and 2017 including CEDS for NO\({}_{\text{2}}\) and CO from fuel combustion ([PERSON] et al., 2018), GFED4 for NO\({}_{\text{2}}\) and CO from open fires ([PERSON] et al., 2015), MEGAN v2.1 for isoprene ([PERSON] et al., 2012), [PERSON] et al. (2012) for lightning NO\({}_{\text{2}}\), and [PERSON] et al. (2012) for soil NO\({}_{\text{2}}\). We increase CO emissions by 19% for fuel combustion and 11% for open fires, following [PERSON] et al. (2017), to account for secondary production of CO from nonmethane volatile organic compounds (NMVOCs). The tropospheric methane concentration is imposed by latitude-dependent surface boundary conditions ([PERSON], 2016). Standard GEOS-Chem modules for dry deposition ([PERSON] et al., 2001) and wet deposition ([PERSON] et al., 2012; [PERSON] et al., 2001) are applied to CH\({}_{\text{2}}\)O, H\({}_{\text{2}}\)O\({}_{\text{2}}\), O\({}_{\text{3}}\), NO\({}_{\text{2}}\) and HNO\({}_{\text{3}}\).
### Machine Learning Neural Network Chemical Solver
Figure 1 shows the ML chemical solver model architecture used in this work. The ML chemical solver consists of three main components: an encoder, an integrator, and a decoder, each of which is a neural network. The encoder and decoder components (referred together as an autoencoder) are used for data compression and decompression, respectively ([PERSON], 1991). The encoder learns to map chemical species to a compressed dimensional representation, the integrator learns to integrate the compressed representation forward in time, and the decoder learns to convert the compressed representation back to the original species. The encoder and decoder are shallow neural networks comprised of a single hidden layer with 16 nodes and linear activation. For the integrator, we use the ResNet residual neural network ([PERSON] et al., 2016) with one block having two hidden layers and 128 nodes per layer, ReLu activation, and the Adam optimizer ([PERSON] & [PERSON], 2017). Each fully connected layer is preceded by a batch normalization operation ([PERSON] & [PERSON], 2015), which normalizes the activations into the ResNet block to create a smoother optimization landscape for improved gradient flow ([PERSON] et al., 2019). After each fully connected layer, a dropout rate of 0.5 is applied to prevent overfitting ([PERSON] et al., 2014). For all ML chemical solvers, we apply stochastic components such as dropout during the entire training process. We refer to the ML parameters as the coefficients of the regression algorithms.
Training of the ML solver involves fitting the chemical evolution in the reference Super-Fast simulation over model time steps. Each GEOS-Chem 1-hr time step output constitutes one training sample, consisting of 20 input variables: Concentrations of the 12 species at the beginning of the time step, 6 photolysis frequencies calculated by Fast-JX in the middle of the chemical time step (for O\({}_{\text{y}}\) H\({}_{2}\)O\({}_{\text{z}}\) NO\({}_{\text{z}}\) CH\({}_{\text{z}}\)O by two branches, and CH\({}_{\text{z}}\)OOH), temperature, and air density. The output variables are the concentrations of the 12 species at the end of the time
Figure 1: Machine learning (ML) chemical solver in Goddard Earth Observing System (GEOS)-Chem. GEOS-Chem computes the evolution of atmospheric composition by successive application over model time steps of components simulating advection, convection, emissions, planetary boundary layer (PBL) mixing, photolysis, chemistry, and deposition. We replace the fourth-order Rosenbrock solver with an ML solver that takes as input the same chemical concentrations and photolysis frequencies. All other model processes are the same as in the original model.
step. Photolysis frequencies can themselves be emulated using neural networks ([PERSON] et al., 2005; [PERSON] et al., 2021; [PERSON], 2020) but their calculation is cheap compared to the chemical calculation.
All ML chemical solver code in this work is written using the Keras package Python ML routines. GEOS-Chem is written in Fortran and there are no programs to easily call Python ML algorithms from Fortran. To couple the ML chemical solver with GEOS-Chem, we use the C Foreign Function Interface for Python (CFFI; [[https://cffi.readthedocs.io](https://cffi.readthedocs.io)]([https://cffi.readthedocs.io](https://cffi.readthedocs.io))) that calls the Python ML code from within Fortran. CFFI includes a process called embedding, which packages Python code into \"dynamic libraries\" that may be included and executed by a Fortran program.
Training of the ML solver to emulate the reference KPP Rosenbrock solver involves minimizing cost functions for the mean square error between output variables, that is, the species concentrations computed at the end of the chemical time step. [PERSON] et al. (2020) found that a cost function that equally prioritizes all species is significantly less accurate than one that is specialized toward a single species of interest. Here, we create 12 separate ML solvers prioritizing each of the output species individually, all with the same 20 input variables listed from above. We apply a log transformation for the concentrations of selected species (H\({}_{\text{O}}\)O\({}_{\text{z}}\), CO, CH\({}_{\text{z}}\)O, NO\({}_{\text{z}}\), CH\({}_{\text{z}}\)OOH, and CH\({}_{\text{z}}\)O\({}_{\text{z}}\)) to obtain more normal distributions that aid in neural network learning before passing these inputs into the encoder. The other species were not sensitive to a log transformation (O\({}_{\text{z}}\)) and HNO\({}_{\text{z}}\)) or were detrimentally affected through decreased sensitivity to the highest concentrations (OH, HO\({}_{\text{z}}\), and C\({}_{\text{z}}\)H\({}_{\text{z}}\)). We use an encoder compression into eight features. For all species, we rescale the inputs and outputs to [0, 1] ranges using min-max normalization for ease of gradient optimization. We use the default Keras weight initializations for the encoder-er-integrator-decoder model.
### Offline and Online Training
We will present results from ML solvers trained in different ways offline and online. The ML solvers are trained over yearlong simulations or for individual seasons (DJF, MAM, JJA, and SON). In standard offline training, we run GEOS-Chem to create a training data set of input and output variables over individual 1-hr chemical time steps. Here, the offline ML chemical solver is trained on batches of data. We use a training data batch size of 1,024 and initial learning rate of 0.001, with learning-rate decay ([PERSON] et al., 2019) occurring every time the validation set error plateaus for 10 epochs (an \"epoch\" is when an entire data set is passed forward and backward through the neural network a single time). We use early stopping ([PERSON] et al., 2019) to halt ML solver training when the absolute error decreases less than \(1\times 10^{-4}\) for 15 epochs.
[PERSON] et al. (2020) found that recursive training of 1-hr chemical time steps over 24-hr time horizons was critical in their box model application to capture slow chemical modes and prevent error growth. We implemented this recursive training here by mimicking the effects of operator splitting between chemistry and other operators in GEOS-Chem. This involved archiving the 24-hr evolution of concentrations over 1-hr time steps from the ensemble of nonchemistry operators and adding it to every hourly time step for recursive 24-hr training of the ML solver. This recursive feedback is solely used for training; we archive the ML results only for the first 1-hr time step and discard the remaining 23-hr time steps. The expectation is that the first 1-hr prediction will have learned from fitting the subsequent 23-hr evolution.
In online training, we call the Python ML routines from Fortran as we run the GEOS-Chem model, sampling the same conditions as the offline training. Here, the online ML chemical solver is trained on the entire 3-D grid up to the tropopause. We employ the same ML solver architecture as the offline-trained ML solver without the recursive time horizon and with a learning rate of \(1\times 10^{-5}\). At each chemical time step, we load the ML solver parameters from the previous training time step, fit the ML solver for one epoch given all the training data at the current chemical time step, then save the ML solver parameters to be loaded in the next chemical time step.
The online framework as described above trains ML solvers from scratch starting from randomly initialized parameters. Recent ML work has suggested starting online training from pretrained offline ML models ([PERSON], 2020; [PERSON] et al., 2021) in order to have a better initialization of ML parameters. We also tried this approach and results will be presented below.
[PERSON] and [PERSON] (2019) previously used a random forest ML solver to emulate the GEOS-Chem mechanism, but here, we employ a neural network ML solver for two reasons. First, random forest algorithms are much slower. [PERSON] and [PERSON] (2019) found that their random forest solver was 85% slower than the reference Rosenbrocksolver, while neural networks should be much faster ([PERSON] et al., 2020; [PERSON] et al., 2021). Second, random forests are not easily amenable to online training because the growing of the architecture to incorporate more trees and branches further slows performance ([PERSON] et al., 2015), whereas online neural network training simply updates parameters. We did not consider the convolutional neural network architectures commonly used in computer vision applications ([PERSON], 2015) because convolutional layers typically perform calculations slower than simple fully connected layers.
## 3 Results
### Reference GEOS-Chem Simulation With Super-Fast Mechanism
We conducted the reference GEOS-Chem simulation using the Super-Fast mechanism integrated with the KPP Rosenbrock solver for 3 years (2015-2017). 2015 was used for initialization, 2016 for training the ML algorithms, and 2017 for testing them. Here, we compare this reference Super-Fast simulation for 2016 with the standard full-chemistry GEOS-Chem simulation in GEOS-Chem 12.0.0 including 228 coupled species to represent oxidant-aerosol chemistry. The intent is to check that the Super-Fast mechanism, although crude, provides a sufficiently reasonable tropospheric simulation in GEOS-Chem to serve as a useful reference for ML application.
Figure 2 compares zonal mean profiles of ozone and NO\({}_{x}\) concentrations for December-February (DJF) and June-August (JJA) 2016. The overall patterns are consistent. The Super-Fast mechanism simulates excessive NO\({}_{x}\) in the Northern Hemisphere winter because it does not include loss from the nighttime N\({}_{x}\)O\({}_{5}\) hydrolysis pathway. This may also explain the higher ozone in winter since N\({}_{x}\)O\({}_{5}\) hydrolysis is a loss of odd oxygen. An additional important ozone and NO\({}_{x}\) sink in the standard mechanism in winter is halogen chemistry ([PERSON] et al., 2016),
Figure 2: Zonal mean concentrations of ozone and NO\({}_{x}\) in Goddard Earth Observing System (GEOS)-Chem. The figure compares GEOS-Chem simulations using the Super-Fast mechanism and the standard full-chemistry mechanism, both integrated with the Kinetic Pre-Processor Rosenbrock solver. Results are for December–February (DJF) and June–August (JJA) 2016. Note different scales between panels.
### Testing of Offline and Online ML Solvers
We first test the accuracy and stability of the different offline and online ML solvers described in Section 2.3 by training a single-species ozone chemical solver with all other species simulated with the Rosenbrock solver. The ML solver training is for JJA 2016 and the testing is for July 2017. Here and elsewhere, we will use four metrics to evaluate the ML solver (ML) relative to the reference Super-Fast simulation (\(R\)) for species \(i\in[I,N]\) in a given grid cell:
\[\text{Normalized mean bias (NMB)}=\frac{\sum_{i=1}^{N}\left(\text{ML}_{i}-R_{i} \right)}{\sum_{i=1}^{N}\left(R_{i}\right)}\times 100 \tag{1}\]
\[\text{Root mean square error (RMSE)}=\sqrt{\sum_{i=1}^{N}\frac{\left(\text{ML}_{i}-R_{i} \right)^{2}}{N}} \tag{2}\]
\[\text{Absolute error}=\text{ML}_{i}-R_{i} \tag{3}\]
\[\text{Fractional error}=\frac{2\left(\text{ML}_{i}-R_{i}\right)}{\left(\text{ ML}_{i}+R_{i}\right)}\times 100 \tag{4}\]
These metrics may be averaged spatially over the global domain and/or temporally over the period of interest. Alternative metrics such as Hellinger distance would also be appropriate but RMSE is similar for assessing accuracy.
Figure 4 shows the error statistics for surface ozone when using the different ML solvers. None of the ML solvers show runaway error growth, unlike in previous studies ([PERSON] and [PERSON], 2019; [PERSON] et al., 2020), which we attribute to the relatively low dimensionality of the Super-Fast mechanism boosted by the use of the encoder/decoder to further reduce dimensionality.
\begin{table}
\begin{tabular}{l r r} \hline & \multicolumn{1}{c}{Super-Fast chemistry} & \multicolumn{1}{c}{Standard chemistry} \\ \hline Sources, Tg a\({}^{-1}\) & & \\ Chemical production & 4,480 & 4,980 \\ Cross-propopause transport\({}^{*}\) & 660 & 670 \\ Total & 5,140 & 5,650 \\ Sinks, Tg a\({}^{-1}\) & & \\ Chemical loss & 3,980 & 4,660 \\ Dry deposition & 1,090 & 920 \\ Wet deposition & 69 & 70 \\ Total & 5,140 & 5,650 \\ Ozone tropospheric mass, Tg & 312 & 314 \\ Ozone lifetime, days & 22.2 & 20.3 \\ \hline \end{tabular} Note. From the GEOS-Chem version 12.0.0 simulation for year 2016 with the standard and Super-Fast chemical mechanisms. The budget is the annual mean for the odd oxygen (O\({}_{\text{r}}\)) chemical family as defined in [PERSON] et al. (2017) to account for rapid cycling between O\({}_{\text{r}}\) components. In the Super-Fast mechanism this family is defined as O\({}_{\text{r}}\) + NO\({}_{\text{r}}\) + HNO\({}_{\text{r}}\).
\end{table}
Table 1: Global Budget of Topospheric Ozone in GEOS-ChemThe offline nonrecursive ML solver shows large positive errors in remote regions, large negative errors in ozone production hotspots, and underestimate of temporal variability. We attribute this to the tendency of the ML solver trained on a randomly ordered ensemble of data to focus on simulating the mean. The offline-trained solver trained using a recursive 24-hr feedback based on [PERSON] et al. (2020) improves the RMSE from 35.6 to 22.4 ppb, which is still very high. It features large positive land and negative ocean biases, as well as a small diurnal pattern in the RMSE. The reduction in error likely reflects better accounting of the predictable diurnal behavior of ozone concentrations.
When the offline 24-hr recursive ML solver is retrained online within GEOS-Chem, we find that the RMSE decreases to 6.1 ppb. The online training on representative realizations in sequence (rather than random samples) prevents under/oversampling of specific chemical environments and captures better the temporal evolution of chemistry. But the patterns of biases learned from the offline training persist and are only partly corrected.
Figure 3: Ozone and NO, concentrations in surface air and at 500 hPa in GEOS-Chem. The figure compares GEOS-Chem simulations using the standard full-chemistry mechanism and the Super-Fast mechanism, both integrated with the Kinetic Pre-Processor solver. Results are means for December–February (DJF) and June–August (JIA) 2016. Note different scales between panels.
The ML solver trained online from scratch within GEOS-Chem performs the best by far and is the only viable solver for further consideration. It achieves a low RMSE of 1.3 ppb with fractional errors lower than 10%, which would be considered adequate for a global tropospheric ozone simulation ([PERSON] et al., 2017). We attribute this success to the nonrandom order of the training, allowing the ML solver to emulate the temporal evolution within the CTM environment. We find that training an ML solver online from scratch provides better performance than retraining an offline ML solver because the bias in the offline solver is difficult to unlearn.
### One-Year Simulation Testing of Online ML Solver
We next apply the online ML solvers trained from scratch for all species to a 1-year GEOS-Chem simulation with the Super-Fast mechanism. We train the ML solvers on January-December 2016 and test them on January-December 2017. We expect that performance gain from using different years for training and testing would be minimal but recognize that validating over added years would increase robustness. In early testing, we found that ML solvers for individual seasons outperformed ML solvers trained for the entire year. We also found that the ML solvers could not capture the discontinuity of hydrogen oxide radical (\(\text{HO}_{\text{g}}\equiv\text{OH}+\text{HO}_{\text{2}}\)) concentrations at sunrise/sunset because the ML training uses low-order continuous functions for its fits. Here, we create separate ML solvers for OH and \(\text{HO}_{\text{2}}\) at night, applying a log transformation to their concentrations in order to capture the fast nighttime decay. In the Super-Fast environment, it would alternatively be acceptable to set these concentrations to zero at night.
The online ML solver embedded within GEOS-Chem performs the chemical integration 5\(\times\) faster than the reference Super-Fast simulation (single Intel Broadwell CPU core; 2.10 GHz). This speedup is smaller than in [PERSON] et al. (2020) and [PERSON] et al. (2021) because the Super-Fast mechanism is simpler and because of the overhead in
Figure 4: Simulation of surface ozone by different machine learning (ML) solvers. The left and middle panels show absolute and fractional errors at the end of a 31-day July 2017 simulation (24:00 UTC on 31 July) relative to the reference Super-Fast baseline simulation using the Kinetic Pre-Processor Rosenbrock solver. The right panel shows the temporal evolution of the global hourly root-mean-square error (RMSE) over the 31-day period. The mean RMSE for the last 10 days of July is given inset. See Section 2.3 for description of the different ML solvers. In this application the ML solver is applied to ozone only.
accessing Python code at each time step. Further speedup could be achieved by reading the trained ML solver parameters through text files or by writing them in Fortran.
Figure 5 shows the daily evolution of the global normalized mean bias (NMB) for Super-Fast species over the full year. The global mean OH concentration computed with the ML solver (\(13.2\times 10^{5}\) molecules cm\({}^{-3}\)) reproduces that in the Super-Fast reference simulation (\(13.1\times 10^{5}\) molecules cm\({}^{-3}\)). Ozone has no significant bias averaged over the year (\(-0.3\%\)) and remains within \(\pm 9\%\) on a daily basis. HO\({}_{z}\) is also successfully fitted, with an average bias of 1% and daily values within \(\pm 6\%\). Other species except HNO\({}_{z}\) are also well fitted and none shows error growth over the course of the simulation. The problem with HNO\({}_{z}\) is that--unlike other Super-Fast species--it does not have a chemical loss and there is therefore no first-order correction to growing biases in the ML solver. We also see in Figure 5 that the seasonal switch between solvers can rapidly erase the error from a poorly performing seasonal solver by switching to another solver in the next season. This suggests for future consideration that alternate application of separately trained solvers, or of the ML and reference solver, could significantly improve accuracy.
Figure 6 compares zonal mean ozone and NO\({}_{z}\) concentrations for DJF and JJA between simulations with the ML online and reference solvers, and Figure 7 compares surface and 500 hPa concentrations. Although the overall patterns are consistent, we find large errors in individual latitudinal bands, up to 20% for ozone and 100% for NO\({}_{z}\). The errors are largest at remote latitudes and high altitudes due to chemical error accumulation as air ages. The largest errors are in polar sunlit conditions where the effect of chemical aging during long-range transport is particularly important.
Figure 8 illustrates the ability of the ML solver to reproduce diurnal and synoptic variations of surface ozone for polluted (Beijing) and remote (Cape Verde) conditions. The Beijing time series shows large diurnal variation due to fast production in the daytime followed by fast loss at night from deposition and reaction with NO. Superimposed on this diurnal variation is synoptic (multiday) variability with pollution episodes approaching 100 ppb. The ML solver reproduces these features without systematic bias. Cape Verde shows by contrast much lower
Figure 5: Evolution of the global normalized mean bias (NMB) over a full-year simulation with the online machine learning (ML) solver. The NMB is the global average calculated daily relative to the reference Super-Fast Goddard Earth Observing System-Chem simulation. Results are shown for the 12 species of the Super-Fast mechanism. NO and NO\({}_{z}\) are grouped as NO\({}_{z}\) and OH and HD\({}_{z}\) are grouped as HO\({}_{z}\). Annual mean biases for each species are indicated in legend. Vertical lines indicate seasonal switches between different ML solvers.
variability and no significant diurnal cycle because of low NO\({}_{z}\) and slow ozone deposition to the ocean, and again this is well reproduced by the ML solver.
### Alternative Configurations
Although the online-trained ML solver as described here enables stable full-year global tropospheric chemistry simulations with reasonable accuracy for the main oxidants ozone and OH, there are large regional inaccuracies for species such as NO\({}_{x}\). We tried different approaches to overcome these inaccuracies but without success. Predicting the change in concentrations for longer-lived species rather than the concentrations themselves ([PERSON] and [PERSON], 2019) worsened the fit. Grouping NO and NO\({}_{z}\) as NO\({}_{z}\) in the prediction did not improve results and required a separate step to resolve the partitioning. Training separate ML solvers for different regions such as land, ocean, and upper troposphere did not improve results and led to high errors at the boundaries. Applying a log transform to all input species or using an L-1 norm (instead of least squares) for fitting prevented successful simulation of polluted grid cells such as ozone in Beijing. Applying \(z\)-score normalization rather than min-max normalization led to instability as \(z\)-scores failed to sufficiently bind the range of possible inputs and outputs.
We found that a yearlong trained ML solver experienced significant bias as the highest concentration observations dominated the learned ML parameters. During online training, new data with relatively lower concentrations (e.g., NO\({}_{z}\) < 0.1 ppb) did not influence the parameters of an ML solver that had already been trained on higher concentrations (e.g., NO\({}_{z}\) > 10 ppb). This led to a seasonal bias in which the yearlong trained ML solver made predictions according to the largest values it had seen (e.g., NO\({}_{z}\) in DIF and ozone in JIA). We do not attribute these errors to 'catastrophic forgetting' but rather to large observations dominating the online learning method. Additional preprocessing transformations to inputs may improve this issue.
Figure 6: Zonal mean ozone and NO\({}_{z}\) concentrations in Goddard Earth Observing System-Chem using the online machine learning (ML) solver and compared to the reference simulation. Results are averages for December–February (DJF) and June–August (JIA) 2017. The reference panels are the same as the Super-Fast panels in Figure 2.
We found that fitting individual seasons with the ML solver, as opposed to the full year, led to significant improvement of results. Some of that improvement may relate to error correction in the switch between solvers from one season to the next (Figure 5). This suggests that alternating between independently trained ML solvers or between the ML solver and the Rosenbrock solver could help to reduce error. A similar approach would be to implement an online bias corrector ([PERSON] and [PERSON], 2020) that either nudges the ML solver toward the Rosenbrock reference or learns to call the Rosenbrock solver when the ML solver starts to fail ([PERSON] et al., 2019). These could be directions for future research.
We did not tune the ML parameters in this work due to lack of computationally efficient optimizations designed for online training. We recognize that parameter tuning has the potential to improve the accuracy of our results. Furthermore, due to computational expense, we were not able to generate an ensemble of ML solvers for each season which may also provide a source of improved accuracy and stability ([PERSON] et al., 2022). These are directions for future research.
Figure 7: Surface ozone and NO, concentrations in Goddard Earth Observing System-Chem using the online machine learning (ML) solver and compared to the reference simulation. Results are averages for December–February (DJF) and June–August (JJA) 2017. The reference panels are the same as the Super-Fast panels in Figure 3.
## 4 Conclusions
This work explored the capability of ML to speed up the kinetic integration of chemical mechanisms in full-year global simulations of atmospheric chemistry. The motivation was to remove a major computational bottleneck in global atmospheric chemistry models and for the inclusion of atmospheric chemistry in ESMs. A challenge was to avoid the runaway error growth that affected previous ML application to global models ([PERSON] and [PERSON], 2019).
Chemical mechanisms in current-generation global atmospheric chemistry models such as GEOS-Chem typically include over 200 species ([PERSON] et al., 2020) and kinetic integration is done with high-order implicit solvers (fourth-order Rosenbrock in GEOS-Chem, implemented through KPP). The high dimensionality of the mechanism represents a major challenge for the application of ML solvers. As a first step and to avoid this complication, we implemented in GEOS-Chem the Super-Fast mechanism including only 12 coupled species to represent tropospheric oxidant chemistry ([PERSON] et al., 2018; [PERSON] et al., 2013). We applied to that mechanism a neural network ML solver equipped with an autoencoder ([PERSON] et al., 2020) and compared the resulting simulation in GEOS-Chem to the reference simulation with the Rosenbrock solver.
We tried two approaches for training the ML solver over the global 3-D domain, offline using archived inputs/outputs from 1-hr chemical integration time steps with the reference simulation, and online synchronously with the reference simulation. We found that the common practice of offline training resulted in large errors. We attributed these errors to training on a randomly ordered ensemble of data, and to overfitting caused by multiple passes through the data. Using a recursive algorithm over 24-hr time horizons to capture diurnal and longer modes ([PERSON] et al., 2020) led to some improvement but errors were still large. The ML solver trained online had much better success, which we attribute to representative sampling of the GEOS-Chem simulation as it progresses in time. Online training from scratch performed much better than pretraining offline.
We applied the online ML solver to a 1-year GEOS-Chem simulation with the Super-Fast mechanism. The ML solver reduced the computational cost of the chemical integration five-fold. We found that training the ML solver for individual species and seasons led to best results. The ML solver achieved a stable simulation over the 1-year simulation period with no error growth. Global biases for ozone and OH were insignificant on an annual basis. Global daily biases for ozone were at most 9%. The ML solver was successful at reproducing the diurnal and synoptic variations of ozone at polluted and clean sites, including events of high concentrations. There were however systematic patterns of biases, worst in chemically aged air such as polar sunlit conditions and the middle/ upper troposphere, and large biases for NO\({}_{x}\). Using different ML solver configurations did not readily solve that problem.
An important outcome of our work was to achieve for the first time a stable global simulation of atmospheric chemistry with an ML solver and with multifold improvement in computational performance. We found in the process that online training of the ML solver is considerably superior to offline training. Online training may achieve even greater computational speedups than demonstrated here by reading the trained ML solver parameters through text files or by writing them in Fortran. Our application was limited to the oversimplified Super-Fast
Figure 8: Hourly time series of surface ozone concentrations in Beijing (39.9 N, 116 E) and Cape Verde (16.5 N, 23.0 W) in July 2017. The Goddard Earth Observing System-Chem simulation using the online machine learning (ML) solver is compared to the reference simulation using the Kinetic Pre-Processor Rosenbrock solver.
mechanism, and even then regional biases could be large. Future work should focus on (a) optimizing the ML parameters during online training, (b) generating an ensemble of ML solvers for each season for improved accuracy and stability, and (c) implementing bias avoidance as there has been some studies to that effect ([PERSON] & [PERSON], 2020; [PERSON] et al., 2019). The curse of dimensionality in full atmospheric chemistry mechanisms could be alleviated by the encoder/decoder processing to reduce dimensionality in the ML solver ([PERSON] et al., 2020).
## Data Availability Statement
The standard GEOS-Chem code is available through [[https://doi.org/10.5281/zenodo.1343547](https://doi.org/10.5281/zenodo.1343547)]([https://doi.org/10.5281/zenodo.1343547](https://doi.org/10.5281/zenodo.1343547)) (version 12.0.0). The KPP implementation of the Super-Fast mechanism and the training and testing methods for the neural network ML solver can be found at Zenodo ([[https://zenodo.org/record/5736524](https://zenodo.org/record/5736524)]([https://zenodo.org/record/5736524](https://zenodo.org/record/5736524))).
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wiley/fed96a22_7008_435c_9fe2_87a6998ab817.md | and salty brine. [PERSON] and [PERSON] (2015) comprehensively evaluated the change from [PERSON] and Lipscomb (1999), (hereafter BL99) thermodynamics, which has a prescribed vertical salinity profile, to MUSHY within the standalone Los Alamos Sea Ice Model CICE ([PERSON] et al., 2015) in global simulations with prescribed atmospheric and oceanic forcing, performing pairs of experiments in which the only difference was the physics change being tested. They tested nine aspects of the thermodynamics parameterization, namely, internal temperature updates; internal salinity updates; the liquidus relation; thermal conductivity; shortwave modification; thickness changes; frazil ice formation; melt pond flushing; and snow-ice formation. In these runs, the atmosphere and ocean were not able to change in response to changes in the sea ice, and their experiments produced thicker and more extensive sea ice in the Arctic with MUSHY, while in the Antarctic there was similar sea ice with MUSHY and BL99. The primary reason behind the Northern Hemisphere differences in their simulations was due to the modification of melt pond characteristics associated with the parameterization of melt pond drainage in the MUSHY configuration. Secondary factors were a shortwave modification near the melt point within the ice and differences in how ice grows (primarily basal) and melts between the formulations. In the Southern Hemisphere they found that snow-ice formation was more important but did not contribute to significant differences in the sea ice volume and area.
The Community Earth System Model version 2 (CESM2; [PERSON] et al., 2020) is one of the first Coupled Model Intercomparison Project Phase 6 (CMIP6) models to move to this newer thermodynamic formulation. CESM2 contains version 5.1.2 of the Los Alamos Sea Ice Model (CICE; [PERSON] et al., 2015) and includes support for the Sea Ice Model Intercomparison Project (SIMIP) variable request ([PERSON] et al., 2016). This version of CICE features a number of new physics options including the MUSHY thermodynamics of [PERSON] et al. (2013) and the level-ice melt pond scheme of [PERSON] et al. (2013). The main change with the new MUSHY physics of [PERSON] et al. (2013) is the inclusion of the variable, prognostic salinity profile. In the BL99 thermodynamic formulation used in CESM1, a fixed prescribed salinity profile based on observations was applied.
This manuscript examines the influence of the new sea ice thermodynamic formulation within the coupled context of CESM2. As discussed in section 2, this involves comparing fully coupled simulations with MUSHY to simulations which use BL99. An assessment of the sea ice mean state and mass budget differences between the simulations in both hemispheres is provided, and the influence on coupled simulation characteristics is discussed. Comparison of CESM2 sea ice mass budgets with other models contributed to CMIP6 are analyzed in [PERSON] et al. (2020), and a number of characteristics of the sea ice as simulated in CESM2 runs are documented in [PERSON] et al. (2020), [PERSON] et al. (2020), and [PERSON] et al. (2020, in press).
## 2 Model and Experiment Description
As described by [PERSON] et al. (2013), the CICE model used here is a dynamic-thermodynamic model which incorporates an ice thickness distribution. Sea ice dynamics is simulated using an elastic-viscous-plastic rheology ([PERSON] & [PERSON], 2002) with a linear remapping advection scheme ([PERSON] & [PERSON], 2004). The ice thickness distribution is resolved with five ice thickness categories and a single open water category.
A new aspect of the CICE model used here is the inclusion of prognostic sea ice salinity and associated changes in the ice thermodynamics. [PERSON] and [PERSON] (2015) fully describe this MUSHY thermodynamic formulation, and here we highlight the primary details. The model simulates time-varying and vertically resolved prognostic salinity and its influence on thermodynamic properties of the sea ice. The migration of water and brine through the ice is handled through drainage and flushing processes, allowing the bulk salinity to change over time. This is in contrast to the BL99 scheme which has a prescribed salinity profile. In both formulations, the ice salinity impacts thermodynamic characteristics, and the internal ice energy is a function of the salt content.
With the prognostic salinity profile there are several associated differences including the freezing point calculation, the thermal conductivity in the sea ice, the growth of sea ice including frazil ice formation, snow-ice formation, gravity drainage and melt pond flushing ([PERSON] et al., 2013). Also, for consistency with the [PERSON] et al. (2013) thermodynamics, the salinity-dependent freezing point of Assur (1958) was used for both the sea ice and ocean components at the sea ice-ocean interface. The melt pond formulation of [PERSON] et al. (2013) considers the fraction of level ice (as a tracer) versus deformed ice, which directly impacts the melt pond concentration and depth. In addition to the new physics, the vertical levels in CESM2 were increased from 4 to 8 in the sea ice and from 1 to 3 in the snow, in order to better resolve the temperature and salinity gradients in the sea ice.
The sea ice mass budget terms are also impacted by the MUBHY formulation in that sea ice forms a mass of solid ice and salty brine. This directly impacts the fluxes of water and heat between the sea ice and ocean. The salt flux is influenced by the mass of water exchange, but a salinity of 4 psi is still assumed here as in BL99 for simplicity of coupling with the ocean model. This is a limitation of the current configuration and means that we do not simulate the full impact of prognostic sea ice salinity on the coupled climate system. While not ideal, the reason for the choice of a constant coupling salinity is practical in that the ocean component of CESM2, the Parallel Ocean Program (POP) model, uses a virtual salt flux at the surface. The POP model is also responsible for computing the fluxes of freshwater and salt due to Brazil ice formation. Hence, the reference salinity of 34.8 in the ocean and 4 psi in the sea ice for computing salt fluxes simplifies salt conservation. Snow ice formation occurs when the weight of the snow pushes the snow-ice interface below the waterline. In this process, the MUBHY scheme explicitly accounts for seawater flooding of the snowpack, thereby affecting the mass of snow-ice formed, whereas in BL99 the snow is just compressed into ice with no addition of seawater. Melt pond properties are also influenced by the MUBHY formulation as it allows melt ponds to drain based on the sea ice porosity, calculated with the prognostic salinity and through parameterized macroscopic holes. On the other hand, the BL99 scheme only allows drainage due to the salinity-based ice porosity.
To diagnose the influence of the new sea ice physics on CESM2, two complementary, preindustrial model experiments were performed: the first with the MUBHY thermodynamics of [PERSON] et al. (2013) and the second with the BL99 thermodynamics of [PERSON] and [PERSON] (1999). In the fully coupled CESM2 experiments presented here, the only difference between the simulations is the value of the CICE parameter \"ktherm,\" which selects the vertical thermodynamics scheme. In other words, both experiments use eight vertical levels in the sea ice and one level in the snow, the level ice melt pond formulation, and a salinity-dependent freezing point at the base of the sea ice. These simulations were both branched from the CESM2 CMIP6 preindustrial control run ([PERSON] et al., 2020) at year 880 and each ran for 50 years. The simulations shown here used only the single-layer snow formulation as compared to three layers in the standard CESM2 simulations, but the simulated climatology was not significantly different from the three-layer simulations (not shown). The reasons for the limited sensitivity to the number of snow layers are uncertain but could arise from the large internal variability in the system or the lack of sophistication in the snow model, which has a constant thermal conductivity and density. Additionally, in the CESM2 version of CICES, we have added a shortwave adjustment for both thermodynamics schemes to overcome a coupled instability that can cause internal sea ice layers to melt completely in a single time step, generating very large fluxes of fresh water. By rerouting excess shortwave (when the internal temperature is very close to melting) from inside the sea ice to the top surface, this change allows the sea ice to melt more gradually. This shortwave adjustment is included in both our MUBHY and BL99 simulations.
## 3 Results
### Sea Ice Mean State and Variability
The annual mean over 50 years shows that sea ice thickness is significantly larger in the MUBHY configuration as shown in Figure 0(a). While the Southern Hemisphere thickness differences are significant in some locations (Figure 0(b)), they are generally small. These coupled results are consistent with [PERSON] and [PERSON] (2015), and the processes/causes leading to the difference will be expanded upon in the next section. Similarly, the annual mean sea ice concentration (Figure 2) is significantly higher in the MUBHY run in the Arctic but smaller in the Antarctic. The snow depth in the Arctic is more complicated. Generally, in the central Arctic, the snow is deeper in the MUBHY run, but is thinner in some of the marginal seas area (Figure 2(a)). The annual northern hemispheric mean snow volume (Table 1) is quite similar in the two runs. The Southern Hemisphere snow cover is thinner in most of the pack in the MUBHY simulation (Figure 2(b)) due to more snow-ice formation.
Considering the annual cycle of ice conditions, we find that the Northern Hemisphere sea ice is significantly more extensive in the MUSHY simulation in all months with the largest changes in summer (Figure 4a). Although it is useful to put these results in the context of the observations, it is worth noting that the NSIDC climatology shown here ([PERSON] et al., 2017) is for present day conditions, while these simulations are preindustrial. Therefore, a direct match between the model and observations should not be expected. More extensive sea ice is consistent with the thicker ice in the MUSHY experiments and the strong coupling
Figure 1: Mean annual (over the 50 years) sea ice thickness (m) and differences for (a) NH and (b) SH. MUSHY is top left and BL99 is top right. Differences, at bottom center, show MUSHY-BL99 and are only shown where significant at the 5% level.
Figure 2: Mean annual (over the 50 years) sea ice concentration (%) and differences for (a) NH and (b) SH. MUSHY is top left and BL99 is top right. Differences, at bottom center, show MUSHY-BL99 and are only shown where significant at the 5% level.
between ice thickness and ice area during summer months. In the Southern Hemisphere (Figure 4b), the sea ice extent in the two simulations is statistically indistinguishable in all months.
Notably, the Northern Hemisphere differences originate almost immediately in the simulations, and the annual mean Arctic sea ice volumes (Figure 5a) and ice area (Figure 5c) are significantly larger in the MUSHY run throughout the entire 50-year experiments. In the Southern Hemisphere, the volume and area are visibly different (Figures 5b and 5d), but the differences are much smaller than in the Northern Hemisphere. The 50-year sea ice volume and snow volume mean differences (Table 1) are all significant to the 5% level in both hemispheres based on a \(t\) test. The 50-year variances (Table 1) are not significantly different in either hemisphere based on an \(F\) test. That is, the sea ice in the MUSHY simulation is thicker and more extensive overall in both hemispheres, but the variability is unchanged. In the MUSHY simulations, the annual hemispheric mean snow volume (Table 1) is much smaller in the Southern Hemisphere but slightly larger in the Northern Hemisphere. However, although these 50-year simulations are designed to account for interannual variability so as to assess differences between the experiments, they do not capture the full extent of decadal variability.
### Mass Budgets
To address the question of why the MUSHY simulation has thicker ice, we examine the mass budgets in our two simulations using the SIMIP ([PERSON] et al., 2016) variables. Figure 6 shows the overall sea ice mass budget components over the central Arctic region (standard NSIDC definition) along with differences (MUSHY minus BL99) of the mass budget terms. The differences are further quantified in Table 2. Sea ice mass budget differences can arise from both the different thermodynamic treatment in the simulations and feedbacks associated with changes in the thickness and concentration mean state due to both dynamics and thermodynamics. The sea ice mass budget is a balance of the growth, melt, and divergence of the sea ice, with divergence associated with the ice motion and considered as the \"dynamic\" contribution to the mass budgets. Ice melt has contributions from the ice surface, the ice base, and the lateral melting of floes. Ice growth has contributions from congelation growth at the base of the ice,
\begin{table}
\begin{tabular}{l l l l l} \hline \hline & BL99 & BL99 & MUSHY & MUSHY \\ & mean & variance & mean & variance \\ \hline NH ice volume & 1.77 & 0.02 & 2.31 & 0.012 \\ NH ice area & 10.13 & 0.06 & 10.72 & 0.055 \\ NH snow volume & 0.14 & 0.0001 & 0.15 & 0.0001 \\ SH ice volume & 1.45 & 0.01 & 1.53 & 0.01 \\ SH ice area & 11.00 & 0.12 & 11.35 & 0.14 \\ SH snow volume & 0.37 & 0.0002 & 0.32 & 0.0005 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Annual Northern Hemisphere (NH) and Southern Hemisphere (SH) Mean Sea Ice Volume (\(10^{13}\) m\({}^{2}\)). Snow Volume (\(10^{13}\) m\({}^{2}\)), and Sea Ice Area (\(10^{12}\) m\({}^{2}\)) and Interannual Variance
Figure 3: Annual total (averaged over 50 years) snow depth (cm) and difference for the NH (a) and SH (b). MUSHY is top left, and BL99 is top right. Differences, at bottom center, are MUSHY-BL99 and are only shown where significant at the 5% level.
frazil ice formation associated with the supercooling of ocean water, and snow ice formation in which snow on the ice surface is flooded and freezes to sea ice.
In the net (black) central Arctic seasonal mass budget (Figure 6a), the BL99 case (solid lines) has a slightly larger amplitude annual cycle as a result of more growth in winter and more melt in summer. The dynamic ice divergence term is not shown here as it is small for the central Arctic domain. The larger summer melt is the result of greater top and bottom melt in the BL99 scheme. The enhanced BL99 growth in winter is largely due to enhanced congelation growth (cyan). This is consistent with the thinner ice and snow in BL99, which allows for more conduction of heat from the ice-ocean interface. The MUSHY scheme has larger frazil ice growth (magenta) in winter, but it is not sufficiently large to lead to more total winter growth. The increased frazil formation is expected because of the way the MUSHY physics functions, forming ice as a combination of solid and liquid sea water. The liquid is trapped within the sea ice, and hence, the net thickness of sea ice
Figure 4: Climatological seasonal cycles of sea ice extent (\(10^{12}\) m\({}^{2}\)) for (a) NH and (b) SH as compared to the satellite observed NSIDC extent ([PERSON] et al., 2017).
Figure 5: Annual mean sea ice volume (top) and area (bottom) time series for MUSHY (red) and BL99 (blue) NH (a and c) and SH (b and d).
and water together is thicker ([PERSON] et al., 2013). The snow and ice mass budget annual totals for each of these components are shown in Table 2.
In the Antarctic (Figure 7), the net sea ice mass budget is similar for the two thermodynamic formulations, but the individual mass budget terms contributing to this are different in BL99 and MUSHY. MUSHY has significantly more frazil growth and snow-ice formation than BL99. This is largely compensated for by decreased congelation growth relative to BL99. There is little difference in top melt, but considerably stronger bottom melt in the MUSHY simulation. The bottom melt in the Southern Hemisphere is stronger in the MUSHY case because the sea ice is saltier than the BL99 sea ice (not shown) and hence begins to melt at a lower temperature, so it is easier to melt overall. The difference in mass budget terms, particularly the frazil ice, appears to play a role in the thinner and less extensive Antarctic sea ice in CESM2 compared to CESM1 ([PERSON] et al., 2020).
There are regional differences in the sea ice mass budgets where frazil ice (Figure 8) is more important near the coast and snow-ice formation (Figure 9) is more important in the open pack. Figure 8 shows the frazil formation in both hemispheres. The NH frazil formation occurs largely in the marginal seas regions and near the coast (Figure 8a), and there is significantly more frazil formation in the MUSHY run as mentioned earlier. The SH frazil formation occurs almost entirely around the coast (Figure 8b). The NH snow-ice formation (Figure 9a) is generally limited to the marginal seas areas and not significant in the central Arctic as mentioned earlier. In the SH, the snow-ice formation is very important in the open pack regions, and there is significantly more frazil ice and snow-ice formation in the MUSHY run (Figure 9b). This snow-ice formation difference leads to less snow overall in the MUSHY as mentioned earlier.
The snow fraction (Figure 10b) is higher in the MUSHY scheme, and when the minimum albedo occurs, snow fraction is about 0.3 in the MUSHY run versus about 0.1 in the BL99 simulation. The radiatively active pond coverage (i.e., the fraction of liquid water not hidden by snow, used in the shortwave radiation computation, Figure 10c) is smaller in the MUSHY simulation with a maximum of approximately 0.25 versus 0.3 in the BL99 run. The combination of reduced melt pond fraction and higher snow fraction leads to a higher broadband albedo in midsummer for MUSHY (Figure 10a). In the fall, the melt pond fraction is slightly greater in the MUSHY scheme, but the resulting lower albedo occurs when sunlight is disappearing rapidly and as a result is not as important for the surface energy balance. The broadband albedo is the sum of the fraction of different surface types multiplied by the albedo for each surface: snow, pond, or bare ice. If we assume the albedo for each surface (a\({}_{\rm surface\,\,type}\)) is approximately the same for each simulation (they use the same radiation model code and physical parameters), then the
Figure 8. Total annual frazil ice formation (averaged over 50 years) in the NH (a) and SH (b) in units of \(10^{4}\) kg/m\({}^{2}\) s. The difference is MUSHY-BL99, and differences are shown only where significant.
Figure 7. SH (a) annual sea ice mass budget and (b) difference in kg/s. In (a) the MUSHY experiment is dashed, and the BL99 experiment is solid. The difference is MUSHY-BL99, and differences that are not significant at the 95% level are set to 0.
difference in broadband albedo (Da) is approximately due to the fractional differences (Df\({}_{\text{surface\_type}}\)) in each surface (see Equation 1).
\[\Delta\alpha=\Delta f_{\text{source}}\,^{*}\alpha_{\text{source}}+\Delta f_{ \text{pond}}\,^{*}\alpha_{\text{pond}}+\Delta f_{\text{iac}}\,^{*}\alpha_{\text{ iac}} \tag{1}\]
Assuming albedos of approximately 0.75, 0.6, and 0.3 for snow, bare ice, and melt ponds in midsummer, values identical in both runs, we can estimate the broadband albedo differences from Equation 1 using the difference in surface fractions between experiments (BL99 minus MUSHY). As shown in Figure 10d, despite its simplicity, this method provides a reasonable approximation to the actual albedo changes calculated in the experiments. Additionally, it allows us to calculate each surface type's contribution (Figure 10d). BL99 has a lower broadband albedo than MUSHY, and the term associated with the snow fraction difference is the largest magnitude contribution to the broadband albedo difference. It is countered by the opposite sign bare ice albedo difference and pond albedo difference. Thus, on average the larger snow fractions in MUSHY lead to higher broadband albedo. The bare ice difference is largely due to smaller snow fraction in the BL99 run versus the MUSHY run, but the melt pond difference requires a bit more detail to understand.
As snow is an important aspect of the seasonal albedo evolution, the snow mass budget on the surface of the sea ice is shown in Figure 11. In addition to snow accumulation, melt, and snow ice formation terms, there is a dynamic loss term associated with transport and ridging of ice which deposits some snow into the ocean. Surprisingly, given the considerable difference in snow fractional coverage, the mass budget terms and the mean annual cycle of snow thickness (Figure 11c) are very similar between the simulations. Note that the snow fraction in the model depends on snow thickness and is always equal to one when snow thickness is above a threshold value of 3 cm. Thus, small differences in snow thickness around this threshold value can have a large influence on the fraction of snow-covered ice.
The primary source of melt ponds is snow melt, and melt ponds can be reduced by both the fraction of level ice and the drainage. The MUSHY scheme also allows for macroscopic drainage of melt ponds, which reduces the depth (volume) of the ponds at a rate of approximately 0.2% every time step in the model, or about 10% each day. This volume loss is offset by the surface melt providing water for the ponds. However, the snow melt and snow depth are nearly the same in each run (not shown), the level ice area is very similar, and hence the pond difference can be explained almost entirely by the drainage. Note also
Figure 9: Total annual snow ice formation (averaged over 50 years) in the NH (a) and SH (b) in units of \(10^{4}\) kg/m\({}^{2}\) s. The difference is MUSHY-BL99, and differences are shown only where significant.
Figure 11: Central Arctic (a) annual snow mass budget and (b) difference in kg/s. In (a) the MUSHY experiment is dashed, and the BL99 experiment is solid. In panel b, the differences are MUSHY-BL99 for the entire central Arctic. Differences that are not significant at the 95% level are set to 0. Panel (c) shows the NH daily mean snow depth from the two simulations in m.
Figure 10: Climatological seasonal cycle of (a) albedo, (b) snow fraction, (c) radiatively active melt pond fraction, and (d) difference in albedo and terms in Equation 1 in a Beaufort Sea region (70–85 N, \(-\)130 to \(-\)180 W), with plus and minus one standard deviation (dashed) for panels (a)–(c).
Figure 12: NH April-May-June mean (a) snow fraction and (b) radiatively active pond fraction. MUSHY is top left, and BL99 is top right. Differences, at bottom center, show MUSHY-BL99 and are only shown where significant at the 5% level.
Figure 13: NH annual mean surface air temperature (K) and difference. MUSHY is top left and BL99 is top right. Differences, at bottom center, are MUSHY-BL99 and are only shown where significant at the 5% level.
that the radiatively active pond fraction shown in Figure 10c will also be reduced from the overall pond fraction due to snow cover on the sea ice. Thus, pond coverage (Figure 12b) is a function of the snow cover, surface melt, pond drainage, and level ice fraction--as ponds are located only on level ice in the melt pond scheme used in both simulations. The MUSHY experiment has slightly less level ice in the central Arctic (not shown), which reduces pond area coverage somewhat. There is a suggestion in the [PERSON] et al. (2013) work that thinner ice leads to less ridging and hence more level ice area. So the thinner ice over all in the BL99 experiment would lead to more level ice. However, the difference in level ice area is quite small overall (less than 10% different). The macroscopic drainage and increased snow fraction are more important differences leading to less ponds in the MUSHY experiment as mentioned earlier. These factors lead to less pond coverage in the MUSHY experiment and hence a higher broadband albedo and less top melt of the sea ice in the central Arctic. Also, the level melt pond formulation ([PERSON] et al., 2013) allows for the pond water to infiltrate the snow cover and hence reduce the snow fraction. So there is an additional feedback here where the greater pond coverage in the BL99 experiment leads to less snow cover. Unfortunately, the pond depth was not saved in these simulations, and hence, the pond volume was not available. The pond depth is used to reduce the snow depth in the level melt pond scheme. When the snow depth reaches a critical threshold of 3 cm, the snow fraction is reduced linearly as mentioned earlier. However, before the critical snow depth is reached, it is also possible for the pond fraction to reduce the snow fraction when the snow fraction is close to one. It is worth noting that the level melt ponds ([PERSON] et al., 2013) have some limitations and potentially a more sophisticated melt pond formulation that takes into account the surface topography (e.g., [PERSON] et al., 2010) might lead to different results. The snow infiltration along with the slightly more rapid decline in snow thickness in the BL99 simulation (Figure 11c) leads to a smaller fraction and hence a lower albedo in BL99 compared to MUSHY. In the Southern Hemisphere, because snow remains longer on the sea ice hiding liquid water, melt ponds are not a dominant factor.
### Coupled Impacts
To assess the potential coupled impacts of the change in the vertical thermodynamic schemes, the Arctic surface air temperature is shown in Figure 13. The thicker ice and deeper snow in MUSHY lead to colder conditions over the ice pack. The differences in surface air temperature (Figure 13) are significant over the central Arctic. The higher surface albedo in the MUSHY case changes the surface energy balance by reflecting more shortwave energy back to the atmosphere, which results in less surface melt, a cooler surface, and
Figure 14: NH July-August-September mean (a) sea surface temperature (°C) and (b) sea surface salinity (psu). MUSHY is top left, and BL99 is top right. Differences, at bottom center, show MUSHY-BL99 and are only shown where significant at the 5% level.
more snow cover. This change has a positive feedback on ice growth and air temperature in the coupled model, because the sea ice melts less in summer, dominating the slower growth of thicker ice in the fall. This feedback is not present in a forced ice-ocean experiment, as was shown by [PERSON] and [PERSON] (2015).
Similarly, the sea surface temperature and salinity (Figure 14) show a colder and saltier central Arctic where the MUSHY has thicker ice due to enhanced ice growth. The colder temperatures are due to lower freezing point temperatures. The North Atlantic is colder and fresher due to increased sea ice export of thicker ice from the Arctic. Note that the salt fluxes are computed using a reference salinity in the ocean and sea ice as mentioned earlier, which may also impact the results here. However, the difference between the sea ice and ocean salinity is large enough that this impact would be relatively small. The differences in the ocean fields are somewhat muted as these were only 50-year simulations and there would likely have been a stronger response in longer, better ocean-equilibrated simulations.
## 4 Discussion and Conclusions
CESM2 ([PERSON] et al., 2020) incorporates a new sea ice model component that includes prognostic salinity and treats sea ice as a two-phase mushy layer following [PERSON] et al. (2013). We find that the MUSHY scheme produces thicker and more extensive ice overall in both hemispheres relative to the Bitz and Lipscomb (BL99) thermodynamics used in earlier CESM versions. While this agrees with the stand-alone sea ice results of [PERSON] and [PERSON] (2015), the reasons for it differ somewhat, partly due to coupled interactions with the atmosphere and ocean. [PERSON] and [PERSON] (2015) found that the difference in melt pond drainage was the leading factor for thicker ice in MUSHY, and changes in the shortwave formulation and the way thickness changes are computed (i.e., the uptake of sea water and ice in the MUSHY scheme) were also found to be important. In our fully coupled CESM2 simulations, both the MUSHY and BL99 thermodynamic schemes use the same shortwave formulation, so this radiative factor has been removed in our comparisons. While the Arctic melt pond coverage is different between the simulations, and contributes to the differences in top melt, the main factor here is the difference in snow fraction between the simulations. The MUSHY simulation has less surface melt and more frazil ice formation (by design), which is partly offset by reduced congelation growth. This balance of melt and growth leads to thicker ice in the MUSHY run. These differences are particularly important in the marginal sea ice regions, where the sea ice is both thinner and less extensive. Draining of melt ponds and reduced surface melt are key differences for the melt pond coverage and hence the surface albedo. Smaller differences in undeformed or level ice also play a role in the melt pond coverage. While the melt pond drainage is determined to be a key aspect as was found in [PERSON] and [PERSON] (2015), it is the snow infiltration from ponds and accumulation of snow impacts on the snow fraction that lead to differences in the broadband albedo and hence the top melt. Unfortunately, the pond volume was not available, but the pond fraction reduction of the snow fraction was shown to be important.
In the Southern Hemisphere, sea ice has much less top melt, and snow-ice formation plays a much larger role in these experiments. While individual mass budget terms differ in the MUSHY simulation relative to BL99, the net budget is similar, and the mean sea ice state differences are much smaller for the Antarctic than the Arctic. Despite the balance in terms being quite similar in the Antarctic sea ice, the regional differences in these terms show both positive and negative differences in the thickness and area. In particular, frazil ice formation is more important near the coast and snow-ice formation is more important in the open pack. Aspects of this are also discussed in [PERSON] et al. (2020).
The change to the thermodynamics with the MUSHY physics does affect the sea ice thickness in CESM2. Despite the thicker sea ice in the MUSHY run, the impacts on the rest of the coupled system are relatively minor. There are small differences in the surface air temperature over the sea ice and the sea surface salinity and temperature. These differences in the atmosphere and ocean also feed back on the sea ice in the coupled system, not present in the simulations of [PERSON] and [PERSON] (2015) as mentioned. However, in comparisons of CESM2 and CESM1, a number of other physics changes are present across the atmosphere and ocean components, and hence, the change to the MUSHY physics in CESM2 is not as large. These changes also have an important influence on the sea ice simulation and its feedbacks within the coupled system ([PERSON] et al., 2020; [PERSON] et al., 2020).
## Data Availability Statement
Previous and current CESM versions are freely available online (at [[https://www.cesm.ucar.edu/models/cesm2/](https://www.cesm.ucar.edu/models/cesm2/)]([https://www.cesm.ucar.edu/models/cesm2/](https://www.cesm.ucar.edu/models/cesm2/))). The CESM data sets used in this study will be made available upon acceptance of the manuscript from the Earth System Grid Federation (ESGF) at [[https://esgf-node.llll.gov/Fsearch/cmip6](https://esgf-node.llll.gov/Fsearch/cmip6)]([https://esgf-node.llll.gov/Fsearch/cmip6](https://esgf-node.llll.gov/Fsearch/cmip6)), or from the NCAR Digital Asset Services Hub (DASH) at [[https://data.ucar.edu](https://data.ucar.edu)]([https://data.ucar.edu](https://data.ucar.edu)), or from the links provided from the CESM website (at [[https://www.cesm.ucar.edu](https://www.cesm.ucar.edu)]([https://www.cesm.ucar.edu](https://www.cesm.ucar.edu))).
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wiley/fecad69a_03a2_46a5_bca1_139bd4304ed6.md | AMOC, Water Mass Transformations, and Their Responses to Changing Resolution in the Finite-Volume Sea Ice-Ocean Model
[PERSON]
1 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1A. M. Obukhov Institute of Atmospheric Physics Russian Academy of Science, Moscow, Russia, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
1 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1A. M. Obukhov Institute of Atmospheric Physics Russian Academy of Science, Moscow, Russia, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
1 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1A. M. Obukhov Institute of Atmospheric Physics Russian Academy of Science, Moscow, Russia, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
4 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
1 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
2 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
1 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1A. M. Obukhov Institute of Atmospheric Physics Russian Academy of Science, Moscow, Russia, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
[PERSON]
2 Affred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany, 1 Department of Mathematics and Logistics, Jacobs University, Bremen, Germany, 1 Department of Physics and Mathematics, University of Alcala, Alcala, Spain, 1 Shirshov Institute of Oceanology, Russian Academy of Science, Moscow, Russia
###### Abstract
The Atlantic meridional overturning circulation (AMOC) is one of the most important characteristics of an ocean model run. Using the depth (z) and density frameworks, we analyze how the sinking and diapycnal transformations defining the AMOC as well as AMOC strength and variability react to mesh refinement from low to higher resolution in two model runs driven by the CORE-II forcing. Both runs can represent the key locations of sinking and diapycnal transformations behind AMOC, that is, northeastern North Atlantic. Although their spatial patterns do not change significantly with resolution in both frameworks as the consequence of the same atmospheric forcing, the quantitative differences, reaching several servderns, are seen in different locations between two model runs for both frameworks. In particular, the refinement leads to the strongest differences in the vertical transport and diapycnal transformations in the latitude range between 30\({}^{\circ}\)N and 55\({}^{\circ}\)N. The z framework emphasizes the role of localized upwelling around the Gulf Stream separation site, whereas the density framework emphasizes the contribution of (spurious) diapycnal mixing around the Grand Banks. Both effects are reduced in the higher-resolution run, leading to higher AMOC south of 26\({}^{\circ}\)N as compared to the low-resolution run, despite the AMOC maxima, located at high latitudes, are higher in the low-resolution run. We suggest that both AMOC frameworks should be used routinely in standard analyses, including forthcoming intercomparison projects.
## 1 Plan Language Summary
In various international programs such as the Climate Model Intercomparison Project (CMIP), climate models are used to assess the past, present, and future climate. The Atlantic meridional overturning circulation (AMOC) is one of the most important characteristics of an ocean model simulation. Commonly, it is computed as a stream function of zonally averaged flow along the constant depth (z-AMOC). However, there are shortcomings related to the inclination of density surfaces in reality, which may lead to the appearance of artificial circulation cells. In order to eliminate these artifacts, it is essential to compute the AMOC along constant density surfaces (g-AMOC). That is why recent studies underlined the importance of the g framework for the AMOC analysis. However, neither the CMIP data nor the native output of most of the ocean circulation models is sufficient for the straightforward computation of g-AMOC. Hence, g-AMOC remains important but rarely computed diagnostics. In this paper we analyze the fundamental differences between both representations of AMOC in order to better understand the role of the spatial resolution of numerical models in representing AMOC formation, strength, and variability. We suggest that the g-AMOC and water mass transformation framework should be used routinely in standard analyses, including forthcoming intercomparison projects.
## 2 Introduction
The Atlantic meridional overturning circulation (AMOC) is an important element of the climate system, determining many aspects of global climate (see, e.g., [PERSON], 2016; [PERSON] et al., 2019; [PERSON] et al., 2007). In particular, the possible decline of AMOC in a warming climate ([PERSON] et al., 2013) might have strong implications for regional climate changes. It is therefore not surprising that AMOC,AMOC variability, and trends are a subject of numerous studies and one of the key diagnostics in different model intercomparison projects such as CORE-II ([PERSON] et al., 2014, 2016, or Climate Model Intercomparison Project (CMIP, see, e.g., [PERSON] et al., 2019).
In ocean models the AMOC is commonly computed as a stream function of zonally averaged flow along the constant depth (hereafter z-AMOC). Either meridional or vertical ocean velocity can be used for computation. Both velocity components are part of the standard output of ocean models, making z-AMOC one of the most widely used diagnostics in ocean and climate modeling. Although the importance of z-AMOC is unquestionable, there are shortcomings related to the fact that ocean flows predominantly follow the inclined isopycnal surfaces, and not z surfaces. In fact, zonal averaging at a constant depth may lead to the appearance of spurious circulation cells (such as the Deacon cell in the Southern Ocean; see e.g., [PERSON], 1994; [PERSON], 1997; [PERSON] et al., 2000). These artifacts are eliminated if the AMOC is computed along isopycnals (\(\uprho\)-AMOC), and frequently potential density referenced to 2,000 dBar is used for that. However, model vertical discretization typically deviates from an isopycnal one (in top layers of hybrid-coordinate models or everywhere in z coordinate models). Since the horizontal transports in isopycnal layers seldom belong to the standard model output, \(\uprho\)-AMOC is a well known but still rarely computed diagnostic.
Even a cursory glance into the results of intercomparison projects is sufficient to conclude that models show a substantial spread in the simulated z-AMOC (see, e.g., [PERSON] et al., 2020); and in many cases, the spread is large even for the same model when tuned differently (see, e.g., [PERSON] et al., 2014, 2016). While there is a general understanding that the magnitude of AMOC is related (among other factors) to surface water mass formation in the northern North Atlantic, the link is not obvious for the simulated z-AMOC, and tuning models to bring their AMOC in correspondence to the observational values at MOCHA-RAPID array (see, e.g., [PERSON] et al., 2007) is difficult. It is generally expected that higher resolution will increase the AMOC strength, leading to closer agreement with observations (see, e.g., [PERSON] et al., 2020; [PERSON] et al., 2016; [PERSON] et al., 2020; [PERSON] et al., 2020). However, the question of how and through which mechanism the simulated AMOC is modified when the resolution is refined is still far from being fully answered.
The framework of \(\uprho\)-AMOC may help in dealing with this question because it directly incorporates surface water mass transformations (see, e.g., [PERSON], 2001, or [PERSON] et al., 2019, for discussion). The recent study of [PERSON] et al. (2018) shows how this framework can be used to map the three-dimensional structure of the total and surface-forced transformations in the North Atlantic setup of HYCOM. It also gains significance in the light of the recent observational study by [PERSON] et al. (2019) that changed our understanding of how AMOC is formed. [PERSON] et al. (2019) emphasize the role of the eastern (east of the tip of Greenland) basin in the northern North Atlantic, showing that \(\uprho\)-AMOC transports with respect to isoneutral surface 27.66 are largely determined by the eastern basin, whereas the role of the Labrador Sea is subdominant. This finding also raises a question as to what extent the models used in climate studies are able to simulate this observed behavior.
In this paper, we use the z and density frameworks to trace how the change in mesh resolution modifies the simulated AMOC in two runs driven by the same forcing, but on different meshes, one coarse (LR), and the other one refined in the regions where the observed eddy variability is high (HR), most importantly, including the Gulf Stream (GS) and adjacent areas. We follow the approach by [PERSON] et al. (2018) to learn about the change in diapycnal transformations and also analyze the change in the simulated pattern of vertical velocities to learn where the differences in z-AMOC are produced. The variability and positions of maxima of z- and \(\uprho\)-AMOC do not coincide, meaning that the same physics is manifested differently in both frameworks. Even though the patterns of diapycnal transformations and vertical velocity simulated in LR and HR runs are very similar, there are systematic differences, most expressed in the range of latitudes between 30\({}^{\prime}\)N and 50\({}^{\prime}\)N, where the resolution of HR is essentially finer, whereby the AMOC at 26\({}^{\prime}\)N in the HR run is about 2 Sv stronger than in LR despite the fact that maximum AMOC at high latitudes is higher in LR.
The paper is organized as follows: Section 2 describes the model simulations. Section 3 summarizes the differences between the simulated z- and \(\uprho\)-AMOC for their mean and variabilities. The contributions to \(\uprho\)-AMOC from surface buoyancy fluxes and internal transformations are discussed in section 4. The role of model resolution in AMOC formation is studied in section 5. The last two sections present the discussion and conclusions.
## 2 Model Simulations
Two global simulations were conducted with the Finite-volumE Sea ice-Ocean Model (FESOM 2.0; [PERSON] et al., 2017; [PERSON] et al., 2019). FESOM is a global sea ice ocean circulation model based on unstructured triangular meshes, which is the first mature ocean climate model allowing for local mesh refinement without traditional nesting ([PERSON] et al., 2004, 2017; [PERSON] et al., 2019; [PERSON] et al., 2009; [PERSON] et al., 2008, 2014). Here, FESOM version 2.0 ([PERSON] et al., 2017; [PERSON] et al., 2019) is used in a standard configuration ([PERSON] et al., 2019) to conduct runs on two different meshes using CORE-II interannual atmospheric forcing (1948-2008) with surface salinity restoring ([PERSON], 2009; [PERSON] et al., 2014). A linear free surface and hence the virtual salinity flux have been used for simplicity, and the K-Profile Parameterization (KPP; [PERSON] et al., 1994) vertical mixing scheme was employed.
Two meshes were used with the horizontal resolution shown in Figure 1. The resolution of the first mesh (LR) varies from nominal 1\({}^{\circ}\) in the interior of the ocean to (1/3)\({}^{\circ}\) in the equatorial belt and 24 km north of 50\({}^{\circ}\)N. The ocean surface in LR is discretized with about 127,000 grid points, and 46 vertical levels are used. This mesh has been used in the CORE-II model intercomparison project (e.g., [PERSON] et al. (2016a, 2016b)) and Ocean Model Intercomparison Project phase 2 (OMIP-2, [PERSON] et al., 2020). The second mesh (HR) resolves the regions of high eddy activity with 10 km, which is finer than internal Rossby radius in low and middle latitudes. The regions of high eddy activity were diagnosed from the variance of sea surface height as derived from satellite altimetry; resolution is also refined in sea ice marginal zones and where mixed layer depth is large according to observations, as described in [PERSON] et al. (2016, 2017). The ocean surface in HR is discretized with about 1,300,000 grid points, and the same 46 vertical levels as in LR are used. To put the number of 2-D grid points into the context, a typical 0.25\({}^{\circ}\) global regular mesh consists of about 900,000 wet grid points. The ocean time step is reduced to 10 min in HR to maintain numerical stability (to be compared to 45 min in LR).
For both meshes, we accumulate and store in run time all necessary variables needed for the computation of AMOC in z and density coordinates. For the computation of z-AMOC we store only the vertical velocity on
Figure 1: Resolution (in km) of the LR and HR ocean meshes. The number of surface vertices is 126,858 in LR and 1,306,775 in HR.
native z levels. For the computation of \(\phi\)-AMOC we store the ocean horizontal velocity divergence together with surface-induced diapycnal transformations ([PERSON], 1982) within the bins of density referenced to a pressure of 2,000 dbar (\(\sigma_{2}\)). The algorithms for AMOC computation on unstructured meshes are described in [PERSON] et al. (2020). Here we calculated the transports in density space during run time, which overcomes a significant weakness of almost all previous work that has used this kind of analysis (see, e.g., [PERSON], 2018).
Figure 2: (upper panel) z-AMOC in LR (left) and HR (right) model runs. (lower panel) Same as the upper panels but for \(\phi\)-AMOC.
The \(\mathfrak{g}\) bins are chosen according to [PERSON] (2018) (72 levels for a good representation of deep and bottom waters) and augmented with density levels to match those presented in [PERSON] et al. (2018). Altogether, we use 85 density bins spanning the range of 30.0 < \(\mathfrak{g}\) < 37.2 kg m\({}^{-3}\).
For the computation of the mean fields we use the time-averaged output over 1960-2008, skipping the first 12 years of model initial adjustment.
## 3 AMOC Frameworks
The middleth cell of AMOC in z coordinates (Figure 2, top panels) is centered around 1,000 m depth in both setups. In LR it contains a recirculation with the maximum at about 40\({}^{\circ}\)N which is absent in HR. The z-AMOC at 40\({}^{\circ}\)N is \(\sim\)15 Sv in LR and is larger than in HR, where it reaches only \(\sim\)12 Sv at this latitude. Such model behavior agrees with that described by [PERSON] et al. (2018) who found a weakening of simulated z-AMOC from \(\sim\)18 to \(\sim\)13 Sv when changing the resolution from 1\({}^{\circ}\) to (1/4)\({}^{\circ}\). Interestingly, because of the absence of the recirculation in HR, the strength of the middleth cell there does not decrease toward the south and is by \(\sim\)2 Sv higher in the southern part of the North Atlantic than in LR.
The simulated \(\mathfrak{g}\)-AMOCs are shown in Figure 2 (bottom panels), which have patterns quite different from those of z-AMOCs. There, the middleth cells are located around \(\mathfrak{g}\) = 36.62 kg m\({}^{-3}\) in both runs. It is noteworthy that the patterns of \(\mathfrak{g}\)-AMOCs are consistent with results from many other models (see, e.g., [PERSON] et al., 2016). Both depict the shallower secondary maximum near 20\({}^{\circ}\)N, which reflects the diapycal component of the subtropical spyre and is consistent with the finding of [PERSON] et al. (2016). In contrast to the z representation, both runs show recirculations which are, however, shifted further north (as compared to z-AMOC in LR) and are found at \(\sim\)55\({}^{\circ}\)N where intense water mass transformations take place. This confirms the generally known fact that the AMOC in density coordinate maps the transformation between different density classes into a zonally mean picture and is more directly connected to the physics of governing processes (see, e.g., [PERSON] et al., 2019; [PERSON], 2014). Also, the values of the northern maximums become higher than those in z representation and, interestingly, do not differ between runs, reaching \(\sim\)16 Sv at \(\sim\)55\({}^{\circ}\) N. Similar to the z-AMOC, however, \(\mathfrak{g}\)-AMOC in HR shows a continuous increase (but of smaller amplitude) of the middleth cell toward the south of 30\({}^{\circ}\)N while a slight decrease is found in LR there.
Figure 3 presents the time series of the subtropical (20-30\({}^{\circ}\)N) and the subpolar (40-60\({}^{\circ}\)N) AMOC maxima in both runs using z and \(\mathfrak{g}\) representations. It illustrates that not only the subpolar maximum and its position but also the variability is affected by the choice of framework. Interestingly, the subtropical maxima is systematically larger in HR than in LR in both frameworks and the opposite is found in the subpolar part.
Figure 3: Time series of the AMOC maximum (in Sv) in z and \(\mathfrak{g}\) representations in LR and HR. The maximum has been computed within the two ranges of latitudes indicated on the top of the figure and within the entire depth.
In the subtropical region, the correlation between z-AMOC and \(\phi\)-AMOC time series are \(\sim\)0.89 which reflects the fact that the density surface is flat across the basin there in both resolution runs. Hence, in the south mainly the resolution sets the difference between time series. The correlation between high and low resolution runs is 0.35 for z-AMOC and 0.61 for \(\phi\)-AMOC time series suggesting that \(\phi\)-AMOC responses more decently to the same atmospheric forcing.
In the subpolar region, the density surface becomes steeper and the correlation between z-AMOC and \(\phi\)-AMOC decreases, reaching 0.55 and 0.64 for the low and fine resolutions, respectively. As in the south, the correlation between high and low resolutions is higher for \(\phi\)-AMOC (0.77) than for z-AMOC (0.48).
## 4 Surface-Forced and Interior Constituents of \(\phi\)-AMOC
Following the water mass transformation framework of [PERSON] (1982) and, more specifically, using the approach of [PERSON] et al. (2009) and thereafter by [PERSON] et al. (2018), we compute the surface-forced diapycal water mass transformations as a function of latitude and density (\(\Psi_{\rm{s}}\) see Appendix 0 for definitions). The transformations are shown in Figure 4 (upper panel) for LR and HR runs. They are driven by the surface buoyancy fluxes with the dominant contribution from the surface heat flux (not shown). We shall note that \(\Psi_{\rm{s}}\), although given in swertdups, is not a stream function but a measure of diapycnal transformations. It does not sum to 0 if integrated from the north to south for the global ocean. Indeed, as has been shown by [PERSON] and [PERSON] (2013), there is a positive surface buoyancy flux into the ocean, and the net budget is largely closed through the interior buoyancy sink caused by cabeling. In the absence of diapycnal mixing and cababeling, however, \(\Psi_{\rm{s}}\) relates directly to \(\phi\)-AMOC and in the observational practice is often used to estimate the AMOC and its variability (see, e.g., [PERSON] et al., 2019).
The patterns of \(\Psi_{\rm{s}}\) in LR and HR are similar to those presented in [PERSON] et al. (2018). They are characterized by three main cells which are all within the upper limb of the AMOC and their difference in density ranges mostly reflects the fact that they are in different latitudinal circulation regimes. The three cells are centered at \(\phi=30.95\) kg m\({}^{-3}\) (equatorial cell), \(\phi=34.3\) kg m\({}^{-3}\) (subtypical cell), and \(\phi=36.8\) kg m\({}^{-3}\) (subpolar cell). The strengths and the density ranges of the cells are, however, different between the runs. In the subpolar cell the transformations take place at \(\sim\)55-60\({}^{\circ}\)N. In LR this cell is stronger and tighter around its maximum as compared to HR. In contrast the formation in HR is more spread toward higher latitudes with some transformation coming from about 70\({}^{\circ}\)N. The subtropical cell represents transformations taking place around the GS, its extension, and the NA Current. In contrast to the subpolar cell, the subtropical one is stronger in HR than in LR. This indicates that the outcrop positions of the isopycnals as well as the surface buoyancy fluxes there are different between runs. Indeed, Figure B2 shows substantial differences in surface hydrography reaching \(\sim\)2\({}^{\circ}\)C in sea surface temperature (SST) in the Nordic (NS) and Labrador (LS) Seas as well as in the GS separation area. The accompanied change in salinity is above \(\sim\)1 psu in the GS. Comparison with climatology (not shown) reveals that the model bias associated with the position of the GS as well as the so-called cold bias around Newfoundland are notably smaller in HR.
In reality, waters modified by \(\Psi_{\rm{s}}\) are advected and further transformed through interior mixing and cabbleing. The interior transformation (\(\Psi_{\rm{I}}\)) is obtained by subtracting \(\Psi_{\rm{s}}\) from the total transformation \(\Psi_{\rm{T}}\). The latter is computed by subtracting the model drift from \(\phi\)-AMOC (see Appendix 0 for definition of \(\Psi_{\rm{T}}\)). For a long-term average, as in this paper, the model drift is becoming negligible and the total water mass transformation \(\Psi_{\rm{T}}\) (not shown) is very similar to \(\phi\)-AMOC. The \(\phi\)-AMOC stream function is presented in Figure 4 (lower panel) for both runs. Once again, qualitatively, patterns of \(\Psi_{\rm{I}}\) look similar to that in [PERSON] et al. (2018). The maximum of \(\Psi_{\rm{I}}\) (\(\sim\)14 Sv) is found at 55\({}^{\circ}\)N in both runs and indicates that the internal transformation works toward denser waters north of 55\({}^{\circ}\)N (toward lighter waters south of 55\({}^{\circ}\)N), as expected. The localized cell here is, however, broader than that in [PERSON] et al. (2018), where the upward (toward lighter water) transformation is found primarily in the North Atlantic Current (north of 42\({}^{\circ}\)N). In LR it extends to \(\sim\)30\({}^{\circ}\)N and even further South in HR. Hence, as it has been mentioned above, the southward stronger middepth cell in HR is induced by \(\Psi_{\rm{I}}\). Note that \(\Psi_{\rm{I}}\) is caused mainly by model interior mixing.
## 5 Spatial Distribution of Vertical Transport and Diapycnal Transformations
Here we are going to learn where the density transformation occurs in more detail. As was shown above, the position of the AMOC middepth cell is located at \(z=\)\(\sim\)1,000 m for z-AMOC and at \(\phi=\)\(\sim\)36.62 kg m\({}^{-3}\) for \(\varphi\)-AMOC. We therefore focus on vertical and diapycnal velocities across these levels. The respective vertical velocities and diapycnal transformations, conservatively remapped onto \(4^{\circ}\times 4^{\circ}\) boxes, are shown in Figure 5. The remapping step reveals a systematic pattern in the vertical velocity which is rather noisy on the native mesh. In contrast, the diapycnal transformations are well defined on the native mesh, as will be discussed below. We begin with the density framework.
The left column of Figure 5 depicts surface transformations across the density class \(\wp=36.62\) kg m\({}^{-3}\) for LR and HR runs. Both patterns are qualitatively similar, being characterized by main regions of surface forced
Figure 4: (top panels) Surface-forced diapycnal transformations (\(\Psi_{\varphi}\)) as a function of latitude and density in LR (left) and HR (right) model runs. (bottom panels) The same as upper panels but for interior-mixing-induced transformations (\(\Psi_{\varphi}\)).
transformations: ocean buoyancy loss along Norwegian coast, in the western Irminger Sea, and in the Labrador Sea and buoyancy gain along east of Greenland and north of the Greenland-Scotland Ridge. The details in the representation of these regions are however different between the runs. The buoyancy gain east of Greenland is weaker in HR compared to LR. The buoyancy loss in the LS continues along the shoreline of the LS in HR while it stops at the southern tip of Greenland in LR. Similar differences between the runs are seen in the maps of the mixed layer depth (not shown) which is not surprising considering how \(\Psi_{\rm{s}}\) is computed (see A5). In both runs, however, \(\Psi_{\rm{s}}\) is nearly 0 south of 50\({}^{\circ}\)N at \(\phi=\) -36.62 kg m\({}^{-3}\) meaning that all transformations through \(\phi=\) -36.62 kg m\({}^{-3}\) south of this latitude are the internal transformations, induced largely through vertical and horizontal mixing.
Note that the places where surface transformations at chosen levels are large do not imply that the \(\phi\)-AMOC is being modified just directly there. Surface transformations happen in succession through all density classes (at all levels) and are further redistributed by interior diapval transformations. The bottom panel of Figure 2 indicates that all surface transformations, beginning from transformation from lighter density classes at around 25\({}^{\circ}\)N to transformations from 35.5 to 36.9 kg m\({}^{-3}\) at higher latitudes (around 55\({}^{\circ}\)N), are important. As concerns the latter transformations, Figure 2 indicates that in density space beginning from 35.5 kg m\({}^{-3}\) water is progressively densified as it moves northward to form the \(\phi\)-AMOC. Surface transformations across density classes \(\phi=\) 35.5 kg m\({}^{-3}\), \(\phi=\) 36.62 kg m\({}^{-3}\), and \(\phi=\) 36.9 kg m\({}^{-3}\) are presented in Figure B3 on native meshes. In the upper density classes (\(\phi=\) 35.5 kg m\({}^{-3}\)) they primarily act to reduce buoyancy in the eastern North Atlantic while in the deeper ones (\(\phi=\) 36.9 kg m\({}^{-3}\)) they reduce it in the LS through the deepwater formation in winter. In the HR, the transformation pattern of \(\phi=\) 36.62 kg m\({}^{-3}\) (middle panel of Figure 3) continues along the Labrador current pointing to the improved realism of HR simulation which can be attributed to the effect of better resolution.
Figure 5.— From left to right: (1) surface-forced diapycnal water mass transformation rate at \(\phi=\) 36.62 kg/m\({}^{3}\), (2) diapycnal velocity at \(\phi=\) 36.62 kg/m\({}^{3}\), and (3) vertical velocity at \(z=\) 1,000 m. The upper and lower panels show results from LR and HR runs, respectively. Vertical and diapycnal velocities have been conservatively mapped onto 4\({}^{\circ}\times\) 4\({}^{\circ}\) boxes before plotting.
Surface transformations are redistributed through internal mixing and augmented by cabeling (we do not specifically analyze it here and refer to Klocker & McDougall, 2010, for more details), giving a total transformation pattern. Patterns of total transformations (diapvcnal velocities) (Figure 5, middle column) qualitatively resemble the respective surface transformation patterns north of 50\"N but are characterized by larger amplitudes of buoyancy loss and more confined upward diapycnal fluxes east of Iceland. This picture is persistent between LR and HR runs. In both runs the upward flux is also found around Grand Banks and at Cape Hatteras. In LR the upward diapycnal velocity follows the whole route of North Atlantic Current, whereas it is much less expressed in HR at these locations. The absence of surface transformations south of Grand Banks means that the diapycnal velocities we see in the GS separation and its extension area are purely due to internal transformations. [PERSON] et al. (2018) suggest that at these locations the likely reason for internal transformations is spurious numerical mixing due to sloping isopycnals that essentially deviate from level surfaces. In z coordinate models, dissipative truncation errors in horizontal advection lead to diapycnal mixing in places where isopycnals are sloping. Smaller internal transformations south of 50\"N in HR compared to LR hence can be attributed to much finer mesh (and reduced spurious dissipation related to the monotone advection scheme in FESOM). This, in turn, correlates well with the recirculation at -55\"N being more expressed in LR.
Total transformations at \(\phi=35.5\) kg m\({}^{-3}\), \(\phi=36.62\) kg m\({}^{-3}\), and \(\phi=36.9\) kg m\({}^{-3}\) are shown in Figure B4 on native meshes. Same as in Figure 5, qualitative similarity between the patterns of total and surface transformations is found for different density classes.
The most obvious difference brought by higher resolution between the diapycnal velocity pattern is much smaller transformations to lighter density classes at \(\phi=35.5\) kg m\({}^{-3}\) and \(\phi=36.62\) kg m\({}^{-3}\) (mentioned above) in HR than in LR. Plotting on the native mesh reveals also the transformations along the GS path starting from the Florida Current in the LR, which are absent in HR. Furthermore, the transformations in the LS at \(\phi=36.62\) kg m\({}^{-3}\) are only around the tip of Greenland in LR, while they continue into the LS toward Davis Strait in HR. Comparing the HR and LR patterns to those presented in [PERSON] et al. (2018) (their Figure 12) at the levels nearest to those used by us (35.413 and 35.98 for 35.5, 36.595 for 36.62, and 36.875 for 36.9), we see that there is much closer agreement for the HR run than the LR run. Taking into account the higher ([1/12]\({}^{\circ}\)) resolution used in [PERSON] et al. (2018), we can conclude that resolution matters and affects the patterns of transformations even though they remain qualitatively similar.
Patterns of total diapycnal transformations are not sign definite. In deeper levels they acquire a \"rim\" structure with regions of buoyancy loss encircled by bands of buoyancy gain, as seen for \(\phi=36.9\) kg m\({}^{-3}\) in the right column of Figure B4 in the LS. This behavior explains why the \(\phi\)-AMOC in Figure 2 is largely confined to density classes lighter than \(\phi=36.9\) kg m\({}^{-3}\). The same behavior is also shown in [PERSON] et al. (2018, see their Figure 12). It shows once again that both the downward (from above) and upward (from below) internal transformations contribute to the total pattern we see at \(\phi=\) -36.62 kg m\({}^{-3}\).
Vertical velocity (Figure 5 third column) at 1,000 m depth indicates that, similar to the \(\phi\)-AMOC, a substantial contribution to z-AMOC in both runs is formed at the southern tip of Greenland. However, the downward flux there is partly counteracted by the upward flux in the nearby regions and in the interior of the LS. Similar to [PERSON] et al. (2018, see their Table 2) sinking along the periphery of the LS is not the major contribution and the contribution from the Labrador Sea decreases with increased resolution. Different from diapycnal velocities, the downward vertical velocity is also found along the GS and its extension. Integrated over the area this contribution is almost as large as the northern one around the tip of Greenland. It corresponds to the southward shift of the z-AMOC recirculation cell as compared to \(\phi\)-AMOC. The recirculation cell in LR is closed by the upward flux at Cape Hatteras. This upward flux, however, is less expressed in HR, and the strong middepth cell there continues further south. As we shall see below, its absence in HR explains why the z-AMOC is larger south of 20\"N in HR.
As already mentioned, for plotting diapycnal and vertical velocities in Figure 5 we remapped them conservatively into \(4^{\circ}\times 4^{\circ}\) boxes. Remapping to finer meshes still showed a rather patchy structure in vertical velocity in regions with steep bathymetry. As is seen from Figure B5, keeping vertical velocity on native mesh fully masks the contribution of the region around the tip of Greenland yet indicates that this contribution is much more localized than the pattern in the right column of Figure 5. Total diapycnal transformations also contain noise on native meshes, yet it does not fully conceal the signal (see Figure B4).
Despite the noisy structure, integrating from north to south for vertical and diapycnal velocities results in smooth stream function patterns which are identical to those derived from the \"smooth\" meridional velocities (not shown).
The left panel of Figure 6 shows integrated (from north to south) diapycnal and vertical velocities (same as \(\phi\)-AMOC and z-AMOC) at levels of z = -1,000 m and \(\varrho\) = -36.62 kg m\({}^{-3}\). The central and right panels of Figure 6 also show separately the cumulative transports for western and eastern basins. We use the longitude 44\({}^{\circ}\)W of the southern tip of Greenland as the separation point between the east and west basins to mimic that of the Overturning in the Subpolar North Atlantic Program (O'SNAP, see, e.g., [PERSON] et al., 2019). Both runs agree with the observational findings by [PERSON] et al., 2019 who claim that the eastern part of the North Atlantic is largely responsible for overturning in the subpolar basin. Combining Figure 6 with the patterns of diapycnal velocities (shown in Figure 5), we again confirm that the maximum of the middepth cell in \(\phi\)-AMOC at -55\({}^{\circ}\)N is primarily caused by the downward flux around the southern tip of Greenland.
Inspecting the pattern of meridional velocity across a section at 60\({}^{\circ}\)N (not shown), we observe that the \(\varrho\) = 36.62 kg m\({}^{-3}\) isopycnal is sufficiently deep east of 44\({}^{\circ}\)W and very shallow in the Labrador Sea. In the western part, almost all northward flowing water is below \(\varrho\) = 36.62 kg m\({}^{-3}\). So the main place where \(\varrho\) = 36.62 kg m\({}^{-3}\) is ventilated is to the north east of the southern tip of Greenland. This agrees with the pattern of diapycnal velocity across \(\varrho\) = -36.62 kg m\({}^{-3}\) in Figure 5, which shows large ocean buoyancy loss along Norwegian coast and in the western Immiger Sea.
The upward flux at GS and its extension leads to the formation of the recirculation cell at -55\({}^{\circ}\)N in LR. In HR the upward flux, responsible for the recirculation, is found east of Grand Banks (Figure 5). It is weaker in total than in LR and explains why the middepth cell in HR is larger south of 50\({}^{\circ}\)N than in LR.
Distinct to \(\phi\)-AMOC, the formation of z-AMOC north of 55\({}^{\circ}\)N is responsible only for a half of its amplitude (Figure 6). The recirculation cell in z-AMOC is caused by the downward flux at GS, its extension, and in the Eastern North Atlantic and the upward flux at Cape Hatteras (Figure 5). The latter is larger in LR compared to HR. The maximum of z-AMOC is therefore found at 40\({}^{\circ}\)N in LR while z-AMOC in HR becomes persistently larger south of 30\({}^{\circ}\)N. This conforms with the modeling studies from ([PERSON] et al., 2020) that higher resolution leads to larger z-AMOC values at 26.5\({}^{\circ}\)N. The reason for higher values of z-AMOC in our case is not the higher formation rate but the lack of upwelling before and in the GS separation area in HR, which is resolved much more finely than in LR.
Figure 6: (left panel) The \(\phi\)-AMOC at \(\varrho\) = 36.62 kg/m\({}^{3}\) and z-AMOC at z = 1,000 m. (middle panel) Transport integrated from north to south for the western basin (tip of Greenland is the separation point for the western and eastern basins). (right panel) Same as middle but for the eastern basin.
## 6 Discussion
Our comparison of AMOC on two different meshes shows that there is much similarity between the patterns of diapycnal transformations and sinking in LR and HR. This is, perhaps, not surprising, given that the runs have been performed with the same model setup and the same atmospheric forcing. However, the patterns do not exactly coincide, and the analysis of diapycnal transformations at selected isopycnals and vertical velocities at fixed depth helps to see why the differences are emerging. The main finding is that despite the AMOC formation in higher latitudes (north of 40\({}^{\circ}\)N for z-AMOC and of 55\({}^{\circ}\)N for \(\sigma\)-AMOC) is larger in LR, AMOC is smaller in lower latitudes in LR as a result of stronger upwelling (z-AMOC) or mixing toward lighter density classes in the 30-50\({}^{\circ}\)N belt which reduces the AMOC in LR. The lack of these effects in HR is obviously related to its high resolution of about 10 km in the western part of this belt, ensuring much better representation of flow structure and dynamics, with locally switched off eddy parameterizations.
Indeed, the maximum of z-AMOC in LR is reached at -40\({}^{\circ}\)N as a result of downwelling along the path of GS extension and North Atlantic Current (NAC) south of -50\({}^{\circ}\)N and concurrent upwelling along Florida at -30\({}^{\circ}\) N. In HR, the upwelling is nearly absent. The comparison in Figure 6 (see also the difference between HR and LR z-AMOCs in Figure B1, left) confirms that the middleton recirculation cell appears only in LR. As a result, z-AMOC in LR is larger than in HR between 30\({}^{\circ}\)N and 50\({}^{\circ}\)N. South of -30\({}^{\circ}\)N, however, the AMOC maximum is larger in HR, in agreement with other studies ([PERSON] et al., 2020).
The total transformations in LR (see Figure B4) are also nonzero in the areas of GS and Florida currents at 36.62 kg m\({}^{-3}\), which approximately corresponds to the depth of the middepth cell. Figure B3 reveals that there are no surface transformations in LR or in HR in this area in density classes around 36.62 kg m\({}^{-3}\) and only the internally caused transformations set the difference between LR and HR there. We therefore speculate that recirculation of z-AMOC in LR centered at -40\({}^{\circ}\)N as well as the reduction of \(\varrho\)-AMOC at latitudes of Grand Banks is likely caused by spurious numerical mixing which is larger in LR.
The observation that not only physical but also spurious numerical transformations set the amplitude of the simulated AMOC deserves attention and calls for further studies aiming at direct estimates of spurious mixing, for example, in the framework of discrete variance decay analysis ([PERSON] et al., 2014), using the concept of reference potential energy (see, e.g., [PERSON] et al., 2012) or using the density framework as has been demonstrated in [PERSON] et al. (2002) and [PERSON] (2018). The latter two present a supplementary tool to assess the total mixing rates--and hence to estimate the numerical mixing--in any given model. The topic of numerical mixing will be addressed in future studies.
In the z framework the vertical velocity is used to compute the AMOC. The vertical transport is accumulated in places of strong downwelling. Binning in Figure 5 hides the true localization of downwelling. Figure B5 shows that on the native meshes in both LR and HR cases strong vertical velocities are localized in narrow areas attached to continental shelf breaks. This agrees with the argument in [PERSON] and [PERSON] (2001) (see also [PERSON] et al., 2018) emphasizing that vertical velocities (\(w\)) can only be large in places where the potential vorticity constraint is violated because of friction. Similar patchy vertical velocities at around the grid scale in a global (1/4)\({}^{\circ}\) model were suggested by [PERSON] (2018) as a source of spurious mixing. Although the resolution of HR is by a factor of 2 higher in the regions of large \(w\) in the LS, there is no qualitative difference between the patterns, and the interior of the LS is largely excluded from the region where AMOC is formed. This is different from the comparison in [PERSON] et al. (2018), which can be explained by the fact that in our case even LR has the resolution of about 25 km in the area of z-AMOC formation. However, as follows from the analysis here, the high latitudes (around Greenland and in LS) are responsible only for a part of z-AMOC, and an even smaller portion of it is accumulated in GS.
The drawback of \(w\) analysis is that the pattern of \(w\) in Figure B5 is patchy even after long-term averaging and only conservative binning in Figure 5 reveals the major accumulation sites. In contrast, the pattern of total transformations in Figure B4 is less noisy and allows for a more consistent view on where total diapycnal transformations reach maximum. In the z framework the simulated \(\varrho\)-AMOCs (see Figures 2, B1 [right], and 6) show recirculation in both model runs, and the maximum values are rather close. The recirculation happens further north as compared to z framework and is found at about 55\({}^{\circ}\)N. From there the LR gradually loses its amplitude and becomes less than HR south of 45\({}^{\circ}\)N which is again in line with many other studies.
In agreement with the picture drawn by [PERSON] et al., 2019, most of the AMOC formation in our simulations occurs east of Greenland, rather than in the Labrador Sea, despite the vigorous convection in the latter location. Major transformations in higher density classes take place as the Atlantic Water is gradually densified on its path into NS and in the Immiger Sea ([PERSON] et al., 2019; [PERSON] et al., 2018). The contributions from the LS basin in our case are relatively high, reaching about 4 Sv in HR g-AMOC, but still smaller than the contributions from the eastern basin, which exceed 10 Sv. If viewed more cautiously, assessing the role of basins has to take into account transformations from lighter density classes in the GS area that contribute to the AMOC formation and indirectly affect the transports shown in Figure 6.
Despite the differences between the z and density frameworks and between the LR and HR configurations, the variability of the AMOC in the south is largely similar in all cases (Figure 3), reflecting the fact that the modeled AMOC variability is forced by the same atmospheric forcing. In the north the AMOC maximum in z- and \(\phi\)-representations shows some differences on decadal time scales. One would expect that using \(\phi\)-AMOC is physically more appealing as it directly accounts for water mass transformations between different density classes (see, e.g., [PERSON] et al., 2019). How AMOC variability depends on the choice of framework will be studied in detail in the future.
Both ways of computing AMOC are valuable, but the water mass transformation framework, leading to \(\phi\)-AMOC, is more insightful, for example, being also able to provide direct assessment of the total mixing rates (see, e.g., [PERSON], 2018). It may also facilitate the study of other topics, such as the effect of numerical diapycnal mixing or the horizontal mixing in the mixed layer (see, e.g., [PERSON] et al., 2018). The work presented in this paper provides an additional value to the density framework. We used it to better understand the impact of model resolution on AMOC.
## 7 Conclusions
We diagnosed AMOC using depth and the potential density (referenced to 2,000 dBar) coordinates. The transports in density space were calculated during run time, which overcomes a significant weakness of almost all previous work that has used this kind of analysis. Comparison of both frameworks for two model runs with coarse and fine resolutions reveals similarities, but also substantial differences. We addressed two questions in this paper: (1) What causes differences in the AMOC between high and low resolution models? (2) Can ocean climate models adequately represent the relative importance of different basins (western vs. eastern northern NA) for the formation of AMOC? For these purposes we employed the unstructured-mesh global model FESOM2. Using two AMOC frameworks facilitated answering these questions.
The most essential differences between the two model runs are found in the latitude belt between 30\({}^{\circ}\)N and 55\({}^{\circ}\)N whereby the z- and \(\phi\)-AMOCs in the high-resolution run attain higher amplitudes at 30\({}^{\circ}\)N than in the low-resolution run despite the higher AMOC maxima in the low-resolution case. South of the 30\({}^{\circ}\)N (away from the deepwater formation) AMOC stays higher in the high-resolution run in both frameworks, in line with many other studies. This behavior is attributed to stronger numerical mixing in the low-resolution case, which returns water upward along the U.S. coast (z-AMOC) or to lighter density classes around Grand Banks (\(\phi\)-AMOC) in the low-resolution case. Counterintuitively, the reason for stronger AMOC in the low-latitude range in the high-resolution run is not related to higher dense water formation rates. This behavior also explains the presence of recirculation in z-AMOC in the low-resolution run.
The spatial patterns of AMOC formation remain similar independent of resolution. In both frameworks and with both resolutions, most of the AMOC formation occurs east of Greenland, rather than in the Labrador Sea, despite the vigorous convection in the latter location. Compared to the z-AMOC framework, the \(\phi\)-AMOC framework better illustrates the importance of AMOC formation east of Greenland.
Although using the water mass transformation framework is cumbersome, the patterns of total diapycnal transformations are much less noisy than the vertical velocity patterns, which is an argument for their more broad use in standard analyses, including forthcoming intercomparison projects. Besides, they are more directly connected to surface transformations and explicitly exhibit relevant processes. Combining this framework with the ability of local refinement on unstructured meshes may help to further deepen our understanding of how numerical details affect the simulated AMOC in future work.
Figure 14: Surface-forced diapycnal water mass transformation rate across three \(\varrho\) levels on native grids. The upper and lower panels show LR and HR runs, respectively.
Figure 14: Same as Figure 13 but for diapynal velocities.
## Data Availability Statement
Data sets related to this article can be found online (at [[https://swiftbrowser.dkrz.de/public/dkrz_035d8f6](https://swiftbrowser.dkrz.de/public/dkrz_035d8f6) ff058403b42f8302e6 badfbc/JAMES_Sidorenkoetal_2020/]([https://swiftbrowser.dkrz.de/public/dkrz_035d8f6](https://swiftbrowser.dkrz.de/public/dkrz_035d8f6) ff058403b42f8302e6 badfbc/JAMES_Sidorenkoetal_2020/)).
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wiley/feae2c2b_b26d_4ebb_a613_b1c1e39e55d5.md | # Identification of synoptic weather types over Taiwan area with multiple classifiers
Shih-Hao Su
Chinese Culture University, Taipei, Taiwan National Science and Technology Center for Disaster Reduction, Taipei, Taiwan National Taiwan University, Taipei, Taiwan
Jung-Lien Chu
National Science and Technology Center for Disaster Reduction, Taipei, Taiwan
[PERSON] Yo
Department of Mathematics, University of Science and Technology, Taipei, Taiwan
Lee-Yaw Lin
National Science and Technology Center for Disaster Reduction, Taipei, Taiwan
###### Abstract
In this study, a novel machine learning approach was used to classify three types of synoptic weather events in Taiwan area from 2001 to 2010. We used reanalysis data with three machine learning algorithms to recognize weather systems and evaluated their performance. Overall, the classifiers successfully identified 52-83% of weather events (hit rate), which is higher than the performance of traditional objective methods.
The results showed that the machine learning approach gave low false alarm rate in general, while the support vector machine (SVM) with more principal components of reanalysis data had higher hit rate on all tested weather events. The sensitivity tests of grid data resolution indicated that the differences between the high- and low-resolution datasets are limited, which implied that the proposed method can achieve reasonable performance in weather forecasting with minimal resources.
By identifying daily weather systems in historical reanalysis data, this method can be used to study long-term weather changes, to monitor climatological-scale variations, and to provide better estimate of climate projections. Furthermore, this method can also serve as an alternative of model output statistics and potentially be used for synoptic weather forecasting.
front, heavy rainfall, machine learning, synoptic weather classification, Taiwan, typhoon 18 September 28 August 2018 24 September 2018 2017 10.1002 hal.861
## 1 Introduction
Most extreme weather events in Taiwan are associated with strong synoptic-scale systems. The fluctuations of these weather systems reflect variations in climatological scale and induce a variety of mesoscale mechanisms. These results in precipitation and temperature change with different temporal and spatial characteristics, and hence are the major cause of natural disasters. Therefore, the recognition of various types of synoptic weather is crucial for weather forecasting, disaster prevention, and climate projections.
Before 1960, the common weather classification techniques used by most meteorologists were mainly manual and subjective methods (e.g., [PERSON], 1950). Since early 1960s, objective diagnosis methods were developed with advances in computer technologies and grid data. [PERSON] and [PERSON] (1965) used spatial gradients of atmospheric thermal and moment parameters to identify weather systems. Their study suggested that using simple thermal and dynamic parameters alone was not robust for the identification of weather fronts.
Meanwhile, other researchers proposed statistical and similarity-based methods for weather typing. Some studies used exemplars of weather systems and similarity metrics, such as spatial correlation ([PERSON], 1963) or sum of squared difference ([PERSON], 1973), to identify their occurrences. Other methods used exploratory analysis techniques toidentify the major spatial patterns of meteorological data and associated them with weather systems [15, 16, 17].
As machine learning gained its popularity in scientific research, techniques such as self-organizing maps was used for weather typing and classifications [10, 11]. In 2016, [PERSON] and colleagues applied convolutional deep neural networks to detect extreme weather systems in simulated and reanalysis datasets [14]. Their results showed that machine learning techniques were suitable for detecting weather systems.
In present study, we proposed a classification-based approach with long-term reanalysis data. We introduced the grid numerical outputs and observational records for model training and used machine learning techniques to classify the synoptic weather types from 2001 to 2010. The climate reanalysis data and surface observational records are described in next section. The automatic analysis methods and the results are presented in sections 3 and 4. Section 5 discusses the results and the usage of the automatic weather classifier.
## 2 Data sources
In this study, we focused on three weather events, namely fronts, typhoons, and heavy rainfall (HR) events. These events are three major weather types associated with nature disasters in Taiwan. The records of these events were sourced from a newly developed dataset referred to as the Taiwan Atmospheric Events Database (TAD, personal connection). This dataset consists of major synoptic-scale weather events in Taiwan area identified with objective and subjective methods. The front events during 2001-2010 were identified with subjective surface analysis of the Central Weather Bureau (CWB) weather maps. The selected domain was used to identify the fronts near Taiwan, in the area 119\({}^{\circ}\)-123\({}^{\circ}\)E and 21\({}^{\circ}\)-26\({}^{\circ}\)N. Typhoon events were determined by the hourly typhoon center position data according to the CWB typhoon database [10]. The CWB hourly precipitation data from 31 manual observation stations and more than 690 automatic rain gauges were used to identify HR events in Taiwan. The criteria of HR, that is, 80 mm/day or 40 mm/hr, was enforced by the CWB of Taiwan.
The National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR; [PERSON] _et al._, 2010; [PERSON] _et al._, 2014) was used for training and evaluation of our statistical model in this study. The CFSR reanalysis data repository provided highly detailed temporal (6 hr) and spatial (0.5 x 0.5\({}^{\circ}\)) information from 1979 to 2010; these datasets are comparable to many other sets of reanalysis data. We also used coarse resolution global grid data from the European Centre for Medium-Range Weather Forecasts (ECWMF), ECMWF's atmospheric reanalysis of the 20 th century (ERA-20C, 2.5 x 2.5\({}^{\circ}\) horizontal resolution; [PERSON] _et al._, 2016) to examine the numerical grid resolution effects. The variables used in this study are summarized in Table 1a.
## 3 Automatic analysis techniques
In this section, the architecture of the proposed weather classification approach is detailed. In addition to the method, a series of experiments was designed to evaluate the effectiveness of the system. We investigated the classification performance of several preprocessing settings, feature sets, and machine learning algorithms.
For a classification task, two types of data are required: input data and output. Input data consists of the feature sets upon which decisions are made. The output variables represent the target decisions or predictions. In the proposed procedure, the output is a set of binary labels indicating whether a weather event occurs.
In this study, we used two sources of data as inputs: coarse resolution global grid data from ERA-20C and fine numerical grid analysis fields from CFSR over the East Asia region. The choice of data sources was made to increase the
\begin{table}
\begin{tabular}{|l l l|} \hline
**(a) Input variable** & **Symbol** & **Selected levels** \\ Zonal and meridional wind components & U, V & 925, 850, 700, and 200 hPa \\ Temperature & T & 925, 850, 700, and 200 hPa \\ Dev point temperature & Td & 925, 850, and 700 hPa \\ Mean sea level pressure & MSLP & Surface \\ Geopotential height & H & 500 hPa \\ \hline
**(b) Input variable** & **Symbol** & **Operational definition** \\ \hline High-resolution grid data & NCEP50 & The principle components that explain 50\% of variance of each variable of NCEP-CFSR grid data \\ & NCEP70 & The principle components that explain 70\% of variance of each variable of NCEP-CFSR grid data \\ \hline Low-resolution grid data & EC50 & The principle components that explain 50\% of variance of each variable of ECMWF ERA-20C grid data \\ & EC70 & The principle components that explain 70\% of variance of each variable of ECMWF ERA-20C grid data \\ Multi-resolution grid data & EC-NCEP50 & The principle components that explain 50\% of variance of each variable of both of CFSR and ERA-20C grid data \\ & EC-NCEP70 & The principle components that explain 70\% of variance of each variable of CFSR and ERA-20C grid data \\ \hline \end{tabular}
\end{table}
Table 1: The list of (a) selected variables of grid data used in experiments and (b) feature sets used in the experimentsvariety of the feature space, so that the classification results can show which type of data is more informative for a certain type of weather event.
The data were further filtered and processed as follows. For the reanalysis data from both ERA-20C and CFSR, 17 vertical levels of 00Z each day were selected. The selected variables consisted of the mean sea level pressure; U, V, Td, and T of 925, 850, and 700 hPa; geopotential height of 500 hPa; and T, U, and V of 200 hPa. The randomized Principal Components Analysis (PCA) was then applied to each variable for dimension reduction ([PERSON] _et al._, 2011; [PERSON] _et al._, 2011). And thus, the first few principal components (PCs) that can explain K% of total variance of each variable were selected as the feature set. The number of PCs selected was decided based on the proportion of variance can be explained, and hence is different for each variable. Generally speaking, most of 17 selected variables can be represented by a few PCs except the humidity parameters and wind field at 200 hPa. Also, the lower-resolution-global-domain dataset required more PCs to explain the same amount of variance compared to the other dataset. We experimented with different \(K\) values and tried to balance between the model accuracy and complexity, and finally decided to present the \(K\) values of 50 and 70, where a limitation of at most 100 PCs can be used for one single variable was enforced.
Table 1b shows six different feature sets used in our experiments. These sets were designed to show what types of data gave the most information indicating the occurrence of a given weather event. The feature set with different grid resolutions helped us determine which resolution of model data is suitable for use in operation.
From the wide variety of algorithms capable of binary classification, three different classifiers were selected for this study, namely the logistic regression model (GLM; R Core Team, 2015), gradient boosting model (GBM; [PERSON], 2015), and support vector machine (SVM; [PERSON] _et al._, 2004) with polynomial kernel. These three classifiers represent three different approaches to classification: a linear model, an ensemble tree-based model, and a nonlinear model. The GLM was chosen because of its simplicity and explainability, and its performance often serves as a baseline for other classifiers. In a thorough review of different classifiers by [PERSON] and his colleagues ([PERSON] _et al._, 2014), random forest and SVM were suggested as the two best classification algorithms for most real-world data. Hence, their R implementations, that is, GBM and SVM, were chosen for the designed experiments.
## 4 Results
Weather forecasts of binary events were conventionally verified with hit rate (_H_), false alarm rate (_F_), false alarm ratio (FAR), and critical success index (CSI; [PERSON] and [PERSON], 2012). In the context of anomaly detection, positive predictive values (PPV) and F-1 score are commonly used for evaluation. Table 2 showed a basic confusion matrix, and its elements are used to explain the measurements of performance as follows.
Hit rate (_H_) is also known as sensitivity. It measures the proportion of positives that are correctly identified as such. Its mathematical form can be written as
\[\text{Hit rate }(H)=\frac{\text{Number of true positive}}{\text{Total of true positives}}=\frac{A}{A+C}.\]
False alarm rate (_F_) measures the proportion of false positives over all negative cases, and a high hit rate represents that most events are detected by the system. The formula of false alarm rate is
\[\text{False alarm rate }(F)=\frac{\text{Number of false positive}}{\text{Total of true negatives}}=\frac{B}{B+D}.\]
FAR measures the proportion of cases identified as positives that are wrong. The mathematical expression of FAR is
\[\text{FAR}=\frac{\text{Number of false positive}}{\text{Total of predicted positives}}=\frac{B}{A+B}.\]
CSI measures the conditional probability of a hit given that the event was either forecast, or observed, or both. CSI is often used for evaluating rare event detection, and can be mathematically expressed as
\[\text{CSI}= \frac{\text{Number of true positive}}{\text{Total of classified positives}}\wedge\text{true positives}\] \[= \frac{A}{A+B+C}.\]
PPV refers the proportion of positive classified results that are true positive results, and it equals to \(1-\text{FAR}\). A high PPV means an event is more likely to occur when the system detects so. The equation for PPV is given as
\[\text{PPV}=\frac{\text{Number of true positive}}{\text{Total of classified positives}}=\frac{A}{A+B}.\]
\(F1\) score is the harmonic mean of hit rate and PPV, and it is commonly used in the field of signal processing for anomaly detection. The \(F1\) score is similar to CSI except it gives higher weight to true positive cases. The mathematical form of \(F1\) score can be written as
\[F1=\frac{2*H*\text{PPV}}{H+\text{PPV}}=\frac{2A}{2A+B+C}.\]
\begin{table}
\begin{tabular}{p{85.4 pt} p{113.8 pt} p{113.8 pt}} \hline \multirow{2}{*}{Classified positive} & Condition positive & Condition negative \\ \cline{2-3} & True positive (hit) A & False positive \\ \cline{2-3} & & false alarm **B** \\ \cline{2-3} \cline{2-All six measures described above, namely the \(H\), \(F\), FAR, CSI, PPV, and F-1, are calculated for each combination of event, feature set, and classifiers.
Besides the performance measures, the sampling scheme used in the experiments also affects the evaluation. Cross-validation ([PERSON], 1974) is a commonly used re-sampling technique known to provide a good estimate of the true out-of-sample performance. In this study, each dataset-classifier combination was evaluated with a 10-fold cross-validation scheme sampled with the same random seed.
Figure 1 depicts the results from the classification experiment. The proposed approach with SVM is shown to identify the typhoon, front, and HR events with hit rate of 37-64%, 26-52%, and 78-83%, and \(F\)1 score of 52-72%, 39-58%, and 77-82%, respectively. While hit rate indicates the ability that the system can identify an event when it occurs, \(F\)1 score balances the hit rate by penalizing false alarms. The results showed that the proposed method gave good hit rate and kept the false alarm rate low at the same time.
Figure 2 shows the \(F\)1 scores over three types of events. As illustrated in the figure, SVM with the PCs explained 70% of variance of NCEP-CFSR data outperformed other feature combinations in most cases. For HR events, SVM with NCEP-CFSR and ECMWF data performed the best, though adding ECMWF data gave only minor improvement. The comparison among the performance of different classifiers showed that the SVM is a capable choice for such tasks.
Results of different grid datasets, NCEP-CFSR and ECMWF, suggest that high-resolution regional data (0.5\({}^{\circ}\) over East Asia) are more informative than low-resolution global data (2.5\({}^{\circ}\) global). Although combining both datasets can provide more information, the improvement is minor or even negative, as shown in Figure 2.
The ROC curve of the results is shown in Figure 3. The figure shows that the proposed method tends to give higher hit rate in general. The overall performance (distance away the no-skill limitation) are much better than the traditional objective methods. Also, we noticed the performance of detecting HR events is more consistent than other events as illustrated in Figure 3.
Figure 1: The (a) hit rate and (b) \(F\)1-score of SVM over three events
Figure 2: The \(F\)1-score of SVM on each feature set over three events
## 5 Discussion and Conclusions
In this paper, we used the machine learning technique to classify three types of synoptic weather events in Taiwan area from 2001 to 2010. The results show better performance in comparison to objective analysis methods, and the details are discussed as follows.
For frontal system, [PERSON] and [PERSON] (1965) first proposed using the \"thermal front parameter (TFP)\" to identify the system from grid data. They manually defined the front location based on TFP and reported a fair accuracy. [PERSON] _et al_. (2014) used multiple TFP-like indices with artificial neural networks to recognize the Australian winter frontal system. They reported the equitable threat score (ETS) as 0.0-0.18 and the best ETS of in our study is 0.33 (SVM with fine-resolution whose PCA modes explained 70% of variance). We applied the TFP-based methods of [PERSON] _et al_. (2014) to the NCEP-CFSR dataset, and the resulting hit rate is 0.17 with a false positive rate of 0.03. The hit rate and false positive rate of our method are 0.52 and 0.06, respectively.
Many methods were proposed to detect the tropical cyclone in the past studies. For comparison, we adopted an objective TC detection method proposed by [PERSON] _et al_. (1997) and applied it to the same NCEP-CFSR dataset. While the SVM showed a hit rate of 0.64, the objective TC detection method gave a hit rate of 0.24 from the same reanalysis inputs.
To compare the ability of recognizing HR events, NCEP-CFSR simulated precipitation rate was used as the baseline ([PERSON] _et al_., 2011). [PERSON] _et al_. (2012) used similar model outputs to evaluate the Quantitative Precipitation Forecast (QPE) skill for multiple global models. According to their results, the QPF with model outputs showed excessive forecasting of light rain, and it had difficulty in predicting heavy rain events. In this study, the best ETS of HR classifiers is 0.48, which is higher than 0.003 directly from the QPF via NCEP-CFSR and 0.30-0.35 reported by [PERSON] _et al_. (2012) with resolution-independent thresholds.
In addition to the performance, the system achieved descent hit rate without high false alarm rate. The results demonstrated that the SVM with the PCs explained 70% of variance of NCEP-CFSR data gave better performance in general. The difference between NCEP-CFSR and ECMWF data can serve as sensitivity tests of grid data resolution. The corresponding results showed that high-resolution regional data is more informative than low resolution data for all events, though the difference was limited. Besides different number of principle components used, we also examined the additional input datasets (7-17 layers) of meteorological fields by selected strategies. The results showed that the classifiers improved by providing more information for most weather events except the frontal system. This may relate to the vertical structure difference of the seasonal frontal systems, suggesting further investigations of sub-types of the front events. In addition, according to our results, increasing the numerical model resolution only brings minor improvement. This suggests that one can obtain reasonable improvement in weather forecasting while adding minimal resources.
In this study, we have successfully demonstrated the use of machine learning methods for synoptic weather classification. The results showed that our method outperformed methods based on traditional objective diagnosis. The proposed method is equivalent to a pattern recognizer that identifies weather events from given reanalysis data, and it has many potential applications. For example, one may apply it to the historical reanalysis datasets and the results can be used to study long-term historical weather changes. This can help to monitor climatological-scale variations as well as to provide better estimation of climate projections. Furthermore, this method can also serve as an alternative of model output statistics (MOS) and potentially be used for synoptic weather forecasting.
## Acknowledgments
We thank Dr. [PERSON] for his helpful comments and suggestions. We thank [PERSON] and [PERSON] for their help in processing the data. This research was supported by the grants from Ministry of Science and Technology of Taiwan through grants MOST-104-2111-M-034-003, MOST-104-2625-M-034-002, MOST-105-2111-M-034-003, MOST-106-2621-M-865-001 and to Chinese Culture University. This study was also collaborating with the Taiwan Climate Change Projection and Information Platform Project (TCCIP). We thank the Central Weather Bureau for their typhoon database and provided the rainfall data.
Figure 3: The relative operating characteristic (ROC) diagram of all experiments. The shaded area marked the no-skill region and gray dash lines were the performance references. The red, green, and blue markers represented the typhoon, front, and HR events. Different symbols indicated three classifiers and black squared mark shows the traditional objective analysis | wiley | Identification of synoptic weather types over Taiwan area with multiple classifiers | Shih‐Hao Su, Jung‐Lien Chu, Ting‐Shuo Yo, Lee‐Yaw Lin | https://doi.org/10.1002/asl.861 | 2,018 | CC-BY |
wiley/feaee070_0e64_4809_82ee_ca336730ae84.md | # IGR Solid Earth
Research Article
10.1029/2023 JB026374
1
Seismic Imaging Beneath Cascadia Shows Shallow Mantle
Flow Patterns Guide Lower Mantle Upwellings
[PERSON]\({}^{\copyright}\)
\({}^{1}\)Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Southampton, UK,
\({}^{2}\)Geology & Geophysics Department, Woods Hole Oceanographic Institution (WHOI), Woods Hole, MA, USA
[PERSON]\({}^{\copyright}\)
\({}^{1}\)Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Southampton, UK,
\({}^{2}\)Geology & Geophysics Department, Woods Hole Oceanographic Institution (WHOI), Woods Hole, MA, USA
[PERSON]\({}^{\copyright}\)
\({}^{1}\)Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Southampton, UK,
\({}^{2}\)Geology & Geophysics Department, Woods Hole Oceanographic Institution (WHOI), Woods Hole, MA, USA
###### Abstract
The mantle transition zone (MTZ) plays an important role in modulating material transport between the upper mantle and the lower mantle. Constraining this transport is essential for understanding geochemical reservoirs, hydration cycles, and the evolution of the Earth. Slabs and hotspots are assumed to be the dominant locations of transport. However, the degree of material transport in other areas is debated. We apply \(P\)-to-\(S\) receiver functions to an amphibious data set from Cascadia to image the MTZ discontinuities beneath mid-ocean ridges, a hotspot, and a subduction zone. We find a MTZ thinned by \(10\pm 6\) km beneath the ridges and by \(8\pm 4\) km beneath the base of the slab, closely resembling the 660 discontinuity topography. Depressions on the 410 discontinuity are smaller, \(5\pm 2\) km on average, focused in the north and the south and accompanied by supra-410 discontinuity melt phases. The depressions occur away from locations of uplifted 660 discontinuity, but near slow seismic velocity anomalies imaged in the upper mantle. This suggests lower mantle upwelling occurs beneath ridges and beneath the base of slabs but stall in the transition zone, with upper mantle convection determining upward material transport from the transition zone. Therefore, upper mantle dynamics play a larger role in determining transfer than typically assumed.
Key Words.:
* [1] 1
## 1 Introduction
The mantle transition zone (MTZ) is the region between the upper mantle and lower mantle bounded by two seismic discontinuities at approximately 410 (the 410) and 660 km (the 660) depth ([PERSON] & [PERSON], 1981). These are typically interpreted as the pressure-induced transformation of olivine grains into denser crystal structures, as predicted by laboratory experiments: \(\alpha\) olivine to \(\beta\)-spinel (wadsleyite) at \(\sim\)410 km depth and ringwoodite to bridgmanite and magnesiosu/stite at \(\sim\)660 km depth ([PERSON], 1975). The MTZ is arguably one of the most important parts of the Earth for understanding its evolution and behavior because: (a) any material moving between the upper and lower mantle has to pass through the MTZ, (b) the MTZ has the capacity for storing huge amounts of water, potentially several oceans worth ([PERSON] & [PERSON], 2009), and (c) the top of the MTZ (and/or the shallow lower mantle) may be a region of widespread deep melts ([PERSON] & [PERSON], 2003; [PERSON] et al., 2014), which may act as geochemical reservoirs and/or alter mantle viscosity.
It is typically assumed that material transfer between the upper and lower mantle occurs where hotspots upwell vertically and where subducting plates descend vertically or sub-vertically. Seismic tomography models also find slow velocities interpreted as ascending material beneath hotspots and fast velocities associated with descending material beneath subduction zones ([PERSON] et al., 2007). Seismic imaging of MTZ discontinuities generallyreflects mineral physics predictions for thickening beneath subduction zones and thinning beneath hotspots ([PERSON] & [PERSON], 2002; [PERSON] et al., 2008; [PERSON] & [PERSON], 2006, 2008).
Several lines of geochemical evidence suggest greater complexity than large, long-lived full mantle convection, or in other words, a well-mixed mantle. These include isotopic differences between ridges and hotspots and bulk compositional discrepancies between the predictions and observations of Earth's interior layering and atmosphere ([PERSON], 1997). Possible explanations include pockets of enrichment, chemical piles, layering of stagnant slabs ([PERSON] et al., 2015; [PERSON] & [PERSON], 2004; [PERSON] et al., 1999; [PERSON] & [PERSON], 2015; [PERSON], 1999), or stable high-viscosity lower-mantle convective cells ([PERSON] et al., 2017). Alternatively, the mantle may pervasively rise across the MTZ, but typically be compositionally filtered during the process ([PERSON] & [PERSON], 2003). Although more intricate convection and alternative locations of material transfer across the MTZ may be implied by these conceptual models, tight constraints have remained elusive.
Seismic observations have also been used to argue for greater complexity than the simple vertical ascent of material beneath hotspots. Deflected upwellings or tree-like upwelling structures have been inferred from global seismic tomography images ([PERSON] & [PERSON], 2015; [PERSON] et al., 2021). Imaged slow velocity regions or MTZ thinning have been interpreted as material upwelling from the lower mantle in alternative locations away from hotspots ([PERSON] et al., 2021; [PERSON] et al., 2006). However, it has also been suggested that some of the observations may also be related to nearby plume material ([PERSON] et al., 2017; [PERSON] et al., 2013) or be artifacts of tomographic inversion ([PERSON] et al., 2016).
Several studies have found seismic phases interpreted as conversions from a melt layer just above the MTZ. This is thought to be the result of hydrated material that upwells through the MTZ, but melts when it enters the lower water solubility conditions shallower than the MTZ. However, the phases have been used to link the presence of a melt layer to a variety of different tectonic environments ([PERSON] et al., 2021; [PERSON] & [PERSON], 1994; [PERSON] & [PERSON], 2011; [PERSON] & [PERSON], 2007) and also to suggest the presence/absence of the melt layer is sporadic without necessarily having a tectonic correlation ([PERSON] et al., 2010; [PERSON] & [PERSON], 2017).
High-resolution in situ imaging of MTZ discontinuities provides independent and tight constraints on material transfer and melt layering. Yet, this imaging has proven challenging given that most seismic stations are located on land, that is, limited to \(\sim\)30% of Earth's surface, and typically away from many tectonic regions of interest.
The Cascadia Subduction Zone lies in the northeastern Pacific where the Juan de Fuca and Gorda Plates subduct beneath the North American Plate (Figure 1). The Cascadia Initiative experiment deployed an amphibious seismic array from the intermediate spreading Juan de Fuca and Gorda Ridges, including the Cobb Hotspot, to the Cascadia Arc and Backarc region ([PERSON] et al., 2014) offering an excellent opportunity to investigate material transfer at a range of tectonic environments. Body wave tomography images high-velocity slabs descending to MTZ depths and slow velocities in the upper mantle beneath the base of the slabs ([PERSON] et al., 2018). However, connections between these shallow mantle dynamics, the MTZ, and the lower mantle have yet to be investigated. Here we image the MTZ discontinuities beneath the Cascadia region using \(P\)-to-\(S\) (\(Ps\)) receiver functions (RF)s from an amphibious data set and compare the variations of these discontinuities and MTZ thickness with the seismic velocity anomalies.
## 2 Data and Methods
### Receiver Functions
In this study, we used an amphibious data set recorded by 202 stations including 136 ocean bottom seismometers (OBS)s and 66 onshore instruments. The data were collected by the Cascadia Initiative (OBSIP, 2011), USArray Transportable Array (Array, 2003), the Pacific Northwest Seismic Network (Washington, 1963), Berkeley Digital Seismic Network (Center, 2014), and the United States National Seismic Network ((ASL)/USGS, 1990). We used earthquakes of magnitudes greater than 5.5 Mw with epicentral distances between 35\({}^{\circ}\) and 80\({}^{\circ}\) that happened during the deployment period of the Cascadia Initiative experiment (Figure 1). These initial parameter cutoffs resulted in seismograms from 29,683 event-station pairs.
Figure 1: Map of the study area. The background shows bathymetry/topography. White inverted triangles represent seismometer locations offshore and white squares represent seismometer locations onshore. Red volcano symbols indicate the locations of major volcanos of the Cascadia Arc and the Axial Seamount (the active volcano associated with the Cobb Hotspot), which is on the Juan de Fuca Ridge. Thick red lines show plate boundaries, and the serrated line shows the trench. Three thick black lines represent the locations of the cross sections in Figures 4 and 6. Black circles along the cross sections correspond to a spacing of 100 km. The inset map shows the locations of earthquakes (red circles) used in this study. Juan de Fuca Ridge (dGFR), Blanco Fracture Zone (BFZ), Gorda Ridge (GR), and Mendocino Fracture Zone (MFZ) are as labeled.
The seismograms located on land were rotated into the \(P\)- and \(S\)-wave components using a transformation matrix ([PERSON], 2005) for the free surface:
\[\begin{bmatrix}P\\ \text{SV}\end{bmatrix}=\begin{bmatrix}\frac{\alpha\ell^{2}}{a}&\frac{1-2\beta \ell^{2}\ell^{2}}{2a_{\text{tr}}a_{\text{tr}}}\\ \frac{1-2\beta\ell^{2}\ell^{2}}{2a_{\text{tr}}}&-\rho\beta\end{bmatrix}U_{x} \begin{bmatrix}U_{R}\\ U_{Z}\end{bmatrix}\]
where \(U_{R}\) and \(U_{Z}\) are the radial and vertical components, \(\rho\) is the ray parameter, \(\alpha\) and \(\beta\) are the \(P\) and \(S\) wave velocities, and \(\eta_{x}\) is given by \(\sqrt{x^{-2}-\rho^{2}}\) (\(x=\alpha,\beta\)). Stations located on the seafloor were rotated using the transformation matrix for the solid Earth-ocean interface:
\[\begin{bmatrix}P\\ \text{SV}\end{bmatrix}=\begin{bmatrix}\frac{\alpha\ell_{x}^{2}}{a_{1}}&\frac{ 1-2\beta\ell_{x}^{2}\ell^{2}}{2a_{1}a_{2}}-\frac{a_{0}\beta_{0}}{2a_{1}a_{0}} &U_{R}\\ \frac{1-2\beta\ell_{x}^{2}\ell^{2}}{2a_{\text{tr}}}&-\rho\beta_{1}-\frac{a_{0} \beta_{0}}{2a_{1}a_{0}\beta_{1}}&U_{Z}\end{bmatrix}U_{R}\\ \begin{bmatrix}P\\ \text{SV}\end{bmatrix}=\begin{bmatrix}\frac{\alpha\ell_{x}^{2}}{a_{1}}&-\frac{ \alpha\ell_{x}^{2}}{a_{1}a_{0}}&-\frac{\alpha\ell_{x}^{2}}{a_{1}a_{0}}\\ \frac{1-2\beta\ell_{x}^{2}\ell^{2}}{2a_{\text{tr}}a_{0}\beta_{1}}&-\frac{ \alpha\ell_{x}^{2}}{a_{1}a_{0}\beta_{1}}&U_{R}\end{bmatrix}U_{R}\\ \begin{bmatrix}P\\ \text{SV}\end{bmatrix}=\begin{bmatrix}\frac{\alpha\ell_{x}^{2}}{a_{1}}&-\frac{ \alpha\ell_{x}^{2}}{a_{1}a_{0}}&-\frac{\alpha\ell_{x}^{2}}{a_{1}a_{0}}&-\frac {\alpha\ell_{x}^{2}}{a_{1}a_{0}}\\ \frac{1-2\beta\ell_{x}^{2}\ell^{2}}{2a_{\text{tr}}a_{0}\beta_{1}}&-\frac{ \alpha\ell_{x}^{2}}{a_{1}a_{0}\beta_{1}}&U_We found the amplitudes of RFs from OBS data were systematically larger than those from land data (Figure 2). This has been observed in previous amphibious experiments, and it is expected for typical sediment/ocean interfaces ([PERSON] et al., 2021). We divided the RF amplitudes by the ratios of the median amplitudes of the offshore and onshore P410s and P660s data, respectively, as done in previous work, in order to meld the data sets ([PERSON] et al., 2021). Our testing with synthetic seismograms indicate this is a reasonable way to deal with the two data sets (Supporting Information S1). Synthetic testing shows that ocean bottom receiver functions are predicted to show a different character than land receiver functions at shallow depths because of the very different shallow layering (Figure S2 in Supporting Information S1). However, this does not affect the resolution of discontinuities at MTZ depths. In addition, reverberations in ocean receiver functions from shallow discontinuities are not expected to strongly influence MTZ discontinuity resolution (Text S1 and Figure S2 in Supporting Information S1).
### Error Bars, Depth Migration, and Tests
Selected RFs were migrated to depth and back-projected along the theoretical raypath and stacked onto a 3-D grid that has a lateral spacing of \(1^{\circ}\) by \(1^{\circ}\) and a 1 km depth spacing. The grid smoothing was determined by the Fresnel zone where the radius is \(\sqrt{\left(\frac{i}{2}+d\right)^{2}-d^{2}}\), and \(\lambda\) is the wavelength and \(d\) is the depth, centered in the grid. Since we used separate data sets for P410s and P660s, two 3-D grids were generated first and then merged into one by using a linear weighing between 410- to 660-km depth of the grids. A weighted average is applied to the 410 and 660 data sets. The weights for the P410s data set grid decrease linearly from 1 to 0 from 410 to 660 km depth, while weights for the P660s data set grid increase linearly from 0 to 1 over the same
Figure 2: Piercing points of RFs at 410 and 660 km depth and corresponding P410s P660s RF amplitudes. (a) Amplitudes of P410s versus longitude. Blue circles show piercing point longitudes at 410 km of RFs from offshore data. Orange squares show piercing point longitudes at 410 km of RFs from onshore data. The red thick line shows the median of P410s RF amplitudes from offshore data, and the black thick line shows the median from onshore data. Numbers on the right side of the lines indicate the corresponding median values. (b) Similar to (a) but for P610s. (c) Spatial distribution of piercing points (blue circles for ocean data and orange squares for land data) at 410 km depth. Red lines show plate boundaries. The black circle indicates the bin used in Figure S2 in Supporting Information S1. (d) Same as (c) but for the P660s data set.
depth range. There are sufficient waveforms (>5) to resolve discontinuities in all bins plotted (Figure S4 in Supporting Information S1). There are no gaps within the model, therefore sampling does not affect our interpretation. The region of overlap of resolved 410 and 660 is >10\({}^{\circ}\) longitude and >20\({}^{\circ}\) of latitude.
The reported error bars in the abstract are the standard errors of the means of each bin across subregions. In the main text, the error bars of the 410 and 660 km discontinuity depths represent the standard error of the mean of the depths of the peaks of the individual waveforms in each bin. These vary across the study area from 1 to 4 and 1 to 7 km for the 410 and the 660, respectively (Figure S5 in Supporting Information S1). The error bars on transition zone thickness reported for a given region in our study area correspond to the errors propagated from the 410 and the 660 discontinuity depths.
We performed tests using different migration models to demonstrate the robustness of our observations (Figure 3). In all tests, we left the sediment and crustal corrections intact, given that these shallow layers are well-constrained by independent observations. We report maximum differences compared to depths assuming the IASP91 model for the mantle, noting that the observed phases and depth anomaly patterns presented and discussed in the following sections remained intact.
We first tested the effect of using the 1-D mantle velocities from the PREM model ([PERSON], 1981) instead of the IASP91 model. The average differences in the depths of the 410 and the 660 between these two models are 1.69 and 3.88 km, respectively, and 3.39 km for the difference of the MTZ thickness.
We also tested a series of 3-D models. We tested the effect of using the regional \(P\)-wave velocity anomalies from model CAS2018_P ([PERSON] et al., 2018) (extrapolating in the western and southern edges to cover our study area), relating the anomalies to P-velocity assuming an IASP91 background model and calculating \(S\)-wave velocities assuming the \(V\)/\(V\)s values from IASP91. The results have a good agreement with migration using the 1-D mantle model. Ninety-five percent of pixel-to-pixel differences of the depths of the 410 and the 660 and the thickness of the MTZ were within 5, 11, and 10 km respectively.
We tested the global model PRI ([PERSON] et al., 2006), which has both \(P\)- and \(S\)-wave velocities. The average differences in the depths of the 410 and the 660 between these two models are 2.50 and 10.24 km, respectively, and 7.08 km for the difference of the MTZ thickness.
We also tested the global \(S\)-wave velocity model SEMum2 ([PERSON] et al., 2013) assuming \(P\)-wave velocities calculated using the _Vp/Vs_ ratio from the IASP91 model. The average differences in the depths of the 410 and the 660 between these two models are 4.40 and 9.61 km, respectively, and 5.58 km for the difference of the MTZ thickness.
Changes in depth resulting from migration model changes are sometimes larger than the reported formal error bars. However, this is a systematic error or bias. The trends are robust regardless of the migration model, and therefore do not affect our interpretation or our understanding of the Earth.
Since the overall observed patterns remain intact, for example, the depressions of the 410 in the north and south and the uplifted 660 beneath the ridges and beneath the base of the slabs, these tests show that the main interpretations of this manuscript are robust. We prefer the IASP91 migration model given that it avoids inherent additional
Figure 3.— Migration tests. Topography maps of the 410, the 660, and mantle transition zone thickness from migration using 1-D mantle models from IASP91 ([PERSON] et al., 1995) (top), PREM ([PERSON] & [PERSON], 1981) (second row), the 3-D \(dVp\) CAS2018_P ([PERSON] et al., 2018) anomaly model related to absolute \(P\)-velocity assuming IASP91 for the reference model and calculating \(S\)-wave velocities assuming the \(V\)/\(V\)s values from IASP91 (third row), 3-D \(Vp\) and \(V\)s models from PRI ([PERSON] et al., 2006) (fourth row), and 3-D \(Vs\) model SEMum2 ([PERSON] et al., 2013) with _Vp/Vs_ ratio from IASP91 (bottom).
uncertainties related to resolution in tomographic models. In addition, it avoids uncertainty related to choosing a _Vp/Vs_ ratio when using local models that are only for _Vp_.
### Temperature Estimates
We estimated temperature anomalies for the MTZ using the relationships of temperature with discontinuity depths applied in previous work ([PERSON] et al., 2021). These include a +2.9 MPa/K slope for the 410 ([PERSON] and [PERSON], 1994) and a \(-\)2.5 MPa/K slope for the 660 ([PERSON] et al., 2014) based on experimental relationships of pressure and mineral phase transitions. The average 5 km depression of the 410 and the 15 km elevation of the 660 correspond to 60 and 190 K thermal anomalies, respectively, using the assumed Clapeyron slopes.
A wide range of Clapeyron slopes has been reported, from 1.5 to 2.9 MPa/K for the phase transition at the 410 ([PERSON] et al., 1989; [PERSON] and [PERSON], 1994) and from \(-\)4.0 to \(-\)2.0 MPa/K at the 660 ([PERSON] and [PERSON], 1994; [PERSON] et al., 1990). The thermal anomalies associated with the average depression and uplift reported above would be 60-115 and 138-276 K, respectively, for these slopes. However, this does not affect our interpretation of upwellings and downwellings based on the topography of the discontinuities and body wave tomography ([PERSON] et al., 2018).
## 3 Results
The main phases that we image are positive phases, or velocity increases caused by the 410 and 660 discontinuities, and these are imaged across the study region. We also image negative phases at \(\sim\) 370 km depth, strongest in discrete locations beneath the Mendocino Fracture Zone and the north-central Juan de Fuca Plate (Figures 4a and 4c). Time-domain deconvolution tests suggest that the strongest supra-410 phases are not sidelobe artifacts, but rather robust features (Text S2 and Figure S3 in Supporting Information S1). We image strong positive phases beneath the 660 at \(\sim\) 750 km depth east of 122\({}^{\circ}\)W and north of 47\({}^{\circ}\)N (Figure 4c). Similar phases were detected in this region by a previous RF study and interpreted as a region of high basalt content ([PERSON] and [PERSON], 2021). We do not interpret these phases further, nor do we interpret the negative phases between the 660 and the positive phases at \(\sim\)750 km depth, given the proximity of those depths and the potential for the interference of sidelobes. Strong
Figure 4: Vertical cross-sections. (a) Top: bathymetry/topography along 40.5”N from 131\({}^{\circ}\) to 115”W. Bottom: Vertical cross-section from 3-D migrated RFs along 40.5”N with location shown in Figure 1. Dashed black lines indicate 410 and 660 km depths. Black circles along the cross sections correspond to a spacing of 100 km. Black arrows indicate supra-410 phases. Small black arrows indicate significantly depressed 410 and uplifted 660. (b, c) the same as (a) but along 45”N (b) and 47.5”N (c), respectively. The plate boundaries are labeled as follows: Gorda Ridge (GR), Mendocino Fracture Zone (MFZ), and Juan de Fuca Ridge (JdFR).
negative phases beneath the 410 are imaged but at the very southeastern corner of our study area (Figure 4a). These could potentially be related to the edge of the slab; although, dipping structures can cause complex receiver function imaging, making definitive interpretation challenging ([PERSON] and [PERSON], 2017). Therefore, we do not interpret further since the phases are not the topic of this work.
The average thickness of the mantle transition of our study area is \(245\pm 1\) km in agreement with the global average observations of \(242\pm 2\) km from \(P_{8}\) RFs ([PERSON] and [PERSON], 2006), \(242\pm 20\) km from SS precursors ([PERSON] and [PERSON], 2002; [PERSON] and [PERSON], 2008), and also the theoretical 250 km thickness ([PERSON] and [PERSON], 1991), with a total range between 231 and 258 \(\pm\) 6 km. East of the Cascadia Volcanic Arc, the MTZ is thinned by 5-10 km in comparison to the theoretical. In the middle of our research area, roughly along the coast, the MTZ is of normal thickness with zones of slight thickening, up to 10 km, in the north beneath south Vancouver Island to the Olympic Peninsula and in the south beneath the Cascadia Arc in northern California. The thickening is mainly because of the depression of the corresponding 660. The greatest amount of thinning (15-20 km) is located beneath the ridges and transform fault system in the west from the junction of the Gorda Ridge and the Mendocino Fracture Zone to the inner corner of the intersection of the Juan de Fuca Ridge and the Blanco Transform Fault. We do not observe focused thinning, uplifted 660 or depressed 410 directly beneath the Cobb hotspot. The 660 topography is uplifted by up to \(15\pm 4\) km in the west and 10-20 \(\pm\) 3 km in the east. The 410 is normal to slightly uplifted (\(4\pm 2\) km) in the west of our research area and uplifted by \(10-15\pm 2\) km in the east. The 410 is depressed in the central parts of our study area, most notably by up to \(13\pm 3\) km in the northern second section in a region below the trench and the ridge and by up to \(11\pm 3\) km in the south beneath the trench east of the Gorda Ridge (Figure 5). The depression of the 410 is \(5\pm 2\) km on average. The thickened MTZ (by 2-12 km) in the center of our study region, primarily related to a depressed 660, corresponds to subtle \(P\)-wave velocity anomalies (0.5%) (Figure 5b). Since this is \(>\)600 km east of the slab inferred from body wave tomography, it would need to be an ancient torn piece of Farallon slabs ([PERSON] et al., 2018). This is not a major feature of our model and we have no strong interpretation of it.
## 4 Discussion
The most prominent anomaly in our result, the thinned MTZ beneath the western portion of our study area by 10-20 km agrees with thinning of 16 km reported in this region by a previous global \(SS\) precursors study ([PERSON] et al., 2019). Finer scale variability in our MTZ discontinuity topography is not likely resolved by the global study. The MTZ discontinuities have been imaged beneath western North America by multiple RF studies with resolutions that are similar to ours. Overall, the magnitudes and patterns of the discontinuity topographies and
Figure 5: Maps of the 410 topography and the 660 topography and the thickness of mantle transition zone (MTZ), (a) Colors show the depths of the 410. Thick black lines represent plate boundaries, and the serrated line shows the trench. Red triangles indicate the locations of major volcanos of the Cascadia Arc and the Axial Seamount. Red contours show \(-0.5\%\)\(P\)-wave velocity anomalies and blue contours show \(+0.5\%\)\(P\)-wave velocity anomalies from body wave tomography ([PERSON] et al., 2018). Gray circles indicate the locations of bins used for time-domain tests (Figure S3 in Supporting Information S1). (b) same as (a), but for the 660. (c) similar to (a), but for the MTZ thickness. Thin black lines show contours of MTZ thickness.
MTZ thickness are variable among these studies, likely owing to differences in data and/or approach, such as data selection (manual vs. automatic) and/or migration assumptions ([PERSON] et al., 2010; [PERSON] & [PERSON], 2014; [PERSON] et al., 2012; [PERSON], 2018). However, we do find some general agreement with previous studies. For instance, two studies found MTZ thinning of 5-10 km in the eastern part of our study region in agreement with the 5-20 thinning observed in our result ([PERSON] et al., 2010; [PERSON] et al., 2012).
### Abnormal Discontinuity Topography and Estimated Temperature Anomalies
The 410 and 660 depths may be affected by temperature and/or composition ([PERSON] et al., 2013; [PERSON], 2002; [PERSON] & [PERSON], 1989; [PERSON] & [PERSON], 1989; [PERSON] & [PERSON], 2002). However, we do not find particularly strong evidence for compositional effects in general, for example, uplifted 410 or depressed 660 accompanied by slow seismic velocities, which would correspond to a water interpretation, or very depressed or broad 660, which would correspond to a basalt interpretation. Instead, the variations of the 410 and the 660 depths are in good agreement with the seismic tomography. The locations of depressed the 410 correspond to low-velocity anomalies. The uplifted and depressed 660 locations correspond to low-velocity anomalies and high-velocity anomalies, respectively (Figures 5a and 5b), which is more consistent with thermal anomalies caused by upwellings or downwellings.
There is a small region on the eastern side of our study area that is characterized by an uplifted 410 and slow velocities in the transition zone (Figures 6b and 6c), that is, indicative of hydration. This could be a possible explanation. However, the thickening could also be related to the nearby slab. If the uplifted 410 in the eastern section of the study area is caused by the slab it would correspond to an anomaly of 121-181 K (Figures 5a and 6). We do not find a corresponding depressed 660 in the east, likely because the slab is located outside our study region at those depths, as suggested by the body wave tomography anomalies (Figure 6) ([PERSON] et al., 2018). Given the ambiguity of the slab location, we do not have a strong interpretation of the observed uplifted 410.
Very large depressions on the 660 are thought to be caused by very high temperatures or basalt contents, for example, where garnet would dominate over olivine at the 660 at 200-300 K above the global average mantle
Figure 6.— Vertical cross-sections compared to anomalies from tomography and inferred dynamics. (a) Top: bathymetry/topography along 40.5”N from 131\({}^{\circ}\) to 115”W. Bottom: Vertical cross-section from 3-D migrated RFs (gray wiggles) along 40.5”N. Background colors are \(P\)-wave velocity anomalies from CAS2018_P ([PERSON] et al., 2018). Semi-transparent gray and black arrows with shades indicate inferred pathways of upwellings and downwellings (slabs). Semi-transparent gray arrow shows suggested upper mantle upwellings ([PERSON] et al., 2018). (b, c) Are the same as (a) but along 45”N (b) and 47.5”N (c), respectively. Plate boundaries are labeled as follows: Gorda Ridge (GR), Mendocino Fracture Zone (MFZ), and Juan de Fuca Ridge (JdF). Black circles at 800 km depth are plotted every 100 km along the cross-sections and correspond to those plotted in Figure 1.
temperature ([PERSON], 2002). This has been observed for instance beneath Iceland ([PERSON] et al., 2016). However, we do not observe this, nor do we necessarily expect very large temperatures or basalt contents.
Therefore, we proceed assuming the temperature-sensitive olivine phase changes are related to the Clapeyron slopes ([PERSON] and [PERSON], 1994), and that compositional effects on the remainder of the study area besides the eastern portion, if any, are minimal.
The thickened MTZ (by 2-12 km) in the center of our study region, primarily related to a depressed 660, corresponds to subtle \(P\)-wave velocity anomalies (0.5%) (Figure 5b). Since this is \(>\)600 km east of the slab inferred from body wave tomography, it would need to be an ancient torn piece of Farallon slabs ([PERSON] et al., 2018). This is not a major feature of our model and we have no strong interpretation of it.
The lack of strong MTZ thinning beneath the Axial seamount, the volcanically active surface realization of the Cobb Hotspot, could be explained by a variety of possibilities. A conduit that is less than \(\sim\)100 km in diameter, the size of one of our bins, is below our resolution. The anomaly could also be muted in magnitude. Gravity arguments have been used to suggest it has an excess temperature of 30\({}^{-}\)40\({}^{\circ}\)C ([PERSON] and [PERSON], 1995), which would correspond to a 3-5 km transition zone thickness anomaly, that is, near the size of our error bars and at the edge of resolution. Alternatively, the hotspot may take a non-vertical path through the upper mantle, crossing the 410 at the location of our anomaly 100 km to the northeast.
The thermal anomalies predicted for the discontinuity topographies are consistent with a previous result from the Mid-Atlantic Ridge, more than that inferred at the East Pacific Rise, and less than inferences from hotspots. The more muted 410 thermal anomalies associated with the depressions in the north and south of the study region (60-97 K) similarly agree with 410 observations at the Mid-Atlantic Ridge, which suggested a 60 K anomaly ([PERSON] et al., 2021), and the predictions are also smaller than estimates based on RF imaging of the 410 beneath hotspots including, for example, 100-165 K in Hawaii ([PERSON] et al., 2017) and 200 K in Iceland ([PERSON] et al., 2016). The result is different than the inferred lack of a thermal anomaly beneath the East Pacific Rise ([PERSON] et al., 1998), which suggests either that faster-spreading centers are not underlain by deep upwellings, or that the upwellings were at the edge of the resolution of the previous work ([PERSON] et al., 2021).
### Dynamics
Several global tomography models also support deep upwellings in this region, finding slow velocities at 660-1,000 km depth (Figure S5 in Supporting Information S1). The variations of the 660 topography contribute more to the MTZ thickness differences as they are correlated at 0.73 with the MTZ thickness (Figure 7). The thinned MTZ and uplifted 660 in our study area suggest that material upwells from the lower mantle beneath the intermediate spreading ridges in Cascadia and beneath the base of the Cascadia Slabs. This expands the interpretation that upwelling occurs beneath slow-spreading environments ([PERSON] et al., 2021) to intermediate-spreading environments. It suggests that sub-slab upwellings inferred from slow velocity anomalies need not necessarily be artifacts of tomography resolution ([PERSON] et al., 2016; [PERSON] et al., 2020). While many geodynamic models predict downwelling sub-slab material, some also suggest that buoyant upwelling material may be possible beneath the base of a subducting slab, which could potentially uplift the 660 ([PERSON] and [PERSON], 2020).
Surprisingly, the 410 depressions do not correspond to the locations of the uplifted 660, and instead, occur roughly between the uplifted 660 regions. This observation is consistent with a non-vertical ascent of material through the MTZ, which is much different from the typical paradigm which includes the simple vertical ascent of material through the MTZ ([PERSON], 1971). However, the observation agrees with observations from the Mid-Atlantic Ridge where the peak 410 topography was offset from that of the 660 ([PERSON] et al., 2021). In our study region, the strongest 410 depressions occur in the north and the south, suggesting a more 3-D flow. In the south, the 410 depression and the eastern 660 uplift occur just beneath the base of the slab as defined by the 0.5% fast contour from body wave tomography ([PERSON] et al., 2018) (Figure 5). In the northern sections, the 660 is uplifted beneath the base of the slab but the 410 depression occurs roughly midway between the ridge and the slab, that is, \(\sim\)500 km west of the base of the slab. One possibility is that the upwellings from the lower mantle in our study region stagnate within the MTZ before reaching 410. The stagnation could occur because the upwellings dehydrate during ascent through the MTZ, as predicted by geodynamics ([PERSON] et al., 2019).
Instead, the locations of thermal upwellings suggested by our 410 depressions are coincident with the locations of slow seismic velocity anomalies from the body wave tomography (Figure 7). The slow velocities were interpretedas buoyant upper mantle flow at \(<\)100-350 km depth. In the north, the inferred flow originates from the west, bending eastward toward the slab as it nears the surface (Figure 6, light gray arrows) ([PERSON] et al., 2018), which is also generally consistent with west-east shear wave splitting directions reported east of the Cobb Hotspot ([PERSON] et al., 2015). In the south, the flow occurs from east to west up the base of the slab (Figure 6, light gray arrows) ([PERSON] et al., 2018), which could also be consistent with complex shear wave splitting directions reported from the eastern side of the Blanco Fracture Zone. Our 410 depressions are coincident with deeper realizations of the slow anomalies associated with the interpreted flow, suggesting that the flow originates from within the MTZ (Figure 6, arrows pointing upwards at 410 km depth).
There are a few possible causes for the inferred reversed flow direction in the north in comparison to the south. The difference may be related to additional buoyancy from the Cobb Hotspot ([PERSON] et al., 2018). Neither our MTZ discontinuity depths nor the body wave tomography detects a strong hotspot anomaly. However, we cannot preclude the possibility that the hotspot causes the variation in dynamics with latitude. An alternative is that the difference in flow direction occurs because the southern edge of our study area is located near the hypothesized southern edge of the Gorda slab, as inferred from tomography ([PERSON] et al., 2018). Toroidal flow around the slab edge could result in more complex mantle flow in the region ([PERSON] et al., 2010).
Figure 7.— Maps of the 410 and the 660 differential topography, the differential thickness of mantle transition zone (MTZ), and average \(P\)-wave velocity anomalies and their correlations. (a) The 410 topography difference compared to 410 km. (b) Average \(P\)-wave anomalies (dVp) from 100 to 410 km ([PERSON] et al., 2018). (c) Regions of 410 depressions and slow average Vp from 100 to 410 km depth (orange) and regions of uplifted 410 and fast average Vp from 100 to 410 km depth (green). (d) The 660 topography difference compared to 660 km. (e) MTZ thickness difference compared to 250 km. (f) Regions of MTZ thinning and uplifted 660 (orange) and regions of MTZ thickening and depressed 660 (green).
The intermittently imaged negative discontinuities at 365-385 km depth may be caused by conversions from the top of a supra-410 melt layer. In the north, the negative phase is strongest directly above the inferred location of upwelling based on 410 topography. In the south, the negative phase exists just to the west of the location of inferred upwelling. Supra-410 melt is predicted to occur when hydrous material upwells from the MTZ into the less-soluble overlying mantle ([PERSON] & [PERSON], 2003), and discontinuities related to such a layer have been imaged by a variety of studies ([PERSON] & [PERSON], 2021; [PERSON], 2017). The observations are consistent with this model and suggest that upper mantle flow may enter the MTZ and entrain hydrous material to shallower depths. A supra-410 discontinuity is not imaged above the inferred upwelling based on the 410 topography at middle latitudes (Figure 4b). Therefore, MTZ hydration may be variable and/or supra-410 melt may be transient in time and/or space possibly owing to melt migration ([PERSON] et al., 2021). Either could explain the wide variety of hypothesized preferential tectonic locations and/or sporadic imaging of supra-410 melt layers ([PERSON] & [PERSON], 2003; [PERSON] & [PERSON], 2017). We note that our testing indicates the supra-410 phases persist regardless of the deconvolution method and migration models used (Text S2, Figure S3 and S7 in Supporting Information S1). However, the melt-layer discontinuities are not necessarily required to support the conclusions of this paper, although they are intriguing and aligned with our interpretation.
## 5 Conclusions
We use extended-time multi-taper _P_s RFs to image the MTZ discontinuities beneath the Cascadia region using an amphibious data set. We interpret phases that are above the formal error bars of the stack, away from the far edges of the model, and at depths deeper than those contaminated by crustal reverberation artifacts. Although migration model assumptions can impact the absolute depths of the imaged discontinuities, the existence of the MTZ phases and the trends of the MTZ discontinuity depths and MTZ thicknesses that we interpret are robust regardless of migration model assumptions.
The MTZ is thinned beneath the Juan de Fuca and Gorda Ridges and beneath the Cascadia Slabs and corresponds to the locations of the uplifted 660. The most depressed 410 lies beneath the northern Juan de Fuca Plate and beneath the Gorda Plate, offset from where the 660 is largely uplifted. The depths of the 410 and the 660 beneath the Cascadia are not anticorrelated as in classical diagrams for regions where ascending/descending happens. However, the variations of the 410 and the 660 topography are in good agreement with thermal predictions based on previous seismic tomography observations. We do not find strong evidence for compositional effects in the central portions of our study region and the locations where our interpretations are focused.
Overall, this suggests that deep upwellings from the lower mantle may occur beneath tectonic locations other than hotspots, including beneath ridges and beneath slabs. However, the upwellings are sluggish and may stagnate in the MTZ, possibly owing to dehydration, instead of continuing to ascend vertically. Instead, upper mantle convection can interact with the shallow MTZ, entraining hydrated MTZ material and transporting it into the mantle above. This provides a new transport mechanism for the redistribution of hydration into the mantle above the MTZ. It suggests that in regions distant from a major hotspot like Hawaii and Iceland, that is, the majority of the Earth, upper mantle dynamics may play a larger role in dictating material transfer from the MTZ into the upper mantle.
## Data Availability Statement
The methods used are standard and widely used ([PERSON], 2006) and are detailed in the Methods section. Data are processed using MATLAB. All the figures were generated using Generic Mapping Tools (www.soest.hawaii.edu/gmt). Data sets are available at the IRIS DMC website ([[http://service.iris.edu/fdsnws/dataset/1/](http://service.iris.edu/fdsnws/dataset/1/)]([http://service.iris.edu/fdsnws/dataset/1/](http://service.iris.edu/fdsnws/dataset/1/))) with network codes 7D ([[https://doi.org/10.7914/SN/7D_2011](https://doi.org/10.7914/SN/7D_2011)]([https://doi.org/10.7914/SN/7D_2011](https://doi.org/10.7914/SN/7D_2011))), TA ([[https://doi.org/10.7914/SN/TA](https://doi.org/10.7914/SN/TA)]([https://doi.org/10.7914/SN/TA](https://doi.org/10.7914/SN/TA))), UW ([[https://doi.org/10.7914/SN/UW](https://doi.org/10.7914/SN/UW)]([https://doi.org/10.7914/SN/UW](https://doi.org/10.7914/SN/UW))), BK ([[https://doi.org/10.7932/BDSN](https://doi.org/10.7932/BDSN)]([https://doi.org/10.7932/BDSN](https://doi.org/10.7932/BDSN))), and US ([[https://doi.org/10.7914/SN/US](https://doi.org/10.7914/SN/US)]([https://doi.org/10.7914/SN/US](https://doi.org/10.7914/SN/US))).
## Appendix A Appendix
### Acknowledgments
[PERSON] and [PERSON] acknowledge funding from the Natural Environment Research Council (EM00350771) and the European Research Council (GA), 2017. Mapping the mantle transition zone beneath Hawaii from Ps receiver functions: Evidence for a hot plume and cold mantle downsellings. _Earth and Planetary Science Letters_, _474_, 226-236. [[https://doi.org/10.1016/j.opl.2017.06.033](https://doi.org/10.1016/j.opl.2017.06.033)]([https://doi.org/10.1016/j.opl.2017.06.033](https://doi.org/10.1016/j.opl.2017.06.033))
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wiley/fea2cef9_3fc6_4ed2_8b74_3f37f217e64d.md | # IGR Earth Surface
Research Article
10.1029/2021 JF006188
###### Abstract
We aim to identify conditions that influence the preservation of a complete record of channel plafforms in the topmost layer of floodplains, prior to the maintenance in the rock record. We have tested a hypothesis that a successive decrease of stream power and channel belt width are necessary to preserve the record of channel plafforms in the topmost floodplain layer over \(10^{3}\) to \(10^{4}\)-year time scales. A literature review was conducted for rivers of the temperate zone of the Northern Hemisphere. Stream power, valley, and channel belt widths, paleodischarges, sediment grain-size, and age of paleodannels were used to identify four groups of rivers with preservation potential ranging from tens of thousands years to annual time scales. The decrease in stream power followed by sustained low stream power, and successive decrease of channel belt width were identified in rivers preserving a \(10^{5}\) to \(10^{4}\)-year record of channel plafforms. River valleys with the record of at least two generations of paleodannels, and valley width/channel belt width ratios between 6 and 12, potentially preserve fluvial records over \(10^{3}\) to \(10^{4}\)-year time scales. We analyzed unusually well-preserved records of channel planforms from the Obra and Sio Rivers (central Europe). A determination of trends in changes of stream power and channel belt widths based on an extensive set of geophysical, geological data, and sediment dating from earlier studies, confirmed the tested hypothesis. The proposed framework can be extended by fluvial records preserved by large, and coastal rivers, with the potential to include ancient fluvial records.
The authors.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
1
## 1 Introduction
A sedimentary record of channel planforms preserved in alluvial sediments provides information about past climate changes. This is because dry and humid periods influence the magnitude of discharge, sediment load, channel width and depth, velocity, slope, and roughness ([PERSON] & [PERSON], 1957). These interactions are recorded in fluvial sedimentary architecture. There are seven orders of elements constituting fluvial sedimentary architecture - from the single lamina, through bar surface, bars, nested channel cuts, channel fills and channel belts, to a nested valley ([PERSON], 1985). The record of channel belts includes information about the type of channel planform including records of past fluvial events that is, channel cutoffs, avulsions, the occurrence of floods, and changes in sedimentation style.
Before this sedimentary information is preserved in the rock record, alluvial sediments undergo eroding and reworking. The completeness of this record depends on the magnitude of erosional events ([PERSON], 1984; [PERSON], 1997), discharge regime (cf. [PERSON] et al., 2016), inter-annual discharge variability (cf. [PERSON] et al., 2018), sediment supply causing the occurrence of aggradation and avulsions (cf. [PERSON] & [PERSON], 2000; [PERSON], 2001; [PERSON] et al., 2016), and the interactions between these factors and base-level changes ([PERSON] & [PERSON], 2000; [PERSON], 1988; [PERSON], 1991). [PERSON] et al. (2018) reported that identification of periods of stasis in fluvial records is important because of the potential to identify events missing in the fluvial sedimentary record. [PERSON] et al. (2018) noted that final preservation of a meandering channel belt requires aggradation, and occurrence of avulsions. [PERSON] et al. (2020) reported that bar deposits are relatively well preserved in avulsion-dominated systems due to slow lateral migration rates ([PERSON] et al., 2020). Despite these studies, it is not fully understood what sequence of changes in flow energy and sediment supply conditions results in the preservation of channel planforms in floodplain sediments prior to their preservation in the rock record.
The main objective of our study is to identify the conditions, the occurrence of which, and changes of which to a new state of flow and sediment transport, resulting in the preservation of a complete record of a channel planform, that can be identified in the topmost part of floodglains. We define the term \"preservation potential\" as the ability to preserve a channel planform in the floodplain surface, and its topmost layer. \"Complete record\" is defined as the sedimentary record of a channel planform maintaining basic features of its geometry (i.e., channel width, thickness, and section connecting at least two inflection points allowing for calculation of sinusosity) preserved in the topmost layer of a floodplain.
Our study aims to test the hypothesis that a successive decrease of specific stream power and channel belt width are necessary conditions to preserve the record of channel planforms in the topmost floodplain layer over \(10^{3}\) to \(10^{4}\) ky time scales. The hypothesis was tested using estimations of stream power, sinusosity and braiding indices for generations of paleochannels identified in the topmost floodplain record of rivers situated in the temperate zone of the Northern Hemisphere. We also studied relations between valley widths, channel belt widths, and the age of paleochannels preserved in the analyzed river floodglains. The data for the estimations originate from the literature review (Table 1), limited to valley-confined rivers. The rivers we analyzed are separated from sea coasts by mountain ranges and moraine uplands, so the influence of the backwater effect is not considered in the present review.
We propose a framework of rivers with preservation potentials varying from tens of thousands years to annual time scales. Four groups of rivers were identified. The obtained results are discussed with reference to identification of potential sites preserving fluvial sedimentary records over \(10^{3}\) to \(10^{4}\) ky time scale, extension of the proposed framework by examples of coastal and large rivers, and implications of our findings for ancient fluvial records.
In the second part of this study, we present a detailed analysis of changes in stream power, aggradation rates, and channel belt widths in unusually well-preserved alluvial fills of the Sio River valley (Transdanubia, southern Hungary), and middle Obra River valley (western Poland). They maintain the sedimentary record of river planforms from the Late Pleniglacial (a period between \(\sim\)30,000 and 14,700 cal. BP) and Late Glacial (\(\sim\)14,700-11,700 cal. BP), respectively. Previous research conducted in these areas referred to the evolution of channel planforms in the Obra ([PERSON], 2013, 2014, 2016a, 2016b, 2018; [PERSON], 2020), and Sio Valleys ([PERSON] et al., 2021). We used ground-penetrating radar (GPR), grain-size, and sediment dating data collected during the earlier studies to estimate the width and thickness of channel fills, values of paleochcharges, stream power, and aggradation rates for identified generations of paleochannels. The goal was to use these data toward testing the hypothesis on a successive decrease of potential specific stream power, and channel belt width, on the preservation of the fluvial record over \(10^{3}\) to \(10^{4}\) ky time scales using an extensive set of geophysical, geological data, and sediment dating, collected during the earlier studies conducted at these sites.
## 2 Materials and Methods
### Literature Review
A literature review was carried out to study time scales of the sedimentary record of channel planforms in rivers of the temperate zone of the Northern Hemisphere (Figure 1; Table 1). We collected data regarding valley and channel belt width, channel width, and depth, grain-size, valley slope, bankfull discharge, paleodischarge, and age of paleochannels. Where not available, widths of channels and channel belts were measured from topographic maps, aerial images, and geological sections, and Google Earth using the \"distance measurement\" tool. These data were used to estimate specific stream power for paleochannels preserved in the valley floors. The literature review was limited by the availability of the data, especially grain-size, aggradation rates, and reconstructions of channel planform changes. We have collected data from the following river valleys:
1. Rivers evolving in a postglacial landscape of central Europe: the Vistula (Wisla; [PERSON], 1991; [PERSON] et al., 1996; [PERSON], 2001), Warta ([PERSON] & [PERSON], 1987), Prosna ([PERSON], 1991; [PERSON] & [PERSON], 1989), middle Obra ([PERSON], 2013, 2014; [PERSON], 2020) and lower Obra Valleys (Poland; [PERSON], 2011, 2016a; 2016b).
2. Rivers of Transdanubia and Great Hungarian Plains (Hungary): the Kapos, Koppany ([PERSON], [PERSON], 2020), Sio ([PERSON] et al., 2021), and Tisza River (Hungary; [PERSON] et al., 2010; [PERSON] et al., 2018).
3. Low-energy rivers of western Europe: the Drentsche Aa and Overjissel Vecht (the Netherlands; [PERSON] et al., 2017, 2018; [PERSON] & [PERSON], 2019).
4. Rivers evolving in valleys confined by mountain ranges or moraine uplands: the Morava (the Czech Republic; [PERSON] et al., 2018), upper Columbia (Canada) ([PERSON] et al., 2002, 2017), Narew (Poland; [PERSON] et al., 2000, 2003).
Figure 1.— World’s climate zones, and situation of rivers selected for review to study changes in stream power and a channel belt width of past channel platforms.
* Rivers characterized by active migration of meanders and formation of cutoffs: the Bollin and Dane Rivers (UK; [PERSON] et al., 2020; [PERSON], 1995, 2004, 2007; [PERSON] et al., 2010); Allier River (France; [PERSON], 1997; [PERSON], 2011).
* 6. Anabranching rivers evolving in floodplains built of coarse sediments, and activating side channels at high flows: the Wear River (UK; [PERSON] et al., 2018).
* 7. Braided rivers reworking their braidplains: the Tagliamento (Italy; [PERSON] et al., 2009, 2010), Kicking Horse (Canada; [PERSON], 2019; [PERSON] et al., 2020), Sagavarnikot (northern slope of Alaska; [PERSON] et al., 2004), and South Saskatchewan River (Canada; [PERSON] et al., 2011).
Sinosity and braiding indices were determined for the channel planforms preserved in the valley floors of the selected rivers (Table 1). Sinuosity was calculated for meandering planforms by dividing the distance along paleochannels by a straight line distance between their upstream and downstream ends. Length-based braiding indices (\(\mathrm{BL_{L}}\)) were determined for braided, and anabranching planforms by dividing the total length of channels in a valley section by the main channel length measured along the centerline of the channels ([PERSON], 1981; in: [PERSON], 2008; [PERSON] & [PERSON], 1993).
\[\mathrm{BL_{L}=\Sigma L_{T}/\Sigma L_{M}} \tag{1}\]
where \(\mathrm{BL_{L}}\) is the length-based braiding index, \(\Sigma L_{T}\) is the total length of channels, and \(\Sigma L_{M}\) is the length of the main channel.
Number-based braiding indices were calculated by counting the number of channels along valley cross-sections. As the number of channels varied between the cross-sections, a range of BI values was given in Table 1 for each of the analyzed rivers. The channel lengths were measured manually using maps and images found in the literature. When clear pictures of paleochannels preserved in valley floors were available in Google Earth, the measurements were carried out using the \"distance measurement tool.\"
Sinuosity and braiding indices were calculated for channel belts preserved in the ancient rock record (Table S1). The aim was to compare geometry of channel planforms preserved in the surface layer of floodplains with the ancient record. An unpaired Welch \(t\)-test was performed to test the hypothesis that sinuosity of channel planforms from the Holocene and Late Glacial is not significantly different from sinuosity of the ancient channel belts (Table S2). The [PERSON]'s \(t\)-test was applied as the number of samples, standard deviation, and variances varied between the analyzed populations. The confidence interval was 95%. The test was run for sinuosity values.
Specific stream power was estimated for all the generations of paleochannels identified in the analyzed rivers (Table 1). Stream power describes the influence of flow energy to move the sediment from river banks and the bottom. This parameter shows how the changes in flow energy exert an influence on the type of channel planform ([PERSON], 1987; [PERSON], 2011; [PERSON], 1995). Specific stream power ([PERSON], 1966) is defined as:
\[\omega=\rho\mathrm{gQ_{H}S/w} \tag{2}\]
where \(\omega\) is potential specific stream power (W m\({}^{-2}\)), \(\rho\) - density of water (g cm\({}^{-3}\)), g - gravitation (m s\({}^{-2}\)), Q\({}_{H}-\) bankfull discharge (m\({}^{3}\) s\({}^{-1}\)), S - slope (m m\({}^{-1}\)), w - bankfull channel width (m).
The uncertainties of bankfull paleocharges, mean velocities and Manning's \(n\) coefficients were determined based on detailed field studies carried out in the Obra and Sio valleys, included in the conducted review (Tables 1, S3, and S4). This was done using an extensive set of geophysical and geological data collected during the earlier studies ([PERSON], 2013, 2014, 2016a, 2016b, 2018; [PERSON], 2020; [PERSON] et al., 2021).
The estimated values of specific stream power were plotted with the median grain-size (D\({}_{\mathrm{sg}}\)) of alluvial sediments on a graph delimiting types and channel planform and sediment load proposed by [PERSON] and [PERSON] (2011). The goal was to compare the identified groups of rivers to types of planform and channel mobility estimated by [PERSON] and [PERSON] (2011). The age of particular generations of the paleochannels was plotted with valley widths and valley width/channel belt width ratios. The aim was to verify how the observed changes in channel planforms are associated with the estimated trends in stream power and channel belt width.
## 3 Results of Literature Review - Conditions to Preserve the Sedimentary Record of Channel Planforms
We identified four groups of rivers characterized by preservation potentials ranging from tens of thousands years to annual time scales have been identified.
Low Energy (0.5-20.0 W m\({}^{-2}\)) Meandering and Anabranching Rivers With a Successive Decrease of Channel Belt Widths
We have found that rivers preserving the record of channel planforms over 10\({}^{3}\) to 10\({}^{4}\) kg time scales are characterized by a decrease in potential specific stream power followed by sustained low stream power (Figure 2a1; Table 1). The decrease in stream power is accompanied by the increase in valley width/channel belt width ratio (Figure 2a2). This is because channel planforms of these rivers produce successively narrower channel belts. This group of rivers evolved from large-scale meanders to small-scale bends or anabranching channels in the Late Plenigalicaal and Late Glacial. These transitions were accompanied by the increase in valley width/channel belt width ratios from 1-2 to 6-12 (Figure 2a2). Stream power decreased, and its low values were maintained in the early and middle Holocene until \(\sim\)4,000 cal. BP.
An increase in stream power can be seen in all the river courses during the last 4,000 years (Figure 2a1). This increase was small (e.g., from 0.5 to 1.0 W m\({}^{-2}\) in the Warta River; Figure 2a1) and did not cause the erosion of the older channel fills. Valley width/channel belt width ratios turned from increasing to constant (Figure 2a2). The ability to preserve sequences of channel planforms by these rivers in a 10-20 kg time scale is confirmed by their locations in the diagram of [PERSON] (2011) (Figure 3). The middle Obra and Si\(\delta\) belong, as well as parts of the Warta, Vistula, and Tisza Rivers, to \"laterally immobile\" rivers. Large-scale meanders, and part of anabranching channels in the Si\(\delta\) Valley, and several channels in the Vistula, Prosna and Tisza Valleys belong to \"moderately braided and meandering with scrolls and chutes\", and \"meandering with scrolls\" (Figure 3). This means that the large-scale bends must have reworked the earlier fluvial record until being replaced by a lower energy planform.
Low and Moderate Energy (0.5-45.0 W m\({}^{-2}\)) Meandering and Anastomosing Rivers With Constant Widths of Channel Belts and Aggrading Conditions
These rivers preserve traces of channel planforms reaching from 7,000 to 4,000 cal. yr BP (Figure 2b1). The Narew, upper Columbia, and Morava evolve through avulsions. Their valley width/channel belt width ratios amount to 1-3, and these values are constant in a millennial-scale. This is caused by constant widths of channel belts which rework the whole or at least half of the valley width (e.g., the lower Obra, Kapos and Koppany, upper Columbia and Narew; Figure 2b2). These rivers are confined by moraine uplands or mountain ranges and are characterized by periods of increased stream power (see Figure 2b1). This is why part of paleochannels preserved in the Narew, upper Columbia and Morava River valleys belong to meandering or moderately braided rivers in the diagram of [PERSON] (2011) (see Figure 3). Such a temporal increase in flow energy may have contributed to the formation of the avulsions, along with the influence of upstream sediment delivery (the upper Columbia River; [PERSON] et al., 2012; [PERSON] et al., 2017), and in-channel vegetation ([PERSON] et al., 2003; [PERSON] et al., 2018).
This group of rivers is characterized by agradding conditions. Aggradation rates amounted to 1.77 mm y\({}^{-1}\) during the last 4,550 cal. yr BP in the upper Columbia River ([PERSON] et al., 2002), 2.8 mm y\({}^{-1}\) in the Morava River ([PERSON] et al., 2018) during the last \(\sim\)7,000 cal. yr BP, and 1.0-1.5 mm y\({}^{-1}\) in the Narew River ([PERSON] et al., 2003) during the last 4,000 cal. yr BP. The aggradation and relatively small valley width (compared to the previous group of rivers; Figure 4), led to the preservation of vertically stacked channel fills in these alluvial fills (multi-storey architecture of floodplains - cf. [PERSON], 2006). Such an architecture also refers to rivers evolving through oblique agradation (Drentsche Aa, the Netherlands; [PERSON] et al., 2017). This process plays an important role in the preservation of channel bodies in the valley floor as the valley width is low (\(\sim\)300 m; Figure 4) and limits the space for the preservation of channel planforms.
It should be noted that rivers evolving in valleys characterized by similar width (2.0-3.0 km) preserve channel planforms at a range of time scales, between 18,000 cal. yr BP and 4,000 cal. yr BP (see, e.g., the Prosna andWorta, and the upper Columbia and Narew Rivers in Figure 4). Here the trends of changes in stream power, and valley width/channel belt width ratio discriminate between the record of channel planforms since the Late Glacial in the Prosna and Warta Valleys, and that since 5,000-4,000 cal. yr BP in the Columbia and Narew Valleys (Figures 2a and 2b).
Part of this group of rivers (Figure 2b1) are courses evolving through a slow migration of meanders, taking a millennial timescale to develop a meander bend. They preserve traces of meander migration from the last 8,000 years (the lower Obra Valley, Poland - [PERSON], 2011) and paleomeanders from the last 13,500 years (Kapos
Figure 2.— Types of rivers characterized by the preservation of channel planforms from millennial to annual time scales. The values of stream power, and valley width/channel belt width ratios were estimated for particular rivers, based on the values of paleodischarges, valley slopes, channel, and channel belt widths, and the age of paleochannels found in the literature (see Table 1 for data and references).
and Koppany Valleys - [PERSON], [PERSON], et al., 2020). These rivers are featured with a constant low stream power not exceeding 1.0 W m\({}^{-2}\) (Figure 2b1). They belong to \"latentially immobile rivers\" (cf. [PERSON], 2011, Figure 3). Again, changes in channel belt width are important. For instance, the valley width/channel belt width ratio of the SiO Valley increases from 1.0 to 8.0 during the last 18,000 years. The ratio is close to constant (1.6-2.7) in the Kapos and Koppany Valleys over the period of 13,000 years. The Kapos and Koppany Valleys do not preserve the record of large-scale meanders from the Late Pleniglacial. High flows going through the Kapos and Koppany valleys formed braided channels at that time. Their traces are marked by layers of coarse sands in the valley bottom (cf. [PERSON] & [PERSON], 2013). The nature of these differences requires further studies.
Moderate and High Energy (30-170 W m\({}^{-2}\)) Meandering and Anabranching Rivers With Constant Channel Belt Widths and Intensive Lateral Migration
These river valleys preserve the record of channel planform changes in centennial time scales. They are characterized by active migration of channels and occurrence of cutoffs. The channel belts of these rivers rework 75%-80% of their valley widths (valley width/channel belt width ratio amount to 1.2-1.7; Figure 2c2 and Table 1). They belong to meandering and moderately braided rivers on the diagram of [PERSON] (2011)
Figure 3.— Specific stream power and median grain-size describing paleochannels preserved in identified groups of rivers.
(Figure 3). The sedimentary record of this type of river corresponds to the type of mobile channel belts (cf. [PERSON], 2006, and see Figure 11b therein). The Allier (France), Bollin (the United Kingdom), and Wear River (the United Kingdom) represent these types of rivers. In the course of the Wear River, single-thread sections are characterized by increased bank erosion and reworking of the river bed ([PERSON] et al., 2018). Thus, near the active channel belt, the scale of preservation can be decadal. Centennial sedimentary records may be preserved within terrace levels within incised sections of the valley. The Bollin and Dane Rivers (the United Kingdom) evolve through series of cutoffs ([PERSON], 2004). As in the previous group of rivers, the width of channel belts is constant. However, these rivers migrate at a pace of 1.25-2.11 m y\({}^{-1}\)([PERSON], 1995), and erode earlier fluvial records. Data shown by [PERSON] (2007; see Figure 2 therein) indicate that the planform of the Dane River from 1840 AD was reworked by later meander migration, and only single fragments of these meanders might be preserved in the alluvial deposits. The Allier River (France) is characterized by bend migration rates between 10.0 and 65.0 m y\({}^{-1}\)([PERSON] & [PERSON], 2011). The intensive migration of meanders means that only single paleomeanders older than 1946 AD might be preserved in lateral parts of the valley (see Figure 1 of van [PERSON] et al., 2012).
High-Energy (60-700 W m\({}^{-2}\)) Braided Rivers With Channel Belts Reworking the Whole Valley Width
These rivers represent the lowest ability to preserve past channel planforms owing to high stream power (Figure 2c1), and frequent eroding and reworking of the earlier fluvial record. The time scale of the preservation is annual to decadal. Valley width/channel belt width ratios amount to 1.0 (Figure 2c2; Table 1). This means that the channel belts of these rivers rework the whole width of these valleys. For instance, the course of the Tagliamento River (Italy) undergoes significant changes in channel width during intensive floods (cf. [PERSON] et al., 2009, 2010). The bankfull stage appears at least once per three years, and a complete reworking of the floodplain happens at least on a 10-20 year scale ([PERSON] et al., 2009). The channels of these rivers migrate rapidly; the average migration rate of the Kicking Horse River amounts from 9.0 to 34.0 m y\({}^{-1}\), and most of the valley floor can be reworked by high flows in a period of 8 years (see Figure 5 in [PERSON] et al., 2020). The channel belt of the Sagavanitkot River (north slope of Alaska) is reworked by flood flows occurring in the ice
Figure 4: Valley widths and maximum age of channel planforms preserved in the alluvial sedimentary record. The valley widths were collected during the literature review or measured in aerial images using Google Earth.
breakup period in May and early June ([PERSON] et al., 2004). Braid bars change their shapes and locations by tens of meters in a 13-year period (see Figure 7 in [PERSON] et al., 2004). Despite dam construction, bed-load transport commences over the entire braidplain of the South Saskatchewan River (Canada) during flood events ([PERSON] et al., 2006). Its anabranches can be abandoned and filled with sediments within a 2-year period ([PERSON] et al., 2011).
## 4 The Middle Obra and Sio Rivers - Examples of High Preservation Potential
We analyzed changes in specific stream power of former channels, widths of channel belts preserved in the valley floor, and aggradation rates in the middle Obra (Poland) and Sio River Valleys (Hungary). This was done in reference to a complex set of generations of paleochannels preserved in both valleys during the last 18,000 years (Figures 5-7). The middle Obra Valley is situated in a postglacial area, within the Warsaw-Berlin ice-marginal valley surrounded by moraine uplands (Figures 5a and 5c). The ice-marginal valley was formed by meltwater outwash of the Last Inland Ice ([PERSON], 2012). The surface area of the catchment measures 4,022 km\({}^{2}\). The width of the valley is \(\sim\)10 km. The valley floor is filled with medium and fine sands, sandy silts, peats, and gyttjas.
Figure 5: Geomorphic maps with the main types of channel planforms, and locations of the study sites. (a) Obra Valley (Poland), (b) Sio Valley (Hungary), (c) traces of a multi-channel connection between the Obra and Obra Rivers, with types of channel planforms identified by [PERSON], [PERSON] and [PERSON] (2020), (d) types of channel planforms preserved in the Sio Valley, identified by [PERSON] et al. (2021). The types of channel planforms distinguished in the maps originate from studies of [PERSON], [PERSON] and [PERSON] (2020 – the middle Obra Valley), and [PERSON] et al. (2021 – the Sio Valley). The main geological and geomorphological features were marked on the maps based on surface sediments geological maps (scale 1:50,000) edited by the Polish Geological Institute, and geological map of Hungary (scale 1:500,000) edited by the Mining and Geological Survey of Hungary.
There are glacial (fragments of morazines) and aeolian (dunes and aeolian sands) landforms on the valley floor (Figure 5c). Alluvial sediments are present in 1-4 km wide \"corridors\", formed among the older landforms, marking locations of former channel belts (Figure 5c). In its western part, traces of a multi-channel connection with the Oda River are preserved in the valley floor ([PERSON], [PERSON], 2020). The middle Obra River formed large-scale meanders in the Late Glacial (Figures 6 and 7). The Sio valley is situated in Transdanubia (Figure 5c).
(Hungary; Figures 5b and 5d). The river, canalized at the beginning of the nineteenth century, flows from Balaton Lake to the Danube River. The valley is surrounded by hills built of loess. Its catchment area measures \(\sim\)9,200 km\({}^{2}\). The valley width varies from 1.5 to 3.0 km. The mean annual discharge in the Sio canal amounts to 39 m\({}^{3}\) s\({}^{-1}\). The valley floor is filled with silts and sandy silts, delivered from loess hills surrounding the valley.
### Data From Previous Studies in the Middle Obra and Sio Rivers
The grain-size data were used by [PERSON] (2014, 2016b) and [PERSON] et al. (2021) to determine trends in vertical changes of mean diameter and standard deviation of the Obra and Sio deposits. The grain-size distributions originated from analyses conducted using laser diffraction technique in a Malvern Mastersizer 3000 Hydro LV
Figure 7: Photographs of paleochannels preserved in the middle Obra and Sio River Valleys: The middle Obra Valley: (a) large-scale meander, (b) oblique aerial photo (taken during an aerial survey on 1 April 2010) showing set of former anharaching channels. They are marked by yellow arrows. The survey was taken in a period of high water levels when the former channels are inundated. The Sio Valley: (c) large-scale meander, (d) anharaching channel, (e) small-scale meander.
(Malvern Inc., Malvern, United Kingdom) particle size analyzer (PSA) at the Szentagothai Research Centre, University of Pecs. In the present study, the grain-size distributions were used to determine the median grain-size \(D_{xy}\) (Table 1) to plot this parameter with the values of stream power. The median grain-size was calculated using GRADISTAT 4.0 software ([PERSON], 2001). The valley slopes were estimated based on topographical maps and using \"show elevation profile\" and \"distance measurement\" tools available in Google Earth. The slopes were measured in valley sections with traces of the former channels.
Age estimation of paleochannel sediments in the middle Obra and Sio Valleys were published by [PERSON] (2014 - the Obra Valley), [PERSON], [PERSON] (2020 - the Obra Valley), and [PERSON] et al. (2021 - the Sio Valley). Accelerator mass spectrometry (AMS) radiocarbon dating (\(n=32\)) was carried out by Poznari Radiocarbon Laboratory (\(n=29\)) and Gliwice Radiocarbon Laboratory (\(n=3\)). Optically stimulated luminescence (OSL; \(n=18\)) age determinations were done by the OSL laboratory in the Department of Physical Geography and Geoinformatics of the University of Szeged (Table 2). They allowed for determining the age of channel planforms identified in both areas. The age of the former channel, and the depths of dated sediments, were used to estimate aggradation rates for the middle Obra and Sio Valleys (Table 2).
Sediment dating provided the time scale of the preservation of the fluvial sedimentary record. All the samples used for AMS radiocarbon analyses were collected from apexes of paleomeanders. These channel sections provided relatively stable depositional conditions compared to limbs of paleomeanders filled by plug bars often reworked in periods of high flows (cf. [PERSON] et al., 2012). A stable deposition in meander apexes usually commences in an oxbow lake (marked by deposition of gyttjas) and is often followed by peatland formation (marked by deposition of peats). Information preserved within such sediments allows for detailed reconstructions of paleoenvironmental changes (e.g., [PERSON] et al., 2018). Moreover, our interpretations are based on extensive sets of radiocarbon data collected in the middle Obra and Sio Valleys, complemented in the Sio Valley by OSL dating.
The values of bankfull paleochscharges (Tables S3 and S4) were published in studies of [PERSON] (2018), [PERSON], [PERSON] and [PERSON] (2020), and [PERSON] et al. (2021) to determine the changes in the magnitude of flows in the identified channel planforms. In the present study, they were used to determine the values of stream power for particular generations of paleochannels identified in the Obra and Sio Valleys. The paleochscharges were estimated using the velocity-area method and [PERSON]'s formula ([PERSON], 1985) to determine the flow conveyed by the identified generations of paleochannels (Tables S3 and S4):
\[Q_{b}=vA_{b} \tag{3}\]
\[v=R^{2/3}S^{1/2}n^{-1} \tag{4}\]
where: \(Q_{b}-\) bankfull discharge (m\({}^{3}\)s\({}^{-1}\)), \(v-\) mean velocity (m s\({}^{-1}\)), \(A_{b}-\) cross-sectional area (m\({}^{2}\)), R - hydraulic radius (m), S - channel slope, n - [PERSON]'s hydraulic roughness coefficient.
The values of the hydraulic radii were calculated using the formula:
\[R=A_{b}/P \tag{5}\]
where P is the wetted perimeter.
GPR images offer the possibility to image outlines of former channels in the Obra and Sio Valleys. The cross-sectional areas and wetted perimeters were calculated using GPR images shown in Slowik (2014), and Slowik, Galka and Marciniak (2020). The imaging of the channels' shapes was possible owing to the difference in dielectric properties of peats and gyttjas filling the paleochannels, and mineral sediments forming their bottoms. In channels filled with mineral sediments the outline of the channel is often marked by a distinct reflection, produced by the difference between the grain-size of channel fill and bed sediments. When the reflections marking the bottom parts of channels were weak, data from boreholes and coring helped identify the interface between channel fill and river bed deposits. Wetted perimeters were measured manually on the GPR images using the identified channel outlines. Next, a mesh of rectangles was placed on the GPR images to determine the cross-sectional areas. Each rectangle corresponded to 2.0 m\({}^{2}\). Paleochannels >100 m wide were covered with 5.0 m\({}^{2}\) rectangles. In the near-bed zone, where the rectangles were incomplete, surfaces of triangles and trapezoids were calculated to obtain a complete surface of a cross-section (see example in Figure S1). In cases when a former channel was
situated lower than the adjacent point bar, its cross-sectional area was determined in reference to the upper part of the point bar to estimate the values corresponding to bankfull conditions.
#### 4.1.1 Estimations of Manning's \(n\) Coefficient
Manning's \(n\) coefficients were estimated for the middle Obra Valley by [PERSON], [PERSON] and [PERSON] (2020), and for the Si\(\delta\) Valley by [PERSON] et al. (2021), based on tables provided by [PERSON] and [PERSON] (1989). The aim was to estimate bankfull paleodischarge conveyed by the types of channel planforms identified in both valleys.
#### 4.1.2 Estimations of Manning's \(n\) Coefficient
Manning's \(n\) coefficients were estimated for the middle Obra Valley by [PERSON], [PERSON] and [PERSON] (2020), and for the Si\(\delta\) Valley by [PERSON] et al. (2021), based on tables provided by [PERSON] and [PERSON] (1989). The aim was to estimate bankfull paleodischarge conveyed by the types of channel planforms identified in both valleys.
\begin{table}
\begin{tabular}{c c c c c c c c c} Sample name/depth & & & & & & & & & & \\ (cm) & Sediment & Material & Nr. Lab. & C14 date & Age (cal yr & rate (mm) \\ MED 8 273–277 & Gytja & Betula sect. albae fruits and fruits scales, charcoal & Poz-111366 & 9,810 \(\pm\) 50 BP & 11,317–11,166 & 0.24 \\ & & & pieces, Pinus sybestris needles & & & & & \\ MED 8 193–197 & Gytja & charcoal pieces, bud scales & Poz-111224 & 7,890 \(\pm\) 40 BP & 8,975–8,590 & 0.24 \\ MED 8 153–161 & Gytja & Rannuculus scaleratus fruits, Utica dioica & Poz-111368 & 6,510 \(\pm\) 40 BP & 7,495–7,323 & 0.21 \\ & & fruits:cj,\(>\)6 jc charcoal pieces & & & & & \\ MED 33 68–73 & Silt & Scheonooplectus lacustruits fruits & Poz-111369 & 1,025 \(\pm\) 30 BP & 1,025–804 & 0.71 \\ MED 33/1 60–65 & Silt & Oearathe aquatic fruits & Poz-111370 & 1,125 \(\pm\) 30 BP & 1,173–959 & 0.55 \\ MED 35 314–320 & Gytja & Lycypous europaeus fruits, Taraxacum sp. seed, & Poz-111372 & 8,740 \(\pm\) 50 BP & 9,903–9,555 & 0.32 \\ & & bud scales & & & & & \\ MED 35 260–266 & Gytja & charcoal pieces, bud scales, Rannuculus sceleratus & Poz-111373 & 8,120 \(\pm\) 50 BP & 9,262–9,891 & 0.26 \\ & & fruits & & & & & \\ MED 54 105–111 & Gytja & Scheonooplectus lacustruits fruits, Rannuculus sp. & Poz-111374 & 1,045 \(\pm\) 30 BP & 1,050–921 & 1.00 \\ & & fruit & & & & & \\ MED 54/1 72–76 & Peat & Scheonooplectus lacustruits fruits, Rannuculus sp. & Poz-111375 & 995 \(\pm\) 30 BP & 964–798 & 0.78 \\ & & fruit, Alsima sp. – fruit & & & & & \\ \hline \multicolumn{2}{l}{SiO valley – OSL dates} & & & & & & & \\ \multicolumn{2}{l}{Sample name/depth} & \multicolumn{1}{c}{Water} & Age & & & & & & \\ (cm) & Nr. Lab. & content (\%) & model & U (ppm) & Th (ppm) & K (\%) & D* (Gy/ka) & De (Gy) & Age & rate (mmy\({}^{-1}\)) \\ \hline MED23/80 & OSZ 1753 & 19 & MAM & 1.85 \(\pm\) 0.02 & 5.34 \(\pm\) 0.09 & 0.92 \(\pm\) 0.04 & 1.6 \(\pm\) 0.11 & 3.1 \(\pm\) 0.23 & 1,940 \(\pm\) 20 & 0.41 \\ MED25/70 & OSZ 1754 & 22 & CAM & 2.23 \(\pm\) 0.03 & 6.47
Hydraulic roughness coefficient describes the frictional resistance exerted by the bed and banks of natural rivers on flow. Elements influencing its values were characterized by [PERSON] (1959 in: [PERSON], 2000):
\[n=(n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{7}+n_{8}+n_{9})\,m \tag{6}\]
where \(n_{f}\) refers to surface roughness caused by the grain-size of sediments at the bottom of the river bed, \(n_{2}\) represents the influence of vegetation on flow conditions, \(n_{3}\) describes channel irregularity caused by bedforms, \(n_{4}\) refers to channel alignment (generated by differences of the river banks from the straight line), \(n_{5}\) is the effect of obstructions (logs, stumps, dams, bridges, etc.). Elements \(n_{6}\)=\(n_{9}\) characterize silting and scouring, stage and discharge, sediment load, and seasonal changes, respectively. Element \"\(m\)\" is a correction factor for channel meandering.
Owing to the intervals in particular n-elements (see [PERSON] & [PERSON], 1989), three discharge values (minimum, average, and maximum discharge) were estimated for particular types of former channels, identified in the middle Obra and Sio Valleys (Tables S3 and S4). The average paleodischarge values were then used to calculate potential specific stream power in the middle Obra and Sio Rivers.
Element n\({}_{1}\) was determined based on the grain-size of sediment samples collected from the bottom of paleochannels. The effect of vegetation (n\({}_{2}\)) was estimated as \"small\" for paleochannels active in the Late Glacial in both valleys, and \"medium\" for anabranching and meandering channels active in the Holocene. Channel irregularity caused by bedforms (n\({}_{3}\)) was determined as \"minor\" for meandering and sunuous channels owing to small or no traces of bedforms and eroding and reworking of the channels identified in the GPR images. The exception was anabranching and crevasse channels owing to the presence of bed forms and erosional surfaces. Channel alignment (n\({}_{4}\)) was negligible or small as variations in channels widths were gradual or large and small cross-section alternated occasionally. This element was inferred from aerial images (source: Google Earth), in which traces of former channel planforms could be identified. The effect of obstructions (n\({}_{3}\)) was defined as negligible, for example, in meanders from the Late Glacial. It was classified as appreciable the case of anabranching channels in the middle Obra Valley because traces of buried objects (possibly logs) were identified in the GPR images. In the case of crevasse channels, the effect was \"severe\" as traces of a dam impeding the flow were spotted on the land surface. Element'm' was defined based on the values of sinuosity.
The roughness coefficients in the middle Obra and Sio Valleys are comparable for the large-scale meanders (see Table S3). In the case of anabranching channels - those evolving in the middle Obra Valley are characterized by higher values of Manning's \(n\) coefficient owing to a higher value of n\({}_{3}\) (effect of obstructions - more buried objects in the channel fills, possibly tree logs) compared to the Sio Valley (Table S3). Small-scale meanders have higher roughness in the Sio Valley compared to the middle Obra owing to a higher channel irregularity (numerous erosional surfaces appearing in the channel fills (cf. [PERSON] et al., 2021).
#### 4.1.2 Standard Errors of Estimations
The estimations of potential specific stream power bear uncertainties delivered by errors in calculations of paleodischarges, Manning's roughness coefficients, and mean velocities (see Equations 1-4). To estimate these uncertainties for the middle Obra and Sio Valleys, we have calculated standard errors for these variables (see Table S4). They were estimated using the formula:
\[\mathrm{SE}=\mathrm{SD}/\sqrt{n} \tag{7}\]
where, \(\mathrm{SE}\) - standard error, \(\mathrm{SD}\) - standard deviation, and \(n\) - number of samples. Standard deviation was determined using the formula:
\[\mathrm{SD}=\sqrt{\Sigma}(\chi_{i}-\mu)^{2}/n-1 \tag{8}\]
where, \(\chi_{i}\) is each value for population, and \(\mu\) is the mean for the population. The samples used for the estimations of standard error and standard deviation originate from multiple locations representing similar types of former channel planforms, active in a similar period (Table S4).
The highest errors refer to the highest volumes of paleodischarge conveyed by large-scale meanders in the middle Obra and Sio Valleys. They reach 25 for the average discharge of 108 m\({}^{3}\) s\({}^{-1}\) (the middle Obra River), and 88 for 335 m\({}^{3}\) s\({}^{-1}\) (the Sio River). This means that the estimated values of the paleodischarge vary between 247 and 423 m\({}^{3}\) s\({}^{-1}\) (335 m\({}^{3}\) s\({}^{-1}\pm 88\)). The error covers 52% of the average value of the paleodischarge. For relatively small discharge values conveyed by small-scale meanders (e.g., 13 m\({}^{3}\) s\({}^{-1}\)) the standard error amounts to 2. Here the error (13 m\({}^{3}\)s\({}^{-1}\pm 2\)) amounts to 39% of the estimated discharge value. In general, the higher the values and range of the variables, the higher the value of the standard errors. This shows that the estimated stream power can be treated as approximate owing to the high standard errors. Therefore, the observed trends in stream power changes were supported with plots of the age of former channels and valley width/channel belt width ratios.
### Width and Thickness of Channel Fills
The width and thickness of large-scale meanders preserved in the middle Obra Valley are 70-80 and 4 m, respectively (Figure 8a, Table 1). The anabranching channels formed within a former subglacial tunnel, have widths
Figure 8: Width, thickness and types of channel planforms identified in the middle Obra (a) and São Valley (b) plotted on diagrams proposed by [PERSON] (2006). The widths and thickness of the channels were measured in the GPR images carried out by [PERSON] (2013, 2014), [PERSON], [PERSON] (2020), and [PERSON] et al. (2021). Aerial images (source: Google Earth) were an additional source to determine the channel widths.
and depths of 120 and 5 m, respectively. The anbranching and sinuous channels, formed after the transition from large-scale bends in the middle Obra Valley, are 50-70 m wide and 2.5-3.0 m thick (Figure 8a). The width of the channel fills in the Si\(\circ\) valley decrease from large-scale meanders (100-120 m), through anbranching channels (60-90 m) to small-scale bends (15-40 m; Figure 8b). A decrease in the channel thickness can also be noted (Figure 8b).
### Stream Power of Channel Planforms Preserved in the Fluvial Record
Large-scale meanders and part of sinuous channels in the middle Obra Valley were characterized by specific stream power of 2.0-3.0 W m\({}^{-2}\) (Figure 9a). When plotted with median grain-size, the channels belonged to
Figure 9: Potential specific stream power and median grain-size of paleochannels preserved in the middle Obra (a) and Si\(\circ\) Valley (b) plotted in a diagram discriminating channel planforms and types of sediment transport proposed by [PERSON] and [PERSON] (2011). The values of stream power were estimated using bankfull padischcharge estimated by [PERSON], [PERSON] (2020), and [PERSON] et al. (2021) (see Table 1). The valley slope was measured on topographic maps. The median grain-size was calculated using GRADISTAT 4.0 software ([PERSON], 2001). The input data were grain-size distributions obtained from analyses conducted at the Szentägorothai Research Centre, University of Pécs.
meandering rivers with scrolls and chutes (Figure 9a). All the anabranching channels were classified as \"laterally immobile, no bars.\" Specific stream power of 7.0-8.0 W m\({}^{-2}\) describes large-scale meanders in the Sio Valley (Figure 9b). The stream power of anabranching channels and small-scale meanders amounts to 1.0-3.0 W m\({}^{-2}\). The multi-channel planform, and part of the small-scale bends belong to the zone \"meandering with scrolls and chutes\" (Figure 9b; cf. [PERSON], 2011). Both middle Obra and Sio Rivers are dominated by a suspended load (Figure 9). The grain size of the Sio sediments is an order of magnitude finer (between 0.00001 and 0.0001 m - from sils to very fine sands) than sediments forming the Obra alluvial fill (0.0001-0.001 m - from very fine sands to coarse sands; see Figure 9). The exception is small-scale bends in the Sio Valley that, owing to bed incision reworked coarser deposits present in the valley floor (cf. [PERSON] et al., 2021).
Changes in Stream Power, Channel Belt Width, and Planform Evolution of the Middle Obra and Sio Rivers
A decrease of stream power from 2.0 to 3.0 W m\({}^{-2}\) to 0.1-0.8 W m\({}^{-2}\) accompanied the transition from large-scale meanders to anabranching and sinuous channels in the middle Obra Valley between 13,300 and 11,200 cal. yr BP ([PERSON], [PERSON], 2020). Valley width/channel belt width ratio increased from 7.0 to 9.0 to 25.0 in that period (Figure 10c). The anabranching channels were active between \(\sim\)11,000 cal. yr BP and the nineteenth century. Aggridation rates amounted to 0.1-0.2 mm y\({}^{-1}\) (with a maximum of 0.8 mm y\({}^{-1}\)) between 11,000 and 4,000 cal. yr BP (Figure 10c). In this period, the valley width/channel belt width ratio ranged from 22.5 to 25.0 (see Table 1). A temporary increase in stream power to 2.0 W m\({}^{-2}\) occurred \(\sim\)3,800 cal. yr BP. Aggridation rates increased to 0.3-0.8 mm y\({}^{-1}\). Valley width/channel belt width ratio remained constant at that time (\(\sim\)22.0; Figure 10c).
The transition from large-scale meanders to anabranching planform in the Sio Valley \(\sim\)18,000 cal. yr BP was accompanied by the decrease in specific stream power from 7 to 8 W m\({}^{-2}\) to 1.0-3.0 W m\({}^{-2}\) (Figures 10b and 10c). Valley width/channel belt width ratio amounted to 1.0 when the large-scale bends were active and increased to 1.5-1.8 after the transition to the multi-channel planform. Aggradration rates increased from 0.1 mm y\({}^{-1}\) to 0.1-0.3 (maximum 0.7) mm y\({}^{-1}\) (Figure 10c). The change of channel planform from the anabranching channels to small-scale meanders took place \(\sim\)12,700 cal. yr BP and was accompanied by sustaining potential specific stream power of 1.0-3.0 W m\({}^{-2}\) (Figure 10c). The stream power was sustained; however, the transition was accompanied by the reduction of bankfull flows to 6.0-12.0 m\({}^{3}\) s\({}^{-1}\) (Table 54 and [PERSON] et al., 2021), a decrease in channel width (Figure 8b), and an increase in valley width/channel belt width ratio to 7.9-8.1 (Figure 10b). The small-scale meanders incised. Aggridation rates amounted to 0.1-0.3 mm y\({}^{-1}\) between 12,000 and 6,000 cal. yr BP (Figure 10c), and increased to 1.0-4.0 mm y\({}^{-1}\) during the last \(\sim\)2,000 cal. yr BP.
## 5 Discussion
### Conditions to Preserve Channel Planform Record in the Obra and Sio Valleys
The sedimentary record of channel planforms preserved in the middle Obra and Sio Rivers confirms the hypothesis that a decrease in potential specific stream power followed by sustained low stream power, and successive decrease of channel belt width results in maintaining the sedimentary record of channel planforms over 10\({}^{3}\) to 10\({}^{4}\)-year time scales. In the Sio Valley, the planform change is accompanied by the decrease in stream power, increased aggradation (Figure 10c), successive decrease of the width and depth of the channels (Figure 9b), and decrease in width of channel bells (Figure 10c). These trends are not so clear in the middle Obra Valley (Figure 8a). This is because large-scale meanders did not rework the whole Obra valley floor. The river flows through the Warsaw-Berlin proglacial stream valley, formed by the activity of glacial meltwater flowers. Part of the channels (i.e., anabranching channels in the bifurcation to the Warta River; [PERSON], [PERSON], & [PERSON], 2020) evolved within larger channel forms inherited from glacial meltwater flows across outwash plains and former subglacial tunnels. A decrease of flows and stream power caused sedimentary structures, that is, fragments of point bars, sets of small bedforms, and smaller-scale channels have been preserved within the 120-m wide channels formed by the meltwater flows (see Figure 4 and II in [PERSON], [PERSON] & [PERSON], 2020). Compared to the Sio Valley, the relatively high values of valley width/channel belt width ratio for the Obra large-scale meanders (\(\sim\)7.0-9.0) show that a significant part of the valley fill contains the fluvialogical record left by meltwater of the last Inland Ice or is occupied by glacial and aeolian landforms (see Figure 5).
Figure 10:
The change from large-scale meanders to anabranching and sinuous planforms in Obra Valley is reflected by the change in fluvial architecture - from multi-storey, represented by fills of the large-scale meanders, to erosion and succession dominated in the cases of the anabranching channels (cf. [PERSON], 2006; see e.g., Figures 4 and 5 in [PERSON], 2013, and Figures 4 and 5 in [PERSON], [PERSON] & [PERSON], 2020). The planform transition was caused by the lowering of the base level, and a period of increased floods (Figure 10d). The anabranching and sinuous channels in the middle Obra Valley, and anabranching channels and small-scale meanders in the SiO Valley, are situated close to the border between meandering rivers and delta distributaries marked by [PERSON] (2006) (see Figure 8). This is consistent with the important role of avulsions, bifurcations and meander cutoffs in the evolution of both rivers.
Figure 11.— Vertical changes in stream power and channel belt width in fluvial record (a) coarse sediments of high-energy braided river overlia by the record of meandering platforms, (b) coarse sediments of high-energy braided river overlia by the record of meandering planforms.
Figure 10.— (a, b) Schematic cross-sections showing types of channel planforms in the middle Obra and SiO Valleys. They were constructed based on the GPR measurements ground-truthed by sedimentary data from coring ([PERSON], [PERSON] & [PERSON], 2020; [PERSON] et al., 2021), topographic maps and aerial images (areial survey conducted on 1 April 2010, and Google Earth images). (c) Potential specific stream power, valley width/channel belt width ratio, and aggradation rate plotted with the age of paleochannels in the middle Obra and SiO Valleys, (d) Base-level changes, the occurrence of flooding/humid phases, and human impact in the middle Obra and SiO Valleys during the last 20,000 cal. BP.
The increase in stream power and sedimentation rates \(\sim\)3,800 cal. yr BP was influenced by periods of flooding ([PERSON], 2001; [PERSON] et al., 2006; see Figures 10c and 10d). The occurrence of the flooding phases was affected by the increase of precipitation and humidity in the European lowlands (e.g., [PERSON] et al., 2012, and references therein; [PERSON] et al., 2015). Moreover, traces of the presence of humans \(\sim\)7,000 cal. yr BP were found in the western part of the middle Obra Valley by [PERSON] et al. (2019). They were marked by types of pollen characteristic of open areas in the forest, species of algae indicative of trophic conditions in lakes, erosional processes in lake catchments, and charred fragments of herbaceous plants derived from marsh vegetation. First human settlements, and potential deforestation accompanied by soil erosion, appeared in the central and eastern part of the middle Obra Valley \(\sim\)2,000 cal. yr BP ([PERSON], 2013). These events could have contributed to increased runoff and sedimentation in valley floors. Along with the human-induced changes, this sedimentation was also influenced by the increase of the base level, conditioned by the rise of the Baltic Sea level ([PERSON], 2004; Figure 10d).
In the Sio Valley, the change from the large-scale meanders to anabranching channels took place during a humid phase that took place between 13,500 and 12,700 cal. yr BP, identified by [PERSON] and [PERSON] (2007) (Figure 10d). The reduction of the stream power was affected by a decrease in bankfull discharge from \(\sim\)250 m\({}^{3}\) s\({}^{-1}\), conveyed by the large-scale meanders, to \(\sim\)10-30 m\({}^{3}\) s\({}^{-1}\), conveyed by the anabranching channels (Table S4). These changes could have been affected by the rise of the local base level, caused by an intensive sedimentation in the Pannonian Basin ([PERSON] et al., 2010; [PERSON] et al., 2015; see Figure 5 for location). This sedimentation could have been interrupted by periods of incision of the Danube River ([PERSON], 1959). The situation of the anabranching channels from the Sio Valley in the \"mandering with scrolls and chutes\" zone of the diagram of [PERSON] (2011) (see Figure 9b) is in agreement with the study of [PERSON] et al. (2021) that the anabranching channels evolved through lateral migration, chute cutoffs, and formation of \"soft avulsions\" maintaining the flow in original channels after cutoff events. The situation of the anabranching channels in the middle Obra Valley (\"laterally immobile, no bars\"; Figure 9a) informs that they were less mobile than the multi-channel planform in the Sio Valley. Indeed, they have no or few traces of lateral migration compared to the Sio anabranching channels, featured with numerous traces of lateral migration, marked by layering patterns preserved in the floodplain (see Figure S2).
The small-scale meanders evolved through lateral migration and cutoffs (cf. [PERSON] et al., 2021). Their incision could have been caused by a temporary decrease of the local base-level, conditioned by the incision of the Danube River (Pecsi, 1959). This incision, in turn, could have been affected by a decrease of the Black Sea level between 12,000 and 11,000 cal. yr BP ([PERSON] et al., 2006; [PERSON] et al., 2020 - see Figure 10d). The local base level further decreased \(\sim\)5,000 cal. yr BP owing to the incision of the Danube River ([PERSON] et al., 2017). Despite this event, an increase of agradation to 1.0-4.0 mm y\({}^{-1}\) took place during the last \(\sim\)2,000 cal. yr BP and was caused by the anthropogenic influence (foreforestation, burning for pastures) that started in Transdanubia 7,000-6,500 cal. BP ([PERSON] et al., 2012; Figure 10d). The human influence was coupled with a humid period that started in central and eastern Europe about 4,000 cal. yr BP ([PERSON] et al., 2018; see also a humid phase identified by [PERSON] and [PERSON], 2007, marked in Figure 10d).
### Applications of the Results
Based on the present study, river valleys with the record of at least two generations of channel planforms, and valley width/channel belt width ratios between 6 and 12, are potential sites preserving fluvial sedimentary record over 10\({}^{3}\) to 10\({}^{4}\)-year time scales. This is supported by the observed increase of valley width/channel belt width ratios after the transitions from large-scale meanders to low-energy meandering and anabranching rivers from 1 to 2 in the Late Glacial to 6-12 in the Holocene (Figure 2a2). The observed trends are the result of the successive decrease in stream power. The decrease was caused by the termination of delivery of glacial meltwater from the last Inland Ice, the appearance of a dense vegetation cover, and \"using\" part of the available water by evapotranspiration as climate warmed (cf. [PERSON], 1991).
The proposed classification may be extended by avulsive river systems formed in coastal zones and affected by the backwater effect owing to sea-level rise (cf. [PERSON] et al., 2012). They may belong to the second of the identified groups of rivers (see Section 3.2). The examples are the anastomosing course of the lower Oda River (Poland) formed \(\sim\)7,000 cal. yr BP; [PERSON] and [PERSON], 2007), and lower Prieglius River (Lithuania). The proposed framework can also be extended by channel planform records preserved in the floodplains of large rivers. For instance, the Mississippippi Valley near New Madrid contains traces of numerous paleomeanders with traces of 16 periods of reworking earlier records and cutoffs ([PERSON] et al., 2018). The channels are fragmentary (valley width/channel belt width ratio can be close to 1.0 based on Figures 11a and 11b in [PERSON] et al., 2018), with the most complete preservation of meanders representing the stage that took place at 500 cal. yr BP. These features show that the section of the Mississippi Valley near New Madrid may belong to the group of actively migrating rivers (Section 3.3). Moreover, rivers classified to one of the identified groups may have sections that indicate a higher preservation potential than indicated by the main trajectory of channel planiform changes. For instance, the whole valley width of the South Saskatchewan River (high-energy braided rivers - Section 3.4) is occupied by braided channels near the town of Outlook. The valley section situated close to Saskatoon preserves traces of paleomeanders along the valley margins (see Figure S3). The age of the paleomeanders and the nature of changes in the preservation potential along this river course require a detailed field study.
The proposed framework of rivers has the potential to be extended by ancient fluvial records. For instance, the Early Cretaceous record of river meanders found in the McMurray Formation (Alberta, Canada; [PERSON] et al., 2018) may belong to the group of actively migrating rivers (Section 3.3) owing to traces of cutoffs, often reworking the earlier record, and preservation of a low-sinusoy channel section (see Figures 7a and 7b in [PERSON] et al., 2018). We conducted a Welch's \(t\)-test to verify whether the sinusosity of ancient channel records is distinguishable from channel belts preserved in the surface layers of the floodplains (see Tables S1 and S2). The test indicated that the difference between the sinusosity of the two groups of rivers is not statistically significant at the 95% confidence interval. This suggests that the sinusosity of ancient channel belts may not undergo significant changes in planiform shape after deposition in the floodplain sediments, if the deposits have already succeeded in being preserved at time scales of thousands to tens of thousands of years. These notions require further verification by more examples from the ancient fluvial record.
The observed changes in stream power and valley width/channel belt width ratio also refer to relations between the fluvial record preserved in the top parts of floodplains, and the underlying fluvial archives. The 10' to 10'-years record of channel planiforms often overlies depos representing the activity of high-energy braided rivers (e.g., the Kapos and Koppany River - [PERSON] & [PERSON], 2013, Figure 11a; the Narev River - [PERSON] et al., 2003; the upper Columbia River - [PERSON] et al., 2002, Figure 11b). These examples represent a vertical sedimentary record of a decrease in stream power during a transition from the braided planform to the overlying record of meanders or anastomosing channels (Figures 11a and 11b). Valley width/channel belt width ratios increased in the vertical record from 1.0 (the whole valley width occupied by the braided system) to 3.0 (large-scale meanders) in course of, for example, the Warta River, and 7.0-8.0 in the course of the middle Obra River. In all these cases the condition to preserve the underlying sedimentary record was that the successive river system (i.e., large-scale meanders or anastomosing system) was featured with lower flow energy than the underlying fluvial record (Figures 11a and 11b).
The findings of our study should be extended beyond the temperate zone. Little is known about controls on the preservation potential of dryland and tropical rivers, especially in intracratonic settings. For instance, the Cooper Creek Basin, Australia, contains traces of a suspended load-dominated anabranching planform that was active at 75,000-55,000 cal. yr BP ([PERSON] et al., 2013). The present anastomosing course (cf. [PERSON] et al., 1998) reworks only the surficial layer of the basin. Sediments filling the Amazon River basin were deposited by megafans and systems of avalive channels coming from the Andes in the Late Miocene (9.0-6.5 Ma). They were reorganized into a transcontinental fluvial basin in the early Pliocene (cf. [PERSON], 2015; [PERSON] et al., 2010). Detailed identification of the controls on the preservation over such long-time scales remains a challenge.
## 6 Conclusions
The main goal of our study was to identify a set of conditions that influence the preservation of channel planform records in the surface and subsurface of river floodplains prior to the maintenance of rock record. We tested a hypothesis that a successive decrease of stream power, accompanied by the increase of valley width/channel belt width ratio, favors the preservation of the sedimentary record of channel planforms over 10\({}^{3}\) to 10\({}^{4}\)-year time scales. Our study is based on a literature review conducted in reference to temperate rivers of the Northern Hemisphere. We collected data regarding paleodischarge, width, and thickness of paleochannels, grain-size, valley widths, channel belt widths, and age of paleochannels preserved in the valley floors. These data were used to estimate specific stream power for generations of paleochannels preserved in the river floodplains.
We developed a framework consisting of four groups of rivers with preservation potentials varying from thousands and tens of thousands years to annual time scales. We found that a decrease of stream power followed by a low stream power, accompanied by a decrease of channel belt widths in successive generations of channel planforms favored the preservation of channel planform records over 10\({}^{3}\) to 10\({}^{4}\) kg time scales. Our study shows that river valleys characterized by valley width/channel belt width ratios between 6 and 12, and traces of channels representing at least two generations of channel planforms, are potential areas containing the preservation of channel planform sedimentary record in thousands to tens of thousands year time scales. Low and moderate energy (0.5-45.0 W m\({}^{-2}\)), meandering and anastomosing rivers with constant channel belt widths preserve the sedimentary record of channel planforms from the last 4,000-7,000 years. They are characterized by periods of increased stream power, contributing to the formation of availusions. Aggrading conditions lead to the preservation of vertically stacked channel fills. Moderate and high energy (30-170 W m\({}^{-2}\)) meandering and anabranching rivers and high-energy (60-700 W m\({}^{-2}\)) braided rivers preserve traces of former channels in centennial and annual to decadal time scales, respectively.
We analyzed in detail the conditions that led to the preservation of 10\({}^{4}\)-year fluvial records of channel planforms using examples of unusually well-preserved paleochannels from the middle Obra River (western Poland) and SiO River (southern Hungary). They represent a sedimentary record of channel planforms reaching back to the Late Glacial and Late Pleniglacial, respectively. Specific stream power decreased from 2.0 to 3.0 W m\({}^{-2}\)-13,000 cal. yr BP to \(<\)1.0 W m\({}^{-2}\) between 11,000 and 4,000 cal. yr BP in the Obra Valley. A decrease from 7.0 to 8.0 W m\({}^{-2}\)-18,000 BP to 1.0-3.5 W m\({}^{-2}\) between 13,000 and 1,000 cal. yr BP took place in the SiO Valley. The decrease was caused by the reduced magnitude of flows, development of vegetation cover, and increase in evapotranspiration in the early and middle Holocene. The maintained low stream power went along with the sustained level of aggradation rates, caused by sediment delivery from morning uplands and loses hills, and successive increase of the base-level, conditioned by the Baltic and the Black Sea levels. The aggradation increased during the last 2,000-3,000 cal. yr BP both in the Obra and SiO Valley owing to increased human impact and climate humidity.
The proposed framework can be extended by examples of paleochannels preserved in floodplains of large rivers, and coastal river valleys. Channel planforms preserved in ancient rock records also may be included in the framework, providing further research on how their geometry is altered by post-depositional processes (i.e., compaction). Extending our results concerning rivers evolving in other geomorphic zones would allow for the identification of controls on preservation of fluvial records in multi-millennial time scales.
## Data Availability Statement
All data sets from this research are available from the ZENODO repository, [[https://doi.org/10.5281/zenodo.6104451](https://doi.org/10.5281/zenodo.6104451)]([https://doi.org/10.5281/zenodo.6104451](https://doi.org/10.5281/zenodo.6104451)). Part of the data, regarding estimations of hydraulic roughness coefficients and paleodischarges, is available in Slowik (2013), [PERSON] et al. (2020) and [PERSON] et al. (2021).
## Supporting Information
Tables S1-S4 can be found in supplementary material [[https://doi.org/10.5281/zenodo.6104451](https://doi.org/10.5281/zenodo.6104451)]([https://doi.org/10.5281/zenodo.6104451](https://doi.org/10.5281/zenodo.6104451))
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wiley/fea5b82e_a24b_4437_bf73_889aa8931d29.md | # Scale effects of topographic ruggedness on precipitation over Qinghai-Tibet Plateau
[PERSON]
1 State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Sciences, Beijing, China 12 Jiangu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, China 201919202019201920192019201920192019201920192019201920201920192020192020192020192020192020192020192020192020192
precipitation through statistical downscaling ([PERSON] _et al._, 2013; [PERSON] and [PERSON], 2014; [PERSON] _et al._, 2016; [PERSON] _et al._, 2016) and numerical model simulation ([PERSON] _et al._, 2003; [PERSON] _et al._, 2006; [PERSON] _et al._, 2008; [PERSON] _et al._, 2014; [PERSON] _et al._, 2016; [PERSON] _et al._, 2018). It is noted that the use of topographical information compensates for the interpolation method to improve the estimation of the extreme rainfall ([PERSON], 1999) and enhances the activities of mesoscale disturbances in the model simulations ([PERSON] _et al._, 2008).
Within those previous studies, scale is important in any precipitation-TR analysis, because TR is usually characterized by index calculated from Digital Elevation Model (DEM), therefore, is naturally scale-dependent. Problems of scale can lead to significant errors for the precipitation estimation because of local differences in TR and elevation ([PERSON], 1984). [PERSON] _et al._ (2016) identified that the appropriate scale at which topographical obstacles impact precipitation is crucial to obtain reliable precipitation distribution. Therefore, it should be considered carefully what scale is most relevant for the phenomenon being analyzed. However, such analyses have not been reported for the precipitation-TR relationship in the Qinghai-Tibet Plateau.
Using quantile regression ([PERSON] and [PERSON], 1978), the appropriate scales for analyzing the relation between precipitation and TR in the Qinghai-Tibet Plateau is investigated in this study based on surface observations of precipitation for 1997-2016. According to observation evidences, the quantile regression method has been applied for investigating mechanisms underlying the increasing intensity of tropical cyclones ([PERSON] _et al._, 2008) and proving the soil-moisture impact on hot extremes ([PERSON] _et al._, 2011). Since precipitation over the Qinghai-Tibet Plateau is variable in summer and winter, high or low precipitation amounts may have distinct relationships with the TR changes. Quantile regression can account for all parts of the precipitation data distribution, and therefore is an appropriate means to investigate the response of precipitation quantiles to the TR changes at different spatial scales.
## 2 Data and methods
### Data
For precipitation measurements, the daily precipitation in a calendar month at each of the 72 meteorological stations located across the Qinhai-Tibet Plateau, are accumulated to obtain the monthly precipitation for the years 1997-2016 (20 years). The monthly precipitation from December, January and February (DJF) are averaged for winter season, and those from June, July and August (JJA) are averaged for summer season. All the stations provide full records without missing values. The geographic locations of these stations with altitude ranging from 1,800 to 8,500 m are illustrated in Figure 1.
The surface elevation is available from the DEM of Shuttle Radar Topography Mission (SRTM), with resolution of three-arc-second (-90 m). The vertical error of the SRTM data is reported to be less than 16 m and the horizontal error less than 20 m ([PERSON] _et al._, 2008). The SRTM data is used to calculate the TR for each grid cell, with the spatial scales changed.
### Methods
The TR metric used in this study is the topographic position index that measures the relative topographic position of the central cell within a specified neighborhood ([PERSON], 2000; [PERSON], 2006). The TR is calculated as follows:
\[\text{TR}=\frac{\text{focalmean}(M)-\text{focalmin}(M)}{\text{focalmax}(M)- \text{focalmin}(M)}, \tag{1}\]
where \(M\) is the matrix of the specified neighborhood. Figure 2 shows the detailed flowchart for the TR calculation. Note that focalmean in Equation (1) actually plays a role to create a smoothed DEM, because smoothing the DEM often
Figure 1: Spatial pattern of surface elevation and topographic rauggedness (scale of 1 km) for the Qinghai-Tibet Plateau.
Superimposed are the mean precipitation of winter (DJF) and summer (JJA) for 1997–2016 produces a more spatially coherent and interpretable roughness raster, which would reduce the within system noise as proposed in [PERSON] _et al._ (2016).
This index is useful for identifying terrain undulation that may correspond with a peak or pit topography and dominant geomorphic process ([PERSON] _et al._, 2013). Scale of TR is changed as the neighborhood varies. For example, 11 cells of \(M\) (including 10 neighborhood cells and 1 central cell) correspond to approximately 1 km TR scale with 90 m resolution of SRTM DEM data. Figure 1 shows the TR for the Qinghai-Tibet Plateau, with a scale of 1 km. Large TR values indicate the severe undulating (rugged) topography.
Quantile regression is used to explore the relationship between TR and seasonal precipitation over the Qinghai-Tibet Plateau. As an extension to the ordinary least square regression, it assumes that a quantile of the response variable \(Y\) (precipitation) is conditional on \(X\) (TR). For each quantile \(\tau\in[0,\,1]\), the linear quantile regression can be written as ([PERSON] and [PERSON], 1978):
\[Q_{\tau}[Y|X]= f(\beta_{\tau}\gamma_{\tau})(X), \tag{2}\]
where \(\beta_{\tau}\) is the slope and \(\gamma_{\tau}\) the intercept, which can be obtained by minimizing the sum of the asymmetrically weighted absolute residuals.
Quantile regression is able to estimate the response not only in the mean of a variable, but also in all parts of the data distribution. Therefore, the change in precipitation quantile can be estimated as a function of TR. A selection of distinct quantiles (i.e., 0.1, 0.3, median [0.5], 0.7 and 0.9) with their regression lines are employed here to show the changes in precipitation with TR. A quantile is a point taken from the inverse cumulative distribution function of the set of seasonal precipitation. So, the 0.9 quantile is the value such that 90% of the precipitation is below this value. For comparison, the regression line for the least squares fitting is also added (black line in Figure 3).
## 3 Results
Figure 1 shows the station-measured mean precipitation of winter (DJF) and summer (JJA) from 1997 to 2016 for the Qinghai-Tibet Plateau. Moisture inflow can reach the region via the Arabian Sea, the Bay of Bengal and the mid-latitude westerlies ([PERSON] _et al._, 2011). Precipitation is relatively abundant in summer (wet season) as the large circulations of Indian and East Asia monsoons transport a vast amount of water vapor to the south and east Qinghai-Tibet Plateau ([PERSON] _et al._, 2014; [PERSON] _et al._, 2015). Indian Ocean is the dominant source region of water vapor and precipitation over the southern Tibet in summer ([PERSON] _et al._, 2018), and the local surface evaporation has a non-negligible effect on the summer precipitation ([PERSON] _et al._, 2017). The mean summer precipitation for 1997-2016 can be up to over 120 mm for the stations in the southern Tibet. Northern Qinghai-Tibet Plateau is relatively dry with much less precipitation in both summer and winter. The standard deviation of the seasonal precipitation shows very similar patterns.
Figure 3a,f show scatter plots of summer and winter data of precipitation from the station observations over the Qinghai-Tibet Plateau versus TR at the scale of 1, 10, and 100 km, respectively. It can be seen that the precipitation-TR relations are different for summer and winter. For winter precipitation (Figure 3b,d), a widening of the precipitation data distributions with more rugged terrain is evidently revealed. This is also apparent in the gradually increasing positive slopes of the quantile regression lines towards higher precipitation quantiles. However, when TR derived from the large spatial scale of 100 km, the features of increasing slope for high precipitation quantile disappeared (Figure 3f), implying that topographic effects on high winter precipitation cannot be revealed for the TR of large scale.
For summer precipitation, high precipitation amounts (0.9 quantile) do not vary as the TR value changes at the scale of 1 and 100 km (Figure 3a,e). While at the scale of 10 km (Figure 3c), the effects of topography emerge, with the pattern of increasing precipitation associated with more rugged terrain for all the quantiles. It is argued that approximately 50% of summer rainfall is maintained by \"up-and-over\" moisture transport lifted by convective storms over central-eastern India and swept over by the mid-tropospheric
Figure 2: Flowchart of topographic ruggedness calculation and quantile regression analysis
circulation, rather than by upslope flow over the Himalayas ([PERSON] _et al._, 2016). In this condition, the effects of topography on precipitation at small scales would be covered up by the large circulation of water vapor mechanisms.
To investigate this relationship further and to identify how precipitation are affected by the TR at different scales as a function of the precipitation-TR regime, the quantile regression slopes of 0.9 and 0.5 for the TR at different scales are shown in Figure 4 for summer and winter, respectively. The 95% confidence intervals of the estimated slopes are shown in shading.
For the relationship between summer precipitation and TR scales (Figure 4a), regression slopes of the 0.9 quantile are almost 0 for the small TR scales (<1 km), indicating that no precipitation-TR relations for the high precipitation are found when TR scales are small. The high precipitation amounts begin to increase 10 mm along with the changes in TR at the scale of 5 km. Thereafter, the slopes vary with the increase in TR scales and drop close to 0 when the TR scale reaches to 100 km. At every scale, it seems that topography influences the median precipitation quantile more than the high precipitation quantile.
For the winter precipitation (Figure 4b), the variations of TR scales almost have no impacts on the median precipitation quantile. On the contrary, the slopes of the high precipitation quantile are relatively steady even if the TR scale is small (e.g., 250 m), and then the obvious precipitation-TR slopes suddenly drop down at the TR scale of 40 km. So, the scale larger than 30 km would not reflect the winter precipitation mechanisms related to topographic variation over the Qinghai-Tibet Plateau. The analysis proves that to investigate the precipitation-TR mechanisms over the Qinghai-Tibet Plateau (e.g., using the climate model), neither too large (e.g., more than 100 km) or too small (e.g., less than 1 km) scales are suitable for exploring the summer precipitation, and the scales would be much better less than 30 km for winter precipitation.
## 4 Discussion
The advantage of quantile regression method here is to diagnose the linear responses of all parts of precipitation amounts to the TR changes, and demonstrate that the precipitation-TR relations indeed vary at different spatial scales. Using advanced methods that developed for the modeling and estimation of nonlinear conditional quantile functions would help analyze nonlinear processes in the precipitation-TR relations.
Figure 4 indicates that the precipitation-TR relations for summer and winter are different as the spatial scales change. The spatial distribution of precipitation resulting from distinct seasonal large-scale circulations may be the major cause. It is suggested that the Indian Ocean is the dominant source region to summer precipitation over the Qinghai-Tibet Plateau through monsoons transport ([PERSON] _et al._, 2013), with a contribution of approximately 30% ([PERSON] _et al._, 2018). Meanwhile, local surface evaporation supplies a substantial component, account for approximately 18% ([PERSON] _et al._, 2017). Most Qinghai-Tibet Plateau areas receive more than 80% of their annual rainfall during summer ([PERSON] and [PERSON], 2010). Therefore, the appropriate spatial scale for the precipitation-TR relations in summer can reach to 100 km. Precipitation distribution during the winter season primarily indicates large-scale patterns due to the westerly circulation ([PERSON] _et al._, 2009; [PERSON] _et al._, 2017). In winter, the westerly circulation transports moisture to the western Tibet, and is disturbed by the high mountains ([PERSON] _et al._, 2015), leading to the precipitation and large precipitation events mainly around the Karakoram and Pamir regions ([PERSON] _et al._, 2014). Thus, the largest spatial scale for the precipitation-TR relations in winter (30 km) is less than summer.
Interestingly, the spatial distribution of seasonal precipitation gives a hint for the selection of appropriate spatial scales. Therefore, the analysis of precipitation-TR relations can be improved by using gridded precipitation data. The great advantage is that the analysis is able to be extended to the vast areas where there are no ground measurements available. However, it is currently limited by accuracy and resolution of the precipitation products. Previous studies evaluate four precipitation products over the Qinghai-Tibet Plateau: TMPA(3B42), TMPART, CMOPRH and PERSIANN ([PERSON] and [PERSON], 2013; [PERSON] _et al._, 2014). They showed that the precipitation products generally tend to overestimate light rainfall (0-10 mm) and underestimate moderate and heavy rainfall (>10 mm), and the correlation coefficients are less than.5 over arid regions. Large errors in these data may affect the exploration of the intrinsic relation between different precipitation quantiles and topographic effects. Moreover, the spatial resolution of these precipitation products is \(0.25^{\circ}\times 0.25^{\circ}\) (i.e., roughly 25 km). Using these gridded data will lead to the lack of analysis for the spatial scales less than 25 km.
The precipitation-TR relationship explored in this study can also be applied to statistical downscaling of precipitation, which remains a challenge in environmental studies. For example, downscaling summer precipitation for the Qinghai-Tibet Plateau at the spatial resolution larger than 1 km would provide valid information that is related to topographic variation. On the contrary, the appropriate spatial resolution should be less than 30 km for downscaling winter precipitation for the Qinghai-Tibet Plateau. It is not the finer resolution but the better. The reason behind is that statistical
Figure 4: Quantile regression slopes of the 0.5 (median) and 0.9 quantiles of summer (a) and winter (b) precipitation in relation to TR at different scales. The 95% confidence intervals of the estimated slopes are shown as shadings for the different quantiles of precipitation
downscaling using information at coarser resolution to derive information at finer resolution, is naturally limited by scale effects.
## 5 Conclusions
In this study, the scales effects of TR on the precipitation over the Qinghai-Tibet Plateau are investigated by using the quantile regression method that can account for the response of different precipitation quantiles to the varied TR scales. Several quantiles (i.e., 0.1, 0.3, median, 0.7 and 0.9) of summer and winter precipitation are selected to analyze the changes in the precipitation-TR relationship at the spatial scale of 1, 10 and 100 km, respectively. Furthermore, the high and median precipitation quantiles are used to diagnose the variations of the precipitation-TR relationship associated with different TR scales.
For summer precipitation, the precipitation-TR relationship would be covered up in the small or large TR scales due to large-scale monsoon circulation. For winter precipitation, an intensification of high precipitation with rugged topographic conditions is found for the TR scales less than 30 km. Those analyses demonstrate that the precipitation-TR relations in the Qinghai-Tibet Plateau are different for summer and winter and varied with the increase in the spatial scales. Therefore, attention should be drawn to the appropriate spatial scales for the validity of discussion about the relationship between different precipitation quantiles and topographic effects. This has important implications for statistical downscaling and model projection of precipitation in the Qinghai-Tibet Plateau.
## Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 41890854) and the Young Talent Fund of Institute of Geographic Sciences and Natural Resources Research, CAS (No. 2015 RC203). The precipitation data were obtained from China Meteorological Administration. SRTM DEM data were available from the U.S. Geological Survey.
## ORCID
_[PERSON]_[[https://orcid.org/0000-0003-1944-5096](https://orcid.org/0000-0003-1944-5096)]([https://orcid.org/0000-0003-1944-5096](https://orcid.org/0000-0003-1944-5096))
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## How to cite this article:
[PERSON] Scale effects of topographic ruggedness on precipitation over
Qinghai-Tibet Plateau. _Atmos Sci Lett._ 2019;20:e904.
[[https://doi.org/10.1002/asl.904](https://doi.org/10.1002/asl.904)]([https://doi.org/10.1002/asl.904](https://doi.org/10.1002/asl.904)) | wiley | Scale effects of topographic ruggedness on precipitation over Qinghai‐Tibet Plateau | Ning Lu | https://doi.org/10.1002/asl.904 | 2,019 | CC-BY |
wiley/fea306cc_ac68_4561_ba94_82351d0bdbb3.md | # Earth and Space Science
Mapping Lava Flows on Venus Using SAR and InSAR:
Hawai'i Case Study
[PERSON]
1 Institute for Geophysics & Planetary Science, Scirpps Institution of Oceanography, University of California San Diego, San Diego, CA, USA, 2 Planetary Science Institute, Tucson, AZ, USA, 3 Department of Earth Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
[PERSON]
1 Institute for Geophysics & Planetary Science, Scirpps Institution of Oceanography, University of California San Diego, San Diego, CA, USA, 2 Planetary Science Institute, Tucson, AZ, USA, 3 Department of Earth Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
[PERSON]
2 Institute for Geophysics & Planetary Science, Scirpps Institution of Oceanography, University of California San Diego, San Diego, CA, USA, 2 Planetary Science Institute, Tucson, AZ, USA, 3 Department of Earth Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
[PERSON]
2 Institute for Geophysics & Planetary Science, Scirpps Institution of Oceanography, University of California San Diego, San Diego, CA, USA, 2 Planetary Science Institute, Tucson, AZ, USA, 3 Department of Earth Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
###### Abstract
We explore the potential for repeat-pass SAR Interferometry (InSAR) correlation to track volcanic activity on Venus' surface motivated by future SAR missions to Earth's sister planet. We use Hawai'i as a natural laboratory to test whether InSAR can detect lava flows assuming orbital and instrument parameters similar to that of a Venus mission. Hawai'i was chosen because lava flows are frequent, and well documented by the United States Geological Survey, and because Hawai'i is a SAR supersite, where space agencies have offered open radar data sets for analysis. These data sets have different wavelengths (L, C, and X bands), bandwidths, polarizations, look angles, and a variety of orbital baselines, giving opportunity to assess the suitability of parameters for detecting lava flows. We analyze data from ALOS-2 (L-band), Sentinel-1 (C-band), and COSMO-SkyMed (X-band) spanning 2018 and 2022. We perform SAR amplitude and InSAR correlation analysis over temporal baselines and perpendicular baselines similar to those of a Venus mission. Fresh lava flows create a sharp, noticeable decrease in InSAR correlation that persists indefinitely for images spanning the event. The same lava flows are not always visible in the corresponding amplitude images. Moreover, noticeable decorrelation persists in image pairs acquired months after the events due to post-emplacement contraction of flows. Post-emplacement effects are hypothesized to last longer on the Venusian surface, increasing the likelihood of detecting Venus lava flows using InSAR. We argue for further focus on repeat-pass InSAR capabilities in upcoming Venus missions, to detect and quantify volcanic activity on Earth's hotter twin.
2024
spreading ridges and on land volcanoes. Based on these arguments, one would expect Venus to have numerous active volcanoes. Indeed a recent study estimates the frequency of volcanic activity on Venus to be as high as 120 eruptions per Earth year ([PERSON] & [PERSON], 2022).
Synthetic aperture radar (SAR) images taken during NASA's Magellan mission (1989-1994) ([PERSON] et al., 1992) indicated that Venus has an extensive history of volcanism, and have enabled comprehensive mapping of lava flows, the ages of which are largely unknown ([PERSON] et al., 1992). The spatial crater density on the surface of Venus is low, and it is not possible to obtain statistically reliable reliable regional surface ages ([PERSON], 1999; [PERSON] et al., 1998; [PERSON] et al., 1992). Based on the low number, area, and density of impact craters, estimates for the average global surface age range from 300 Ma to \(\sim\)1 Ga ([PERSON] et al., 1997; [PERSON] et al., 1992; [PERSON] et al., 1992). Analysis of Magellan radar emissivity data, showing variations spatially correlated with individual features on the ground, suggests the youngest flows on Maat Mons are younger than 60 million years old, and perhaps as young as 9 million years old ([PERSON] et al., 2021). There is also circumstantial evidence for even more recent volcanism on Venus. Thermal emissivity anomalies detected by ESA's Venus express mission could result from lava flows younger than 250,000 years old ([PERSON] et al., 2010), and these anomalies have been used to map the location and extent of younger versus older lava flows ([PERSON] et al., 2017). The venus monitoring camera aboard Venus express also detected local fluctuations in surface temperature on a time scale of days to months, located along the Ganiki Chasma rift zone, suggesting the presence of volcanic activity related to the rift ([PERSON] et al., 2015). Atmospheric evidence also suggests the presence of recent volcanism, such as the episodic injection of sulfur dioxide ([PERSON], 1984). Recent comparisons of two Magellan SAR images of Atla Regio suggest that a volcanic event occurred in the 8-months gap between acquisitions ([PERSON], 2023). These observations indicate a volcanic event increasing 4 km\({}^{2}\) in area, the first direct indication of volcanic activity on the Venusian surface. Still, the exact age of Venus' lava flows and the frequency with which they are emplaced now or in the past remains a mystery.
Detection of present and past volcanism is a major goal of upcoming SAR missions to Venus, namely NASA's VERITAS mission (X-band, [PERSON] et al., 2022) and ESA's EnVision mission (S-band, [PERSON] et al., 2017). These may have the capabilities to detect volcanism within the mission lifetime using repeated SAR imagery amplitude and possibly SAR Interferometry (InSAR) ([PERSON], 2012).
The primary focus of the Magellan mission was on imaging and mapping Venus using SAR, but not InSAR, as the use of amplitude and phase data for InSAR at Earth was first tested only around the time of the Magellan mission ([PERSON] & [PERSON], 1993), and the orbital characteristics of the Magellan mission, as with most planetary missions, were not optimal for doing so. Measuring changes in radar backscatter amplitude has been used to accurately detect lava flows in previous terrestrial studies, including on the island of Hawai'i ([PERSON], 2022; Poland, 2022). However, only using radar backscatter amplitude differences to identify lava flows has many challenges. Radar backscatter is most sensitive to the roughness of the surface at the wavelength of the radar--fresh lava flows can therefore prove difficult to map, disappearing in the radar image where their flow becomes smooth, and reappearing in a \(\alpha\) or pabenhoe-textured areas ([PERSON] et al., 2023). Although very large changes in the shape of the surface can be seen in radar backscatter amplitude changes, such as those found by [PERSON] and [PERSON] (2023), smaller, or relatively flat lava flows are difficult to detect. In short, if the surface texture remains roughly the same before and after a lava flow is emplaced, it may go undetected.
Previous studies show InSAR is very effective for mapping lava flows ([PERSON] et al., 2012; [PERSON] et al., 2000; Poland, 2022; [PERSON] et al., 2003; [PERSON] et al., 1996), and can be used when changes cannot be distinguished in radar backscatter. InSAR measures surface change by comparing radar phase between two co-registered SAR scenes collected at different times. Where the surface scatterers have not changed orientation with respect to the satellite view between two images, coherence will be high, but where the surface has changed in the time between acquisitions, coherence will be low. The phase can be computed at a single pixel but the coherence requires averaging or filtering over an area of several pixels. The coherence will remain high as long as the phase variations are relatively uniform within the averaging area. We smooth the coherence with a Gaussian filter having 0.5 gain at 75 m half wavelength, which is comparable to a 36 m boxcar filter, a commonly used length scale for multilook averaging ([PERSON] & [PERSON], 1992). Moreover, the phase of the overall interferogram can be highly distorted by atmospheric phase delays while the corresponding coherence image will be largely insensitive to the atmospheric distortions and more sensitive to changes in the surface scatterers. This coherence is measured with a value from 0 to 1 referred to as correlation ([PERSON] & [PERSON], 1992). On Earth, decorrelation between two SAR images of the same area is often caused by water and vegetation, which causes surface changes between SAR scenes ([PERSON] & [PERSON], 1992). Variations in the position of the satellite also affect correlation, and the larger the distance between the satellite positions at different acquisition times, known as the \"physical perpendicular baseline,\" the lower the overall correlation and its maximum possible value ([PERSON] et al., 1994). The length of time between acquisitions, or \"temporal baseline,\" also lowers correlation, because of small surface changes accumulating over time ([PERSON] & [PERSON], 1998).
New lava flows cause substantial decorrelation of SAR images by repaving the surface, completely changing the ground's scattering properties between images collected before and after flow emplacement. However, once a flow becomes inactive, and the lava completely cools and subsides, its surface remains stable between image acquisitions, yielding high correlation in subsequent acquisitions, at least in arid regions ([PERSON] et al., 2012). It is this effect that makes InSAR correlation useful in lava flow mapping, as new, active lava flows will exhibit very low correlation compared to old, inactive lava flows around them (Figure 1).
Venus provides unique challenges for an InSAR mission; physical perpendicular baselines may be large because of the highly eccentric orbits common to planetary missions. Furthermore, Venus' slow rotational period means that the matching tracks (descending or ascending) of an orbiting satellite only passes over the same location once every 243 days, constraining the temporal baseline, and limiting the total number of repeat passes over the mission lifetime to \(\sim\)5 at best ([PERSON] & [PERSON], 2012). Despite these challenges, NASA plans to utilize InSAR on VERITAS ([PERSON] et al., 2022) and there was initially discussion of using InSAR on EnVision ([PERSON] et al., 2017). Although InSAR is no longer a planned mission activity for EnVision (ESA/SCI, 2021) because no near repeat orbits are planned (ESA/SCI, 2023), repeat orbits with short interferometric baselines may occur, especially at high latitudes where the orbital tracks converge. In this study, we aim to inform potential future Venus InSAR efforts to detect lava flows by exploring the most effective radar bands, orbits, temporal baselines, and analysis tools.
We use the Island of Hawai'i as a natural laboratory for the following reasons: (a). It is heavily studied, including other InSAR lava flow tracking experiments ([PERSON] et al., 2012; [PERSON], 2004; Poland, 2022; [PERSON] et al., 1996); (b). It is an open data supersite; and (c). It is a volcanically active area with new lava flows frequently covering older emplaced flows. To investigate the optimal methods for lava flow detection with InSAR, we use data from three satellites, namely Sentinel-1 operating at C-Band (5.6 cm), ALOS-2 operating at L-Band (23.6 cm), and COSMO-SkyMed operating at X-band (3.1 cm). These satellites travel in orbits having near-exact repeats, so interferometry is commonly possible. We employ two methods, InSAR correlation and SAR amplitude, to investigate and monitor lava flows from two separate eruptions (Figure 2).
## 2 Methods
We consider two main eruption phases on the island of Hawai'i to characterize changes in SAR amplitude and correlation. The 2018 eruption has the best temporal coverage, especially at C-band. This enables us to compare
Figure 1: Schematic of the correlation of InSAR image pairs over active and inactive volcanic flows. The InSAR correlation of an active lava flow area of an image taken before the eruption with all following images will drop dramatically after the event, and stay low for any interferogram made between the first, pre-eruption acquisition and any acquisition taken after the volcanic event, no matter the length of time that has transpired. In contrast, for inactive lava flow areas, the InSAR correlation will initially be high but decrease steadily with time in subsequent interferograms due to small, accumulating changes in the surface scatterers ([PERSON], 1998).
amplitude and coherence changes before, during and long after the eruption. The 2022 eruption at the summit of Mauna Loa provides excellent spatial mapping of amplitude and coherence in L, C, and X-band.
### C-Band Analysis of the 2018 Eruption
To study the May 2018 Kilauea Lower East Rift Zone Eruption ([PERSON] et al., 2021; [PERSON] et al., 2019; [PERSON] et al., 2019), we assembled more than 200 Sentinel-1 (C-band) SAR images from both A and B satellites for times when both were operational, with a 6-12 days repeat pass period over the Island of Hawai'i spanning March 2018-December 2021. We used only data from a descending orbit (track 87). Using the software GMTSAR ([PERSON] et al., 2011), we processed all possible 20,000+ combinations of InSAR image pairs. We used a Gaussian filter with a 0.5 gain at a wavelength of 120 m for multi-look averaging amplitude, phase, and coherence, and used the shuttle radar topography mission (SRTM1) 30 m data for our digital elevation model (DEM) to remove the topographic phase ([PERSON] et al., 2007).
Having assembled all InSAR pairs and calculated phase differences, radar amplitude differences, and correlation, we then computed the average correlation for specific regions of interest on the map for each pair. Our two main regions of interest were one. \"Active lava flow areas,\" consisting of an old lava flow or bare ground that was largely covered by new lava during the eruption event, contrasted with two. \"Inactive lava flow areas,\" consisting of old lava flow or bare ground that was completely untouched by new lava flows for the entire duration of the data set, as sketched in Figure 1. The locations of all \"active\" and \"inactive\" areas sampled are shown in Figure 2.
For the 2018 eruption, our active lava flow area is the old 1955 lava flow and parts of the 1960 flow, which were largely devoid of vegetation before the eruption and completely covered by new lava during the event (Figure 2). The presence of extensive vegetation in this area made analysis difficult, as only small areas could be sampled and studied. Our inactive lava flow area was an unvegetated slope of Mauna Loa, which had no new lava flows during this time period (2018-2021).
Figure 2: Location and extent of the two lava flows analyzed in this paper. Left: United States Geological Survey (USGS) map of Hawai’i showing all lava flows in the past 1000 years in red (USGS, n.d.). Boves 1 and 2 show the approximate extents of the USGS maps for the 2018 and 2022 events shown in Top Right and Bottom Right respectively. Top Right: USGS map of the 2018 Kilauea Lower East Rift Zone eruption final extent (USGS, 2018). Purple shows old emplaced lava flows, pink shows the 2018 flow, and overlaid green oval marks the general location from which SAR amplitude and InSAR correlation values were sampled over the new lava flow. Bottom Right: Published USGS map of the 2022 Mauna Loa lava flow, showing extent by 12 December 2022 in pink and red (USGS, 2022). Overlaid yellow oval marks the general location of the area from which SAR amplitude and InSAR correlation values were sampled. Overlaid black ring marks the general location from which values were sampled over the older, inactive surface.
For each pair of SAR images, we also computed the relative change in SAR amplitude between the two images, by taking the absolute difference between them and dividing by their average to normalize to one. In the same way we sampled average correlation, we sampled the average amplitude difference of each image pair, for both the active and inactive lava flow areas. No radiometric or other corrections were performed on the amplitude data beforehand.
### L, C, and X-Band Spatial and Temporal Analysis of the 2022 Mauna Loa Eruption
The November-December 2022 eruption of Mauna Loa (Figure 2) provided an opportunity to explore the strengths and weaknesses of imaging an eruption using three radar wavelengths L, C, and X-band. There is little water or vegetation on the slopes of Mauna Loa, so the inherent correlation of the old emplaced flows is very high at all three radar wavelengths, similar to conditions expected on Venus, making this eruption an ideal case study for our method. As discussed above, the orbits of the reference and repeat images must be within the critical baseline to recover interferometric phase and coherence. The critical baseline ([PERSON], 1992) is given as
\[b_{\rm crit}=(\lambda\,r)/(2 Rcos^{2}\theta) \tag{1}\]
where \(c\) is the speed of light, \(r\) is the slant range (\(\sim\)600 km), \(\theta\) is the look angle (\(\sim\)20-45\({}^{\circ}\)), \(\lambda\) is the wavelength, and \(R\) is the pulse length = 1/bandwidth. The maximum coherence of an interferogram is
\[\tau=1-(b_{\rm perp}/b_{\rm crit}) \tag{2}\]
where \(b_{\rm perp}\) is the range-perpendicular distance in space between the reference and repeat orbits. For similar orbital geometry, the main factors controlling the critical baseline are the radar bandwidth and the radar wavelength. The radar wavelengths of L, C, and X-band are 30-15, 7.5-3.75, and 3.75-3.5 cm, respectively, so all else being equal, the critical baseline for L-band will be four times longer than C-band and eight times longer than X-band.
At L-band, the 2022 eruption site was imaged only six times with JAXA's ALOS-2 spanning June 2022-July 2023. From this limited set, we generated 15 interferograms spanning the eruption and lava flow event. The perpendicular baseline of all the interferograms was well within the critical baseline of \(\sim\)6.5 km.
At C-band the 2022 eruption site was imaged 23 times by Sentinel-1 spanning October 2022-June 2023. Because of the relatively short perpendicular baselines, we processed 162 InSAR pairs. Once again, we calculated and sampled the average correlation and average amplitude difference at an active and inactive lava flow area for each InSAR pair.
At X-band we assembled 10 images from ASI's COSMO-SkyMed, spanning October 2022-April 2023. Each sequential image pair had a temporal spacing of around 15 days. Unfortunately, the repeat orbits of COSMO-SkyMed (CSK) are not normally controlled within the relatively small critical interferometric baseline of around 1.3 km, so only a fraction of the interferograms are useable. Many have maximum correlation far less than one, so the correlation contrast can be low. Of the 45 interferograms we processed, fewer than 15 had sufficiently high correlation to distinguish surface features, with many being completely decorrelated. Still, those well-correlated interferograms gave us an opportunity to compare interferograms of the 2022 eruption in all three bands, L, C, and X. This also gave us a unique opportunity to test the effects of high physical baselines on our detection method, as this will be a major hurdle of any Venus InSAR mission.
## 3 Results
### Analysis of 2018 Eruption
Our schematic (Figure 1) for how new emplacement of lava flows would affect the correlation between InSAR image pairs is supported quantitatively by the Sentinel-1 data for the 2018 eruption (Figure 3). The correlation of the inactive area stays high, slowly decreasing, on average, in a linear fashion over several years. The correlation of the active area however, drops substantially with the emplacement of new lava, and remains low more than a 1,000 days later. Substantial noise is present due to baseline effects, and because of the presence of some light vegetation and water in these areas, both of which cause rapid decorrelation in InSAR images, however, neither are present on the Venusian surface. All things being equal, a higher signal-to-noise ratio in such derived products might be expected from a Venus mission. Venus' atmosphere may cause significant variability in the strength of the coherence signal, leading to lower signal-to-noise overall ([PERSON] & [PERSON], 2012).
The average correlations of all possible image pairs for both the active and inactive areas is shown in Figure 4. There are three distinct types of correlation in relation to the lava flow: (a). The inactive area (Figure 4, right) has no notable correlation changes between pairs. There are some bands of relatively lower correlation believed to be caused by rainfall, which can reduce correlation ([PERSON], 2023); (b). All interferograms spanning the event have low correlation as seen in area B of Figure 4 left; (c). There is an interesting pattern in correlation for interferograms with both acquisitions after the event. The coherence between sequential SAR images does not immediately return to the high value of \(\sim\)0.8 because the surface scatters of the lava flow are still in motion. This is due to cooling and settling of the lava which can take several years depending on thickness of the flow as noted in previous studies ([PERSON] et al., 2012; [PERSON] et al., 2001). These post-emplacement signatures can also be seen in our results for the other eruption and are discussed in more detail in Section 4.1.
### Analysis of 2022 Eruption
Figure 5 shows the average correlations of all possible C-band image pairs for both the active and inactive areas for the 2022 eruption data set. As with the 2018 eruption, there is a clear pattern of the correlation dropping and staying low after the eruption is present in the active lava flow area but not the inactive area. Bands of lowered correlation in the inactive area data are, as in the previous example, most likely caused by moisture and ordinary noise.
Figure 3: Average InSAR correlation over active (red) and inactive (blue) lava flow areas, between one image before the 2018 eruption (1 March 2018) and every other image in the data set, showing the evolution in time of correlation in both areas. Lava emplacement occurred around day 190 (9 July 2018). Time on the \(x\)-axis refers to the date of second acquisition.
Figure 6 shows InSAR Correlation maps of Mauna Loa made using ALOS-2 (L-band), Sentinel-1 (C-band), and CSK (X-band). All three maps were generated using images with as close to a 243 days temporal baseline as possible to simulate the aforementioned temporal baseline issues of a Venus mission. The differences between L-band and C-band are minimal, both showing the 2022 lava flow clearly. A dark halo of low coherence surrounds the summit of Mauna Loa in the L-band image, which is not volcanic in origin but results from the late December snowfall. The same snowfall signal is visible in C-band images made around the same time. X-band has significantly lower overall correlation, being far more affected by baseline effects than the other two bands. However, the new lava flows are still seen via their correlation contrast with the surrounding area.
Figure 4: Plots of average correlation over specified area for all possible InSAR pairs in the data set for 2018 eruption. Blue line marks day 190 (9 July 2018), the approximate date at which lava flows completely covered the active lava flow area sample region. Left: samples over an active lava flow area, specifically parts of the old 1955 lava flow that were completely covered by the 2018 eruption. Green letters show regions of interest representing certain snapshots of lava flow evolution which are further discussed in Section 4.1. Region A, represents both acquisitions taken before the eruption, B one acquisition taken before and one after, C long time-span acquisitions taken after the eruption and D short time-span acquisitions taken after the eruption respectively. Right: samples over inactive lava flow area.
Figure 5: Plots of average correlation over active (left) and inactive (right) lava flow areas for all possible InSAR pairs in the 2022 Mauna Loa eruption data set. The blue line marks day 330 (26 Nov 2022), the approximate date at which lava flows completely covered the active lava flow area sample region.
### Amplitude Difference Versus Correlation
Figure 7 shows the average amplitude differences of all possible image pairs for both the active and inactive areas, for both eruptions, in the C-band.
For the 2018 and 2022 eruption data sets, the difference between active and inactive volcanic areas is far more pronounced and temporally obvious in the average correlation data compared with the amplitude difference. In all data sets, active lava flow areas appear to have larger and more frequent changes in SAR amplitude than inactive areas. However, large amplitude differences in all three instances do not match well in time with the date of the volcanic event--it is difficult from amplitude data alone to distinguish where and when lava flow emplacement is occurring, from other events that may cause a change in backscatter (e.g., precipitation). Conversely, differences in average correlation before and after a volcanic episode are immediately noticeable, and show a clear evolution in time. As is discussed in further detail in Section 4.1, post-emplacement effects from the lava cooling and settling can be also clearly seen in the correlation data-- something that is not visible in the amplitude difference data.
Figure 8 shows a map of the 2022 lava flow in both correlation and amplitude difference. In InSAR correlation data (Figure 8 top left), the decorrelated lava flow is clearly visible against the surrounding highly correlated rock. In the SAR amplitude difference data (Figure 8 top right), the lava flow is less visible, appearing similar to the surrounding surface making it more difficult to ascertain what is and is not new lava emplacement. This is reflected in the histogram distributions of each image. The correlation data shows a clear bimodal distribution (Figure 8 bottom left), meaning there is a sharp difference between low and high correlation areas. In comparison, the distribution of the amplitude difference data is unimodal (Figure 8 bottom right), meaning there are no sharp distinctions between different areas on the map. This amplitude also has a substantially lower signal-to-noise ratio compared to the correlation data.
## 4 Discussion and Conclusions
### Post-Emplacement Signal in Correlation
Because InSAR correlation is not just a function of eruption time spans, it is not necessary to detect a volcanic event during its eruption. Instead, thermal effects on correlation mean that recent flows can be detected and their
Figure 6: Left: interferogram correlation using 2 ALOS-2 L-band SAR acquisitions, one before the eruption (19 June 2022) and one after the eruption (1 January 2023), a temporal baseline of 196 days, the closest to 240 days possible with ALOS-2 data. Center: interferogram correlation using 2 Sentinel-1 C-band SAR acquisitions, one about 240 days before the eruption (8 April 2022) and one during (4 December 2022), representing 2 repeat passes of a typical Venus satellite. Straight lines going across the image mark the boundary of the Terrain Observation with Progressive Scans (TOPS) mode radar burst, and are not signals. Right: interferogram correlation using 2 CSR X-band SAR acquisitions, one during the eruption (2 December 2022) and one after (25 April 2023), a temporal baseline of 144 days, the closest to 240 days possible with our limited number of well correlated interferograms.
emplacement time constrained long after the event that created them. As discussed in [PERSON] et al. (2012), there is a temporal delay in the recovery of high coherence. Similar delay signatures, seen in the phase of interferograms following eruptions in Iceland were attributed to cooling and thermal contraction of the lava ([PERSON] et al., 2017). These post-emplacement effects are visible in Figures 4 and 5. Here, even image pairs for which both images are taken after the volcanic event have a drop in correlation that does not appear in the data for the inactive area.
For both image acquisitions post-emplacement, an interferogram taken over a new lava flow will have high correlation over short time intervals, but over longer time intervals the correlation will rapidly decrease because of the instability of the subsiding surface (see the correlation change from region D to C, Figure 4 left). However, the longer a lava flow has been emplaced, the higher the stability of the surface, and therefore the smaller the resulting drop in correlation over time. This can be seen along the diagonal (Figure 4 left,
Figure 7: Plots of average SAR amplitude differences over specified areas for all possible InSAR pairs for both eruptions. Right Column: average amplitude differences of the active lava flow areas for each of two eruptions, 2018 (top) and 2022 (bottom). Left Column: average amplitude differences of the inactive lava flow areas for each of two eruptions. Red lines show the time of the volcanic event for each data set.
region D), where interferograms are initially highly correlated before dropping off with time (Figure 4 left, region C), but the magnitude and rate of the drop decreases the further the date of the first acquisition is from the date of the eruption.
Figure 9 shows the evolution in time of the InSAR correlation of the 2022 Mauna Loa lava flow. The correlation gradually recovers over time as the lava settles and cools. Even when capturing both pre- and post-eruption acquisitions a couple of months later, the distinct outline of the lava flow remains clearly visible, exhibiting lower correlation compared to the surrounding rock (Figure 9 right). The northern, thicker and more distal part of the flow also continues to have consistently lower correlation (Figure 9).
Figure 8.— Top left: interferogram correlation using 2 Sentinel-1 C-band SAR before (8 April 2022) and during (4 December 2022) the eruption (same as Figure 6 left), representing 2 repeat passes of a typical 243 days repeat interval at Venus. Straight lines through the image are data radar burst boundaries. Bottom left: histogram shows the bimodal distribution of correlation. The low peak is the reduced correlation over new flows, and is smaller in amplitude because of the relatively small area of the image taken up by new flows. Top right: absolute amplitude difference for the same pair of images, over the same geographic extent. Bottom right: histogram shows the unimodal distribution of amplitude difference.
If both SAR acquisitions are taken before the eruption, the correlation of the resulting interferogram will be very high (see region A, Figure 4 left). If one acquisition is taken before the eruption and the other acquisition taken any time after the eruption, the InSAR correlation will be very low (see Figures 3, Figure 4 left region B, and Figure 9 left). If the first acquisition is taken relatively shortly after the eruption and second acquisition taken long after, then the resulting InSAR correlation will be low, though higher than the previous scenario (see region C, Figure 4 left, and Figure 9 center). If both the first and second acquisitions are taken long after the eruption, then the correlation will be higher as the new lava flow becomes more and more stable. Long time scale cooling effects on correlation would only be seen if the time between acquisitions was great, but short temporal baselines would show high correlation (see region D, Figure 4 left).
It is therefore important to know how quickly a lava flow settles and stops having any effect on InSAR correlation. How long a lava flow takes to become stable is dependent on its thickness, its rate of thermal subsidence, and the wavelength of the radar band detecting the change. [PERSON] et al. (2017) used InSAR phase to detect an exponential decay time in the thermal subsidence of 4-6 years following eruptions in Iceland having a thickness of 8-30 m. The thickness of the 2022 Mauna Loa flow is similar, ranging from 5 to \(-\)25 m and up to 40 m in some areas (NASA Earth Observatory, 2022), meaning the thermal subsidence time of this flow should be similar.
As shown by [PERSON] et al. (2012), there is a linear relation between the length of time an emplaced lava flow is decorrelated in sequential InSAR data, and the lava thickness. This relation is also dependent upon the band of radar used--the post-emplacement change in coherence differs among wavelengths because of their different
Figure 9: Time evolution of InSAR correlation over 2022 lava flow. Left: InSAR correlation map of Mauna Loa lava flow using two Sentinel-1 C-band SAR acquisitions, November 21 through 3 December 2022. Center: InSAR correlation map of the same area, 27 December 2022 through 8 January 2023. Right: InSAR Correlation map of the same area, February 1 through 12 February 2023. Lines through each image mark the boundary of the TOPS mode radar burst and are not signals.
servations of the flow. Though the results of [PERSON] et al. (2012) were done using L-band, our own C-band results from the 2018 eruption fit broadly well with their linear model. Our active lava flow area for the 2018 eruption had a lava flow thickness of around 10-15 m and took around 175-200 days to recover sequential InSAR correlation (Figure 10). This duration of decorrelation versus lava flow thickness value is the same as that predicted by the model of [PERSON] et al. (2012).
Figure 11 shows the evolution of correlation of sequential interferograms versus time for various lava thicknesses for each radar band. Slight, episodic decreases in correlation can be seen, particularly in the C-band area D sample data, which are most likely due to noise and not weather, as area D is too far from the summit of Mauna Loa to be covered by snowfall. For all lava thicknesses, longer wavelengths have shorter durations of decorrelation. X-band decorrelation signatures possibly remain for longer than at L-band or C-band, however it is difficult to state this for certain due to the paucity of X-band data. L-band has the shortest decorrelation duration, at just \(\sim\)30 days for Area A. This is due to the same phase changes corresponding to smaller line-of-sight ground motions. As expected, for all bands, increased lava thickness leads to longer duration of decorrelation, as the thicker the lava flow is, the longer it takes to cool and settle. This is most notable in the C-band, where area A exhibited high correlation after \(\sim\)50 days, area \(B\) after \(\sim\)75 days, and area C did not achieve high correlation until \(\sim\)150 days post-emplacement.
### Relevance to Future Venus Missions
Our results from Hawai'i indicate that InSAR correlation is more informative than SAR amplitude differences for detecting and mapping lava flows, because differences in correlation can more readily distinguish between volcanically active and inactive surfaces. The occurrence of a new lava flow will have a far larger effect on correlation than on amplitude because any new lava flow changes the random scattering properties of the surface and will cause a change in InSAR coherence. Amplitude difference primarily detects changes in the overall statistical roughness properties of the surface which stay largely the same for similar types of lava flows. Furthermore, on Earth, InSAR correlation also allows the detection of post emplacement signals, which can last several months or even years depending on lava flow thickness and radar wavelength, as discussed in Section 4.1.
The following considerations are critical to a future Venus mission. First, any relevant scenarios from our analyses of data over Hawai'i must fit with the necessarily large temporal baselines. Second, use of InSAR correlation
Figure 10: Average InSAR correlation for sequential interferograms over active (red) and inactive (blue) lava flow areas, between sequential images in the 2018 data set (C-band), showing the evolution in time of correlation in both areas. Lava emplacement occurred around day 190 (9 July 2018). Inset: United States Geological Survey (USGS) lava flow thickness map for the 2018 eruption (USGS, 2020). Black circle shows the general location of the active lava flow area.
for lava flow detection on Earth is most effective in arid areas and the application to Venus requires consideration of any environmental factors that could decrease coherence on the Venus surface, especially over time scales on the order of several months to years. Third, identification of volcanic activity via detection of post-emplacement signals is dependent on the cooling and subsidence rate of new flows, that in turn depend on surface conditions, the likely thicknesses of lava flows, and the radar wavelength used (Section 4.1). Finally, physical baselines and decorrelation from atmospheric disturbances need to be considered in future InSAR studies at Venus. We discuss each of these considerations below.
As noted in the introduction, same-look, repeat-pass SAR acquisitions at Venus will be separated in time by at least \(\sim\)240 days, 1 Venus sidereal day. Therefore for Venus, one should not expect to detect any scenarios that require observations taken within a short temporal baseline (e.g., see region D, Figure 4 left and Figure 9). If the first SAR acquisition is around the time of an eruption, then the second SAR acquisition will be at minimum several months post emplacement. The resulting interferogram would have low correlation within the lava flow, and higher correlation outside the lava flow.
Changes in the radar properties of the Venus surface relevant to InSAR analyses could also result from changes in the cm-scale morphology of flows (fresh or ancient) that in turn occur because of chemical weathering or wind erosion (e.g., [PERSON] et al., 2023), and/or changes in radar emissivity from surface-atmosphere chemical interactions. The latter have been known since early during the Magellan mission to occur over the limited surface area of the planet at altitudes corresponding to planetary radii greater than \(\sim\)6,054 km (e.g., [PERSON] et al., 1992; [PERSON] and [PERSON], 2004). More generally, chemical reactions that could occur anywhere on the planet and affect radar emissivity or cm-scale roughness are the topic of considerable recent analog experimental and theoretical work (e.g., [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2023). These studies are motivated by the implications of weathering for identification of major compositional units (felsic vs. mafic) and weathering state (fresh vs. weathered) across the planetary surface via near-IR emissivity (e.g., [PERSON] et al., 2010). The time-scales over which chemical weathering occurs are currently unclear and estimates range from a few hours ([PERSON] et al., 2020), to days ([PERSON] et al., 2023) to up to 0.5 Ma to affect a \(\sim\)30 micron-thick surface layer
Figure 11.— Evolution of average correlation of sequential interferograms over multiple areas of the 2022 Mauna Loa eruption event for 3 different bands. Lava emplacement around day 330. Left: lava flow thickness map for the 2022 Mauna Loa eruption (NASA/JPL, 2022). Lava flow thickness map generated using UAVSAR and TanDEM-X ([PERSON] et al., 2019). Circles A, B, C, and D represent sample areas, each with different flow thicknesses: 10, 15, 20, and 0 (no lava) meters respectively. Right: Average correlation versus time for areas A, B, C, and D from (top) ALOS-2 data L-band, (center) Sentinel-1 data C-band, and (bottom) CSK data X-band data. The cyan line on all three subplots represents the time of emplacement.
Mauna Loa 2022 lava flow may still be visible in InSAR correlation data. InSAR correlation thus also allows for the detection of post emplacement signals which can last several months or even years depending on lava flow thickness, and radar wavelength.
The use of InSAR correlation to detect new flows during or post-emplacement does not appear limited by radar wavelength, as pronounced decorrelation appears in all three bands we tested. Shorter bands have the benefit of post-emplacement signals lasting longer, while longer bands have the benefit of higher overall correlation. ESA's EnVision, although not currently planned to perform InSAR, possesses a radar that is InSAR capable. This SAR instrument will utilize S-band (9.4 cm), between the C-band and L-band tested in this paper (ESA/SCI, 2021). NASA's VERITAS, which is planned to perform some InSAR, will be on the boundary between X and C bands (3.8 cm) and be more similar to terrestrial C-band satellites in terms of performance ([PERSON] et al., 2022).
As expected, large physical perpendicular baselines remain the largest hurdle in a potential Venus InSAR mission. Large physical perpendicular baselines have a far larger effect on InSAR correlation than temporal baselines, making the highly elliptical orbit of a Venus mission a greater challenge than the long time spans between repeat acquisitions. Distinguishing between uncorrelated, new lava flows and correlated, old inactive surfaces is more difficult when the overall correlation threshold is lowered by large baselines. X-band in particular is very sensitive to this issue, as smaller wavelengths lead to smaller critical baselines. An example of a poorly correlated X-band interferogram can be seen in Figure 12.
Even though the image is poorly correlated, evidence of new lava flows emplaced on older lava flows can still be seen, though it is difficult to distinguish from baseline-related noise. Still, even one repeat pass with a reasonable perpendicular baseline would allow for the detection of newly emplaced lava flows, and potentially the age and thickness of flows. VERITAS, and, depending on the final reconstructed spacecraft trajectories, EnVision could
Figure 12.— Interferogram correlation using 2 CSK X-band SAR acquisitions, focused on the summit of Mauna Loa. First image acquisition on 14 October 2022, second image acquisition on 18 January 2023, with a perpendicular baseline of around 747 m.
potentially perform repeat pass SAR observations with moderately low physical perpendicular baselines over a few select regions of the Venusian surface, allowing for InSAR correlation analysis of such areas ([PERSON] et al., 2022; ESA/SCI, 2023).
There is a benefit to using longer wavelength radars for InSAR, as longer wavelengths have longer critical baselines, allowing InSAR to be done at higher physical perpendicular baselines, which lessens the need for precise orbit control. As high physical perpendicular baseline to critical baseline ratios have a detrimental effect on InSAR correlation, we believe that longer radar wavelengths are optimal for our lava detection method. Longer radar wavelengths also travel more easily through Venus' atmosphere, reducing the impact of attenuation on the signal to noise of the correlation signal ([PERSON] et al., 2010; [PERSON] & [PERSON], 2012). A higher radar bandwidth also linearly increases the length of the critical baseline, however higher bandwidth radar produces a higher volume of data, requiring the satellite to have a faster data downlink.
Finally, the thick and turbulent atmosphere of Venus may affect the InSAR phase severely ([PERSON] & [PERSON], 2012), creating complications to detect phase signals, for instance thermal subsidence with the method of [PERSON] et al. (2017). However, as long as atmospheric phase distortions occur over length scales greater than the multilook averaging length scale (\(\sim\)150 m), the correlation signals would survive ([PERSON] & [PERSON], 2012). Alternatively, if the atmospheric phase distortions occur over length scales less than the multilook averaging length scale, coherence will be diminished.
The potential use of InSAR correlation to detect and track lava flows on Venus should be given more attention. The recent discovery of modern-day volcanic activity on Venus ([PERSON] & Hensley, 2023) comes at a time of renewed scientific interest in Earth's sister planet, with VERITAS and EnVision planned to perform detailed SAR imaging of Venus in the next decades. InSAR, although not a priority for these upcoming missions, can provide indisputable evidence for volcanic activity because, as we have shown, InSAR correlation can be used to accurately detect and map these lava flows, even with only post-emplacement data acquisitions.
## Data Availability Statement
Sentinel-I image and orbital data was accessed via the ESA's Copernicus Open Data Hub via the Alaska Satellite Facility Vertex Data Search (ASF/ESA, 2022). CSK data was accessed from the Hawai'i Volcano's Supersite via the ESA Geohazard Exploration Platform (GEO-GNSL, 2023). ALOS-2 data was accessed via an individual proposal to JAXA (JAXA, 2022), and was the only data set we used in this paper which is not open access. Our DEM was generated using the SRTM1 model, as accessed through the GMTSAR website's DEM generator ([PERSON] et al., 2022).
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wiley/fe7cd712_ac13_4f49_8172_14fa055617f2.md | The GFDL Global Atmospheric Chemistry-Climate Model AM4.1: Model Description and Simulation Characteristics
[PERSON]
1 NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA, 1 Department of Chemistry and Biochemistry and Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK, USA, 1 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA, 1 Department of Earth and Planetary Sciences and Institute for Sustainable and Energy, Northwestern University, Evanston, IL, USA, 1 Department of Earth and Planetary Sciences and Institute for Sustainable and Energy, Northwestern University, Evanston, IL, USA, 1 Department of Earth and Planetary Sciences and
weaknesses of CM3 chemistry, including the critical role of prognostic aerosol interactions (e.g., [PERSON] et al., 2013; [PERSON], [PERSON], et al., 2013). As such, interactive aerosols were included in all of GFDL's fourth-generation atmospheric model development efforts, targeted for the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The high computational cost of interactive atmospheric chemistry, however, was avoided in GFDL's recent CM4.0 development ([PERSON] et al., 2019) by prescribing ozone and other oxidants. A full, interactive chemistry representation, along with a comprehensive carbon cycle, was reserved in this generation of GFDL models for Earth System Model development in ESM4.1 ([PERSON] et al., 2020). Thus, CM4 included a focus on ocean resolution, while ESM4.1 focused on a comprehensive representation of the Earth system.
The overall goal of AM4.1 development was to merge a suite of mostly parallel sets of updates and innovations into GFDL's fourth-generation atmospheric model. These updates include a revised chemical mechanism from AM3 to AM4.1 to take advantage of new laboratory kinetic data (e.g., [PERSON], [PERSON], et al., 2013; [PERSON] et al., 2011; as implemented by [PERSON] et al., 2016), in particular for photooxidation of biogenic volatile organic compounds (BVOCs). Analysis of deficiencies in AM3 chemistry has pointed out improper treatment of nitrate aerosols and gas-aerosol interactions and biases in wet and dry deposition. We also wanted to leverage successful follow-on development efforts from AM3 targeted to implement reduced nitrogen cycling ([PERSON] et al., 2016; [PERSON], [PERSON], et al., 2017) and improved representation of the seasonal cycle in sulfate ([PERSON], [PERSON], & [PERSON], 2017). Finally, we wanted to provide the ability for the atmospheric model to handle a more diverse suite of land-atmosphere and ocean-atmosphere linkages for comprehensive Earth system representation of not only heat and hydrology but also CO\({}_{2}\), dust, reactive nitrogen, and organic carbon.
The focus of the present study is to document the atmosphere physics and chemistry developed for AM4.1, as distinguished from the physical climate-focused AM4.0 ([PERSON] et al., 2018a, 2018b), for standalone atmospheric applications. A more comprehensive discussion of coupled atmosphere-ocean-land Earth system interactions in ESM4.1 is provided by [PERSON] et al. (2020). We focus our analysis on evaluating the AMIP configuration of AM4.1 used for CMIP6, and document the differences in results between AM4.1 and other GFDL CMIP models, including AM4.0 (CMIP6) and AM3 (CMIP5). In the case of comparisons with AM3, the differences in results reflect updates to both the model configuration and the emissions (as discussed in section 2.4).
## 2 Model Description
A general schematic of AM4.1 forcing, dynamics, physics, aerosol, and chemistry interactions is provided in Figure 1. The following sections discuss the formulations for these components in reference to their AM4.0 ([PERSON] et al., 2018a, 2018b) counterparts.
### Physical Model Formulation
The physical formulation of AM4.1 is similar to that of AM4.0, but the model top has been raised from 100 Pa (\(\sim\)45 km) to 1 Pa (\(\sim\)80 km), and the number of vertical levels has been increased from 33 to 49, similar to the 48-level structure of AM3. This enhanced vertical extent and resolution allows AM4.1 to represent stratospheric dynamics and chemistry and stratosphere-troposphere coupling. The time step used in the dynamical core for gravity wave and the Lagrangian dynamics is reduced from 150 s in AM4.0 to 130 s in AM4.1 for increased numerical stability.
Like AM4.0, AM4.1 includes five tracers for water (specific humidity, liquid water, ice water, cloud amount, and liquid droplet number concentration) and uses the same large-scale and convective cloud parameterizations as in AM4.0. Cloud parameterizations in AM4.1 were retuned slightly compared to AM4.0 in order to improve agreement with observed top-of-atmosphere shortwave and longwave radiative fluxes, in response to initially excessive reflection from convective clouds over sub-Saharan Africa, North Indian Ocean, and the western tropical Pacific. In particular, the scale factor applied to the fall speed of ice clouds (_c1_ in [PERSON] et al., 2018b) was reduced from 0.90 in AM4.0 to 0.85 in AM4.1 to increase ice water path and decrease outgoing longwave radiation. The cloud erosion timescale (\(\tau_{\text{eros}}\)) in convectively active regions is decreased slightly from 6.9 to 5.6 h to increase the absorbed shortwave radiation. The cloud erosion timescale under other conditions is unchanged from AM4.0.
As described by [PERSON] et al. (2018b), nonorographic gravity wave drag in AM4.0/AM4.1 is parameterized following [PERSON] and [PERSON] (1999), but the parameters used in AM4.1 are modified from those in AM4.0 to improve stratospheric circulation. In AM4.1, the magnitudes of the nonorographic gravity wave flux above 350 hPa for the tropics, northern extratropics, and southern extratropics (_St_, _Sn_, and _Ss_) are set to 0.004, 0.005, and 0.0035 m\({}^{2}\) s\({}^{-2}\), respectively.
Land hydrology and ecosystem dynamics are represented in AM4.1 by the GFDL Land Model version 4.1 (LM4.1; [PERSON], personal communication), replacing the LM4.0 model used in AM4.0 ([PERSON] et al., 2018). LM4.1 includes advanced vegetation and canopy competition, fire, land-use representation, and dynamic atmospheric dust coupling.
### Atmospheric Chemistry and Aerosol Scheme
AM4.1 includes interactive tropospheric and stratospheric gas-phase and aerosol chemistry. The bulk aerosol scheme, including 18 transported aerosol tracers (see Table S1 in the supporting information), is similar to that in AM4.0 ([PERSON] et al., 2018), with the following updates: (1) ammonium and nitrate aerosols are treated explicitly, with the sulfate-nitrate-ammonia thermodynamic equilibrium simulated using ISORROPIA ([PERSON] & [PERSON], 2007), as described by [PERSON] et al. (2016); (2) oxidation of sulfur dioxide and dimethyl sulfide to produce sulfate aerosol is driven by the gas-phase oxidant concentrations (OH, H\({}_{2}\)O\({}_{2}\), and O\({}_{3}\)) and cloud pH simulated by the online chemistry scheme ([PERSON] et al., 2016); and (3) the rate of aging of black and organic carbon aerosols from hydrophobic to hydrophilic forms varies with calculated concentrations of hydroxyl radical (OH), as described by [PERSON] et al. (2011).
Unlike AM4.0, the AM4.1 model has an online representation of gas-phase tropospheric and stratospheric chemistry. The combined tropospheric and stratospheric chemistry scheme includes 18 prognostic (transported) aerosol tracers, 58 prognostic gas-phase tracers, five prognostic ideal tracers, and 40 diagnostic (non-transported) chemical tracers (Table S2), with 43 photolysis reactions, 190 gas-phase kinetic reactions, and
Figure 1: Schematic description of forcing, dynamics, physics, aerosol, and chemistry interactions in AM4.1. Terms depicted in gray (left) are prescribed as inputs to the model, while chemical processes included in the orange box are calculated interactively within the atmospheric model. The light blue box (top) includes physical processes calculated in AM4.1. The green box (bottom left) represents the land component (LM4.1), which is coupled to AM4.1. The dark blue box (bottom right) includes specified ocean-surface boundary conditions.
15 heterogeneous reactions (Table S3). The tropospheric chemistry includes reactions of the NO\({}_{x}\)-HO\({}_{x}\)-O\({}_{\rm x}\)-CO-CH\({}_{4}\) system and oxidation schemes for other nonmethane volatile organic compounds. The stratospheric chemistry accounts for the major ozone loss cycles (O\({}_{\rm ox}\), HO\({}_{\rm ox}\), NO\({}_{\rm ox}\), CLO\({}_{\rm ox}\), and BrO\({}_{\rm 3}\)) and heterogeneous reactions on liquid and solid stratospheric aerosols as in [PERSON] et al. (2013). The base chemical mechanism is updated from that in AM3 ([PERSON], [PERSON], et al., 2013), using gas-phase and heterogeneous chemistry updates from [PERSON], [PERSON], et al. (2013) and [PERSON], [PERSON], et al. (2013), similar to the configuration described by [PERSON] et al. (2018). We include heterogeneous reactions of HO\({}_{2}\), NO\({}_{2}\), N\({}_{2}\)O\({}_{\rm s}\), and NO\({}_{3}\) on the surfaces of all simulated aerosol types, with specified gamma values (given in Table S3). Note in particular that \(\gamma\) (HO\({}_{2}\)) is reduced from the value of 1 recommended by [PERSON], [PERSON], et al. (2013) to 0.2. We also include the heterogeneous oxidation of SO\({}_{2}\) on aerosols following [PERSON] et al. (2015). The heterogeneous chemistry included in AM4.1 has a much stronger effect on oxidant levels than that in AM3, which used \(\gamma\)(N\({}_{2}\)O\({}_{\rm s}\)) = 0.1, \(\gamma\)(NO\({}_{3}\)) = 0.1, \(\gamma\)(NH\({}_{3}\)) = 0.05, \(\gamma\)(HO\({}_{2}\)) = 0, and \(\gamma\)(NO\({}_{2}\)) = 0, applied only to sulfate aerosols. The chemical system is solved using an implicit Euler backward method with Newton-Raphson iteration, as in [PERSON] et al. (2003). Photolysis rates are calculated interactively using the FAST-JX version 7.1 code, as described by [PERSON] et al. (2016), accounting for the radiative effects of simulated aerosols and clouds.
Dry deposition velocities for all aerosols are calculated interactively using a wind-driven resistance method ([PERSON] et al., 2002), accounting for the effect of whitecaps over the ocean ([PERSON], 1982). The treatment of wet deposition accounts for slower removal by frozen precipitation due to the Bergeron process in mixed-phase clouds ([PERSON] et al., 2011). Dry and wet deposition for gases are as described by [PERSON] et al. (2016).
Optical properties of aerosols are precalculated, as in AM4.0, using Mie theory assuming sphericity. The extinction efficiency, single scattering albedo, and asymmetry parameter are tabulated as a function of wavelength, aerosol type, aerosol size (for dust and sea salt), and relative humidity. Sulfate is assumed to be internally mixed with black carbon for the calculation of optical properties. Unlike AM4.0, radiative effects of nitrate aerosol are included in AM4.1 (as in [PERSON], [PERSON], et al., 2017).
### 2.3. AMPP (1980-2014) Simulation Configuration
We conduct AMIP simulations with AM4.1 over the period 1979-2014 using observed gridded sea surface temperature (SST) and sea-ice concentration boundary conditions from the reconstructions of [PERSON] et al. (2000). Historical reconstructions of monthly solar spectral irradiances are from [PERSON] et al. (2017). For radiation calculations, global monthly mean concentrations of greenhouse gases (GHGs), including nitrous oxide (N\({}_{2}\)O), and ozone-depleting substances (ODSs, including CFC-11, CFC-12, CFC-113, and HCFC-22) are specified from [PERSON] et al. (2017). Global mean mixing ratios of methane (CH\({}_{4}\)) and N\({}_{2}\)O are specified at the surface as lower boundary conditions for chemistry. Carbon dioxide (CO\({}_{2}\)) mixing ratio is restored to observed global-mean values with a one-year timescale. The simulated global-mean CO\({}_{2}\) and CH\({}_{4}\) concentrations are used for radiation calculations.
### Emissions
Annually varying time series of monthly anthropogenic and biomass burning emissions of ozone precursors and aerosols (and their precursors) are from the Community Emissions Data System (CEDS; [PERSON] et al., 2018) and the data set of [PERSON] et al. (2017), respectively, developed in support of CMIP6. Wildfire emissions are distributed vertically between the surface and 6 km, with location- and biome-dependent vertical profiles, as recommended by [PERSON] et al. (2006), similar to the treatment in AM3 ([PERSON] et al., 2011; [PERSON], [PERSON], et al., 2013). Natural emissions of NO\({}_{x}\), CO, non-methane volatile organic compounds (NMVOC), hydrogen (H\({}_{2}\)), and ammonia (NH\({}_{3}\)) are generally the same as those considered by [PERSON], [PERSON], et al. (2013), namely from the Precursors of Ozone and their Effects in the Troposphere (POET) inventory for present day (corresponding to year 2000) ([PERSON] et al., 2003). Emissions of NH\({}_{3}\) from sea bird colonies, not accounted for in AM3, are included in AM4.1 following [PERSON] et al. (2012). The treatment of marine ammonia emissions is also revised as described below.
Biogenic emissions of isoprene and monoterepnees are calculated online using the Parameterized Canopy Environment Emission Activity (PCEEA algorithm; [PERSON] et al., 2006) in the Model of Emissions of Gases and Aerosols from Nature (MEGAN v2.1; [PERSON] et al., 2012) as a function of simulated air temperature and shortwave radiative fluxes, implemented as described by [PERSON] et al (2012). Leaf area indices for 17 plant functional types are based on AVHRR and MODIS data and are mapped to five vegetation types ([PERSON] et al., 2010). These vegetation types and leaf area indices are independent of those simulated by the LM4.1 dynamic vegetation model, due to a lack of coupling between the dynamic vegetation properties simulated by LM4.1 and the atmospheric emissions module. We do not apply the soil moisture or CO\({}_{2}\) responses from [PERSON] et al. (2012). Future model development plans include coupling biogenic emissions to LM4.1. Sea salt emissions are based on the parameterization of [PERSON] et al. (1986) as in CM3 ([PERSON] et al., 2011), but are modulated by sea surface temperature following [PERSON] et al. (2011). Ocean ammonia emissions are calculated following [PERSON] et al. (2015), using the simulated seawater concentration of NH\({}_{4}^{+}\) in ESM4.1. Other marine emissions, including primary organic aerosols (POA) and dimethyl sulfide (DMS), are calculated similarly to in CM3. DMS emissions are calculated using an empirical formula as a function of a prescribed monthly climatology of DMS concentration in sea water ([PERSON] et al., 2011) and calculated wind speed at 10 m, as described by [PERSON] et al. (2002). Thus, oceanic emissions of POA, DMS, ammonia, and sea salt are dependent on the simulated meteorology in the model.
Emission totals for year 2014 are shown in Table 1. Time series of annual global emissions in AM4.1 (using CMIP6 inventories) are shown for select species in Figure 2 and compared with corresponding totals in AM3 (using CMIP5 inventories).
Sources of secondary organic aerosols (SOA) include an anthropogenic source from oxidation of the simulated C\({}_{4}\)H\({}_{10}\) hydrocarbon tracer by hydroxyl radical (with a 10% per-carbon yield) and a biogenic pseudo-emission assuming a 10% per-carbon yield from emissions of BVOCs, including isoprene and monoterpenes, from vegetation. This yield is in the range of values suggested by recent studies using more detailed schemes for SOA production (e.g., Bates & Jacob, 2019; [PERSON] et al., 2020). In year 2014, the sources of SOA are 83.84 Tg a\({}^{-1}\) from BVOCs and 3.49 Tg a\({}^{-1}\) from anthropogenic hydrocarbon oxidation.
Lightning NOx emissions are calculated interactively as a function of subgrid convection in AM4.1, as diagnosed by the double-plume convection scheme described by [PERSON] et al. (2018b). The lightning NOx source is calculated as a function of convective cloud-top height, following the parameterization of [PERSON] et al. (1997), and is injected with the vertical distribution of [PERSON] et al. (1998), as in AM3 ([PERSON], [PERSON], et al., 2013). The global total production of NOx by lightning is 3.59 Tg N for year 2014.
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline Species & Units & Anthro & Biomass burning & Biogenic/natural & Ocean & Animals & Soil & Ship & Aircraft & Total \\ \hline ACET & Tg Ca\({}^{-1}\) & 1.47 & 0.98 & 15.09 & 0 & 0 & 0 & 0 & 0 & 17.53 \\ BC & Tg Ca\({}^{-1}\) & 7.83 & 1.77 & 0 & 0 & 0 & 0 & 0.17 & 0 & 9.76 \\ C2H4 & Tg Ca\({}^{-1}\) & 4.88 & 3.82 & 0 & 0 & 0 & 0 & 0.14 & 0 & 8.83 \\ C2H50 & Tg Ca\({}^{-1}\) & 2.40 & 0.07 & 4.82 & 0 & 0 & 0 & 0 & 0 & 7.29 \\ C2H6 & Tg Ca\({}^{-1}\) & 5.22 & 2.71 & 0.80 & 0.78 & 0 & 0 & 0.17 & 0 & 9.67 \\ C3H6 & Tg Ca\({}^{-1}\) & 9.50 & 5.85 & 0.85 & 1.29 & 0 & 0 & 0.16 & 0 & 17.66 \\ C3H8 & Tg Ca\({}^{-1}\) & 5.05 & 0.53 & 1.63 & 1.05 & 0 & 0 & 0.49 & 0 & 8.76 \\ C4H10 & Tg Ca\({}^{-1}\) & 52.93 & 2.34 & 0 & 0 & 0 & 0 & 1.10 & 0 & 56.38 \\ C1 OH16 & Tg Ca\({}^{-1}\) & 0 & 1.24 & 57.37 & 0 & 0 & 0 & 0 & 0 & 58.61 \\ CH2O & Tg Ca\({}^{-1}\) & 1.00 & 1.94 & 0 & 0 & 0 & 0 & 0 & 0 & 2.94 \\ CH3 OH & Tg Ca\({}^{-1}\) & 0.30 & 3.24 & 85.61 & 0 & 0 & 0 & 0 & 0 & 89.14 \\ CO & Tg\({}^{-1}\) & 612.40 & 356.68 & 159.24 & 19.80 & 0 & 0 & 0.69 & 0.57 & 1,149.37 \\ DMS & Tg Ca\({}^{-1}\) & 0 & 0 & 0 & 42.72 & 0 & 0 & 0 & 0 & 42.72 \\ DUST & Tg a\({}^{-1}\) & 0 & 0 & 0 & 0 & 0 & 2,507.67 & 0 & 0 & 2,507.67 \\ H2 & Tg a\({}^{-1}\) & 24.50 & 9.01 & 0 & 2.98 & 0 & 2.98 & 0.03 & 0 & 39.48 \\ ISOP & Tg a\({}^{-1}\) & 0.00 & 0.57 & 499.78 & 0 & 0 & 0 & 0.00 & 0 & 500.36 \\ NH3 & Tg a\({}^{-1}\) & 0.682 & 4.30 & 0 & 3.89 & 0.15 & 2.95 & 0.02 & 0 & 72.13 \\ NO & Tg N a\({}^{-1}\) & 35.52 & 6.23 & 3.29 & 0 & 0 & 3.59 & 6.89 & 0.93 & 56.45 \\ OM & Tg a\({}^{-1}\) & 31.26 & 26.81 & 0 & 16.21 & 0 & 0 & 0.20 & 0 & 74.48 \\ SSALT & Tg a\({}^{-1}\) & 0 & 0 & 0 & 6,254.24 & 0 & 0 & 0 & 0 & 6,254.24 \\ SO2 & Tg a\({}^{-1}\) & 51.26 & 1.14 & 3.59 & 0 & 0 & 0 & 4.44 & 0.14 & 60.56 \\ \hline \end{tabular}
\end{table}
Table 1: Annual Total Emissions for Year 2014 in AM4.1 Dust emissions are calculated dynamically online in the land component, LM4.1, as a function of wind speed, topography, vegetation cover, snow cover, soil moisture, and land type, as described by [PERSON] et al. (2016).
As in AM3, direct stratospheric injection of SO\({}_{2}\) from volcanic eruptions and emissions of carbonyl sulfide (COS) are not considered in AM4.1. Instead, we specify time series of stratospheric aerosol optical properties, accounting for not only the volcanic contribution to stratospheric aerosol abundance but also other natural and anthropogenic contributions. Tropospheric emissions of SO\({}_{2}\) from continuously degassing and explosive volcanoes are treated in the same way as in AM3 ([PERSON] et al., 2011), with a climatological total of 3.59 Tg S a\({}^{-1}\).
## 3 Results: Physical Climate Simulation (AMIP, 1980-2014)
### Surface Air Temperature
Comparison of surface air temperature over land with observations from CRU TS (Figure 3) illustrates the substantial decrease in overall root mean square error (RMSE) achieved in AM4.1 (RMSE = 1.92\({}^{\circ}\)C) from the previous generation full-chemistry AM3 (RMSE = 2.18\({}^{\circ}\)C) and similar, if slightly degraded, pattern to AM4.0 (RMSE = 1.85\({}^{\circ}\)C). The most notable difference from AM3 to AM4.0 and AM4.1 is an improvement in boreal warm biases and South American cold biases.
### Precipitation
Comparison of precipitation with observations from GPCP v2.3 (Figure 4) also illustrates the substantial decrease in overall RMSE achieved in AM4.1 (RMSE = 0.83 mm d\({}^{-1}\)) from the previous generation full-chemistry AM3 (RMSE = 1.02 mm d\({}^{-1}\)) and a similar pattern to AM4.0 (RMSE = 0.85 mm d\({}^{-1}\)). The most notable difference from AM3 to AM4.0 and AM4.1 is an improvement in Amazon dry biases and in wet biases over Australia and the Indian Ocean.
Figure 2: Global annual totals (in Tg a\({}^{-1}\), using mass as indicated on y-axis label) for anthropogenic (fossil fuel + biomass burning + ship + aircraft) emissions of NO, CO, SO\({}_{2}\), NH\({}_{3}\), BC, and primary OM in AM3 (blue, CMIP5 emissions) and AM4.1 (red, CMIP6 emissions) AMIP simulations.
### Circulation
Comparison of zonal mean zonal winds with the ERA40 reanalysis (Figure 5) illustrates a substantial decrease in overall RMSE in AM4.1 (RMSE = 1.32 m s\({}^{-1}\)) from the previous generation high-top full-chem-istry AM3 (RMSE = 1.75 m s\({}^{-1}\)). The AM4.1 RMSE is greater than that in the low-top AM4.0 (RMSE = 1.00 m s\({}^{-1}\)), owing to a westerly wind bias in the equatorial stratosphere, and a weak, equatorward-shifted Arctic stratospheric jet in AM4.1. The representation of the stratospheric wintertime westerly polar jet associated with the Antarctic vortex is significantly improved in AM4.1 (not shown) compared with AM3 ([PERSON] et al., 2011), in which the westerlies were excessively strong (leading to a too-cold Antarctic vortex). We plan to work towards further improving the stratospheric circulation in future versions of AM4.1 through improvement in our representation of parameterized gravity wave drag. Tropospheric circulation patterns in AM4.1 are very similar to those in AM4.0.
Figure 3: Annual mean surface air temperatures (\({}^{\circ}\)C) in AM4.1 AMIP simulation (1980–2014) and CRU-TS-3.22 observations (1979–2013). Differences between simulated and observed surface air temperatures in AM4.1, AM4.0, and AM3 AMIP simulations.
### Stratospheric Variability
Comparison of statistics for sudden stratospheric warmings with the ERA40 reanalysis (Figure 6) illustrates an improvement in AM4.1 with respect to capturing events in the coldest months (December-January), which were largely missed in AM4.0 ([PERSON] et al., 2018), even though AM4.0 already performs quite well among low-top atmospheric models ([PERSON] et al., 2013). In the surrounding months (November, February), AM4.1 overestimates warming events, whereas AM4.0 matches the reanalysis data fairly well.
### Radiation Fluxes
Comparison of top-of-atmosphere (TOA) net radiation with CERES EBAF observations (Figure 7) illustrates the substantial decrease in overall root mean square error (RMSE) achieved in AM4.1 (RMSE = 7.2 W m\({}^{-2}\))
Figure 4: Annual mean precipitation (mm day\({}^{-1}\)) for 1980–2014 in AM4.1 AMIP simulation and GPCP v2.3 observations. Differences between simulated and observed precipitation in AM4.1, AM4.0, and AM3 AMIP simulations.
from the previous generation full-chemistry AM3 (RMSE = 8.6 W m\({}^{-2}\)) and similar, if slightly degraded, pattern to AM4.0 (RMSE = 6.8 W m\({}^{-2}\)). The most notable difference from AM3 to AM4.0 and AM4.1 is associated with an improvement in areas of tropical convection along the interotropical convergence zone (ITCZ) that had previously been too absorbing and increased absorption in northern boreal regions that had been previously too reflective, as discussed by [PERSON] et al. (2018). The most notable differences between AM4.0 and AM4.1 are associated with a decrease in the global TOA from a near-zero bias in AM3 (0.02 W m\({}^{-2}\)) to a slight negative bias in AM4.0 (\(-\)0.14 W m\({}^{-2}\)) and substantial low bias in AM4.1 (\(-\)0.80 W m\({}^{-2}\)). This increase in bias is due in part to the increased albedo of northern boreal regions associated with snow masking depth in LM4.1 ([PERSON], personal communication and also in part to differences over Antarctica associated with the prescribed albedo of snow on glaciers that was modified late in the development cycle of ESM4.1 to address Southern Ocean dynamics, as discussed by [PERSON] et al. (2020).
Figure 5: Annual mean zonal mean zonal wind (m s\({}^{-1}\)) in AM4.1 AMIP simulation (1980–2014) and ERA40 reanalysis (1981–2000). Differences between simulated and observed zonal winds in AM4.1, AM4.0, and AM3 AMIP simulations.
### Lightning Flash Frequency
Figure S1 shows the lightning flash frequency retrieved from the spaceborne Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) ([PERSON] et al., 2014), compared with simulated values from AM3 and AM4.1. In both AM3 and AM4.1, lightning flash frequency is parameterized as a function of convective cloud top height, following [PERSON] et al. (1997), but the two models use different parameterizations of cumulus convection ([PERSON] et al., 2018b). While the overall correlation between model and observations is lower in AM4.1 than AM3, there are some notable areas of improvement in the representation of flash frequency, including a reduction of the high biases present in AM3 over the Amazon and the maritime continent, improving agreement with observations.
## 4 Results: Simulation of Atmospheric Composition
### Ozone
In this section, we evaluate model simulations of ozone, including surface ozone concentrations relevant for air quality and column ozone abundances relevant for climate.
#### 4.1.1 Surface Ozone
We focus on the seasonal mean of the maximum daily 8-h average (MDA8) surface ozone over the period 2005-2014, when observations are available from densely clustered monitoring sites across northern mid-latitude populated regions (Figure 8 for MAM, Figure 9 for JJA). Observations were obtained from the Tropospheric Ozone Assessment Report (TOAR) Database for 2005-2014 ([PERSON] et al., 2017) and a monitoring network operated since 2013 by China's Ministry of Environmental Protection (CNMEP, [[http://106.37.208.233:20035/](http://106.37.208.233:20035/)]([http://106.37.208.233:20035/](http://106.37.208.233:20035/))). Observations are averaged onto the same 1\({}^{\circ}\)\(\times\) 1\({}^{\circ}\) grid as AM4.1. We compare simulated ozone from the AM4.1 AMIP simulation with that from the AM3 AMIP simulation.
Surface MDA8 ozone in AM3 is biased high by 12 ppb on average during MAM (Figure 8b) and by up to 20 ppb over the eastern U.S. during summer (Figure 9b), as documented in previous studies ([PERSON] et al., 2014; [PERSON], [PERSON], [PERSON], et al., 2012; [PERSON], [PERSON], [PERSON], et al., 2012; [PERSON] et al., 2017; [PERSON] et al., 2015). AM4.1 shows substantially reduced biases in mean ozone for both spring and summer over the eastern U.S. and Europe (Figures 8c and 9c). This dramatic improvement in the simulation of surface ozone concentrations results from a combination of updates to the chemical mechanism from AM3 to AM4.1, including updates to the isoprene oxidation scheme ([PERSON], [PERSON], et al., 2013) and the representation of heterogeneous reactions ([PERSON], [PERSON], et al., 2013), and the change from CMIP5 emissions in AM3 to CMIP6 emissions in AM4.1 (section 2.3). The shallow surface layer of the model (30 m thick) may also have an impact on the comparison with surface sites. [PERSON] et al. (2018a) found a significant improvement in diagnosed 2-m temperatures associated with this shallower surface layer.
To further explore the causes of the differences in surface ozone abundances between AM3 and AM4.1, we conduct two additional simulations--an AM4.1 simulation with nudged meteorology and an additional AM4.1 nudged simulation with AM3-like chemistry (AM4.1_AM3 Chem; [PERSON] et al., 2019). The two experiments use the same CMIP6 emissions and have nearly identical meteorology (as a result of the nudging), allowing us to isolate the influence of changes in chemistry alone. Seasonal-mean MDA8 ozone from these simulations are plotted in Figures S2-S5.
Similar to the results from AM3 (Figures 8b and 9b), surface MDA8 ozone in AM4.1_AM3 Chem is biased high by 11 ppb on average during spring (Figure S2b) and by up to 20 ppb over the eastern U.S. during summer (Figure S3b). Switching the chemistry scheme from AM3 to AM4.1 leads to substantial reductions in mean ozone biases for both spring and summer over the eastern U.S. and Europe (Figures S2c and S3c), but the model underestimates springtime MDAS ozone over central eastern China by 20 ppb (Figure S2c versus CNMEP observations in Figure S2a).
Figure 6: Monthly and annual (ANN) stratospheric sudden warming (SSW) frequency for 1870–2014 from AM4.0 and AM4.1, and 1957–2002 from ERA40. SSW is defined as in [PERSON] and [PERSON] (2007). Error bars indicate the 95% confidence interval (the statistical test of the SSW frequency is calculated as in [PERSON] et al., 2007).
Observations show more severe springtime ozone pollution over central eastern China and Mexico than in the U.S. and Europe. This regional contrast is not simulated in either of our experiments. Particularly, the enhanced heterogeneous chemistry in AM4.1 (section 2.2; [PERSON], [PERSON], et al., 2013; [PERSON], [PERSON], et al., 2013) likely leads to excessive heterogeneous loss of HOx and NOx radicals over eastern China and Mexico, where aerosol loadings are high during the spring season. For summer over the southeastern U.S., where high mean-state ozone biases are found in many current-generation CTMs and CCMs ([PERSON] et al., 2009; [PERSON] et al., 2018), the AM4.1 experiment shows remarkable agreement with observations. However, on the basis of analysis conducted for an intensive field campaign, [PERSON] et al. (2016) suggested that the common model biases in simulating summertime ozone over the southeastern U.S. may reflect a combination of excessive NOx emissions (too high by 50%) and the deep model surface layer that cannot resolve near-surface ozone gradients. A balanced view is needed to interpret the reduced ozone biases in the AM4.1 experiment.
Figure 7. Annual mean net radiation flux at top of atmosphere (W m\({}^{-2}\)) in AM4.1 AMP simulation (1980–2014) and CERES EBAF v2.8 observations (2000–2015). Differences between simulated and observed net radiation flux in AM4.1, AM4.0, and AM3 AMP simulations.
Our results suggest the complexity of various sources, sinks, transport, and chemistry in influencing the simulation of surface ozone. In the future, process-based assessments, not only for means but also for variability and extreme events, are needed to fully evaluate how the choices of different emission data sets, chemical mechanisms, and deposition schemes affect simulations of surface ozone and related tracers.
#### 4.1.2 **Tropospheric Ozone Column**
We compare climatological annual mean tropospheric ozone columns simulated by AM3 (mean over 2000-2008) and AM4.1 (2005-2014) with those derived from the OMI-MLS ([PERSON] et al., 2019) (Figure 10). In the analysis shown here, AM3's native ozone output on model levels is used to calculate tropospheric ozone
Figure 8: MAM mean surface MDA8 ozone mixing ratios (ppbv) for 2000–2008 from (a) TOAR observations regridded to the same \(1^{\circ}\times 1^{\circ}\) grid as AM4.1, (b) AM3 AMIP simulation, (c) AM4.1 AMIP simulation. Here, mn is the mean and rmsd is the root-mean-square deviation between observations and simulations.
column using the WMO tropopause definition, while for AM4.1, the tropospheric ozone column (tropoz) is diagnosed at every time step, by applying the WMO tropopause definition using model simulated temperature. The global mean tropospheric ozone columns simulated by AM3 and AM4.1 are 35 DU and 31 DU, respectively, compared to the OMI/MLS value of 30 DU. While AM3 showed consistent high biases globally except over the Antarctic, AM4.1 shows an interhemispheric pattern in the biases with high values in the Northern Hemisphere mid-latitudes and over continents and low values in the Southern Hemisphere extra-tropics. This pattern is consistent with global chemistry-climate models evaluated against the OMI/MLS climatology by [PERSON] et al. (2013) for a slightly different time period. An interesting feature in AM4.1 is the strong positive bias over Oceania, possibly related to the different
Figure 9: Same as Figure 8, but for JJA.
biomass burning emissions applied in the two models. AM3 exhibited an average high bias of 21.7%, which has been reduced to 7.3% in AM4.1; accordingly the RMSE has been reduced considerably, from 7.1 DU in AM3 to 4.6 DU in AM4.1.
#### 4.1.3 Total Ozone Column
Figure 11 shows the evaluation of modeled time series of total column ozone against two data sets for 1980-2015, namely, Multi-Satellite Merged Total Column NASA and NOAA product from Frith (2013; SBUV; open triangles) and version 3.4 of the National Institute of Water and Atmospheric Research--Bodeker Scientific (NIVA-BS; closed circles) total column ozone database. AM3 results are plotted for 1980-2008 period, while AM4.1 results are for 1980-2014. The comparison is shown for the annual average globally, in the tropics, and in southern and northern mid-latitudes, and for March in the Arctic and October in the Antarctic. Globally (Figure 11a), absolute values of total column ozone for AM3 were biased high compared to both data sets, whereas AM4.1, on the other hand, is biased low. Both models generally capture the trend in total column ozone, although the evaluation of AM3 is truncated at 2008. As suggested by the greater correlation coefficients for AM4.1 compared with AM3, AM4.1 is better able to capture the observed interannual variability and trends of global mean total column ozone. In the tropics (Figure 11b), total ozone column values remain lower than observed in AM4.1, as opposed to higher in AM3. Consistent with observations, both models simulate negligible trends in total column ozone in the tropics; however, AM4.1 exhibits greater skill in capturing the observed evolution of total column ozone. In the northern mid-latitudes (Figure 11c), AM4.1 differs more from observations than AM3 does, although with fairly similar skill in simulating the observed time evolution of total column ozone. The comparison is opposite for the southern mid-latitudes (Figure 11d), where AM4.1 is much closer to observed values than AM3 with similar correlations. In the Arctic in March (Figure 11e), AM4.1 reproduces the observed total ozone column values slightly better than AM3, however both have fairly low skill in reproducing the observed evolution. In the Antarctic in October (Figure 11f), AM4.1 exhibits greater skill in simulating ozone depletion compared to AM3 both in terms of trends and absolute values. This improvement likely results from the improved dynamical representation of the Antarctic polar vortex in AM4.1 (section 3). Overall, AM4.1 compares slightly better against observations of total column ozone than AM3.
Figure 10: Climatological mean tropospheric ozone column in AM3 (upper left; Dobson Units, DU), AM4.1 (lower left; DU), and the % bias compared to the OMI/MLS satellite estimate of the tropospheric Ozone Column ([PERSON] et al., 2019) for AM3 (upper right; %) and AM4.1 (lower right; %). RMSE is provided in DU.
### Carbon Monoxide
The simulated tropospheric CO columns are evaluated against CO retrievals from the MOPITT (Measurements of Pollution in The Troposphere) instrument in Figure 12. We use the MOPITT V8 Joint (NIR + TIR) retrievals ([PERSON] et al., 2019) during 2001-2014, which are available from the
Figure 11: Comparison of time series of total ozone column (DU) for the annual mean (a) global mean (90\({}^{\circ}\)S–90\({}^{\circ}\)N), (b) tropics (25\({}^{\circ}\)S–25\({}^{\circ}\)N), (c) northern mid-latitudes (35\({}^{\circ}\)N–60\({}^{\circ}\)N), (d) southern mid-latitudes (33\({}^{\circ}\)S–35\({}^{\circ}\)N), and for the (e) March mean in the Arctic (60\({}^{\circ}\)N–90\({}^{\circ}\)N), and (f) October mean in the Antarctic (60\({}^{\circ}\)S–90\({}^{\circ}\)S) from AM3 (red) and AM4.1 (blue) against NASA and NOAA observations from the multisatellite merged ozone total column ([PERSON], 2013) (SBUV; open triangles) and version 3.4 of the NIWA-BS total column ozone database ([PERSON] et al., 2005) (NIWA; closed circles). The numbers in each panel indicate linear correlation coefficient (\(R\)) for model against each of the measurement data sets (top for NIWA and bottom for SBUV).
NASA Earthqu archive ([[https://earthdata.nasa.gov](https://earthdata.nasa.gov)]([https://earthdata.nasa.gov](https://earthdata.nasa.gov))). The model is interpolated to the gridded monthly MOPITT observations and the averaging kernel for each grid is applied to the simulated monthly mean CO profiles.
The tropospheric CO columns are in general higher in AM4.1 than AM3, in better agreement with MOPITT retrievals in terms of magnitudes (RMSE reduced from \((2.6\)-\(2.7)\times 10^{17}\) cm\({}^{-2}\) to \((1.6\)-\(1.8)\times 10^{17}\) cm\({}^{-2}\)) and spatial distribution (\(r^{2}\) increased from 0.7-0.9 to 0.8-0.9). Compared to AM3, AM4.1 reduces the underestimations in column CO in the Northern Hemisphere, but overestimates column CO in the Southern Hemisphere, especially during summer. This is in part due to lower OH levels in AM4.1 than AM3.
To evaluate surface CO, we use measurements from a globally distributed network of air sampling sites maintained by the Global Monitoring Laboratory (GML) of the National Oceanic and Atmospheric Administration (NOAA) ([PERSON] et al., 2019; data available at [[ftp://aftp.cmdl.noaa.gov/data/trace_gases/co/flask/](ftp://aftp.cmdl.noaa.gov/data/trace_gases/co/flask/)]([ftp://aftp.cmdl.noaa.gov/data/trace_gases/co/flask/](ftp://aftp.cmdl.noaa.gov/data/trace_gases/co/flask/))). Surface CO observations during 1988-2014 are used to evaluate model performance (Figure 13).
AM4.1 simulates higher surface CO concentrations than AM3 over the Southern Hemisphere, and slightly overestimates surface CO concentrations by \(<\)5 ppb when compared to surface observations. Over the Northern Hemisphere, AM4.1 largely reduces the negative biases that occurred in AM3, with a mean bias of \(\pm 20\) ppb over most GMD sites. This is consistent with the comparisons to the MOPITT retrievals shown above. In addition, compared to AM3, AM4.1 better captures the seasonal cycles (with correlation coefficient \(R>0.5\)) at most sites and better captures the latitudinal gradient as well (\(R=1.0\) versus \(R=0.9\)).
Comparisons of surface CO concentrations over pristine sites show significant improvement in AM4.1 over AM3 across latitudes from South to North. In the Southern Hemisphere, such as at South Pole (SPO), Ushuaia (USH), and Easter Island (EIC) sites, the underestimation of surface CO concentrations by AM3 are reduced in AM4.1. In the Northern Hemisphere, such as at Mauna Loa (MLO), Barrow (BRW), and Alert (ALT) sites, both surface concentrations and monthly variations are improved significantly in AM4.1 compared to AM3. These improvements are mainly associated with improved chemistry in AM4.1.
Figure 12. Absolute difference in tropospheric CO column between AM3 and MOPITT (left panel) and AM4.1 and MOPITT (right panel) for winter (December-January–February, DJF, top) and summer (June–July–August, JJA, bottom).
### Aerosols
We first evaluate concentrations of aerosols in surface air. Figure 14 (top panels) compare simulated concentrations of sulfate and nitrate aerosols from AM4.1 with observations over the United States from the IMPROVE network. The model successfully captures the wide range of observed sulfate aerosol concentrations. While nitrate concentrations are well correlated with observations (\(R=0.74\)), simulated concentrations are generally too high (normalized mean bias [NMB] \(=+80\%\)). This bias is larger than in [PERSON] et al. (2016), where nitrate aerosols are assumed to deposit rapidly like nitric acid. Simulated concentrations of sulfate and nitrate in precipitation are compared with observations from the NADP network in the lower panels of Figure 14. The rainwater abundances of sulfate and nitrate are well correlated with observations, but with a low bias for sulfate (NMB \(=-19\%\)) and a high bias for nitrate (NMB \(=+35\%\)).
Figure 15 compares simulated concentrations of sulfate, dust, and sea salt aerosols from AM3, AM4.0, and AM4.1 with observations from the University of Miami network ([PERSON], 1977). The model successfully captures the wide range of observed sulfate aerosol concentrations. For sulfate, the RMS error versus observations is reduced in AM4.1 (0.20 \(\mu\)g m\({}^{-3}\)) from AM3 and AM4.0 (both 0.22 \(\mu\)g m\({}^{-3}\)), and the correlation is improved (\(r=0.93\) in AM4.1, \(r=0.89\) in AM3 and AM4.0). The agreement between simulated and observed dust improves from AM3 to AM4.0, but then degrades in AM4.1, reflecting the shift from prescribed to interactive source regions for dust in LM4.1. The RMSE for simulated sea salt is reduced significantly in AM4.1 (0.35 \(\mu\)g m\({}^{-3}\)) compared with AM3 (0.47 \(\mu\)g m\({}^{-3}\)) and AM4.0 (0.49 \(\mu\)g m\({}^{-3}\)), as a result of updates to the emissions and deposition parameterizations in AM4.1.
We next evaluate the simulated AOD against measurements from the AERONET sunphotometer network ([PERSON] et al., 1998) in Figure 16. Here we use the quality assured and cloud screened level 2 version 2 AOD data ([PERSON] et al., 2000). For comparison, we also show the results from AM4.0 (middle) and AM3 (bottom). Both AM4.0 and AM4.1 exhibit higher correlation (0.89 and 0.9) and lower RMS (0.07 and 0.08) with AERONET observations than AM3 (0.81 and 0.09, respectively). In particular, the large positive biases in the tropics and equatorial regions are reduced, which reflects the more efficient removal of aerosol by convective precipitation ([PERSON] et al., 2016). AM4.1 exhibits a greater positive bias than AM4.0 over the Midwest United States, associated with higher dust loading and nitrate aerosol (not included in AM3 and AM4.0).
Figure 13: Comparison of surface CO mixing ratios (ppbv) from AM4.1 (red) and AM3 (blue) against NOAA Global Monitoring Division (GMD) flask observations ([PERSON] et al., 2019, for 1988–2014). Left panels show model bias (top) and correlation coefficient (bottom) versus observations, plotted by station latitude. Right panels show monthly time series comparisons at selection stations. The root mean square error (RMSE) and correlation coefficient (\(R\)) are indicated on plots.
Figures 17 and S6 and compare the regional monthly mean AOD simulated by AM3, AM4.0, and AM4.1 with observations from the MODIS ([PERSON] et al., 2007) and MISR ([PERSON] et al., 2009) instruments. AM4.0 and AM4.1 have reduced the seasonal contrast between winter and summer months, in better agreement with observational constraints. The spring maximum over East Asia and the North Pacific is also better captured with AM4.0 and AM4.1. The AM3 high biases over the Caribbean Sea and maritime continent are reduced consistent with the comparison against AERONET.
These improvements primarily reflect changes in the treatment of aerosol removal, including reduced removal by frozen precipitation formed by the Bergeron process and more efficient scavenging by convective precipitation ([PERSON] et al., 2016). AM4.1 exhibits greater bias over Asia than AM4.0, which primarily reflects higher optical depth from dust and ammonium nitrate. Uncertainties in Asian SO2 and NH3 emissions ([PERSON] et al., 2009) and aerosol hygroscopic growth may also contribute to the AM4.1 high bias over this region ([PERSON] et al., 2018).
Figure 14.— Comparison of AM4.1 (2000–2014) against IMPROVE (a,b) and NADP (c,d) observations of concentrations in surface air (top) and in precipitation (bottom) of sulfate (left) and nitrate (right).
Figure 15: Comparison of simulated (AM3, 1979–2008; AM4.0, 1980–2014; and AM4.1, 1980–2014) and observed (University of Miami) annual mean surface concentrations (\(\rm{ag\ m^{-3}}\)) of (first row) sulfate, (second row) dust, and (third row) sea salt sodium at 28 locations and (bottom) their ratios (simulated/observed) at each location (for AM4.1 only). Shaded contours indicate simulated surface concentrations (top colorbar) and symbols indicate the ratio of simulated/observed concentrations (bottom colorbar, symbol points upwards if ratio greater than one, downwards if less than one).
Figure 16: Comparison of simulated aerosol optical depths (550 nm) with AERONET observations over the 2000–2014 period for (top) AM4.1, (middle) AM4.0, and (bottom) AM3 AMIP simulation. Dashed lines in left panels denote slopes of 0.5 and 2. Color in right panels shows the percentage difference between model and AERONET (i.e., \(100\%\times[\text{model}-\text{AERONET}]/\text{AERONET}\)).
### Hydroxyl Radical (OH) and Methane Lifetime
Here, we evaluate the climatological mean hydroxyl (OH) radical simulated by AM4.1, as OH is the primary atmospheric oxidant determining the abundance and lifetime of several short-lived climate forces, including methane. The simulation of OH depends on the chemical mechanism, particularly the representation of isoprene photoxidation ([PERSON] et al., 2010; [PERSON], 2019). Differences in emissions, meteorology, and photochemical mechanisms across models also lead to differences in OH ([PERSON] et al., 2020). Climatological mean (1980-2014) global airmass-weighted tropospheric OH simulated by AM4.1 is \(10.4\times 10^{5}\) molecules cm\({}^{-3}\), about 18% lower than that simulated by AM3, but is within the range of values reported for ACCMIP models for the 2000s ([PERSON], [PERSON], et al., 2013). Consequently, the mean whole-atmosphere chemical lifetime of methane (calculated as the global methane burden divided by global total loss) in AM4.1 is 8.5 years; lifetime against loss by reaction with tropospheric OH is 9.7 years, which is 13% greater than the AM3 value of 8.6 years (1981-2000), but still lower than the observationally derived estimate of \(11.2\pm 1.3\) years ([PERSON] et al., 2012). Figure 18 shows the comparison of tropospheric OH distribution for 12 regions simulated by AM4.1 with estimates from AM3, ACCMIP ensemble mean, and the climatology of
Figure 17: Monthly climatology (2003–2014) of aerosol optical depth simulated by AM3 (purple line), AM4.0 (green line) and AM4.1 (orange line) and measured by MODIS (TERRA: star, AQUA: cross) and MISR (filled circles) satellite instruments. Each panel represents a spatial average over the corresponding region on the background map. The numbers in each box show the correlation coefficients (left) and normalized root mean square error (right) compared to MODIS-TERRA (purple: AM3, green: AM4.0, orange: AM4.1).
[PERSON] et al. (2000). AM4.1 simulates reduced OH levels compared to AM3 throughout the troposphere, possibly because of differences in emissions and chemical mechanisms between the two model versions. In particular, the lower lightning NO\({}_{\rm x}\) in AM4.1 versus AM3 acts to lower OH because of the strong sensitivity of OH to lightning NO\({}_{\rm x}\) emissions ([PERSON] et al., 2013). Relative to the [PERSON] et al. climatology, AM4.1 exhibits a reduced high bias compared with AM3, but has too low OH, particularly in the tropical upper troposphere.
## 5 Sensitivities to Greenhouse Gases, Aerosols, and SST Perturbations
Table 2 shows the net radiative flux perturbations that result from historical changes in anthropogenic forcing agents and from idealized changes in CO\({}_{2}\) and SST. Comparison of these radiative metrics between AM3, AM4.0 and AM4.1 indicates that effective radiative forcings (ERF) from preindustrial to present-day changes in greenhouse gases and aerosols are nearly identical between AM4.0 and AM4.1. However, the ERF from quadruping CO\({}_{2}\) is significantly lower in AM4.1, mostly because of the inclusion of interactive ozone (colder stratospheric temperatures reduce the rate of ozone chemical loss) but also partially resulting from increased dust emissions from LM4.1 (related to increased fires under elevated-CO\({}_{2}\) conditions). The Cess feedback, the change in net radiative flux resulting from an increase of SSTs by 2K, is significantly more negative in ESM4.1 (corresponding to a weaker Cess sensitivity), likely resulting from increased emissions of salt, dust, and BVOCs with increasing temperatures in ESM4.1. While comparison with previous-generation models is complicated by changes in the AMIP configuration since the AM3 model simulations were conducted (in particular, updating the \"present-day\" conditions from representing 1990 conditions to 2014 conditions), some assessment of these differences can be made using AM4.0 simulations conducted for 1990 conditions (as in [PERSON] et al., 2018a). The most important differences between AM3 and AM4.0 are a
Figure 18: Climatological (1980–2014) annual mean airmass-weighted tropospheric OH concentration averaged globally (top-most row) and regionally for individual atmospheric subdomains from AM4.1 (black) compared with those from AM3 (1980–2008, red), ACCMIP ensemble mean (orange), and climatological mean values from [PERSON] et al. (2000) (purple). Values for AM4.1 and AM3 also show \(+/-\) standard deviation about the mean.
decrease in the magnitude of the negative aerosol ERF from AM3 to AM4.0, an increase in the 4 xCO2 ERF consistent with an update to the treatment of CO\({}_{2}\) radiative bands ([PERSON] et al., 2018b), and a strengthening of the negative Cess feedback. The decrease in the magnitude of the aerosol ERF from AM3 to AM4.0 has been attributed by [PERSON] et al. (2018b) to a decrease in the strength of the aerosol indirect effect, resulting from the increase in horizontal resolution and improvements to the representations of aerosol convective wet deposition ([PERSON] et al., 2016) and aerosol activation.
## 6 Summary
AM4.1 includes considerable advances in resolution and physics as in AM4.0 ([PERSON] et al., 2018a, 2018b) as well as a comprehensively revised suite of chemistry parameterizations to improve consistency in treatment across species and with advances in the underlying science over the last decade. AM4.1 is able to maintain the fidelity of AM4.0 while substantially increasing in comprehensiveness and associated climate-chemistry interactions and feedbacks. This development effort has also led to considerable improvement in model fidelity compared to GFDL's previous-generation coupled chemistry-climate model (AM3) with respect to observed atmospheric composition for aerosol, CO, ozone, as well as climate phenomena such as sudden stratospheric warnings.
## Data Availability Statement
Data are provided at 10.22033/ESGF/CMIP6.1407. Model code is provided at [[https://data1.gfdl.noaa.gov/nomads/forms/esm4/](https://data1.gfdl.noaa.gov/nomads/forms/esm4/)]([https://data1.gfdl.noaa.gov/nomads/forms/esm4/](https://data1.gfdl.noaa.gov/nomads/forms/esm4/)). The input data are provided at [[ftp://data1.gfdl.noaa.gov/users/ESM4/ESM4](ftp://data1.gfdl.noaa.gov/users/ESM4/ESM4) Documentation/GFDL-ESM4/inputData/ESM4_rundir.tar.gz]([ftp://data1.gfdl.noaa.gov/users/ESM4/ESM4](ftp://data1.gfdl.noaa.gov/users/ESM4/ESM4) Documentation/GFDL-ESM4/inputData/ESM4_rundir.tar.gz).
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wiley/fe77ce08_d16e_4b2b_bf7f_6e687fab8cfc.md | # IGR Oceans
Research Article
10.1029/2023 JC020013
[PERSON]\({}^{1,2}\), [PERSON]\({}^{2}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{1,3}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{2}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{2}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{2}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{2}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
[PERSON]\({}^{1}\)
\({}^{1}\)Ocean University of China, Qingdao, China, \({}^{2}\)Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), Bremerhaven, Germany, \({}^{3}\)Jacobs University, Bremen, Germany
###### Abstract
Despite the importance of the Arctic Ocean for the large-scale circulation and climate, there is still a knowledge gap in our understanding of the spatial characteristics of the Arctic Ocean circulation, especially for the mesoscale. This paper investigates the spatial characteristics of the Arctic Ocean circulation using a simulation with 1 km horizontal resolution. We revealed that there are two peaks in the kinetic energy (KE) spectral density at the 400 m depth, one at the gyre scale of the Arctic Circumpolar Boundary Current (centered at 1,700-2,000 km), and the other associated with the mesoscale (at about 60 km). However, at the 70 m depth, the boundary currents tend to mask the spectrum peak associated with the mesoscale. The KE spectrum exhibits a power-law scaling typical for ocean eddies. We found that about 80% (50%) of the KE is on scales smaller than 100 km (30 km). The maximum KE content is in the 10-20 km scale band in most of the eddy-rich regions of the abyssal ocean. The seasonality of the KE spectrum and KE content inside the Arctic Ocean follow the seasonality of eddy activity and baroclinicity, with low values in spring and maxima in late summer to autumn, and the seasonal variation is stronger at the 70 m depth than the 400 m depth. The strong concentration of KE on the very small spatial scales warrants future studies on energy transfer between scales in the Arctic Ocean.
## Plain Language Summary
We identified the two dominant spatial scales of the Arctic Ocean circulation, the gyre scale of the Arctic boundary currents and the mesoscale, on the energy spectrum of the Arctic Ocean circulation. We found that most of the kinetic energy in the Arctic Ocean is on scales smaller than 100 km, and about half of the kinetic energy is on scales smaller than 30 km. The findings help improve our understanding of the spatial characteristics of the Arctic Ocean circulation and kinetic energy.
## 1 Introduction
The Arctic Ocean has a strong halocline that insulates the cold mixed layer and sea ice above from the underlying warm Atlantic Water layer ([PERSON] et al., 1996). The Arctic Circumpolar Boundary Current, as one of the major large-scale circulations in the Arctic Ocean, has an Arctic shelf break branch in the halocline and a Fram Strait branch in the Atlantic Water layer ([PERSON] et al., 2011; [PERSON], 2002; [PERSON], 2012). The maintenance of the Arctic halocline and the Atlantic Water layer circulation is contributed by mixing induced by mesoscale eddies ([PERSON], 2013), while eddy formation hotspots in the Arctic Ocean are along the Arctic boundary currents ([PERSON] et al., 2012; [PERSON] et al., 2005; [PERSON] et al., 2018; [PERSON] et al., 2008; [PERSON] et al., 2020; [PERSON] et al., 2014).
Available observations, despite being sparse in space and time, indicate that mesoscale eddies are ubiquitous in the Arctic Ocean, including the halocline and the depth range of the Atlantic Water layer ([PERSON] and [PERSON], 1985; [PERSON] et al., 2018; [PERSON] et al., 2008; [PERSON] et al., 2001; [PERSON] et al., 2014, 2016; [PERSON] and [PERSON], 2015). Some recent studies investigated the role of Arctic Ocean eddies using eddy-permitting or eddy-resolving model simulations ([PERSON] and [PERSON], 2022; [PERSON] et al., 2021; [PERSON] et al., 2020). Both model simulations and observations indicate that Arctic eddy activity is highest in Fram Strait and along topography slopes inside the Arctic Ocean, including the Eurasian continental slope, the Lomonosov Ridge and the western Arctic continental slope ([PERSON] et al., 2020).
Ocean kinetic energy (KE) is distributed over a wide range of spatial scales, covering large and gyre scales, mesoscale and even smaller scales. Currently there is a lack of understanding of the spatial scales of Arctic Ocean KE, and in general there is a great challenge in studying the mesoscale in the Arctic Ocean. Firstly, there are no sufficient observations of eddies in the Arctic due to sea ice cover and very limited instruments ([PERSON] et al., 2022). The issue of data scarcity is further complicated by the small horizontal scales of mesoscale dynamics in high-latitude regions, with the first baroclinic Rossby radius of deformation around 7-15 km in the
## 2 Data and Methodology
### Model Simulation at 1 km Resolution
The model data used here is from the Finite-Element/volumE Sea ice-Ocean Model version2 (FESOM2) simulation. FESOM2 is a multi-resolution sea ice-ocean model that solves the ocean primitive equations on unstructured meshes ([PERSON] et al., 2017). Its sea ice module is formulated on the same unstructured meshes as the ocean ([PERSON] et al., 2015). FESOM2 can reasonably represent the global ocean and sea ice ([PERSON] et al., 2019; [PERSON] et al., 2019, 2022; [PERSON] et al., 2024).
The model configuration has horizontal resolutions of 1 km in the Arctic and 30 km in the rest of the global ocean. In the vertical it has 70 \(\mathrm{\SIUnitSymbol2}\)-levels with 5-m spacing in the upper 100 m. It is driven by the atmospheric reanalysis fields from ERA5 ([PERSON] et al., 2020). Free-slip boundary condition was used at the ocean boundary. The simulation was initialized from the PHC3 climatology ([PERSON] et al., 2001) starting from 2010 and has been run for 11 years. The first 4 years are considered model spinup and the last 7 years (2014-2020) are analyzed in this study. The snapshots of ocean current speed and relative vorticity in Figure 1 obtained from this model simulation clearly indicate the eddy activities in the Arctic Ocean, with a spatial pattern consistent with previous studies ([PERSON] et al., 2020; [PERSON] et al., 2022).
The Arctic Ocean in this study is defined as the region north of \(77^{\circ}\mathrm{N}\) in the Fram Strait, east of \(20^{\circ}\mathrm{E}\) in the Barents Sea Opening, and north of the Bering Strait, which has 1 km horizontal resolution (inset in Figure 1a).
### Coarse-Graining Method
We employ the coarse-graining method proposed by [PERSON] (2019) to study the spatial scales of the Arctic Ocean circulation. This method has been successfully applied to understand the multiscale dynamics of the ocean ([PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON] & [PERSON], 2018; [PERSON] et al., 2020; [PERSON] et al., 2022). Coarse-graining can be considered a \"blurring\" process (analogized with taking off one's glasses to have a blurrier picture) ([PERSON] et al., 2022). Mathematically, its main idea is to apply a low-pass filter with a convolution approach.
First, we define the convolution kernel \(G\) centered at point \(\mathbf{x}\) for the scale \(\ell\),\[G_{\ell}(\mathbf{r})=\frac{A}{2}[1-\tanh((|\mathbf{r}|-\ell^{\prime}/2)/S_{\
u})], \tag{1}\]
where \(|\mathbf{r}|\) is the geodesic distance from the point \(\mathbf{x}\), the transition scale \(S_{\
u}=2\) km, and \(A\) is the normalization factor that guarantees \(\sum G_{\ell}(r)=1\) (where the sum is over all the elements of the matrix) ([PERSON], 2019; [PERSON] et al., 2021). Then one can obtain the low-pass filtered field \(\overline{\varphi}\) after the convolution operation (*) over the original field \(\varphi\) as
\[\overline{\varphi}_{\ell^{\prime}}=G_{\ell}*\varphi. \tag{2}\]
\(\overline{\varphi}_{\ell^{\prime}}\) contains length scales larger than \(\ell\).
\(G_{\ell}(\mathbf{r})\)is expected to be uniform when \(|\mathbf{r}|\) is smaller than \(\ell/2\) and smoothly decrease to zero when \(|\mathbf{r}|\) approaches \(\ell/2\). As we will calculate the coarse-grained field \(\overline{\varphi}_{\ell^{\prime}}\) at scales as small as a few kilometers, the value of \(S_{\
u}\) is chosen to be small as well.
Before the coarse-graining is performed, we transformed the spherical coordinate so that the Arctic Ocean is centered at the equator. That is, in the new coordinate, the equator crosses the center of the Arctic Ocean, and the Arctic Ocean spans a latitude range of about \(\pm 20\). In this case, we can coarse-grain the two velocity components separately, with the spherical effect, the impact of the metric term, neglected. When analyzing a large domain such as the global ocean or studying energy transfer across scales, one needs to employ Helmholtz decomposition before performing convolution ([PERSON], 2019), or use implicit filters by solving Laplacian equations formulated in spherical coordinates ([PERSON] et al., 2024).
### Kinetic Energy Spectrum and Content
After obtaining the coarse-grained velocity \(\overline{\mathbf{u}}_{\ell}\) from daily velocity fields, the coarse KE contained in scales larger than \(\ell^{\prime}\) is calculated as
\[\mathcal{E}_{\ell^{\prime}}=\frac{1}{2}|\overline{\mathbf{u}}_{\ell}(\mathbf{ x},\,t)|^{2}. \tag{3}\]
Figure 1: Eddies are ubiquitous in the Arctic Ocean. A snapshot on 1 October 2017 from FESOME 1 km-resolution simulations: (a) ocean current speed at 70 m depth and (b) Rossby number at the same depth. Several regions of high eddy activity studied in this paper are denoted by boxes in (b), including Fram Strait (black), central Nansen Basin (purple), east Eurasian Basin (blue), Makarov Basin (yellow), Chukchi Borderland (red) and Beaufort Sea (green). Note that 1 km resolution is only applied inside the Arctic Ocean in the global simulation. The inset in (a) shows the horizontal resolution and the locations of the Arctic boundary defined in this study.
## 3 Results
### Kinetic Energy Spectrum and Power Spectral Density Peaks
In this study, we focus on the 70 and 400 m depths, representing the upper halocline and the Atlantic Water layer, respectively. The upper depth is consistent with the typical core depths of eddies in the halocline observed by mooring instruments and Ice Tethered Proffers ([PERSON] and [PERSON], 2015; [PERSON] et al., 2014, 2016). The warm Atlantic water layer is located in the depth range of approximately 150-800 m, with maximum temperature in the depth range of 200-400 and 400-600 m in the Eurasian Basin and Amerasian Basin, respectively ([PERSON] et al., 2024). Therefore, we choose 400 m depth to represent the Atlantic Water layer in our analysis.
Figure 2 shows an example of applying coarse-graining to the velocity at 70 and 400 m depths on 1 st October 2017. The used filter scale is 100 km. The low-pass filtered velocity (Figures 1(a) and 1(c)) depicts the large-scale circulation in the Arctic, including the inflow through Fram Strait and the Barents Sea in the Atlantic sector, the cyclonic circumpolar boundary current along the continental slope, and the return flow along the Lomonosov Ridge, consistent with what we know about the Arctic Ocean circulation ([PERSON] et al., 2011; [PERSON] and [PERSON], 2002; [PERSON], 2012; [PERSON] and [PERSON], 2020; [PERSON] and [PERSON], 2022). Meanwhile, the fine-scale velocity (Figures 1(b) and 1(d)) presents the flows at the scales smaller than 100 km. In the deep basin area, the fine-scale flows are dominated by mesoscale eddies in the vicinity of continental slopes in both the western and eastern Arctic, over the Chukchi Borderland and along the Lomonosov Ridge of the Siberian continental shelf, consistent with the eddy field shown by relative vorticity on the same day (Figure 0(b)). The above example illustrates the success of the method in separating the flow spatial scales. Note that, in the Barents Sea, the first baroclinic Rossby radius is smaller than in the deep basin ([PERSON] and [PERSON], 2014; [PERSON] and [PERSON], 2020) and 1 km resolution might be insufficient for fully resolving mesoscale eddies.
As shown in Figure 3, the KE spectral scaling for both the 70 m depth and the 400 m depth lies between \(k^{-5/3}\) and \(k^{-3}\) for wavenumbers larger than \(3\times 10^{-2}\) km\({}^{-1}\) (i.e., smaller than about 30 km in scales), a typical power-law scaling range at mesoscales and smaller scales in the geophysical flow ([PERSON] and [PERSON], 2009). In lower
Figure 2: Gyre-scale and mesoscale flows of the Arctic Ocean for the day on 01 October 2017 obtained from the coarse-graining method. Velocity magnitude for (a) spatial scales larger than 100 km and (b) smaller than 100 km at 70 m depth. (c) and (d) are same as (a) and (b), but at 400 m depth. White contours in (a) (c) denote the streamlines of the coarsened velocity, with arrows showing the direction of the flow.
postsess mesoscale peaks at the spatial scale of approximately 60 km for the 70 m depth (see Section 3.4). This implies that it is the inclusion of the boundary currents when analyzing the whole Arctic domain that masks the mesoscale peak for the 70 m depth in Figure 3. When the boundary currents are relatively strong as they are at the 70 m depth (Figure 2a), the KE spectrum does not drop from 60 to 200 km (Figure 3, red line). At 400 m depth on the other hand, the boundary currents are relatively weaker, so the mesoscale peak is visible in the KE spectrum (Figure 3, black line).
As we can see in Figures 2b and 2d, after removing the velocity coarsened at 100 km, the remaining velocity is dominated by eddies and filaments. We therefore also calculated the KE spectrum by first removing velocity coarser than 100 km. In this case, spectrum peaks are present for both depths and located at about 60 km (Figure 3, orange and blue lines). Removing velocity coarsened at 100 km before analyzing the spectrum effectively eliminates the impact of boundary currents during the coarse-graining. We note that the exact information on the location of spectrum peaks associated with mesoscale eddies should rely on analysis performed for small regions excluding boundary currents as we did in Section 3.4. Our test here by removing the velocity coarsened at 100 km serves as an illustration about the impact of boundary currents on the spectrum. The fact that the obtained peaks are located at 60 km, the same as the results of analysis for small regions, indicates that the energy associated with boundary currents is largely removed with the choice of the scale of 100 km. This choice was made to have results consistent with analysis of small regions shown in Section 3.4.
The KE spectrum has another peak in the range of 1,700-2,000 km for both the depths considered (Figure 3). This scale can be considered the mean gyre scale of the Arctic-wide boundary currents. Being able to reveal both the mesocales and gyre scales in the KE spectrum is one of the advantages of the coarse-graining method ([PERSON] et al., 2022). However, as shown above, the spectrum peak representing the upper bound range of mesoscales is rather absent for the Arctic flow at the 70 m depth due to the relatively strong boundary current and relatively weak eddy intensity in the Arctic. This issue is not present for lower latitudes where eddy intensity is relatively high ([PERSON] et al., 2022).
### Kinetic Energy Content in Scale Bands
Figure 4 shows that the scales smaller than 10 km contains the highest KE among all the 10 km scale bands for the 70 m depth, while the 10-20 km band has the highest KE at the 400 m depth. On scales larger than 20 km, the KE content decreases with the increase in the scales for both the depths considered. At the 70 m depth, 47% of the total KE is contained in the scale band smaller than 30 km, 22% in the scale band of 30-60 km, 12% in the scale band of 60-100 km, and the remaining 19% in all scales larger than 100 km. The KE content distribution for the 400 m
Figure 3: Kinetic energy (KE) spectrum for the Arctic Ocean at 70 m (red) and 400 m (black) depths. The KE spectra are also computed from the fine velocity after removing velocity coarser than 100 km scale, as shown by orange and blue lines for the two depths. The results are averaged over 7 years (2014-2020). Shading colors are inter-quartile range (25 th-75 th percentiles) of temporal variation. The two gray lines indicate the slopes of \(k^{-50}\) and \(k^{-3}\), respectively.
depth similarly shows that more than 80% of the KE is contained in scales smaller than 100 km and nearly 50% in scales smaller than 30 km.
With the traditional method such as Fourier analysis, one only gets spectrum plots like our Figure 3. One major advantage of the coarse-graining method is that it preserves the 2D information of the filtered fields and thus allows us to analyze maps of KE contained in different scale bands as defined in Equation 5. The result is shown in Figure 5. In the three scale bands below 100 km, KE is mainly distributed in the vicinity of the circumpolar boundary current and Lomonosov Ridge, and over the Chukchi Borderland, consistent with the spatial distribution of eddies (Figures 1 and 2). These are the regions where previous studies have shown high conversion from eddy available potential energy to eddy kinetic energy ([PERSON] et al., 2020). Figure 4 shows that the KE content in the three scale-bands decreases with the increase in the scale. Figure 5 further demonstrates that this relation applies to all the areas with high KE content. In the scales above 100 km, the highest KE is associated with the main currents. The KE spatial distributions in each scale-band are similar between the two ocean depths.
### Seasonality of Kinetic Energy Spectrum and Content
There is a clear seasonal variation in the KE spectrum at the 70 m depth (Figure 6a). The spectrum value is lower in spring and higher in late summer to autumn for all wavenumbers larger than \(10^{-2}\). Accordingly, the slope of the spectrum is steeper from late summer to autumn. The spectrum peak is located at about 60 km all year round. At the 400 m depth, the seasonal variation in the KE spectrum has a phase similar to the 70 m depth, but with a clearly smaller magnitude. The fact that the spectrum peak is located in the same period (September-October) for all spatial scales (Figure 6a) indicates that there is no clear spectral lag time inside the Arctic Ocean, different from what was found for the lower latitudes of the global ocean ([PERSON] et al., 2022). The exact reasons for the spectral lag time in the global ocean is not yet fully understood ([PERSON] et al., 2022) and the difference of the Arctic Ocean also remains an open question.
The KE content in different scale bands has a seasonal variation phase similar to that of the KE spectrum, and the magnitude of the seasonal variation is much stronger at the 70 m depth than at the 400 m depth (Figure 6b). In all months, the KE content is the highest in the scale band of 10-20 km at the 400 m depth and in the scale band of 1-10 km at the 70 m depth, and further decreases with the increase in the scales.
The seasonal variation in the KE spectrum and content is consistent with that of the EKE in the halocline and Atlantic Water layer of the Arctic Ocean ([PERSON] et al., 2022; [PERSON] et al., 2020), which can be attributed to the seasonal variation in the conversion rate from eddy available potential energy to EKE ([PERSON] et al., 2020). Sea ice cover can dissipate existing eddies and prevent the growth of eddies, so the seasonal variation of EKE in the upper few tens of meters is expected to follow the seasonal changes in sea ice cover ([PERSON] et al., 2021). However, for ocean depth below about 50 m, the direct impact of sea ice on eddy activity is small, so the variability of EKE is largely determined by the baroclinic energy conversion rate. Therefore, the seasonal variation of the KE spectrum and content for the two depths considered here is not correlated with sea ice cover seasonal changes.
### Kinetic Energy Spectra and Contents in Eddy-Rich Regions
The seasonal variability of KE spectrum and content at 70 m depth is shown in Figure 7 for six eddy-rich regions, including Fram Strait (the deepest Arctic Ocean gateway) and five regions inside the Arctic Ocean. The locations of the six regions are shown in Figure 1b. For these regions, the spectrum peak is similarly located at the scale of about 60 km, and the spectral scaling lies between \(k^{-5/3}\) and \(k^{-3}\) for wavenumbers larger than 3 \(\times\)\(10^{-2}\) km\({}^{-1}\) (Figure 7, left column). These properties are the same as the Arctic-wide mean properties (Figure 3). The spectrum magnitudes are different among the regions, with the Beaufort Sea region showing the largest magnitude inside the Arctic, exceeded only by the spectrum magnitude in Fram Strait. Note that, we don't need to
Figure 4: Kinetic energy (KE) content in different spatial-scale bands for 70 m depth (solid blue line) and 400 m depth (dashed blue line). The respective cumulative energy contents (in percentage) are also shown in red lines with y axis on the right side. The KE contained the scale bands of 1–30 km, 30–60 km, and 60–100 km for 70 m depth is indicated on the top of the plot. Note that the scales bins are 10 km wide below 100 km and go higher beyond. The result is averaged over 7 years (2014–2020).
remove the velocity coarser than 100 km when doing coarse-graining for the selected subdomains, as we strategically excluded the boundary currents in the analysis of subdomains.
The seasonal variability of the KE spectrum at 70 m depth in the five eddy-rich regions inside the Arctic Ocean is similar, with low values in spring and the maximum located in late summer to autumn as in the Arctic-wide mean seasonality (Figure 7, middle column). In the Fram Strait, the KE spectrum seasonality is different from that inside the Arctic Ocean. Here, the maximum spectrum peak value occurs in winter, consistent with the seasonality of the EKE in this region, which is elevated by increased baroclinic instability associated with the increase in mixed layer depth in winter ([PERSON] et al., 2016; [PERSON] et al., 2017, 2020).
The KE content shows a seasonality similar to that of the KE spectrum (Figure 7, right column). In most regions, the KE content has a maximum in the 10-20 km scale band and decreases with the increase in the spatial scale.
Figure 5: Spatial distribution of KE in different scale bands following Equation 5 at 70 m depth (a–d) and 400 m depth (e–h). The result is averaged over 7 years (2014–2020).
Figure 6: Seasonal variability of (a) kinetic energy (KE) spectrum and (b) KE content for the 70 m depth (upper row) and 400 m depth (lower row). In (a), both the seasonal-mean KE spectrum (left) and the annual cycle of the KE spectrum (right) are shown. The pink shading and blue shading in the KE spectrum denote the standard deviation for the corresponding months. The black dashed lines in the plot of the annual cycle indicate the beginning of February and August, respectively. The results are the average over 7 years (2014–2020).
The KE content better illustrates that the Fram Strait has a maximum in winter, different from the regions inside the Arctic. And the Beaufort Sea has larger KE content than other regions inside the Arctic for all shown scales.
For the 400 m depth level, the properties of the power spectrum (power-law scaling and location of the peak) and its seasonality phase are very similar to those at the 70 m depth (Figure 8). However, the seasonal variations of both the KE spectrum and content are much weaker than at the 70 m depth, consistent with the weaker seasonality in eddy generation and EKE at depth ([PERSON] et al., 2020). The KE content in different scale bands is higher at the 400 m depth than at the 70 m depth in the Eurasian and Makarov basins and in the Beaufort Sea, indicating that the eddy activity in the Atlantic Water layer in these regions is high in the studied period.
Figure 8: Same as Figure 7, but for the 400 m depth.
Figure 7: Kinetic energy (KE) spectrum and content for the 70 m depth in 6 regions with high eddy activity. (left) KE spectrum separately for two seasons: August-January and February–July. (middle) Annual cycle of KE spectrum. (right) Annual cycle of KE content in scale bands. The locations of the regions are denoted in Figure 10. The results are the averages over 7 years. In the right column, the upper colorbar is only for the Fram Strait (the first row), and the lower colorbar is for all other panels.
The KE contents averaged over each region clearly indicate that the maximum is in the 10-20 km band for both ocean depths and in most regions, expect for the 70 m depth level in the central Nansen Basin (Figure 9). On the contrary, the mean KE content averaged over the whole Arctic Ocean shows that the maximum is located in the 1-10 km band at 70 m depth (Figures 4 and 6b). The reason is that there are large areas where the KE content maximum is located in the 1-10 km band, including the Barents-Kara seas and the central Nansen Basin. In particular, when excluding the Barents-Kara seas, the mean KE content becomes similar between the 1-10 km band and 10-20 km band (Figure 10). This is consistent with the fact that Rossby radius in the shelf seas is smaller than in the abyssal ocean. The cumulative KE in scale bands in different regions similarly shows that about 50% of the KE is on the scale is on the scale s smaller than 30 km and about 80% of the KE is on the scales smaller than 100 km (Figure 9), consistent with the Arctic mean KE content (Figure 4).
## 4 Summary
In this paper we applied the coarse-graining method to study the spatial scales of the Arctic Ocean circulation and KE at two ocean depths. Satellite observations and typical high-resolution simulations cannot resolve mesoscale eddies in the Arctic Ocean, so there was a knowledge gap in the understanding of the spatial characteristics of the Arctic Ocean circulation. By using a novel decade-long global simulation with 1 km horizontal resolution in the Arctic Ocean, we filled the knowledge gap in this paper.
Our result shows that the KE spectrum of the Arctic Ocean circulation at 70 m depth has one peak at the scale of about 1,700-2,000 km, which is the gyre scale of the Arctic Circumpolar Boundary Current. The KE spectrum at 400 m depth has two peaks, one at the same scale as the 70 m depth corresponding to the large-scale circulation, the other is centered at 60 km, roughly representing the upper bound of the mesoscales in the Arctic Ocean. The reason for missing the spectrum peak associated with the mesoscale at the 70 m depth is that the boundary current is relatively strong compared with the eddy velocity. Indeed, when analyzing different small regions for the 70 m depth with
Figure 10: Kinetic energy (KE) content in scale bands for the 70 m depth. The results for the whole Arctic Ocean (black), the abyssal ocean (blue) and the Barents-Kara seas (red) are shown separately. The results are averaged over 7 years (2014–2020). The inset indicates different Arctic regions.
Figure 9: Kinetic energy (KE) content in scale bands in six eddy-rich regions for the 70 m depth (solid blue lines) and 400 m depth (dotted blue lines). The cumulative energy contents (in percentage) are also shown for the 70 m depth (solid red lines) and 400 m depth (dotted red line) with \(y\)-axis on the right side. The results are averaged over 7 years (2014–2020). Note that the \(y\)-axis range for the Fram Strait in (a) is different from other panels.
boundary currents excluded, we can get a spectrum peak at 60 km, similar to the 400 m depth. The KE spectrum exhibits a similar power-law scaling typical for ocean eddies for both the considered depths.
We found that about 80% of the KE is on the scales smaller than 100 km and about 50% of the KE is on the scales smaller than 30 km at the two depths of the Arctic Ocean. The high concentration of KE on the very small spatial scales is consistent with observed small size of eddies in the Arctic Ocean ([PERSON] et al., 2014). When separating the KE into scale bands of every 10 km, the maximum KE content is in the 10-20 km band for both the 70 and 400 m depths in most of the Arctic eddy-rich regions. However, because the maximum KE is in the scale band of 1-10 km in some regions such as the Barents-Kara seas, averaged over the whole Arctic Ocean, the maximum KE content is in the 1-10 km band for the 70 m depth.
The seasonality of the KE spectrum and KE content is similar inside the Arctic Ocean in the five eddy-rich regions we analyzed. It follows the seasonality of EKE and baroclinicity, with low values in spring and maximum in late summer to autumn. The maximum magnitude of the KE spectrum and the maximum KE content in the Fram Strait are in winter, when eddy activity is the strongest ([PERSON] et al., 2016; [PERSON] et al., 2017). The seasonal variation is stronger at the 70 m depth than the 400 m depth, consistent with that the conversion rate from eddy available potential energy to EKE has a weaker seasonal variability at depth as found before ([PERSON] et al., 2020).
In this paper, we studied the spectrum and spatial scales of the KE and their seasonal cycle in the Arctic halocline and Arctic Atlantic Water layer. We found that KE in the Arctic Ocean is strongly concentrated on very small scales, while the ocean receives energy from winds on large spatial scales ([PERSON] et al., 2021). Therefore, energy transfer between scales, interaction between surface mixed layer and eddies, and vertical energy fluxes through the water column need dedicated studies in future work. Our decade-long simulation is still relatively short, which does not allow us to study trends in eddy activity associated with the ongoing climate change. Long historical simulations to be carried out in the future will allow us to look into changes in eddy properties and KE spatial scales over the past few decades when the Arctic Ocean physical environment experienced dramatic changes.
## Data Availability Statement
The data and the scripts that used to produce the figures in the paper are available at [PERSON] et al. (2024) ([[https://doi.org/10.5281/zenodo.7895619](https://doi.org/10.5281/zenodo.7895619)]([https://doi.org/10.5281/zenodo.7895619](https://doi.org/10.5281/zenodo.7895619))).
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## Erratum
The originally published version of this article contained a typographical error. Coauthor [PERSON]'s name should be spelled [PERSON]. The error has been corrected, and this may be considered the authoritative version of record. | wiley | Spatial Scales of Kinetic Energy in the Arctic Ocean | Caili Liu, Qiang Wang, Sergey Danilov, Nikolay Koldunov, Vasco Müller, Xinyue Li, Dmitry Sidorenko, Shaoqing Zhang | https://doi.org/10.1029/2023jc020013 | 2,024 | CC-BY |
wiley/fe74b748_8359_4083_af34_bdbdbf1f0334.md | # Effects of Surface Heating on Coastal Upwelling Intensity
[PERSON]
School of Earth and Environmental Sciences, Research Institute of Oceanography, Seoul National University, Seoul, Republic of Korea
[PERSON]
School of Earth and Environmental Sciences, Research Institute of Oceanography, Seoul National University, Seoul, Republic of Korea
###### Abstract
Numerical experiments were conducted to evaluate the effects of surface heating on coastal upwelling intensity. Offshore transport, isopycnal slope, and the sea surface temperature (SST) difference between coastal and offshore regions, which represent the upwelling intensity, were estimated. Surface heating decreases Ekman transport but increases Ekman pumping by changing air-sea stability conditions. However, offshore transport does not change significantly with surface heating. Our experimental results revealed that the increase in surface heating decreases the isopycnal slope but increases the SST difference. Both the isopycnal slope and SST difference are closely related to the change in the surface boundary layer (SBL). Strong surface heating thins the surface-mixed layer, which decreases the vertical eddy viscosity. The decreased vertical eddy viscosity thins the SBL and enhances its offshore velocity. The isopycnal slope weakens because of the thin SBL, while the SST difference becomes stronger because of the enhanced offshore velocity despite the same offshore transport. The present study may be relevant to the change in upwelling systems as the increase in surface heating under future global warming.
25 APR 2022
Accepted 27 JAN 2023
## Author Contributions
[PERSON]
Formal analysis: [PERSON]
Finding acquisition: [PERSON]
Washington: [PERSON], [PERSON]
The effect of wind stress on upwelling intensity has been widely investigated ([PERSON] et al., 2013; [PERSON] and [PERSON], 1995; [PERSON] and [PERSON], 1974; [PERSON], 1997). Surface offshore transport, which increases the upwelling intensity in coastal regions, largely depends on the alongshore surface wind stress ([PERSON], 1981).
A change in stratification can alter the upwelling source depth ([PERSON] and [PERSON], 2021; [PERSON] and [PERSON], 2011) and surface offshore velocity ([PERSON], 1973; [PERSON] et al., 1995; [PERSON] et al., 2019; [PERSON] and [PERSON], 1972; [PERSON] and [PERSON], 2004). Upwelling source depth has been shown to decrease as stratification intensifies ([PERSON] and [PERSON], 2011; [PERSON] and [PERSON], 2004). Intensified stratification in the water column confines the cross-shore circulation to a shallower near-surface layer ([PERSON] and [PERSON], 1972). The change in the upwelling source depth and surface offshore velocity due to a change in stratification can affect the coastal upwelling intensity.
Changes in the upwelling intensity by increased surface heating, which frequently occur under global warming, are poorly understood. Previous studies have focused on the role of surface heating in warming the cold coastal SSTs related to coastal upwelling ([PERSON] et al., 1987; [PERSON] and [PERSON], 2016). Surface heating may warm the upwelled cold water and decrease the SST difference between the cold coastal and warm offshore regions.
However, a recent observational result demonstrated that the SST difference between the cold coastal and warm offshore regions increased during strong surface heating ([PERSON] and [PERSON], 2020). A strong coastal upwelling along the southern coast of the Korean Peninsula was reported during the hot summer of 2013 (Figure 1). The air temperature and offshore SST in the summer of 2013 were higher than those of the climatological (2006-2015) mean by approximately 2\({}^{\circ}\)C. Despite the strong surface heating, the SST in the coastal upwelling region was lower than the climate SST by 2\({}^{\circ}\)C, resulting in a large temperature difference between the coastal and offshore regions.
In the present study, simplified numerical experiments were conducted to explore the effect of surface heating on coastal upwelling intensity. The upwelling intensity was measured via offshore transport, isopycnal slope, and the SST difference between coastal and offshore regions. The change in upwelling intensity, at various wind speeds and surface heating levels, was investigated based on the upwelling condition in the southern coast of the Korean peninsula ([PERSON] and [PERSON], 2020).
This study does not consider other potential causes of upwelling, focusing on the effect of surface heating on the wind-driven upwelling intensity.
This paper proceeds as follows: In Section 2, the numerical model configuration is described. Section 3 describes upwelling responses according to various wind speeds and surface heating levels, including momentum and heat budgets. Section 4 is a discussion of the causes pertaining to the change in upwelling intensity. Section 5 provides a conclusion to this study.
## 2 Model Setup
The numerical model utilized in this study is the Regional Ocean Modeling System (ROMS), which is a free-surface, split-explicit, and hydrostatic ocean model ([PERSON], 2005). The model domain is 500 km in length and 200 km in width (Figure 2a) with a grid resolution of 1 km horizontally with 30 vertical layers. To capture the surface boundary structure precisely, fine vertical grid spacing (approximately 1 m)
Figure 1: (a) Climate (2006–2015) sea surface temperature (SST) in August, (b) SST in August 2013, and (c) SST anomaly in August 2013 in the southern coast of the Korean Peninsula. Black dots indicate the observation stations.
was implemented near the surface. The bottom topography is flat with a uniform depth of 120 m to exclude the topographic effect. Vertical mixing was calculated using the MY-2.5 turbulent closure scheme ([PERSON], 1982). The background vertical eddy viscosity and diffusivity were set to \(10^{-5}\) m\({}^{2}\)s\({}^{-1}\). The Coriolis parameter, \(f=10^{-4}\) s\({}^{-1}\), was utilized, and the southern and northern boundaries were closed; the eastern and western boundaries were configured with periodic boundary conditions. The horizontal viscosity coefficient was set to 20 m\({}^{2}\)s\({}^{-1}\), and the diffusivity coefficient was set to 2 m\({}^{2}\)s\({}^{-1}\) ([PERSON] et al., 1998). The initial temperature as a function of depth (Figure 2b) was:
\[T(z)=5\times\arctan\left(\frac{z+25}{15}\right)+21, \tag{1}\]
which represents a typical summer temperature profile on the southern coast of the Korean Peninsula. The salinity was set to a constant of 32 during the 25 numerical experiments, which were conducted with various wind speeds and surface heating values (Table 1). A bulk-flux formula was adapted to calculate the surface flux ([PERSON] et al., 1996, 2003). The wind stress, sensible heat, and latent heat were calculated using the Coupled Ocean-Atmosphere Response Experiment (COARE) 3.0 algorithm ([PERSON] et al., 2003). The bulk formulas for wind stress, sensible heat, and latent heat are given as follows:
\[\tau_{z}=\rho_{x}C_{d}SU, \tag{2}\]
\[Q_{s}=\rho_{x}\rho_{c}\rho_{x}S(\mathrm{SST}-T_{air}), \tag{3}\]
\begin{table}
\begin{tabular}{l c c c c c} Wind & \multicolumn{5}{c}{AirT and SWrad} \\ \cline{2-6} speed & 26°C & 27°C & 28°C & 29°C & 30°C \\ m/s & 100 W/m\({}^{2}\) & 150 W/m\({}^{2}\) & 200 W/m\({}^{2}\) & 250 W/m\({}^{2}\) & 300 W/m\({}^{2}\) \\ \hline
4 & W4\_S1 & W4\_S2 & W4\_S3 & W4\_S4 & W4\_S5 \\
5 & W5\_S1 & W5\_S2 & W5\_S3 & W5\_S4 & W5\_S5 \\
6 & W6\_S1 & W6\_S2 & W6\_S3 & W6\_S4 & W6\_S5 \\
7 & W7\_S1 & W7\_S2 & W7\_S3 & W7\_S4 & W7\_S5 \\
8 & W8\_S1 & W8\_S2 & W8\_S3 & W8\_S4 & W8\_S5 \\ \hline \end{tabular} _Note._ The surface heating varies according to the air temperature (AirT) and shortwave radiation (SWrad).
\end{table}
Table 1: Numerical Experimental Cases According to Wind Speed and Surface Heating
Figure 2: (a) A schematic of the model domain and wind direction. (b) Cross-shore section of initial temperature. (c) Comparison of the mean power imposed on the layer from the surface to 20 m by the surface wind stress and heating during the experiments. The red and blue lines represent the imposed power by surface heating and wind stress, respectively.
\[Q_{l}=\rho_{x}L_{x}C_{c}S(q_{\rm{ex}}-q_{\rm{ix}}), \tag{4}\]
where \(\tau_{x},Q_{x}\) and \(Q_{l}\) are zonal wind stress, sensible heat flux, and latent heat flux, respectively; \(\rho_{a}\) is the density of air, \(C_{d}\) is the drag coefficient, \(S\) is the wind speed at a 10 m height, and \(U\) is the zonal wind speed at a 10 m height; \(c_{P}\) is the specific heat of air, \(C_{h}\) is the transfer coefficient for sensible heat, SST is the sea surface temperature, and \(T_{\rm{air}}\) is the air temperature at a 2 m height; \(L_{x}\) is the latent heat of evaporation, \(C_{c}\) is the transfer coefficient for latent heat; and \(q_{\rm{as}}\) and \(q_{\rm{air}}\) are the saturation specific humidity at the surface and at a 2 m height, respectively. The longwave radiation was calculated using the Berlind formula ([PERSON], 1952) assuming zero cloud fraction.
The surface heating varied with air temperature and shortwave radiation. The air pressure and relative humidity for the bulk-flux formula were set to constants of 1007.5 hPa and 86.7%, respectively. The ranges of wind speed, air temperature, and shortwave radiation were based on the upwelling conditions on the southern coast of the Korean Peninsula during the summer ([PERSON] & [PERSON], 2020). Shortwave radiation was imposed using a diurnal cycle. In each experiment, spatially uniform air temperature, shortwave radiation, and upwelling-favorable (eastward) wind were applied after 10 days of adjustment for the initial conditions without any external forcing. The wind speed increased linearly to the assigned value for 3 days and was maintained for 3 days in each experiment.
The energy ranges of the wind stress and surface heating imposed on the surface during the experiments were compared using the method reported by [PERSON] et al. (1978). The mean power ranges imposed by the wind stress and surface heating were comparable (Figure 2c).
Zonally averaged model results were analyzed. The daily mean results of the experiments on the final day were considered.
## 3 Results
### Vertical Cross-Sections of Temperature and Velocities
The vertical cross-sections of temperature, alongshore velocity, cross-shore velocity, and vertical velocity for cases employing weak (W4_S1 and W4_S5) and strong (W8_S1 and W8_S5) winds are displayed in Figures 3 and 4, respectively. The temperature sections exhibit coastal upwelling with the tilting of isopycnals (isotherms) toward the coast (Figures 3a, 3e, 4a, and 4e). The isopycnal slope steepens as the wind speed increases and the surface heating decreases.
Figure 3: Cross-shore sections of temperature (Temp.), alongshore velocity (vel.), cross-shore velocity (vel.), and vertical velocity (vel.) on day 6 for W4_S1 (top) and W4_S5 (bottom). Positive values represent the eastward, northward (onshore), and upward directions in the alongshore, cross-shore, and vertical velocities, respectively.
The SST of weak surface heating cases (Figures 3a and 4a) is lower than that of strong surface heating cases (Figures 3e and 4e) in both coastal and offshore regions. The surface-mixed layer becomes thicker with the increase in wind speed and decrease in surface heating. The temperature at a depth of 20 m exhibits insignificant change in all cases.
The alongshore velocities (Figures 3b, 3f, 4b, and 4f) exhibit jet flow along the coast as a result of geostrophic adjustment by coastal upwelling. The maximum speed and thickness of the coastal jet are enhanced as the wind speed increases and the surface heating decreases. The cross-shore velocities (Figures 3c, 3g, 4c, and 4g) display the offshore transport (negative value) driven by the alongshore wind near the surface. The surface boundary layer (SBL), where the offshore transport exists, becomes thicker as the wind speed increases and surface heating decreases. However, the maximum speed of the offshore velocity increases with an increase in surface heating. The vertical velocities (Figures 3d, 3h, 4d, and 4h) exhibit upward motion of subsurface water to compensate for the offshore transport. The vertical velocities increase as the wind speed increases. This results in an increased supply of subsurface water to the surface. The vertical velocity increases at a shallower depth but decreases at a deeper depth as the surface heating increases.
To clarify the changes in upwelling circulation, streamfunctions (\(\psi\)) combining cross-shore and vertical velocities are displayed in Figure 5. The streamfunction is defined as \(-\partial\psi/\partial z=v\) and \(\partial\varphi/\partial y=w\) where \(v\) is the cross-shore velocity and \(w\) is the vertical velocity. When the surface heating is strong (Figures 5b and 5d), the streamlines near the surface become denser, but the streamlines near the coast become sparser. This suggests that upwelling cells with strong surface heating are concentrated at shallower depths.
### Change in Upwelling Intensity According to Wind Speed and Surface Heating
Three upwelling indices were used to quantify the upwelling intensity in this study. The first upwelling index is offshore transport (\(V^{\prime}\)). The offshore transport was estimated as the transport above the shallowest zero crossing of the cross-shore velocity during three windy days ([PERSON] & [PERSON], 2004):
\[V^{\prime}=\int_{z_{0}}^{0}v\,dz, \tag{5}\]
where \(v\) is the cross-shore velocity, and \(z_{0}\) is the depth of the shallowest zero crossing of the cross-shore velocity.
The calculated offshore transport in each experimental case is displayed in Figure 6a. The horizontal and vertical axes represent the variation in the maximum wind speed during each experiment and net surface heat flux
Figure 4: Cross-shore sections of temperature (Temp.), alongshore velocity (vel.), cross-shore velocity (vel.), and vertical velocity (vel.) on day 6 for W8_S1 (top) and W8_S5 (bottom). Positive values represent the eastward, northward (onshore), and upward directions in the alongshore, cross-shore, and vertical velocities, respectively.
(NSHF) on the first model day, respectively. The offshore transport does not change significantly according to the surface heating at the same wind speed, whereas it increases remarkably with the wind speed. The difference in the offshore transport is below 10% for cases with the same wind speed.
The second upwelling index is the isopycnal slope. The isopycnal slope was directly calculated assuming linearity using the 20\({}^{\circ}\)C isotherm line, which was not outcropped during the 6 days of the model run.
\[\frac{\partial z}{\partial y}\Big{|}_{T_{20}}=\frac{z_{e}-z_{d}}{d}, \tag{6}\]
where \(z_{e}\) is the depth of the 20\({}^{\circ}\)C isotherm line at the coast, and \(z_{d}\) is the depth of the 20\({}^{\circ}\)C isotherm line at \(d\) km from the coast. The value of \(d\) was set as 20 km for the isopycnal calculation because the depth of the 20\({}^{\circ}\)C isotherm line hardly changes at this distance during the model run.
Figure 5: Calculated streamfunctions on day 6 for (a) W4_S1, (b) W4_S5, (c) W8_S1, and (d) W8_S5. The contour intervals are 0.03 m\({}^{2}\)/s for W4 cases and 0.1 m\({}^{2}\)/s for W8 cases.
Figure 6: (a) Offshore transport, (b) isopycnal slope, and (c) sea surface temperature (SST) difference between the coastal and 50 km offshore regions on day 6 according to the wind speed and net surface heat flux (NSHF). Table 1 lists the wind speed and surface heating of each experimental case.
The calculated isopycnal slope in each experimental case is displayed in Figure 6b. The isopycnal slope increases as the wind speed increases, which corresponds to increased offshore transport. However, the slope decreases as the surface heating increases, as displayed in the thickness of the SBL (Figures 3c, 3g, 4c, and 4g), which indicates that the change in isopycnal slope is caused by the changes in the thickness of the SBL.
The last upwelling index is an SST difference between coastal and offshore regions.
\[\Delta\mathrm{SST}=\mathrm{SST}_{e}-\mathrm{SST}_{c}, \tag{7}\]
where the SST\({}_{e}\) and SST, are the SST at the 50 km offshore and coastal regions, respectively.
The time series of SST in the coastal and offshore (50 km from the coast) regions for four cases (W4_S1, W4_S5, W8_S1, and W8_S5) are displayed in Figure 7. When the surface heating is weak (S1), the offshore SSTs change slightly, while coastal SSTs decrease because of coastal upwelling. When the surface heating is strong (S5), the coastal SSTs decrease along with the weak surface heating cases, while the offshore SSTs increase because of the strong surface heating. Both coastal and offshore SSTs of the strong surface heating cases are higher than those of the weak surface heating cases. However, the increments of offshore SSTs are more pronounced compared with those of coastal SSTs, which means greater decreases in coastal SSTs because of active coastal upwelling under strong surface heating.
The SST differences between the coastal and offshore regions on the final day for varying wind speed and surface heating are displayed in Figure 6c.
The SST difference increases as the wind speed increases, along with the isopycnal slope, which corresponds to the increased offshore transport. Notably, the SST difference increases as the surface heating increases for all wind speeds.
To quantify the relationship of the surface heating to the change in upwelling intensity, the offshore transport, isopycnal slope, and SST difference were reconstructed using linear regression analysis based on the surface heating for each wind speed case as in Equation 8:
\[\mathrm{Upwelling\ index}=a\times\mathrm{NSHF}+b, \tag{8}\]
where \(a\) is the slope of the line, and \(b\) is the intercept.
Before the linear regression analysis, the three upwelling indices were normalized by their maximum values. The results of linear regression are summarized in Table 2. As shown in Figure 6, the offshore transport is relatively unaffected by the change in surface heating. Under stronger wind speed conditions, the decrease in isopycnal slope becomes more susceptible to the surface heating. In contrast, the increase in the SST difference is less sensitive to the surface heating under the stronger wind speed conditions.
### Momentum Balance
Alongshore and cross-shore momentum balances in the cross-shore section were calculated to understand the upwelling dynamics that determine the upwelling intensity in response to the changes in wind speed and surface
Figure 7: Time series of the sea surface temperature (SST) in the (a) coastal and (b) offshore (50 km from the coast) regions for four cases (W4_S1, W4_S5, W8_S1, and W8_S5). The horizontal axis represents the days after surface forcing is applied.
heating. The nonlinear advection term in the alongshore momentum balances is significant near the upwelling front region when the wind speed is strong. However, except that region, the advection term is small, on the order of \(\text{O}\left(10^{-9}\right)\text{m}/s^{2}\), while the other significant terms have orders of \(\text{O}\left(10^{-6}\right)\text{m}/s^{2}\). The momentum equations neglecting the small advection, diffusion, and horizontal viscous force terms can be expressed by Equations 9 and 10:
\[\frac{\partial u}{\partial t}=-\frac{1}{\rho}\frac{\partial P}{ \partial x}+fv+\frac{\partial}{\partial z}\Big{(}A_{z}\frac{\partial u}{ \partial z}\Big{)}, \tag{9}\] \[\frac{\partial v}{\partial t}=-\frac{1}{\rho}\frac{\partial P}{ \partial y}-fu+\frac{\partial}{\partial z}\Big{(}A_{z}\frac{\partial v}{ \partial z}\Big{)}, \tag{10}\]
where \(u\) and \(v\) are the alongshore and cross-shore velocity components, respectively, \(\rho\) is the density of seawater, \(P\) is the pressure, \(f\) is the Coriolis parameter, and \(A_{z}\) is the vertical eddy viscosity. Because the acceleration terms are balanced by a combination of the pressure gradient force (PGF), Coriolis force, and vertical viscous force terms, only the right-hand side terms in Equations 9 and 10 are plotted. The alongshore and cross-shore momentum balances on the final day for the four cases (W4_S1, W4_S5, W8_S1, and W8_S5) are displayed in Figures 8 and 9.
In the alongshore direction (Figure 8), the PGF of each case has an order of \(\text{O}\left(10^{-12}\right)\text{m}/\text{s}^{2}\), which is small enough to be neglected. However, the Coriolis and vertical viscous forces are balanced near the surface, which results in the development of the SBL. The SBL becomes thicker as the wind speed increases and thinner as the surface heating increases. However, the Coriolis and vertical viscous forces become stronger with the increase in surface heating, as shown in the offshore velocities (Figures 3c, 3g, 4c, and 4g) and SST difference (Figure 6c). This implies that the offshore velocities and SST difference are closely related to the thickness of the SBL.
In the cross-shore direction (Figure 9), a geostrophic coastal jet exists in which the PGF and Coriolis force are balanced during the wind-driven upwelling. The PGF and Coriolis force in the coastal region become stronger as the wind speed increases and the surface heating decreases, as displayed in the alongshore velocities (Figures 3b, 3f, 4b, and 4f) and isopycnal slope (Figure 6b).
\begin{table}
\begin{tabular}{l c c c c} \hline Normalized upwelling index & Wind speed (m/s) & \(a\) (\(/\text{W}\cdot\text{m}^{-2}\)) & \(b\) & Root mean square error (RMSE) \\ \hline Offshore transport & 4 & \(0.04\pm 0.04\times 10^{-3}\) & \(0.22\pm 0.01\) & \(0.0022\) \\ & 5 & \(-0.03\pm 0.08\times 10^{-3}\) & \(0.35\pm 0.01\) & \(0.0044\) \\ & 6 & \(-0.03\pm 0.14\times 10^{-3}\) & \(0.52\pm 0.01\) & \(0.0046\) \\ & 7 & \(-0.25\pm 0.07\times 10^{-3}\) & \(0.74\pm 0.01\) & \(0.0039\) \\ & 8 & \(-0.36\pm 0.06\times 10^{-3}\) & \(1.01\pm 0.01\) & \(0.0033\) \\ Isopycnal slope & 4 & \(-0.26\pm 0.07\times 10^{-3}\) & \(0.18\pm 0.01\) & \(0.0041\) \\ & 5 & \(-0.48\pm 0.11\times 10^{-3}\) & \(0.30\pm 0.02\) & \(0.0065\) \\ & 6 & \(-0.78\pm 0.14\times 10^{-3}\) & \(0.48\pm 0.03\) & \(0.0084\) \\ & 7 & \(-1.20\pm 0.23\times 10^{-3}\) & \(0.74\pm 0.04\) & \(0.0133\) \\ & 8 & \(-1.49\pm 0.31\times 10^{-3}\) & \(1.08\pm 0.06\) & \(0.0179\) \\ SST difference & 4 & \(1.54\pm 0.21\times 10^{-3}\) & \(0.10\pm 0.04\) & \(0.0120\) \\ & 5 & \(1.40\pm 0.29\times 10^{-3}\) & \(0.21\pm 0.05\) & \(0.0165\) \\ & 6 & \(1.16\pm 0.34\times 10^{-3}\) & \(0.36\pm 0.06\) & \(0.0195\) \\ & 7 & \(0.87\pm 0.30\times 10^{-3}\) & \(0.57\pm 0.05\) & \(0.0176\) \\ & 8 & \(0.63\pm 0.25\times 10^{-3}\) & \(0.81\pm 0.05\) & \(0.0146\) \\ \hline \end{tabular}
\end{table}
Table 2: Results of Linear Regression of Upwelling Intensity Indices Versus Net Surface Heat Flux (NSHF) as a Function of Wind Speed With 95% Confidence Intervals
### Heat Balance in the Surface Layer
The heat balance in the surface layer was calculated to investigate the main causes of SST variations in the coastal and offshore regions. The heat balance equation, neglecting the small alongshore advection and horizontal diffusion terms, can be expressed by Equation 11:
\[\frac{\partial T}{\partial t}=-\frac{\partial(tT)}{\partial y}-\frac{\partial(uT )}{\partial z}+\frac{\partial}{\partial z}\left(A_{\mathrm{u}}\frac{\partial T }{\partial z}\right). \tag{11}\]
The surface and bottom boundary conditions are as follows:
\[\left(A_{\mathrm{u}}\frac{\partial T}{\partial z}\right)_{z=0}=\frac{Q_{ \mathrm{net}}}{\rho_{0}C_{p}} \tag{12}\]
\[\left(A_{\mathrm{u}}\frac{\partial T}{\partial z}\right)_{z=-k}=0, \tag{13}\]
where \(T\) is the temperature, \(v\) is the cross-shore velocity, \(w\) is the vertical velocity, \(A_{\mathrm{u}}\) is the vertical diffusivity, \(Q_{\mathrm{net}}\) is the NSHF, \(\rho_{0}=1025\,\mathrm{kg\,m^{-3}}\) is the reference density, and \(C_{p}=3985\,J\) (\(\mathrm{kg^{-}C^{-1}}\) is the specific heat capacity of seawater.
To evaluate the effect of surface heating on SST variations, the third term on the right-hand side of Equation 11 was decomposed into downward vertical heat diffusion from the uppermost model layer to the second layer (V_DIFF\({}_{\mathrm{down}}\)) and the difference between NSHF to the first layer and transmission of solar radiation to the second layer in the model (V_DIFF\({}_{\mathrm{sur}}\)).
V_DIFF\({}_{\mathrm{down}}\) was calculated using the following equation:
\[\mathrm{V_{-}DIFF_{\mathrm{down}}=\frac{1}{\partial z}\left(-A_{\mathrm{u}} \frac{\partial T}{\partial z}\right).} \tag{14}\]
Figure 8: Alongshore momentum balance terms with the (a) pressure gradient force, (b) Coriolis force, and (c) vertical viscous force on day 6 for four cases (W4_S1, W4_S5, W8_S1, and W8_S5).
V_DIFF\({}_{\rm SiWF}\) was calculated using the following equation:
\[\text{V\_DIFF}_{\rm SiWF}=\frac{1}{\partial z}\left(\frac{Q_{\rm ee}}{\rho_{0}C_{ p}}-\frac{Q_{\rm i,1}}{\rho_{0}C_{p}}\right), \tag{15}\]
where \(Q_{\rm i,1}\) is the solar radiation penetrating the bottom of the first layer.
The cumulative time integrals of heat balance in the offshore and coastal regions on day 6 are displayed in Figure 10.
The cross-shore advection (H_ADV) and vertical advection (V_ADV) terms were combined into the total advection (ADV) term (Figure 10) to evaluate the net effect of advection.
Figure 10: Cumulative time integrals of heat balance in the (a) coastal and (b) offshore regions on day 6 for four cases (W4_ S1, W4_ S5, W8_ S1, and W8_ S5). The horizontal axis represents the heat balance terms in Equations 14–16.
Figure 9: Cross-shore momentum balance terms with the (a) pressure gradient force, (b) Coriolis force, and (c) vertical viscous force on day 6 for four cases (W4_ S1, W4_ S5, W8_ S1, and W8_ S5). The contour intervals are \(4\times 10^{-4}\) m/s\({}^{2}\) for W4 cases and \(10\times 10^{-6}\) m/s\({}^{2}\) for W8 cases.
\[\text{ADV}=\text{H\_ADV}+\text{V\_ADV}=-\frac{\partial(eVT)}{\partial y}-\frac{ \partial(\omega T)}{\partial z}. \tag{16}\]
The change in offshore SST (Figure 7b) depends on the surface heat flux and downward vertical diffusion (Figure 10b). When the surface heating is strong, the SST increases because of the surface heat flux but decreases because of the downward vertical diffusion. The effect of advection on the change in offshore SST (ADV in Figure 10b) is negligible and can be ignored. There is no significant change in offshore SST in the weak surface heating cases (Figure 7b) because of the balance between the surface heat flux and downward vertical diffusion.
The change in coastal SST (Figure 7a) depends on not only the surface heat flux and downward vertical diffusion but also advection (Figure 10a). Except for case W4_S1, SST increases owing to the surface heat flux and decreases owing to the downward vertical diffusion. For W4_S1, the surface heating is not strong enough to increase the SST. When the surface heating is strong, an increase in SST caused by the surface heat flux is more pronounced compared with that in weak surface heating cases. The impact of advection on SST change becomes significant in the coastal region (ADV in Figure 10a). A decrease in SST caused by advection is more obvious when the surface heating is strong.
## 4 Discussion
### Effect of Surface Heating on Total Upwelling Transport and Surface Boundary Layer Thickness
The offshore transport calculated by model velocities (Figure 6a) was compared with total upwelling transport, which is the sum of Ekman transport (\(V^{\text{LK}}\)) and Ekman pumping transport. The Ekman transport, which was calculated as described by [PERSON] (1968), is defined in Equation 17:
\[V^{\text{LK}}=\frac{\tau_{\text{const}}^{x}}{\rho_{0}f}, \tag{17}\]
where \(\tau_{\text{const}}^{x}\) is the alongshore surface wind stress in the coastal region.
The Ekman pumping velocity, \(\omega_{E}\left(\text{m/s}\right)\), which was also calculated as described by [PERSON] (1968), is defined in Equation 18:
\[w_{E}=\frac{1}{\rho_{0}f}\left(-\frac{\partial\tau^{x}}{\partial y}\right), \tag{18}\]
where \(\tau^{x}\) is the alongshore surface wind stress.
The wind stress from the numerical model output was used for the calculations. The Ekman pumping velocities were integrated from the coastal grid to the 50 km offshore grid for the Ekman pumping transport. The calculated results are displayed in Figure 11. The total upwelling transport (Figure 11a) is comparable to the offshore transport in Figure 6a (\(R^{2}=0.9995\,\text{and}\,\text{RMSE}=0.0153\)). Although the total upwelling transport exhibits little change as the surface heating increases, the Ekman transport decreases (Figure 11b) but the Ekman pumping transport increases (Figure 11c). Thus, the surface heating can change the Ekman transport and Ekman pumping transport at the same wind speed.
In the ROMS model, surface wind stress is calculated using the bulk-flux formula. As seen in Equation 2, the surface wind stress changes with the drag coefficient (\(C_{d}\)), which depends on the air-sea stability conditions
Figure 11: (a) Total upwelling transport, (b) Ekman transport, and (c) Ekman pumping transport on day 6 according to the wind speed and net surface heat flux (NSHF). Table 1 lists the wind speed and surface heating for each experimental case.
([PERSON] et al., 2003). COARE3.0 \(C_{d}\) was parameterized as a function of air-sea stability, gustiness, and surface roughness as in Equation 19, based on the Monin-Obukhov similarity theory:
\[{C_{d}}^{1/2}(\zeta)=\frac{{C_{d}}^{1/2}}{\left[1-\frac{{C_{d}}^{1/2}}{\kappa} \psi_{d}(\zeta)\right]}, \tag{19}\]
where \(\zeta\) is a stability parameter, the subscript \(n\) refers to neutral stability, \(\kappa\) is [PERSON]'s constant, and \(\psi_{d}\) is an empirical function describing the stability dependence of the mean profile. The \(C_{d}\) calculated from the COARE algorithm can be expressed as a function of air-sea temperature difference ([PERSON] et al., 2005). Assuming constant air pressure (1007.5 hPa) and relative humidity (86.7%), the \(C_{d}\) for various wind speeds is displayed in Figure 12 as a function of air-sea temperature difference. As the stability increases due to decreasing SST by upwelling, the \(C_{D}\) decreases, which results in weak wind stress. Colder coastal water caused by coastal upwelling decreases the wind stress in coastal regions, which weakens the Ekman transport. However, the increased stability by the cold surface water induces the wind stress curl and enhances Ekman pumping. Strong surface heating, which results in a larger SST difference between coastal and offshore regions, increases Ekman pumping. The increase in Ekman pumping and decrease in Ekman transport due to the air-sea stability are consistent with the findings of previous studies that used an empirical SST-wind interaction relationship ([PERSON] et al., 2007; [PERSON] et al., 2009). This stability-induced wind stress curl can significantly affect the upwelling source depth ([PERSON] & [PERSON], 2012) and the subsurface density structure ([PERSON] et al., 2004).
As shown in Figures 3, 4, and 8, the thickness of the SBL (\(H_{\text{SBL}}\)) decreases but the maximum speed of the offshore velocity increases with surface heating. The scale of \(H_{\text{SBL}}\) is \(\sqrt{2A_{s}/f}\), where \(A_{s}\) is the vertical eddy viscosity ([PERSON], 1905; [PERSON], 1999). Thus, the \(H_{\text{SBL}}\) and vertical eddy viscosity display a proportional relationship. The offshore velocity in the SBL is closely related to the vertical eddy viscosity ([PERSON] & [PERSON], 2002; [PERSON], 1995). [PERSON] and [PERSON] (2002) reported an inverse dependence of vertical eddy viscosity on water column stratification. The vertical eddy viscosity is considered proportional to the mixing length in the surface-mixed layer, which is bounded by the air-sea interface ([PERSON], 1948). Below the surface-mixed layer, the vertical eddy viscosity decreases with an increase in Richardson number (Ri) ([PERSON] et al., 2013; [PERSON] et al., 2005).
The cross-shore sections of the vertical eddy viscosity for four cases (W4_S1, W4_S5, W8_S1, and W8_S5) are displayed in Figure 13. The vertical eddy viscosities have an order of \(\text{O}\left(10^{-5}-10^{-3}\right)\text{m}^{2}/\text{s}\), which are typical values of other upwelling regions ([PERSON], 1989; [PERSON] et al., 2017).
The vertical eddy viscosity is prominent from the surface to the depth at which the Coriolis and vertical viscous forces are in balance (Figure 8). The threshold depths of the prominent vertical viscous force are consistent with the depth of Ri = 1 (lower red dashed lines in Figure 13). The vertical eddy viscosity increases as the wind speed increases and the surface heating decreases. When the surface heating is weak (Figures 13a and 13c), the mixed layer depth (MLD) is relatively thick, and vertical surface mixing is enhanced. The enhanced vertical mixing comprises an increase in the vertical eddy viscosity because of an increase in the mixing length ([PERSON] & [PERSON], 1948) and a decrease in Ri ([PERSON] et al., 2013; [PERSON] et al., 2005). The increased vertical eddy viscosity increases the SBL thickness but decreases the offshore velocity, while the offshore transport remains unchanged.
In contrast, when the surface heating is strong (Figures 13b and 13d), the MLD becomes thinner, and vertical mixing is inhibited. The inhibited vertical mixing comprises a decrease in the vertical eddy viscosity because of the decreased mixing length and increased Ri in the SBL. Owing to the decreased vertical eddy viscosity, the surface stress is limited to the shallow surface, which results in a thin SBL but enhanced offshore velocity.
Vertical profiles of the offshore velocities calculated by a simple analytical model for the Ekman layer ([PERSON] & [PERSON], 2016) were compared with our model results (Figure 14). Wind stress and vertical eddy viscosity
Figure 12.— Drag coefficients for various wind speeds. The horizontal axis represents the difference between sea surface temperature (SST) and air temperature (Tair). Color indicates the wind speed as shown in the legend.
calculated from the numerical model were used as input parameters for the analytical model. Depth-averaged vertical eddy viscosity was used for surface (\(z=0\)) vertical eddy viscosity in this study. \(\delta\) and \(f/\omega\) were set to 0.75 and 0.9, respectively ([PERSON] & [PERSON], 2016). Although there are differences in absolute values, the changes in the speed and thickness of the SBL caused by the surface heating are comparable in both models. The differences may be attributable to the space-time coupling of vertical eddy viscosity calculated from the numerical model.
### Change in Isopycnal Slope According to the Surface Boundary Layer Thickness
The isopycnal slope may result from the vertical and horizontal scales of upwelling motion ([PERSON] & [PERSON], 2004). The isopycnal slope should be proportional to the water depth divided by the baroclinic Rossby radius of deformation (\(L_{d}\)) ([PERSON] & [PERSON], 2004). The \(H_{\text{SBL}}\), which determines the depth from which fluid is drawn into the SBL, was selected as the vertical scale of upwelling motion in this study because it is closely related to the isopycnal slope. \(L_{d}\) is a horizontal scale for sloping isopycnals during upwelling ([PERSON], 1980; [PERSON], 1978). The \(L_{d}\) for the two-layer fluid is defined as:
\[L_{d}=\sqrt{\frac{g^{\prime}\left(\frac{n_{1}n_{2}}{H_{1}+H_{2}}\right)}{f^{2 }}}, \tag{20}\]
where \(g^{\prime}\) is the reduced gravity, \(f\) is the Coriolis parameter, and \(H_{1}\) and \(H_{2}\) are the thicknesses of the upper and lower layers, respectively ([PERSON] & [PERSON], 1974).
Figure 13: Cross-shore sections of the vertical eddy viscosity (Az) on day 6 for (a) W4_S1, (b) W4_S5, (c) W8_S1, and (d) W8_S5. The upper and lower red dashed lines represent the air-sea interface and depth of Ri = 1, respectively.
To calculate \(L_{d}\), \(H_{1}\) was chosen as \(H_{\text{SBL}}\) at 50 km offshore where the subsurface density changes little during the experiments; \(g^{\prime}\) was calculated utilizing the mean densities of \(H_{1}\) and \(H_{2}\). \(H_{\text{SBL}}\) is defined as the depth of Ri = 1. Ri is defined as:
\[Ri=\frac{N^{2}}{\left(\frac{\omega_{\text{R}}}{a\pi}\right)^{2}+\left(\frac{ \omega_{\text{R}}}{a\pi}\right)^{2}}, \tag{21}\]
where \(N\) is the buoyancy frequency, \(u\) is the alongshore velocity, and \(v\) is the cross-shore velocity.
The ratio of \(H_{\text{SBL}}\) to \(L_{d}\), assuming \(H_{1}\ll H_{2}\), can be expressed as:
\[\sqrt{\frac{H_{1}}{g^{\prime}}}f. \tag{22}\]
\(H_{\text{SBL}}\) and \(L_{d}\) were calculated for each experiment (W4_S1, W4_S5, W8_S1, and W8_S5) as displayed in Table 3. The change in \(L_{d}\) due to surface heating is noticeably smaller than that of \(H_{\text{SBL}}\). This is due to the effect of increasing \(g^{\prime}\) being offset by decreasing \(H_{1}\)(= \(H_{\text{SBL}}\)) in Equation 20. The smaller variation in \(L_{d}\) relative to that in \(H_{\text{SBL}}\) suggests that \(H_{\text{SBL}}\) is crucial in determining the isopycnal slope during surface heating. This results in a gentle isopycnal slope with the increase in surface heating because surface heating forms a thinner SBL.
The ratio of \(H_{\text{SBL}}\) to \(L_{d}\) was plotted with the model-calculated isopycnal slope (Figure 15). The isopycnal slope and ratio of \(H_{\text{SBL}}\) to \(L_{d}\) show a proportional linear relationship consistent with the results of [PERSON] and [PERSON] (2004). The proportionality constants with 95% confidence intervals for wind speeds of 4, 5, 6, 7, and 8 m/s are \(0.06\pm 0.01\), \(0.11\pm 0.01\), \(0.18\pm 0.01\), \(0.29\pm 0.02\), and \(0.38\pm 0.08\),
Figure 14: Vertical profiles of the offshore velocities (50 km from the coast) on day 6 for (a) W4_S1, (b) W4_S5, (c) W8_S1, and (d) W8_S5. Blue lines represent cross-shore velocities from the numerical model, and orange dotted lines represent the cross-shore velocities calculated from the analytical model.
### Limitations and Implications
Model results from the simplified model, assuming a flat bottom and no alongshore variability, may differ from the realistic responses in the coastal region. Steep bottom topography leads to narrow and intense upwelling circulation, whereas gentle bottom topography results in broad and weak upwelling circulation ([PERSON] et al., 1995; [PERSON] et al., 2013; [PERSON] et al., 2008). Thus, the model results with a flat bottom may weaken the cross-shore return flow because the bottom Ekman transport cannot be considered, potentially weakening the effect of surface heating compared with the realistic response in the coastal region. The presence of the alongshore pressure gradient can also affect the near surface cross-shore transport ([PERSON] et al., 2018; [PERSON] & [PERSON], 2010) and surface temperature in the true coastal region ([PERSON] & [PERSON], 2002; [PERSON] et al., 1987). Therefore, the findings in this study may not be applicable when the effect of alongshore pressure gradient is significant.
The numerical model results are transient states in this study. In a stratified ocean, cross-shore circulation induced by upwelling-favorable wind is unsteady and exhibits offshore movement for the sloping isopycnals and upwelling front ([PERSON] et al., 1995; [PERSON] & [PERSON], 2004). The unsteady response of numerical models precludes the
Figure 16: Time series of the differences in the heat balance between coastal and offshore regions presented as a cumulative time integral. (a) Changes in sea surface temperature (SST) difference from vertical diffusion. (b) Changes in SST difference from advection. (c) Changes in SST difference. The horizontal axis represents the days after surface forcing is applied.
Figure 15: Isopycnal slope as a function of the ratio of thickness of surface boundary layer (\(H_{\text{sat}}\)) to Rossby radius of deformation (\(L_{d}\)) on day 6. Color indicates the wind speed as shown in the legend.
quantitative generalization of model results. However, when the model was run longer, no changes in the relative effect of surface heating on the offshore transport, isopycnal slope, and SST were observed. The main factors controlling the offshore transport and isopycnal slope are the alongshore wind stress in the offshore region and SBL thickness. The relative effect of these factors continues for a longer time. Although the lower temperature waters in the upwelled region absorb heat faster than warmer offshore waters over time, the faster offshore velocity continuously maintains a larger cross-shore temperature difference.
In spite of these limitations, the findings presented in this study can help us understand the role of surface heating in changing the upwelling system for the future climate scenarios. Strong surface heating enhances the surface offshore velocity, which suggests that the surface coastal water can move farther offshore while the upwelling source depth decreases. This change can significantly affect the circulation and ecosystem in the coastal upwelling region ([PERSON] et al., 2007; [PERSON] et al., 2010).
## 5 Conclusions
To investigate the effects of surface heating on coastal upwelling intensity, simplified three-dimensional numerical experiments were conducted. Offshore transport, isopycnal slope, and the SST difference between coastal and offshore regions were evaluated.
Surface heating decreases Ekman transport but increases Ekman pumping transport owing to the increase in the air-sea stability. However, surface heating does not change net offshore transport significantly.
The isopycnal slope increases as the wind speed increases and surface heating decreases. The change in isopycnal slope is more vulnerable to the change in surface heating under strong wind speed conditions. The regression coefficients from the linear regression of isopycnal slope versus NSHF are \(-0.26\pm 0.07\times 10^{-3}\), \(-0.48\pm 0.11\times 10^{-3}\), \(-0.78\pm 0.14\times 10^{-3}\), \(-1.20\pm 0.23\times 10^{-3}\), and \(-1.49\pm 0.31\times 10^{-3}\) for wind speeds of 4, 5, 6, 7, and 8 m/s, respectively. Our modeling experiments demonstrate that \(H_{\text{SBL}}\) is crucial in determining the isopycnal slope. Surface heating, which forms a thinner SBL, results in a gentle isopycnal slope.
The SST difference between coastal and offshore regions increases as the wind speed increases, as with the isopycnal slope. However, the SST difference also increases as the surface heating increases. The change in SST difference is more susceptible to the change in surface heating under weak wind speed conditions. The regression coefficients from the linear regression of SST difference versus NSHF are \(1.54\pm 0.21\times 10^{-3}\), \(1.40\pm 0.29\times 10^{-3}\), \(1.16\pm 0.34\times 10^{-3}\), \(0.87\pm 0.30\times 10^{-3}\), and \(0.63\pm 0.25\times 10^{-3}\) for wind speeds of 4, 5, 6, 7, and 8 m/s, respectively. Model results indicate that vertical diffusion plays a key role in determining SST in the offshore region, but advection becomes impactful in the coastal region. Surface heating has two opposing effects on the SST difference. The SST difference decreases with an increase in the NSHF in the coastal region but increases because of the advection induced by enhanced offshore velocity in the SBL simultaneously.
Both the \(H_{\text{SBL}}\) and offshore velocity in the SBL are closely related to the vertical eddy viscosity, which, in turn, depends on the mixing length and Ri. When the surface heating is weak, the vertical eddy viscosity increases and forms a thicker SBL which reduces the offshore velocity of the SBL. The isopycnal slope becomes steep because of the thick SBL, whereas the SST difference decreases because of the reduced offshore velocity. When the surface heating is strong, the vertical eddy viscosity decreases and forms a thinner SBL, resulting in an enhanced offshore velocity. The isopycnal slope becomes gentle because of the thin SBL, and the SST difference increases because of the enhanced offshore velocity despite the same offshore transport. The increase in the SST difference due to the enhanced offshore velocity overwhelms the decrease in the SST difference by NSHF.
Although our study focused on local stratification, our findings could be beneficial for studying larger and longer timescale implications concerning global warming in the future. The effect of surface heating could affect the upwelling source depth and flushing time of the subsurface in a coastal upwelling region, which affects the coastal ecosystem. Hence, additional research, including observations, is necessary to better understand the effect of surface heating on coastal upwelling.
## Data Availability Statement
The observational temperature data set was derived from the serial oceanographic observations obtained from the National Institute of Fisheries Science ([[https://www.nifs.go.kr/kodc/index.kodc](https://www.nifs.go.kr/kodc/index.kodc)]([https://www.nifs.go.kr/kodc/index.kodc](https://www.nifs.go.kr/kodc/index.kodc))). The serial oceanographic data have been routinely observed on a bimonthly basis at standard ocean depths around the Korean Peninsula. The numerical model used in this study uses an open-access source code. The source code can be downloaded from [[https://www.myromms.org/](https://www.myromms.org/)]([https://www.myromms.org/](https://www.myromms.org/)).
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wiley/fe324c86_8c3a_43a3_bdba_2b868ab26117.md | # Geochemistry, Geophysics, Geosystems'
Salt Diapir-Driven Recycling of Gas Hydrate
[PERSON]
1
[PERSON]
1 Department of Earth and Planetary Sciences, Stanford University, Stanford, CA, USA, 1 Department of Earth and Planetary Sciences, Stanford
trapped in the sediment matrix moves downward relative to the pressure and temperature conditions to a part of the subsurface where hydrate is no longer stable (below the BGHSZ), leading to GH decomposition and release of gas and water. This buoyant gas may then migrate upward and be reincorporated as hydrate at the new BGHSZ (i.e., the BGHSZ now located in relatively shallower sediment) or may be trapped as free gas beneath the BGHSZ. Numerous processes can drive GH recycling. It has most often been described as a response to sedimentation and sediment burial (e.g., [PERSON] et al., 2017; [PERSON] et al., 2019; [PERSON] et al., 2007, 2008; [PERSON], 1983; [PERSON], 1989; [PERSON] et al., 2018; [PERSON] et al., 1994; [PERSON] et al., 2022; [PERSON], 2021), but also as a response to tectonic uplift-driven pressure reduction ([PERSON] et al., 2007; [PERSON], 1989), sea-level fall-driven pressure reduction ([PERSON] et al., 2007), bottom-water warming ([PERSON] et al., 2007; [PERSON] et al., 2017), deglaciation ([PERSON] et al., 2008), and changes in geothermal gradients ([PERSON] et al., 2008). However, although salt bodies (including domes and diapirs) are known to modify local to regional temperature fields and heat flow, the potential impact of salt tectonics-driven temperature changes on the GH recycling process has not yet been explored.
Due to its high thermal conductivity, salt promotes enhanced heat flux in sedimentary basins, resulting in local heat flow anomalies and elevated temperatures above salt diapirs (e.g., [PERSON], 1995; [PERSON], 1983, 1990; [PERSON] et al., 1992; [PERSON], 1984, 1988; [PERSON], 1966; [PERSON] et al., 1985; [PERSON] et al., 1992). Salt can therefore impact the stability of GH systems. For instance, salt diapir-modulated heat flows are speculated to influence gas hydrate stability zone (GHSZ) thickness in the Barents Sea ([PERSON] et al., 2008), while salt diapir-associated heat flux (and flux of saline waters) is speculated to impede hydrate formation in the northern Gulf of Mexico's Garden Banks and Mississippi Canyon areas ([PERSON] et al., 2005). Salt diapir-driven upwarping of the BGHSZ is observed in the Gulf of Mexico's Green Canyon and Walker Ridge areas (possibly causing hydrate dissociation; [PERSON] et al., 2020) and at the Blake Ridge Diapir ([PERSON] et al., 2005; [PERSON] et al., 2000). Nonetheless, the impact of salt (via its modulation of heat flow) on GH system dynamics is relatively underexplored. Furthermore, previous studies have primarily documented the _destructive_ effects of salt-mediated temperature changes on GH systems, whereas the potential for salt-mediated temperature changes to have a _constructive_ effect on GH systems by causing GH recycling has, to the best of our knowledge, never been documented.
In this paper, we investigate the influence of salt diapir movement and associated changes to basin thermal conditions on the GH recycling process. Using the commercial basin simulation and petroleum system modeling software PetroMod(tm), we build and interrogate various two-dimensional theoretical (synthetic) basin-scale GH system models to assess the impact of salt diapirism--as well as variations in basal heat flow, salt diapir diameter, salt stock height, and sediment thermal conductivities--on hydrate formation and the potential for GH recycling. We then conduct two real-world case studies of Green Canyon (Gulf of Mexico) and Blake Ridge (U.S. Atlantic coast) salt diapirs, modeling salt movement and GH system evolution through time and deriving quantitative estimates of hydrate and free gas saturations at these locations. We compare the Green Canyon and Blake Ridge model results with previous modeling work, seismic data, and drilling data on the distribution and saturation of GH and free gas at these localities.
## 2 Methods
We use the PetroMod(tm) v. 2019 basin and petroleum system modeling software suite (e.g., [PERSON] et al., 2008; [PERSON] & [PERSON], 2008; [PERSON], 2009), provided by Schlumberger, for the 2-D modeling described herein. All modeling was performed using the Sherlock High Performance Computing Cluster at the Stanford Research Computing Center.
The GH module within PetroMod(tm) is a joint development of Schlumberger GmbH (Aachen, Germany) and GEOMAR Helmholtz-Zentrum fur Ozeanforschung Kiel ([PERSON] et al., 2016). The module has been successfully applied to numerous investigations of GH systems, including both synthetic modeling approaches (e.g., [PERSON], 2022; [PERSON] et al., 2016) and a diversity of real-world case studies (e.g., [PERSON], 2022; [PERSON] et al., 2020; [PERSON] et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2016; [PERSON] et al., 2018, 2020; [PERSON] et al., 2015, 2017, 2019, 2022; [PERSON] et al., 2020). PetroMod(tm) can model hydrate formation via GH recycling ([PERSON] et al., 2019), and two of the aforementioned studies use the software to demonstrate sedimentation-driven GH recycling ([PERSON] et al., 2017; [PERSON] et al., 2022).
### Synthetic Modeling Approach
We construct various purely synthetic, geologically reasonable 2-D basin and GH system models to investigate numerous scenarios for the interaction of salt diapirs, heat flow, and GH systems through time. In addition to modeling salt diapir movement and its corresponding influence on temperature and hydrate stability, we examine, via model scenarios detailed below, the impact of variations in (a) basal heat flow, (b) salt diapir diameter, (c) salt stock height, and (d) sediment thermal conductivity on GH stability and corresponding hydrate and free gas accumulations.
#### 2.1.1 Synthetic Model Dimensions and Surfaces
Synthetic model dimensions are provided in Table 1, and a standard base case synthetic model is illustrated in Figure 1. Model layers, as well as their corresponding ages and properties, are listed in Table 2. Synthetic models include domed sediment above the salt diapir crest, creating positive bathymric relief of \(\sim\)200 m, consistent with observations of domed sediment associated with various salt diapirs (e.g., [PERSON] et al., 1996; [PERSON] & [PERSON], 1998).
#### 2.1.2 Stratigraphy, Lithologies, and Rock Properties
Sediment thicknesses, sedimentary facies, sedimentation rates, and rock properties used for the base case synthetic models are listed in Table 2. Table 3 provides different sediment thermal conductivity combinations tested for the synthetic modeling scenario implemented to investigate the impact of variable sediment thermal conductivities on GH stability and distribution.
#### 2.1.3 Salt
Salt diapir geometries and dimensions vary greatly ([PERSON], 2007; [PERSON] & [PERSON], 1983; [PERSON] & [PERSON], 1986). Mature diapir stocks range from \(<\)1 km to \(>\)10 km in diameter ([PERSON] & [PERSON], 1986). Salt diapir symmetry is highly variable, ranging from symmetrical, vertical stocks to asymmetrical, curved stocks ([PERSON] & [PERSON], 1986). Salt diapir shape is also highly variable, including conical, cylindrical, bulb-topped, and teardrop-shaped ([PERSON] & [PERSON], 1986; [PERSON], 1998).
Here, we use a base case salt diapir diameter of 2 km for most synthetic modeling, but also specifically test the influence of salt diapir diameters in one set of modeling scenarios. For this scenario set, we test six diapir diameters: 1 km, 2 km, 4 km, 6 km, 8 km, and 9 km. For all modeling, we assume salt diapirs are characterized by axially symmetrical vertical stocks. We assume diapirs to be slightly conical in shape, consistent with, for instance,
\begin{table}
\begin{tabular}{l c c c} \hline Model width & Model height & Salt diapir width & Depth of diapir crest \\ \hline Synthetic Models & & & \\
10 km (49 cells, each \(\sim\)204 m wide) & Up to \(\sim\)10 km (2.2 km water depth; 7.5 km sediment) & 2 km\({}^{\rm st}\) & – \\ Green Canyon Model & & & \\
10 km (49 cells, each \(\sim\)204 m wide) & 9.5 km (2 km water depth; 7.5 km sediment\({}^{\rm st}\)) & 2 km\({}^{\rm st}\) & 1.5 km below seafloor\({}^{\rm st}\) \\ Blake Ridge Model & & & \\
10 km (49 cells, each \(\sim\)204 m wide) & \(>\)10 km (2.16 km water depth; \(\sim\)8 km sediment\({}^{\rm st}\)) & 2 km\({}^{\rm st}\) & 1 km below seafloor\({}^{\rm st}\) \\ \hline \end{tabular} \({}^{*}\)Except for the variable salt diapir diameter modeling scenarios, in which we test six different diapir diameters (1, 2, 4, 6, 8, and 9 km), as described in the text. \({}^{\rm t}\)Consistent with 1.5 km of sediment above the diapir crest, and a diapir height of 6 km ([PERSON] et al., 2020). \({}^{\rm th}\)Based on a 2–3 km diapir width estimated from seismic data and modeling by [PERSON] et al. (2020); however, it must be noted that assigning an essentially constant diapir width is a highly simplified assumption, given the substantially complex diapir geometries imaged at Green Canyon ([PERSON] et al., 2020). \({}^{\rm st}\)[PERSON] et al. (2020). \({}^{\rm st}\)[PERSON] et al. (1996) and [PERSON] et al. (2005). \({}^{\rm th}\)See text for explanation.
\end{table}
Table 1: _Model Dimensions_
Figure 1: Base case 2-D synthetic model geometries, including \(\sim\)1.3 km of shallow 5.6–0 Ma sediment and \(\sim\)6 km of deep 20–5.6 Ma sediment, as well as the 2-km-wide salt diapir.
observations that a majority of \(>\)120 salt diapirs in South Louisiana are conical ([PERSON] & [PERSON], 1986) and that \"upward-narrowing\" diapirs dominate in passive margin settings ([PERSON], 1998).
Various studies have successfully utilized basin modeling approaches to model salt evolution (e.g., [PERSON] et al., 2009; [PERSON] et al., 2012; [PERSON], 2012; [PERSON] et al., 2013; [PERSON] & [PERSON], 1997; [PERSON] et al., 2012). In terms of capturing salt movement through time, PetroModT software utilizes sequential back-stripping to interpolate salt restoration timesteps in between a pre-defined present-day salt geometry (i.e., diapir geometry at 0 Ma) and a pre-salt-movement geometry (a flat-lying, undeformed source salt layer in both our synthetic and real-world models) with the assumption that salt volume is constant through time. This methodology need not discriminate between mechanisms for salt movement (i.e., differential loading-driven vs. buoyancy-driven salt ascension; e.g., [PERSON], 1986; [PERSON] & [PERSON], 2007; [PERSON] et al., 1993), instead acting to capture the physical geometry of a deforming salt body at various timesteps.
Because rates of salt flow are extremely variable (e.g., [PERSON] & [PERSON], 1986), we adopt a base case for our synthetic modeling efforts whereby salt ascends at a rate of \(\sim\)300 m/Myr, compatible with rates of 10 m to 2 km/Myr ([PERSON] et al., 1994).
#### 2.1.4 Heat Flow and Other Boundary Conditions
Because the major salt basins containing confirmed or inferred GH deposits occur in thermally subsiding (i.e., postrift) passive margin settings ([PERSON] et al., 2015; [PERSON] & [PERSON], 2007; [PERSON] & [PERSON], 2020), we adopt heat flow values typical of such settings, which average 50 mW/m\({}^{2}\) with a typical range of \(\sim\)35-65 mW/m\({}^{2}\)([PERSON] & Allen, 2013). We also investigate the impact of variations in heat flow by testing the following basal heat flow scenarios: 35, 45, 50, 55, 65, and 80 mW/m\({}^{2}\). Treatment of heat flow and the thermal modeling approach implemented within PetroModT\({}^{\text{m}}\) are described in detail by previous workers (e.g., [PERSON] et al., 2010; [PERSON] & [PERSON], 2009).
A constant sediment-water interface temperature (SWIT) of 4\({}^{\circ}\)C was used, as in [PERSON] et al. (2017), and consistent, for instance, with estimates of Pliocene bottom-water temperatures at depths of \(\sim\)2.0-2.5 km ([PERSON] et al., 2009). A constant temperature was assigned to negate the effects of changing SWIT on GH stability.
Water depth is held constant at 2.2 km in all synthetic models described here, a simplification made to negate effects of changing water depth on GH stability.
### Synthetic and Real-World Modeling Approach to Gas Generation, Migration, and Hydrate Formation
The synthetic and real-world models implement a similar approach to modeling biogenic gas generation, gas migration, and the GH formation and recycling process, as detailed below.
#### 2.2.1 Organic Properties and Kinetics
We confine the synthetic and real-world models to the generation of biogenic gas; thus, the kinetics of Middelburg (1989)--which consider burial depth, sedimentation rate, and age of organic matter--are applied.
\begin{table}
\begin{tabular}{l l l l} \hline Scenario 1 & Shallow sediment: 1.8 W/m/K & Scenario 5 & Shallow sediment: 1.4 W/m/K \\ & Deep sediment: 1.6 W/m/K & & Deep sediment: 1.6 W/m/K \\ Scenario 2 & Shallow sediment: 1.8 W/m/K & Scenario 6 & Shallow sediment: 1.8 W/m/K \\ & Deep sediment: 2.0 W/m/K & & Deep sediment: 1.6 W/m/K \\ Scenario 3 & Shallow sediment: 1.8 W/m/K & Scenario 7 & Shallow sediment: 2.2 W/m/K \\ & Deep sediment: 2.4 W/m/K & & Deep sediment: 1.6 W/m/K \\ Scenario 4 & Shallow sediment: 1.8 W/m/K & Scenario 8 & Shallow sediment: 2.6 W/m/K \\ & Deep sediment: 2.8 W/m/K & & Deep sediment: 1.6 W/m/K \\ \hline \end{tabular} _Note._ Values listed are for thermal conductivity at 20\({}^{\circ}\)C, and are consistent with values reported in the literature.\({}^{\text{a}}\)
\({}^{\text{a}}\)[PERSON] (1971) and [PERSON] (2000).
\end{table}
Table 3: _Eight Sediment Thermal Conductivity Scenarios Tested via Synthetic Modeling_This kinetic rate law relates the reactivity of organic material to its depositional age. These kinetics have been implemented and validated in studies of GH systems, including PetroMod(tm)-based studies (e.g., [PERSON] et al., 2017; [PERSON] et al., 2019; [PERSON] et al., 2016). In the synthetic models, a TOC (total organic carbon) of 1 wt. % and an HI (hydrogen index, used to calculate the generation potential of biogenic methane) of 100 mg HC/g TOC are used as the base case (Table 4), as in PetroMod(tm)-based studies of GH by [PERSON] et al. (2015) and [PERSON] et al. (2017), and as is consistent with the average TOC of continental margin sediments (Emerson & Hedges, 1988), the general range of TOC for siliceous marine sediments (e.g., [PERSON], 1982), and preliminary work on TOC of global hydrate-associated sediments ([PERSON], 2020). Organic properties used in the real-world models are listed and explained in Table 4.
It should be noted that while we do not consider thermogenic gas contributions in our synthetic or real-world modeling efforts, the integration of deeper thermogenic sources of gas could exert an effect on the formation of hydrate (and corresponding saturations and volumes), and in a limited number of locations has been suggested to represent an important contribution to the GH system (e.g., [PERSON] et al., 1984, 1986; [PERSON] et al., 2006; [PERSON] et al., 2015; [PERSON], 1995; [PERSON] et al., 2020). However, GH at Green Canyon is predominantly biogenic ([PERSON] et al., 2017; [PERSON] et al., 2022), as is GH at Blake Ridge ([PERSON] et al., 1996), and in general, most recovered samples of GH from global continental margins indicate biogenic rather than thermogenic sources ([PERSON] et al., 2016; [PERSON] et al., 2011; [PERSON], 1995, 1998; [PERSON] & [PERSON], 2001; [PERSON], 2003).
#### 2.2.2 Gas Hydrate Formation and Recycling
Several methods are available to simulate fluid flow and migration within PetroMod(tm). Here, free gas migration is modeled as two-phase Darcy flow. Cell-to-cell, pressure-gradient-driven Darcy flow is considered the best migration modeling approach for fine-grained and mixed (i.e., lower permeability) lithologies and for GH modeling ([PERSON] & [PERSON], 2018; [PERSON] & [PERSON], 2009; [PERSON] et al., 2000; [PERSON] et al., 2016). A relatively low critical gas saturation value (i.e., the saturation at which the gas phase becomes mobile; discussed in [PERSON] and [PERSON] (2009) and [PERSON] et al. (2018)) of 1 vol. % is assigned to enhance gas migration potential and to permit small gas bubbles to flow (as in [PERSON] et al. (2017)), and methane is permitted to travel either as a free gas phase (according to [PERSON]'s law) or in solution (according to [PERSON]'s law). The assumption of negligibly small critical gas saturation values is common practice ([PERSON] & [PERSON], 2009). It should be noted that modeled gas migration within the GHSZ is impacted by the presence of GH (e.g., [PERSON] et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2022) because hydrate changes bulk sediment properties by reducing porosity, reducing permeability, and increasing capillary entry pressure ([PERSON] & [PERSON], 2007; [PERSON], 2003).
The PetroMod(tm) GH module integrates PetroMod(tm)'s basin and migration modeling approach with low-temperature microbial methane generation kinetics ([PERSON], 1989) and the physical, thermodynamic, and kinetic properties of GHs to simulate hydrate formation and dissociation ([PERSON] et al., 2016). In the module, the formation and presence of GH is determined according to the equilibrium between methane dissolved in seawater (porewater) and methane hydrate ([PERSON] et al., 2016), with this equilibrium in turn governed by the dissociation pressure of methane hydrate in seawater ([PERSON] et al., 2005). GH formation from available
\begin{table}
\begin{tabular}{l c c c c} \hline Facies & Thickness & TOC content & HI & Hydrocarbon generation kinetics \\ \hline Synthetic Models & & & & \\ Siltstone (Organic Lenan)\({}^{*}\) & \(\sim\)7.3 km & 1 wt. \%\({}^{*}\) & 100 mg HC/g TOC\({}^{*}\) & Middelburg (1989)\({}^{*}\) \\ Green Canyon Model & & & & \\ Shale-dominated\({}^{*}\) & \(\sim\)1.3 km & 1 wt. \%\({}^{*}\) & 100 mg HC/g TOC\({}^{*}\) & Middelburg (1989) \\ Blake Ridge Model & & & & \\ Siltstone (Organic Lenan)\({}^{*}\) & \(\sim\)8 km & 0.5 wt. \%\({}^{*}\) & 100 mg HC/g TOC\({}^{*}\) & Middelburg (1989) \\ \hline \end{tabular}
* \({}^{*}\)See text for explanation. \({}^{*}\)Consistent with regional geochemical work, and as modeled for Green Canyon by [PERSON] et al. (2017); [PERSON] et al. (2017). \({}^{*}\)TOC contents of shallow sediments at the site are generally \(<\)0.5 wt. \% but may be higher in deeper sediments, and are less than those at other Blake Ridge ODP sites ([PERSON] et al., 1996). Nonetheless, we conservatively adopt a uniform sediment TOC content of 0.5 wt. \%. \({}^{*}\)No data are available for HI values at this site, but HIs at other Blake Ridge sites are atl\(\gtrsim\)100 ([PERSON] et al., 1996); thus, we adopt a uniform sediment HI of 100.
\end{table}
Table 4: _Sediment Organic Properties Assigned to the Models for Biogenic Gas Generation_methane is simulated for each cell and each time step by calculating the dissolution of methane in water and the dissociation pressure of methane hydrate depending on pressure and temperature (using the equations established by [PERSON] et al. (2005)). Within the GHSZ, GH forms whenever the saturation of methane is greater than the solubility of methane in aqueous solution and conversely dissociates when the solubility exceeds saturation ([PERSON] et al., 2005). Due to the large timesteps (i.e., >10,000 years) typically used in basin modeling, hydrate formation is assumed to be instantaneous rather than kinetically controlled ([PERSON] et al., 2017). In other words, all methane that enters the GHSZ and exceeds the CHI, solubility limit is immediately converted to hydrate ([PERSON] et al., 2017). Here, the minimum gas saturation for hydrate formation is set at 1%, which allows a small portion of free and dissolved gas to be present in the GHSZ (a minimum gas saturation of 0% for hydrate formation, by contrast, would mean all methane entering the GHSZ forms hydrate, with no free gas able to occur). Relevant GH phase properties are provided in Table 5.
PetroModTurk's ability to simulate complex geological basin evolution (including burial and salt movement histories), hydrocarbon generation, multiphase flow, and the temperature- and pressure-dependent stability, formation, and dissociation of GH means that the software can be used to model GH recycling ([PERSON] et al., 2019). During recycling, GH accumulations initially within the GHSZ are shifted downward, below the BGHSZ (i.e., the BGHSZ is shifted upward relative to the hydrate-bearing sediment), placing the hydrate under conditions at which it is no longer stable. The destabilized hydrate dissociates into water and free gas, and the liberated methane becomes available to migrate buoyantly upward and recrystallize GH at the new upward-shifted BGHSZ. Released gas may also be trapped as free gas beneath the BGHSZ, due to the scaling properties (i.e., capillary entry pressure effects; [PERSON] and [PERSON], 2007; [PERSON] and [PERSON], 2003) of the overlying hydrate (e.g., [PERSON], 1993; [PERSON], 1984; [PERSON] et al., 2003; [PERSON], 2001; [PERSON] et al., 2004; [PERSON] and [PERSON], 2003). PetroModTurk predicts temperature and pressure changes through time to model GHSZ evolution and can thereby capture hydrate recycling driven by numerous processes that might modify temperature- and pressure-dependent hydrate stability, including sediment burial-driven temperature changes (e.g., [PERSON] et al., 2007; [PERSON] et al., 2018; [PERSON] et al., 1994) as well as salt movement-driven temperature changes. This capability has been successfully employed by a limited number of studies ([PERSON] and [PERSON], 2021) that model sedimentation-driven (burial-driven) GH recycling and development of high-saturation hydrate deposits, including work on the Gulf of Mexico's Green Canyon area ([PERSON] et al., 2017), work on two thrust ridges of New Zealand's Hikurangi Margin ([PERSON] et al., 2022), and our preliminary work on the Gulf of Mexico's Terrebonne Basin ([PERSON], 2021).
Porewater salinity is used by PetroModTurk in conjunction with pressure and temperature properties to calculate GH stability and solubility, in accordance with the equations set forth by [PERSON] et al. (2005). PetroModTurk assumes prowewater salinity to be constant through time. Because processes are being modeled at the resolution of the model cell size (on the order of tens of meters), PetroModTurk does not account for microscale changes in porewear chemistry due to GH formation and dissociation (other than methane content) ([PERSON] et al., 2015) or due to the presence of salt diapirs. For the synthetic models, a salinity of 35% (standard for seawater; e.g., Lyman and Fleming, 1940) was applied. Salinities applied to the real-world models are discussed below.
### Real-World Modeling Approach
We construct two 2-D basin and GH system models based on known salt diapir-associated GH localities at Green Canyon (Gulf of Mexico) and Blake Ridge (offshore Carolinas).
#### 2.3.1 Green Canyon
The Green Canyon area is located within the northern Gulf of Mexico salt province, and at the Green Canyon Block 955 site studied here, contains a prominent salt diapir ([PERSON] et al., 2020). GH occurs throughout the northern Gulf of Mexico, and has been recovered from multiple sites in the Green Canyon area ([PERSON] et al., 1986).
Geophysical, drilling, and previous modeling work in the area supply the inputs necessary for the construction of a 2-D model of the Green Canyon diapir and associated GH system. Green Canyon model dimensions are provided in Table 1. Green Canyon sediment characteristics and rock properties are listed in Table 2, while sediment organic properties and biogenic gas generation kinetics are listed in Table 4. Table 5 provides computational parameters for gas migration and hydrate formation.
We present model scenarios including the Green Canyon site salt diapir as well as a model scenario completely excluding the salt diapir (see below). As at the Blake Ridge site, it is noted that salt diapirism in the Green Canyon area causes doming of sediments, including expression as domes at the seafloor ([PERSON] and [PERSON], 1998). The depth of the underlying salt layer at the site seems poorly constrained, as [PERSON] et al. (2017) adopt a salt layer depth of \(\sim\)2,400 m below seafloor (mbsf) in their modeling effort, whereas [PERSON] et al. (2020) mention that the salt diapir has an apparent height of \(\sim\)6 km, suggesting an underlying source salt layer depth of \(\sim\)7,500 mbsf. Because the focus of our work is on salt diapir-related effects (and not on underlying source salt layer effects), we conservatively adopt a source salt layer depth of 7,500 mbsf. The age of this underlying salt layer is approximately Late Jurassic (\(\sim\)145-164 Ma) (Salvador, 1987). Salt movement in the northern Gulf of Mexico is inferred to have initiated in the Mesozoic and early Cenozoic ([PERSON] et al., 2013), although movement specifically within the Green Canyon area is said to have initiated in Neogene times ([PERSON] et al., 2017). We model salt movement starting at 20 Ma. Salt movement in the Green Canyon area has continued through recent times and is likely to be active today ([PERSON] et al., 1998; [PERSON], 1992).
We run one salt diapir model scenario that includes a \(\sim\)30-m-thick sand-dominated layer at the approximate level of the BGHSZ and within the upper 1.5 km of shale-dominated sediment, consistent with drilling results and seismic stratigraphic analysis at this site ([PERSON], [PERSON], et al., 2012; [PERSON] et al., 2012; [PERSON] et al., 2017; [PERSON] et al., 2020), and also run a model scenario that excludes this sand-dominated layer, so as to examine in relative isolation the potential lithological control of a sand-rich reservoir on GH saturations (a mechanism suggested for this site by [PERSON], [PERSON], et al., 2012).
Both biogenic and thermogenic GHs have been recovered in the Green Canyon area ([PERSON] et al., 1986), though most hydrate is likely of biogenic origin ([PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2022). Notably, BSR depth above the salt diapir is estimated at \(\sim\)450 mbsf ([PERSON], [PERSON], et al., 2012), which is significantly (\(\sim\)400 m) shallower than predicted based solely on standard temperature and pressure gradient assumptions ([PERSON] et al., 2020). GH saturations at the BGHSZ are as high as 90 vol. % in the domed sediments overlying the diapir, and average 50 to over 80 vol. % in the \(\sim\)30-m-thick GH reservoir identified here ([PERSON] et al., 2012; [PERSON] et al., 2020; [PERSON] and [PERSON], 2012; [PERSON] et al., 2022; [PERSON] et al., 2020), while saturations in the overlying sediments (183-266 mbsf) are estimated to be either negligible, based on P-wave velocity logs, or about 20 vol. %, based on a resistivity log ([PERSON] and [PERSON], 2012). [PERSON] et al. (2017) hypothesize that elevated GH saturations at the BGHSZ are in part due to recycling driven by high Neogene sedimentation rates, in conjunction with lithological control due to sandier reservoir sediments at this depth (e.g., [PERSON], [PERSON], et al., 2012). Notably, it is inferred that a substantial amount of free gas is trapped beneath the BGHSZ by the overlying, relatively impermeable hydrate accumulation ([PERSON], [PERSON], et al., 2012). Also of relevance to salt-influenced GH occurrence at this site is the postulation that continued salt diapir growth may continue to thin the GHSZ ([PERSON] et al., 2020). A water depth of 2,000 m is used for this site ([PERSON] et al., 2020), and is treated as constant through the time interval modeled here. We make this simplified assumption to negate the potential influence of changing hydrostatic pressure on the GHSZ. This approach of assuming a constant water depth follows the practice of [PERSON] et al. (2017), who took a more extreme approach and modeled a relatively constant water depth for the Green Canyon area from 100 Ma to present. Nonetheless, we acknowledge that sea level has in fact been highly variable during the Cenozoic ([PERSON] et al., 1987; [PERSON] et al., 2005, 2020), including recent high-magnitude fluctuations in the northern Gulf of Mexico (e.g., [PERSON] et al., 1998; [PERSON] and [PERSON], 1991). Water temperature at the seafloor is treated as 4\({}^{\circ}\)C throughout the modeled time interval ([PERSON] et al., 2017; [PERSON] et al., 2020). Basal heat flow in the Green Canyon area is 42 mW/m\({}^{2}\) at present day ([PERSON] and [PERSON], 2016), and heat flow is inferred to have decayed slightly from a value of \(\sim\)50 mW/m\({}^{2}\) at 100 Ma to the present-day value ([PERSON] et al., 2017). Here, we conservatively treat basal heat flow as constant through time at 42 mW/m\({}^{2}\). Geothermal gradients immediately above the diapir crest are over twice the regional geothermal gradient, and gradients in the overlying domed sediment at the level of the BSR are nearly twice the regional gradient ([PERSON] et al., 2020). Accordingly, heat flow in the sediments overlying the diapir crest up to the level of the BGHSZ is around twice that of the basal heat flow. Salinity at this site is conservatively assumed to be 35% (standard for seawater; e.g., [PERSON] and Fleming, 1940), consistent with values of 17-35% measured in the area ([PERSON] et al., 2020).
#### 2.3.2 Blake Ridge Diapir
The Blake Ridge Diapir occurs as one of more than two dozen salt diapirs located in the Carolina Trough ([PERSON] et al., 1982). GH occurs in the sediments overlying the diapir, and was recovered from multiple holes drilled at Site 996 of ODP Leg 164 ([PERSON] et al., 1996).
Drilling information and additional work at the site provide the suite of inputs necessary for the construction of a 2-D model of the Blake Ridge Diapir and associated GH system. Blake Ridge model dimensions are provided in Table 1. Blake Ridge sediment characteristics and rock properties are listed in Table 2, while sediment organic properties and biogenic gas generation kinetics are listed in Table 4. Computational parameters for gas migration and hydrate formation are provided in Table 5.
The diameter of the salt diapir itself is not fully constrained, but may be as much as \(\sim\)3.5 km based on seismic data presented in [PERSON] et al. (2000). We adopt a conservative diapir diameter of 2 km, as used by [PERSON] et al. (2005). Similarly, the depth of the crest of the diapir is unknown but is modeled as 1 km beneath the seafloor by [PERSON] et al. (2005) based on previous work suggesting that salt diapirs reach neutral buoyancy at \(\sim\)1 km depth ([PERSON], 1993). We adopt this estimate, assuming a 1,000 mbsf diapir crest depth, though it bears mentioning that diapirs can rise above the level of neutral buoyancy due to differential loading of sediment ([PERSON] & [PERSON], 2007; [PERSON] & [PERSON], 1986; [PERSON] et al., 1993; [PERSON], 1993). Diapirism causes doming of sediment at Blake Ridge, including expression as positive bathymmetric relief on the seafloor at this site ([PERSON] et al., 1996). The top of the diapir source (i.e., the underlying salt layer) is estimated at 8,000 mbsf ([PERSON] et al., 1996), while the age of this salt is estimated to be Middle Jurassic (\(\sim\)164-174 Ma) or older ([PERSON] et al., 1982). Here, we model salt movement beginning \(\sim\)23 Ma.
GH recovered at the site is of predominantly biogenic origin ([PERSON] et al., 1996). Importantly, the BSR occurs at \(\sim\)400 mbsf away from the diapir, but shallows to \(\sim\)245 mbsf above the diapir ([PERSON] et al., 2005). [PERSON] et al. (2000) note that salinity likely has little influence on this observed upwardping of the BGHSZ, and previous studies suggest that the upwardping is instead due to diapir-driven heat flow effects ([PERSON] et al., 2005; [PERSON] et al., 2000). The BSR was not reached during drilling, and thus, concentrations at the BGHSZ are unknown ([PERSON] et al., 1996). While GH and free gas saturations are not available from Site 996 of ODP Leg 164, estimations from nearby sites 994, 995, and 997 suggest hydrate saturations of \(\sim\)3%-8% of the pore space above the BSR, and free gas saturations of up to 14% of the pore space below the BSR ([PERSON] & [PERSON], 2002), although earlier work suggests that these hydrate and free gas values could be slightly higher ([PERSON] et al., 1997).
A water depth of 2,160 m is adopted for the site ([PERSON] et al., 2005; [PERSON] et al., 1996). Water temperature at the seafloor is 3.5\({}^{\circ}\)C ([PERSON] et al., 1996), and is treated as such throughout the modeled time interval. A heat flow of 40 mW/m\({}^{2}\) was assumed by [PERSON] et al. (2000) for sediments away from the diapir, while [PERSON] et al. (2005) used a similar basal heat flow of 38 mW/m\({}^{2}\). We use this basal heat flow of 38 mW/m\({}^{2}\) throughout the time interval modeled here. Importantly, [PERSON] et al. (2000) document a salt-influenced heat flow of 70 mW/m\({}^{2}\) in the sediments above the salt diapir and near the seafloor. A salinity of 35% is adopted, as in [PERSON] et al. (2000).
### Model Limitations
Numerous assumptions and their attendant uncertainties are embedded within the basin and GH system modeling process, including certain computational limitations and simplifications (e.g., [PERSON] et al., 2017; [PERSON] & [PERSON], 2009; [PERSON] et al., 2019). Within the description of our synthetic and real-world modeling approaches, above, we have detailed numerous assumptions made for the purposes of this study. Basin and salt geometries are inherently simplified during the modeling process, and in the case of the real-world models described here, are subject to assumptions made due to lack of data, such as poorly constrained salt geometries and depths at Green Canyon ([PERSON] et al., 2017; [PERSON] et al., 2020) and Blake Ridge ([PERSON] et al., 2005; [PERSON] et al., 2000). In the PetroMod\({}^{\text{TM}}\) backstripping-based interpolations of salt diapir geometries through time, we do not consider the possibility that the salt becomes emergent at the seafloor (e.g., [PERSON] & [PERSON], 2007; [PERSON] et al., 1994; [PERSON] et al., 1993; [PERSON] & [PERSON], 1992). We do not consider the possibility that salt diapirism could be promoting faulting (e.g., [PERSON] et al., 2018; [PERSON] et al., 1994; [PERSON] et al., 1996; [PERSON] et al., 1993; [PERSON] et al., 2000; [PERSON] et al., 2009), and we do not consider the influence of faults (e.g., as permeable pathways for the enhanced migration of gas) on GH formation (e.g., [PERSON], 2022; [PERSON], 1993; [PERSON] et al., 2020; [PERSON] et al., 2007; [PERSON] & [PERSON], 1996; [PERSON] et al., 2002). Integration of faults could be important to future modeling efforts, as, for example, the complex network of faults at Green Canyon has been invoked as a possible migration mechanism to help explain elevated hydrate concentrations found there (e.g., [PERSON] et al., 2017; [PERSON] et al., 2022), and the potential importance of fault-mediated gas migration to the hydrate system has likewise been discussed for Blake Ridge (e.g., [PERSON] et al., 2002; [PERSON] et al., 2000;[PERSON] & [PERSON], 2000). Relatedly, we do not investigate the possibility of advective heat transport by warm fluids moving along permeable faults, which can have detrimental effects on hydrate stability (e.g., [PERSON] et al., 2014; [PERSON] et al., 2012), including as a possible contributing factor to BGHSZ upwarping at Blake Ridge ([PERSON] et al., 2000). Importantly, we do not consider salt diapir-driven changes to porewater salinity, a limitation of PetroMod(tm) ([PERSON] et al., 2019) that is unfortunate, as the impact of salinity on GH stability, such as inhibition of hydrate formation due to ions released into brines from dissolution of diapir-related salt, is well-established (e.g., [PERSON] et al., 1999; [PERSON], 1997; [PERSON], 1990; [PERSON] & [PERSON], 1986; [PERSON] et al., 1981; [PERSON] et al., 2005; [PERSON] et al., 2015), and has also been invoked as a possible contributor to BGHSZ upwarping at Blake Ridge ([PERSON] et al., 2000), though not at Green Canyon, where we nonetheless assume a salinity at the uppermost limit of actual on-site measurements ([PERSON] et al., 2020). As discussed above, PetroMod(tm) does not account for microscale hydrate- or diapir-mediated changes to porewater chemistry, due to model cell resolutions ([PERSON] et al., 2015). PetroMod(tm) does not model capillary effects on hydrate solubility and the hydrate phase boundary ([PERSON] et al., 2019), which can be significant and have been invoked to help explain hydrate occurrence at Blake Ridge (e.g., [PERSON] et al., 1999; [PERSON] & [PERSON], 2011), while capillary inhibition is unlikely in explaining reservoir-interval Green Canyon hydrate saturations ([PERSON] et al., 2022). GH modeling in PetroMod(tm) does not incorporate types of hydrate-forming gases other than methane (e.g., carbon dioxide, ethane, propane, and other C\({}_{\pm}\) hydrocarbon gas molecules; e.g., [PERSON], 1995; [PERSON] & [PERSON], 1983; [PERSON], 2005; [PERSON], 1998), and the software is unable to simulate the formation of structure II or structure H GH, which are present in some parts of the Gulf of Mexico (e.g., [PERSON] et al., 2010; [PERSON] & [PERSON], 1994; [PERSON] et al., 2001). As discussed above, we focus on microbial gas generation, and do not model thermogenic gas generation. Anaerobic oxidation of methane is not modeled in PetroMod(tm), meaning hydrate saturations in the uppermost (seafloor to \(\sim\)50 mbsf) sediments are likely overestimated ([PERSON] et al., 2017). As discussed above, PetroMod(tm) assumes that methane entering the GHSZ and exceeding the solubility limit is instantaneously converted to hydrate, and therefore does not consider the kinetically feasible coexistence of hydrate and free gas phases within the GHSZ ([PERSON] et al., 2017) or, for instance, the migration of gas through the GHSZ, invoked at Blake Ridge ([PERSON] et al., 2002). We make various assumptions by assigning model boundary conditions, as detailed above, including the assumption of constant basal heat flows, sediment-water interface temperatures, and water depths through time, and we do not explicitly consider, for instance, impacts of sea-level fluctuations on variable delivery of organic matter or coarse-grained sediment to our real-world model areas (e.g., [PERSON], 2009; [PERSON] et al., 2023; [PERSON] et al., 1996), though we do seek to replicate corings- and geophysical data-based interpretations of stratigraphy and lithology, as detailed above.
## 3 Results
### Synthetic Models
We report results from synthetic modeling aimed at examining the influence of salt diapirism on GH formation by modeling variations in relevant parameters, including (a) basal heat flow, (b) salt diapir diameter, (c) salt stock heights, and (d) sediment thermal conductivities.
#### 3.1.1 Variable Heat Flows
As anticipated, variations in basal heat flow exert a marked influence on the thickness of the GHSZ as well as on the nature of GH accumulations (Figures 2 and 3; Table 6; Figure S2 in Supporting Information S1).
For scenarios with modeled movement of a salt diapir, the GHSZ thins directly above the crest of the diapir from 890 m at \(\sim\)3.1 Ma to 725 m at present (\(\sim\)19% reduction in thickness) for the 35 mW/m\({}^{2}\) heat flow scenario, from 495 to 410 m (\(\sim\)17% reduction) for the 50 mW/m\({}^{2}\) scenario, and from 375 to 280 m (\(\sim\)25% reduction) for the 65 mW/m\({}^{2}\) scenario (Figure 2; Table 6; Figure S2 in Supporting Information S1). The GHSZ also thins at the edges of the model over the modeled time interval, but only by \(\sim\)6%-11% for the three aforementioned heat flow scenarios (Table 6).
By contrast, the scenarios excluding a salt diapir show only minimal reductions in GHSZ thickness over the same time interval, showing reductions in the range of \(\sim\)7%-12% at the center of the model and \(\sim\)0%-14% at the edges of the model (Figure 2; Table 6; Figure S3 in Supporting Information S1).
With-salt versus no-salt synthetic modeling scenarios (i.e., salt diapir-driven recycling vs. only sedimentation-/burrial-driven hydrate recycling scenarios) reveal a significant difference in predicted GH satu
to 1.64 TCF at present (\(\sim\)8% decrease), although free gas column height increases from 90 to 120 m during this same time. For all no-salt heat flow scenarios from \(\sim\)3.1 Ma to present, free gas accumulations are non-existent or negligible (0 TCF with a column height of 0 m).
#### 3.1.2 Variable Salt Diapir Diameters
Interestingly, variations in salt diapir diameter seem to exert control on the efficacy with which diapirs cause recycling and concentration of GH. For the 1 and 2 km salt diapir diameter scenarios, saturations of GH exceeding 90 vol. % occur above the crest of the diapir (Figure 5). At diapir diameters of 4 km and wider, increasing diapir diameter has the effect of creating lower, more diffuse hydrate concentrations, such that for the maximum diameter tested (9 km), GH occurs at saturations restricted to <20 vol. % diffusely throughout the model (Figure 5). This is perhaps explained by the salt-mediated heat flow being less focused or less spatially concentrated: the 2-km-wide diapir is most effective at channeling heat flow from its crest, and therefore most effective in creating the highest saturations of hydrate. At 9 km, heat flow radiates upward from the salt across the entire width of the model, preventing appreciable focusing and accumulation of GH.
As might be predicted, in the 1-8 km diapir diameter scenarios, the shape of the GHSZ corresponds to the shape of the top of the diapir, with the upward base of the GHSZ becoming increasingly wide from 1 to 8 km (Figure 5). At the edges of the models in the 1-6 km diapir diameter scenarios, the depth of the BGHSZ is relatively constant at \(\sim\)3.2 km, but in the 8 and 9 km scenarios, the BGHSZ shallows \(\sim\)3.1 and \(\sim\)2.95 km, respectively.
#### 3.1.3 Variable Salt Stock Heights
For salt stock heights from 0 to 1 km, stock height exerts some influence on GHSZ thickness, whereby the GHSZ is somewhat thicker than for greater stock heights. For instance, GHSZ thickness is 300 m for the 0.25 and 0.5 km salt stock heights and 270 m for the 1 km stock height, but shrinks to 240 m for the 3, 5, and 7 km stock heights (for stock heights \(\geq\)3 km, changing stock height seems to exert no influence on GHSZ thickness).
#### 3.1.4 Variable Sediment Thermal Conductivities
Unsurprisingly, increasing sediment thermal conductivity in the deeper silt to either side of the diapir (while holding shallow silt conductivity constant) leads to decreasing GHSZ thickness in the overlying sediment away from the salt diapir (Figure S7 in Supporting Information S1). For instance, for a lower conductivity of 1.6 W/m/K, the GHSZ away from the salt diapir (i.e., toward the edges of the model) is 450 m thick, while it is 390 m thick for a conductivity of 2.0 W/m/K, and 360 m thick for conductivities of 2.4 and 2.8 W/m/K (Figure S7 in Supporting Information S1). However, directly above the diapir crest, GHSZ thickness is actually greater (at 270 m) for the two higher deeper silt thermal conductivity scenarios of 2.4 and 2.8 W/m/K than for the 1.6 and 2.0 W/m/K scenarios (240 m). This is perhaps because the flux of heat entering the base of the model is impeded to a greater degree by lower thermal conductivities in the sediment, and is accordingly channeled through the highly conductive salt to a greater degree than if the sediment itself were more conductive.
By varying the thermal conductivity of the shallow silt (i.e., varying conductivities at depths shallower than the salt diapir crest, while holding deeper silt conductivity constant), we observe that higher shallow sediment thermal
Figure 2: Summary of predicted with-salt (pink color) versus no-salt (tan color) changes to gas hydrate stability zone (GHSZ) thickness (measured above the salt diapir crest; at the center of the model) and maximum GHat saturation since \(\sim\)3 Ma for three modeled heat flow scenarios: (a) 35 mW/m\({}^{2}\), (b) 50 mW/m\({}^{2}\), and (c) 65 mW/m\({}^{2}\). Decreases in GHSZ thickness (in %) are computed as the percentage change in GHSZ thickness from 3.1 to 1.5 Ma and from 1.5 to 0 Ma; changes in hydrate saturation (in vol. % per Myr) express the maximum absolute change in hydrate saturation per unit time, computed separately for 3.1–1.5 Ma and 1.5–0 Ma. Predicted GHSZ thicknesses and hydrate saturations are also listed in Table 6.
conductivities lead to higher GHSZ thicknesses, both immediately above the salt crest and toward the edges of the model. For instance, GHSZ thickness increases from 240 m above the diapir crest and 360 m at the model edges for the 1.4 W/m/K scenario to 300 m above the crest and 630 m at the edges for the 2.6 W/m/K scenario (Figure S7 in Supporting Information S1).
Figure 3.— Modeled salt diapir-associated gas hydrate (GH) saturations from \(\sim\)3 Ma to present for three heat flow scenarios: (a–c) 35 mW/m\({}^{2}\), (d–f) 50 mW/m\({}^{2}\), and (g–i) 65 mW/m\({}^{2}\). Hydrate saturation scale in (i) applies to all panels. Thin black lines indicate sediment layers; note that the salt diapir crest is beneath the field of view. The corresponding GH stability zone simulations are displayed in Figure S2 of Supporting information S1.
Figure 4: Model results (gas hydrate (GH) saturations) from identical scenarios as in Figure 3, but without inclusion of a salt diapir. The corresponding GH stability zone simulations are displayed in Figure S3 of Supporting information S1.
Figure 5: Present-day (0 Ma) modeled gas hydrate saturations for (a) 9, (b) 8, (c) 6, (d) 4, (e) 2, and (f) 1 km salt diapir diameters. Hydrate saturation scale in (f) applies to all panels. Note that the salt diapir crest is beneath the field of view in all panels.
### Green Canyon Model
Our Green Canyon model simulates salt movement concurrent with sedimentation from 20 Ma to present (Figure 6).
At present day, our model captures the influence of salt diapir-channeled heat on the distribution and thickness of the GHSZ (Figures 7a and 7b). We predict a BGHSZ depth of \(\sim\)470 mbsf directly above the diapir crest, compared to a BSR depth of \(\sim\)450 mbsf estimated by [PERSON], [PERSON], et al. (2012), and we predict a BGHSZ depth of \(\sim\)860 mbsf in the sediment away from the diapir, compared to a depth of \(\sim\)850 mbsf predicted via
Figure 6: Green Canyon salt diapir movement modeled from (a) 20 Ma to (f) present.
temperature and pressure gradient assumptions by [PERSON] et al. (2020). By contrast, running a model scenario that excludes the diapir but is otherwise identical fails to accurately predict a GHSZ thickness compatible with the literature: the BGHSZ depth at the center of the domed sediment is overestimated by \(\sim\)470 m and the BGHSZ depth at the edges of the model is underestimated by \(\sim\)120 m (Figure 7c). This corresponds directly to temperature distributions associated with the no-salt scenario (Figure 7d), which are markedly different from temperature distributions in the with-salt scenario (Figure 7b).
Figure 7: Predicted gas hydrate stability zone extent (in red) for Green Canyon (a) with and (c) without salt diapir and temperature distribution (b) with salt and (d) without salt. Scale applies to (b and d).
Our Green Canyon model predicts GH saturations ranging from \(\sim\)30 to 90 vol. %, and averaging \(\sim\)60 to \(>\)70 vol. %, at the depth of the sand-rich reservoir layer within the domed sediment (which coincides with the depth of the BGHSZ) (Figures 8 and 9), as compared to estimated average saturations of 50-80 vol. % and highs exceeding 90 vol. % for the reservoir ([PERSON] et al., 2012; [PERSON] et al., 2020; [PERSON], 2012; [PERSON] et al., 2022; [PERSON] et al., 2020). We predict negligible hydrate saturations above this reservoir interval (Figures 8 and 9), consistent with the observed average saturations.
Figure 8.— Modeled Green Canyon diapir-associated (a–c) gas hydrate and (d–f) free gas saturations from \(\sim\)1 Ma to present. Saturation scale in (f) applies to all panels.
with P-wave velocity log interpretations ([PERSON], 2012). By contrast, performing an identical simulation of our Green Canyon model, but excluding salt, we find that hydrate saturations are completely underpredicted, with saturations reaching no greater than \(\sim\)30 vol. %, with any saturations >15 vol. % being extremely spatially limited, and with any >15 vol. % saturations occurring in the silty sediment \(\sim\)0.1-0.4 km beneath the sandy
Figure 9. Zoomed-in view of modeled Green Canyon gas hydrate saturations from \(\sim\)1 Ma to present for (a–c) with-salt, with-sand and (d–f) no-salt, with-sand scenarios. Saturation scale in (c) applies to all panels.
reservoir layer due to a BGHSZ that is deeper than in the with-salt scenario (Figures 7 and 9f). Notably, results from an identical simulation to the Green Canyon with-salt model, and merely excluding the \(\sim\)30-m-thick sandy reservoir interval, yield hydrate saturations up to \(\sim\)75 vol. % and averaging \(\sim\)50 vol. % at the BGHSZ (Figure S9 in Supporting Information S1). Interestingly, our modeling of Green Canyon suggests that GH saturations in the with-salt, with-sand scenario have jumped from \(\sim\)15 to 60 vol. %, with an average of \(\sim\)40 vol. %, at \(\sim\)1 Ma to the present-day values of \(\sim\)30-90 vol. %, averaging \(\sim\)60 to \(>\)70 vol. % (Figures 8 and 9). By contrast, the hypothetical no-salt scenario actually suggests that maximum saturations have dropped from \(\sim\)40 vol. % at \(\sim\)1 Ma to \(\sim\)30 vol. % at present-day, and that saturations throughout the modeled section have dropped somewhat (Figure 9).
Estimations of GH volumes for both with- and without-salt scenarios add some nuance to the saturation results. Interestingly, present-day hydrate volumes are almost identical, and even slightly higher in the no-salt scenario, at 0.67 and 0.68 TCF for with- and without-salt, respectively. This can be attributed to the distribution of hydrate saturations predicted throughout each 2-D model transect. In the with-salt scenario, hydrate saturations are high and are essentially exclusively focused within the \(\sim\)30-m-thick sand-rich reservoir interval at the BGHSZ (Figure 9). In the no-salt scenario, hydrate saturations at the BGHSZ are much lower, but in the entire \(\sim\)500 m (at the center of the domed sediment) to \(\sim\)300 m (adjacent the domed sediment) thickness of sediment overlying the BGHSZ, hydrate saturations are \(\sim\)10-15 vol. % (whereas saturations in this sediment are \(\sim\)0 vol. % in the with-salt scenario) (Figure 9). Neither saturation scenario--whether \(\sim\)0 vol. % or \(\sim\)10-15 vol. % in sediment overlying the BGHSZ--can be excluded based on drilling data, as saturations in this overlying sediment are estimated to be either \(\sim\)0 vol. % (via P-wave velocity logs) or \(\sim\)20 vol. % (via a resistivity log) ([PERSON] & Collett, 2012). Nonetheless, it is clear that even in the scenario whereby total hydrate volumes for with- and without-salt scenarios are equal for Green Canyon at present-day, accumulations of GH are much more concentrated for the with-salt scenario, and much more diffuse for the no-salt scenario (Figure 9). Interestingly, the with-salt scenario suggests the same trend of increasing hydrate volumes through time as is described for our synthetic modeling heat flow scenarios, whereby GH volume increases from 0.64 TCF at 0.98 Ma to 0.66 TCF at 0.16 Ma to 0.67 TCF at present-day (\(\sim\)5% increase since \(\sim\)1 Ma). By contrast, the no-salt scenario shows the opposite trend, whereby GH volume decreases from 0.71 TCF at 0.98 Ma to 0.69 TCF at 0.16 Ma to 0.68 TCF at present (\(\sim\)4% decrease since \(\sim\)1 Ma).
Notably, both free gas volumes and column heights increase over this time interval for the with-salt scenario (Figure 8), whereas neither \(>\)0-TCF volumes nor \(>\)0-m column heights are predicted for the no-salt scenario (Figure S8 in Supporting Information S1). Our with-salt model therefore appears compatible with work by [PERSON], [PERSON], et al. (2012), suggesting that a significant amount of free gas is trapped beneath the hydrate reservoir at Green Canyon, whereas our no-salt model fails to predict free gas accumulation of any size. Free gas volumes predicted by the with-salt scenario increase from 1.44 TCF at 0.98 Ma to 1.57 TCF at present (\(\sim\)9% increase), while column heights increase from 90 to 120 m during the same period.
### Blake Ridge Model
We model salt movement from 23 Ma to present in our Blake Ridge Diaipr model (Figure S10 in Supporting Information S1).
Our model successfully captures the diapir-related upwarping of the BGHSZ (Figure S11a in Supporting Information S1) previously described at Blake Ridge ([PERSON] et al., 2005; [PERSON] et al., 2000). We predict a BGHSZ depth of \(\sim\)240 mbsf directly above the salt diapir crest (and predict the GHSZ here has thinned by \(\sim\)16% since 0.65 Ma), compared to a BSR depth of \(\sim\)245 mbsf given by [PERSON] et al. (2005), and we predict a BGHSZ depth of \(\sim\)390 mbsf in the sediment toward the edges of the model (and predict the GHSZ here has thinned by \(\sim\)6% since 0.65 Ma), compared to a BSR depth of \(\sim\)400 mbsf given by [PERSON] et al. (2005). As with the Green Canyon model, running a model scenario that excludes the salt diapir but is otherwise identical fails to predict a GHSZ thickness consistent with the literature: BGHSZ depth at the center of the domed sediment is predicted as \(\sim\)360 m (unchanged since 0.65 Ma) and BGHSZ depth at the edges of the model is predicted as \(\sim\)330 m (also unchanged since 0.65 Ma) (Figure S11c in Supporting Information S1). As at Green Canyon, this is due to the influence of the diapir on temperature distributions (Figure S11b vs. Figure S11d in Supporting Information S1).
Predicted thinning of the GHSZ (i.e., upwarping of the BGHSZ) above the salt crest as it ascends also corresponds to a shallowing of the top of the single GH reservoir (\(>\)20 vol. % saturation) layer through time in the with-salt scenario, whereby the shallowest portion of the reservoir progressively migrates upward through the sediment
0.65 Ma to \(\sim\)2.50 km at 0.33 Ma to \(\sim\)2.50-2.51 km at present-day, though present-day also includes a secondary (>15 vol. % saturation) reservoir layer with the shallowest depth at \(\sim\)2.44 km (Figure 10d-10f). Furthermore, at present, the single >20 vol. % reservoir layer in the with-salt scenario has expanded laterally to greater than twice the horizontal extent of the previous two timesteps (>2-km extent at present-day vs. \(\sim\)1-km extent at 0.65 Ma and 0.33 Ma), whereas the no-salt scenario sees an evolution from two >10 vol. % saturation reservoirs at 0.65 Ma to one such reservoir at 0.33 Ma to two such reservoirs at present-day, and also sees no change in horizontal extent of any of these reservoir layers, which stay constant at \(\sim\)1-km widths (Figure 10).
The greater areal extent of the with-salt, single reservoir layer at present-day corresponds to a slightly higher (albeit quite low in comparison to the Green Canyon model) total GH volume of 0.07 TCF versus 0.06 TCF for the no-salt, multiple-reservoir layers. Both the with-salt and no-salt hydrate volumes have increased by 0.01 TCF since 0.65 Ma, representing a \(\sim\)17% increase for the with-salt scenario and a 20% increase for the no-salt scenario.
Also of potential relevance is the observation that only in the with-salt scenario are modeled free gas volumes and column heights greater than zero at present-day. Nonetheless, this with-salt free gas volume (at 0.03 TCF with a maximum saturation <30 vol. %) and column height at 30 m, or the minimum possible layer thickness) are both relatively minimal (Figure S12 in Supporting Information S1). Free gas volumes and column heights are 0 TCF and 0 m, respectively, for with-salt timesteps at 0.65 and 0.33 Ma (indicating an increase to present-day values) and for all no-salt timesteps (Figures S12 and S13 in Supporting Information S1).
Figure 11. Conceptual illustrations of sedimentation-/burial-driven gas hydrate (GH) recycling versus salt diapir-driven hydrate recycling. During sedimentation-driven recycling, hydrate-bearing sediment is buried below the base of the hydrate stability zone (BGHSZ), destabilizing and dissociating the hydrate into free gas and water. This free gas may then migrate upward and be incorporated as higher-concentration hydrate at the new BGHSZ. During diapir-driven recycling, the ascent of the salt diapir causes progressive upwarping of the BGHSZ. As the BGHSZ is pushed above hydrate-bearing sediment, the hydrate decomposes, releasing free gas that may be recycled into the new shallower BGHSZ as hydrate. Free gas may preferentially migrate along and toward the apex of sediment domed/folded by diapir ascent, promoting both formation of high-saturation hydrate and accumulation of a free gas column beneath the recycled high-saturation GH seal. Note that both sediment burial-driven and salt diapir-driven recycling, as illustrated here, involve temperature-driven hydrate destabilization. Abbreviations and symbols: GH, gas hydrate; sat, saturation; ; sed., sediment; \(T\), temperature; \(t_{p}\), time at present (on left, present-day seafloor/scliment surface; on right, present-day salt diapir crest depth); \(t_{i}\) and \(t_{p}\) time intervals in the past, with \(t_{b}\) being the oldest (indicating older, buried sediment surfaces on the left, and previous, deeper diapir crest depths on the right).
Though yielding quite low GH and free gas saturations for the with-salt scenario (especially compared to Green Canyon) and low hydrate saturations for the no-salt scenario, our model estimates (at 10-20 vol. % or more maximum hydrate saturation for with- and without-salt scenarios) are at the upper end of previous estimates for nearby sites at Blake Ridge, which postulated \(\sim\)3-8 vol. % ([PERSON] & [PERSON], 2002) or possibly slightly higher ([PERSON] et al., 1997) hydrate saturations above the BSR. However, because the BSR was not encountered during drilling at the Blake Ridge Diparir site, concentrations at the BGHSZ (such as those predicted in the with-salt scenario modeled here) are unknown, as are potential underlying free gas saturations ([PERSON] et al., 1996). Estimates at nearby sites, also performed by [PERSON] and [PERSON] (2002), approximate free gas saturations up to 14 vol. % below the BSR (about half the value of the maximum saturations predicted in our with-salt model, but higher than the 0 vol. % saturations predicted in our no-salt model), although, as with hydrate saturations, earlier work by [PERSON] et al. (1997) suggested slightly higher free gas saturations might be present at these adjacent sites. In any case, it is of note that only the with-salt scenario produces any free gas accumulation, which is more consistent with the inference that, however minimal, free gas accumulations are present at at least some of the Blake Ridge sites.
## 4 Discussion
### Salt Diapir-Driven Gas Hydrate Recycling Demonstrated via Synthetic and Real-World Models
Through numerous synthetic basin and GH system models as well as real-world models from Green Canyon and Blake Ridge, we confirm that salt diapir movement causes an upwarping of the BGHSZ and an overall thinning of the GHSZ through time, as demonstrated in numerous previous studies (e.g., [PERSON] et al., 2008; [PERSON] et al., 2005; [PERSON] et al., 2020; [PERSON] et al., 2000). However, while previous work has described the influence of salt diapirism as a cumulatively destructive mechanism within the context of GH systems (e.g., [PERSON] et al., 2020; [PERSON] et al., 2005), we show through our combined synthetic and real-world modeling that salt diapirs can serve as a constructive mechanism by promoting GH recycling (Figures 2 and 11).
Previous work demonstrates recycling as a mechanism for concentrating (i.e., increasing through time) GH saturations at the BGHSZ (e.g., [PERSON] et al., 2017; [PERSON] et al., 2008; [PERSON] et al., 1994; [PERSON] et al., 2022; [PERSON] & [PERSON], 2021). Here, we present a newly described mechanism for GH recycling: salt diapirism. We show that the movement of salt diapirs and resultant changes to local heat flows lead to GH recycling and produces elevated saturations and volumes of GH at the BGHSZ and elevated volumes of free gas beneath the BGHSZ (Figure 11). We demonstrate that this salt diapir-driven GH recycling is a mechanism by which saturations of hydrate accumulations at the BGHSZ may reach >90 vol. % (vs. saturations limited to <30 vol. % in synthetic scenarios that exclude a salt diapir) and by which volumes of both GH at and free gas beneath the BGHSZ may be significantly elevated through time. Notably, a comparison of with-salt model scenarios (i.e., salt diapir-driven hydrate recycling scenarios) against no-salt model scenarios (i.e., burial-driven hydrate recycling scenarios, in which recycling occurs at a background rate paced by sedimentation) indicates a significant contrast between the rates of hydrate recycling in each scenario (Figure 2). In our synthetic models, salt diapir-driven hydrate recycling increases maximum GH saturations by 20-30 vol. % per Myr, whereas solely sedimentation-driven recycling increases maximum saturations by no more than 7 vol. % per Myr since 1.5 Ma (Figure 2).
By examining the influence of salt diapir-mediated temperature changes on the GH recycling process, this work represents an investigation into the poorly understood ([PERSON] et al., 2022) influence of local GHSZ perturbations on the recycling process. Furthermore, the demonstration of salt diapir-driven hydrate recycling provides an effective recycling mechanism that may lead to locally elevated hydrate saturations on old, rifted continental margins (i.e., where many major global salt basins are located; [PERSON] & [PERSON], 2007) where rates of recycling due to non-diapir-related processes are otherwise thought to be low ([PERSON] et al., 2007, 2008).
### Salt Diapir-Driven Gas Hydrate Recycling Can Explain Observations at Green Canyon
A close agreement between our Green Canyon model results (GHSZ thicknesses) and geophysical observations (BSR depths from seismic data; [PERSON], [PERSON], et al., 2012) and between our model results (GH saturations, and presence of free gas accumulations) and logging-while-drilling data (estimates of GH saturations from P-wave velocities and a resistivity log, and the inference of a substantial sub-hydrate free gas accumulation; [PERSON], [PERSON], et al., 2012; [PERSON] et al., 2012; [PERSON] & [PERSON], 2012), as well as a close adherence to model input data available from previous work in the region and at the Green Canyon diapir modeled here, lend confidence to the results and interpretations described herein.
We show that lithological control on observed GH saturations ([PERSON], [PERSON], et al., 2012; [PERSON] et al., 2022) is important--here, the with-salt, with-sand scenario (Figure 9) is estimated to account for hydrate saturations elevated by \(\sim\)10-15 vol. % beyond the with-salt, no-sand scenario (Figure S9 in Supporting Information S1)--but that salt diapir-driven recycling may be a more important control in the case of the Green Canyon diapir: we show that the diapir may account for saturations elevated by \(\sim\)35-45 vol. % (derived by comparing the with-salt, no-sand scenario with the no-salt, with-sand scenario; Figure 9 and Figure S9 in Supporting Information S1). In our modeling work presented here, it is only by combining the effects of lithological control ([PERSON], [PERSON], et al., 2012) and salt-driven recycling control (this study)--and not by considering either control in isolation--that our Green Canyon model accurately predicts the average and maximum GH saturations estimated from logging data during previous studies of the site. This said, there are various processes in addition to lithological control and salt diapirism that could help explain observed present-day hydrate saturations at Green Canyon, and while our modeling does account for the process of sedimentation-driven recycling invoked for the site ([PERSON] et al., 2017), we do not, for example, investigate the possible role of faults (e.g., [PERSON] et al., 2017; [PERSON] et al., 2022). Overall, however, recycling is acknowledged as a plausible explanation for observed elevated hydrate saturations at Green Canyon ([PERSON] et al., 2022; [PERSON] et al., 2022), and may be more compatible with findings of predominantly biogenic gas at the site ([PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2022) than fault-mediated gas migration (as noted by [PERSON] et al., 2022).
We also find that sedimentation-driven recycling (e.g., Figure 11) need not fully explain the elevated hydrate saturations observed within the sandy reservoir interval here (e.g., [PERSON] et al., 2017). We arrive at this conclusion through the consideration of a Green Canyon model that excluded salt but would be able to capture sedimentation-driven recycling (the \"no-salt, with-sand\" scenario; Figure 9), in which average predicted reservoir-interval saturations were at least \(\sim\)35% lower and maximum reservoir-interval saturations were at least \(\sim\)60% lower than saturations estimated from logging data by previous workers. Although the influence of sedimentation-driven recycling could potentially be enhanced by very high sedimentation rates (i.e., greater than the \(\sim\)0.3-0.4 km/Myr modeled here for Green Canyon), the influence of heat flow-driven (i.e., salt diapir-driven) recycling seems inextricable from the case of Green Canyon GH saturations. Furthermore, the influence that diapir movement has on the observed doming of overlying sediment at this locality, which--as demonstrated by our models--controls focused gas migration into the GHSZ (this focusing is also illustrated by [PERSON] et al., 2022), and without which hydrate saturations would be much more diffuse across the \(\sim\)10-km-wide modeled transects, must be considered. This diapir-driven sediment folding and focused gas migration may provide a mechanism for overcoming the initial hydrate saturation needed to initiate an effective recycling process at the BGHSZ ([PERSON] et al., 2017). Finally, failure to consider salt influence (i.e., the \"no-salt, with-sand\" model scenario; Figure 9) also means that the significant sub-hydrate free gas accumulation interpreted by [PERSON], [PERSON], et al. (2012) for this site is completely missed, with neither \(>\)0 TCF free gas accumulations nor \(>\)0-m column heights produced by this no-salt scenario.
### Salt Diapir-Driven Gas Hydrate Recycling May Explain Some Observations at Blake Ridge
For the with-salt scenario, progressive upward migration of the \(>\)20 vol. % saturation GH reservoir layer from 0.65 Ma to present (Figures 10a-10c) is consistent with GHSZ thinning due to upward migration of the salt diapir crest and is consistent with repeated BGHSZ upwarping-driven disassociation of GH into free gas and re-accumulation as hydrate at stratigraphically shallower depths (i.e., GH recycling). Additionally, the consistent localization of any appreciable (\(>\)10 vol. % saturation) amount of hydrate into this single hydrate reservoir layer through the three timesteps examined for the with-salt scenario (as reflected by the doubling in horizontal extent of this single reservoir from \(\sim\)1 km at 0.65 Ma to \(>\)2 km at present-day) versus the somewhat more diffuse, dispersed distribution of hydrate-bearing reservoir (\(>\)10 vol. % saturation) layers in the no-salt scenario (and as reflected, by contrast, in the unchanging \(\sim\)1-km extent of the various reservoirs) at various timesteps is consistent with recycling in the with-salt scenario driving progressive focusing of and concentration of GH accumulations specifically at the BGHSZ, rather than a lack of recycling leading to a less focused distribution of hydrate saturations throughout the GHSZ as in the no-salt scenario (Figure 10a). The observation of predicted present-day free gas accumulation (albeit small in volume) in the with-salt scenario (Figure S12 in Supporting Information S1)but the lack of any free gas accumulation in the no-salt scenario (Figure S13 in Supporting Information S1) may provide additional evidence for some amount of salt diapir-driven recycling and locally elevated hydrocarbon saturations at and below the BGHSZ at the Blake Ridge Diapir site.
This said, for the no-salt scenario, the observed secondary (>15 vol. % saturation) GH reservoir layer with apex at a shallower, \(\sim\)2.44 km [PERSON] may indicate some degree of sedimentation-driven (i.e., burial-driven) recycling (Figure 10f) (e.g., as discussed by [PERSON] and [PERSON] (2019)), which potentially explains the downward migration (burial?) of the primary (>20 vol. % saturation) hydrate reservoir since 0.65 Ma (Figure 10d-10f), and may partially explain the observed increase in no-salt GH volume from 0.65 Ma, though it should be noted that these sorts of relatively small magnitude increases in GH saturation and volume through time can also be products simply of continued biogenic gas generation, migration, and accumulation in the [PERSON].
In general, previous estimates of <10 vol. % hydrate saturations and <20 vol. % free gas saturations at Blake Ridge GH sites ([PERSON] et al., 1997; [PERSON] and [PERSON], 2002) and our estimates of maximum hydrate saturations of \(\sim\)10-20 vol. % (for both with- and without-salt scenarios) and free gas saturations no greater than \(\sim\)30 vol. % (for the with-salt scenario) as well as our estimates of present-day GH volumes of 0.07 TCF or less and free gas volumes of 0.03 or 0 TCF for both scenarios suggest that Blake Ridge Diapir may not be of particularly high resource prospectivity, with neither compelling unconventional nor conventional hydrate-associated natural gas potential.
### Implications of Salt Diapir-Driven Gas Hydrate Recycling for Resource Exploration
Given particular relevance to both conventional and unconventional resource exploration, it bears mentioning again that, through numerous synthetic and real-world basin and GH system models, we demonstrate that salt diapir-driven GH recycling is a mechanism by which saturations and volumes of hydrate accumulations near the BGHSZ (as an unconventional exploration target) can be significantly elevated beyond a no-salt baseline (with saturations attaining >90 vol. %) and by which volumes of free gas trapped beneath the BGHSZ (as a conventional exploration target) may likewise be significantly elevated. With regard to resource accumulation, we demonstrate through synthetic models and Green Canyon and Blake Ridge models that GH can act as a feedstock in producing appreciable free gas accumulations via salt-driven decomposition and recycling, and may concurrently act as a seal (in the classical petroleum system sense; [PERSON] and [PERSON], 1994; [PERSON] and [PERSON], 2014) to allow build-up of an underlying free gas column (Figure 11). Due to the particularly elevated saturations that may be found within salt diapir-associated recycled GH (as demonstrated here), salt-associated recycled hydrate near the BGHSZ may represent a sealing element of particularly high integrity (at least within the context of considering GH as a potential seal). This inference is supported by the finding that throughout our synthetic and real-world modeling efforts, predicted free gas columns were consistently and exclusively observed in connection with modeling scenarios that included a salt diapir and that showed some amount of inferred GH recycling near the BGHSZ.
Because of elevated hydrate saturations and volumes and elevated free gas volumes and column heights associated with salt diapir-driven recycled hydrates, we suggest that salt diapir-associated hydrate deposits and free gas accumulations represent an attractive exploration target for future marine drilling efforts. This is relevant both to industry interests from a resource exploitation perspective, and to scientific and academic interests, particularly for real-world, targeted testing of the salt diapir-driven GH recycling hypothesis presented here. Interestingly, our scenario-testing of variable salt diapir diameters seems to suggest there is an ideal diapir diameter (<4 km, and perhaps most ideally \(\sim\)2 km) for promoting recycling, which has implications both in helping guide hydrate-related exploration and for the Green Canyon and Blake Ridge diapirs discussed here, both of which fall within this ideal diapir diameter range (with Green Canyon's diapir width estimated at 2-3 km by [PERSON] et al. (2020), and Blake Ridge Diapir's width estimated at 2 km by [PERSON] et al. (2005), or a maximum of \(\sim\)3.5 km by [PERSON] et al. (2000)). Our study has particular implications for major salt basins with known or inferred hydrate occurrences, such as basins of the Gulf of Mexico, of southeastern Brazil, and off the west coast of Africa ([PERSON] et al., 2015; [PERSON] and [PERSON], 2007; [PERSON] and [PERSON], 2020). These linked salt-GH systems represent particularly attractive localities for examining potential salt-driven hydrate recycling, and for associated future resource exploration.
## 5 Conclusions
We use synthetic basin and GH system models and real-world models to demonstrate a salt diapir-driven mechanism for the recycling of GH (Figure 11). This salt diapir-driven GH recycling serves as a mechanism that can elevate hydrate saturations above 90 vol. % and can significantly elevate free gas saturations and volumes. Comparison of salt diapir-driven recycling and sediment burial-driven recycling suggests markedly higher rates of hydrate recycling in diapir-driven versus burial-driven scenarios (e.g., respective hydrate saturation increases of 20-30 vol. % per Myr vs. less than 7 vol. % per Myr in our synthetic models since 1.5 Ma; Figure 2). Using case studies of Green Canyon and Blake Bridge, we demonstrate how GH recycling can help explain concentrations of GH observed during drilling. Overall, GH recycling due to salt diapir activity implies that hydrate and free gas above salt diapir crests may represent attractive targets for scientific and academic drilling as well as for unconventional and conventional hydrocarbon resource exploration.
## Data Availability Statement
Data inputs and references used in constraining synthetic and real-world models are provided in Section 2 (Methods) of this paper and in Tables 1-5. Specifically, synthetic models are based on data and information from the following references: [PERSON] and [PERSON] (1983), [PERSON] and [PERSON] (1986), [PERSON] et al. (1994), [PERSON] et al. (1996), [PERSON] (1998), [PERSON] and [PERSON] (1998), [PERSON] and [PERSON] (2007) (for model geometries, namely salt diapir geometry); [PERSON] (1930), [PERSON] (1971), [PERSON] and [PERSON] (1979), [PERSON] and [PERSON] (1982), [PERSON] and [PERSON] (1998), [PERSON] et al. (1998), [PERSON] (2000), [PERSON] et al. (2004), [PERSON] et al. (2007), [PERSON] and [PERSON] (2009), [PERSON] et al. (2017) (for stratigraphy, lithologies, and rock properties); [PERSON] et al. (2009), [PERSON] and [PERSON] (2013), [PERSON] et al. (2017) (for heat flow and boundary conditions); [PERSON] (1982), [PERSON] and [PERSON] (1988), [PERSON] (1989), [PERSON] et al. (2015), [PERSON] et al. (2017), [PERSON] (2020) (for organic properties and kinetics); [PERSON] and [PERSON] (1940), [PERSON] et al. (2005), [PERSON] and [PERSON] (2007), [PERSON] and [PERSON] (2009), [PERSON] et al. (2016), [PERSON] et al. (2017), [PERSON] and [PERSON] (2018), [PERSON] et al. (2018) (for gas migration modeling, simulation of hydrate stability, formation, and dissociation, and hydrate kinetics and phase properties). The Green Canyon model is based on data and information from the following references: [PERSON] and [PERSON] (1998), [PERSON] et al. (2017), [PERSON] et al. (2020) (for model geometries, namely salt diapir geometry); [PERSON] (1930), [PERSON] (1971), [PERSON] and [PERSON] (1975), [PERSON] and [PERSON] (1982), [PERSON] and [PERSON] (1996), [PERSON] and [PERSON] (1998), [PERSON] et al. (1998), [PERSON] (2000), [PERSON] and [PERSON] (2008), [PERSON] and [PERSON] (2009), [PERSON], [PERSON], et al. (2012), [PERSON], [PERSON], et al. (2012), [PERSON] et al. (2012), [PERSON] et al. (2017), [PERSON] et al. (2017), [PERSON] et al. (2020), [PERSON] et al. (2020) (for stratigraphy, lithologies, and rock properties); [PERSON] and [PERSON] (2016), [PERSON] et al. (2017), [PERSON] et al. (2020) (for heat flow and boundary conditions); [PERSON] (1989), [PERSON] et al. (2017), [PERSON] et al. (2020), [PERSON] et al. (2022) (for organic properties and kinetics); [PERSON] et al. (2005), [PERSON] and [PERSON] (2007), [PERSON] and [PERSON] (2009), [PERSON] et al. (2016), [PERSON] et al. (2017), [PERSON] and [PERSON] (2018), [PERSON] et al. (2018) (for gas migration modeling, simulation of hydrate stability, formation, and dissociation, and hydrate kinetics and phase properties). The Blake Ridge Diapir model is based on data and information from the following references: [PERSON] (1993), [PERSON] et al. (1996), [PERSON] et al. (2000), [PERSON] et al. (2005) (for model geometries, namely salt diapir geometry); [PERSON] (1930), [PERSON] (1971), [PERSON] and [PERSON] (1979), [PERSON] and [PERSON] (1982), [PERSON] et al. (1996), [PERSON] et al. (1996), [PERSON] and [PERSON] (1998), [PERSON] (2000), [PERSON] and [PERSON] (2009), [PERSON] et al. (2017) (for stratigraphy, lithologies, and rock properties); [PERSON] et al. (1996), [PERSON], [PERSON], [PERSON] et al. (2009), [PERSON] et al. (2005) (for heat flow and boundary conditions); [PERSON] (1989), [PERSON] et al. (1996) (for organic properties and kinetics); [PERSON] et al. (2005), [PERSON] and [PERSON] (2007), [PERSON] and [PERSON] (2009), [PERSON] et al. (2016), [PERSON] et al. (2017), [PERSON] and [PERSON] (2018), [PERSON] et al. (2018) (for gas migration modeling, simulation of hydrate stability, formation, and dissociation, and hydrate kinetics and phase properties). Model simulations described herein are available as figures in the main text of this paper (Figures 3-10) and in Figures S1-S13 of Supporting Information S1. All model simulations were generated with the Petrodot(tm) v. 2019 Petroleum Systems Modeling Software ([[https://www.software.slb.com/products/petromod](https://www.software.slb.com/products/petromod)]([https://www.software.slb.com/products/petromod](https://www.software.slb.com/products/petromod))), provided courtesy of Schlumberger. The modeling work was performed using the Sherlock High Performance Computing Cluster at the Stanford Research Computing Center.
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wiley/fe14bb62_1773_4414_9bee_f06dc09a49a4.md | that hampers important yet time-consuming analysis of biogeochemical models (e.g., parameter perturbation experiment (PPE) and model-data fusion) ([PERSON] et al., 2023).
To resolve the \"spin-up problem,\" a variety of methods have been proposed over the past two decades to improve the computational spin-up efficiency. The simplest method is native dynamics spin-up (ND). ND takes hundreds to thousands of years of model simulation, running under recursive external forcing ([PERSON] et al., 2007; [PERSON] et al., 2009). The accelerated decomposition (AD) spin-up approach was developed by temporarily assuming higher decomposition rates ([PERSON] and [PERSON], 2005) and has been successfully applied to both the Biome-BGC and Community Land Model (CLM) to reduce 70% spin-up time ([PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON] et al., 2013; [PERSON] and [PERSON], 2005). It should be noted that both AD approaches require an additional period of ND simulation (the post-AD spin-up process) to further adjust the quasi-steady-state from the accelerated mode to a real steady-state, which is sometimes accompanied by a great computing burden. Some models are initiated with observations of plants, litter and soil in previous regional experiments ([PERSON] et al., 2014; [PERSON] and [PERSON], 2000; [PERSON] et al., 2002). However, the model still take a long time to come to equilibrium so that this method may not practically improve efficiency ([PERSON] et al., 2013; [PERSON] and [PERSON], 2007).
In addition, a suite of approaches has been proposed based on the formulated carbon balance equation to solve the steady state in an analytical or semi-analytical manner. The approach works because most of the current generation of terrestrial carbon and nitrogen cycle models use the first-order kinetics to describe terrestrial carbon and nitrogen dynamics ([PERSON] et al., 2008; [PERSON] et al., 2013; [PERSON] et al., 2018) while some of the nonlinear models also can be analytically solved to obtain steady state ([PERSON] et al., 2017). Full analytical spin-up method such as gradient projection approach ([PERSON] et al., 2015), numerically solves matrix-based expressions via the Jacobian matrix or Gauss-Jordan elimination algorithms ([PERSON] et al., 2011; [PERSON] et al., 2007; [PERSON] et al., 2018), which could save up to 85%-90% of the computational cost. However, the fully analytical method requires a series of complicated mathematical operations and currently it is only tested at a few sites ([PERSON] et al., 2015; [PERSON] et al., 2011) and North America ([PERSON] et al., 2018). Based on the matrix representation of biogeochemical models in the terrestrial ecosystems ([PERSON] et al., 2003, 2017), [PERSON] et al. (2012) first developed a semi-analytical spin-up (SASU) using the Australian Community Atmosphere Biosphere Land Exchange (CABLE) model. SASU offers great potential to effectively reduce the spin-up time of global models, which saves up to 92.4% and 86.6% of computational time in CABLE ([PERSON] et al., 2012).
As more ecological processes are integrated, increasing complexity of current biogeochemical model structures further introduce substantial difficulties to achieve efficient spin-up. For examples, in recognition of the importance of vertical distribution and exchange of soil organic matter (SOM) ([PERSON] and [PERSON], 2007; [PERSON] et al., 2018; [PERSON] and [PERSON], 2000), vertically resolved SOM structure has been implemented in land models ([PERSON] et al., 2011; [PERSON] et al., 2008). In CLM Version 5 (CLM5), [PERSON] et al. revised the vertically resolved structure ([PERSON] et al., 2013), which can simulate dynamic changes of soil carbon up to 8.6 m deep ([PERSON] et al., 2019). In addition, different from fixed carbon-nitrogen ratios in most of the current carbon-nitrogen coupled models ([PERSON] et al., 2011; [PERSON] et al., 2010; [PERSON] et al., 1993; [PERSON], 1993), CLM5 improved global carbon-nitrogen coupling simulation by defining flexible carbon-nitrogen ratios and adding a Fixation and Uptake of Nitrogen (FUN) module ([PERSON] et al., 2015; [PERSON] et al., 2019). All of the above advancements in representing biogeochemical processes lead to relatively longer carbon turnover times and more complex carbon-nitrogen interactions than its predecessors ([PERSON] et al., 2015), which bring greater computational burden to the spin-up. Implementing SASU to such a complicated biogeochemical model like CLM will benefit future biogeochemical model development ([PERSON] et al., 2015; [PERSON] et al., 2018).
In this study, we propose a new SASU framework by combining the AD method and semi-analytical algorithm based on the CLM5 matrix version ([PERSON] et al., 2020). We found that this new SASU framework further accelerates spin-up of global carbon-nitrogen coupled models over that introduced by [PERSON] et al. (2012). Computational efficiency and steady-state consistency of ND, AD, and SASU approaches are evaluated using CLM5 at both one-site and the global scale. In addition, we applied SASU to a PPE using CLM5, which is designed to examine the parameter sensitivity and provide a pathway for systematic parameter calibration. Our results provide strong support for the applications of SASU to complicated biogeochemical models with vertically resolved structure and flexible carbon to nitrogen ratio representations.
## 2 Materials and Methods
### Model Description
This study is based on CLM5, which is widely used and incorporate comprehensive biogeochemical processes. Similar to other land surface models, CLM5 represents the terrestrial carbon cycle via multiple carbon and nitrogen pools. The dynamics of pools can be characterized by the difference between carbon input and output (Figure 1). Terrestrial organic carbon is originally produced by photosynthesis of plants and distributed to six main pools (leaf, fine root, live stem, dead stem, live coarse root, dead coarse root). Vegetation carbon pools are regulated by multiple processes such as phenology, nutrient constraints, fire, etc. Subsequently, carbon is directly transferred from the vegetation or indirectly through the Coarse Woody Debris (CWD) pools to three different litter pools, including labile, cellulose and lignin. Downstream of the litter pools are three SOM pools with fast, slow, and passive decomposition. To simulate advection and diffusion of organic matter along a soil vertical profile, CLM5 divides soil into 20 layers that are up to 8.5 m along depth ([PERSON] et al., 2019). The carbon turnover time varies in different pools, which depends on the transfer coefficients regulated by the availability of soil nutrients and environmental factors (such as temperature and moisture). Limited by depth and environmental factors, SOM in deep layers typically has little carbon input and low decomposition rates.
In addition to having the same structure as the carbon cycle described above, the nitrogen cycle in CLM5 also regulates the availability of mineral nitrogen in the soil through immobilization and denitrification, which will constrain the photosynthesis of plants to form a relatively complete carbon-nitrogen coupling cycle. In particular, compared to CLM4, CLM5 has been updated in nutrient dynamics to model the nitrogen limitation in plant growth. In CLM4, denitrification was handled through a time constant applied to a bulk soil mineral \(N\) pool, and static carbon-nitrogen ratio is used to indicate that the availability of soil mineral nitrogen limits potential photosynthesis; in CLM4.5 nitrification and denitrification were modified based on CENTURY model from distinct and vertically resolved NO\({}_{3}\) and NH\({}_{4}\) pools ([PERSON] et al., 2013; [PERSON] et al., 2019). In CLMS, the FUN module proposes that plants will consume a certain amount of carbon when they uptake nitrogen based on the reality of symbiotic nitrogen fixation ([PERSON] et al., 2014). The description of biogeochemical processes in CLM5 has been well documented in [PERSON] et al. (2019) and more details can be found on this site ([[https://escomp.github.io/ctsm-docs/versions/release-clm5.0/html/](https://escomp.github.io/ctsm-docs/versions/release-clm5.0/html/)]([https://escomp.github.io/ctsm-docs/versions/release-clm5.0/html/](https://escomp.github.io/ctsm-docs/versions/release-clm5.0/html/))).
### The Matrix Representation of the Terrestrial Carbon and Nitrogen Cycle
In the carbon-nitrogen coupled cycle model, multiple carbon/nitrogen balance equations are used to calculate the dynamics of each carbon or nitrogen pool, which can be mathematically expressed by a matrix equation ([PERSON] et al., 2003, 2017, 2022). The vegetation simulation in CLM5 contains six tissue pools (leaf, fine root, live stem, dead stem, live coarse root, dead coarse root) and each tissue pool is accompanied by a storage and a transfer pool to facilitate the description of vegetation biomass growth and other phenological processes. An additional nitrogen pool is used to store reusable nitrogen (Figure 1). These 18 Carbon (C) pools and 19 Nitrogen (N) pools are represented by \(18\times 1\) vector \(C_{\rm{veg}}(t)\) and \(19\times 1\) vector \(N_{\rm{veg}}(t)\). Following two matrix equations are constructed to track the state variables of carbon and nitrogen in CLM5 matrix version ([PERSON] et al., 2020):
\[\frac{dC_{\rm{veg}}}{dt}=B_{\rm{C}}(t)U_{\rm{Na}}(t)+\big{(}A_{\rm{Cpl}}(t)K_{ \rm{Cpl}}+A_{\rm{Cpl}}(t)K_{\rm{Cpl}}+A_{\rm{Ccl}}(t)K_{\rm{Ctl}}\big{)}C_{\rm {veg}}(t) \tag{1}\]
\[\frac{dN_{\rm{veg}}}{dt}=B_{N}(t)U_{\rm{Na}}(t)+\big{(}A_{Npl}(t)K_{Npl}+A_{Npl }(t)K_{Npl}+A_{Npl}(t)K_{Npl}\big{)}N_{\rm{veg}}(t) \tag{2}\]
\(t\) represents each simulated timestep, which is half an hour in this study. A state variable with \(t\) will change dynamically with time. \(B_{\rm{C}}(t)\) (\(18\times 1\) vector) and \(B_{N}(t)\) (\(19\times 1\) vector) indicate input allocation fractions of Total vegetation carbon (TOTVEGC) or nitrogen. \(U_{\rm{Ccn}}(t)\) and \(U_{\rm{Na}}(t)\) are total amount of carbon/nitrogen inputs to the system. In general, carbon input refers to the net primary productivity (NPP) and the sources of nitrogen input are usually nitrogen absorption and fixation. \(A\) are \(18\times 18\) matrices for vegetation carbon pools and 19 \(\times\) 19 matrices for \(N\) pools, representing carbon/nitrogen transfer coefficients along prescribed pathway between pools. All \(A\) matrices have \(-1\) diagonally, and the element \(a_{ij}\) (in row \(i\) and column \(j\)) in the matrix represents transfer coefficient from the pool \(j\) to \(i\). \(A_{\rm{Cpl}}\) and \(A_{Npl}\) are used to quantify carbon and nitrogen fluxes among plant pools controlled by phenology processes. \(A_{\rm{Cpl}}(t)\) and \(A_{\rm{Spm}}(t)\) describe the gap-mortality transfer fractions and fire-induced process is indicated by \(A_{\rm{Ctl}}(t)\) and \(A_{Ntl}(t)\).
Figure 1:
\(K\) are diagonal matrices (\(18\times 18\) matrices for carbon pools and \(19\times 19\) matrices for nitrogen pools) with each diagonal element representing the turnover rate of each plant carbon and nitrogen pools. Phenology matrices \(K_{\mathrm{Cyl}}(t)\) and \(K_{N\mathrm{yl}}(t)\) represent plant tissue turnover rates according to phenology principles. Harvest rates and natural mortality are all included in gap mortality matrices \(K_{Cpm}(t)\) and \(K_{N\mathrm{yl}}(t)\). Fire matrices \(K_{C\mathrm{tl}}(t)\) and \(K_{N\mathrm{yl}}(t)\) refer to vegetation carbon/nitrogen losses from fire.
The soil carbon and nitrogen biogeochemical processes in CLM5 follow the CLM4.5 bge matrix structure developed by [PERSON] et al. (2018), which includes CWD pool, three litter pools (metabolic litter, cellulose litter and lignin litter) and three SOM pools (fast SOM, slow SOM and passive SOM). Each pool can be subdivided into 20 layers along soil depth so that the carbon/nitrogen pools are represented by a \(140\times 1\) vector, that is, \((\mathrm{C}_{1}(t),\mathrm{C}_{2}(t),\mathrm{C}_{3}(t),\dots,\mathrm{C}_{140}(t ))^{T}\). The matrix equation for litter and SOM can be organized as following:
\[\frac{dC_{\mathrm{col}}}{dt}=I_{\mathrm{coal}}+\left(A_{\mathrm{Cyl}}\xi(t) K_{\mathrm{a}}+V(t)+K_{f}(t)\right)C_{\mathrm{soil}}(t) \tag{3}\]
\[\frac{d\,N_{\mathrm{soil}}}{dt}=I_{N\mathrm{sol}}+\left(A_{N\mathrm{a}}\xi(t) K_{\mathrm{a}}+V(t)+K_{f}(t)\right)N_{\mathrm{soil}}(t) \tag{4}\]
where \(I_{\mathrm{coal}}\) and \(I_{N\mathrm{sol}}\) are \(140\times 1\) vector, representing vegetation carbon and nitrogen inputs to litter or CWD, respectively. As with vegetation, \(A_{\mathrm{Cyl}}\) and \(A_{N\mathrm{a}}\) a matrix of size (\(140\times 140\)), which is used to represent the transfer coefficient of carbon/nitrogen between pools. \(K_{\mathrm{a}}\) are diagonal matrices (\(140\times 140\)), representing the potential decomposition coefficient of litter and soil pools. \(K_{f}\) refers to litter and SOM carbon/nitrogen loss induced by fire. \(\xi(t)\) is a diagonal matrix (\(140\times 140\)) reflecting the environmental factors. Each element is a number from 0 to 1 to indicate the degree of carbon/nitrogen cycle affecting by environment such as soil temperature and moisture. \(V(t)\) is a \(140\times 140\) matrix, used to capture carbon and nitrogen dynamics in the vertical soil profile through mixing mechanisms (i.e., diffusion and advection).
The above matrix equations have been successfully constructed and verified in previous studies ([PERSON] et al., 2018; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2022). More details about CLM5 matrix version can be found in [PERSON] et al. (2020).
### Spin-Up Methods
This study evaluated three spin-up methods, which are ND spin-up, AD spin-up, and semi-analytic spin-up (SASU). These three methods adopt the same spin-up criterion (the mean change in total ecosystem carbon over last two loops \(\Delta C_{\mathrm{TOTECOSYC}}\lesssim 1.0\) g C \(\mathrm{m}^{-2}\) yr\({}^{-1}\) for the Brazil site and each gird cell in global verification), which is one of criteria in [PERSON] (2005) and [PERSON] et al. (2013). Below is a description of the three methods.
#### 2.3.1 Native Dynamics (ND) Spin-Up
The ND spin-up is simple and universal. It keeps default model running from arbitrary initial conditions until steady-state is reached under cycled meteorological forcing ([PERSON] and [PERSON], 2005). Recursive forcing provides similar environmental conditions over time. With no additional disturbance, the state variables (carbon and nitrogen pools) in terrestrial model will gradually approach the quasi-equilibrium state after long-time simulation. It relies entirely on internal dynamics and results in high computation cost, but it is a reliable reference for other spin-up methods.
#### 2.3.2 Accelerated Decomposition (AD) Spin-Up
Accelerated decomposition spin-up was first described by [PERSON] and [PERSON] (2005) and was implemented into CLM4. The approach was slightly modified by [PERSON] et al. (2013) to use different acceleration factors for
Figure 1: Diagram of the carbon and nitrogen processes of Community Land Model version 5 model. (a) The vegetation module tracks 18 carbon pools, 18 corresponding nitrogen pools, and an additional retransallocated nitrogen pool, which are controlled by phenology, gap-mortality and fire processes. L, leaf pool; L,X, leaf transfer pool; L,S, leaf storage pool; Fr, fine root; Fr,X, fire, fire root transfer pool; Fr,S, fire root storage pool; L, live stem transfer pool; L\({}_{\mathrm{s}}\),X, live stem transfer pool; L\({}_{\mathrm{s}}\),S, live stem storage pool; Ds, dead stem pool; Ds, X, dead stem transfer pool, Ds, S, dead stem storage pool; Lcr, live coarse root pool; Lcr,X, live coarse root transfer pool; Lcr,S, live coarse root storage pool; Dcr, dead coarse root transfer pool; Dcr,S, dead coarse root transfer pool; Dcr,S, dead coarse root transfer pool; Dcr,S, dead coarse root storage pool. (b) The soil module tracks 7 carbon and 7 corresponding nitrogen pool categories that into 20 soil profiles, resulting in 140 pools in the matrix representations. SOM, soil organic matter; CWD, coarse woody debris. Figures are originally from [PERSON] et al. (2020) and [PERSON] et al. (2018).
each soil pool, leading to a 70% reduction in computational cost from ND. The spin-up efficiency is mainly limited by the pools with long turnover times. Thus, AD defines a series of fixed scaling scalars for litter and SOM pools to accelerate carbon decomposition while vegetation pools maintain their default turnover timescales. In this solution, the vegetation states achieve quasi-equilibrium quickly, but the litter and SOM carbon and nitrogen predicted state are inversely proportional to the decomposition scaling factors ([PERSON] and [PERSON], 2005). The scaling scalars can vary considerably for different pools and regions. For example, for passive soil organic carbon pool, the acceleration factor is higher to make it similar to the decomposition rates of other fast pools. Geographically, the decomposition rates at high latitude are much lower than in the tropics, where temperature and moisture factors strongly limit the carbon decomposition. In CLM5, these areas were assigned higher scalars to ensure spin-up efficiency, by adding a latitudinal dependence to the acceleration. Introducing scaling factors, the model will converge to a steady state in a short time due to the fact that fast SOM decomposition provides sufficient mineralized nitrogen for rapid plant growth ([PERSON] et al., 2013). Consequently, a quasi-steady state can be obtained by multiplying by the corresponding scaling scalars. Thus, the model continues to run at the ND model after the end of the AD simulation until a steady state is reached.
To evaluate computational efficiency in this study, we used the same AD scaling scalars as [PERSON] et al. (2019) and followed 2 spin-up steps suggested by [PERSON] et al. (2020) to do AD spin-up: (a) 200 years of AD phase in which both carbon decomposition and vertical transport rates are accelerated by a set of scaling factors to ensure sufficient mineral nitrogen availability. At the end of AD spin-up, an exit-AD phase is executed automatically in the model to obtain quasi-steady-state values by multiplying the soil carbon and nitrogen states from the AD spin-up step by the scaling factors; (b) a long-time (at least 400 years) post-AD spin-up in normal mode (ND) to reach final equilibrium.
#### 2.3.3 Semi-Analytical Spin-Up (SASU)
[PERSON] et al. first proposed SASU for CABLE based on matrix equation ([PERSON] et al., 2012). Fundamentally, litter and soil organic carbon decomposition in terrestrial models limits the spin-up efficiency due to the long carbon turnover time. The default first-order dynamical scheme can efficiently simulate the decay of litter and SOM, which can be described by the following matrix equation:
\[\frac{dC_{\text{soil}}}{dt}=B(t)U(t)+A\xi(t)KC_{\text{soil}}(t) \tag{5}\]
where \(C_{\text{soil}}(t)\) is a vector of pool sizes; \(U(t)\) is the total carbon input from vegetation, usually referring to NPP; \(B(t)\) is a vector of allocation fraction to each pool; \(A\) is a matrix of transfer coefficients (or microbial carbon use efficiency) to quantify carbon transition; \(\xi(t)\) is a diagonal matrix of environmental scalars. \(K\) is a diagonal matrix, representing the potential decomposition coefficient of litter and soil pools. It has been well documented and validated in different models ([PERSON] et al., 2018; [PERSON] et al., 2020; [PERSON] et al., 2003; [PERSON] et al., 2012).
Mathematically, theoretical steady state can be calculated by making Equation 5 equal to zero. As there are several time-dependent variables (\(U(t)\), \(B(t)\), and \(\xi(t)\)), we treated them by mean values during the forcing loops (\(\overline{U}\), \(\overline{B}\), \(\overline{\xi}\)) so that we can solve the equation as:
\[C_{ss}=-\left(A\overline{\xi}K\right)^{-1}\overline{BU} \tag{6}\]
where \(C_{ss}\) is the theoretical steady state, assuming that the carbon input is equivalent to the output. The dynamic changes of environmental factors \(\xi(t)\) in the same climate loop are very similar and will be relatively stable after averaging. In addition to environmental factors, dynamic variables (e.g., \(B(t)\) and \(U(t)\)), which are associated with the plant input and allocation, are also subject to feedback regulation of mineralized nitrogen. When vegetation growth is deficient in available mineral nitrogen, reduced gross primary productivity will lead to dynamic changes of downstream pools. In other words, the organic carbon and nitrogen produced by vegetation vary nonlinearly and generally dominate in the simulations. Regularly, the vegetation becomes stable within several atmosphere loops as it grows rapidly. Indeed, \(\overline{B}\) and \(\overline{U}\) will be close to steady state, which makes the analytical solution more accurate. The actual equilibrium can be achieved quickly when the analytical solution is applied as initial value for next simulation loop.
In the CLM5.0 matrix version, by setting Equations 3 and 4 to 0, at the end of each climate loop, the analytical solution of soil carbon and nitrogen can be calculated based on matrix operation as:
\[C_{\text{soil}}^{ss}=-\left(A_{Cs}\overline{\xi}K_{Cs}+\overline{V}+ \overline{K_{f}}\right)^{-1}\overline{I_{\text{Coul}}} \tag{7}\]\[N_{\text{sol}}^{\text{s1}}=-\left(A_{N\#}\overline{\overline{\overline{\overline{ \overline{\overline{\overline{\overline{\overline{\overline{\overline{\overline{\overline{ \overline{\overline{\overline{\overline{\overline{\overline{\overline{\overline{{\overline{\overline}}}}}}}{{{\overline{ \overline{\overline{\overline{\overline{{\overline{\overline{}}}}}}}{{{\overline{{ \overline{\overline{\overline{\overline{{\overline{\overline{{\overline{\}}}}}}}}{{{\overline{{ \overline{\overline{\overline{{\overline{\overline{{\overline{\}}}}}}}}}{{{\overline{{ \overline{\overline{\overline{{\overline{\overline{{\overline{{\}}}}}}}}}}}}{{{{\overline{{ \overline{\overline{{\overline{{\overline{{\overline{{\overline{\overline{{\}}}}}}}}}}}}}}}}}}}}}}}}}}}}} \right)^{-1}\overline{I_{N\text{sol}} \tag{8}\]
In this study, we combined AD, semi-analytical and native dynamic modes to become a new SASU framework as the following three steps (Figure 2):
**Step 1.**: Accelerated decomposition mode: We used the same AD scaling scalars from [PERSON] et al. (2020) and [PERSON] et al. (2019) to accelerate soil decomposition and provide enough mineral nitrogen for plants to grow rapidly. Thus, model will quickly obtain a near steady-state estimate of NPP (or all plant pools), which usually takes 100-200 years (looping over 20 years of atmospheric forcing).
**Step 2.**: Semi-analytical (SA) mode: Calculate the analytical solutions of soil organic carbon and nitrogen pools based on matrix equations at the end of every atmosphere forcing loop. Figure 2 shows an overview diagram of the SASU mode used in CLM5 matrix version.
**Step 3.**: Native dynamic mode: Reach the final equilibrium by taking the analytical carbon and nitrogen pools as initial values and then cycling over repeat-forcing until the total ecosystem carbon meets the spin-up criterion.
We tested and adjusted the required simulation time in the three steps to maximize the spin-up efficiency. The following procedure was identified as the best-performing for site and global simulation: (a) 160 years of AD and the exit-AD mode as described in Section 2.3.2; (b) 200 years of semi-analytical mode, updating soil organic carbon and nitrogen pools with analytical solutions every forcing loop; (c) at least 40 years ND mode to reach final equilibrium.
### Evaluation of These Three Spin-Up Methods
To evaluate the computational efficiency of different spin-up approaches, we ran AD and SASU at a Brazil site (55\({}^{\circ}\)W, 7\({}^{\circ}\)S). They are driven by recursive meteorological forcing from 1901 to 1920 of the Global Soil Wetness Project Phase 3 dataset (GSWP3) ([PERSON] et al., 2006). In addition, we conducted the ND, AD and SASU for a 400-griddell sparse grid (\(1.9^{\circ}\times 2.5^{\circ}\)) ([PERSON] et al., 2013) that is used for parameter perturbation studies with CLM. The 400 grid cells that are used were identified using a cluster analysis and represent a minimum number
Figure 2: Procedures of the semi-analytical spin-up (SASU) method used in this study. There are three steps in SASU, including accelerated decomposition mode, semi-analytical (SA) mode, and native dynamics mode.
of grid cells that can reasonably capture model behavior across different cooregions around the globe (Figure 5). They are driven by repeated meteorological forcing from 2005 to 2014 to compare these approaches. All spin-up methods are initiated with cold-start, which means that plants will grow from beer land.
### Parameter Perturbation Experiment (PPE) in CLM5
With the growing of complexity and comprehensiveness of land models, land carbon dynamics simulated by earth system models are highly variable and fit poorly with observations ([PERSON] et al., 2015; [PERSON] and [PERSON], 2021; [PERSON] et al., 2015). It is crucial to understand sources of uncertainties. There are more than 200 crucial parameters in CLM5 and the contribution of parameter uncertainty to total uncertainty expected to be large, but unquantified ([PERSON] et al., 2016). Parameter values in the current land models are mostly determined on an ad hoc basis and may be derived from the results of field experiments, other models, or informed from scientific studies ([PERSON] et al., 2001). Systematic parameter calibration will enhance the accuracy of simulations, and increase suitability and accessibility of models for actionable science. Parameter perturbation experiment on CLM5 is proposed to examine the parameter importance and sensitivity on model results by ensemble analysis under parameter perturbation. Steady state under each parameter perturbation should be estimated to give us insight into how carbon cycle response to parameter change. PPE considered total 197 parameters in CLM5 across 14 categories and thousands of spin-up tasks are required for this ensemble analysis.
We applied SASU to PPE protocol based on a global 400 grid cell sparse grid driven by repeated meteorological forcing from 2005 to 2014. The test was to start from an equilibrium with default parameterization and we modified a model parameter (the changed parameter _stem_leaf_ in this test was reduced by 50%, which is an allocation parameter that controls the amount of new stem carbon per new leaf carbon). We used the SASU method to achieve a new equilibrium with this modified parameter. We tested a range of simulation times in the three SASU method steps and identified the following procedures as optimal: (a) 20 years of AD phase and exit-AD spin-up as described in Section 2.3.2; (b) 120 years of semi-analytical mode, updating soil organic carbon and nitrogen pools with analytical solutions every forcing loop; (c) at least 20 years ND mode to reach final equilibrium. It is worth to noticed that the time allocation among these steps is not quite the same as description in Section 2.4. The time of step 1 (AD mode) is greatly reduced in PPE due to the relative mature vegetation but no growing from beer land.
## 3 Results
### Spin-Up at the Brazil Site
We first compared the computational cost of each spin-up method at the Brazil site. For the Brazil site, the AD spin-up scaling scalars were set to 1, which means that it is fundamentally the same as ND. To reach the spin-up threshold (\(\Delta\)C\({}_{\rm TOTECOSVSC}\) \(<\) 1.0 g C m\({}^{-2}\) yr\({}^{-1}\)), we ran SASU and took ND spin up as a control. We recorded the first year when the growth rate of total ecosystem carbon storage is below the spin-up criterion. Generally, it took SASU 420 years and ND 3,000 years to achieve the same steady state (Figure 3a). ND kept a slow growth rate for about 2,000 years to reach steady state. In SA mode, all the carbon pools quickly approached a quasi-steady-state after 360 years (Figure 3a). Moreover, in the following simulation of step 3, the state variables maintained a dynamic balance and the change rate approached zero (Figure 3b). Compared with ND, SASU significantly reduced the computational cost, saving 2,580 years (86.0% simulation time) to reach the same state (Figures 3a and 4). The steady-state estimations from ND and SASU are consistent, just with small bias. TOTVEGF reached the same equilibrium of 15.37 kg C m\({}^{-2}\). Total ecosystem carbon (TOTECOSYSC) is 25.25 kg C m\({}^{-2}\) with ND and 25.28 kg C m\({}^{-2}\) with SASU. Even the same spin-up criterion is adopted, SASU has reached the equilibrium with 0.56 g C m\({}^{-2}\) yr\({}^{-1}\) of change rate, while total ecosystem carbon in ND still increases with 1.00 g C m\({}^{-2}\) yr\({}^{-1}\).
When a smaller criterion of the steady state (\(\Delta\)C\({}_{\rm TOTECOSVSC}\) \(<\) 0.05 g C m\({}^{-2}\) yr\({}^{-1}\)) was set to evaluate computational efficiency of the two spin-up methods at the Brazil site, it took SASU a total of 480 years and ND 4,720 years to meet the smaller criterion (Figures 3a-3c). It took an additional 1720 years to reach the new criterion of \(\Delta\)C\({}_{\rm TOTECOSVSC}\)\(<\) 0.05 g C m\({}^{-2}\) yr\({}^{-1}\) beyond the 3,000 years to reach the original criterion of (\(\Delta\)C\({}_{\rm TOTECOSVSC}\)\(<\) 1.0 g C m\({}^{-2}\) yr\({}^{-1}\)) for ND (Figure 3c). It only took an additional 60 years to reach the new criterion of \(\Delta\)C\({}_{\rm TOTECOSVSC}\)\(<\) 0.05 g C m\({}^{-2}\) yr\({}^{-1}\) beyond the 420 years to reach the original criterion of (\(\Delta\)C\({}_{\rm TOTECOSVSC}\)\(<\) 1.0 g C m\({}^{-2}\) yr\({}^{-1}\)) for SASU (Figure 3c). Biases of the steady-state pool sizes are reduced to a minimal for both the methods. Totalecosystem carbon from both ND and SASU are 25.28 kg C m\({}^{-2}\). The difference of total ecosystem carbon is about 0.001 kg C m\({}^{-2}\), which is less than 0.005% of the pool size (Table 1). Each individual carbon pool (i.e., CWD, TOTVEGC, each litter and soil pool) was consistent as well (Table 1). The difference of CWD pools between the two methods was \(6.51\times 10^{-5}\) kg C m\({}^{-2}\), while the difference of total soil carbon (TOTSOMC) was about \(1.45\times 10^{-3}\) kg C m\({}^{-2}\). In general, the good agreement demonstrated that SASU can reach the same steady state as with the ND method but with much higher computational efficiency.
### Spin-Up at Global Scale
We selected 400 sparse grid cells at global scale to compare the spin-up performance among ND, AD and SASU methods. All of grid cells were under \(1.9^{\circ}\times 2.5^{\circ}\) resolution and the same for three spin-up approaches (Figure 5). For the global test, spin-up ends when \(\Delta\)C\({}_{\rm TOTVEGCSVRC}\) is less than 1.0 g C m\({}^{-2}\) yr\({}^{-1}\) for more than 97% grid cells. The traditional ND and AD spin-up method spent 19,840 and 3,200 simulation years to reach equilibriums,
Figure 3: Carbon state trajectories (a, d, g) and the change of carbon between loops for semi-analytical spin-up (SASU) (b, e, h) and native dynamics (ND) (c, f, i) on the Brazil site. Results are organized as total ecosystem carbon (a–c), total vegetation carbon (d–f) and total soil carbon (g–i). These two methods ended up with the same steady state (horizontal black dashed line in a, d, g) on the Brazil site. Blue dots in a, d indicate where the SA mode starts. To reach the criterion of 1.0 g C m\({}^{-2}\) yr\({}^{-1}\) (horizontal gray dashed line in b, c, c, f, h), SASU took 420 years (b) and ND took 3,000 years (c), which were marked with gray arrows in (b, c). To meet a smaller criterion of 0.05 g C m\({}^{-2}\) yr\({}^{-1}\) (horizontal brown dashed line in b, c, e, f, h, i), SASU took 480 years (b) and ND took 4,720 years (c), which were marked with brown arrows in (b, c).
190 years by SASU from the default to a new steady state (Figure 6c). There were 2.61% of global areas that did not meet the spin-up criterion (\(\Delta C_{\rm TOTECOSYSC}<1.0\) g C m\({}^{-2}\) yr\({}^{-1}\)) (Figures 6c and 6d).
## 4 Discussion
### Improved Computational Efficiency for CLM5 With Vertical Structure
The development of vertical structure in SOM models posed great challenges to spin-up. Most terrestrial models regard the soil as a bulk without description of vertical distribution of SOM along the depth ([PERSON] et al., 1987; [PERSON] et al., 1994). Recently, with increasing awareness of the importance of deep soil organic carbon, more and more models include an explicit representation of the vertical SOM distribution to improve predictions of carbon cycling, as well as facilitate the addition of new process descriptions ([PERSON] et al., 2011; [PERSON] respectively (Figure 4). For SASU, it took a total of 400 years, including 200 years for AD mode, 160 years for SA mode and the last 40 years for ND. At the end of the spin-up, the number of grid cells that did not reach the spin-up criterion was 2.50% of the 400 grid cells for ND, 2.78% for AD, and 2.57% for SASU.
For the 400 global sparse grid cells, the steady states obtained by the three methods were similar (Figure 5). Total ecosystem carbon density was high in northern North America, northern Asia and the Tibetan Plateau, but low in the Sahara and Australia (Figures 5a, 5c, and 5e). Total soil organic carbon and total ecosystem carbon was mainly stored at high-latitude regions (\(\sim\)60\({}^{\circ}\)N), especially in Asia and northern North America (Figures 5b, 5d, and 5f).
### Application of SASU in Parameter Perturbation Experiment (PPE)
When the parameter in plant processes was perturbed, gross primary productivity and total ecosystem carbon had changed compared with the default steady state. Total ecosystem carbon increased to 317.83 Pg C (Figure 6a) and NPP quickly approached relative equilibrium (from 1.97 \(\times\) 10\({}^{-7}\) to 2.03 \(\times\) 10\({}^{-7}\) g C m\({}^{-2}\) s\({}^{-1}\)) (Figure 6b). The whole spin-up process took 190 years by SASU from the default to a new steady state (Figure 6c). There were 2.61% of global areas that did not meet the spin-up criterion (\(\Delta C_{\rm TOTECOSYSC}<1.0\) g C m\({}^{-2}\) yr\({}^{-1}\)) (Figures 6c and 6d).
et al., 2011; [PERSON] et al., 2018; [PERSON] et al., 2013). However, the vertically resolved structure strictly limited the decomposition of deep soil by environmental factors, especially in high latitudes, resulting in little carbon input and output in deep soil and long carbon turnover time ([PERSON] et al., 2008; [PERSON] et al., 2017), which means native dynamic simulation need an extremely long time to bring the SOM to the final steady state.
In CLM5, the extremely long turnover time in vertical structure brings a heavy computational burden on spin up and makes it difficult to accurately assess the steady state ([PERSON] et al., 2019). ND is really a time-consuming method, requiring 19,840 years for the sparse grid, which took about 40 days of real time on a high-performance computing system. The widely used AD spin-up method was 6.2 times faster than ND (Figure 4), which took about a week of real time. However, due to the extremely long turnover time of deep SOM, the acceleration factors of deep soil layers are particularly high (greater than 200 in CLM5) to accelerate the decomposition and
Figure 5.— Global distributions of steady-state carbon density (G C m\({}^{-3}\)) from native dynamics (a, b), accelerated decomposition (c, d) and semi-analytical spin-up (e, f) at 400 global grid cells. The figure is organized as the global carbon density of total ecosystem carbon (a, c, e), total soil carbon (b, d, f).
SOM cycling ([PERSON] et al., 2013). Microbial activities are generally less active in deep soil, resulting in low SOM decomposition rates and small environmental factors (e.g., temperature, water and oxygen scalar), especially in high latitudes with permafrost ([PERSON] et al., 2013, 2015; [PERSON] et al., 2015). In contrast, not limited by the long turnover time, SASU can estimate the theoretical steady-state once the annual soil carbon inputs and losses are obtained ([PERSON] et al., 2012), which reduced the real running time to less than a day. The analytical principle of SASU is more conducive to solving the \"spin up problem\" brought by vertical structure in terms of computational efficiency and simulation accuracy in the context of model development.
The SASU method saved 86\(\%\) of the computational time at the Brazil site, and 98.0\(\%\) at 400 sparse grid cells worldwide than traditional ND spin-up. Compared to the efficient method explored by [PERSON] and [PERSON] (AD method), SASU saved 87.5\(\%\) of computational time at global scale. It is more efficient than methods currently reported in the literature. Our results are consistent with the results recorded in previous studies. AD can be successfully applied to land model and the calculation time is saved by 84\(\%\) compared with the traditional ND method, which also showed the high efficiency of AD method as documented ([PERSON] and [PERSON], 2005). [PERSON] et al. (2012) first applied SASU to CABLE and sped up spin-up by 20 times ([PERSON] et al., 2012). To adapt to the strong carbon-nitrogen coupling cycle, compared with [PERSON] et al. (2012), we introduced the AD step at the beginning of spin up, which can help the system stability in a short time. In this study, the computational efficiency is greatly improved, which is 50 times higher than 20 times in CABLE ([PERSON] et al., 2012).
### Applications of SASU to Various Biogeochemical Models
The developed SASU is directly applicable to most of terrestrial biogeochemical models that followed similar first-order decay principle with CLM5 in this study ([PERSON] et al., 2012). The application of SASU in microbial models is under explored. With the increasing recognition of the role of microbial processes in soil carbon dynamics, dozens of microbial models have been developed in the past decades to consider microbial traits and nonlinear kinetics in simulating biogeochemical cycle ([PERSON] et al., 2010; [PERSON] et al., 2015). For example, the rate of carbon assimilation by microbes and decomposition catalyzed by extracellular enzymes are not constant as assumed in linear model such as CLM5 but dependent on the substrate concentration (e.g., Michaelis-Menten Kinetics). Nevertheless, the nonlinear microbial models still can be represented in the matrix form (Sierra and
Figure 6: The application of semi-analytical spin-up in parameter perturbation experiment. Total ecosystem carbon (a) and net primary productivity state trajectories (b) in whole spin-up process. Changes in land area percentage of disequilibrium (c) and disequilibrium area distribution (d). Gray line in (c) is the threshold of 3\(\%\) disequilibrium regions.
[PERSON], 2015) with either logistic or Michaelis-Menten equations in recent examples ([PERSON] et al., 2022b; [PERSON] et al., 2023). While various methods have been explored to obtain the steady state of microbial models, [PERSON] et al. (2017) have developed a similar semi-analytical solution for accelerating model spin-up by solving differential equations and their method can be used to different microbial models ([PERSON] et al., 2023). Thus, the SASU approach is likely appliable to different microbial models in the future.
The application of SASU to a dynamic global vegetation model (DGVM) is mathematically possible. However, it is still technically challenging. The development of DGVM in land models has expanded greatly in recent years, especially the vegetation demography model (VDM) ([PERSON] and [PERSON], 2020; [PERSON] et al., 2018; [PERSON] et al., 2020). VDM introduces new representation of spatially heterogeneous canopy, which describes vegetation dynamics in two dimensions, individual plant size and the age of a forest gap since last disturbance. The steady state of vegetation dominancy hierarchy could be obtained by solving partial differential equations, which assume at long time scale that both plant size changes and gap age changes equal to zero at steady state. Although SASU is theoretically applicable on aboveground carbon cycle spin-up, the impact of weak nonlinearity or discretization in the VDM could still prevent the aboveground ecosystem from an immediate approaching to the steady state. Regardless, final convergence to the unique steady state should be still guaranteed based on the theory of compartmental model. Then, steady states of belowground soil carbon and nitrogen can be finally approached after plant size and age both reach the steady states.
For similar reasons, incorporating SASU into Community Earth System Model (CESM) may potentially increase the spin-up efficiency, but the acceleration rates will be negatively impacted by the nonlinearity. Compared to the offline version CLMS, the CESM add the feedback of the land surface change to the atmosphere. For example, an increase in leaf area index induced under climate change would also enhance latent heat fluxes ([PERSON] et al., 2020), increase local precipitation ([PERSON] and [PERSON], 2011) and consequently alter the vegetation productivity patterns ([PERSON] et al., 2013). These feedbacks introduce nonlinearity into land carbon cycle, which therefore affect SASU spin up efficiency. Nevertheless, most of the new nonlinearity in CESM is external to land carbon cycle, so a quasi-steady state could still be derived from SASU.
### Implications for Model Improvement
Acceleration of spin-up for biogeochemical models make some of the computationally costly studies possible, such as parameter sensitivity analysis ([PERSON] et al., 2018), model inter-comparison ([PERSON] et al., 2022a; [PERSON] et al., 2018) and data assimilation with complicated carbon cycle models ([PERSON] et al., 2014; [PERSON] et al., 2018; [PERSON] et al., 2023). SASU accelerates spin-up, thus makes it computationally feasible to assimilate both flux- and pool-based big data to constrain full-dynamic model (e.g., earth system model) prediction through data assimilation and machine learning ([PERSON] and [PERSON], 2020; [PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). Constrained parameter values after data assimilation will improve SOM storage estimates and yielded better spatial and vertical distributions of SOM than the original model ([PERSON] et al., 2020, 2023). In addition, SASU provides the possibility to implement parameter sensitivity analysis of complicated earth system models, such as PPE in CLM5. The total spin-up time of CLMS was reduced to 190 years under parameter variations. Thus, computational resources can be reallocated to do more parameter perturbation experiments and ensemble analysis. SASU offers a new technical solution for most of terrestrial biogeochemical models that follow the first-order decay function in Equation 1 to increase the applicability of biogeochemical models toward an improved understanding of the land carbon cycle.
## 5 Conclusions
We applied a SASU framework to CLM5 to accelerate the spin-up of biogeochemical cycle to steady states. The SASU framework combined the AD mode, semi-analytical mode, and ND mode to improve the spin-up efficiency. SASU is 7.1 times faster than the AD spin-up to reach the same steady state at Brazil site. For the global simulation at 400 grid cells, SASU is 49.6 times faster than the ND method and 8.0 times faster than the AD method. Overall, the SASU method, to the best of our knowledge, is the most efficient spin-up method in comparison with all previously reported methods. Our study suggested that SASU is applicable to most of the biogeochemical models with the first-order kinetics and possibly with nonlinear microbial models and, thus, enabling computationally costly research, such as parameter sensitivity analysis and data assimilation with complex models.
## Data Availability Statement
All simulations used in this work were performed using Version 5.0 of CLM [[https://ecomp.github.io/tcsm-docs/versions/release-clm5.0/html/](https://ecomp.github.io/tcsm-docs/versions/release-clm5.0/html/)]([https://ecomp.github.io/tcsm-docs/versions/release-clm5.0/html/](https://ecomp.github.io/tcsm-docs/versions/release-clm5.0/html/)) ([PERSON] et al., 2018). The code of the matrix model of CLM5 are available at this site [[https://github.com/chriskj/ctsm/tree/cn-matrix_v3](https://github.com/chriskj/ctsm/tree/cn-matrix_v3)]([https://github.com/chriskj/ctsm/tree/cn-matrix_v3](https://github.com/chriskj/ctsm/tree/cn-matrix_v3)) ([PERSON], 2020). The model output data this study at [[https://zenodo.org/record/75931844.Y9](https://zenodo.org/record/75931844.Y9) oTTOxBy3J]([https://zenodo.org/record/75931844.Y9](https://zenodo.org/record/75931844.Y9) oTTOxBy3J) ([PERSON], 2023) as an archival repository.
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* [PERSON] et al. (2013) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2013). Extreme precipitation patterns and reductions of terrestrial oxygen production across biomass. _Journal of Geophysical Research: Biosciences_, _118_(1), 148-157. [[https://doi.org/10.1029/0212](https://doi.org/10.1029/0212) ja002136]([https://doi.org/10.1029/0212](https://doi.org/10.1029/0212) ja002136) | wiley | Matrix Approach to Accelerate Spin‐Up of CLM5 | Cuijuan Liao, Xingjie Lu, Yuanyuan Huang, Feng Tao, David M. Lawrence, Charles D. Koven, Keith W. Oleson, William R. Wieder, Erik Kluzek, Xiaomeng Huang, Yiqi Luo | https://doi.org/10.1029/2023ms003625 | 2,023 | CC-BY |
wiley/fe0e27b0_74fe_4d62_84ac_5f40ba4969c0.md | # IGR Solid Earth
Research Article
Opening in the Reykjanes Peninsula Rift Zone, SW Iceland
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###### Abstract
We analyze seismicity and centroid moment tensors (CMTs) on the Reykjanes Peninsula, Iceland, during the early phase of a widespread unrest period that led to multiple fissure eruptions between 2021 and 2024. We use a dense temporary seismic array, together with fiber-optic distributed acoustic sensing data, and incorporate first-motion polarities into the CMT inversion to improve accuracy, generating a total of 300 robust CMT solutions for magnitudes \(M_{W}\)\(>\) 2.5, focusing on 83 reliable \(M_{W}\)\(>\) 2.7 earthquakes for interpretation. The CMTs predominantly exhibit shallow strike-slip faulting, with a few normal faulting events compatible with tectonic stress. Interestingly, significant positive isotropic components are resolved, contributing up to 15% of the moment release. We also develop a new high-resolution seismic catalog of 34,407 events and show that larger shallow earthquakes at the plate boundary are preceded by the slow upward migration of microearthquakes from below, suggesting that intruding magmatic fluids interact with the oblique plate boundary to trigger slow slip events. We interpret our results as the seismic response to transtensional motion at the plate boundary in the brittle upper crust under shear, in response to stress changes induced by the intrusion of pressurized fluids in the lower crust. The complex interaction of multiple subparallel dikes with the plate boundary fault contributes to a broader deformation band that accommodates both tectonic and magmatic stresses. While the location and magnitude of the CMTs correlate with reactivated surface fractures and faults, the locations of intense, deep microseismic swarms indicate the sites of future fissure eruptions.
Key Points:
* [1] 1 German Research Centre for Geosciences (GFZ), Potsdam, Germany, \"Institute of Geosciences, University of Potsdam, Potsdam, Germany, \"NORSAR, Kjeller, Norway, \"Instituto Andaluz de Geofisica, Universidad de Granada, Granada, Spain, \"Departamento de Fisica Teorica y del Cosmos, Universidad de Granada, Granada, Spain, \"Institute of Geophysics, Czech Academy of Sciences, Prague, Czech Republic, \"Tecland GeosCurrey (ISOR), Kopayougur, Iceland
## 1 Introduction
The Reykjanes Peninsula (RP) in southwestern Iceland represents a transstensional plate boundary between two offset spreading axes of a mid-ocean ridge system, influenced by seismicity, deformation, geothermal activity, and volcanism (Figure 1). The north-trending mid-Atlantic ridge emerges from the ocean at the southwestern corner of the RP, turning into a 60-km-long N70\({}^{\circ}\) - 75\({}^{\circ}\)E-trending plate boundary, highly oblique to the spreading direction of N(121 \(\pm\) 3)\({}^{\circ}\)E ([PERSON] et al., 2009). The minimum compressive stress \(S_{\rm shrink}\) from microearthquakes indicates an average of N(120 \(\pm\) 6)\({}^{\circ}\)E. Kinematic plate boundary models based on GNSS indicate a 18 \(\pm\) 2 mm/yr left-lateral motion and 7 \(\pm\) 1 mm/yr opening along the central part of the plate boundaryon the RP ([PERSON] et al., 2009). The predicted average \(S_{limit}\) from this model trends N(132 \(\pm\) 1)degE and would favor rupture on N-S right-lateral and NE-SW left-lateral conjugate faults, if a friction coefficient of 0.6 is assumed.
Figure 1.— Seismicity and distribution of seismic stations in the study area in 2020. The red rectangle and black line in the inset figure show our study area and the plate boundary axis on the RP ([PERSON] et al., 2022). Triangles show the locations of broadband seismic stations; orange, purple, and blue colors indicate the seismic networks of Academy of Sciences of the Czech Republic (REFKJANET), Icelandic Meteorological Office (IMO), and MAGA-GEOPON (Germany GeroFchungszentrum, GFZ), respectively. Pink diamonds indicate the GNSS stations operated by MO, and white inverted triangles show the 40 virtual (selected) channels on the fiber-optic cable operated by GFZ (MAGIC). The colored circles show the seismicity in 2020 for depth. Three swarm periods are highlighted (July 19–22, red: August 26–29, green: October 20–21, yellow). The yellow star indicates the location of the 20 October 2020, Mw = 5.6 event at Kryswka. The cyan lines show the eruptive fissures active from 2021 to 2024. The areas within the red lines show the volcanic systems of Reykjanes, Svartsengi, Fagradalsfjal, Kršššššššššššššššššššššššššššššššššššššššššššššššššššššššš
The oblique plate boundary manifests as a 5- to 10-km-wide wide seismic zone and a series of volcanic systems, including Reykjanes, Svartsengi, Fagradalsfjall, Krysuvik, Brennisteinsfjoll, and Hengill (see Figure 1; [PERSON] and [PERSON], 2013), accompanied by high-temperature geothermal fields ([PERSON] et al., 2022). These volcanic systems are arranged in an en-echelon pattern relative to the plate boundary ([PERSON], 2006; [PERSON], 2008) and comprise eruptive fissures, tectonic faults, and fractures created during repeated basaltic eruptive phases. Over the last 4,000 years, historical volcanism has been episodic, with rifting and volcanic episodes lasting 400-600 years, interspersed with periods of dormancy lasting 600-800 years ([PERSON] et al., 2020; [PERSON] and [PERSON], 2013).
Intense earthquake swarms frequently occur on the RP ([PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 1977), where the transcurrent motion of the plate boundary is accommodated by either left-lateral motion along the plate boundary or by right-lateral motion on N-S striking rupture planes of earthquakes with magnitudes up to M 6 ([PERSON] et al., 2004; [PERSON] et al., 2023; [PERSON] et al., 2009) at depths between 2 and 67 km ([PERSON], 1991). The latest cycle of seismic unrest began in late 2019 in the area of Porphorn-Svartsengi, characterized by cycles of local surface uplift and subsidence with rates of 3-4 mm/day ([PERSON] et al., 2021; [PERSON] et al., 2022). Seismicity intensified in early 2020, particularly in the Fagradalsfjall volcanic system, indicating active deformation and unrest linked to magma inflation and the ascent of magma through the upper crust. Initially, the focus was placed on the Svartsengi volcanic system due to shallow seismicity suggesting stress build-up from deep magma intrusion; however, the first volcanic eruption occurred more than 10 km east of Svartsengi.
On 19 March 2021, a first fissure eruption occurred in the Fagradalsfjall volcanic system near Geldingadalir (Figure 1), releasing 150 Mm\({}^{3}\) of lava over six months and covering an area of 5 km\({}^{2}\)([PERSON] et al., 2022). Seismic activity before to this eruption had intensified in 2020, indicating the climax of magmatic processes at depth. Two further eruptions occurred in the same region on 3 August 2022 and 11 July 2023, a few kilometers northeast of the 2021 Fagradalsfjall eruption (e.g., [PERSON] et al., 2023). In late 2023 and early 2024, volcanic activity shifted west of Svartsengi, with fissure eruptions taking place at Sundhankar near Grinadvik. These ongoing eruptions and seismic activity suggest that the RP remains in a phase of tectonic and magmatic unrest.
Recent advancements in monitoring techniques, such as TerraSAR-X interferometry, have documented wide-spread fault and surface fracture movements during the volcano-tectonic unrest on the RP between 2019 and 2021 ([PERSON] et al., 2024). Movements occurred both within the active plate boundary segment and to the north, primarily in the Svartsengi volcanic system and in Grindavik, which experienced the 2023 and 2024 fissure eruptions. While the movements at the Fagradalsfjall eruption site were smaller than in surrounding areas, surface fracture movements occurred in regions without major earthquakes, indicating long-term stress build-up. These observations provide crucial insights into understanding both near-surface tectonic strain and deeper magmatic processes.
A key question arising from this ongoing unrest is why relative opening and shear plate motion in the RP is accommodated by en-echelon fault systems and differently oriented crack modes, and whether co-seismic opening is observed. Factors such as plate boundary flexure, lithospheric structure, and rheology are likely critical. The upper crust of the RP, estimated to be 3-5 km thick and composed of basaltic extrusives, overlies the lower crust and Moho at approximately 15 km depth ([PERSON], 2024; [PERSON] et al., 2001). The brittle-ductile transition (BDT) is thought to occur at a 6-7 km depth but rises to between 3 and 5 km beneath high-temperature geothermal fields ([PERSON] et al., 2022), where temperatures are estimated to reach 600 degC ([PERSON] et al., 2012). These factors, along with the interaction of faulting and magmatic processes at different depths, are likely to explain the transressional dynamics of the plate boundary and are key to predicting future volcanic and seismic hazards.
In 2020, an extensive network of seismic sensors (Figure 1) was installed to provide comprehensive data on the RP transtenional rifting episode and the associated seismicity and seismic swarms in the Svartsengi and Fagradalsfjall volcanic systems. Additionally, repeated gravity experiments and InSAR studies offered critical data on cyclic surface deformation ([PERSON] et al., 2022). These data sets have the potential to elucidate how magmatic fluid input, intrusions, and plate motion release shear and tensional stresses at different depths. Seismic swarms and microearthquake seismicity enable researchers to investigate how localized strain from ascending magma interacts with tectonic forces along the plate boundary. A thorough understanding of these dynamics is essential for addressing potential future eruptions.
Volcano-tectonic (VT) earthquakes provide further evidence of the complex interactions between tectonic and magmatic systems. Centroid moment tensor (CMT) analysis, based on full waveform inversions, has been crucial for understanding these dynamics. CMT can be decomposed into isotropic (M\({}_{low}\)) and deviatoric tensors (M\({}_{dr}\)), with the latter composed of double-coule (M\({}_{dc}\)) terms and compensated linear vector dipole (M\({}_{chd}\)) terms ([PERSON] and [PERSON], 1989). Non-double-coule (_nonDC_) terms, represented by M\({}_{iso}\) + M\({}_{chd}\), often arise in VT earthquakes where magma-induced pressure and tensile opening play a role in faulting processes. These (_nonDC_) can also originate from non-planar faults or multi-subevent earthquakes on parallel fault planes. Some studies even indicate mixed-mode ruptures on shear-tensile cracks for RP, with co-seismic opening and closing mechanism in the same region along the transtransitional rift zone, associated to normal and thrust faulting, respectively ([PERSON] et al., 2021). These microcarbusake source mechanisms, however, have not yet been confirmed by independent studies. A key question for the study at the RP is whether and at what depth _nonDC_ terms and co-seismic opening have occurred, how it works, and what role it plays in understanding transtransitional plate motion.
This research thus aims to address key aspects of how the transtransitional opening of the brittle part of a plate boundary is mechanically realized, to explore the interaction between ascending melt batches, slow slip events, and the seismicity at the BDT, and to examine the consequences of the interaction between sub-parallel intrusions at depth and shear faults above. Leveraging an extensive seismic data set, including full moment tensors, microseismic catalogs, and distributed acoustic sensing (DAS) deployed in 2020, we aim to understand how magma-tectonic interactions drive fault formation, stress accumulation, and seismicity. These insights are critical for forecasting future volcanic and seismic activity in the RP.
## 2 Data and Methods
### Detection and Location of Seismicity
The RP was seismically highly active during 2020, with several intense swarm episodes. According to the catalog of the Icelandic Meteorological Office (IMO, 1992), approximately 19,534 events were detected within 10 months in the area from 21.8\({}^{\circ}\) to 22.85\({}^{\circ}\)W to 63.78\({}^{\circ}\)and 64.10\({}^{\circ}\)N (Figure 1). We analyzed seismic data acquired by three different seismic networks deployed on the RP - REYKJANET (7E; [PERSON], 2013), GFZ - MAGIC (9H; [PERSON] et al., 2020) and the IMO Icelandic National Network (SIL; Icelandic Meteorological Office, 1992). The data set consists of 27 stations distributed across the RP, each with a different installation period (Figure 1, Figure S1 and Table S1 in Supporting Information S1).
The high signal-to-noise ratio (SNR) facilitated the reliable picking of P-wave onsets at most of the stations (Figure S2 in Supporting Information S1). The azimuthal coverage of each event is abundant, which is essential to obtain reliable earthquake locations and source parameters with low uncertainties. In addition to these stations, DAS strain-rate recordings from a 21-km-long fiber-optic cable (Figure 1) were included. We used a subset of 40 spatially stacked channels downsampled to 100 Hz. The DAS interrogator was operated by GFZ Potsdam as part of the MAGIC HART Rapid Response Action.
[PERSON] et al. (2022) integrated DAS data to study very low magnitude seismicity and identified up to approximately 40,000 events with M \(>\) -1 within 7 months (January 1 to 1 September 2020). The study shows a concentration of shallow earthquakes (less than 4 km deep) near the center of uplift in Svartsengi. Deeper seismic events were rare during the 244-days monitoring period. Although the waveform stacking approach used by [PERSON] et al. (2022) to detect and locate seismicity was promising and successful, the earthquake catalog had some shortcomings. First, magnitudes were not included in the analysis. Second, the static grid points used to search for centroids were relatively sparse, which did not allow for detailed analysis of the spatial distribution of the earthquakes or their spatiotemporal migration.
In this study, we derive an earthquake catalog using _Qosek_--an automatic and waveform--based earthquake detector and locator (Figure 1, Figures S3 and S4 in Supporting Information S1). _Qosek_ combines seismic phase arrivals provided by neural network phase pickers and waveform stacking with an efficient adaptive octree search. The resolution of the search volume is iteratively refined toward the seismic source location, allowing for a fast and accurate search. Calculation of moment and local magnitude from peak ground motions is included ([PERSON] et al., 2024). Location accuracy is improved by incorporating station-specific corrections (SST) and source specific station terms (SSST) into the search. The method has been demonstrated and validated for several large seismic data sets in different regions and geological settings ([PERSON], [PERSON], [PERSON], et al., 2024; [PERSON], [PERSON], [PERSON], et al., 2024). Our seismic catalog was generated using the local velocity model reported by [PERSON] et al. (2021). A comparison of the IMO and _Qseek_ locations is shown in the Figure S5 of Supporting Information S1. A comparison of the local \(M_{L}\) model from [PERSON] et al. (2020) and the \(M_{W}\) scale from _Qseek_ with the seismic moment derived from CMT employing _Grond_ is demonstrated in the Figure S6 of Supporting Information S1.
### Centroid Moment Tensor Inversion
#### 2.2.1 Method
We apply CMT inversion to earthquakes larger than \(M=2.5\) that occurred in 2020 and were captured by our combined network (Figure 1). We use a joint waveform and polarity inversion method (Figures 2 and 3) to retrieve the CMTs of earthquakes on the RP. To quantify the uncertainties of the retrieved results, a combination of non-linear inversion and bootstrap technique is applied, as it is implemented in the open-source software Grond ([PERSON] et al., 2018). A small subset of the waveform fits and CMT solution are shown in Figure 2 for a selected event. The full online report of CMT results produced in this study can be found at the link [[https://data.pyrocko.org/publications/grond-reports/2020-iceland-reykjanes/](https://data.pyrocko.org/publications/grond-reports/2020-iceland-reykjanes/)]([https://data.pyrocko.org/publications/grond-reports/2020-iceland-reykjanes/](https://data.pyrocko.org/publications/grond-reports/2020-iceland-reykjanes/)) and as a Table in Supporting Information S1.
We solve the inverse problem of determining a source model given a set of observations using a probabilistic optimization approach ([PERSON] et al., 2022; [PERSON] et al., 2023; [PERSON] et al., 2021). It consists of repeatedly searching for the model that minimizes the misfit between observed and forward modeled data, each time using a different perturbation of the objective function used in the data fitting. The results of these optimizations form an ensemble of source models that all explain the observations satisfactorily well. From this ensemble, it is possible to determine the uncertainties of the source model parameters and also the possible trade-offs between them. We call this method Bayesian bootstrap optimization BABO and it is explained in [PERSON] et al. (2018) and [PERSON] et al. (2020). It is based on the concept of [PERSON] (1981), who showed that, with a certain choice of weights, the resulting ensemble of bootstrap solutions can be treated as a non-parametric posterior distribution.
The source model parameterization consists of the location, depth, and time of the point-like earthquake origin (centroid) and of the six independent components of the moment tensor. Optionally a source duration can be added to the inversion parameters.
The forward modeling of synthetic waveforms uses an approach based on precalculated Green's functions (GFs; [PERSON] et al., 2019). We use the QSEIS code of [PERSON] (1999) to compute the GFs. It uses the orthonormal propagator method to solve the wave equation for a layered viscoelastic half-space model. For the forward modeling of seismic phase onset polarities and travel times), we use the Cake tool, which is part of the Pyrocko software suite ([PERSON] et al., 2017).
The optimization is based on minimizing the misfit between observed and synthetic data. Following [PERSON] et al. (2020), we design the objective function to be minimized using an L1 norm as
\[M=\frac{\sum_{i}|w_{i}m_{i}|}{\sum_{i}|w_{i}n_{i}|}\, \tag{1}\]
where \(m_{i}\) is the misfit for a specific recorded seismic waveform or phase attribute, \(n_{i}\) is a corresponding normalization factor, and \(w_{i}\) is a weighting factor. For seismic waveforms, the \(m_{i}\) and \(n_{i}\) are defined as (not showing the index \(i\))
\[m=\sum_{j}|o_{j}-s_{j}|\quad\text{and}\quad n=\sum_{j}|o_{j}|\, \tag{2}\]
where \(o_{j}\) and \(s_{j}\) are observed and synthetic samples, respectively. The samples are taken from filtered and tapered displacement waveform snippets or amplitude spectra. For seismic phase polarity records, we use Figure 2:
\[m=\frac{1}{2}|o-s|\quad\text{and}\quad n=1\, \tag{3}\]
where o and \(s\) are the observed and synthetic polarities \(\{+1,\ -1\}\).
Also following Equation 4 in [PERSON] et al. (2020), the weights \(w_{i}\) in (1) are composed as
\[w_{i}=w_{\text{balance},i}\ w_{\text{manual},i}\ w_{\text{bioetrap},i} \tag{4}\]
where the \(w_{\text{balance},i}\) balance the contribution due to expected signal amplitude, depending on source-receiver distance, phase type, and applied signal processing; the \(w_{\text{manual},i}\) can be used subjectively, and \(w_{\text{bioetrap},i}\) are assigned by the BABO algorithm to perturb the objective function, a requirement for the bootstrap technique which is used to obtain uncertainties. Details are described in [PERSON] et al. (2020).
#### 2.2.2 Data
We analyzed CMT for 300 events with magnitudes \(M>2.5\) using permanent and temporary seismic stations (27 stations in total) as well as DAS data measured along a 21 km long fiber optic cable running across the center of the seismic swarms (Figure 1). Full waveforms consisting of body and surface waves at broadband seismic stations, and first motion polarities are jointly inverted to resolve a full moment tensor. Seismic data quality assessments were performed visually. About 7,000 P-wave arrivals were manually identified and picked. The frequency ranges of 0.7-2.0 Hz and 0.04-0.2 Hz (hereafter referred to F1) were selected for body and surface waves, respectively.
#### 2.2.3 Application and Parameters
Synthetic seismograms are calculated based on the local velocity model reported by [PERSON] et al. (2021) for a 250 m grid spacing from 1 to 50 km source-receiver distance and 0.1-10 km source depth for a sampling rate of 25 Hz. Theoretical arrival times for S-wave and surface waves were calculated using Cake software ([[https://pyrocko.org/docs/current/apps/cake/index.html](https://pyrocko.org/docs/current/apps/cake/index.html)]([https://pyrocko.org/docs/current/apps/cake/index.html](https://pyrocko.org/docs/current/apps/cake/index.html))).
Waveforms (Figure 2) and polarities (Figure 3) are combined to provide more detailed information about the source process ([PERSON] et al., 2018). While the surface waves were inverted in the time and frequency domains using the R, T, and Z components for the full waveforms, the body waves were inverted in the time domain using the T and Z components in time windows ranging from 0.1 s before to 0.3 s after the P and S arrivals, respectively. This setup was chosen as a result of sensitivity analysis, testing the stability of the result in terms of waveform fits when using different phases, amplitudes, and input data types. Synthetic traces are allowed to be shifted by up to \(\pm 0.2\) s relative to observed data. Balancing weights are applied to ensure an optimal weighting of different phases and distances ([PERSON], 2011). In addition, manual weights were defined for each input data type ([PERSON] et al., 2020) giving more weight to the waveforms since they carry more reliable information on the source (Table 1). For the first motions, take-off angles were computed using the same velocity model as for the waveform GFs database. The parameters used in the CMT inversion are summarized in Table 1.
We applied 200,000 iterations in the inversion. The inversion provides the best and mean solutions besides source parameter uncertainties. Finally, 83 earthquakes (M\({}_{w}>2.7\)) out of 300 (Figures 4 and 5) were selected for a
Figure 2.— Small subset of the Grond report for the 2020–07–20 (UTC) 08:15:12 M\({}_{\text{W}}=3.3\) earthquake. Waveform fits for station 7E.ELB for (a) vertical (\(Z\)) and transverse (T) waveforms of the body waves in the time domain, (b) Z, T, and radial (R) waveforms of the surface waves in the frequency domain, and (c) the time domain, respectively. Information (left side, from top to bottom) gives station name with the component, distance to the source, azimuth of the station with respect to source, target weight, target misfit, and start time of the waveform relative to the origin time. The background gray area demonstrates the applied taper function. The bottom panel shows sample-wise residuals in time domain (red-filled), and amplitude spectra of observed and synthetic traces (gray and red-filled, respectively). Colored boxes to the upper right show the relative weight of the target during optimization within the entire data set (top box, orange) and the relative misfit contribution to the global misfit (bottom box, red). (d) Location of the ensemble of best solutions. Symbols show the best double-couple mechanisms, and colors indicate low (red) and high (blue) limits. (e) Ensemble best and mean solutions decomposed into M\({}_{\text{tot}}\), M\({}_{\text{dver}}\), M\({}_{\text{dver}}\), and M\({}_{\text{dver}}\) parts. Symbol size indicates relative strength of the components.
common interpretation based on the robust centroid locations, convergence of model parameters, low misfit, and sufficient azimuthal coverage (Figure 4). The full reports of waveform fits for all 83 events are provided in the link repository as interactive web reports (see Open Research). They include the waveform and station distribution assessments, waveform and spectral fits of the best and ensemble models, information on the convergence and statistics of the optimization, and the evaluation of the contribution of the individual input data, and model parameters uncertainties, including centroid locations and CMT components.
## 3 Results
### Event Locations
The high-resolution earthquake catalog derived by _Qseek_ with the applied SSST corrections is shown in Figure 1. The catalog consists of 34,407 locations for the period from January 1 through 31 October 2020 (Figure S5 in Supporting Information S1). [PERSON] et al. (2022) detected slightly more events with the predecessor method of _Qseek_ (_Lassie_) including additional DAS data. However, we omitted the DAS data here because the neural phase picker is not trained on DAS data. The earthquake hypocenters in the IMO catalog were determined manually using the single-event location method, with approximately 15,000 coinciding with those in the Qseek catalog. However, _Qseek_ earthquake locations are more clustered and events are better aligned on 2D structures that can be
Figure 3: Lower-hemisphere projection of the P-wave radiation pattern of the full moment tensor (FULL) and the double-couple (DC) along with the first motion polarities for six selected earthquakes in 2020 a) 2020–07–19T23:36:13, M\({}_{\rm w}\) 4.6, (b) 2020-10-20T15:32:46, M\({}_{\rm w}\) 4.3, (c) 2020-07:20T06:23:00, M\({}_{\rm w}\) 4.1, (d) 2020-07:20T00:08:19, M\({}_{\rm w}\) 3.9, (e) 2020-07: 20T07:09:13.16, M\({}_{\rm w}\) 3.7, (f) 2020-07:20T08:20:30, M\({}_{\rm w}\) 3.5. The black circles with white outlines and white circles with black outlines demonstrate the upward and downward motion of the first polarities, respectively.
interpreted as faults or fissures. The number of isolated deep events is smaller in the new _Qseek_ catalog, which has a narrower depth range. The mean depth of all events is slightly greater in the new _Qseek_ catalog compared to the previous _Lassie_ catalog ([PERSON] et al., 2022), which may be explained by the inclusion of DAS data in the latter, which allowed for the detection of local, shallow microearthquakes situated below the fiber cable.
### Centroid Moment Tensors
Figure 4 shows the statistics of the decomposed source parameters. Our results indicate positive \(M_{iso}\) components (Figure 4a) around \(14.5\pm 4.9\%\). In contrast, M\({}_{tnd}\) components fluctuate around zero, ranging between \(-50\%\) and \(60\%\), with a mean of \(6.9\pm 12.9\%\) (Figure 4b). No significant correlation (\(R=-0.02\)) is observed between the two _nonDC_ components (Figure 4c). The centroid depths of the events are mostly located in the shallow 4 km, with a mean value of 3.0 km (Figure 4d) and a depth uncertainty of 0.2 km (Figure 4e). We also compared the _nonDC_ components with centroid depths (Figures 4f and 4g) and magnitudes (Figures 4h and 4i). Larger magnitude events tend to have lower M\(clvd\) components, likely due to improved SNR. In contrast, M\(iso\) shows a slight increase as centroid depth increases. No temporal variation is recognizable in either of the components (Figure S7 in Supporting Information S1). The complete list of CMT inversion parameters and their uncertainties is provided in Supporting Information S2 and visualized in Figures 4 and 5. Different analyses show that the source parameters remain stable. We varied the selection of stations, phases, data types, frequency ranges, and performed inversions using different velocity models. The CMTs remain consistent across these tests, irrespective of the velocity models and frequency bands used (see Supporting Information S1, Figures S8 and S9).
Figure 5 depicts the Hudson plot for the _nonDC_ source components ([PERSON] et al., 1989). The origin of the Hudson plot represents a source with a pure double-couple moment tensor (DC = 100%). Crack opening is located in the upper-left near the positive dipole and the crack closing is in the lower-right near the negative dipole. Pure explosions and implosions emerge on the vertical axis of the diagram, +Isotropic and -Isotropic, respectively. The solutions consistently cluster in the upper half of the Hudson plot, indicating that a positive M\({}_{iso}\) component is prominent. On the contrary, the scatter for the horizontal axes is symmetric, indicating that a non-zero M\({}_{chd}\) component is not resolved.
Figure 6 shows well-resolved CMTs. They represent predominantly strike-slip earthquakes on either EW (left-lateral) or NS (right-lateral) rupture planes. The centroid locations derived from moment tensor inversion align in the N70 degE direction along the plate boundary on a segment within \(\pm 15\) km of the 2021 eruption site (Figure 6). The average centroid location uncertainties are \(\pm 0.3\) km (N) and \(\pm 0.2\) km (E), respectively. We do not observe a systematic change in the orientation of the DC component in the region near Svartsengi, which experienced strong uplift-subsidence cycles in 2020.
Several sensitivity analyses were applied to the data set to understand the reliability of our results, because in the case of earthquakes with significant _nonDC_ components, the magnitude of M\({}_{dc}\) and M\({}_{iso}\) components can vary significantly for small perturbations of the inversion parameters ([PERSON] & Dreger, 2006; [PERSON] et al., 2008). To evaluate the dependence of the results on the velocity model, we inverted the events employing three additional velocity models (Model 2, Model 3, Model 4) in Figure S8 of Supporting Information S1 derived from [PERSON] et al., 2021; [PERSON] et al., 1993; [PERSON] et al., 2002). GFs were generated with the same
Figure 4.— The full CMT decomposition results are shown in dark green. The red dashed lines represent the mean, while the orange lines show the median values. Histograms of (a) M\({}_{iso}\) and (b) M\({}_{iso}\) (for definitions see e.g., [PERSON] & Krüger, 2014); (c) M\({}_{tot}\) vs. M\({}_{iso}\); histograms of (d) centroid depths compared to hypocentral depths reported by MO (light green color) and (e) depth uncertainty. Centroid depth (f), (g) and magnitude (h), (i) versus M\({}_{iso}\) and M\({}_{tot}\) components, respectively.
parameters for all models. For Model 2, a shallow low-velocity layer was added to Model 1 to see the effect of near-surface properties on the inversion. The M\({}_{\rm iso}\) components are estimated to be 14.6 \(\pm\) 4.6%, 15.8 \(\pm\) 5.2%, and 15.7 \(\pm\) 5.2% for the Model 2, Model 3, and Model 4, respectively, while the M\({}_{\it cid}\) components are estimated to be 7.6 \(\pm\) 12.3%, 6.0 \(\pm\) 12.6%, and 6.0 \(\pm\) 12.7%. The mean centroid depths are 3.1 \(\pm\) 0.2 km, 2.8 \(\pm\) 0.2 km, and 2.8 \(\pm\) 0.0001.
Figure 5: Non-Double Couple components of all CMT inversion results in the Hudson diagram. The beach-balls depicting double-couple part of the mean CMT solutions of all bootstrap-chains, colored by centroid depth. Dotted lines indicate the uncertainties in the M\({}_{\rm iso}\) and M\({}_{\it cid}\) components.
Figure 6: The beach-balls depicting double-couple part of the CMT solutions (lower hemispheric projections) of 83 selected earthquakes (M\({}_{\rm w}\)\(>\) 2.7) retrieved in this study. The colors of the beach-balls indicate the centroid depths of the earthquakes. The black beach-ball indicates the CMT of the 20 October 2020 Mw = 5.6 event at Krjsurk (GEOPON). Gray and black lines indicate surface fissures and faults that were active in 2019 and 2020–2021, respectively ([PERSON] et al., 2024). Red lines indicate eruptive fissures active from 2021 to 2024.
0.2 km for the three different velocity models (Figure S8 in Supporting Information S1). In summary, the sensitivity analysis confirmed the presence of positive _Miso_ components around 10%-20%, shallow centroid depths, and nearly zero _Mclvd_ components on average.
The frequency band used in the CMT inversion can also affect the results and interpretation. For this reason, we evaluated the CMT inversion results obtained with three additional different frequency bands depending on the source-receiver distance, F2: 0.7-2.0 Hz and 0.1-0.2 Hz for body and surface waves, respectively, F3: 1.0-2.5 Hz and 0.1-0.2 Hz, and F4: 1.0-2.5 Hz and 0.05-0.15 Hz (Figure S9 in Supporting Information S1). The means of the _nonDC_ components are estimated as follows: M\({}_{iso}\) = 14.7 \(\pm\) 4.5% and M\({}_{chd}\) = 8.0 \(\pm\) 11.8% for F2, M\({}_{iso}\) = 14.1 \(\pm\) 4.7% and M\({}_{chd}\) = 8.4 \(\pm\) 12.5% for F3, and M\({}_{iso}\) = 15.7 \(\pm\) 4.4% and M\({}_{chd}\) = 5.6 \(\pm\) 13.2% for F4, respectively. The means of centroid depths are 3.1 \(\pm\) 0.2 km, 3.0 \(\pm\) 0.3 km, and 3.2 \(\pm\) 0.2 km for the three different filter ranges, respectively (Figure S9 in Supporting Information S1). We observe no discernible dependence of the parameters on the frequency bands, increasing the confidence in the accuracy and reliability of our results.
Furthermore, inversion results for small magnitude events (\(M<4.0\)) can be affected by ambient noise. For example, in Iceland, the microseosin noise from oceanic waves during storms can dominate the signals in the 0.04-0.2 Hz frequency range, which was used for surface wave inversion. Such unwanted noise can lead to artificial _nonDC_ components. To understand the impact of microseissions caused by oceanic waves, we first invert all earthquakes with magnitudes larger than 2.5 (300 events). Subsequently, we inverted microseism signals contaminated by noise in the frequency band of 0.04-0.2 Hz. For both analyses, the mean of the distribution of _nonDC_ components is zero, thus demonstrating that moment tensor solutions are not systematically biased by noise in this frequency band, and the volumetric components found during the inversion of the events are reliable (see Figure S10 in Supporting Information S1).
Events are clustered in both time and space. For example, major earthquake sequences occurred in July, August, and October 2020, represented by red, green, and yellow in Figure 7. Figure 7a shows the dominant mechanisms and the distribution of the CMTs in a triangular diagram. Pressure, tension, and null axes (P, T, and B axes, respectively) are indicated in Figure 7b. The P axes display a NE-SW alignment, while the T axis is sub-horizontal with an azimuth of \(\sim\) 130 deg, which roughly corresponds to the direction of the least principal stress on the RP ([PERSON] et al., 2009). In Figure 7c, we present the mean full moment tensor solutions of the clusters.
## 4 Discussion
### Evolution of Seismicity Along Tectonic and Volcanic Structures
Figure 7c shows four selected profiles to discuss the spatiotemporal evolution of seismicity and the occurrence of larger magnitude earthquakes with possible future fissure eruptions. Profile p1 trends \(E15\,\mathrm{\SIUnitSymbolCelsius}\,N\) and lies along the oblique plate boundary. Profiles p2, p3, and p4 run along the Reykjanes, Svartsengi and Krysuvik volcanic systems, respectively, and are oriented perpendicular to \(S_{\mathrm{main}}\), approximately aligning with the mean direction of the P-axes in Figure 7a. Thus, shear stresses are assumed to be low or negligible on profiles p2-p4, while they are significant along or perpendicular to profile p1. Earthquakes rupturing the plate boundary in p1 are assumed to release shear stress directly, while migrating seismicity along profiles p2-p4 is interpreted as being induced by hydraulic or magmatic fracture growth at depth.
A second measure for distinguishing between intrusion-induced and tectonic earthquakes is the rate of migration of seismic fronts and back-fronts. While most aftershocks are activated immediately or shortly after the occurrence of a major tectonic event and sample approximately the size of the rupture plane of the main shock, the migration of intrusion-induced earthquakes is much slower, in the range of a few hundred meters or kilometers per hour for magma dikes rising from depth ([PERSON], 2000; [PERSON] & [PERSON], 2006) and about 10-15 km/hr for lateral propagating dikes near the surface ([PERSON] & [PERSON], 1980; [PERSON] et al., 2024). In the following, we select time windows of a few days or weeks along the specific profiles (Figure 7d) and project the seismicity and CMTs along horizontal and vertical sections. Only a few sections are included in the main text, while more examples are provided in the Supporting Information S1. For each profile, a girl animation of the time-space evolution of the seismicity is provided as a Zenodo repository [[https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152)]([https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152)), as it would be difficult to present it with static figures.
Figure 8 shows the seismicity at p1 during the first quarter of 2020 until April 24 (day 114). During this period, only three CMTs with \(M_{\mathrm{W}}\) \(>\) 2.7 were retrieved, often in the boundary region of a developing swarm, and all
occurring at depths of about 3.8 km. Interestingly, the first moderate microearthquake swarm started in the east beneath Krysauvik at a profile length of 10 km (day 12) and 15 km (day 15). Subsequently, the swarm activity seems to jump westward (e.g., swarm at \(-\)2 km between Grindavk and Fagradalsfjall on day 22, at \(-\)7 km beneath Svartsengi on day 24 or at \(-\)15 km beneath Reykjanes on day 47). Over time, however, the seismic
Figure 7.— (a) The triangle diagram displays the distribution of strike-slip, normal, and thrust fault mechanisms, with circles representing the earthquakes. (b) P, T, and B axes of the earthquakes. (c) Selection of profiles p1 (blue), p2 (purple), p3 (light green), and p4 (orange), which run along the main plate boundary, Reykjanes, Svartsengi, and Krysauvik volcanic systems, respectively. The crossing points of profiles p2-p4 with p1 are marked by inverted triangles. Earthquakes are indicated by black circles, while larger ones\(-\)83 events with CMTS of \(M_{\rm w}>2.7\), retrieved in this study—are plotted in magenta. The composite full moment tensor solutions for activity during July 19–22 (red), August 26–29 (dark green), and October 20–21 (yellow), 2020, are provided. The red lines show the eruptive fissures active from 2021 to 2024, while gray lines indicate surface fissures and faults that were active from 2019 to 2021 ([PERSON] et al., 2024). (d) Time evolution of the seismic activity is illustrated to discuss the swarm phases, marked by color-filled circles in (c), with light blue indicating activity between January 1 and April 23. The remaining events are drawn in black, and larger events with CMTS are represented by magenta squares in the \(M_{\rm w}\) over time plot.
swarms occurred along the entire plate boundary, except for a segment between 3 and 13 km, where the first microearthquake swarms appear in our catalog.
The earthquakes often occur at depths between 1 km and 6-7 km. A very interesting observation from Figure 8 is that individual swarms during this time typically sample a large depth range, but have little lateral extent along the plate boundary so that they appear as sub-vertical channels of 3-4 km length in the vertical section of p1. In the map view (upper panel in Figure 8), they activate elongated structures of about 2-3 km in length that cross p1 and trend toward the volcanic fissure zones. These are typical dimensions and shapes of buoyancy-driven dikes ([PERSON], 2000). The swarm activity is therefore interpreted as intrusive, sub-vertical fractures (dikes) crossing the plate boundary and fed by magmatic reservoirs below 7 km depth. For instance, the swarm that became active later on day 187.9, at a profile length of 15 km generated a \(M_{\rm w}\) 3.1 normal faulting event at a depth of 3.4 \(\pm\) 0.5 km (Figure S11, see also S15 in Supporting Information S1), with nodal planes striking in the direction of the p2 hydrofractures (e.g., Figure 7c).
We observe no clear correlations between GNSS deformation and larger earthquakes in a swarm, except for the \(M_{\rm w}\) 5.6 earthquake on October 20. This earthquake produced co-seismic displacements on the horizontal components at the nearby GNSS station KRIV (see Figure S12 in Supporting Information S1). Apart from this example, GNSS stations were often many kilometers away from the moderate-sized earthquakes. The expected surface displacement from the deep and small-sized intrusions with only 2 km width and 3-4 km vertical length is very small, such that the GNSS apparently may not resolve an individual deep intrusion. For example, using a 2D boundary element method, we simulated a dike with a vertical length of 5 km and an overpressure of 1 MPa, with its upper tip located 6 km below the surface (half-space model, Young's modulus 50 GPa, Poisson ratio 0.25). This dike produces a maximum vertical and horizontal displacement of \(\pm\)3 mm and \(\pm\)1.5 mm at the surface, respectively, which is then distributed over a distance of more than 20 km. The displacement from a 3D dike simulation would be even smaller. Variations in daily and hourly GNSS station data are too large to resolve such small intrusions. However, the July 2020 swarm near the future eruption site at Fagradalsfjall may have triggered a trend change at the GPS stations SKSH and SENG, west and north of Mt. Porbjorn, respectively (see Figure S12 in Supporting Information S1).
A notable observation is that these repeated \"intrusion events\" are widespread across the en-echelon structures. As we will see, this type of distributed intrusive activity continues throughout the analysis period in 2020, including at sites where fissure eruptions occurred in 2021, 2022, 2023, and 2024. If the massive intrusions at
Figure 8.— Profile p1 (blue dashed line), trends \(E15\,^{\circ}N\) and lies along the oblique plate boundary, showing seismicity up to day 114 (\(t\) = 2020-04-24 13:38:08.4). The size of the circles represents \(M_{\rm w}\), while the color indicates the time of occurrence in days before the selected day (here, day 114). Earthquakes for which moment tensors were computed are indicated by beach-balls. Upper panel: p2 (purple), p3 (green), and p4 (orange) profiles are plotted and marked by inverted triangles where they cross p1. Thick black dashed lines and thinner black lines indicate volcanic fissure zones and elongated structures, based on interpretations from this study. Bottom panel: The crossing points of p2 (purple), p3 (light green), and p4 (orange) with p1 are marked again by inverted triangles at the top of the depth section. Black dashed lines show sub-vertical channels (dikes), as discussed in our study. Black triangles indicate where eruptive fissures at Fagradalsfjall (2021–2023) and Svartsengi (2023–2024) cross p1.
depth are all related to magma migration, the system of sub-parallel magma likes likely forms reservoirs ([PERSON], 2008) that are emptied by fissure eruptions. In addition, sill-type reservoirs may have formed.
In Figures 9 and 10, we unravel the details of a swarm's evolution, focusing on the example from July 19-22, 2020, when a significant number of stronger earthquakes were induced at the plate boundary, preceded by a deep, upward-migrating swarm. Two snapshots are shown just 2 hours apart. Unlike before, the colored circles show the number of events that occurred before the current time allowing the progression of activity to be resolved. Note that the shallowest earthquake for which a moment tensor could be resolved (\(M_{W}\) 3.7) occurred on July 18 (day 200) at a depth of only 558 \(\pm\) 154 m (white circle at \(-\)6 km distance in Figure 9), just beneath the site of the future Svartsengi eruptive fissure, and is likely related to the swarm activity described here. In the first image (47.6 hr after July 18, 00:00), a vertical cluster of microearthquakes can be seen in cube volume 1, which is delineated based on our observational data of seismicity patterns similar to cube 2). This volume encompasses depths from approximately 4.5-6.5 km, highlighting areas where seismic activity is concentrated. In this phase, the calculated
Figure 10.— Same as Figure 9, but 2 hr later.
Figure 9.— Snapshot of seismicity along profile p1 (blue dashed line) 47.6 hr after 18 July 2020. The color scale represents the number of events that occurred just before the given time (t). Two cube volumes are indicated by the gray and yellow areas with dashed lines, which define the volumes for the projection onto vertical and horizontal lines in Figure 11 based on our interpretation for further discussion. For an explanation of symbols, please see Figure 8.
b-value is higher than 1.5, indicating a relatively higher proportion of smaller earthquakes compared to larger ones (Figure S13 in Supporting Information S1). In map view, the events extend on a fracture structure that crosses the plate boundary profile p1 with a trend of \(E35^{\circ}N\). A few minutes before the snapshot time, three larger earthquakes occurred at the top of the seismic cloud, for which moment tensors could be computed. As we show below, the cluster of microcarbauskes was migrating upward before the larger events were triggered as illustrated in the animations (available at [[https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152)]([https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152))).
Figure 10 shows the situation almost 2 hr later (49.5 hr after July 18, 00:00). In this short time, the plate boundary itself has been activated by a number of larger events between 2 and 4 km depth and by microearthquakes in the depth layer below. The b-value in this phase is lower, at around 1.0, indicating a shift in the earthquake size distribution (Figure S13 in Supporting Information S1). The highest event rates and the most recent events occur in a circular spreading front. In map view, the seismicity is now aligned along the p1 profile. The strike-slip solutions of the moment tensors agree very well with the elongated pattern of seismicity, indicating that shear stress is being released at the plate boundary. The projection of the moment tensor events in the vertical section orthogonal to p1 allows the dip angle and geometry of the plate boundary fault to be inferred. It is very likely that the moment tensor events ruptured EW planes and not NS-oriented en-echelon structures as is often assumed, for the larger earthquakes in the South Iceland seismic bookshelf transform zone to the east of the Hengill system. However, we will later discuss the largest \(M_{W}\) 5.6 earthquake, which may also have involved NS-oriented rupture planes.
In Figure 11, we finally project the seismicity onto vertical and horizontal cross-sections. Earthquakes occurring within a cube volume surrounding the projection axes are represented by colored circles; others are represented by open circles. Prior to 47 hr (July 18, 00:00), the swarm is concentrated at a depth of about 4.5-7 km and produces microearthquakes. At hour 47, an upward migration of microearthquakes begins with a mean velocity of the distribution of about 1.4 km/h (gray dashed line in Figure 11b). The earthquakes also become larger. Lateral growth starts at 47.7 hr with a propagation velocity between 10,km/h and 15,km/h (yellow-dashed line in
Figure 11: Deep intrusion phase between July 19 and 20, 2020. (a) Time-distance plots for earthquakes (circles) projected along profile p1 onto horizontal line at a depth of \(z=3\) km) and (b) vertical line (at \((x,y)=(2,9)\) km). The filled yellow and gray circles in (a) and (b) are events projected to the x and z axes from the cubes 2 and one indicated in Figures 9 and 10, respectively. The magenta beach-balls represent larger earthquakes (M\({}_{W}\)\(>\) 2.7) for which CMTs could be calculated in this study. The gray-dashed and yellow-dashed lines indicate migration velocities of about 1.36 km/h and 10 \(-\) 15 km/h, respectively. The continuous black line in (b) shows the least squares filtered average of events inside cube 1 using a window length of 150 m and a polynomial order of 3.
Figures 11a and 11b). Lateral growth in the brittle part of the plate boundary above 4 km depth is characterized by larger magnitude earthquakes. Comparable intrusions occurred later to the east, in some cases rupturing the brittle part of the plate boundary (e.g., days 239 and 242), and in others not (e.g., day 203). Examples are shown in Figures S11 and S14 in the Supporting Information S1.
Snapshots projected along the crossing profiles p2-p4 show that en-echelon structures have developed not only for shear fractures parallel to the plate boundary but also for intrusive fractures sub-parallel to the fissure swarms of the volcanic systems (see Figures S15, S16, and S17 in Supporting Information S1).
### Centroid Moment Tensors
#### 4.2.1 Reliability, Consistency, and Significance of Moment Tensor Solutions
A well-distributed network of high-quality seismic stations at regional and local distances is required to calculate well-constrained CMTs for small-magnitude earthquakes. The solutions are only reliable if both P- and S-waves, and preferably also surface waves, are used. The limitation of body-wave inversion is that one usually has to work in a frequency range above 0.5 Hz, which requires very well-tested and accurate velocity models. Inversions with dominant frequencies above 4 Hz are usually not reliable in our experience. Regional distance surface waves can be inverted at much lower frequencies, for example, between 0.04 and 0.2 Hz, which lessens the impact of inaccuracies in the velocity model, but requires wide- or broadband recordings and shallow earthquakes. Joint inversion of amplitude spectra and full waveforms is recommended. In addition to the second-order moment tensor, source studies should simultaneously invert for the centroid location and the centroid time. Otherwise, the interpretation of the _nonDC_ components is questionable in particular, since third and higher-order terms in the moment tensor multiple expansion do not vanish and can be mapped into virtual _nonDC_ components. It is also very important to sample the full model space to capture uncertainties and trade-offs of solutions. Finally, reliability and robustness testing with bootstrapping of input data and variation of velocity models is recommended. All these recommendations and conditions were taken into account in our case, making our study one of the most careful source mechanism studies on the RP. For instance, we were able to use 25 high-quality stations with good azimuthal coverage complemented by 40 virtual channels of DAS strain-rate recordings over a length of 21 km close to the epicentral area. We combined P- and S-wave amplitude spectra and full waveforms with Rayleigh and Love waves, P-wave arrival times, and first motion polarities in a joint inversion (Table 1). The centroid location and time are estimated in a probabilistic parameter search. The azimuthal coverage of the stations is exceptionally good, and the waveform fits are very convincing. The different data types can be fit very consistently so that we get very small error bounds.
Earthquake depths on the RP are usually shallow, with the BDT estimated at 6-7 km depth ([PERSON] et al., 2022). The hypocentral depths of the studied events is reported by IMO to be between 4 and 7 km. In contrast, the centroid depths are systematically shifted to shallower depths in the range of 0.6-5.0 km, mainly ranging from 2 to 5 km, with the median of the depth uncertainties being only 0.2 km (Figures 6d and 6e). The shallowest event, with a magnitude of \(M_{W}\) 3.7, occurred on 18 July 2020 at 5:54 UTC, just beneath the site of the future eruptions on the Sundhnakkar crater row in Svartsengi, expected in 2023 and 2024. The shallower depth can be explained by the much denser network of temporary stations we could use for the centroid location. Furthermore, the DAS cable runs almost across the epicentral region, imposing additional constraints on the depths of the earthquake. Earthquakes confined to a depth layer between the surface and 4 km indicate a hot crust and a shallow BDT, doming up to roughly 3-5 km depth beneath the geothermal fields on the RP ([PERSON] et al., 2022).
#### 4.2.2 Robustness and Reliability of _nonDC_ Components
The robustness and reliability of the components _nonDC_ in general and the isotropic components, in particular, have been debated in previous studies ([PERSON] and [PERSON], 1997; [PERSON] et al., 2020; [PERSON] et al., 2008). Systematic errors such as inaccurate velocity models, the lack of near-surface information in the vicinity of the station, and inconsistent centroid locations can cause spurious _nonDC_ components ([PERSON], 1994). Therefore, we performed different sensitivity analyzes to obtain the most accurate results. First of all, our method inverts for centroid location and moment tensor simultaneously using the same waveforms and filters, so that a bias from inconsistent centroid locations can be excluded. Additionally, we considered various different velocity models and concluded that _nonDC_ components are stable and not affected by the choice of the velocity models. However, M\({}_{chd}\) components show higher uncertainty up to by 13% than M\({}_{iso}\) components. Hudson plots of the ensemble of bootstrap solutions also confirms a systematic positive sign of isotropic components for single event, while M\({}_{chd}\) components scatter around zero (Figure 5). We also conducted tests of the effect of different frequency ranges on M\({}_{chd}\) and M\({}_{iso}\) components and found almost no influence on the M\({}_{iso}\) component. This indicates that the volumetric source component is generated instantaneously together with the shear rupture. Furthermore, errors due to stations and sensors can introduce systematic artifacts in the CMT results. Therefore, we carefully evaluated the quality of the data and tested that the arbitrary exclusion of different sensors and networks from the waveform inversion did not significantly change the existence of M\({}_{iso}\) components.
In addition, from theoretical considerations, it can be expected that the inversion of amplitude spectra may generate artificial M\({}_{iso}\) components if the ambient noise level is high. For instance, in Iceland, strong primary and secondary microseisms may be generated by oceanic waves in the Atlantic Ocean with dominant frequencies between 0.04 and 0.2 Hz (e.g., [PERSON] et al., 2006). Although we combine the amplitude spectra inversion with time-domain full waveforms, we want to exclude any possible influence from microseismic noise, especially for the surface waves. Therefore, we conducted a test in which only signals of microseisms were inverted with the same Bayesian method, using the same frequency band and window length for surface waves as in our earthquake study. Our results were conclusive: microseisms do not produce any significant M\({}_{iso}\) components during inversion, as shown in Figure S9 of Supporting Information S1. After these investigations, we are confident that the positive isotropic component is not an artifact generated by noise or by the selection of data and sensors.
Previous studies show the existence of _nonDC_ components in CMTs near volcanic areas. For instance, [PERSON] et al. (2000) observed significant volumetric expansion from moment tensors indicating a direct link between the seismicity and hydrothermal or magmatic processes in the Long Valley Calder in 1997. [PERSON] et al. (2018) found \(\sim\) 50% _nonDC_ components corresponding to a fault opening at the Jailolo Volcano, Indonesia. [PERSON] et al. (2021) showed that the microearthquakes in Kolumbo and Anydros in the Santorini-Amargos zone at the Hellenic volcanic arc have positive _nonDC_ components, which are possibly indicative of volcanic activity. [PERSON] et al. (2010) revealed that the percentage of _nonDC_ components of the swarm-earthquakes substantially increased before the 2001 CMT. [PERSON] and [PERSON] (2009) observed \(-\)30% M\({}_{chd}\) components at the Nyiargongo Volcano just after the eruption in 2002 suggesting the collapse of the roof of a shallow magma chamber.
Figure 5 presents the ensemble means of the M\({}_{iso}\) component of 83 studied events. They are all above zero with a mean ratio between the moment of the isotropic and full moment tensor of \(\approx\)15% indicating a volume expansion. \(\pm\)Isotropic in Figure 5 is defined by \(\frac{\sigma}{\mu!}\frac{M_{\
u}}{M_{\
u}!}\), with \(tr=(M_{11}+M_{22}+M_{33})/3\) and \(M_{T}=\sqrt{M_{T\mu}^{2}M_{T\mu}^{2}/2}\) and \(M_{iso}=tr/\sqrt{6}\)(see e.g., [PERSON] & Kruger, 2014). The volume can be estimated by \(\Delta V=tr/(\lambda+2\mu/3)\) for a tensile crack and \(\Delta V=tr/(\lambda+2\mu)\) for an explosion source ([PERSON], 2001). Using [PERSON]'s constants of \(\lambda\approx\mu\approx 30\ GPa\) and events with a moment magnitude of \(M_{W}=3.5\) (20 July 2020) and \(M_{W}\approx 4.5\) (19 July 2020), the co-seismic volume expansion is in the range of 800 \(m^{3}\) and 26,000 \(m^{3}\), respectively. For comparison, the estimated co-seismic volume expansion (ISO = 8%) accompanying an \(M_{L}\) 2.3 earthquake beneath Eyjafjallajokull volcano in June 1994 was 35 \(m^{3}\)([PERSON] & Brandsdottir, 1997).
#### 4.2.3 The Usage of DAS Data in Centroid Moment Tensor Inversion
At a first glance, first motion polarities extracted from the 21 km long dark fiber (DAS) are compatible with the results of the CMT inversion. We were therefore interested in investigating whether DAS data could be employed to further improve the quality of solutions. To this end, we analyzed which features of the DAS data may be used in seismic source studies. During the period of operation, most earthquakes (\(M_{W}\) > 2.5) occurred in the eastern part of the DAS cable and therefore, showed clear strain rate polarities along the cable. However, most of the virtual stations are unfortunately aligned on the nodal planes between the compressional and dilatational quadrants of the moment tensor and therefore show only emergent first motions.
In general, the DAS data was of lower quality and possessed a lower SNR. Other unknowns in the use of DAS data were the coupling to the ground, site conditions and the particular layout of the buried dark fiber cable. We recommend that these aspects are considered prior to any DAS cable installation, especially in a volcanic environment, in order to perform reliable seismic source studies (see also, [PERSON] et al., 2021). If the DAS cable had been positioned more advantageously in relation to the nodal planes, waveforms recorded on the DAS could potentially be used as cross-correlation traces jointly with other types of waveforms in the CMT inversion, despite the instrument response not being known. On the other hand, the limitations are less severe for methods that use travel time and azimuth information, for example, for event detection or location ([PERSON] & [PERSON], 2018). Thus, we only included DAS-based P-wave first arrival times as an additional target group (Table 1) in the joint inversion and excluded polarities. Especially, the arrival times of the P-waves along the dense array of virtual sensors of the DAS provide additional constraints on the epicentral location and depth. In turn, a better understanding of the centroid location helps to further constrain the moment tensor parameters, and we could verify a further improvement in the fit and a reduction of uncertainties in the source parameters.
### What CMTs and Swarms Tell About the Transtensional Opening Mechanisms?
Seismicity in 2020 is distributed in a 5 km wide zone along the oblique plate boundary on RP. Figure 12 shows the magnitude distribution, rate and isotropic components of events in our catalog along profile p1 (see Figure 7).
The earthquake rate and magnitudes in 2020 were high at and between the Svartsengi and Fagradalsfjall volcanic systems. The highest rates of microearthquakes correlate with locations where fissures occurred in 2021-2024 (Figure 12b). A third spot of high earthquake rate and large magnitudes is the Krysuvik system, where no eruption has occurred so far.
The density of activated surface faults ([PERSON] et al., 2024) crossing p1 follows the general trend of higher magnitudes and seismic activity, and shows a peak at about 10 km where the largest earthquake (\(M_{\mathrm{W}}\) 5.6) occurred (Figure 12c). Isotropic components (Figure 12d) do not correlate directly with specific eruption sites but are more generally linked to larger earthquakes triggered near the upper tip region of deep intrusions.
[PERSON] et al. (2022) pointed out the shallow micro seismicity occurring beneath Svartsengi related to the three uplift-subsidence cycles and the associated bending of the uppermost layers resulting from a pressure increase in a still-shaped area at about 4 km depth. Geodetic observations of the uplift cycles also suggest still-type intrusions beneath Svartsengi: Interestingly, the source region causing the uplift beneath Svartsengi did not show earthquakes below roughly 4 km depth, and the catalog of confined locations in this study indicates an up-doming of the deepest earthquakes beneath Svartsengi from about 7 to 4 km. The majority of the deeper seismicity and the largest events occurred east of Svartsengi, near the future eruption sites of Fagradalsfjall, and also close to Krysuvik, 10 km east of Fagradalsfjall. According to [PERSON] et al. (2023), these deep microearthquakes were possibly associated with mid-crustal magmatic intrusions at a depth of 6 km. Our analysis supports this model and
Figure 12: (a) Magnitude (\(M_{\mathrm{W}}\)) and seismicity, (b) the earthquake rate, (c) the density of active surface faults and fractures from 2019 to 2020, and (d) the volumetric source component (\(M_{\mathrm{iso}}\)) as a function of the length along profile p1. The magenta beach-balls in (a) represent events with high-quality CMT solutions. The black triangles in (b) indicate the crossing points of eruption fissures at Svartsengi (\(-5\) km) and Fagradalsfjall (0 km). The surface fault data set was taken from [PERSON] et al. (2024).
provides more details on where and how the intrusions were taking place and how they interact with the plate boundary.
The deeper seismicity beneath Fagradalsfjall is in a similar location as a group of long period earthquakes imaged at 10-12 km depth prior to and during the 2021 eruption, likely linked to the magma plumbing system beneath Fagradalsfjall ([PERSON] et al., 2022). Our seismic catalog resolves that most deep intrusions in the beginning phase of the unrest occurred in vertical, en-echelon planes striking sub-parallel to the volcanic fissure swarms of the Reykjanes, Svartsengi, Fagradalsfjall, and Krysvukir systems, perpendicular to the least compressive stress. The swarm-like seismicity in narrow bands with a width of only 1 km or smaller and the upward migration of the seismic front with velocities of only a few kilometer per hour suggest that these were ascending, buoyancy-driven magma-dikes, possibly accompanied by \(CO_{2}\) degassing. Our study indicates that multiple, small-sized dikes ascended over a broader region of the plate boundary and formed distributed magmatic reservoirs in the lower and upper crust that were possibly depleted during later fissure eruptions.
The distribution of larger events is reflected in the 83 moment tensor solutions with M\({}_{W}>2.7\) which align along a narrow, 30 km long segment centered on the 2021-2023 eruption sites at Fagradalsfjall and trending about \(N80^{\circ}E\) (Figures 6 and 7). Interestingly, the CMT events occurred mainly at depths between 2 and 5 km, with the shallowest event at 0.6 km, and often sample the uppermost parts of the microearthquakes associated with intrusions. According to the well-resolved CMT inversions, most earthquakes occurred in the Fagradalsfjall segment, indicating \(NS\)-trending right-lateral or approximately N80\({}^{\circ}\)E trending left-lateral strike-slip faulting (Figure 6). This pre-dominance of strike-slip faulting in the transcurrent plate boundary zone is well known and has been explained by systems of sub-parallel, northerly striking right-lateral transcurrent faults that generate the largest earthquakes ([PERSON], 2006; [PERSON], 1991; [PERSON] et al., 2020, 2023). However, we cannot confirm northerly striking rupture planes for the events along the Fagradalsfjall segment but see indications of shear rupture along the plate boundary. We presented examples showing that the shear motion in the plate boundary was triggered by intrusions from depth. The formation of en-echelon structure, both from opening fractures by intrusions above or below a ductile shear zone, and from shear cracks associated with earthquakes above a ductile shear zone or above dikes (see Figure 13a), is well known from laboratory experiments in structural geology in the brittle layer above ductile shear zones.
The CMTs of the \(M_{W}>2.7\) earthquakes are predominantly strike-slip with positive isotropic components indicating co-seismic volume expansion. While the \(\sim\)N80\({}^{\circ}\)E striking nodal plane agrees surprisingly well with the spatial alignment and migration direction of microearthquakes in the upper crust, the co-seismic volume expansion needs further discussion. A simplest approach would be to interpret the increase in volume by shear-tensile crack in which the ratio of opening to shear is equal to the ratio of plate movement of 7 mm/yr versus 18 mm/yr = 0.38. However, the isotropic component of such a mixed mode rupture would be about 34%, about
Figure 13: Sketch to demonstrate possible mechanisms for generating en-echelon faulting and diking and positive M\({}_{\rm iso}\) components. (a) Shear cracks can form in the border region of dikes or above ductile shear zones (Mode I, Mode III, Riedel shears). Opening cracks can form en-echelon structures above or below these ductile shear zones. (b) Four models explain co-seismic volume expansion. See the text for further explanation.
twice the observed one. More critically, it would not be trivial to fill a compact fracture surface at a depth of 3-4 km with a frictional fluid in a few milliseconds if the fluid had to flow into the fault first.
Only a few mechanisms can be considered to explain a co-seismic volume expansion during the short duration of a shear rupture. Model (1) in Figure 12(b) depicts the aforementioned mixed-mode dislocation on the seismic fault at depth. Overpressure may be generated by an influx of magmatic fluids or gases from a deeper reservoir. The mixed-mode failure can be shown by a decomposition into a general dislocation source ([PERSON], 1980; [PERSON], 1996; [PERSON], 2015), for which the magnitude of the positive M\({}_{iso}\) component has a specific ratio to the moment of the _nonDC_ component depending on the elastic properties of the media. Also, a positive M\({}_{iso}\) should correlate with a positive M\({}_{fold}\). Magma or water is ruled out as fluid because the flow velocity is too slow. However, if gas has previously intruded into the fault zone, then the co-seismic expansion of the gas in the shear fracture can proceed rapidly and open the fault surface during rupture.
Model (2) in Figure 12(b) assumes that a fluid-filled crack already exists close to the shear fault and possibly triggered the earthquake nearby. The fluid-filled crack may be a magmatic dicke or still under overpressure in its upper tip. As a response to shear failure in its vicinity, the dicke will instantaneously expand and generate a co-seismic M\({}_{iso}\) component. The dicke expansion can be fast, even if magma-filled, because the fluids do not need to flow through narrow channels behind the rupture front, and only a small opening over the full surface of the dicke is needed to explain a large M\({}_{iso}\). The model has been suggested by [PERSON] and [PERSON] (1997) to explain positive volumetric source components of microearthquakes beneath Eyjafallajokull volcano at the eastern tip of the South Iceland Seismic Zone.
Models (3) and (4) in Figure 12(b) both display non-localized processes occurring remotely from the earthquake rupture. Based on the double-couple source assumption for a seismic source, which includes two quadrants--dilatant and compressional--that represent the areas of dilation and compression, Model (3) assumes a gas-saturated pore space in a dilatant quadrant for the rupture, where pore volume may expand when the rupture propagates. The gas may consist of \(CO_{2}\) that migrated upward from the magmatic reservoirs in the lower crust and mantle and is trapped in the upper crust. The model predicts a positive M\({}_{iso}\) component if the expansion of the pore gases outweighs the contraction of the pore space in other quadrants. A broad distribution of M\({}_{fold}\) components can be explained if the orientation of the fractures forming the pore space varies. Model (4) assumes that the volume expansion is generated near the surface. For instance, as the compressive pressure is small, opening cracks could appear with the arrival of seismic waves. This would be expected particularly if the uplift of the surface leads to tensile stresses. Model (4) is not very likely as a time delay can be expected between the seismic waves and the reaction of the aquifer close to the station.
Earthquakes in Iceland often display M\({}_{iso}\) components due to volume changes, for instance in Krafla ([PERSON] et al., 2016; [PERSON] et al., 2016), at the Eyjafallajokull volcano ([PERSON], 1997), and in Hengill ([PERSON] et al., 1998). [PERSON] et al. (1989) observed microearthquakes in the Krafla area that had a variety of _nonDC_ mechanisms, including explosive tensile-crack events and implosive events due to cavity collapse at depth. The existence of _nonDC_ mechanisms on the RP was previously observed in the study of [PERSON] et al. (2021). They showed different signs of M\({}_{iso}\) components associated with inflation (positive) and deflation (negative) during the swarm activity in 2017 related to a vertical magmatic dicke.
Since in our study, most of the earthquakes have positive M\({}_{iso}\) components with strike-slip mechanisms, confined to a very narrow zone both in time and space at a shallow depth, indicating a link between the magmatic system, vertical dikes, and earthquake activity, we infer that the M\({}_{iso}\) component can be associated with a co-seismic widening of dikes and a possible volume increase of gas-saturated pore space close to the fault.
Returning to our key questions, how does the transtensional opening of the brittle part of a plate boundary work mechanically? Melt transfer in the lower crust occurs along the 70 km length of the plate boundary in the form of multiple, vertically extended, buoyancy-driven intrusions, with their horizontal axes oriented in the direction of the maximal compressive stress (\(\sigma_{1}\)), slowly ascending (\(<2\) km/hr) to the brittle-ductile transition of the plate boundary, and in some cases, at shallower depths. The intrusions are accompanied by tiny earthquake swarms with magnitudes smaller than about 2. At the depth of the brittle-ductile transition, we observe a strong interaction of dikes with the plate boundary fault, which is tilted about 30\({}^{\circ}\) with respect to \(\sigma_{1}\). Melt appears to infiltrate the fault from below, inducing shear in the fault that propagates laterally and upward at velocities of 10-15 km/hr. The slow slip events are accompanied by larger earthquakes, reaching magnitudes of five or greater. These eventsindicate co-seismic volume expansion, which may result from the interaction of melt and fluids or gases in neighboring dikes and pore space. The complex interaction of multiple subparallel dikes with the plate boundary leads to the formation of fault systems that together create a wider deformation band accommodating tectonic stresses from surface asesismic faults and shallow microearthquakes.
## 5 Conclusions
This study enhances our understanding of seismogenic processes and their interplay with magmatic and tectonic activities on the Reykjanes Peninsula in Iceland. It elucidates how transtensional opening in the brittle part of a plate boundary is driven by the interaction between melt-induced dike intrusions and tectonic stresses. In oblique spreading zones like the Reykjanes Peninsula rift, this interaction leads to a complex system of faulting and deformation that accommodates both the ascent of magma and the lateral propagation of shear slip along the plate boundary. These mechanisms contribute to the development of broader deformation zones of sub-parallel fissures and earthquake faults where tectonic and magmatic activities are intricately linked at various depths, ultimately influencing both seismic, asesismic, and volcanic phenomena.
The 2020 unrest marked the beginning of a longer process which culminated so far in several eruptions from 2021 to 2024 at different sites along the obliquely rifting plate boundary of the Reykjanes Peninsula. We developed a catalog of microearthquakes from an automatic processing of waveform data from 2020 with a new method involving machine learning and waveform attribute stacking with an octal tree search for location. This high-resolution, high-quality catalog gives insights into the interaction of magmatic dikes with microearthquakes and shear ruptures. From this we see deep, swarm-like, precursory seismicity at sites of impending eruptions in the Svartsengi-Fagradals/jall volcanic systems. In addition, our results indicate that the Krysuvik volcanic system could be preparing for a possible future eruption already since 2020. While the plate boundary and deformation zone trend at depth in a N70'E-direction, obliquely to the spreading of N121\({}^{\circ}\), the magmatic intrusions into the crust form systems of sub-parallel, en-echelon dikes approximately in the NE-SW direction. They induce earthquakes at shallow depths in the uppermost crust, which in turn generate en-echelon fault systems in the EW and possibly NS direction.
Centroid moment tensor inversion has become a basic tool to analyze earthquake sources and their possible _nonDC_ components, while their errors are rarely reported. In our study a probabilistic moment tensor inversion method is used providing uncertainties by exploiting data from several dense networks. We found very consistent orientations of the strike-slip mechanism along the plate boundary, including positive, isotropic components (M\({}_{iso}\)) with an average fraction of 15% of the total seismic moment, indicating a co-seismic volume expansion between about 800-26,000 \(m^{3}\).
The M\({}_{iso}\) components are uncorrelated with the M\({}_{clnd}\) components, implying that they cannot be explained by mixed-mode dislocation on a single plate boundary fault. We explain the isotropic component by an interaction between magmatic intrusions and the derived magmatic gases with shear fractures in the disk damage zone. Additionally, void space and fissure formation at the surface may contribute to M\({}_{iso}\) components in regions affected by uplift-induced tensile stresses.
This study has also shown that DAS data can provide valuable input to determine the centroid location and the position of nodal planes on the focal sphere with high accuracy. However, the integrating of strain-rate amplitudes measured on DAS into the CMT inversion was problematic, even after careful data evaluation and sensitivity analysis, indicating that the installation of high-quality seismic sensors with good azimuthal coverage is important for moment tensor studies and cannot be substituted by DAS.
## Data Availability Statement
The supporting information includes Figures S1-S17 and Table S1 in Supporting Information S1, which can be found in Supporting Information S1. Compiled waveforms for the CMT inversion can be found for target events in the GFZ data library [[https://doi.org/10.5880/GFZ.2.1.2024.002](https://doi.org/10.5880/GFZ.2.1.2024.002)]([https://doi.org/10.5880/GFZ.2.1.2024.002](https://doi.org/10.5880/GFZ.2.1.2024.002)). The CMT results obtained in this study are available as interactive online reports via the link [[https://data.pyrocko.org/publications/gromd-reports/2020-ice-land-reykjanes](https://data.pyrocko.org/publications/gromd-reports/2020-ice-land-reykjanes)]([https://data.pyrocko.org/publications/gromd-reports/2020-ice-land-reykjanes](https://data.pyrocko.org/publications/gromd-reports/2020-ice-land-reykjanes)). Seismic data from the permanent national seismic network in Iceland are available in the open database Icelandic Meteorological Office (1992). Data from temporary stations operated by the GeophysicalInstitute of the Academy of Sciences of the Czech Republic ([PERSON], 2013) are under embargo until April 2026. However, data for 2013-2020 are scheduled to be released on 1 January 2025 via an EIDA node. Until then, they are available on request from [PERSON]. Seismological data from temporary GFZ stations analyzed during the current study are available in the GEOFON repository ([PERSON] et al., 2020). Fiber optic data are available at [PERSON] et al. (2020). For each profile, p1, p2, p3, p4, a GIF animation of the time-space evolution of the seismicity is available in the Zenodo repository ([PERSON], [PERSON], [PERSON], et al., 2024; [[https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152)]([https://doi.org/10.5281/zenodo.13882152](https://doi.org/10.5281/zenodo.13882152))).
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wiley/fe119459_40ec_4c53_951a_20d2831e5828.md | # IGR Solid Earth
Research Article
10.1029/2023 JB027676
Relating Hydro-Mechanical and Elastodynamic Properties
of Dynamically Stressed Tensile-Fractured Rock in Relation
to Applied Normal Stress, Fracture Aperture, and Contact Area
Clay [PERSON]
1 Department of Geosciences, Pennsylvania State University, University Park, PA, USA, 2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 1 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 2 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
3 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 3 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
2 Department of Geosciences, Pennsylvania State University, University Park, PA, USA, 2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 3 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
1 Department of Geosciences, Pennsylvania State University, University Park, PA, USA, 2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 3 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
1 Department of Geosciences, Pennsylvania State University, University Park, PA, USA, 2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 3 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
[PERSON]
1 Department of Geosciences, Pennsylvania State University, University Park, PA, USA, 2 Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA, 3 Chevron ETC, San Ramon, CA, USA, 3 Department of Energy and Mineral Engineering, EMS Energy Institute, G3 Center, The Pennsylvania State University, University Park, PA, USA, 2 Dipartimento di Scienze della Terra, La Sapienza Universita di Roma, Rome, Italy
###### Abstract
We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PETs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10-20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for \"true\" contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.
We report laboratory experiments with fractured rock to understand the relation between fluid flow, fracture openness, and elastic properties under oscillating stresses. These experiments are conducted on rough, pre-fractured granite specimens under normal stress conditions similar to those found in the shallow earth, a few kilometers in depth. Fluid pressure in the fracture is oscillated at various amplitudes at a fixed frequency. During this dynamic stressing, we use an ultrasonic device to monitor the evolution of the fracture interface. We examine the influence of fracture aperture and contact area by conducting measurements at increasing normal stress state. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film, showing an image of where the two halves of the fracture are in contact. The ultrasonic monitoring reveals spatial variations in contact properties, which is informed by fracture contact area measurements. These measurements are also related to the fluid-flow in response to dynamic stressing and similar comparisons are made for how the fracture interface evolves, recovers, following the stress perturbations.
Footnote †: 02024 The Author(). This is an open access article under the terms of the Creative Commons Attribution-Non Commercial License, which permits use, distribution and reproduction in any medium, provided the original work is not used for commercial purposes.
Footnote †: 020024 The Author(). This is an open access article under the terms of the Creative Commons Attribution-Non Commercial License, which permits use, distribution and reproduction in any medium, provided the original work is not used for commercial purposes.
Footnote †: 02024 The Author(). This is an open access article under the terms of the Creative Commons Attribution-Non Commercial License, which permits use, distribution and reproduction in any medium, provided the original work is used for commercial purposes.
et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 1976; [PERSON] et al., 1988; [PERSON] & [PERSON], 2003; [PERSON], 2015). Also, fault stability may even be perturbed by elastic waves propagating from earthquakes ([PERSON] & [PERSON], 2004; [PERSON] et al., 2016; [PERSON] & [PERSON], 2007) thus triggering seismicity ([PERSON] & [PERSON], 2013; [PERSON] et al., 2013). This is often observed with co-seismic velocity variation, or \"elastic softening,\" typically in the shallow crust ([PERSON] et al., 2008a, 2008b, 2014; [PERSON] et al., 2010; [PERSON] et al., 2013; [PERSON] et al., 2012; [PERSON] et al., 1998, 2006; [PERSON] et al., 2008; [PERSON] et al., 2009; [PERSON] et al., 2016). This co-seismic softening, an instantaneous wave speed change (typically a decrease), is then followed by a time-logarithmic post-seismic recovery of the fractured rock stiffness for example, [PERSON] et al. (2008a); [PERSON] et al. (2021).
Experimental and field studies have use seismic wave velocity and attenuation to estimate fracture stiffness ([PERSON] et al., 2008; [PERSON] et al., 1990). These and other observations demonstrate that fracture topology, and its changes with stress, is central to the poromechanical response ([PERSON], 1987; [PERSON] & [PERSON], 1985; [PERSON] et al., 2013; [PERSON] & [PERSON], 1996). Other experimental studies have investigated the changes in elastic properties of faults during shear ([PERSON] & [PERSON], 1971), usually with some amount of gauge or wear product. Other studies has demonstrated, with similar monitoring techniques, the relation between wave speed and amplitude and the following: contact area (evolution) ([PERSON] & [PERSON], 2006), gauge layer dilation ([PERSON] & [PERSON], 2013; [PERSON] et al., 2016), degree of surrounding bulk damage ([PERSON] et al., 2021), and stress state ([PERSON] et al., 2021). In the work of [PERSON] et al. (2021), it was demonstrated in quasi-static experiments that elastic stresses in bulk rock exert significant control on transmitted wave velocity, but near-fault properties strongly influenced transmitted wave amplitude (attenuation). All of these studies provide rich information regarding the role of discontinuities in rocks and the role their topology plays in deformation (stress distribution) and fluid flow. However, these observations of planar, rough fractures are not necessarily indicative of their poor-elastic response under dynamic conditions (strain). Recently, dynamic acousto-elastic testing (DAET) has been used to study the nonlinear elastodynamic response of fractured rock under different stress and saturation conditions ([PERSON] et al., 2021, 2022). In these studies, the nonlinear elastic responses can be activated with dynamic strains on the order of \(10^{-6}\)([PERSON], 2009; [PERSON] & [PERSON], 2005; [PERSON] et al., 2015). The nonlinear elastodynamic behavior of rock, intact or fractured, is modulated by minute features such as apertures (governing flow transport, asperity compliance) and higher-order effects such as nonlinear effective stiffness (impacted by rate and state-dependent friction and healing). Laboratory experiments implementing DAET ([PERSON] et al., 2021, 2022; [PERSON] et al., 2016; [PERSON], [PERSON], [PERSON], & [PERSON], 2017; [PERSON] et al., 2021), show that transmitted ultrasonic wave velocity decreases in response to stress oscillations followed by a time logarithmic recovery, similar to the aforementioned field observations.
In the context of subsurface storage and energy recovery, dynamic stressing can result in permeability enhancement or reduction. Elastic waves from earthquakes may also induce pore pressure oscillations sufficiently large to change permeability ([PERSON] & [PERSON], 2013; [PERSON] et al., 2012). The underlying mechanism dominating empirical observations of permeability enhancement (and reduction) is postulated to be mobilizing and arresting of particles in porous media ([PERSON] et al., 2014, 2015; [PERSON] et al., 2011; [PERSON] & [PERSON], 2009; [PERSON], 2005; [PERSON] & [PERSON], 2009). This effect of clogging and unclogging of pore throats has been observed experimentally ([PERSON] et al., 2014; [PERSON] et al., 2011), but the relation between these observations and elastic properties of fractured rock is not well understood. Other mechanisms could account for the changes in transmissivity of rough fractures such as: fracture orientation to flow ([PERSON] & [PERSON], 2000), evolution of fracture geometry (i.e., roughness, contact area) ([PERSON] et al., 2020; [PERSON] & [PERSON], 1996).
The similar poromechanical responses (permeability change and elastic softening) of faults and fractured rock to dynamic stressing sources indicate that these mechanisms--stiffness and fluid transport--are correlated ([PERSON] et al., 2006; [PERSON], 2002; [PERSON] et al., 2002; [PERSON], 1987; [PERSON] & [PERSON], 1995; [PERSON], 1982; [PERSON] & [PERSON], 2003; [PERSON] et al., 2005; [PERSON] et al., 1987; [PERSON] et al., 1980; [PERSON] et al., 2006; [PERSON] & [PERSON], 1996), much like the connection under static conditions ([PERSON], 2013; [PERSON] et al., 2011; [PERSON] et al., 2013; [PERSON] & [PERSON], 2016). In this work we seek to decouple the nonlinear elastic and fluid flow responses to dynamic stressing under different applied normal stresses. To address this, we perform laboratory experiments on a tensile-fractured specimen of Westerly granite, where pore pressure perturbations were applied at different applied stress states. An array of cross-fracture ultrasonic sensors and through-fracture fluid flow measurements allow us to characterize the elastodynamic and permeability responses to the pore pressure oscillations. A unique contribution of this study is relating the nonlinear elastic and fluid flow changes to fracture contact area with the implementation of pressure sensitive films. This allows us to connect the inherent spatial variability of fracture geometry to applied stress state and the variability of observed nonlinear elasticity (for respective ultrasonic sensor locations).
## 2 Experimental Setup
We conducted a series of highly constrained laboratory experiments on a pre-fractured sample of Westerly granite. For the first experiment (p5483), nonlinear elastic properties and flow rates were simultaneously measured under true triaxial stresses. Another experiment (p5596) was conducted to estimate the real area of contact of the fracture as a function of applied normal stress.
The sample was cut into a L-shaped block \(69\times 45\times 50\times 26\) mm (Figures 1a and 1b) that we grooved along the perimeter and split in Mode I over a knife-edge to create a rough quasi-planar fracture. The pre-fractured sample was re-maated, placed between two loading platens, and then sealed with a latex membrane (separating pore fluid from confining fluid). The steel loading platens include piezoelectric transducers (PZTs) embedded 3 mm from the on-rock faces as well as internal conduits to provide a distributed line source of fluid at both ends of the fracture, Figure 1b (using a modified version of the method of [PERSON] et al., 2011).
After placing the sample between steel loading platens, it was sealed inside a latex membrane, and then placed inside a pressure vessel, Figures 1b and 1c; more details regarding sample preparation can be found in Shokouhi
Figure 1: (a) Pre-fractured L-shaped Westerly granite sample. (b) Transmitter-receiver pairs used in active source ultrasonic monitoring embedded inside loading blocks (inactive sensors are dark-gray). (c) Biaxial loading apparatus with pressure vessel in Penn State’s Rock Mechanics Laboratory. After sample preparation and installation in the pressure vessel, the fracture was saturated with deionized water. Imposed dynamic oscillations of pore pressure with amplitudes ranging from 0.2 to 1 MPa at 1 Hz. (d) Overview of the experiment showing the applied normal stress levels (10, 12.5, 15, 17.5, 20 MPa) in red and pore pressure oscillations in blue. Normal stress oscillations at the beginning of each stress level were performed for a separate study. (e) Pore pressure oscillations at 15 MPa \(\sigma_{\text{eff}}\)
et al. (2020); [PERSON] et al. (2021); [PERSON] et al. (2021). Leveling blocks below the bottom faces of the loading platens act to minimize tilting during the application of normal stress. Each loading axis is independently servo-controlled, including upstream and downstream fluid flow from pressure intensifiers. Mechanical displacements and stresses are measured with direct current displacement transducers (Trans-Tek Series 240 DCDT) as well as custom-built load cells and recorded by a 24-bit analog-to-digital data acquisition system at 100 Hz. Active source ultrasonic monitoring was conducted using a VantageTM Research Ultrasound (Verasonics) system and PZTs (APC International Ltd. 6.35 mm diameter compressional crystals) with a nominal center frequency of 500 kHz. PZTs are adhered to the steel loading blocks with conductive epoxy and back-filled with seal epoxy. The transmitting PZTs were successively pulsed every 0.2 ms and the ultrasonic response is recorded at the receiving PZTs at 25 MHz. A triggering signal from the Verasonics system is also recorded by the mechanical data acquisition system, allowing data synchronization. More details for the data acquisition are found in [PERSON] et al. (2020); [PERSON] et al. (2021); [PERSON] et al. (2021).
### Experimental Procedure
After sample preparation and installation into the pressure vessel, the experiment commenced with the application of a normal stress of \(\sim\)10 MPa followed by a confining pressure of \(\sim\)5 MPa. Next, the inlet (\(P_{ph}\) = 2.5 MPa) and outlet (\(P_{ph}\) = 1.5 MPa) pressures were applied to provide a pressure differential across the sample, Figure 1. The large difference in confining and pore fluid pressures prevents fluid from flowing around the outside of the sample and/or along the grooved contour around the sample (used during tensile fracture). Pore pressure oscillations were applied via servo control by feeding a sinusoidal command signal to the inlet pressure intensifier \(P_{ph}\). \(P_{ph}\) stress oscillations ranged in amplitude from 0.2 to 1 MPa at 1 Hz while holding \(P_{ph}\) constant, Figure 1d. All oscillations throughout the experiment are composed of 20 cycles, which allows for direct comparison in this experiment and to other studies ([PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2021). The first pore pressure oscillation set is preceded by a normal stress oscillation set, which is used in the analysis of [PERSON] et al. (2021), and can be seen in the effective normal stress plot in Figure 1d. Afterward, the effective stress state was increased for a total of five different stress levels [10, 12.5, 15, 17.5, 20] MPa. Due to operational constraints, the effective stress state was decreased to \(\sim\)1 MPa and held over several hours, before resuming the experiment at 17.5 MPa. Three sets of pore pressure oscillations of varying amplitudes were repeated three times at each normal stress level when stresses were incremented and four sets when decremented, Figures 1d and 1e. The decremental stress levels [17.5, 15, 12.5, 10] MPa, were conducted in order immediately proceeding largest stress, 20 MPa, and with an hour hold at 12.5 MPa. This protocol is designed to investigate the repeatability of measurements and to determine the effect, if any, of loading and unloading on the fracture properties (elastic nonlinearity, permeability).
### Steady-State Permeability Measurements
Independent measurements of volumetric inflow (\(Q_{A}\)) and outflow (\(Q_{B}\)) rates are made using Linear Variable Differential Transformers (LVDTs) attached to the pistons of the pressure intensifiers. Our flow rate measurements are continuous, but we only consider data for steady-state flow conditions defined by: \(Q_{A}-Q_{B}\leq 5\%\). [PERSON]'s law is used to calculate permeability \(k\):
\[k=\frac{\mu L\,Q}{A\Delta P_{P}} \tag{1}\]
where \(Q=\frac{1}{2}(Q_{A}+Q_{B})\) is the average flow rate, \(\mu\) is the fluid viscosity (\(10^{-3}\) Pa \(\cdot\) s) at 20\({}^{\circ}\)C, \(L\) is the length of the flow path along the fracture plane (50 mm) and \(A\) is the cross-sectional area perpendicular to the flow path (45 mm \(\times\) 26 mm), which includes both the fracture and granite wall rock. This gives fracture permeability assuming that flow through the surrounding rock matrix is negligible, which is consistent with previous work showing permeability values of order \(10^{-21}\) m\({}^{2}\)([PERSON], 1987). The fracture permeability could also be calculated using other approaches ([PERSON] et al., 2018; [PERSON]. [PERSON] et al., 2017) which isolate the fracture but our focus is on relative _changes_ in fracture permeability, rather than the absolute values, and for our work the changes are dominated by the stress-sensitive fracture. We note that permeilities and transmissivities are intrinsically linked through aperture. Permeability scales with aperture (b) as \(\frac{b^{2}}{12}\) and transmissivity scales as \(\frac{b^{2}}{12}\). Furthermore, bulk permeability (inclusive of the frontal solid area) scales as \(k_{bulk}=\frac{b^{2}}{12}\) where s is the equivalent spacing between fractures, or in our experiments the thickness of the sample perpendicular to the fracture. This thickness remains constant throughout the experiment and thus our measurements of changes in \(k_{bulk}\) scale directly with transmissivity.
### Dynamic Permeability Measurements
In addition to measuring the steady-state permeability before and after oscillations, we use the flow-analysis technique as described in [PERSON] (2007) to calculate the \"dynamic\" permeability, \(\hat{k}\), during the pore pressure oscillations. The frequency of the imposed pore pressure oscillations, 1 Hz, is sufficiently fast enough to be nonsteady-state (i.e., \(Q_{A}\
eq Q_{B}\)). The following equation is employed to quantify the permeability during oscillatory flow conditions:
\[\hat{\delta}_{Q}=\left|\frac{Q_{A}(t)}{P_{A}(t)}\right|=\frac{1}{2}\Bigg{|} \frac{(1-i)\sqrt{\hat{\eta}\hat{\xi}}\ \mathrm{sinh}\left(1+i\sqrt{\hat{\xi}/\hat{\eta}}\ \right)\Bigg{|}}{\mathrm{cosh}\left(1+i\sqrt{\hat{\xi}/\hat{\eta}}\ \right)\Bigg{|}}, \tag{2}\]
where \(\hat{\eta}=\left(AT\hat{k}/\pi\mu L\right)\) and \(\hat{\xi}=AL\hat{s}\). Here, \(T\), \(\hat{k}\), and \(\hat{s}\) are the oscillation period (1 s), dynamic permeability, and hydraulic storage, respectively. This analytical expression is the solution to harmonic flow through a porous medium via diffusion. The hydraulic parameter \(\hat{\delta}_{Q}\) is the ratio between imposed upstream pore press (\(P_{A}\)) and the resulting fluid flux \(Q_{A}\), measured by LVDTs attached to the pressure intensifier pistons. Both the dynamic permeability, \(\hat{k}\), and hydraulic storage, \(\hat{s}\), are calculated from a least-squares minimization between the measured hydraulic parameter \(\hat{\delta}_{\mathrm{Qexp}}\) and the analytically calculated \(\hat{\delta}_{Q}(\hat{k},\hat{s})\) :
\[\left(\hat{\mathbf{k}},\hat{s}\right)_{\mathrm{opt}}=\underset{\hat{\mathbf{ k}},\hat{\mathbf{s}}}{\mathrm{arg}\ \mathrm{min}}\sqrt{\left|\hat{\delta}_{\mathrm{Qexp}}^{2}-\hat{\delta}_{Q}^{2} \left(\hat{\mathbf{k}},\hat{s}\right)\right|}. \tag{3}\]
In subsequent sections, we report results of dynamic permeability, \(\hat{k}\), under different stress conditions and in relation to active source ultrasonic measurements during oscillations.
## 3 Active Source Ultrasonic Measurements
Active source ultrasonic data are continuously recorded before, during and after the pore pressure oscillations. P-wave, transmitting PZTs are successively excited with half-sine pulses at 96 V having a center frequency of 500 kHz. Having an array of transmitters and receivers allows us to capture the spatial variability of the fracture's elastodynamic properties (i.e., wave speed and amplitude). Various limitations prevented the use of all possible transmitter-receiver pairs; we report the results from 7 transmitter-receivers pairs.
The ultrasonic data are processed as previously documented ([PERSON] et al., 2021; [PERSON] et al., 2013; [PERSON] et al., 2021), where all waveforms are cross-correlated with a reference waveform (constructed by averaging 50 recorded waveforms at the beginning of each experimental run before stress oscillations) to determine a time shift. Since the time shift is typically smaller than the signals' sampling time, often on the order of 1 ns, the resolution is improved with a second-order polynomial fit to the peak of the cross-correlation function ([PERSON] et al., 1995). Figure S1 in Supporting Information S1 shows the raw waveforms for one transmitter-receiver pair during a 1 MPa amplitude pore pressure oscillation, which highlights minute changes we are able to measure. The absolute arrival time is obtained by adding the relative time shift to the p-wave arrival time of the reference waveform (obtained using a threshold). To obtain (corrected) p-wave wave speed, the sample thickness (corrected for compaction/dilation from internal DCDT which has \(\pm 0.1\) \(\mu\)m resolution) is divided by the absolute arrival times. The RMS amplitude is calculated over an approximately 10 \(\mu\)s time window including the p-wave arrival and one full period of the waveforms. Additionally, as part of a previous study ([PERSON] et al., 2021), tests were conducted using a stainless steel specimen (of same dimensions) and concluded that the nonlinearity of the entire experimental apparatus is negligible compared to the nonlinearity measured in intact and fractured rock samples.
### Fresnel Zone Imaging
A key aim of this study is relating p-wave velocity and permeability changes to changes in the fracture contact area. To accomplish this, we need to determine the size of the fractured region probed by a given ultrasonic transmitter-receiver pair in our experimental configuration. It is common to implement ray theory approximations of acoustic wave propagation for active-source monitoring, that connects changes in wave velocity and amplitude to changes in experimental fault contact area ([PERSON] et al., 2014; [PERSON] et al., 2021), for example, In this approximation, waves propagating from source to receiver are considered to be in the high-frequency limit and thus the wavefield is collapsed into a raypath approximated as an infinitesimally thin line ([PERSON], 2004). In reality, elastic waves propagate within a finite volume whose width is frequency-dependent, rather than the volumeless trajectory of a raypath. The region around the propagation trajectory responsible for diffraction in a medium is called the Fresnel zone or Fresnel volume. The region around a ray that mostly influences the propagation of a band-limited wave is called the first Fresnel zone. Previous studies estimated the ellipsoidal Fresnel volume for active-source monitoring ([PERSON] et al., 2015) by assuming point sources for transmitters and receivers, which may underestimate the region or volume probed by finite-sized transducers.
Here, we numerically model the Fresnel zone resulting from our finite-sized transmitter-receiver PZTs through the bulk rock sample using a sensitivity kernel (SK) to later estimate perturbations in the wavefield amplitude arising from heterogeneities at the fracture interface. The SK also provides insight on how other types of diffractors, that is, wave speed or density, affect acoustic wave propagation ([PERSON] et al., 2013). The SK in Figure 2b shows the variation in transmitted wavefield amplitude, where red colors indicate increased amplitude and blue colors correspond to reduced relative amplitude (from scattering). It is important to note that in our model we treat our transmitter and receiver as a collection of point sources and consequently the Fresnel zone is a superposition of their respective wavefields. The relative transmitted wave amplitude SK along the fracture profile is shown in Figure 2c, where the width of the half-power bandwidth of the first Fresnel zone (blue) is delineated by dashed gray lines. For a given transducer pair, we consider this region within the Fresnel zone to substantially contribute to the recorded changes in transmission characteristics along the transmitter-receiver travel path.
Figure 2: (a) Diagram of L-shaped configuration with region of interest outlined in red. (b) Amplitude sensitivity kernel (SK) model across granite block, where intensity represents response of transmitted wave to perturbation. (c) Profile of SK along the fracture plane (denoted by dashed black line in panel (b)). Dashed gray vertical lines indicate the half-power bandwidth of the Fresnel zone, where the transmitted waves are most sensitive to perturbations along the travel path (left to right).
## 4 Fracture Contact Characterization
After conducting the dynamic stressing experiment described above, we conducted additional multi-step experiments to characterize the real area of contact for the tensile fracture specimen under load. This was accomplished by designing a system to insert Fuji Prescale(r) Medium Film (9.7-49 MPa) between the two halves of the fracture and loading the specimen to a range of stresses. The pressure sensitive film is a \(\sim\)100 \(\mu\)m thick plastic film containing capsules that rupture and react with an agent to produce the a color that is proportional to force (Figure 3b) when a sufficient force is applied, \(>\)9.7 MPa. The spatial resolution is 5 \(\mu\)m, which corresponds to approximately \(\pm\)1.5 Pa stress resolution ([PERSON] & [PERSON], 2015). For our measurements, mating the fracture exactly the same way, in the same location repeatable is imperative so that the same asperity contacts form each time, maintaining the same location of voids. To achieve this, we installed locating pins in each fracture to ensure that they mated the same way each time and we used them with the pressure sensitive film. The pins were installed by drilling 1.588 mm diameter holes through the shorter sample half and blind holes in the taller half, such that the locating pins could be inserted to ensure alignment (Figure 3a). A blank pressure sensitive film was cut to size and then inserted between the two fracture halves before loading to the desired target stress. This procedure was repeated with a new pressure sensitive film for each stress ranging from 9 to 21 MPa in increments of 1 MPa. Figure 3b shows representative data from pressure sensitive film loaded to 20 MPa; magenta color corresponds to regions of the fracture interface in contact and the remaining areas are void space. We digitized the pressure sensitive film using a Epson Perfection 3200 Photo color scanner at 3200 dpi resolution. Digitized scans were aligned using cross-correlation (with the lowest stress, 9 MPa, as the reference) and then binarized using an algorithm that generates a threshold value based on mean pixel intensity. Figure 3c shows an overlay of the fracture contacts (shades of blue) for 10, 15, and 20 MPa (data from experiment p5596).
Figure 3: (a) Sketch of fracture and locating pins to insert pressure sensitive film. (b) Example of pressure sensitive film after loading to 20 MPa. Magenta regions represent contact and remaining areas are voids. (c) Superimposed images showing the evolution of contact area with applied stress at 10, 15, and 20 MPa. (d) Colored circles represent fracture regions probed by the array of transmitter-receiver pairs, where the footprint size is calculated from the Fresnel zone. (e) Real contact area from film measurements (as in panel (b)) relative to nominal total area as a function of applied stress. The dashed lines show cubic and linear fits to these data, suggesting a Hertzian-contact relation between area and stress.
## 5 Results
Our data include measurements of fracture permeability, p-wave velocity and fracture contact area. The transducer array and pressure sensitive film provide information on the spatial variability of fracture properties and its evolution during dynamic stressing. We integrate that data with fluid flow measurements to develop a detailed understanding of fracture properties.
### Static Hydraulic and Elastic Responses
We quantify the overall linear elastic and hydraulic changes in responses to static loads. In Figure 4a, compaction, \(\delta\), is measured during the beginning of each effective stress level for both the loading and unloading phases of the experiment. We observe fracture closure (positive) from 10 to 15 MPa, and then this trend changes, most likely in response to unloading the sample and holding at \(\sim\)2 MPa for several hours and then subsequent reloading of the specimen to 17 MPa. Despite this long hold time, there is a small effect on the stress-displacement relationship. During the unloading portion, the fracture aperture opens nearly linearly with decreasing stress. Overall, there is minor hysteresis at 10 MPa and minimal on-fault compaction. This is supported by our observations in Figure S2 in Supporting Information S1, which shows the effective stress as a function of on-fault displacement for experiment p5483. This, along with the stress-displacement curves in Figure S2 in Supporting Information S1, demonstrates that our observations are repeatable and that fracture misalignment is minimal and not dominating the overall elastic deformation. Figure 4b shows the evolution of static permeability, \(k\), with increasing and decreasing effective stress. Static permeability decreases non-monotonically with increasing stress and is nearly invariant with decreasing effective stress. Interestingly, there is more hysteresis present compared to on-fault displacement, but the ending permeability measurement is within 30% of the minimum starting value.
### Connecting Sensor Footprint and Contact Area
A crucial component to this study is connecting fracture contacts to the active-source monitoring data. We estimate the real fracture contact area probed by each transmitter-receiver pair by superimposing the calculated PZT footprints (Section 3.1) onto the digitized and binarized pressure sensitive films. Figure 3d shows an example of fracture contacts (black indicates regions of contact and white indicates void) with locations and sizes of sensor footprints highlighted. This demonstrates the highly variable spatial distribution of contacts across the fracture. Additionally, the estimated total area of contact as a function of applied stress is shown in Figure 3e. We show a linear fit and a cubic fit (dashed red line) to these data (Figure 3). Each of them fits equally well, suggesting a Hertzian-contact relation between real contact area (from pressure sensitive films) and nominal applied stress ([PERSON], 1881). Furthermore, we quantify the change in real contact area within PZT footprints with stress, see Figure 5, with respective dashed lines are cubic fits. As expected, the contact area within each PZT footprint generally increases with stress with a few exceptions, possibly due to the inevitable variations in mating of the two fracture surfaces at each stress level. A comparison between the regions probed by sensors highlighted with dark green (top right) and light orange (bottom left) illustrate the disparity of contact area. The relation between these results and nonlinear elastodynamic measurements are detailed in the Discussion section. The measured contact
Figure 4: (a) Compaction, \(\delta\), at each effective stress level during the loading and unloading phase. (b) Static permeability, \(k\), as a function of effective stress.
area (Figures 3d and 5) is consistent with previous studies using similar contact registration methods ([PERSON] et al., 2009) and rough surfaces ([PERSON] & [PERSON], 1987) to quantify stress-contact area relationships, with approximately 10% area in contact at 10 MPa applied normal stress.
### Hydraulic and Nonlinear Elastodynamic Responses
Rocks exhibit nonlinear elastic behavior due to the nonlinear response of their constituent minerals and structures, namely, microcracks and compliant grain boundaries ([PERSON] & [PERSON], 2009; [PERSON] et al., 2015). When rocks are fractured, as in nature, this nonlinearity is compounded by contact acoustic nonlinearity (CAN) at fractured interfaces. Figure 6 shows characteristic responses to dynamic pore fluid pressurization upstream (blue) where transient softening and modulation of baseline velocity ([PERSON] et al., 2013) are manifest with slow recoveries to the pre-oscillation condition. In comparison, a linear elastic response would be effectively stress invariant, not showing any of the aforementioned characteristics. Thus, nonlinear elasticity reveals much about the rock micro-structure, fractures, and inter-grain contacts ([PERSON], 2009), all of which also modulate the hydraulic properties. Both fluid and acoustic transmission characteristics are highly sensitive to pore/ fracture apertures and contact condition. Thus, we seek to link the effect of
Figure 5: Percent area of fracture in contact within each piezoelectric transducer ”footprint area” as a function of applied stress for one experiment. Contact area is directly estimated by pressure sensitive films at each stress. Note spatial variations in contact, as expected for a rough fracture, and also non-linear changes with stress. Each measurement involves re-mating the fracture and thus some variability is expected.
Figure 6: Excerpt of data from experiment p5483 illustrating the effect of (a) pore pressure oscillation (1 MPa amplitude at 1 Hz) on (b) ultrasonic p-wave velocity and (c) permeability at applied normal stress of 20 MPa. A 1 s window preceding the oscillation is used to calculate the pre-oscillation values of velocity (\(c_{0}\)), highlighted in gray. Changes in permeability are calculated from pre-oscillation, \(k_{\varphi}\) and post-oscillation magnitudes, \(k_{1}\), averaged in 5 s windows, respectively. Long-term post-oscillation evolution in wave velocity and permeability (\(c\), \(k\), respectively) are illustrated with arrows. The first 10 s of post-oscillation recovery for p-wave velocity and permeability are shown in panels (d) and (e), respectively.
stress state and resulting fracture aperture and contact to the elastodynamic and hydraulic properties of dynamically stressed fractured rock. The nonlinear elastic response to dynamic stressing is characterized by the following: (a) relative change in wave velocity, \(R_{0}=\Delta c/c_{\mathrm{op}}\) (b) the wave velocity amplitude modulation \(R_{1}\), and (c) the evolution of slow dynamics or post-oscillation recovery of wave velocity \(c_{r}\). Both \(R_{0}\) and \(R_{1}\) are extracted using a projection procedure following ([PERSON] et al., 2013). The long-term recovery, or slow dynamics, is observed to be logarithmic in time ([PERSON], [PERSON], [PERSON], & [PERSON], 2017; [PERSON], [PERSON], [PERSON], et al., 2017; [PERSON] & [PERSON], 1996) and is recorded in a 90 s window following each oscillation, although the time to full recovery may be much longer ([PERSON], [PERSON], [PERSON], & [PERSON], 2017). Besides the nonlinear elastodynamic measures described above, the relative stress-induced change in permeability \(\Delta k/k_{0}\) and log-time recovery \(k_{r}\) are quantified, as noted in the permeability subplot of Figure 6.
### Dynamic Stress-Induced Changes in Permeability
The relation between relative change in permeability (\(\Delta k/k_{0}\)) and pore pressure (\(P_{\mathrm{pk}}\)) oscillation amplitude for each effective normal stress (\(\sigma_{\mathrm{eff}}\)) ranging from 10 to 20 MPa in 2.5 MPa increments is shown in Figure 7a. All oscillations were applied with the same frequency of 1 Hz to allow direct comparison. As expected ([PERSON] et al., 2020; [PERSON] et al., 2021), we observe increasing permeability enhancement with increasing amplitude of the applied pore pressure oscillation, though, in some cases this reaches a plateau. Additionally, the scaling between \(\Delta k/k_{0}\) and oscillation amplitude (least-squares fit) varies with the stress state of the fracture, generally decreasing with increasing stress and assumed greater fracture closure, Figure 7b. This relationship is nearly monotonically decreasing with applied stress except for the increase in \(\varphi\) from 15 to 17.5 MPa. Though the overall permeability (Figure 4b) is not sensitive to the long hold after 15 MPa, perhaps the relative change in permeability is very sensitive to minute changes in fracture mating or indentation creep ([PERSON], 1994).
The dynamic permeability, \(\hat{k}\), calculated using Equations 2 and 3, is a measure of permeability during oscillations. As with permeability, \(k\), we observe that \(\hat{k}\) monotonically increases with pore pressure amplitude, Figure 8a. Whereas, \(k\) is a measure of a transient response, \(\hat{k}\) corresponds to the actuation of the fracture aperture, flow pathways, during oscillations. Furthermore, the nominal values of \(\hat{k}\) at the lowest oscillation amplitude, 0.2 MPa, are consistent with the nominal static permeabilities, see Figure 4b. Also, the slope of dynamic permeability with respect to oscillation amplitude, indicated with dashed blue lines in Figure 8a decreases with applied stress and
Figure 7: (a) Relative permeability change (\(\Delta k/k_{0}\)) as a function of pressure oscillation amplitude for each applied normal stress. For all applied normal stresses, permeability changes increase with increasing pressure oscillation amplitude. Error bars are one standard deviation from mean for oscillations with repetitions. (b) The ratio of change in relative permeability with pore pressure amplitude, \(\varphi\), generally decreases with applied stress, except from 15 to 17.5 MPa.
remains nearly invariant during the unloading phase. This slope, \(\phi\) is summarized in Figure 8b and is consistent with our measurements of static permeability throughout the experiment, 4b.
### Dynamic Stress-Induced Changes in P-Wave Velocity
One of the measures of elastic nonlinearity, the relative change in velocity (\(R_{\text{0}}\)) for all transmitter-receiver pairs as a function of pore pressure oscillation amplitudes are shown in Figure 9a. As noted previously ([PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2021), the magnitude of \(R_{\text{0}}\) clearly increases with increasing
Figure 8: (a) Dynamic permeability, \(\hat{k}\), as a function of pore pressure oscillation amplitude for each effective stress level, circles indicate loading phase and squares indicate unloading phase. (b) Slope of dynamic permeability, \(\phi\), for the loading and unloading phases.
Figure 9: (a) Relative velocity change (\(R_{\text{0}}\)) averaged over repetitions at each oscillation amplitude as a function of amplitude. Symbol colors correspond to the highlighted transducer footprint locations (see legend). (b) Slope of \(R_{\text{0}}\), \(\alpha\), versus oscillation amplitude for each normal stress, a measure of hysteretic nonlinearity. \(\alpha\) decreases, then increases for most transmitter-receiver pairs. This represents a presumed fracture closure and increase in specific stiffness.
pressure oscillation amplitude. Furthermore, after an initial increase, increasing effective stress generally reduces the magnitude of \(R_{\rm{up}}\) as seen in Figure 9b in agreement with previous observations ([PERSON] et al., 2021; [PERSON] et al., 2016). The data in Figure 9 are colored by location of the PZTs along the fracture plane (see scaled version in figure legend) to reveal the spatial variability of the measured nonlinearity. One observations across all stress levels is that the nonlinearity (larger magnitude \(R_{0}\)) measures the highest for the transducer pair at the bottom left corner (light pink color). In contrast, the nonlinearity measured by the transducer pair at the top right corner (dark green color) is among the lowest at all stress levels.
Another measure of elastodynamic nonlinearity that we investigate is the relative change in the average amplitude of the wave velocity change, \(R_{1}\). Figure 10a shows \(R_{1}\) as a function of pore pressure oscillation amplitude for all transmitter-receiver pairs. Like \(R_{0}\), the average amplitude wave velocity \(R_{1}\) scales linearly with increasing pore pressure oscillation amplitude, as expected ([PERSON] et al., 2013, 2015). As the fracture is closing with the increased applied stress, the slope of \(R_{1}\) with respect to the oscillation amplitude denoted as \(\beta\) increases at 12.5 MPa, decreases, and then slightly increases again at 17.5 MPa, see Figure 10b. The trend is slightly different for different transducer pairs. Overall, the magnitude of the nonlinear elastic parameters are consistent with previous studies on fracture rock specimens, for the respective stress levels ([PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2021).
### Measurements During Loading Versus Unloading Phase
A key part of this study is understanding the effect of fracture aperture, degree to which the fracture is closed or open under different applied stresses, on the stiffness and hydraulic properties of the fracture interface. Besides measurements at increasing effective stress levels (loading), we performed a subset of the pore pressure oscillation protocol while unloading the sample. During the unloading phase, the confining stress was decreased incrementally to the stresses previously used during the loading phase (17.5, 15, 12.5, 10) MPa. Figure 11 shows summarized results of the \(\Delta k/k_{0}\) slope, \(\varphi\), as a function of applied stress for both the loading (circle markers) and unloading (square markers) phases of experiment p5483. There is some hysteresis comparing the loading phase to the unloading phases with nearly an order of magnitude difference between \(\varphi\) at the beginning and end of the loading cycle. During the loading phase, there is a large increase in \(\varphi\) from 15 to 17.5 MPa, which we attribute to the long hold after 15 MPa. We posit that the \(\Delta k/k_{0}\) measurement is sensitive to on-fault properties such as surface mating, creep, or fine wear products (breakage of asperities). However, during the unloading phase, \(\varphi\) generally increases with decreasing applied stress, but does not return to the initial value at 10 MPa. This hydraulic
Figure 10: Relative change in the average amplitude of the wave velocity change (\(R_{1}\)) as a function of pressure oscillation amplitude. Symbol colors correspond to various raypath locations across the fracture. (b) Slope of \(R_{1}\), \(\beta\), versus pressure oscillation amplitude for increasing applied normal stress.
measurement could be, to some extent, influenced by deformation that occurs at 20 MPa, marginally changing preferential fluid pathways.
This hysteresis is also observed in the measures of nonlinearity, \(R_{0}\) and \(R_{1}\) albeit less pronounced. Figure 12 shows \(\alpha\) measured for each transmitter-receiver pair as a function of applied stress for the loading and unloading phases of experiment p5483. During the loading phase, there is a characteristic decrease at \(\epsilon_{\mathrm{eff}}\) = 12.5 MPa (higher nonlinearity) and then an increase at \(\sigma_{\mathrm{eff}}\) = 20 MPa (lower nonlinearity) for most of the transducer pairs. However, during the unloading phase, the change in \(\alpha\) is either nearly invariant with applied stress (light blue, dark red) or linearly increases in magnitude. A common observation across all transducer pairs is the slightly higher measured nonlinearity during unloading than that during the loading phase at a given stress. Possibly, the asperities break and deform when loading leading to a larger instantaneous stress-induced stiffness change \(R_{0}\) during unloading and therefore, larger \(\alpha\) magnitudes.
Similarly, Figure 13 shows \(\beta\) as a function of applied stress for each transmitter-receiver pair during the loading and unloading phases of the
Figure 11: Slope of \(\Delta k/k_{0}\), \(\varphi\), as a function of applied stress for loading and unloading phases of the experiment.
Figure 12: \(\alpha\) versus applied stress for loading and unloading phases of the experiment. A lower value of \(\alpha\) corresponds to a larger nonlinearity. We see an overall decrease in nonlinearity with applied stress (\(\alpha\) tends toward zero) for some of the pairs (e.g., dark green), while no clear trend can be seen for other pairs (i.e., light blue).
experiment. The measured \(\beta\) and hysteresis vary significantly for different transducers. The pairs in the two upper rows with \(\beta\) close to zero show nearly stress-invariant wave velocity amplitude modulation, whereas others in the bottom row show greater nonlinearity and hysteresis loops. As previously noted, the measured \(\beta\) during the loading phase is mostly insensitive to the effective stress level except for a local increase at 12.5 and a slight increase at 17.5 MPa for some transducer pairs. During the unloading phase, \(\beta\) generally increases returning to the initial value measured at 10 MPa. The observed hysteresis loops appear larger for transducer pairs with a larger measured \(\beta\). Unlike what is observed for \(\alpha\), \(\beta\) measures consistently lower during unloading than loading. Previous studies relate \(\beta\) to opening and closing of fractures ([PERSON] et al., 2015). We hypothesize that the broken and deformed fracture asperities during loading facilitate the mating of the two fracture surfaces, making it harder for the fracture to close, thus smaller \(\beta\). We note that for both \(\alpha\) and \(\beta\), the nonlinearity measured during unloading increases with decreasing stress, which is expected due to fracture opening. Though, we did not quantify the damage and did not observe noticeable damage while conducting the experiment or pressure sensitive film testing. Upon visual inspection gouge material (from broken asperity tips) was not present in the down-stream reservoir, indicating that the concentration is low and particle size is <\(\mu\)m.
### Permeability Recovery and Slow Dynamics
The post-oscillation evolution of permeability and p-wave velocity is related to how the fracture contact asperities have been transiently or irreversibly changed during the imposed oscillations. Also, the time-dependent
Figure 13: Nonlinearity parameter \(\beta\) versus applied stress for loading and unloading phases of the experiment, shows the hysteresis in changes in fracture stiffness.
phenomenon provides an indication of the rate of healing ([PERSON], 1994) and recovery at the perturbed interface. Here, this is measured as the slope of the recovery in logarithmic time. Our observations indicate that log-time permeability recovery \(k_{r}\) is mostly invariant to the amplitude of pore pressure oscillations at higher normal stresses (>12.5 MPa), Figure 14a. At lower normal stresses, the log-time evolution recovers more quickly at lower pore pressure oscillation amplitudes. These overall trends are summarized in Figure 14b with the slope of \(k_{r}\) as a function of applied stress, which also includes results from the unloading phase of the experiment.
The p-wave velocity recovery \(c_{r}\) for all transmitter-receiver pairs as a function of pore pressure oscillation amplitude is shown in Figure 15a. The measured recovery rate slightly increases with increasing pressure oscillation amplitude that is, the wave velocity returns to the pre-oscillation value quicker after larger amplitude oscillations. The slopes change slightly and unsystematically with fracture closure, Figure 15b, but during the unloading phase, there is much less spread between the transmitter-receiver pairs and more systematic evolution with applied stress (fracture opening). In Figures 14b, 15b, and 15c, both \(k_{r}\) and \(c_{r}\) slopes show a hysteretic relationship with fracture closing and opening (increasing and decreasing applied stress).
## 6 Discussion
### Elastic Deformation of Fracture and Bulk
We observe that the hydraulic and elastodynamic measurements scale with applied stress. On-fault compaction (Figure 4a) shows minimal hysteresis in loading and unloading the fractured rock specimen. This, along with the stress-displacement curves in Figure S3 in Supporting Information S1, demonstrates that our observations are repeatable and the fracture is well-mated. A common observation in experimental studies is that fracture specimens must be \"pre-conditioned\" with an initial load/unload cycle with the purpose of optimally mating the two fracture faces ([PERSON] et al., 1983; [PERSON], 2017). Importantly, these studies find that subsequent loading cycles produce reversible (as a function of stress) elastic or hydraulic properties. Our results depart from these observations as seen in Figure 4a and Figure S3 in Supporting Information S1, which show that despite reducing the stress after the 15 MPa stress level and holding at 2 MPa for several hours before increasing the stress to 17 MPa, that the overall elastic deformation is not dominated by severe misalignment. An additional observation is a minor degree of compaction unloading the sample from 20 to 17.5 MPa. We surmise that the sudden increase in pore pressure after the last pore pressure oscillation sequence (before the normal stress reduction) may have an influence on compaction of the fracture sample. This effect is minor in that it is a couple microns and it
Figure 14: (a) Log-time recovery of permeability after pressure oscillations for each normal stress. The recovery rate is oscillation amplitude-dependent at lower stresses (<15 MPa), but not at higher normal stresses (>12.5 MPa) and with relatively little change up to the largest normal stress (20 MPa). (b) Slopes of \(k_{r}\) as a function of applied stress for the loading and unloading phases of the experiment.
does not have a noticeable effect on permeability or the dynamic measurements (Figures 12-15). Furthermore, the hydraulic measurements of this study (static and dynamic permeabilities) do no exhibit a significant (order of magnitude) difference in loading and unloading phases of the experiment, like in [PERSON] and [PERSON] (2017). We interpret the reduction in permeability (static and dynamic) during the loading phase as being dominated by fine-scale asperity deformation, likely plastic ([PERSON] et al., 1951).
As previously stated in Section 5.3, the nonlinearity in the elastic response of rocks arises from the compliant features in their matrix structure (microcracks and grain boundaries) ([PERSON] and [PERSON], 2009; [PERSON] et al., 2015). Fracture interfaces introduce additional nonlinearity (CAN). However, as shown in our previous work, the influence of a fracture on the overall elastodynamic behavior of fractured rock depends on the applied stress as well as the number and size of asperities in contact. In [PERSON] et al. (2022), a similar set of experiments were conducted, in which the nonlinear response of intact Westerly granite was compared to that of fractured (fluid-filled and dry) specimens at 10, 15, and 20 MPa normal stresses. At all stresses and excitation frequencies (0.1, 1, and 10 Hz) considered, the nonlinearity in the elastodynamic response (measured in terms of relative wave speed change) of the dry intact specimen was larger than that measured in the tensile-fractured specimen. To explain this counter-intuitive observation, a 2D finite element analysis on simplified models of intact and fractured rock with different roughness under static stress was conducted. The numerical modeling and simulation results illustrated that the fracture significantly modifies the strain distribution in the bulk of the stressed rock in our test configuration as later reported by [PERSON] et al. (2021) as well. It appeared that intact samples could experience larger strain in their bulk compared to fractured samples, where strain is largely concentrated on the asperities in contact at the fracture interface. As a result, a larger change in wave speed may be measured in bulk, where a larger area is strained above \(10^{-6}\), the widely accepted threshold for activating elastic nonlinearity. Interestingly, the relative change in wave amplitude measured larger for dry fractured sample under 10 and 15 MPa at low frequencies, contrary to what was consistently observed for the wave speed change. Although not discussed in [PERSON] et al. (2022), this apparent contradiction is in agreement with [PERSON] et al. (2021) and [PERSON] et al. (2021)'s conclusions that wave amplitude is more affected by on-fault properties while wave speed reflects the strain distribution in the bulk. At 20 MPa, both relative wave speed and wave amplitude are smaller for fractured sample indicating that the strain in the bulk under this larger stress dominates the strain of the in-contact asperities, possibly because of their larger contact areas. In sum, there is no simple way to disentangle nonlinearity of the bulk from the fracture interface in our experimental observations. The partitioning is controlled by the strain distribution in the bulk versus the strain concentrated at the fracture
Figure 15: (a) Log-time recovery rate for all transmitter-receiver pairs. Positive values indicate a transient change to the fracture asperities and negative values indicate irreversible changes to fracture contacts. (b) The slope of \(c_{s}\) as a function of applied stress does not seem to systematically evolve with increasing \(\sigma_{\text{eff}}\) (c) Slopes of \(c_{s}\) as a function of applied stress during the unloading phase of the experiment.
interface (asperities) which depend on the amount of stress applied, the overall contact area and the size of individual asperities in contact.
### Linking Stress-Induced Elastodynamic and Hydraulic Changes
To investigate the coupling between fluid flow changes and elastodynamic nonlinearity, we analyze how the observed stress-induced changes in p-wave velocity is connected to changes in permeability at different normal stress levels. Figure 16a relates stress-induced changes in p-wave velocity to changes in permeability (\(\Delta k/k_{0}\)) for each effective applied stress. In this figure, \(\overline{R_{0}}\) denotes \(R_{0}\) averaged over all transmitter-receiver pairs. Both of these parameters measure average changes along the fracture in response to stress perturbations. We observe a linear correlation between \(\overline{R_{0}}\) and \(\Delta k/k_{0}\), which appears to be mostly independent of the stress level. In addition to the transient changes, we relate the stress-induced changes in p-wave velocity and dynamic permeability during the oscillations. Figure 16b shows the nonlinear elastic parameter \(R_{1}\) averaged over all transmitter-receiver pairs as a function of \(\bar{k}\). Again, we observe a monotonic relationship between the magnitude of nonlinearity, \(\overline{R_{1}}\), and dynamic permeability, \(\bar{k}\). Furthermore, in both plots in Figure 16 show that increasing applied stress reduces both the elastodynamic response (\(\overline{R_{0}}\) and \(\overline{R_{1}}\)) and permeability enhancement (\(\Delta k/k_{0}\) and \(\bar{k}\)), consistent with the idea that these are measures of the degree to which the fracture aperture is modulated.
### Relating Contact Area to Elastodynamic Properties
True fracture contact area constrain many of the elastodynamic and hydraulic observations. Figures 3c-3e show that the estimated true contact area using pressure sensitive film increases as a function of applied stress in a Hertzian-contact-like manner (cubic relationship), effectively reducing aperture and enlarging individual contact areas. Defining Fresnel rayptunnels between transmitters and receivers (PZT footprints) projected on the pressure sensitive film images allows us to investigate the true contact area and its evolution for individual transducer pairs. The estimation of fracture contact area is limited by two main factors: (a) spatial/stress resolution of the pressure sensitive film and (b) physical characteristics of the pressure sensitive film (i.e., film thickness and stiffness), which determine how the plastic film deforms between the fracture halves and registers local stresses. We observe that nearly all asperities register the maximum stress >49 MPa, therefore limiting analysis to a binary contact/void image. The ideal application of such pressure sensitive films is between two nominally planar surfaces, however, despite some deformation or crinkling of the films, we emphasize its utility in reliably
Figure 16: (a) Relation between relative changes in velocity, \(R_{0}\) and permeability, \(\Delta k/k_{0}\) for each normal stress level. (b) Relation between relative changes in velocity, \(R_{1}\) and dynamic permeability, \(\bar{k}\), for each normal stress level. Circle markers correspond to loading phase and square markers correspond to the unloading phase of the experiment.
-pressure sensitive films, we are not able to register the real area of contact while unloading. Compared to roughened planar surfaces, it is more challenging to measure the real area of contact for tensile fractures with long wavelength roughness.
Next, we investigate the relationship between the nonlinear parameters and estimated contact area. Since stiffness is defined as \(\kappa=\frac{F}{\beta_{0}}\), where \(\delta\) is displacement, assuming a nominal unit area and considering the dependence of the contact force \(F\) on the number and radii of asperities in contact ([PERSON] et al., 2020), we may take contact area \(S_{0}\) to be a proxy for the interface stiffness at rest \(\kappa_{0}\). It is important to make the distinction that this is not the only source of nonlinearity ([PERSON] and [PERSON], 2009; [PERSON] and [PERSON], 2005). Previous studies ([PERSON] et al., 2020; [PERSON] et al., 2022) show that intact specimens exhibit a greater degree of nonlinear elastic response to dynamic stress compared to fractured specimens. Nonetheless, a fracture with a larger true contact area is expected to be stiffer and therefore is more difficult to induce changes. Since the nonlinearity parameter \(R_{1}\) is believed to be related to the opening/closing of the fracture, it is considered to be a measure of \(\Delta\kappa/\kappa_{0}\). Therefore, an important question to ask is whether our data show a correlation between \(R_{1}\) and \(S_{0}\). That is to say, what is the correlation between elastodynamic changes and initial contact area. To our knowledge, this is the first experimental investigation of the relation between contact area and elastic nonlinearity of a fracture. The expectation is that regions of the fracture with a larger true contact area, \(S_{0}\), should be stiffer and therefore, more difficult to open and close (at a given dynamic stress level). This reasoning is supported by our observations shown in Figure 17, which shows \(S_{0}\) as a function of \(\beta\) during the loading phase of the experiment. This illustrates that regions with a smaller contact area (pale orange) for a given stress level exhibit larger nonlinearity compared to those with larger contact area (dark green). Results for contact area as a function of \(\beta_{unload}\) are plotted in Figure S4 in Supporting Information S1. Despite the caveats to this technique (see Section 5.2 for details), we emphasize the utility in estimating the distribution of contacting asperities to interpret, with greater certainty, the causes of spatial variability in ultrasonic measures of fracture properties. Furthermore, Figure 17 suggests that over the range of normal stresses explored in our experiments, fracture topology (contact area and roughness) is the primary control on fracture stiffness and also fluid flow ([PERSON], 2019).
### Broader Impacts and Insights
Dynamic stressing of pore pressure at a range of amplitudes in our experiment allows simulates dynamic stressing in field conditions and the observed hydraulic and elastic responses. Furthermore, repeating this pore pressure oscillation protocol at different applied stresses simulate conditions at different (shallow) depths in the crust. Figure 6 demonstrates many qualitative similarities between experiment and field observations. The transient decrease in cross-fault wave velocity is reminiscent of field observations of co-seismic elastic softening ([PERSON] et al., 2008, 2008, 2014; [PERSON] et al., 2010; [PERSON] et al., 2013; [PERSON] et al., 2012; [PERSON] et al., 2022; [PERSON] et al., 1998, 2006; [PERSON] et al., 2008; [PERSON] et al., 2009; [PERSON] et al., 2016). Figure 6 also shows through-fault permeability enhancement, much like what is observed in the subsurface ([PERSON] and [PERSON], 2013; [PERSON] et al., 2012). Importantly, the fractured specimen in our experiment did not contain real or simulated gouge material, further demonstrating that many of the complex field conditions can be approximated with a \"bare\"
Figure 17: Regions with larger contact area (\(S_{0}\)) exhibit smaller measure of nonlinearity, \(\beta\), and regions with small \(S_{0}\) exhibit larger nonlinearity during the loading phase of the experiment.
-fracture under similar stress conditions and evolution of fracture geometry (roughness, contact area) may be a prevailing factor.
Another quality produced in our experimental configuration is the log-time recovery of velocity and permeability (slow dynamics) toward their respective pre-oscillation values. The magnitude of velocity recovery is comparable to previous observations of rough fractures ([PERSON] et al., 2022; [PERSON] et al., 2021), similar to post-seismic recovery of rock stiffness ([PERSON] et al., 2008; [PERSON] et al., 2021). However, permeability recovers much quicker than previous observations where gauge/wear material is present at rough fracture interface ([PERSON] et al., 2011; [PERSON] et al., 2021). A pressure-solution mechanism ([PERSON] et al., 2020) is assumed to not play a role in contact area changes in our experiment due to insufficient conditions--low temperature and stress and non-reactive pore fluid (deionized water). This highlights the degree to which chemo-mechanical ([PERSON] and [PERSON], 2008; [PERSON] et al., 2004) and gauge transport (clogging/unclogging) ([PERSON] et al., 2014, 2015; [PERSON] et al., 2011) dominate field observations of permeability enhancement induced by seismicity ([PERSON] and [PERSON], 2013; [PERSON] et al., 2012).
## 7 Conclusion
We present tightly constrained experiments to investigate the role of aperture and real contact area on hydraulic and elastodynamic properties of dynamically stressed fractured rock. Conditions are representative of fractures at various depths and therefore stresses. Simultaneous measurements of fluid flow and active-source ultrasonic transmission show how these mechanisms are coupled--potentially linking permeabilities with elastodynamic characteristics. Additionally, we quantify the heterogeneity of the fracture contacts at discrete stresses in order to better interpret our observations from multiple transducer pairs probing different parts of the fracture.
Fractured Westerly granite exhibits characteristic mesoscopic elastic nonlinearity when subjected to pore pressure oscillations, revealing rich information about the contact mechanics of the asperities. Our observations, as found in [PERSON] et al. (2020) and [PERSON] et al. (2021), show a nearly monotonic relationship between increased permeability enhancement and increased pressure oscillation amplitude. We add to the work of [PERSON] et al. (2021); [PERSON] et al. (2020); and [PERSON] et al. (2021) by documenting a reduction in pore pressure oscillation-induced permeability enhancement with increasing normal stress on the fracture and related fracture closure. Similar trends are observed for the nonlinearity parameters \(\alpha\) and \(\beta\). For some transmitter-receiver pairs, the nonlinearity parameters depend on the degree of fracture openness (in the corresponding region of the fracture) immediately before oscillation. There is a noticeable increase in nonlinearity, \(\alpha\) and \(\beta\), from 10 to 12.5 MPa, for example, (see Figures 8(b) and 9(b)). That is to say, the dominating factor is not necessarily the stress state, but the local fracture aperture.
We investigate the spatial heterogeneity of nonlinearity parameters with regard to actual estimations of fracture contacts and voids. To that end, pressure sensitive film images are related to ultrasonic measurements; a smaller initial contact area (\(S_{0}\)) is associated with higher nonlinearity \(\beta\) and a larger \(S_{0}\) with a smaller \(\beta\). Importantly, the estimate of fracture contact area over the range of normal stresses explored in our experiments demonstrates that fracture topology is a primary control on the observed elastodynamic and hydraulic responses.
Finally, we document the rate of recovery from post-oscillation state of permeability and wave velocity. The rate of permeability recovery (log-time) increases above \(\sim\)0.4-0.6 MPa amplitude oscillations at lower stresses (\(\sigma_{\text{eff}}<17.5\) MPa) and is oscillation amplitude-invariant at higher stresses (\(\sigma_{\text{eff}}>15\) MPa) (see Figure 14). These recovery rates are orders of magnitude smaller than those reported in previous studies ([PERSON] et al., 2020; [PERSON] et al., 2021), where gauge present at the fracture interface dominated permeability changes. During the unloading phase, the rate of recovery increases with decreasing stress state. These recovery rates are also smaller than in previous studies ([PERSON] et al., 2020; [PERSON] et al., 2021), suggesting \"accumulated deformation\" throughout the loading phase of the experiment.
## Data Availability Statement
Hydraulic, mechanical, and ultrasonic (time delay) data for this research are available at ([PERSON] et al., 2024).
## Appendix A Journal of Geophysical Research: Solid Earth
### Acknowledgments
Technical assistance from [PERSON] is gratefully acknowledged. This work was fully supported by a grant from DOE Office of Basic Energy Science (DG-SC01758) to PS. CM acknowledges support from the European Research Council Advance Grant R335012 (CTCTN075) and US Department of Energy Grants DE-SC02002512 and DE-SC020042-8 EB008763.
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wiley/fe0a3786_06de_4e6f_bd42_66faf3211592.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly.
energy, provides a widely-used framework for understanding these flows of energy, which we summarize as follows. The radiative imbalance from equator to pole generates mean available potential energy, which is transformed into eddy available potential energy and eddy kinetic energy through baroclinic instability; the eddy kinetic energy then maintains the zonal-mean kinetic energy against dissipation by friction through barotropic processes. If the atmosphere were adiabatic and frictionless, the sum of available potential and kinetic energy would be conserved: energy would only be transformed from one type to the other. Diabatic processes (radiation, condensation of water vapor, or conduction from the surface) affect only the generation of available potential energy; and the kinetic energy is altered by diabatic heating indirectly, through its effect on available potential energy.
The purpose of this study is to clarify the effect of variations of atmospheric radiative heating on the extratropical circulation, using the framework put forward by [PERSON] (1955). We show, in an experiment where the radiative cooling profile is overwritten with the climatological mean from a control experiment, that synoptic-scale eddies are more vigorous when radiative feedbacks are suppressed. We find that radiative cooling near the surface and tropopause in low-pressure systems destroys eddy available potential energy by removing temperature anomalies. We propose this as a possible mechanism by which radiative heating weakens midlatitude cyclones.
## 2 Methods
The Geophysical Fluid Dynamics Laboratory High-Resolution Atmosphere Model (HiRAM; see [PERSON] et al., 2009) is used to determine the effect of atmospheric radiative heating on midlatitude cyclones. The model has \(\sim\)0.5\({}^{\circ}\) horizontal resolution and 32 vertical levels. The (relatively) high spatial resolution of HiRAM is advantageous because the storm tracks in climate models are better simulated at higher resolutions than coarser ones ([PERSON] et al., 2013). At the lower boundary the model is forced by monthly-mean observed sea surface temperatures and sea ice from the HadISST data set ([PERSON] et al., 2003) between 1986 and 2005. Land surface temperatures are interactive and respond to surface radiative fluxes.
The experiments used in this study were first described by [PERSON] et al. (2021). In the control simulation the radiative transfer calculation is interactive, and the radiative heating and cooling rates at each time-step respond to the instantaneous conditions in the column at that time (e.g., specific humidity and cloud cover). In a perturbation experiment, referred to as \"climatological radiation,\" the model is rerun, but at each time-step the total radiative heating or cooling rate (longwave plus shortwave) is overwritten with the monthly mean, calculated from the final 20 years of the control run, and interpolated to the current time-step. The virtue of this approach is that the time-mean radiative cooling rates are identical in the control and climatological radiation experiment. This stands in contrast to other experiments which make clouds transparent to radiation (set the cloud radiative heating rates to 0), and therefore introduce a disparity in the total heat input from radiation into the system. In the climatological radiation experiment, the radiative heating and cooling rates are prescribed from the control climatology at all but the top two model levels; radiation at upper levels is left interactive to ensure that surface fluxes exactly balance outgoing radiation, and there is no unusual surplus or deficit of energy in the atmosphere. A related experiment, in which the radiative cooling rates are prescribed only in the troposphere, is described in Section 3.3. We note that only the atmospheric radiative cooling rates are overwritten in these experiments and at the land surface the radiative fluxes are interactive.
For the analysis it is necessary to calculate mean and eddy quantities related to available potential and kinetic energy. As discussed by [PERSON] (1964), eddies can be defined from the space, time, or mixed space-time domains. Here we consider transient eddies, that is, departures from the time mean. Therefore the eddy kinetic energy is given by
\[K_{E}=\frac{1}{2g}\int\overline{[u^{2}+v^{2}]}dp,\]
where the overbar and bracket represent the time and zonal means, respectively, and the prime indicates the difference from the monthly mean ([PERSON] et al., 2022).
## 3 Results
### Eddy Kinetic Energy
The vertically-integrated zonal-mean eddy kinetic energy of the control and climatological radiation experiment is reported in Figure 1. When radiative interactions are suppressed, the eddy kinetic energy is enhanced in the midlatitudes. This is consistent with the findings of [PERSON] and [PERSON] (2018). In general, the zonal-mean vertical structure of eddy kinetic energy is characterized by two teardrop lobes of high eddy kinetic energy located at \(\sim\)40 N/S, with maxima near the tropopause. The change of eddy kinetic energy between the control and climatological radiation experiment is concentrated at upper levels in the troposphere (Figure S1 in Supporting Information S1), and in the midlatitudes can be thought of as intensifying the eddy kinetic energy where it is largest. We note there is some change of the eddy kinetic energy observable in the tropics, which may influence eddies in the midlatitudes. However, the mean tropical circulation and temperature profile are nearly constant between the control and climatological radiation experiment ([PERSON] et al., 2021).
### Generation of Eddy Available Potential Energy
If the atmosphere were adiabatic and frictionless, the sum of available potential and kinetic energy would be conserved, and the two forms of energy could only be converted from one to the other. It is through diabatic processes (radiative heating or cooling, latent heat release, sensible heat transfer) that available potential energy is generated; and the kinetic energy can only be altered by diabatic heating through its indirect effect on available potential energy. The generation of available potential energy can be partitioned into mean and eddy components. Because the time-mean radiative cooling profile is constant between the control and climatological radiation experiment, it is only the generation of eddy available potential energy that is directly altered in the climatological radiation run. All accompanying changes to the flows of energy in the atmosphere must be responses to this initial perturbation. An expression for the globally-averaged generation of eddy available potential energy is given by [PERSON] (1964):
\[G(P_{E})=\int\overline{\gamma\left[T^{\prime}Q^{\prime}\right]}dm,\]
Figure 1: The vertically-integrated zonal-mean eddy kinetic energy for the control (blue), where the radiative heating rate responds to instantaneous conditions of moisture and cloud cover, and the climatological radiation experiment (orange), where the radiative heating rate is fixed to the monthly mean.
where \(Q^{\prime}=c_{p}\hat{T}^{\prime}\) is the departure of the heating rate from the zonal mean, \(dm\) is an increment of mass, and \(\gamma\propto\left(\frac{Q}{T}\right)^{2}\) is a term arising from the derivation of available potential energy from the thermodynamic equation (see [PERSON], 1964). The interpretation of \(G(P_{E})\) is straightforward: when \(T^{\prime}\) and \(\hat{T}^{\prime}\) are of the same sign, then either there is heating where it is warm or cooling where it is cold, and eddy available potential energy (i.e., the variance of temperature within latitude circles) is generated. The reverse--heating where cold or cooling where warm--destroys eddy available potential energy.
To quantify the contribution of radiative heating to the generation of eddy available potential energy we use the model-calculated temperature tendency due to longwave and shortwave radiation (\(\hat{T}_{RAD}\)). Figure 2 shows the difference of the generation of eddy available potential energy due to radiation, \(G_{R}(P_{E})\), between the control and climatological radiation experiment. By design, the temperature and radiative heating anomalies are uncorrelated in the climatological radiation experiment, so \(\overline{T^{\prime}\times\hat{T}_{RAD}}\approx 0\) (see Figure S2 in Supporting Information S1). Consequently the change in the generation of eddy available potential energy in Figure 2 resembles the distribution of that quantity in the control. The vertical structure of \(G_{R}(P_{E})\) is worth calling attention to. In the midlatitudes \(G_{R}(P_{E})\) is positive at mid-levels but negative near the surface and tropopause. We also note that there are two regions of strongly negative \(G_{R}(P_{E})\) in the northern and southern polar stratosphere; we will return to this in Section 3.3.
Because the climatological radiation experiment does not directly alter the mean climate, we analyze temperature and radiative heating anomalies on the scale of the cyclone (e.g., [PERSON] et al., 2020) rather than in the zonal mean (e.g., [PERSON] and [PERSON], 2019; [PERSON] and [PERSON], 2008). To visualize these anomalies we generate composites of low-pressure systems in the midlatitudes. Low-pressure systems can be identified in a variety of ways ([PERSON] et al., 2020); in this study we elect for the simplest procedure possible and define a low as the local minimum of sea-level pressure in each 20\({}^{\circ}\)\(\times\) 20\({}^{\circ}\) box from 30 to 70 N/S. This provides a large sample of lows (\(\sim\)8-10 per day, in each hemisphere), and is sufficient to illustrate a \"typical\" low-pressure system. We note that there is approximately the same number of lows between the control and climatological radiation experiment (the difference is \(<\)0.5%).
Figure 2: The difference of the generation of eddy available potential energy due to radiation between the control and climatological radiation experiment. In the midlatitudes, radiative interactions generate eddy available potential energy at mid-levels but destroy it near the surface and tropopause.
Composites of low-pressure systems in the Northern Hemisphere are reported in Figure 3 on a 30\({}^{\circ}\)\(\times\) 30\({}^{\circ}\) domain (the corresponding plots in the Southern Hemisphere are given in Figure S3 in Supporting Information S1). The temperature anomalies (departures from the monthly mean) at (a) 925 hPa and (b) 200 hPa are provided for reference. These show the typical characteristics of midlatitude cyclones, including warm and cold sectors near the surface, separated by fronts, and westward tilt of the temperature anomaly with height. The radiative cooling anomalies are shown in panels c and d. Near the surface there is anomalous cooling in the warm sector and warming in the cold sector, due to the dependence of radiative emission on temperature (the Stefan-Boltzmann law), humidity, and cloud cover. At upper levels there is anomalous cooling, possibly associated with the tops of the atmosphere.
Figure 3: The temperature and radiative heating anomalies in the control, and the covariance between them, in composites of Northern Hemisphere low-pressure systems. The left column is at 925 hPa, the right column at 200 hPa. The covariance between temperature and radiative heating anomalies is negative throughout the domain, indicating that warm air is being cooled and cool air warmed in the control compared to the climatological radiation experiment.
deep clouds forming near the cyclone center. The difference of the covariance of the temperature and radiative heating anomalies, between the control and climatological radiation experiment, is shown in panels e and f. At both 925 hPa and 200 hPa the covariance is everywhere negative, meaning that warm air is cooled and cool air warmed in the control. Finally the domain-averaged \(T^{\prime}\times\dot{T}^{\prime}_{RAD}\) versus height is shown in Figure 4. In the control the covariance is positive at mid-levels but negative near the surface and tropopause. This supports the idea that radiative heating weakens midlatitude cyclones by destroying eddy available potential energy at upper and lower levels, as suggested by Figure 2.
It is not entirely clear, however, why the destruction of eddy available potential energy near the surface and tropopause seems to prevail over the generation of eddy available potential energy at mid-levels. The change of eddy kinetic energy is concentrated at upper levels in the troposphere, and it is tempting to say that the destruction of eddy available potential energy near the tropopause is responsible for it. However, the relationships between the available potential energy and kinetic energy are only defined for the global average, and not at each location. It is possible that the generation of available potential energy in one part of the atmosphere could alter the kinetic energy in another ([PERSON] et al., 2002). It is also possible that radiative heating could alter other diabatic heat sources, such as latent heat, and thereby indirectly alter midlatitude cyclones ([PERSON] et al., 2023). How the vertical structure of \(G_{\beta}(P_{E})\) affects large-scale eddies remains an open question. We note that a similar idea has been explored with regard to baroclincity: namely, whether large-scale eddies are more sensitive to changes of the upper- or lower-level horizontal temperature gradient ([PERSON] et al., 2019; [PERSON] & [PERSON], 2016). Finally, it is worthwhile to compare our results to those of previous studies which have examined the effect of cloud radiative heating on midlatitude cyclones. Using different methods, [PERSON] and [PERSON] (2018), [PERSON] et al. (2019) and [PERSON] et al. (2023) found conflicting responses of the eddy kinetic energy to suppressed cloud radiative interactions. [PERSON] et al. (2023) attempted to reconcile these results by showing the opposing influences of low and high clouds in cyclone intensification. They argued that the cooling of low cloud tops weakens cyclones, while the cooling of high cloud tops strengthens them, by modifying the static stability near the boundary layer and tropopause. Our results, by contrast, indicate that radiative cooling at upper levels in the warm sector (likely by high clouds) destroys eddy available potential energy, and that radiative cooling at mid-levels in the cold sector (possibly by low clouds) generates eddy available potential energy (see Figures S4 and S5 in Supporting Information S1). Future work in which we explicitly separate the cloud and clear-sky components of radiative heating may help to resolve this apparent contradiction and reconcile the energetic approach of this paper with the momentum approach favored in prior studies.
Figure 4.— The domain-averaged covariance of temperature and radiative heating anomalies for composites of low-pressure systems. In the control the covariance is positive at mid-levels but negative near the surface and tropopause.
### The Role of the Stratosphere
In Figure 2 there can be observed in the northern and southern polar stratosphere two regions where the covariance of temperature and radiative heating anomalies is strongly negative. It is conceivable that the loss of eddy available potential energy in one part of the atmosphere could affect the eddy kinetic energy in another, since the two forms of energy are only related when integrated over the entire mass of the atmosphere, and not at each location. Two questions follow: what causes the regions of negative \(G_{R}(P_{E})\) in the polar stratosphere, and what effect do they have on the kinetic energy of the troposphere?
The stratosphere is thought to exist in \"radiative-dynamical equilibrium\"; low-wavenumber Rossby waves from the troposphere propagate vertically into the stratosphere, depositing their momentum and inducing a meridional circulation which leads to sinking motion and adiabatic warming ([PERSON], 2022). This is the process behind \"sudden stratospheric warmings.\" These warm events cool, in part, by enhanced thermal emission of radiation (the Planck feedback); and therefore positive temperature anomalies in the stratosphere are associated with negative radiative heating anomalies, leading to the negative covariance (\(G_{A}(P_{E})<0\)) observed in Figure 2. In the climatological radiation experiment, however, the radiative cooling rate in the stratosphere is fixed, so transient warm events are unable to cool off by the Planck feedback. This leads to more persistent warm events in the climatological radiation experiment, and a higher mean temperature in the polar stratosphere, particularly in winter in the Northern Hemisphere, when vertical propagation of planetary waves is most prevalent (Figure S6 in Supporting Information S1).
Because the troposphere and stratosphere are coupled, it is conceivable that an alteration to the stratosphere in the climatological radiation experiment could affect tropospheric eddies ([PERSON] and [PERSON], 2004). We therefore perform a second experiment, in which the radiative cooling profile is fixed to the monthly mean only in the troposphere (Figure S7 in Supporting Information S1). To demarcate the troposphere from the stratosphere, we define a monthly-varying tropopause as the height above 400 hPa where the lapse rate falls to 2\({}^{\circ}\)C/km, based on the definition from the WMO (1957). In the troposphere-only climatological radiation experiment we find an increase of the globally-averaged eddy kinetic energy by \(\sim\)4% compared to the control. This is slightly smaller than the \(\sim\)6% increase found in the full-column climatological radiation experiment, and the difference arises mainly in the midlatitudes in the Northern Hemisphere (Table S1 in Supporting Information S1; Figure S8 in Supporting Information S1). This finding suggests a role for the stratosphere in setting the kinetic energy of tropospheric eddies, particularly in the Northern Hemisphere; however, the details of this mechanism are at this point uncertain.
## 4 Conclusions
Using a high-resolution general circulation model we have shown that, when atmospheric radiative heating is fixed to its climatology, the globally-averaged eddy kinetic energy is enhanced by \(\sim\)6%. This supports the findings of [PERSON] and [PERSON] (2018) and suggests that, unlike tropical cyclones, midlatitude cyclones are weakened by radiative interactions. It has been the purpose of this study to develop a framework for understanding this result, based on the concept of available potential energy put forward by [PERSON] (1955). Our picture of the effect of radiative heating on midlatitude cyclones can be summarized as follows. In a cyclone's warm sector there is convergence of moisture and rising motion leading to deep clouds, while in the cold sector the atmosphere is dry and contains low clouds. In the warm sector there is anomalous radiative cooling, and in the cold sector anomalous radiative heating, near the surface and tropopause. This cooling of warm air and heating of cold air causes a destruction of eddy available potential energy, which offsets the generation of eddy kinetic energy by baroclinic instability. We suggest that the destruction of eddy available potential energy by radiative cooling explains the weakening of midlatitude cyclones when radiative interactions are permitted. Unlike previous studies, which have related the eddy kinetic energy to the mean horizontal temperature gradient or mean available potential energy ([PERSON] and [PERSON], 2008), we have shown that radiation weakens the horizontal temperature gradient on the scale of the cyclone.
We have, throughout this article, adopted an \"energy viewpoint\" for understanding the effect of atmospheric radiative heating on large-scale eddies in the midlatitudes. However, that is only one perspective. Another viewpoint, such as that of momentum (i.e., potential vorticity), is likely to offer complementary insights. How the vertical structure of temperature and radiative heating anomalies affects midlatitude cyclones, and how clouds contribute to radiative heating anomalies, are questions that may benefit from such another perspective.
## Data Availability Statement
The HiRAM simulations were performed on Princeton University Research Computing systems. The zonal-mean eddy kinetic energy data set, the zonal-mean generation of eddy available potential energy data set, and the covariance between temperature and radiative heating anomalies data set are available at Mischell (2024).
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wiley/fde9368d_876e_4d93_a0d8_673852534670.md | # Water Resources Research
Research Article
10.1029/2023 WR036038
[PERSON]
1 Hydrology and Environmental Hydraulics, Wageningen University and Research, Wageningen, Netherlands 1
[PERSON]
1 Hydrology and Environmental Hydraulics, Wageningen University and Research, Wageningen, Netherlands 1
[PERSON]
1 Hydrology and Environmental Hydraulics, Wageningen University and Research, Wageningen, Netherlands 1
###### Abstract
Acoustic Doppler current profilers (ADCPs) are a global standard in observing flow fields in rivers, estuaries and the coastal ocean. To date, it remains a labor intensive challenge to isolate mean flow fields governed by river discharge, tides and atmospheric forcing on the one hand, from small-scale turbulence, positioning imprecision, Doppler noise and erroneous backscatter, on the other hand. Here, we introduce a generic, new method of combining raw shipborne ADCP transect data with continuity and smoothness constraints to obtain better estimates of turbulence-averaged three-dimensional flow velocities in any type of open water body. The physical constraints are enforced with variable relative importance via generalized Tikhonov regularization. We demonstrate that in complex estuarine flow, this procedure allows for more reliable estimates of tidal amplitudes, phases and their gradients than what is possible with a purely data-based approach, by testing the method's generalization capabilities and robustness to turbulence and measurement noise on a data set retrieved at a tidal channel junction. The increased adherence to mass conservation and robustness to noise of various kinds allows for more reliable and verifiable estimates of Reynolds-averaged flow components, and subsequently, of terms in the Navier-Stokes equations.
2023 WR036038201 14 SEP 2023 21 NOV 2024 21 NOV 2024 21 NOV 2023
[PERSON], [PERSON], [PERSON], [PERSON].
suitable for further estimating terms in the Reynolds-averaged Navier-Stokes equations by incorporating assumptions on temporal evolution and directly estimating spatial gradients. The method combines the tidal projection method employed by for example, [PERSON] et al. (2005); [PERSON] et al. (1992); [PERSON] (2000); [PERSON] et al. (1990) and [PERSON] (2006) to capture temporal variability, and the mesh-based and partitioning method previously used by [PERSON] and [PERSON] (1990); [PERSON] and [PERSON] (1990); [PERSON] et al. (2013) and [PERSON] et al. (2014) regarding the spatial variability of the velocity field.
The derived empirical model is regularized using the framework of generalized Tikhonov regularization ([PERSON] and [PERSON], 2019; [PERSON], 1943). By employing physical laws as constraints to the optimization problem, the estimated flow velocity field is biased toward physically realistic solutions ([PERSON] and [PERSON], 1970; [PERSON], 1970; [PERSON], 1986). In that sense, the method acts as a physics-based filter of the data. Importantly, this filtering is based on a priori principles rather than an a posteriori smoothing of the solution. Moreover, the constraints are applied in a \"weak\" sense: regularization weights act as adjustable parameters governing the solution of the inverse problem. As the constraints themselves are also subject to numerical approximations and errors, strong enforcement may lead to over-regularization. The obtained flexibility through adjusting regularization weights makes the presented method applicable to a wide range of problems.
The use of regularization to obtain filtered flow estimates has already been proposed by various researchers ([PERSON] et al., 1992; [PERSON], 2006), who used a purely data-driven method (SVD/PCA analysis) to obtain a better-posed inverse problem. In contrast, in the current work, the regularization conditions are derived from physical constraints such as the incompressible continuity equation and kinematic boundary conditions, and subsequently applied in a weak sense. We demonstrate this leads to more reliable and robust estimates of Reynolds-averaged tidal flow. Herein, we draw inspiration from heuristic techniques (e.g., K-fold cross-validation) ([PERSON] and [PERSON], 2019) as well as more rigorous statistical approaches ([PERSON], 1970; [PERSON], 1986; [PERSON] and [PERSON], 2007). In the end, the \"real\" Reynolds-averaged flow of any highly turbulent real-life system is never fully known at all times and places. We can only illustrate the validity of the presented estimation method using heuristic and statistical techniques.
This paper is organized as follows. In Section 2 the method of data-based tidal flow field parameter estimation is explained. Next, we present assumptions and derivations leading to the regularization constraints. Subsequently, the actual model inversion and flow field parameter estimation is detailed. In Section 3, we present the result of the regularized tidal projection method on a high-resolution estuarine data set. The method is validated and goodness-of-fit metrics of the proposed method are discussed. Results are interpreted in Section 4, wherein recipes for choosing regularization weights for practical applications of the present method are also provided. We conclude with presenting the methodology in an open-source toolbox and drawing conclusions in Section 5.
## 2 Method
### Radial Beam Velocities to Local Flow Velocities
The present section details the assumptions and conventions employed in the current work. In their paper, [PERSON] et al. (2014) introduced a method to estimate three-dimensional flow fields from ADCP beam data, schematically depicted in Figure 1.
By manipulating Doppler frequency shifts, one ADCP measurement (one 'ping' from one of the transducers) produces one beam velocity estimate. They are linearly related to the local flow velocity \(\mathbf{u}\) by the inner product relation
\[b(t,\mathbf{x})=\frac{\mathbf{x}-\mathbf{x}_{b}(t)}{\|\mathbf{x}-\mathbf{x}_{ b}(t)\|}\cdot\mathbf{u}(t,\mathbf{x})=\mathbf{q}^{T}\mathbf{u} \tag{1}\]
where \(b\) is a beam velocity scalar, \(\mathbf{q}\) is a unit vector pointing from one of the ADCP sensors to the velocity sample. \(\mathbf{x}=(x,y,z)\) is the location of backscattering and hence the flow velocity sample, where an instantaneous velocity \(\mathbf{u}\) is measured. The flow velocity \(\mathbf{u}(t,\mathbf{x})\) is expressed in an orthonormal basis that is assumed to be aligned with the channel geometry: \((x,y,z)\) forms a right-handed coordinate system where \(x\) points along-channel, \(y\) points along the lateral dimension and \(z\) points upwards. Finally, \(\mathbf{x}_{b}(t)\) is the transducer location at time \(t\). Importantly, the present study focuses on repeat transect cross-sectional data, but the resolved velocity field is three-dimensional.
The along-channel velocity component (i.e., orthogonal to the cross-section) and its gradients can be resolved due to beam spread and small streamwise variations in the positioning of the vessel tracks. When multiple transects are repeatedly measured, the complete three-dimensional flow field can be resolved.
### Derivation of the Empirical Model
Our aim is to estimate three-dimensional turbulence-averaged flow velocities in time and space. Typically, a field experiment only produces a sparse data set, that is, the measurement locations and times are only a small subset of four-dimensional \((t,\mathbf{x})\) space. In steady-state or tidal environments, this can partly be mitigated with prior information on tidal motion using a set of pre-determined tidal constituents. These also capture steady-state or subtidal behavior because a time-independent component is always included. First, the water level, in general described by \(z=\zeta=\zeta(t,x,y)\) can be parametrized by a set of \(N_{t}\) tidal constituents:
\[\zeta(t,x,y)=\zeta_{0}(x,y)+\sum_{n=1}^{N_{t}}f_{n}^{z}(x,y)\cos\left(\omega_{ n}t\right)+g_{n}^{z}(x,y)\sin\left(\omega_{n}t\right). \tag{2}\]
The method outlined in the present work operates on the basis of \(\sigma\) coordinates, which is a transformed vertical coordinate. Temporal and horizontal coordinates are unaffected by the coordinate transformation. However, they are implicitly coupled by the vertical \(\sigma\) coordinate:
\[\sigma=\frac{z-z_{0}(x,y)}{\zeta(t,x,y)-z_{0}(x,y)}. \tag{3}\]
Herein, \(z_{0}\) denotes the (fixed) bed level height relative to a reference datum. In the present work, \((t,\mathbf{x})\) denotes a point at time \(t\) in Cartesian space, while \((t,\mathbf{r})\) denotes a location in \(\sigma\) space, with \(\mathbf{r}=(x,y,\sigma)\). From Equation 3, the inverse transformation is given by
\[z=z_{0}+(\zeta-z_{0})\sigma=z_{0}+H\sigma, \tag{4}\]
where \(H=H(t,x,y)=\zeta(t,x,y)-z_{0}(x,y)\) is the instantaneous water depth. The flow velocities \(\mathbf{u}=(u,v,w)^{T}\) respectively in the \((x,y,z)\) directions are parametrized using the same set of tidal constituents as the water level (Equation 2):
\[u(t,\mathbf{r})=A_{0}(\mathbf{r})+\sum_{n=1}^{N_{t}}A_{n}( \mathbf{r})\cos\left(\omega_{n}t-\phi_{n}^{x}(\mathbf{r})\right) \tag{5}\] \[=f_{0}^{x}(\mathbf{r})+\sum_{n=1}^{N_{t}}f_{n}^{x}(\mathbf{r}) \cos\left(\omega_{n}t\right)+g_{n}^{x}(\mathbf{r})\sin\left(\omega_{n}t\right) \tag{6}\]
where the superscript \(x\) may be replaced by \(y,z\) for lateral and vertical flow velocities \(v,w\), respectively. In the above, the two equivalent representations are related by
\[A_{0} =f_{0}^{x},\] \[A_{n}^{2} =\left(f_{n}^{x}\right)^{2}+\left(g_{n}^{x}\right)^{2}, \tag{7}\] \[\phi_{n}^{x} =\arctan\left(\frac{g_{n}^{x}}{f_{n}}\right).\]
Figure 1: Based on their locations of backscattering (in \(\sigma\)-space), radial beam velocities are converted to flow velocity estimates within pre-defined cells.
Importantly, the \(\sigma\) coordinate transformation is only used to transform the spatial domain from time-varying to constant in time. The velocities \(\left(u,v,w\right)^{T}\) are still expressed in the orthonormal basis associated to the Cartesian coordinates \(\left(x,y,z\right)\).
To transform the inverse problem to a discrete state estimation problem, the spatial amplitudes \(\left(f_{u}^{x},g_{u}^{y},f_{s}^{z}\right)\) and \(\left(g_{u}^{x},g_{u}^{y},g_{u}^{z}\right)\) require a parametric representation. To this end, the cross-sectional domain \(\Omega\) is partitioned in \(N_{c}\) hexagonal cells which have fixed \(\sigma\) coordinates. Hence in \(z\) space, move along with the tide ([PERSON] et al., 2014). A computational mesh used in the current work is plotted in Figure 2.
In each of the cells indexed by \(c\), \(1\leq c\leq N_{c}\), we denote the cell center by \(\mathbf{r}_{0}^{c}=\left(x_{0}^{c},\ y_{0}^{c},\ \sigma_{0}^{c}\right)^{T}\) and we prescribe a linear flow velocity profile, based on a first-order Taylor expansion around the cell center. For a point \(\mathbf{r}\) in cell \(c\), we denote \(d\mathbf{r}=\mathbf{r}-\mathbf{r}_{0}^{c}\) and we expand up to first order in \(x\), \(y\) and \(\sigma\):
\[\begin{split} f_{w}^{x}(\mathbf{r})&=f_{w}^{x} \left(\mathbf{r}_{0}^{c}\right)+\
abla f_{w}^{x}\left(\mathbf{r}_{0}^{c} \right)\cdot d\mathbf{r}+O\big{(}\|d\mathbf{r}\|^{2}\big{)}\\ &=f_{w}^{x}\left(\mathbf{r}_{0}^{c}\right)+\frac{\partial}{ \partial x}f_{w}^{x}\left(\mathbf{r}_{0}^{c}\right)\,dx+\frac{\partial}{ \partial y}f_{w}^{x}\left(\mathbf{r}_{0}^{c}\right)\,dy+\frac{\partial}{ \partial\sigma}f_{w}^{x}\left(\mathbf{r}_{0}^{c}\right)\,d\sigma+O\big{(}\|d \mathbf{r}\|^{2}\big{)}.\end{split} \tag{8}\]
In words, \(\
abla f_{w}^{x}\left(\mathbf{r}_{0}^{c}\right)\) is the spatial gradient of the \(u\)-cosine-component of constituent \(n\) in cell \(c\), where the gradient is taken with respect to the \(\sigma\) coordinate system. The same procedure can be carried out for the sine-component of the tidal constituents. Given a mesh cell \(c\), we proceed to collect all radial velocity measurements from the ADCP at all times. These \(n_{c}\) radial velocity measurements are collected in a vector. We formulate a large, sparse linear system of equations connecting all radial velocity measurements to their respective tidal flow field parameters within corresponding computational cells:
\[\vec{b}=M\vec{p}+\vec{\epsilon}. \tag{9}\]
Herein, \(\vec{b},M\) and \(\vec{p}\) are called data vector, model matrix and state vector, respectively. The residual is modeled as \(\vec{\epsilon}\sim\mathcal{N}\big{(}\vec{0},\Sigma\big{)}\) with expected value \(\vec{0}\) and covariance matrix \(\Sigma\). The derivation of the model matrix \(M\) is detailed in Appendix A. The state vector \(\vec{p}\) contains all flow characteristics that need to be estimated and depends on the choice of empirical model. All entries of \(\vec{p}\) have a physical interpretation as either flow magnitudes or gradients. For example, if first-order spatial Taylor expansions of tidal amplitudes of M\({}_{0}\) and M\({}_{2}\) are desired to be estimated, we have
\[\vec{p}=\left(\delta_{01}^{x}\quad f_{11}^{x}\quad g_{11}^{x}\quad\frac{ \partial}{\partial x}f_{01}^{x}\quad \quad\frac{\partial}{\partial\sigma}f_{ \mathrm{ir}_{\mathrm{ir}_{\mathrm{ir}_{\mathrm{ir}_{\mathrm{ir}}}}}}^{x}\quad \frac{\partial}{\partial\sigma}g_{\mathrm{ir}_{\mathrm{ir}_{\mathrm{ir}}}}^{x} \right)^{T}. \tag{10}\]
In the present work, elements of the vector \(\vec{p}\) are often denoted \(p_{i}^{x}\), where subscript \(c\) refers to the cell index and superscript \(j\) refers to the index of a physical quantity (e.g., flow velocity amplitude). The dimension of the state vector is the product of the number of flow field parameters per cell times the number of computational cells in the mesh: \(N_{p}=n_{p}N_{c}\). Since \(\vec{b}\) and \(M\) are obtainable from the ADCP, the state vector \(\vec{p}\) can be estimated using ordinary least squares. As such, tidal amplitudes, phases and their spatial structure can be directly obtained from ADCP data. In practice, there is a degree of mis-specification and error in the above model, which in the present
Figure 2: An equivalent computational mesh in \(z\) - coordinates (left) and \(\sigma\)-coordinates (right). The mesh is constructed such that an approximately equal amount of measurements fall within each mesh cell. The blue line denotes the water level, the black line the channel bottom. Empty space depicts the blind area of the ADCP, either being too close to the water surface or bottom.
work is modeled using the multivariate normally distributed vector \(\vec{e}\). The goal is to find a vector \(\vec{p}\) that robustly, accurately and meaningfully captures the Reynolds-averaged flow.
### Constraining the System of Equations
In general, the linear system of equations Equation 9 is ill-conditioned, that is, small perturbations in the data \(\vec{b}\) lead to large fluctuations in least squares estimated state vector. In other words, parts of the state vector \(\vec{p}\) are nearly non-observable from the data \(\vec{b}\). This fundamental problem causes direct inversion of Equation 9 via a least squares objective function to be problematic and often meaningless ([PERSON], 1970; [PERSON], 1986). The problem of ill-posedness can partly be mitigated by \"nudging\" the solution toward physical realism, that is, to make the inverse problem \"physics-informed\". This is an example of a regularization approach. We assume that the unknown vector \(\vec{p}\) approximately (to be quantified later) satisfies a number of physical constraints, detailed in the following. The constraints are based on rectangular approximations of mesh cells in \(\sigma\) coordinates. This assumption is valid as long as bathymetric gradients remain small relative to the mesh cell size, motivating the choice of high-resolution meshes. Modeling choices are further commented upon in Section 4.
#### 2.3.1 Physics-Informed Nudging: Conservation of Mass
Open channel flow must conserve mass by satisfying the incompressible continuity equation
\[\
abla_{z}:\mathbf{u}=0, \tag{11}\]
where the subscript \(z\) refers to the \(z\) coordinate system. As detailed in Appendix B, certain assumptions lead to the following characterization of continuity in the \(\sigma\) coordinate system, where partial derivatives are symbolized by subscript notation
\[H_{u_{x}}+(1-\sigma)H_{u}u_{x}+Hv_{y}+(1-\sigma)H_{y}v_{x}+w_{\sigma}=0. \tag{12}\]
Substitution of the tidal expansions of \(u,v,w\) (Equation 6) and \(H\) (Equation B16) yields an expression for mass conservation in terms of amplitudes of tidal constituents, hence in terms of the state vector \(\vec{p}\). In order to remove time dependence from the resulting equations, we collect all terms containing the same time dependence and equate their amplitudes, that is, we require term-by-term equality of the series expansion. This can be viewed as a truncation method, in which higher-order temporal correlations, which are nonlinear in \(\vec{p}\), are ignored. These cross-correlations are likely to cause net contributions on the subtidal and tidal timescales captured in the equations that follow, however, these effects are assumed small. The subtidal condition is given by equating all time-independent terms in Equation 12 after substitution of the different tidal expansions, yielding
\[H_{0}f_{\mathrm{M}_{\mathrm{M}}}^{x}+(1-\sigma)H_{\mathrm{M}_{\mathrm{M}_{ \mathrm{M}}}}f_{\mathrm{M}_{\mathrm{M}}}^{x}+H_{0}f_{0}^{y}+(1-\sigma)H_{0}f_{ \mathrm{M}_{\mathrm{M}}}^{x}+f_{0}^{z}f_{0}^{z}=0. \tag{13}\]
Using the truncation assumption considering the expansion of \(H\) in tidal constituents yields the equations involving the amplitudes of the harmonic constituents:
\[\begin{split} H_{0}f_{\mathrm{M}_{\mathrm{M}}}^{x}+(1-\sigma)H_ {\mathrm{M}_{\mathrm{M}}}f_{\mathrm{M}}^{x}+H_{0}f_{0}^{y}+(1-\sigma)H_{0}f_{ \mathrm{M}_{\mathrm{M}}}^{y}+f_{\mathrm{M}_{\mathrm{M}}}^{z}+f_{0}^{z}f_{0}^{ z}=0,\\ H_{0}g_{\mathrm{M}_{\mathrm{M}}}^{x}+(1-\sigma)H_{0}g_{\mathrm{M} _{\mathrm{M}}}^{x}+(1-\sigma)H_{0}g_{\mathrm{M}_{\mathrm{M}}}^{y}+g_{\mathrm{M }_{\mathrm{M}}}^{z}+g_{\mathrm{M}_{\mathrm{M}}}^{z}+f_{0}^{z}g_{\mathrm{M}}^{ z}+f_{0}^{z}g_{\mathrm{M}}^{z}=0,\end{split} \tag{14}\]
for all constituents \(1\lesssim n\lesssim N_{r}\), yielding \(2N_{t}\) additional equations per computational cell. The set of Equations 13 and 14 are (weakly) required to hold at two spatial scales, the first of which is the mesh cell scale. As such, they provide \(N_{c}\left(2N_{t}\right.+1\left.\right)\) extra equations that constrain the tidal velocity field parameters. Partial derivatives of the tidal constituent amplitudes are present in the vector \(\vec{p}\) (See Equation 8), hence the constraining equations can be written using a sparse matrix \(C_{cc}\) with \(N_{c}\left(2N_{t}\right.+1\left.\right)\) rows and \(N_{p}\) columns:
\[C_{cc}\vec{p}=\vec{0}. \tag{15}\]
In the following, we refer to the above as a \"continuity constraint\" (hence the \"cc\" subscript).
#### 2.3.2 Physics-Informed Nudging: Kinematic Boundary Conditions
As a second regularization term, we constrain the problem by adding no-transport boundary conditions at the bottom and surface boundaries of the domain at hand. This constraint is intimately related to the continuity constraint and likewise obtained from fundamental principles. In terms of instantaneous velocities, kinematic boundary conditions are given by
\[\mathbf{u}\cdot\mathbf{n}=\begin{cases}0,&\text{for $\sigma=0$},\\ \zeta_{r},&\text{for $\sigma=1$}.\end{cases} \tag{16}\]
The outward normal vector pointing at the bottom is given by \(\mathbf{n}_{0}=(-z_{bs},\ -z_{bs},1)^{T}\), while the outward normal vector at the surface is given by \(\mathbf{n}_{0}=(0,0,\ -1)^{T}\), neglecting surface gradients. The flow velocity at the bottom is approximated by \(\mathbf{u}_{0}\ -\ d\sigma\mathbf{u}_{c}\), and vice versa for the surface velocity. Herein, \(\mathbf{u}_{0}\) represents the velocity at cell centers, \(\mathit{d}\sigma\) represents the \(\sigma\)-distance to the bottom and \(\mathbf{u}_{c}\) the estimated partial derivative w.r.t. \(\sigma\). Kinematic boundary conditions are enforced for the subtidal flow and for each tidal constituent. Bottom boundary conditions are applied at \(\sigma=0\):
\[\begin{split} f_{h}^{x}z_{bs}-\mathit{d}\sigma_{nn}^{x}z_{bs}+f_ {h}^{z}z_{bs}-\mathit{d}\sigma_{nn}^{y}z_{bs}-f_{h}^{z}+\mathit{d}\sigma_{nn}^{ z}=0,&\ n=0,1,2,\ldots\\ g_{h}^{x}z_{bs}-\mathit{d}\sigma_{nn}^{y}z_{bs}+g_{h}^{z}z_{bs}- \mathit{d}\sigma_{nn}^{z}z_{bs}-g_{h}^{z}+\mathit{d}\sigma_{nn}^{z}=0,& \ n=1,2,\ldots.\end{split} \tag{17}\]
Kinematic surface boundary conditions neglecting water level gradients are inhomogeneous due to the time-varying water level, that is, for the subtidal flow as well as for constituent \(1\leq n\leq N_{t}\) we prescribe for \(\sigma=1\):
\[\begin{split} f_{\widetilde{0}}^{c}+\mathit{d}\sigma_{nn}^{z}& =0,\\ f_{n}^{c}+\mathit{d}\sigma_{nn}^{c}&=\xi_{n}^{c} \omega_{n},\\ g_{h}^{z}+\mathit{d}\sigma_{nn}^{z}&=-f_{h}^{c} \omega_{n},\end{split} \tag{18}\]
where the factors \(f_{n}^{z},g_{h}^{z}\) are a priori retrieved from water level data (Equation 2). The above conditions constrain the vertical velocities just below the water surface, which is the region in the water column often affected by boat and device fluctuations. Assembling the regularization matrix as before, the fifth regularization condition reads, using a subscript referring to \"boundary conditions\":
\[\mathcal{C}_{bc}\vec{p}=\vec{\zeta}. \tag{19}\]
Herein, \(\vec{\zeta}\) contains the inhomogeneous surface forcing terms appearing on the right-hand side of Equation 18.
#### 2.3.3 Smoothness Nudging: Flow Coherence
In cell-based estimation of Reynolds-averaged flow velocity parameters, a degree of coherence across cells can be expected. Abrupt flow transitions may exist and be realistic, but Reynolds averaged flow in an individual cell will not deviate from all neighboring cells. We construct a third regularization matrix that encodes this as follows. Consider a computational cell having index \(c\), with neighboring indices \(\Gamma=\{c_{-},c_{-},c_{\uparrow},c_{\downarrow}\}\). Then, given a element of the state vector \(p_{c}^{j}\), we require the expression
\[p_{c}^{j}-\sum_{i\in\Gamma}w_{i}^{j}p_{i}^{j}=0 \tag{20}\]
to approximately hold, where \(w_{i}^{j}\) are non-negative weights associated to the relative importance of the coupling between cell \(c\) and \(i\in\Gamma^{c}\) regarding flow field parameter \(p^{j}\), with \(\sum_{i\in\Gamma}w_{i}^{j}=1\) for all \(c\) and \(j\). If cell \(c\) is a boundary cell, the set \(\Gamma^{c}\) is smaller. Specifying the weights \(w_{i}^{j}\) biases \(\vec{p}\) toward specific solutions. For instance, suppose the weights associated to the lateral direction are large compared to the ones associated with the vertical direction. This will nudge the solution toward lateral uniformity. This regularization term acts as an a priorismoothing filter in the \(\sigma\) coordinate system by simultaneously penalizing large fluctuations and gradients in state space, and most closely resembles standard gradient Tikhonov regularization. As before, the constraint is linear in \(\vec{p}\) and can be written as
\[C_{j}\vec{p}=\vec{0}, \tag{21}\]
where the subscript \"fs\" refers to \"flow smoothness\".
#### 2.3.4 Smoothness: Gradient Consistency
As a fourth and final regularization constraint, central differences across cells in the cross-sectional domain must approximately equal the cell-based estimated partial derivatives of the flow velocities. For example, regarding the along-channel velocity \(u\), centered differences across a cell \(c\) are given by
\[\frac{\Delta u}{\Delta y}\coloneqq\frac{u_{|_{c_{u}}}-u_{|_{c_{u}}}}{y_{0}^{c_ {u}}-y_{0}^{c_{u}}},\ \ \text{and}\ \ \frac{\Delta u}{\Delta\sigma}\coloneqq\frac{u_{|_{c_{u}}}-u_{|_{c_{u}}}}{ \sigma_{0}^{c_{u}}-\sigma_{0}^{c_{u}}} \tag{22}\]
We thus require
\[u_{y}=\frac{\Delta u}{\Delta y},\ \ \text{and}\ \ \ u_{a}=\frac{\Delta u}{\Delta\sigma} \tag{23}\]
to approximately hold (similarly for the velocity components \(v\), \(w\)). Importantly, the left-hand sides of the above approximate equalities are elements of the state vector \(\vec{p}\), while the right-hand sides are central differences consisting of multiple elements in the state vector. Conversion to (sub) tidal amplitudes is straightforward from Equation 6. Because of linearity, the constraint can again be written as
\[C_{\mu}\vec{p}=\vec{0}, \tag{24}\]
where the subscript \"\(gs\)\" refers to gradient smoothness.
### Objective Functional Definition
The functional to be minimized is defined as a linear combination of individual square loss functionals, each measuring the adherence of the state vector to different constraints.
\[J_{\lambda}(\vec{p})=\underbrace{\left\|M\vec{p}-\vec{b}_{||}\right\|^{2}}_{ \text{data}}+\underbrace{\lambda_{cc}\left\|C_{cc}\vec{p}\right\|^{2}}_{ \text{continuity}}+\underbrace{\lambda_{cc}\left\|C_{\text{k}\vec{p}}-\vec{ \gamma}\right\|^{2}}_{\text{kinem, b.c.}}+\underbrace{\lambda_{j_{f}}\left\|C_ {f,j}\vec{p}\right\|^{2}}_{\text{flow smoothness}}+\underbrace{\lambda_{g} \left\|C_{g}\vec{p}\right\|^{2}}_{\text{gradient smoothness}}. \tag{25}\]
The penalty parameters, hereafter called regularization weights \(\lambda_{i}\geq 0\) determine the relative importance of the applied constraints. As such, this constitutes a regularized linear least squares formulation with weak constraints ([PERSON], 2019; [PERSON] et al., 2006), also interpretable as generalized Tikhonov regularization. If for some \(i\), \(\lambda_{i}\ \to\ \infty\), constraint \(i\) is strongly enforced. For example, \(\lambda_{j_{f}}\ \to\ \infty\) would result in uniform flow in space, with no variation between cells. The optimal estimate of the state vector \(\vec{p}\), given regularization weights \(\lambda\) is given by
\[\vec{p}_{\lambda}=\underset{\vec{p}\in\mathbb{R}^{\times}}{\arg\min}J_{ \lambda}(\vec{p}). \tag{26}\]
The functional \(J_{\lambda}\) has a unique minimum, depending on the data and on \(\lambda\). Hence, \(\vec{p}_{\lambda}\) is the unique solution of the system of equations ([PERSON] et al., 2006):
\[\left(M^{T}\Sigma^{-1}M+\sum_{i\in[c_{u},\lambda_{c}/(s,s)]}\lambda_{i}C_{i} \right)\vec{p}_{\lambda}=M^{T}\Sigma^{-1}\vec{p}+\lambda_{cc}C_{\mu}^{T}\vec{ \gamma}. \tag{27}\]To facilitate further discussion, we define the aggregate regularization matrix (viewed a weighed Gramian matrix of the regularization constraints, hence \(G\)) as
\[G_{\lambda}=\sum_{i\in[c_{i},c_{i},c_{j},c_{j}]}\lambda_{i}C_{i}^{T}\,C_{i}, \tag{28}\]
and the regularized system matrix, governing the present method, as
\[\begin{split} A_{2}&=\,M^{T}\Sigma^{-1}M+\sum_{i\in[ c_{i},c_{i},c_{j},c_{j}]}\lambda_{i}C_{i}^{T}\,C_{i}\\ &=\,M^{T}\Sigma^{-1}M+G_{\lambda}.\end{split} \tag{29}\]
Hence, the present method can be succinctly formulated as the system of linear equations
\[A_{2}\tilde{p}_{\lambda}=\overline{r}_{\lambda} \tag{30}\]
\(A_{2}\) is a \(N_{p}\times N_{p}\) symmetric non-negative definite matrix with properties such as condition number and eigenvalues depending on the model design matrix \(M\), data covariance matrix \(\Sigma\) and weights \(\lambda\), reducing to the unregularized ordinary least squares problem if \(\lambda=\mathbf{0}\). \(\overline{r}_{\lambda}\) is the left-hand side of Equation 27. The linear system can be solved by either direct or iterative methods. In this work, we employ the iterative method of preconditioned conjugate gradients (MATLAB: pcg), which is optimal for \(A_{2}\) being large, sparse and nonnegative definite. As a preconditioner, the incomplete Cholesky decomposition of \(A_{2}\) is used. These algorithmic choices cause computation times to remain low and do not influence the actual result of the state estimation significantly.
### Data Set
A 13 hr repeat transect data set from a field campaign in the Hartel Canal, retrieved on the twelfth of August 2014, is used to test the presented method. This canal connects the Old Meuse river to the mouth of the New Waterway toward the harbor of Rotterdam, and forms the east branch of the Old Meuse - Hartel Canal tidal junction within the greater Rotterdam urban area (Figure 3). The complex geometry at the tidal junction causes the flow field to show considerable variations in the cross-section.
### Empirical Model Selection
For the test case experiments, we have chosen a mesh resolution of 25 mesh cells in the lateral and at most 13 in the vertical direction, for the system under study corresponding to mesh sizes of 12 m wide and 60 cm high
Figure 3: Location of the field campaign within the Rotterdam harbor area, The Netherlands. The area of the repeat transects is depicted by the green rectangle in the detailed view. The bathymetry is visualized by light-blue (shallow) to purple (deep) colors.
(Figure 2). This mesh size allows for identifying details in the flow, that is, it is not too coarse. On the other hand, the linear systems of equations involved are small enough to be solved on a standard laptop in order demonstrate the proposed method. The influence of mesh resolution on the solution will be discussed in Section 4. For the tidal constituents in the empirical model, we have chosen the subtidal (M\({}_{0}\)), semidivantant (M\({}_{2}\)) and quarterdiurnal (M\({}_{4}\)) tide as the tidal constituents on which to project the temporal variation of flow velocity. These constituents are known to be dominant at this location from a harmonic analysis of water level data. The selected constituents result in five parameters (one for M\({}_{0}\), two for M\({}_{2}\) and two for M\({}_{4}\)) to be estimated in each mesh cell, for each velocity component \(u,v\) and \(w\). Considering also the spatial gradients in the constituents, this results in 60 flow field parameters to be estimated per mesh cell. Multiplying by the number of mesh cells (in this experiment \(N_{c}~{}=~{}216\)) we end up with a total of \(N_{p}~{}=~{}12960\) flow field parameters to be estimated, which is the dimension of the state vector. On the other hand, the dimensionality of the data vector \(\vec{b}\) is \(N_{s}~{}=~{}166996\). The matrices and vectors involved in the inverse problem Equation 30 all have row dimension \(N_{p}\), with the model matrix \(M\) and regularization matrices \(C_{cc}\), \(C_{bc}\), \(C_{fs}\), \(C_{gs}\) having column dimensions \(166996\), \(1080\), \(1080\), \(12960\) and \(6480\), respectively. The inverse problem is over-determined and the Gramian model matrix \(M^{T}M\) appearing in the inverse problem (Equation 30) has condition number greater than \(10^{12}\), indicating an ill-conditioned problem. Therefore, we expect the introduced regularized inversion algorithm to be useful on this data set. The combined effect of turbulence and noise is modeled using a diagonal covariance matrix \(\Sigma~{}=~{}\sigma^{2}I\) (not to be confused with the vertical coordinate). This considerable simplification allows for rescaling the functional Equation 25 and the system of equations Equation 30 with the scalar \(\sigma^{2}\). In turn, the regularization weights are scaled with the same factor. In the following, regularization weights are always scaled w.r.t. some data variance \(\sigma^{2}\). Owing to this scaling, we pick \(\sigma^{2}~{}=~{}1\) without loss of generality. This choice is further motivated in Section 3.2.2.
## 3 Results
### Solution of the Flow
We estimated the state vector of flow field parameters from the raw velocity data using three degrees of regularization (Figure 4). Regularization weights in the following figures are (\(\lambda_{N}=\textbf{0}\)), (\(\lambda_{L}=(30,30,3,3)^{T}\)) and \(\lambda_{H}~{}=~{}(250,250,250,250)^{T}\), with subscripts referring to \"None\", \"Low\" and \"High\", respectively.
The larger the regularization weights, the more the state vector adheres to the constraints. Most apparent are the increased spatial coherence and the change in boundary cell flow with increasing regularization weights (represented by the matrices \(C_{js}\) and \(C_{ks}\)).
Next, some flow gradients are plotted in Figure 5, again regularized by the same regularization weights as in Figure 4. Typically, regularization greatly helps in observing small flow field parameters such as horizontal gradients, which are nearly unobservable from the raw data. The emergence of large vertical flow gradients, enforced by the kinematic boundary condition constraint, is readily apparent and may provide further estimates of bottom shear stresses (this being outside the scope of present research).
From Figures 4 and 5, it is clear that, given the empirical model defined in Section 2.6, regularized flow field estimation outperforms unregularized data-only estimation in terms of likeness to familiar Reynolds-averaged flow fields. However, this intuition is just based on visual inspection. In the following, we empirically validate the present method.
### Method Validation
The additional control over the solution provided by the regularization weights introduces the danger of over-regularization or underfitting. In that case, the estimated state vector does not represent the retrieved data anymore. In the following, the detailed behavior of the estimation procedure as a function of the regularization weights is discussed. We vary the regularization weights \(\lambda\) over many orders of magnitude to observe their influence on the corresponding optimal estimated state vector \(\vec{p}_{s}\). This can be considered as a heuristic way of investigating relevant sensitivities: the data and mesh size influence the result. Section 4 analytically derives statistical properties of the regularized state estimator following studies of [PERSON] et al. (1979), [PERSON] (1997) and [PERSON] (2010). To be able to visualize the behavior of the present method, we restrict the regularization weights to two degrees of freedom:Figure 4: (Sub) tidal flow field parameters plotted on the cross-sectional mesh, estimated using the three different regularization weights \(\lambda_{w}\), \(\lambda_{k}\) and \(\lambda_{H}\). The colors depict the flow velocity (gradients) using the same color bar scale per row. The upper five rows show the along-channel flow velocity \(u\) in terms of its (sub) tidal amplitude and phase (M\({}_{0}\) - M\({}_{2}\) - M\({}_{A}\)) - retrieved from the state vector \(\vec{p}_{1}\) using Equation 7. The lower three rows show the subtidal lateral and vertical velocities, respectively. Going from left to right, the increased flow coherence is striking. Units are m/s for the amplitudes and rad for the phase.
\[\lambda=\begin{pmatrix}\lambda_{c}\\ \lambda_{c}\\ \lambda_{d}\\ \lambda_{e}\end{pmatrix} \tag{31}\]
Figure 5. Estimated vertical gradients of the amplitudes of the along-channel flow \(u\) (top three rows), and three of the terms that are dominant in the subtidal continuity equation (bottom three rows). The bottom three gradients, scaled by the \(\sigma\)-coordinate Jacobian, are constrained to approximately sum to zero by increasing \(\lambda_{cc}\). Units of the horizontal gradients are \(\varsigma^{-1}\), of the vertical gradients m/s.
Herein, the positive scalars \(\lambda_{c}\) (with subscript \"c\" referring to continuity) and \(\lambda_{s}\) (with subscript \"s\" referring to smoothing) capture physics-based and smoothness-based regularization, respectively. In principle however, they can be varied independently and the influence of each element of \(\lambda\) may be investigated.
In the present section, two empirical measures of goodness-of-fit are analyzed.
#### 3.2.1 Generalization Error
The generalization error of a regression model refers to the ability of the model at hand to capture unseen data. A small generalization error indicates good extrapolation qualities of the model, roughly equivalent to the prevention of under- and overfitting ([PERSON] and [PERSON], 2019). A bootstrapping method to estimate the generalization error of the algorithm as function of regularization weights \((\lambda_{c},\lambda_{s})\) is achieved by partitioning the data vector \(\vec{b}\) and model matrix \(M\) in two: One training data set for computing the optimal state vector, and a validation data set for assessing the model's capability of capturing unseen data. Denoting the number of data by \(N_{s}\), the data are partitioned \(K\) times by two disjoint sets of indices \(T_{k}\) (training) and \(V_{k}\) (validation), such that for each \(k\), \(T_{k}\cup V_{k}=\{1,\ldots,N_{s}\}\), with \(1\leq k\leq K\). The number of data points in the validation set \(V_{k}\) is taken to be \(N_{s}/10\). First, for any cross-validation iteration \(k\), the index sets are formed randomly, the training model matrix and training data vector are obtained by eliminating rows/entries indexed by the validation index set. The obtained matrix and vector are denoted by \(M_{T_{k}}\) and \(\vec{b}_{T_{k}}\), respectively. The system of equations Equation 30 is solved using this model matrix and data vector. The obtained state vector estimate, using regularization weights \(\lambda\), is denoted \(\vec{b}_{T_{k}}(\lambda)\). The ensemble-averaged training error is defined as
\[E_{b}^{\text{train}}(\lambda)=\frac{1}{K}\sum_{k=1}^{K}\left\|M_{T_{k}}\vec{b} _{T_{k}}(\lambda)-\vec{b}_{T_{k}}\right\|^{2}. \tag{32}\]
The subscript \(b\) refers to the fact that the above error metric is derived from the norm in data space, inhabited by \(\vec{b}\). By construction, the training error on the data is minimized by the unregularized state vector \(\vec{b}_{T_{k}}(\mathbf{0})\). This is not the case for the generalization error, demonstrating the use of regularization in our method. Using repeated cross-validation with different randomized data partitions, an estimate of the model's generalization capacity may be obtained. We define the generalization error as the ensemble-averaged mean-squared prediction error on an ensemble of \(K\) validation data sets
\[E_{b}^{\text{gen}}(\lambda)=\frac{1}{K}\sum_{k=1}^{K}\left\|M_{N_{s}}\vec{b} _{T_{k}}(\lambda)-\vec{b}_{V_{k}}\right\|^{2}. \tag{33}\]
If the above metric is small as a function of \(\lambda\), it means that the training set estimate generalizes well to unseen data indexed by the sets \(V_{k}\), and one can have confidence in the vector \(\vec{b}_{k}(\lambda)\) to represent the underlying dynamics well, that is, that no over- or underfitting is present. Results of the training and generalization error metrics are shown in Figure 6.
In Figure 6, the region of feasible regularization weights is enclosed by the black line, where \(E_{b}^{\text{gen}}(\lambda)=E_{b}^{\text{gen}}(\mathbf{0})\) in \((\lambda_{c},\lambda_{s})\) - space. Whereas points close to (0,0) may lead to overfitting, the red area represents the underfitting region in regularization weight space: the state vector does not meaningfully represent the data anymore. From the data, there is no specific reason to choose any set of regularization weights over another within this region. The three state vector locations in \((\lambda_{c},\lambda_{s})\) space that were used to generate Figures 4 and 5 are depicted by the black dots. The results of Figure 6 imply that for example, the middle plots in Figure 4, while introducing more bias with respect to the full data set, are better in predicting unseen data than the unregularized estimates given in the left plots. This observation is further commented upon in Section 4.
#### 3.2.2 Sensitivity to Noise
One key aspect of standard Tikhonov regularization is a decreased sensitivity to measurement noise. As a trade-off, a bias with respect to the measured data is introduced. In this work, we employ multiple generalized Tikhonov regularization matrices \(C_{cc},\ldots,C_{bc}\), complicating a straightforward analysis of estimated flow field robustness to noise. We can, however, empirically visualize the sensitivity to noise by generating an ensemble of known state
estuarine scales ([PERSON] et al., 2001; [PERSON], 2006) to high-resolution riverine scales ([PERSON] et al., 2019). However, their common goal is to convert a large number of Doppler frequency shift data to human - intelligible information, such as horizontal or vertical velocity profiles, discharge time series or flux decompositions ([PERSON] et al., 2001). Both the choice of the empirical model (in this work, the matrix \(M\)), and the choice of regularization method (in this work, generalized Tikhonov regularization using the matrices \(\lambda_{i}C_{i}\)) must be made by the modeler, depending on the scale, a priori information and purpose of the study. In this work, the problem statement, solution and validation methods are set up as general as possible, partly incorporating past scientific studies.
#### 4.1.1 Choice of Empirical Model
The choice of empirical model in ADCP processing differs per study. Regarding the temporal aspects of the flow to be estimated, two cases can be considered. In case of single transect experiments such as large-scale offshore experiments, locations in space are often visited once, and there is no other option than to fit one flow vector per spatial location ([PERSON] et al., 2001; [PERSON], 1982). In case of repeat transect experiments, there are several options. In quasi-stationary (i.e., non-tidal) environments such as inland rivers, data are often just averaged in time to represent stationary dynamics ([PERSON] et al., 2019). In estuarine, tidally influenced regions, the practice of detiding comes down to projecting raw velocity data on a subtidal and one or more tidal constituents, thereby essentially transforming a time-varying estimation problem to a stationary estimation problem ([PERSON] et al., 1992; [PERSON] et al., 2005; [PERSON], 2000; [PERSON] et al., 1990; [PERSON], 2006). If a priori knowledge justifies fitting other (e.g., linear or higher-frequency) temporal dynamics, this can be straightforwardly included in the empirical model matrix \(M\). Hence, our method includes all of the approaches.
Regarding the spatial aspects of flow velocity estimation from ADCP data, the estimated flow is often projected on a set of spatial basis functions. First, spatial binning methods make use of a set of basis functions that are only nonzero on independent computational mesh cells ([PERSON], 1990; [PERSON] et al., 2004; [PERSON], 1990; [PERSON] et al., 2013). Benefits of this method include a potentially finer resolution of complex flow
Figure 7: Logarithm of the MSE metric as defined by Equation 34. \(\lambda_{i}\) varies between the subfigures, with sensitivity to \((\sigma,\lambda_{i})\) plotted. It is clear that the coherence regularization weight \(\lambda_{i}\) exerts the strongest influence on the model’s ability to retrieve the ‘true’ state vector.
at the cost of low spatial coherence, possibly, due to noise and turbulence influencing measurements. Second, non-binning methods such as domain-covering polynomials ([PERSON] et al., 2001; [PERSON] et al., 1992; [PERSON] et al., 1992) and node-based radial basis functions (RBFs) ([PERSON] et al., 2016; [PERSON], 2006), automatically satisfying the continuity equation, are employed often in large-scale experiments with sparse data. This projection method may yield smooth results across the domain of interest, parametrized by fewer flow field parameters, at the cost of possibly lacking model generality.
Within this variety of spatial projection methods, we strike a balance by using a spatial binning method with inter-cell connectivity due to the regularization constraints. This connectivity can be tuned a priori. This constitutes a difference with for example, the method described by [PERSON] et al. (2013), who use a posterior filtering to obtain smooth flow velocity estimates. A prerequisite for a posteriori moving averaging is that the estimated state vector on average represents actual dynamics. However, if the chosen mesh resolution is too fine or the data is too sparse, the problem of ill-conditionedness causes a posteriori averaging to yield erroneous results. The estimated state vector itself is then heavily influenced by noise smeared out over a large domain. A priori regularization fundamentally helps constraining the solution vector to a realistic subspace of the full solution space and is superior to a posteriori averaging.
#### 4.1.2 Regularization
Since the introduction of regularization by [PERSON] (1943), and subsequent work by [PERSON] and [PERSON] (1970) [PERSON] (1970), [PERSON] et al. (1978), [PERSON] et al. (1979), and [PERSON] (1986), various techniques have been applied to the inverse ADCP flow velocity estimation problem. Purely data-driven methods such as SVD and PCA approaches were already conducted by [PERSON] et al. (1992); [PERSON] and [PERSON] (2006) and subsequent authors. Locally weighed classical Tikhonov regularization was used by [PERSON] and [PERSON] (2004) to obtain a multiscale resolving flow velocity estimation algorithm. A posteriori validation based on physical principles such as the continuity and momentum conservation equations has been conducted by [PERSON] et al. (2001), [PERSON] et al. (1998) and [PERSON] and [PERSON] (2006). To our knowledge, the excellent method of [PERSON] et al. (2012) is the only study that a priori incorporates physical constraints with variable weights in the inverse ADCP problem. However, their method requires calculating gradient terms based on measured flow velocities a posteriori. As they point out, this is problematic in case of data sparsity. By incorporating the constraints in a weak sense via generalized Tikhonov regularization, our method can handle data sparsity more effectively.
### The Bias-Variance Decomposition
In Section 3, a general trend was discussed. Regularized state estimation achieves a reduction of solution variance and an improved robustness to measurement noise, as well as increased adherence to a priori physical information, at the cost of a bias introduction with respect to the data. This resulted in an improved generalization capacity of regularized state vectors.
Because of linearity of the state estimation problem Equation 30, we can actually derive some analytical characterizations of both bias and variance of the regularized estimators for \(\vec{p}\). This has great benefit as it helps understanding the state estimation problem, moreover it is also practically useful, as the empirical bootstrapping performed in Section 3 is computationally expensive. To explain the results in a more analytical way, we first consider the data-to-state vector mapping (Equation 9), with a theoretical 'true' vector \(\vec{p}\)\({}^{\text{true}}\), which is unknown and which we wish to estimate under the influence of turbulence and noise:
\[\begin{split}\vec{b}&=M\vec{p}\ ^{\text{true}}+\vec{\epsilon}\\ \vec{\epsilon}&\sim\mathcal{N}\big{(}\mathbf{0}, \sigma^{2}I\big{)}\end{split} \tag{35}\]
Importantly, \(M\) and \(\vec{p}\)\({}^{\text{true}}\) are assumed nonrandom, with \(\vec{b}\) and \(\vec{\epsilon}\) being viewed as stochastic vectors. \(M\) is known as the design matrix in statistical nomenclature, required to have linearly independent columns. For purposes of simplicity, we (as before) assume the residual vector \(\vec{\epsilon}\) to have an i.i.d. multivariate normal distribution with (unknown) variance conditioned on the data: the noise covariance matrix \(\Sigma\) is given by \(\sigma^{2}I\). Estimating \(\Sigma\) from instrument and flow properties falls outside the scope of the present research, but may be derived from studying the measurement processes influencing raw data retrieval as discussed by for example, [PERSON] et al. (2004), who list a large number of different sources of measurement uncertainty and compute error propagation formulas. We introduce the estimator for the unknown true state vector \(\widehat{p}^{\text{true}}\) by using regularization weights \(\lambda\) as \(\widehat{\widehat{p}}_{\lambda}\), and we wish to study the behavior of this estimator, which, in this section, is considered a \(N_{p}\)-dimensional stochastic random variable.
Under key assumptions on the (conditional) distribution of the residuals ([PERSON], 2007), which are assumed in this work, by the Gauss-Markov theorem the ordinary least squares estimator
\[\begin{split}\widehat{\widehat{p}}_{0}&=\ \big{(}M^{T}M \big{)}^{-1}M^{T}\widehat{b}\\ &=\ \widehat{p}^{\text{true}}+\big{(}M^{T}M\big{)}^{-1}M^{T}\widehat{ \varepsilon}\end{split} \tag{36}\]
is the best unbiased estimator for the 'true' state vector \(\widehat{p}^{\text{true}}\), in the sense that it minimizes the expected mean-squared error. It has a multivariate normal distribution with
\[\begin{split}\mathbb{E}\big{[}\widehat{\widehat{p}}_{0}\big{]}& =\ \widehat{p}^{\text{true}}\Rightarrow\text{Bias}\big{[}\widehat{ \widehat{p}}_{0}\big{]}=\mathbb{E}\big{[}\widehat{\widehat{p}}_{0}\big{]}- \widehat{p}^{\text{true}}=0\\ \text{Var}\big{[}\widehat{\widehat{p}}_{0}\big{]}& =\ \sigma^{2}\big{(}M^{T}M\big{)}^{-1}\end{split} \tag{37}\]
An unbiased estimator for the residual variance is given by the reduced chi-square statistic
\[\hat{s}^{2}=\frac{\widehat{\varepsilon}^{T}\widehat{\varepsilon}}{N_{b}-N_{p }}, \tag{38}\]
in the sense that \(\mathbb{E}\big{[}\hat{s}^{2}\big{]}=\sigma^{2}\), from which an estimate of \(\text{Var}\big{[}\widehat{\widehat{p}}_{0}\big{]}\) may be generated by substituting \(\hat{s}^{2}\) for \(\sigma^{2}\). Subsequently, confidence intervals for the flow field parameters can be computed.
Having established the properties of \(\widehat{\widehat{p}}_{0}\), let us analyze the behavior of the regularized estimator \(\widehat{\widehat{p}}_{\lambda}\). Following the derivation detailed in Appendix C, a characterization of the regularized estimator \(\widehat{\widehat{p}}_{\lambda}\) is given by
\[\widehat{\widehat{p}}_{\lambda}=\widehat{\widehat{p}}_{0}-\sigma^{2}\big{(}M^ {T}M+\sigma^{2}G_{\lambda}\big{)}^{-1}\big{(}G_{\lambda}\widehat{\widehat{p}} _{0}-\lambda_{bc}C_{bc}^{T}\widehat{\varepsilon}\big{)} \tag{39}\]
Recall that \(\widehat{\widehat{p}}_{0}\) is unbiased for \(\widehat{p}^{\text{true}}\). As a result, when applying the linear expectation operator, \(\widehat{\widehat{p}}_{\lambda}\) is a biased estimator with bias
\[\begin{split}\text{Bias}\big{[}\widehat{\widehat{p}}_{\lambda} \big{]}&=\ \mathbb{E}\big{[}\widehat{\widehat{p}}_{\lambda}\big{]}-\widehat{p}^{\text{true} }\\ &=\ -\sigma^{2}\big{(}M^{T}M+\sigma^{2}G_{\lambda}\big{)}^{-1}\big{(}G_{ \lambda}\widehat{p}^{\text{true}}-\lambda_{bc}C_{bc}^{T}\widehat{\varepsilon} \big{)}.\end{split} \tag{40}\]
The estimator bias is nonzero if any of the \(\lambda_{i}\) is nonzero, and we observe the residual variance \(\sigma^{2}\) controlling the relative importance of the data in the estimator bias.
Second, the variance - covariance matrix of \(\widehat{\widehat{p}}_{\lambda}\) can be computed by considering an equivalent characterization of \(\widehat{\widehat{p}}_{\lambda}\), directly obtainable from Equation 30:
\[\widehat{\widehat{p}}_{\lambda}=\big{(}M^{T}M+\sigma^{2}G_{\lambda}\big{)}^{- 1}\big{(}M^{T}\widehat{b}+\sigma^{2}\lambda_{bc}C_{bc}^{T}\widehat{\varepsilon }\big{)} \tag{41}\]
This expression is equivalent to Equation 39. Standard matrix-vector algebra for covariance matrices and the symmetry of various matrices involved, yields the covariance matrix of the estimator \(\widehat{\widehat{p}}_{\lambda}\):\[\begin{split}\text{Var}[\widehat{\widehat{p}}_{\,\lambda}]& =\,\sigma^{2}\Big{(}M^{T}M+\sigma^{2}G_{\lambda}\Big{)}^{-1}\,M^{T}M \big{(}M^{T}M+\sigma^{2}G_{\lambda}\big{)}^{-1}\\ &=\,\sigma^{2}\Big{(}M\big{(}M^{T}M+\sigma^{2}G_{\lambda}\big{)}^ {-1}\Big{)}^{T}M\big{(}M^{T}M+\sigma^{2}G_{\lambda}\big{)}^{-1}\\ &=\,\sigma^{2}\,M^{T}\,\tilde{M},\end{split} \tag{42}\]
with \(\tilde{M}\) representing a'regularized design matrix', coinciding with \(M\) if either \(\sigma^{2}=0\) or if all regularization weights are zero. Again, the residual variance may be estimated from Equation 38, from which an actual estimate of the estimator bias, covariance matrix and MSE may be computed. Knowledge of estimator bias and variance is important because of the matrix-valued bias-variance decomposition of the mean-squared error (MSE), defined as the expectation of the squared norm of the difference between estimator and parameter. More specifically:
\[\begin{split}\text{MSE}(\widehat{\widehat{p}}_{\,\lambda}, \widehat{p}^{\text{max}})&=\,\mathbb{E}\left[\,\left\|\,\widehat{ \widehat{p}}_{\,\lambda}-\widehat{p}^{\text{max}}\,\right\|^{2}\right]\\ &=\,\left\|\,\text{Bias}\big{[}\widehat{\widehat{p}}_{\,\lambda} \big{]}^{2}+\text{Tr}\big{(}\text{Var}\big{[}\widehat{\widehat{p}}_{\,\lambda }\big{]}\big{)},\right.\end{split} \tag{43}\]
where Tr denotes the trace operator. The above relation explains the results of the current work in the most concise way. Although hard to prove in more detail due to the complex nature of the matrices \(C_{ce},\dots,C_{gr}\), the characterizations of bias, variance-covariance and MSE associated to the regularized estimator \(\widehat{\widehat{p}}_{\,\lambda}\) given here confirm the observed patterns in Section 3 and can be used, and tuned using the \(\lambda_{i}\)'s, to further study and improve the inverse state estimation problem.
### Computational Aspects
The toolbox and regularization module presented in the present research operate on the basis of a number of computational choices. Some of these are discussed briefly.
#### 4.3.1 Pre-Processing
The vector of raw ADCP beam velocity data \(\vec{b}\), corresponding backscattering locations, GPS vessel track coordinates and knowledge of the local bathymetry are all prerequisites for the present framework. Care must especially be taken in transforming between vessel, Earth, cross-section and beam coordinates. A variety of pre-processing utilities is automated in the ADCPTools package ([PERSON], 2023).
#### 4.3.2 Computational Mesh
The conversion from raw beam velocity data to the model state vector is encoded in the model matrix \(M\). The dimension of this matrix as well as the state vector are dependent on the underlying empirical model (e.g., the number of tidal constituents and order of the spatial Taylor expansion), which is a choice left to the user. A key part of the empirical model is the computational, hexagonal mesh as introduced by [PERSON] et al. (2014). It is a hybrid between \(z\) and \(\sigma\)-coordinates. This ensures an approximately equal number of data is present in each cell, improving state estimation properties. However, the geometry of the mesh introduces a discretization error in the derivation of some of the regularization matrices. Rather than hexagonal cells, the regularization equations implicitly assume rectangular mesh cells in Cartesian \((x,y,z)\) space. The discretization error remains small if bathymetric gradients are small. We have the following trade-off.
* Low-resolution mesh: Many data points per mesh cell, fast computation times, less need for regularization. Less risk of over- and underfitting. However, this comes at the cost of reduced flow field estimation resolution, and increased mesh discretization errors.
* High-resolution mesh: Allows for high-resolution flow field estimation and decreases mesh discretization errors. This comes at the cost of there being fewer data points per mesh cell and slower computation times. The number of regularization equations is proportional to the number of mesh cells: The regularization matrices will become more important with respect to the data. This introduces a higher risk of both under- and overfitting: the generalization error and state vector covariance matrix has to be studied to avoid erroneous conclusions.
These trends qualitatively apply to any ADCP data set. Quantitatively, empirical optimal regularization weights may differ widely between data sets. Every data set brings its own challenges. The current work provides a unified framework, which may afterward be applied to specific data sets.
It is outside the scope of the present work to simultaneously optimize the computational mesh resolution and the regularization weights. However, one can visualize the combined behavior by choosing three representative mesh resolutions: coarse, moderate (used thus far) and fine, with the number of cells increasing fourfold when refining. This is depicted in Figure 8.
#### 4.3.3 Over- and Underfitting: Recipes on Choosing \(\lambda\)
Over- and underfitting pose a realistic pitfall in high-dimensional state estimation. How to regularize the problem in such a way that terms in the Reynolds-averaged momentum equation may be estimated smoothly, without losing the opportunity to be'surprised' by the data?
Regarding the model matrix \(M\) that incorporates the empirical model, a key assumption must be that the model is well-specified, that is, the dynamics encoded in \(M\) must at least asymptotically represent the real-world dynamics within an estuary or river. This includes theoretical considerations such as the number of tidal constituents that can realistically be resolved (the Nyquist criterion). The choice of empirical model in this work is very general: Mesh-based Taylor expansions may approximate any flow field for high enough mesh resolution. Regarding the regularization matrices encoding the conservation of mass \(C_{cc}\) and bottom and surface boundary conditions \(C_{bc}\), local truncation errors of spatial expansions and the truncation approach of neglecting high-order correlations between tidal constituents introduce an error that motivates not letting \(\lambda_{c}\) become too large. Lastly, the intersection of null spaces of the coherence matrix \(C_{fs}\) and consistency matrix \(C_{sp}\) consists of only partially constant state vectors across the computational cells. Hence, in regions of known flow variation in space (e.g., stratified flow), it is advisable to not increase \(\lambda_{s}\) too much, as it is known to be the most sensitive regularization weight from our experiments.
As stated in the previous paragraph, the higher the mesh resolution and resulting complexity of the empirical model, the higher the risk of overfitting. This problem calls for enhanced regularization, again introducing the risk of underfitting. This delicate balance calls for an optimization of regularization weights by minimization of the MSE of the regularized estimator (Equation 43). In practice, this is infeasible. Rather, the generalization error is an often-used heuristic tool to choose feasible regularization weights. A large generalization error is introduced by both underfitted (due to a large bias) and overfitted (due to a large variance) state vectors. The empirical validation metrics of Section 3 and analytical expressions in the current section can help in conducting a meaningful fit. These validation metrics are all included in the ADCPTools ([PERSON], 2023).
Figure 8: Generalization error for three different mesh resolutions as a function of the smoothing regularization weight \(\lambda_{s}\). Note the difference in vertical scales: A fine mesh resolution causes a highly ill-posed problem, needing more regularization. These experiments employed a fixed value of \(\lambda_{s}=5\) for the physics-informed constraints.
#### 4.3.4 Post-Processing
After regularized solutions to the state vector are obtained, a number of post-processing tools for visualization and validation can be employed. For instance, the state vector in the current work uses the cosine - sine representation of harmonic tidal constituents. A nonlinear mapping must be applied to obtain the amplitude - phase representation of tidal flow. Second, to estimate terms in the Reynolds-averaged Navier-Stokes equations, the state variables have to be further transformed. A number of these post-processing tools as well as scripts for merging different ADCP data sets for combined processing is contained in the ADCPTools ([PERSON], 2023).
### Application: Estimation of Terms in the Vertical Momentum Balance
As a proof of concept to demonstrate the benefit of the proposed method in estimating terms in the momentum balance, we compare estimates of the vertical acceleration term using the three regularization weight vectors provided in the present work. The vertical Reynolds-averaged momentum balance is given by
\[\frac{Dw}{Dt}=-\frac{1}{\rho}\frac{\partial p}{\partial z}+\frac{1}{\rho} \cdot\dot{r}-g, \tag{44}\]
where \(p\) is the pressure and \(\dot{r}\) the vertical component of the Reynolds stress tensor. Pressure can be decomposed in a hydrostatic and a non-hydrostatic component \(p=p_{h}(z)\ +\ p_{\mathrm{ul}}(x,y,z)\). The hydrostatic pressure is derived from the hydrostatic balance
\[\frac{1}{\rho}\frac{\partial p_{h}}{\partial z}=-g. \tag{45}\]
The equation for the non-hydrostatic pressure is obtained after subtracting Equation 45 from Equation 44:
\[\frac{1}{\rho}\frac{\partial p_{\mathrm{ul}}}{\partial z}=-\frac{Dw}{Dt}+ \frac{1}{\rho}\
abla\cdot\dot{r}^{2}, \tag{46}\]
Subsequently, the magnitude of the terms in the hydrostatic balance \(\big{(}\sim\!10\ \mathrm{m}/\mathrm{s}^{2}\big{)}\) to the magnitude of the instantaneous acceleration term in the RANS equations, which can be obtained accurately using the presented method:
\[\frac{Dw}{Dt}=\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v \frac{\partial w}{\partial y}+\frac{w}{H}\frac{\partial w}{\partial\sigma}, \tag{47}\]
Higher-order contributions arising from the \(z\ -\ \sigma\) coordinate transformation are neglected in the characterization above. Terms in the above equation are all contained in the state vector \(\vec{p}\). The term is plotted in Figure 9.
Figure 9: Estimate of the instantaneous vertical acceleration term of the flow \(\left[\mathrm{m}/\mathrm{s}^{2}\right]\) in the Hartel Canal at 12:00 \(\sigma\)clock in the afternoon, estimated using the three different regularization weights of Section 3. The figure demonstrates a negligible contribution of the vertical acceleration terms to the vertical momentum balance, illustrated by the difference in order of magnitude between the unregularized and regularized estimates. The depicted magnitude is representative of the term’s magnitude throughout the measurement campaign.
Assuming the magnitude of the vertical acceleration term to be indicative of the importance of non-hydrostatic effects in the flow, we may conclude from Figure 9, together with the arguments from Section 3 in which the validity of the proposed method was studied, that non-hydrostatic effects are small in the flow.
### Outlook
The present method was applied to cross-sectional repeat transect data. However, there is no restriction to semi-two-dimensional data such as the data set employed here. In principle, this method may be applied to a wide class of geophysical flows in which ADCP field campaigns may be used. The empirical model matrix \(M\) can be formulated for any experiment, depending on the choice of empirical model. Regularization matrices may encode different constraints, depending on a priori available information. Regarding the time-independence of the state vector, the presented method can be used in all sorts of estuarine or riverine environments, as long as there is sufficient knowledge of temporal dynamics to project the data on. In that sense, also stationary or short-duration experiments may benefit from the present approach. All regularization matrices may be employed to achieve a more reliable estimate of turbulence-averaged tidal and subtidal flows and gradients, and relative to the unregularized inverse problem, a finer mesh may be constructed, allowing for high-resolution flow inspection. In turn, this may help in estimating terms in the momentum balance in more detail. The improved toolbox presented in this research may be valuable for academics and researchers that often conduct ADCP field campaigns and especially wish to have a high degree of control over ADCP processing.
## 5 Conclusion
We introduce a method capable of solving the three-dimensional, turbulence averaged velocity field from raw ADCP beam velocity data, while including prior knowledge about the physics governing the flow. Continuity, kinematic boundary conditions, spatial coherence and temporal dynamics can help constrain the solved velocity field yielding more realistic solutions. Unlike many existing methods and data processing procedures, the degree of adherence of the solved flow field to prior knowledge is explicitly included and can be tuned a priori and validated a posteriori. The estimated uncertainty gives direct insight in the capability to resolve flow field parameters from the measured data. This dramatically eases comparison of field based results with conceptual and numerical models.
The regularized estimator for the three-dimensional flow amplitudes, phases and their gradients introduces a bias with respect to the data, but has better generalization, robustness and physical properties. The performance of the proposed estimator is verified using multiple generalized cross-validation, empirical sensitivity analyses and bias-variance analysis.
The proposed method is applied to cross-sectional repeat transect data and can be extended to general field campaigns. The method is contained in the open-source toolbox ADCPTools ([PERSON], 2023).
## Appendix A Derivation of Empirical Model Matrix M
Equation 8 may be written as a matrix - vector product, in which the entries of the matrix are measurable by the ADCP and the vector elements are 'parameters' to be estimated: the state variables. Capturing the spatially uniform and first order terms in a vector \(\mathbf{p}\), the above equation may be written out as
\[\begin{split} f_{y_{0}}^{x}(\mathbf{r})&=p_{y_{0}, i}^{x,a}+\left(p_{y_{n},i}^{x,a}\;\;p_{n_{x},i}^{x,a}\right)\;J\mathbf{r}+O \big{(}\|d\mathbf{r}\|^{2}\big{)}\\ &=p_{y_{0},i}^{x,a}+p_{y_{n},i}^{x,a}dx+p_{y_{n},i}^{x,a}dy+p_{y_ {n},i}^{x,a}d\sigma+O\big{(}\|d\mathbf{r}\|^{2}\big{)}\;\;=\;\big{(}1\;\;\;dx \;\;\;dy\;\;\;\;\;d\mathbf{e}\big{)}\;\mathbf{p}_{y_{0},i}^{x,a}=S(d\mathbf{ r})\mathbf{p}_{y_{0},i}^{x,a}\,,\end{split} \tag{1}\]
where the second-order residual term was neglected. Herein, the \(1\times 4\) matrix name \(S\) refers to the spatial part (hence \(S\)) of the cosine-amplitude (hence \(a\)) of the \(u\)-component (hence \(x\)) of the flow velocity of the \(n\)-th constituent included, within cell \(j\). Similarly, we write for the sine-amplitude in (6)
\[g_{y_{0}}^{x}(\mathbf{r})=S(d\mathbf{r})\mathbf{p}_{y_{0}}^{x,b} \tag{2}\]
with \(n\geq 1\). Substitution of Equation 1 and Equation 2 in Equation 6 leads to \[u(t,\mathbf{r})=S(d\mathbf{r})\mathbf{p}_{ij}^{c+}+\sum_{n=4}^{N_{c}}S(d\mathbf{r}) \mathbf{p}_{ij}^{c+}\cos\omega_{n}t+S(d\mathbf{r})\mathbf{p}_{ij}^{c,b}\ \sin\omega_{n}t \tag{10}\]
which can be written using Kronecker product notation as
\[u(t,\mathbf{r}) = \left(T(t)\otimes S(\mathbf{r})\right)\mathbf{p}_{j}^{i}=m_{j}^{T }(t,\mathbf{r})\mathbf{p}_{j}^{i}, \tag{11}\]
where the \(1\ \times\ (2N_{i}\ +\ 1)\) matrix \(T(t)\) is given by
\[T_{j}^{c}(t) = \left(1\quad\cos\omega_{1}t\quad\sin\omega_{1}t\quad \quad\cos \omega_{N_{i}}t\quad\sin\omega_{N_{i}}t\right) \tag{12}\]
and \(m^{T}\) has size \(1\ \times\ (14N_{i}\ +\ 7)\). Taking together the mappings for the \(x,y\) and \(z\) components of flow velocity:
\[\mathbf{u}(t,\mathbf{r}) = \begin{pmatrix}m^{T}(t,\mathbf{r})&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&m^{T}(t,\mathbf{r})&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&m^{T}(t,\mathbf{r})\end{pmatrix}\mathbf{p}_{j}=M(t, \mathbf{r})\mathbf{p}_{j} \tag{13}\]
Combination with Equation 1 gives for a single measured radial velocity component. \(b_{i}\)
\[b_{i} = \mathbf{q}_{i}^{T}\mathbf{u}_{j}(t_{i},\mathbf{r}_{i}) \tag{14}\] \[= \mathbf{q}_{i}^{T}M_{i}(t,\mathbf{r})\mathbf{p}_{j}\] (15) \[= \left(q_{i}^{T}m^{T}(t_{i},\mathbf{r}_{i})\quad q_{i}^{T}m^{T}(t _{i},\mathbf{r}_{i})\quad q_{i}^{T}m^{T}(t_{i},\mathbf{r}_{i})\right)\mathbf{ p}_{j} \tag{16}\]
Collecting all radial velocities within a specific mesh cell \(c\) in a vector \(\mathbf{b}_{c}\), we write Equation 8 as a linear system of \(n_{c}\) equations with \(n_{p}\) unknowns:
\[\mathbf{b}_{c}=M_{c}\mathbf{p}_{c}\ \ \text{for}\ c\in\{1,\ldots,N_{c}\} \tag{17}\]
The procedure is finalized by collecting all beam velocity vectors \(\mathbf{b}_{c}\) in one vector \(\vec{b}\), assemble the corresponding block diagonal empirical model matrix \(M\) from the \(M_{c}\) matrices and collecting all cell-based state vectors \(\mathbf{p}_{i}\) in one large state vector \(\vec{p}\), for \(c=1,\ldots,N_{c}\). We obtain a system of equations, where \(M\) has size \(N_{s}\ \times\ N_{c}n_{p}=N_{s}\ \times\ N_{p}\). This is the model equation Equation 9 in the main text.
## Appendix B Derivation of Continuity Constraints in \(\sigma\) Coordinates
In the present section, the Reynolds-averaged continuity equation is transformed to a \(\sigma\)-coordinate system in order to be used in the estimation of tidal flow field parameters from ADCP data. In standard \(x,y,z\) coordinates, the continuity equation reads
\[\
abla\cdot\mathbf{u}=0 \tag{18}\]
The method outlined in the present work operates on the basis of \(\sigma\) coordinates, which is a transformed vertical coordinate. Temporal and horizontal coordinates are unaffected by the coordinate transformation. However, they are implicitly coupled by the vertical \(\sigma\) coordinate:
\[t = t \tag{19}\] \[x = x\] (20) \[y = y \tag{21}\]\[\sigma=\frac{z-z_{b}(x,y)}{\zeta(t,x,y)-z_{b}(x,y)} \tag{10}\]
with inverse transformation
\[\sigma(t,x,y,z)=\frac{z-z_{b}(x,y)}{\zeta(t,x,y)-z_{b}(x,y)}\Longleftrightarrow z =z_{b}+(\zeta-z_{b})\sigma=z_{b}+H\sigma \tag{11}\]
The above spatial coordinate transform has an associated Jacobian matrix:
\[J=\frac{\partial(x,y,z)}{\partial(x,y,\sigma)}=\begin{pmatrix}\frac{\partial x }{\partial x}&\frac{\partial x}{\partial y}&\frac{\partial x}{\partial\sigma} \\ \frac{\partial y}{\partial x}&\frac{\partial y}{\partial y}&\frac{\partial y}{ \partial z}\\ \frac{\partial z}{\partial x}&\frac{\partial z}{\partial y}&\frac{\partial z} {\partial\sigma}\\ \end{pmatrix}=\begin{pmatrix}1&0&0\\ 0&1&0\\ z_{bx}+\sigma H_{x}&z_{by}+\sigma H_{y}&H\\ \end{pmatrix} \tag{12}\]
The Jacobian determinant of the above coordinate transform is given by the product of diagonal elements of the Jacobian matrix:
\[|J|=\det(J)=H>0 \tag{13}\]
Inverting the above Jacobian matrix yields the Jacobian matrix of inverse transform
\[J^{-1}=\frac{\partial(x,y,\sigma)}{\partial(x,y,z)}=\begin{pmatrix}\frac{ \partial x}{\partial x}&\frac{\partial x}{\partial y}&\frac{\partial x}{ \partial z}\\ \frac{\partial y}{\partial x}&\frac{\partial y}{\partial y}&\frac{\partial y}{ \partial z}\\ \frac{\partial\sigma}{\partial x}&\frac{\partial\sigma}{\partial y}&\frac{ \partial\sigma}{\partial z}\\ \end{pmatrix}=\begin{pmatrix}1&0&0\\ 0&1&0\\ -\frac{z_{bx}+\sigma H_{x}}{H}&-\frac{z_{by}+\sigma H_{y}}{H}&\frac{1}{H}\\ \end{pmatrix} \tag{14}\]
Partial derivatives in Cartesian space are transformed to partial derivatives in transformed space with the help of Jacobian matrices provided above. First, we have
\[\frac{\partial\sigma}{\partial t}=-\frac{\sigma}{H^{\alpha_{x}}} \tag{15}\]
From this, we obtain for any differentiable function \(f\)
\[\frac{\partial f}{\partial t}=\frac{\partial f}{\partial t}\frac{\partial t} {\partial t}+\frac{\partial f}{\partial\sigma}\frac{\partial\sigma}{\partial t }=\frac{\partial f}{\partial t}-\frac{\sigma}{H^{\alpha_{x}}}\frac{\partial f }{\partial\sigma} \tag{16}\]
\[\frac{\partial f}{\partial x}=\frac{\partial f}{\partial x}\frac{\partial x} {\partial x}+\frac{\partial f}{\partial\sigma}\frac{\partial\sigma}{\partial x }=\frac{\partial f}{\partial x}-\frac{z_{bx}+\sigma H_{x}}{H}\frac{\partial f }{\partial\sigma} \tag{17}\]
\[\frac{\partial f}{\partial y}=\frac{\partial f}{\partial y}\frac{\partial y} {\partial y}+\frac{\partial f}{\partial\sigma}\frac{\partial\sigma}{\partial y }=\frac{\partial f}{\partial y}-\frac{z_{by}+\sigma H_{y}}{H}\frac{\partial f }{\partial\sigma} \tag{18}\]
\[\frac{\partial f}{\partial z}=\frac{\partial f}{\partial\sigma}\frac{\partial \sigma}{\partial z}=\frac{1}{H}\frac{\partial f}{\partial\sigma} \tag{19}\]Applying the above transformation to Equation 1 and multiplying by the local depth \(H\), we obtain Equation 12. To use this equation in the estimation of the state vector, we use a truncation approach to convert the above nonlinear, time-dependent equation to a linear equation in \(\widetilde{p}\). First, since \(H=\zeta-z_{b}\):
\[\left(\zeta-z_{b}\right)u_{+}-\left(z_{bx}+\sigma\big{(}z_{x}-z_{bx}\big{)} \right)u_{+}+\left(\zeta-z_{b}\right)v_{y}-\left(z_{by}+\sigma\big{(}z_{y}-z_{ by}\big{)}\right)v_{x}+w_{x}=0. \tag{11}\]
Substitution of Equation 2 and neglecting water level gradients by assuming that bathymetric gradients dominate depth gradients, the local water depth and its gradient is given by
\[\begin{split} H(t,x,y)&=\,H_{0}(x,y)+\sum_{n=4}^{N }f_{n}^{\zeta}\cos\left(\omega_{n}t\right)+g_{n}^{\zeta}\sin\left(\omega_{n}t \right)\\ H_{x}(t,x,y)&=\,\frac{\partial H_{0}}{\partial x }(x,y)=-\frac{\partial z_{b}}{\partial x}=-z_{bx}\\ H_{y}(t,x,y)&=\,\frac{\partial H_{0}}{\partial x }(x,y)=-\frac{\partial z_{b}}{\partial y}=-z_{by}\end{split} \tag{12}\]
with \(H_{0}(x,y)=\hat{f}_{0}^{\zeta}-z_{b}(x,y)\). Consequently, inserting the above expressions for all tidal constituents indexed by \(n\), and neglecting nonlinear temporal cross-correlations, yields Equations 13 and 14.
## Appendix C Derivation of Regularized Estimator Characterizations
To derive a useful characterization of the regularized estimator \(\widehat{\widehat{p}}_{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\
## Data and Software Availability Statement
Software for this research is available in the in-text data citation reference [PERSON] and Jongbloed (2023) under the GNU General Public License v3.0. Scripts to recreate the figures and processed data using the software can be found in the in-text data citation reference [PERSON] (2024). The dataset for this research is available in the in-text data citation reference [PERSON] et al. (2023), under the GNU General Public License v3.0.
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wiley/fdec7061_44ec_4fea_94b9_0d41d6ece735.md | Cold surge invading the Beijing 2022 Winter Olympic Competition Zones and the predictability in BCC-AGCM model
[PERSON] [PERSON]
###### Abstract
The 24 th Olympic and Paralympic Winter Games will be held at three competition zones in North China. The cold surge is considered as the most dominant weather affecting the game schedule by the Organizing Committee of Beijing Olympic Games. In this article, both the frequency of 124 cold surge cases invading the competition zones and the corresponding atmospheric circulation during the winters of 1985-2020 are first analyzed. The results show that the frequency has not been reduced by the global warming. On the contrary, it has been increasing slightly in recent decade. By verifying the forecast skill of temperature drop at the zones in Beijing Climate Center-Atmospheric General Circulation Model (version 2.2), it is found that the average efficient forecast leading time with persistent temperature drop exceeding 1\({}^{\circ}\)C is about 7 days, but significant differences exist among the individual cases. The 20 best forecasts and the 20 worst forecasts were selected for further analysis. In the 20 worst forecasts, the cold surge processes cannot be forecasted even 1 day in advance. It is mainly due to the great deviation of the simulated circulation from the observation, especially the failure to forecast the enhancement of the Siberian High especially in its southeast part before the cold surge occurrence. While in the 20 best forecasts, the model can capture the cold surges 9 days before the occurrence, owing to its skill in forecasting the positive sea level pressure anomalies from the southern Barents Sea and the Kara Sea to eastern China. Above evaluations can provide useful information to the forecast of cold surge invading the competition zones beyond 1 week.
BCC-AGCM model, cold surge, competition zones of Beijing Olympic and Paralympic Winter Games, Siberian High 202122103
## 1 Introduction
The cold surge is one of the most common disastrous weather in winter in the middle and high latitudes of the Northern Hemisphere. Its frequency decreased remarkably since the 1980s due to global warming. However, recent studies show that extreme cold events in the middle latitudes of the Northern Hemisphere have been increasing again since the early 21 st century, when the global warming slows down. Both statistical results ([PERSON] _et al._, 2015; [PERSON] _et al._, 2018) and typical cases in Europe ([PERSON] _et al._, 2013; [PERSON] _et al._, 2015), North America ([PERSON] _et al._, 2016; National Weather Service, 2019) and Asia ([PERSON] and [PERSON], 2019; [PERSON] _et al._, 2019) indicate that the cold surges and cold winters in above regions occur more frequently in the latest decade than in the first decade of the 21 st century, which can be partly attributed to the recent Arctic warming or the Arctic amplification caused by the rapid loss of the Arctic sea ice ([PERSON] _et al._, 2012, 2020; [PERSON] _et al._, 2012; [PERSON] _et al._, 2013; [PERSON] _et al._, 2014; [PERSON] _et al._, 2018; [PERSON] _et al._, 2019). In China, the extremely strong cold surges are also more frequent during this period, resulting in severe low-temperature and freezing disasters, which badly harm the national economy and people's lives ([PERSON], 2019). For example, China experienced an unprecedented low-temperature and snowstorm disaster in early 2008 caused by four successive cold surges, resulting in 133 deaths and direct economic losses of over 20 billion dollars ([PERSON] and [PERSON], 2008; National Climate Center, 2008; [PERSON] _et al._, 2009). In January 2016, the extreme \"Boss-level\" cold surge also caused similar economic losses ([PERSON] _et al._, 2016; [PERSON] _et al._, 2018; [PERSON] and [PERSON], 2019). [PERSON] (2015) pointed out that five out of the seven regions in China will suffer from severe cold surges and freezing disasters in the future under the warming scenarios. Therefore, forecast of the cold surges is quite important in China.
In the 1950s, the pioneering studies of [PERSON] (1956) and [PERSON] (1959) revealed the sources and three tracks of the cold surges invading China. [PERSON] _et al._ (2010) also pointed out that the sources of cold air affecting China could be traced back to the Barents Sea, the Kara Sea and southern Iceland, with the strongest and the most frequent cold air from the Barents Sea. The cold air from the three sources converges in western Siberia and strengthens the Siberian High, which affects East Asia through three paths ([PERSON] and [PERSON], 1987). These results provided synoptic basics for the cold surge forecasts in the 1980s and 1990s in China ([PERSON], 1985; [PERSON] and [PERSON], 1985; [PERSON] _et al._, 1987; [PERSON], 1996). In the 21 st century, numerical models have become the primary tool for the forecast and early warning of cold surges. However, the numerical models perform poorly in directly forecasting the events with a leading time exceeding 1 week, even for the extreme case ([PERSON] _et al._, 2003; [PERSON] _et al._, 2017).
Recently, long-term forecasts of cold surge events in China based on the interpretation and application of the climate model products have been conducted. The climate models can well reproduce the basic characteristics of the East Asian winter monsoon ([PERSON] _et al._, 2016; [PERSON] _et al._, 2017), and can also capture the East Asian cold surges 2 weeks in advance ([PERSON] _et al._, 2019). However, the forecast skill differs greatly owing to different verification and evaluation criteria utilized in different studies. For example, [PERSON] _et al._ (2017) focused on the annual number of cold surge days and events in East Asia, which reflects the prediction skills for the seasonal large-scale circulation system rather than the synoptic cold surge process. Besides, the skill is also related to the cases selected and the predictability of the influencing circulation systems of cold surges. For example, [PERSON] _et al._ (2011) classified East Asian cold surges into wave-train type and blocking type. In both of the observation and climate models, the blocking cold surges tend to be more intense and last longer compared to the wave-train type. These researches suggest that the cold surge forecast should focus on not only the temperature itself but also the influencing circulations.
From 4 to 20 February and from 4 to 13 March 2022, the 24 th Olympic and Paralympic Winter Games will be hosted in Beijing, China, respectively (BJ2022 in the following). According to the weather and wind analysis report issued by the Beijing Organizing Committee of the Olympic Games, there are six weather patterns notably affecting the game schedule in total, four of which are closely related to cold surges ([PERSON] and [PERSON], 2019). Owing to the influence of the East Asian winter monsoon, the three competition zones of BJ2022 (Beijing, Yanqing and Zhangjiakou) are all vulnerable to the cold extremes. Recently, [PERSON] _et al._ (2020a) explored that the pre-signal of cold surges invading the competition zones of BJ2022 from the Novaya Zemlya could have a leading influence exceeding 10 days. Therefore, forecast skills of influencing circulations should be considered when analyzing the intra-seasonal forecast skills of cold surges.
The Beijing Climate Center-Atmospheric General Circulation Model (BCC-AGCM) has become one of the main operational models for the sub-seasonal prediction in China. The simulation results well demonstrate the actual geographic distributions and the prominent annual cycle characteristics of the variables ([PERSON] _et al._, 2009; [PERSON] _et al._, 2016). The model can reproduce the basic patterns of the winter circulations in the Northern Hemisphere and the dominant mode ([PERSON] _et al._, 2012). It is also skill in forecasting severalextreme temperature indices in China, including the daily minimum temperature associated with the cold surge ([PERSON] _et al._, 2012). Therefore, in this article, we first evaluate the simulations of the latest version of the model (BCC-AGCM 2.2) for the 124 cold surge events at the BJ2022 competition zones during the winters of **1985-2020**. Then we analyze the forecast skills for the influencing circulation in the cold surge events with a leading time from 1 day to 20 days, aiming to provide useful information of the cold surge forecast based on dynamic models.
## 2 Data and method
The BCC-AGCM 2.2 is an improved version of the Community Atmosphere Model Version 3 (CAM3) from the National Center for Atmospheric Research (NCAR) ([PERSON] _et al._, 2006). Its simulation of intra-seasonal variations is significantly improved compared with CAM3. The model has a horizontal resolution of T106 and includes 26 vertical levels ([PERSON] _et al._, 2014). The initial field of the model is derived from the T639 operational forecast model developed by the China National Meteorological Center. The optimal interpolated sea surface temperature (SST) data is adopted ([PERSON] _et al._, 2002). The model hindcast starts from 1 January 1983, with the forecast length of 55 days in each simulation. On each day, the forecasts are conducted four times at 00Z, 06Z, 12Z and 18Z, respectively. The arithmetical average of all the four members is calculated as the daily average. In the analysis, the daily geopotential height (GPH) at 500 hPa, the sea level pressure (SLP) and the air temperature in the hindcast are applied. Daily data of SLP, 500 hPa GPH and 850 hPa horizontal winds are extracted from the NCEP/NCAR reanalysis project and used as the observation ([PERSON] _et al._, 1996; [PERSON] _et al._, 2001).
In this article, three meteorological stations (WMO station code #54406, 54433 and 54401) are used to represent the three competition zones of BJ2022, respectively ([PERSON] _et al._, 2020a). The daily average temperature data are used to calculate the temperature drop over two successive days in each winter. Here the winter of 1985 denotes December 1984-January 1985-February 1985.
## 3 Cold surge frequencies at BJ2022 competition zones and the atmospheric circulations
Intra-seasonal and interannual variations of the cold surge frequencies at BJ2022 competition zones during the winters of 1985-2020 are first analyzed. Due to their much high consistency of daily variability, here we use the average of air temperature at above three stations instead of individual station. Since the top 10% threshold of daily temperature drop magnitude is about 3.8\({}^{\circ}\)C, in the following analysis a cold surge event is identified if the drop is over 4\({}^{\circ}\)C, then 124 cold surge events are obtained (Figure 1). In the 124 cases, temperature drop (negative temperature change between two successive days) occurred in all stations, and the occurrence probability of cold surge events in each station was about 70-80%. Among the 124 events, the frequencies with temperature drop magnitude of 4-5\({}^{\circ}\)C, 5-6\({}^{\circ}\)C, 6-7\({}^{\circ}\)C and over 7\({}^{\circ}\)C are 65, 29, 15 and 15, respectively. The upper left panel of Figure 1 shows the 36-year cumulative frequency in each day. In the first half of winter (December to early January), the frequency demonstrates a slight decreasing change, while in the second half the frequency shows fluctuation. The annual frequency of cold surge events (right panel) shows an average number of 3.4 during 1985-2020. It displays a significant interannual variation, with the maximum number of 7 in 2009 and 2016, and the minimum number of 1 in 1989, 2002 and 2008. Moreover, the frequency has been increasing slightly since 2009. The average numbers during 1985-2008 and 2009-2020 are 3.2 and 4, respectively. This result is consistent with the cold surge frequency in North China ([PERSON] _et al._, 2020b).
To better characterize the atmospheric circulation caused the cold surge event at the competition zones, a composition analysis on the occurring day of the 124 cases is performed (Figure 2). Before the composition, the correlation coefficients between different East Asian winter monsoon indices and the temperature changes in the competition zones are compared. The indices include the East Asian trough, the Siberian High and the westerly jet index. It could be found that the Siberian High has the strongest correlation with a leading time of 2 days (figures not shown). This also indicates that the Siberian High is a dominant factor, which is consistent with the result of [PERSON] _et al._ (2020c). Therefore, only the SLP field is provided here. According to the climatological position, here the Siberian High is defined as the average SLP in (40-60\({}^{\circ}\)N, 80-120\({}^{\circ}\)E), as shown by the dashed box in Figure 2. The typical circulation pattern corresponding to the cold surge is characterized with two positive SLP anomaly centers from North China to Mongolia and from Novosibirsk to Barents Sea, accompanied with a negative anomaly center over Japan and its eastern ocean, that is, the west part of the Aleutian low pressure. In winter, the cold high dominates over Eurasia continent and the warm low dominates over the Pacific Ocean. Therefore, the SLP anomaly distribution in Figure 2 is favorable for increasing the land-sea pressure contrast, contributing to the deepening of the East Asian trough in the middle troposphere and the enhancement of the strong northerly wind. Composition analysis of the 500 hPa GPH anomaly (figure not shown) indicates that the values between the negative and positive SLP anomaly centers shown in Figure 2 is less than \(-\)80 gpm. The location of this negative GPH anomaly center is consistent with that of the climatic East Asian trough. The average anomaly of the 850 hPa northwesterly wind in the west of the trough exceeds 3 m\(\cdot\)s\({}^{-1}\) (figure not shown). This circulation pattern is favorable for the cold air invading the competition zones along the northwesterly airflow.
## 4 Verification of the cold surge events at Bj2022 competition zones forecasted by bcc-agcm 2.2
Based on the selected 124 cases, the forecast skill of the BCC-AGCM 2.2 is evaluated with a leading time of 1-20 days. Figure 3 presents the forecast of the average daily temperature change for the 124 events, as well as the average of the 20 best and the 20 worst forecasts. The efficient leading forecast time is defined as the maximum leading days when the model can continuously forecast the cold surge events. Since the daily variability of the predictand in the model decreases rapidly with the increasing of the leading time (figure not shown), the threshold of temperature drop in the model is set to 1\({}^{\circ}\)C. For a cold surge event, if the model continuously forecasts a negative temperature change below \(-\)1\({}^{\circ}\)C (temperature drop over 1\({}^{\circ}\)C) with the leading time less than or equal to \(N\) days, but forecasts a positive temperature change (temperature increase) or a slight temperature drop less than 1\({}^{\circ}\)C on the \(N+1\) days in advance, the efficient forecast leading time is \(N\). Based on this method, the model forecast and efficient leading time for all the 124 events is calculated and ranked. The longer forecast efficiency indicates an earlier forecast of the cold surge,Figure 3: Average daily temperature change for the 124 cold surge cases (histogram), the 20 best forecasts (solid line) and the 20 worst forecasts (dashed line) with the leading time of 1–20 days by the BCC-AGCM 2.2. The dotted line indicates \(-1^{\circ}\)C (units: \({}^{\circ}\)C)
which can provide an earlier warning for the possible future impacts. Conversely, the shorter forecast leading time means a later response of the model to the cold surge. The 20 cases with the longest forecast leading time are defined as best forecasts and the 20 cases with the shortest leading time are defined as worst forecasts.
The histogram in Figure 3 shows the average daily temperature change for all the 124 cold surge events forecasted by the model. It is noted that the temperature change in the model generally decreases with the increasing of the leading time in the first 10 days, at a decreasing rate of 0.45\({}^{\circ}\)C-day\({}^{-1}\). The model can continuously forecast the 2\({}^{\circ}\)C temperature drop within 5 days in advance and the 1\({}^{\circ}\)C drop within 7 days. This is generally consistent with previous studies ([PERSON] _et al._, 2003; [PERSON] _et al._, 2017). Beyond 10 days, although the forecasted average temperature change of the 124 cases is still negative, its intensity is significantly weaker than that within 10 days. In the 20 best forecasts, the model produces significantly stronger temperature change. The temperature drop magnitude decreases slowly within the first 9 days compared with the 124-case mean. In the 20 best forecast type, the average forecast leading time for the 1\({}^{\circ}\)C temperature drop can be up to 15 days. Conversely, the 20 worst forecasts demonstrate warming even when the leading time is 1 day. The most extreme cases with the 30 greatest temperature drops are also analyzed. The average leading time in these cases is 7 days, which is similar with the 124-case average.
The circulations in the good forecasts and the poor forecasts are analyzed to figure out the reasons for the significant difference in their forecasts. Figure 4 presents the SLP and its anomalies averaged in the 20 worst forecasts and the 20 best forecasts with the leading time of 1 day. Comparing it with Figure 2, we can find a significant difference in the SLP between the two types of forecasts. There are negative anomalies over most regions of East Asia in the 20 worst forecasts. Specifically, the anomaly is below \(-4\) hPa on the east of the Siberian High, which is the most dominant atmospheric circulation affecting the cold surge at the zones. This anomaly pattern weakens and even reverses the land-sea pressure gradient in the middle latitudes of East Asia in winter, which is not favorable for the southward movement of the cold air. It is the reason for the incorrect forecast even 1 day in advance. On the contrary to Figure 4a, the SLP anomalies in the 20 best forecasts are all positive over the north of 40\({}^{\circ}\)N in Eurasia (Figure 4b). The pressure anomaly exceeds 4 hPa in the central Siberian High, which is higher than the observation in Figure 2. The negative SLP anomaly to the east of the Sea of Japan in the observation is not forecasted in Figure 4b, suggesting that the accurate forecast of the Siberian High is the key for forecasting the cold surge at the zone.
Figure 5 presents the SLP and its anomalies in the 20 best forecasts, with the leading time of 5, 7, 9 and 11 days. The forecasted circulation anomalies with the leading time of 5 and 7 days are comparable to those in Figure 4b, demonstrating positive SLP anomalies dominant from the Ural Mountains to Lake Baikal. The SLP anomaly exceeds 4 hPa in the eastern part of the Siberian High. The forecast field with the leading time of 9 days shows that the area of positive SLP anomalies is located significantly more northwestward than the observation, so the Siberian High is weaker than the observed high. Since the land-sea pressure contrast corresponding to the cold surge in winter is mainly determined by the Siberian High, the temperature drop magnitude is weakened in the model due to the northwestward movement of the high pressure and the intensity decrease in its eastern part. Even in the best forecasts, the average temperature drop magnitude is only 1.5\({}^{\circ}\)C (Figure 3). In the forecasted circulation with the leading time of 11 days, the SLP anomalies to the east of Lake Baikal transform from positive to negative, and the Siberian High is nearly normal. From Figure 5, it could also be found that the SLP over the south of Barents Sea has a 4-day leading influence on the Siberian High. That means the high SLP center has a southeastward propagation from the south of Barents Sea, which is similar with the 500-hPa cyclone center in [PERSON] _et al._ (2020). Statistical results of the paths of all the 124 cases indicate that the northwest and west paths can account for about 78.5%, which also demonstrates the importance of the Siberian High in causing the cold surges invading the zones. Forecast skill of the Siberian High is also assessed between the 20 best and 20 worst forecasts. In the 20 best cases, the model can well capture the positive daily pressure change (\(>1\) hPa) since 9 days before the cold surge occurrence (figure not shown). However, in the 20 worst cases, the intensity of the Siberian High in the model is quite weak even with a leading time of 1 day. Thus, the forecast skill of the model for the cold surge at BJ2022 competition zone depends on its ability to predict the strength of the eastern Siberian High. So it could be considered that the forecast of Siberian High rather than other circulation members determines the efficient skill or leading time of the cold surges in BCC-AGCM 2.2.
## 5. Conclusions and Discussion
According to the weather report issued by the Beijing Organizing Committee of BJ2022, six weather patterns can notably affect the game schedule in total, four of which are closely related to cold surge events ([PERSON] and [PERSON], 2019). It has great importance to analyze the predictability of cold surge events at the BJ2022 competition zones by dynamic models. Therefore, the intra-seasonal and interannual variations of the cold surge frequency during 1985-2020 at the competition zones and the corresponding atmospheric circulation are first analyzed. It can be found that the cold surge frequency in winter has not been reduced with the global warming. On the contrary, it has been increasing slightly since 2009, with the average frequency increasing from 3.2 during 1985-2008 to 4.0 after 2009. When a cold surge event occurs at the zones, positive SLP anomalies dominate from the Barents Sea and the southern Kara Sea to eastern China, while negative SLP anomalies dominate to the east of Japan. In the middle troposphere the geopotential height anomalies usually demonstrate a positive center in Central Siberia and a negative center over the Sea of Japan. The circulation pattern is favorable for a further increase of the land-sea pressure gradient in winter, thereby prompting the high-latitude northerly wind to invade southward to China and inducing cold surge at the zones.
By further analyzing the efficient forecast leading time of the BCC-AGCM 2.2 for the cold surges at the zones, we found that the average forecast leading time in the model for the temperature drop exceeding \(1^{\circ}\)C is about 7 days, but there are significant differences among the individual cases. In the 20 worst forecasts, the cold surge processes cannot be forecasted even 1 day in advance. It is mainly due to the great deviation of the simulated circulation from the observation, especially the failure to forecast the strengthening of the SLP in the southeastern side of Siberian High before the cold surge. In the 20 best forecasts, the drop over \(1^{\circ}\)C can be forecasted 15 days in advance, and the \(2^{\circ}\)C drop can be forecasted 8 days in advance. In the good forecasts, the model well captures the positive SLP anomalies from the southern Barents Sea and the Kara Sea to eastern China. These circulation anomalies can originate and persist 9 days in advance, which is probably the main reason. The above evaluations can be the reference for the model-based forecasts of cold surge on the leading time over a week. Further analysis reveals that, even in the 20 best forecasts, the model fails to reproduce the distribution of geopotential height anomalies at middle levels. It falsely distributes the positive and negative anomaly centers, especially the East Asian trough.
The cold surge invading northern China has complex paths and different duration length ([PERSON] _et al._, 2020c). Due to the limited area of the BJ2022 competition zones, the cold surge influence usually lasts only 1 day and then moves eastward or southward. Thus, only the occurring day of cold surge invasion is considered in this article. In the future study, we will evaluate the forecast of the cold surge process from northwestern China to southern China based on the BCC-AGCM 2.2. Although the Siberian High is the dominant factor for the cold events in northern China including the competition zones, the cold surges are also influenced by other circulation systems, such as the blocking high ([PERSON] and [PERSON], 2015; [PERSON] and [PERSON], 2017), the East Asian jet stream ([PERSON] and [PERSON], 2017) and the polar jet ([PERSON] and [PERSON], 2013). For example, [PERSON] and [PERSON] (2017) revealed the common features and the differences of the blocking activities between ordinary and extensive cold surge. For the ordinary type, the blocking is limited in the Ural Mountains and exhibits a regional feature, while for the extensive type the blocking can extend eastward into Northeast Asia. Besides, the position or the shape of the Siberian High especially its spatial extension also has significant impacts to the temperature besides the intensity. [PERSON] and [PERSON] (2020) explored that a stronger Siberian High with an expanding eastern edge is coupled with the East Asian trough and results in a colder winter in Northeast China. Results also indicate that the horizontal extent of the Siberian High corresponds well with the zonal extents of the large-scale tilted ridge and trough, and the latter could be caused by the abnormal blocking high ([PERSON] and [PERSON], 2015). But compared with the intensity, the skillful forecast of the Siberian High shape is still a big challenge in almost all the climate models. These will also be analyzed in the future to obtain a more comprehensive understanding of the circulation patterns under which the model can better forecast the cold surge invading the competition zones.
## Acknowledgements
This research was supported by the National Key R&D Program of China (2018 YFC1505600).
## Conflict of Interest
The authors declare no potential conflict of interest.
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**How to cite this article:** [PERSON], [PERSON], [PERSON].
Cold surge invading the Beijing 2022 Winter
Olympic Competition Zones and the predictability
in BCC-AGCM model. _Atmos Sci Lett._ 2021;22:
e1039. [[https://doi.org/10.1002/asl.1039](https://doi.org/10.1002/asl.1039)]([https://doi.org/10.1002/asl.1039](https://doi.org/10.1002/asl.1039)) | wiley | Cold surge invading the Beijing 2022 Winter Olympic Competition Zones and the predictability in <scp>BCC‐AGCM</scp> model | Xiang Li, Hui Gao, Ting Ding | https://doi.org/10.1002/asl.1039 | 2,021 | CC-BY |
wiley/fdcd95c9_f6f8_4d1c_ae8a_62ccdd597c9a.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Iridescence Reveals the Formation and Growth of Ice Aerosols in Martian Noctilucent Clouds [PERSON]. [PERSON]
1 Space Science Institute, Boulder, CO, USA, 1 Centro de Astrobiologia (CAB), CSIC-INTA, Torrejon de Ardoz, Spain, 1
[PERSON]
2 Space Science Institute, Boulder, CO, USA, 2 Centro de Astrobiologia (CAB), CSIC-INTA, Torrejon de Ardoz, Spain, 2
[PERSON]
3 NASA Goddard Space Flight Center, Greenbelt, MD, USA, 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 3
[PERSON]
4 Research & Development Development of the National Science Foundation, funded by
et al., 1997; [PERSON] et al., 2023), and spectral interference effects that suggest iridescence have been reported in daytime CO\({}_{2}\) clouds ([PERSON] et al., 2019).
InSight detected noctilucent clouds at solar longitude (\(L_{\rm S}\)) 16\({}^{\circ}\) in Mars Year (MY) 35 (25-04-2019; [PERSON] et al., 2020). Given InSight's location 600 km north of Curiosity, such \(>\)50-km altitude clouds were plausibly visible from Curiosity's Gale-crater location (137\({}^{\circ}\)E, 5\({}^{\circ}\)S). Before this, there were few reports of mesospheric clouds around Gale crater in early southern autumn. Such clouds were not expected due to the influence of Martian topography on tides, which suppresses gravity wave propagation to the mesosphere except around 0\({}^{\circ}\) and 270\({}^{\circ}\)E longitudes ([PERSON] et al., 2012). [PERSON] et al. (2018) reported an \(L_{\rm S}\) = 20-30\({}^{\circ}\) peak in afternoon mesospheric CO\({}_{2}\) clouds near 0\({}^{\circ}\) longitude with moderate optical depths that would be visible in the daytime. While the Opportunity rover imaged daytime cirrus clouds in that region in the same season ([PERSON] et al., 2015), Curiosity has not seen similar clouds. [PERSON] et al. (2021) reported on twilight clouds at midlatitudes and not around the Curiosity site.
Using Curiosity data, we report the first images of naccrous clouds on Mars and use a long-term photometry record to show that the noctilucent cloud season was typical. Section 2 describes the observations of iridescence. Section 3 describes the environmental context for the clouds. Section 4 discusses the constraints on cloud characteristics and the window into cloud physics such data provides. Section 5 summarizes our conclusions.
## 2 Iridescence
### Mastcam Images and Image Processing
Mastcam is Curiosity's color and multispectral stereo camera ([PERSON] et al., 2019). Color images were obtained with a short-pass filter in series with Bayer-pattern microfilters (639 \(\pm\) 44, 553 \(\pm\) 38, and 494 \(\pm\) 38 nm for red, green, and blue) on the pixels ([PERSON] et al., 2019). Due to the wider field of view (FOV) of the 34-mm focal length left eye, we used it for cloud imaging. The FOV, as commanded, was 16.6 \(\times\) 14.8\({}^{\circ}\) and was sampled by 1,328 \(\times\) 1,184 pixels with projected sizes of 74 \(\upmu\)rad. Images were calibrated to radiance and _I/F_ (radiance, or intensity, normalized to solar flux) using solar fluxes for each bandpass ([PERSON] et al., 2019; [PERSON] et al., 2022).
We used panoramic imaging to see clouds across the sky, emphasizing the sunset azimuth. Over mission sols 2,422-2,448 (2019-05-30 to 2019-06-26, \(L_{\rm S}\) = 33-45\({}^{\circ}\)), two imaging strategies were used. One used 23 images to obtain a 360\({}^{\circ}\) mosaic (23 \(\times\) 1) covering \(\sim\)13-27\({}^{\circ}\) elevation; the other used a westerly 3 \(\times\) 2 mosaic, repeated to show motion (3 \(\times\) 2 \(\times\) 2). A second campaign over sols 3,047-3,091 (2021-03-03 to 2021-04-17, \(L_{\rm S}\) = 12-33\({}^{\circ}\)) included the 23 \(\times\) 1 and 3 \(\times\) 2 \(\times\) 2 images as well as a small number of other mosaics. Panoramic images were processed into cylindrical mosaics using geometric information in image headers. The Sun was \(<\)\(-\)5.7\({}^{\circ}\) elevation for the observations reported here, meaning the sunlit clouds were noctilucent and above \(\sim\)40 km altitude (looking west, 20\({}^{\circ}\) above the horizon).
All images were inspected in several color modes, including a linear I/F stretch, a gamma-corrected approximate true color stretch, and a normalized, chromaticity-like image (see Figure S1 in Supporting Information S1). Chromaticity, which represents color information after the removal of intensity, is useful for objective studies of the color of noctilucent clouds ([PERSON] et al., 2022; [PERSON], 1993). While it is formally based on human color vision, we used the Mastcam color bands such that the color transform for each pixel was {_r, g, b_} = {_R, G, B_}/(R+G+B), where _RGB_ represents _I/F_ values for the red, green, and blue channels, and _rgb_ represents the normalized color.
### Iridescence and Coronae
We report the first images of naccrous clouds on Mars and of Martian scattering coronae (Figure 1). Images show clouds that were both noctilucent and iridescent, which are referred to as naccrous clouds on Earth ([PERSON] et al., 2021). As used here, the terms noctilucent (night-shining), iridescent (colorful due to diffraction), and naccrous (both) refer to the physical and geometric conditions and not to the composition or altitude of analogous terrestrial clouds. For the five mosaics in Figure 1, each image shows a linear stretch of _I/F_ that preserves color, enhancing highlights relative to true color. Based on experience imaging terrestrial iridescent clouds, we estimate that the color variations in these clouds would have been visually detectable.
Noctilucent clouds were seen on sol 2,422 (\(L_{\rm g}\) = 33\({}^{\circ}\)) and were widespread on sol 2,425 (\(L_{\rm g}\) = 34\({}^{\circ}\)) but were not abundant after that during the first season (MY-35). The sol-2,425 images near the sunset azimuth provided the first evidence for iridescence, and low-scattering-angle images showed the first corona.
Color imaging was initiated earlier in the second season (MY-36). Over several weeks, widespread iridescent clouds and some coronae were seen. On sol 3,063 (\(L_{\rm g}\) = 19\({}^{\circ}\)), the rover was kept awake for several hours from before sunset until dark as a large set of imaging was done under cloudy skies. Clouds became rarer later in the season.
Iridescence in clouds is a diffraction phenomenon ([PERSON], 2003). Locally (e.g., within a few pixels), particle sizes have low variance. Diffraction variations at similar scattering angles indicate a changing size parameter (\(\alpha\) = 2\(\alpha\)/\(h\), where \(a\) is the particle radius and \(\lambda\) is the wavelength of light). A large local particle-size variance would eliminate iridescence due to the overlap of different-sized diffraction patterns. The low variance suggests that the particles have a similar and short formation history without time to diverge.
A corona in clouds (Figure 1e) is a diffraction phenomenon with low variance in particle size locally and over large areas of the sky ([PERSON] & [PERSON], 1991). Color variations appear due to the different widths of the diffraction rings with different wavelengths. Where iridescence indicates that particles locally have the same formation, coronae indicate that a widespread haze has a similar formation history.
## 3 Environmental Context
### Ultraviolet Photometry
The seasonality of the clouds is important for aiding inferences about their properties and as a tool for planning further studies. While imaging in MY-35 showed evening twilight clouds appeared over \(L_{\rm g}\) = 16-33\({}^{\circ}\), no image-based constraints existed before MY-35.
The Rover Environmental Monitoring Station (REMS; [PERSON] et al., 2012) includes an Ultraviolet Sensor (UVS; [PERSON] et al., 2016; [PERSON] et al., 2017). REMS has typically monitored the first 5 min of each hour (in local mean solar time) and several complete hours each sol on a rotating basis. UVS has six photodiode-based sensors covering different spectral ranges with an FOV \(\pm\)30\({}^{\circ}\) from the rover's zenith. The ABC and A sensors, 200-380 nm and 320-380 nm, have the greatest response to twilight due to the combination of bandwidth and available solar flux. Digitized UVS data are truncated at 0 on the rover, making all negative measurements indistinguishable. The A and C (200-280 nm) sensors have the highest 0-points and are thus most useful for low-light studies as they do not saturate low as easily. We use partly calibrated data, showing the current from each
Figure 1: Iridescent clouds are shown in cylindrical projection. Mosaics are shown from sols (a) 3,047, (b) 3,048, (c) 3,050, (d) 2,425, and (e) 3,049. The axes are at azimuth 270\({}^{\circ}\), elevation 15\({}^{\circ}\), with tick marks every 5\({}^{\circ}\) (azimuth) and 1\({}^{\circ}\) (elevation). Scattering-angle contours are at 5\({}^{\circ}\) intervals with a yellow 30\({}^{\circ}\) contour. The image in (d) is shown at twice the resolution of the others.
photodiode (TELRDR data set) instead of the fully corrected data with unwanted spatial corrections based on the assumption the light source is direct sunlight. For the brighter clouds, all UVS channels responded the same way; we chose to use channel A as a reference for its combination of response and zero point. Data were taken at 1 Hz; we used 60-s averages (roughly averaging over 0.25 deg in solar elevation).
We determined that the UVS was sensitive to the clouds present during the imaged period and had recorded cloud-related signals before MY-35. As an initial screen, we averaged the UV-A current when the Sun was 5.5-6.5 deg down. Figure 2a shows this UV-A current across seasons, demonstrating that there are systematically higher (and variable) signals in the \(L_{\rm S}\) = 0-45 deg period compared to surrounding periods, as well as sporadic high signals near mid-year and a longer period of elevated signals in the second half of the year.
Inspection of the UV-A profile on all nights with appropriate measurements showed a seasonal pattern. For \(L_{\rm S}\) = 0-45 deg, most nights showed a falling signal due to sunset, then a pause or even reversal (see Figure 2b) followed by a brightness peak. This was also true for some of the sporadic high signals. For most nights from \(L_{\rm S}\) = 150-300 deg, any high signals were consistent with dust extending to higher altitudes at this time of year. Figure 2b shows an example from each Mars year of a signal with a post-sunset peak as well as two out-of-season examples and a dusty season example.
We infer that the sols with a brightness maximum after sunset generally show cloud formation. A uniform spherical shell would have a monotonically decreasing brightness as the Sun lowered. Clouds could advect into or out of the FOV to cause brightness variations. However, if advection were the explanation, clouds would be equally likely to enter or leave the FOV just before the Sun got to \(-6\)deg. No sudden, early darkening was observed over the \(L_{\rm S}\) = 0-45 deg timeframe. On the other hand, clouds that form at or after sunset should lead to brightening for as long as they are illuminated, followed by darkening based on when the Sun is obscured at their altitude.
### Navcam Images and Image Processing
The rover's navigation camera, Navcam, was used as a cloud survey camera due to its wide FOV. Navcam takes monochrome (600-800 nm bandpass) images with a 45 deg FOV and 1,024 \(\times\) 1,024 detector ([PERSON] et al., 2012). Initial surveys were multi-frame time-lapse images in a single direction, frequently eight images looking northward toward InSight's location (1 \(\times\) 1 \(\times\) 8). Other surveys included 3 \(\times\) 1 panoramas that were repeated some number of times (3 \(\times\) 1 \(\times\) N), and there was occasional use of larger panoramas. Mean-frame subtraction techniques used for daytime images ([PERSON] et al., 2015) were unnecessary for these high-contrast clouds. The cloud contrast was such that autoexposure was an efficient cloud detector: it resulted in short exposures of 1-10 s in the presence of clouds and long exposures of up to 4-5 min on cloud-free nights (cf., typical daytime exposures
Figure 2: REMS-UVS current indicates clouds. (a) The UVS signal at a solar depression angle of 6° is shown across solar longitudes showing a cloudy season for \(L_{\rm S}\) \(<\) 45°. Elevated values for \(L_{\rm S}\) \(>\) 150° mostly correspond to high-altitude dust. (b) UVS profiles for five nights in the incolitement cloud season are shown with solid lines, two nights with unesasonal notillement clouds are shown with dash-dot lines, and a representative dusty season night is shown with a dashed line. One degree corresponds to \(\sim\)4 min.
near 0.5 s). As sequence execution windows were based on rapid imaging, the sequences did not run to completion on cloud-free nights.
Imaging campaigns were initiated with Navcam on sols 2400 (\(L_{\mathrm{S}}\) = 22\({}^{\circ}\)) and 3,046 (\(L_{\mathrm{S}}\) = 11\({}^{\circ}\)). The initial goals were to confirm that Curiosity's position allowed images of the clouds previously seen by InSight looking to the south ([PERSON] et al., 2020) and then to further characterize them. With iridescence that could only be observed with Mastcam, the role of Navcam shifted to providing contextual information. The 3 \(\times\) 1 \(\times\) N image sequences were chosen as a standard that could show both low-scattering angle bright sky and high-scattering angle sky that might include the projection of the terminator on clouds. As with Mastcam, geometric information in the image headers was used to create cylindrical mosaics.
### Cloud Morphology, Altitude, and Optical Depth
Shadows cast upward onto the clouds were the most direct clues to altitude in the imaging or UVS photometry. Within the UVS profiles, the rapid brightness fall-off at low solar elevations was interpreted to be caused by the setting of the Sun as seen from the cloud altitude, 30-40 min after sunset. In time-lapse images, clouds could be seen going dark over time. In some cases (with appropriate contrast settings), a terminator-like line could be seen across the sky.
We modeled recollectment cloud brightness as singly scattered sunlight. For a grid of cloud altitudes (arbitrarily using 1-km cloud thickness), solar zenith angles, and atmospheric optical depths, we constructed look-up tables of cloud illumination. We estimated transmission to the cloud layer, scattering by the cloud, and transmission to the rover using measured atmospheric optical depths ([PERSON] et al., 2024). We used the look-up tables to associate altitudes with UVS profiles and images with the terminator (see Text S1 in Supporting Information S1 for more detail). For Mastcam images, we determined path optical depths through selected locations in clouds using the computed transmissions, the I/F difference between the cloud and the background, and the radiative transfer equation for single scattering. Typical optical depths for the iridescent clouds were 10\({}^{-3}\) to 10\({}^{-2}\).
Figure 3 shows a set of Navcam mosaics with candidate terminators superposed on the images and the resulting height measurements. We assigned a height measurement in a set of images if clouds could be seen to vanish over time (to differentiate changing illumination from patterns in the clouds). We assigned a lower limit to individual images or to a set of images that did not meet that criterion if recollectum clouds were present. We note that in Figure 2(a), there are both waveform and ciriform clouds (cf., Supporting Information Movie S1). The waves disappear at 50-55 km, while the ciriform clouds disappear at 60-65 km. We chose the ciriform value for the summary in Figure 2(b), but note that sols 3,054, 3,063, 3,075, and 3,081 had waveform clouds near 50 km. Clouds moved east-to-west on all nights when motion could be determined.
We tested all sols with \(>\)600 s of UVS data while the Sun was 4-8\({}^{\circ}\) below the horizon. We identified 131 profiles during \(L_{\mathrm{S}}\) = 0.45\({}^{\circ}\): 84 had no identified clouds and 47 had clouds for which we determined a height (36%); 30 of those had a brightness reversal. We identified 802 profiles during \(L_{\mathrm{S}}\) = 45-360\({}^{\circ}\), of which 14 gave a height (1.7%) and 6 had a brightness reversal. This reinforces that \(L_{\mathrm{S}}\) = 0-45\({}^{\circ}\) is a distinct cloud season.
## 4 Results and Discussion
### Cloud Characteristics
These images include at least two cloud populations: common ciriform clouds and occasional waveform clouds. We do not exclude clouds below 40 km, but due to the detection method, we focus on those above 40 km. Due to the low cloud optical depths, images show a superposition of illuminated clouds. Coronae may be associated with the waveform clouds.
Ciriform clouds at 55-80 km were likely CO\({}_{2}\) ice, but H\({}_{2}\)O ice cannot be ruled out from altitude alone. [PERSON] et al. (2018) reported daytime mesospheric clouds of sub-\(\mu\)m CO\({}_{2}\) east of the site for early autumn, while [PERSON] et al. (2019) found H\({}_{2}\)O ice below 55 km and sub-\(\mu\)m CO\({}_{2}\) up to 70 km at \(L_{\mathrm{S}}\) = 30-60\({}^{\circ}\).
Waveform clouds, some below 55 km, may have been H\({}_{2}\)O ice. Such clouds are seen in daylight, mostly with optical depths near 0.01 around the equinox, transitioning to 0.1 in mid-autumn and winter ([PERSON] et al., 2024; [PERSON] et al., 2018). However, these clouds are mainly around 20-40 km altitude ([PERSON] et al., 2020). [PERSON] et al. (2018) suggested H\({}_{2}\)O ice clouds, as opposed to high and cold CO\({}_{2}\) clouds, cause warming of overnight minimum surface temperatures during \(L_{\rm S}\) = 20-50\({}^{\circ}\). We note that coronae are common in terrestrial wave clouds due to their tendency to monodisperse particle sizes ([PERSON] & [PERSON], 2003). Projecting the images to the 50-km level, we find mean wavelengths of 7.5 km, with a range of 5.4-10.8 km, and an orientation consistent with mean motion from 80\({}^{\circ}\) azimuth (east).
### Cloud Particle Size and Evolution
While size controls the observed diffraction pattern, a unique interpretation of the diffracted light requires identifying the diffraction pattern over some scale. We calculated the single-scattering phase function for diffraction following [PERSON] (2015) for the relevant scattering angles and a range of sizes, using the camera's spectral response and a log-normal size distribution with \(\sigma\) = 0.005, and converted them from linear _RGB_ color to normalized _rgb_ color (Figure 4a). Other than the number of fringes that can be seen, the width of the distribution has little effect on the colors ([PERSON] et al., 2015). Large-scale patterns, such as a corona, could indicate size equilibria, while small-scale patterns could indicate nucleation areas or growth in fall streaks (e.g., [PERSON], 1979).
We looked for a diffraction fingerprint in the clouds, either local color changes at similar scattering angles or larger coronae. Figure 4 shows details (individual images) from several panoramas (also see Figures S2-S4 in Supporting Information S1). Most show iridescent fall streaks, and two show a corona. A fall streak similar to those commonly seen as a result of icy precipitation in terrestrial cirrus clouds in Figure 4b (and partly 4c) shows a blue-green-red variation. The blue is distinctive in the diffraction calculation and anchors our interpretation that the particles grow from \(\sim\)0.75 to \(\sim\)1.2 um as they fall. However, different assumptions in the diffraction calculation might allow a 1.2-1.8 um interpretation. Options in between are ruled out by the blue, and growth is required by the blue-green-red sequence. Other scenes are more complicated: Figure 4d shows clouds 40-50\({}^{\circ}\) from the Sun, where the relative blueness of ice compared to background dust dominates, but color variations along fall streaks are still present at the top; Figure 4e shows a set of partially superposed clouds with most of the color variation organized by scattering angle, but some cloud-to-cloud and intracloud variation. The ellipse in Figure 4f (like 4c) crosses a diffraction fringe in the corona. A single fringe is difficult to interpret given the background light, but examination of several color stretches led to the conclusion that \(\sim\)1.1 um was likely, \(\sim\)0.6 um less likely, and larger was unlikely. The most intriguing suggestion about cloud physics information that could be teased out of the data was a small color change in the sol-3063 3 \(\times\) 2 \(\times\) 2 (Figure 4g). Over 62 s, a greenish area expanded on the left of the red-toned cloud. A possibility is that small particles were actively nucleating in this cloud and became visible at \(<\)1 um.
The linking of size and color through diffraction gives us a window into otherwise hidden cloud formation. While some size interpretations are non-unique, the main conclusion is that there are narrow size distributions, and the colors change with changing size. [PERSON] (2022) suggested a possible mechanism: once there are sufficient ice nuclei, further nucleation can be inhibited in favor of uniform depositional growth. The images show evolving clouds, and the colors provide a way to constrain size and growth.
Figure 3: Cloud altitudes are estimates from UV signals and images. (a) Three Navcam twilight mosaics taken over 7.5 min on sol 3.075 are shown in cylindrical projection with white contours indicating the position of the terminator for cloud altitudes of 50, 55, 60, and 65 km and 10\({}^{\circ}\) grid spacing. (b) Cloud altitudes derived from REMS, Navcam, and Mascam are shown. For REMS-UVs, filled circles indicate nights with brightness reversals, and open circles indicate nights without. For the cameras, filled symbols indicate heights measured in time-lapse imaging, and * and \(\times\) indicate lower limits from single images.
### Open Questions
Additional observations from November 2024 to March 2025 and October-December 2026 could expand the utility of the initial data. (a) How extensive are these clouds, vertically and horizontally? Curiosity and InLight data only pertain to a few hundred km around their landing sites. Orbiters capable of sunset and twilight times could constrain the cloud altitude. (b) How fast do particles evolve in these clouds? Time-lapse imaging, perhaps at a higher resolution, could acquire a significant sample of case studies. (c) What is the nature of the corona-forming layer? The low sample size precludes a convincing association with the waveform clouds, and a larger sample could d'sambiguate whether the corona is related to the currform clouds or if a second process
Figure 4: Color constraints on size are shown. (a) Diffraction colors are shown for a narrow log-normal size distribution. Individual M-34 images are shown for sols 2,425 (b), 2,425 (c), 3,047 (d), 3,048 (e), 3,049 (f), and 3,063 (g) with a linear _RGB_ stretch above and normalized _rgb_ below. Linear stretches are color-neutral from 0.5% to 99.5% brightness levels. The _rgb_ stretches are 0.30-0.3667. Contours are every 5\({}^{\circ}\) in scattering angle. The yellow ellipse (b) shows color variation in a fall streak represented by the yellow arrow in (a). The magenta ellipse (c) and blue ellipse (f) indicate coronae that correspond to the blue and magenta lines in (a). The green ellipse in (g) shows a region with new small particles.
produces a narrow distribution of ice particles. A convincing size for the coronal clouds would require seeing more diffraction rings and, thus, a wider range of angles.
## 5 Conclusions
The Curiosity rover obtained the first images of iridececence in clouds on Mars and the first detection of a Martian scattering corona. The iridecent clouds were seen in twilight in the early southern autumn of two Mars years, and a five-Mars-year record of ultraviolet photometry shows that this is a consistent and distinctive cloud season. Ciririform clouds at 60-80 km were likely CO\({}_{2}\) clouds, although such clouds were not previously expected. Waveform clouds below 55 km may have been H\({}_{2}\)O ice also seen in daytime rover imaging. The diffraction color fringes illustrate size evolution in the clouds, but a larger sample is needed to address timescales for growth and sedimentation.
## Data Availability Statement
All Curiosity data used in this study are publicly available via the Planetary Data System ([PERSON], 2013; [PERSON], 2018; [PERSON], 2013).
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wiley/fdc81e9e_723b_4d57_b37d_55e3c64cbb62.md | Walruses from space: walrus counts in simultaneous remotely piloted aircraft system versus very high-resolution satellite imagery
[PERSON]
1 British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0 ET, UK 1
[PERSON]
1 British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0 ET, UK 1
[PERSON]
2 Norwegian Polar Institute, Fram Centre, 9296, Tomsa, Norway 2
[PERSON]
2 Norwegian Polar Institute, Fram Centre, 9296, Tomsa, Norway 2
[PERSON]
3 WWF-UK, Living Planet Centre, Rufford House, Brewery Road, Woking GU21 4 LL, UK 3
[PERSON]
2 British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0 ET, UK 2
###### Abstract
Regular counts of walruses (_Odobenus rosmarus_) across their pan-Arctic range are necessary to determine accurate population trends and in turn understand how current rapid changes in their habitat, such as sea ice loss, are impacting them. However, surveying a region as vast and remote as the Arctic with vessels or aircraft is a formidable logistical challenge, limiting the frequency and spatial coverage of field surveys. An alternative methodology involving very high-resolution (VHR) satellite imagery has proven to be a useful tool to detect walruses, but the feasibility of accurately counting individuals has not been addressed. Here, we compare walrus counts obtained from a VHR WorldView-3 satellite image, with a simultaneous ground count obtained using a remotely piloted aircraft system (RPAS). We estimated the accuracy of the walrus counts depending on (1) the spatial resolution of the VHR satellite imagery, providing the same WorldView-3 image to assessors at three different spatial resolutions (i.e., 50, 30 and 15 cm per pixel) and (2) the level of expertise of the assessors (experts vs. a mixed level of experience - representative of citizen scientists). This latter aspect of the study is important to the efficiency and outcomes of the global assessment programme because there are citizen science campaigns inviting the public to count walruses in VHR satellite imagery. There were 73 walruses in our RPAS 'control' image. Our results show that walruses were under-counted in VHR satellite imagery at all spatial resolutions and across all levels of assessor expertise. Counts from the VHR satellite imagery with 30 cm spatial resolution were the most accurate and least variable across levels of expertise. This was a successful first attempt at validating VHR counts with near-simultaneous, in situ, data but further assessments are required for walrus aggregations with different densities and configurations, on different substrates.
R 29 September 2023; Revised 7 March 2024; Accepted: 19 March 2024
## 1 Introduction
Walruses (_Odobenus rosmarus_) live throughout much of the circumpolar Arctic, where they use sea ice to meet various biological needs such as giving birth and resting ([PERSON], 1982; [PERSON] et al., 1995). However, sea ice in the Arctic is declining at a rapid rate in terms of extent, thickness and seasonal presence ([PERSON] et al., 2019). Understanding how these important habitat modifications are affecting walruses is essential for management authorities to safeguard their existence. Ideally, walrus monitoring would be performed on a regular basis to capture impacts of the rapid and highly dynamic changes in sea ice conditions.
During late summer and early autumn, when sea ice is at a seasonal minimum, walruses tend to return to terrestrial haul-out sites that they have previously occupied. Therefore, counting them at their terrestrial haul-out sites during this period is the preferred abundance assessment method (e.g., [PERSON] et al., 2022; [PERSON] et al., 2016; [PERSON] et al., 2014; [PERSON] et al., 2008). Regional population surveys are conducted in some areas for walruses, but the logistical challenges (including financial costs) limit the frequency and extent of such surveys ([PERSON] et al., 2016; [PERSON] et al., 2014). Satellite imagery has the potential to be a non-invasive solution to monitor large areas more frequently. However, further work is required to better understand what level of monitoring (e.g., haul-out occupation, herd size, abundance) is feasible using space-borne technologies. Earth-observing satellites that orbit the Earth are capable of imaging the whole walrus distribution range within one season. For instance, the Maxar constellation of very high-resolution (VHR) multispectral satellites captures images below 50 cm spatial resolution (i.e., GeoEye-1, WorldView-2 and WorldView-3) and could capture images of all known walrus haul-out sites in a 3 month period in ideal conditions, with the possibility for regional populations to be imaged within much shorter time frames (pers. comm. Maxar, 2022). Other VHR satellites, such as those operated by Airbus and Planet, may offer similar capabilities (Airbus, 2022; Planet, 2018). As more VHR satellites are launched into space and become operational ([PERSON] et al., 2021), the time coverage is expected to improve, which would facilitate synoptic surveys on shorter time scales. If VHR imagery is not required for a particular study (e.g., assessing haul-out site occupation), satellites with lower spatial resolution can be used, such as Sentinel-2 (10 m resolution; ESA, 2015) operated by the European Space Agency, or PlanetScope (3 m resolution; Planet, 2023) operated by Planet, both of which provide daily imagery for Arctic areas.
Very high-resolution satellites have already proved to be a useful complementary tool for monitoring wildlife such as penguins ([PERSON] et al., 2012; [PERSON] & [PERSON], 2014) and elephant seals (_Mirounga_ spp. [PERSON] et al., 2023), and for finding walruses ([PERSON] et al., 2012; [PERSON] & [PERSON], 2005; [PERSON] & [PERSON], 2021; [PERSON] et al., 2022; [PERSON] et al., 2020). This new tool could provide a non-invasive mean to assess walruses, which can be disturbed easily by noise from boats or arircrafts traditionally used in surveys ([PERSON] et al., 2021). However, work is needed regarding the feasibility of using VHR satellite imagery to count the number of individuals in haul-out groups accurately. In particular, it is necessary to validate the counts in satellite imagery with near-simultaneous aerial imagery that can provide an accurate baseline count ([PERSON] & [PERSON], 2021; [PERSON] et al., 2023). Some previous attempts to count walruses from space ([PERSON] et al., 2012; [PERSON] et al., 2020) could not provide validation of their counts due to the difficulty of acquiring near-simultaneous aerial imagery. Other studies ([PERSON] & [PERSON], 2021; [PERSON] et al., 2023) were able to pair their satellite imagery with aerial imagery acquired 1.5-9 h apart from each other, but uncertainty in the accuracy of the satellite imagery herd size estimate remained due to the known dynamic nature of walrus aggregations and the likelihood of different numbers of walruses being present between the satellite and aerial imagery ([PERSON] & [PERSON], 2021).
Further considerations for counting walruses across a whole population, sub-species, or their entire pan-Arctic distribution using VHR include the feasibility of efficiently reviewing vast numbers of images. Two potential solutions are to use automated systems, or the power of the crowd, through citizen science projects. No automated systems currently exist, due to the requirements for large amount of training data, particularly for Convolutional Neural Networks, which are proving successful for the detection of wildlife in VHR satellite imagery ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2023). The other solution resides with citizen science campaigns. Recently, Weddell seals (_Letponychotes weddellii_) were censed across the ice shelves surrounding the entire Antarctica continent through a crowdsourcing campaign ([PERSON] et al., 2020). A similar campaign, Walrus from Space (WWF, 2023; [[https://www.wwf.org.uk/learn/walrus-from-space](https://www.wwf.org.uk/learn/walrus-from-space)]([https://www.wwf.org.uk/learn/walrus-from-space](https://www.wwf.org.uk/learn/walrus-from-space))), is currently inviting citizen scientists to search for and count Atlantic walruses (_O. rosmarus rosmarus_) in VHR satellite imagery. However, walrus counts made by the public need to be validated.
In this study, we aimed to validate walrus counts made by experts and citizen scientists in satellite imagery, using a 'control count' obtained using a remotely piloted aircraft system (RPAS) captured simultaneously with the satellite imagery. We assessed the accuracy of the walrus counts depending on the spatial resolution of the VHR satellite imagery (i.e., 50, 30 and 15 cm), and the experience level of the assessors (experts with or without field knowledge and non-expert/citizen scientists).
## Materials and Methods
### Study location
Walruses regularly haul out during summer at Sarstangen (78.72\({}^{\circ}\) N, 11.44\({}^{\circ}\) E), a narrow band of light beige and grey sand and gravel on the western shores of Spitsbergenin the Svalbard Archipelago, Norway, extending into Forlandsundet (Fig. 1).
## RPAS and satellite imagery acquisition
On 15 July 2022, we visited Sarstangen and flew a DJI Mavic 3 (Hasselblad camera sensor: 4/3 CMOS, effective pixels: 20 MP, focal length: 12 mm, image width: 5280 pixels, image height: 3956 pixels; for further detailed specifications, see: [[https://www.dji.com/uk/mavic-3/specs](https://www.dji.com/uk/mavic-3/specs)]([https://www.dji.com/uk/mavic-3/specs](https://www.dji.com/uk/mavic-3/specs))) under Permit No. 22/00507-2 from the Governor of Svalbard (RiS number 11906). [PERSON] et al. (2021) tested the level of disturbance in response to RPAS flights undertaken above walruless in Svalbard and observed no disturbance when RPAS were flown at altitudes above 50 m. We added a precautionary 5 m and flew at 55 m above the walruses in our study. We observed no disturbance (e.g., no head lifting) during our RPAS flights within view of the remote pilot and observers on the ground. We piloted the RPAS to take off and land downwind, at
Figure 1: Map showing the Sarstangen walrus haul-out site, where RPAS and VHR satellite imagery were acquired (large red dot). Other known walrus haul-out sites are shown as small grey dots and human settlements are indicated by block stars. Basemap and walrus haul-out sites © Norwegian Polar Institute (2014, 2024).
distances greater than 300 m from the walruses. Herein, we used an image of the haul-out site that was captured at 13:10 UTC on 15 July (2022-07-15T13:10Z; Table 1) because it was closest in time to the satellite image acquisition. The image was captured at radii.
A WorldView-3 image of the Sarstangen walrus haul-out site was captured on 15 July 2022, at 13:25 UTC (2022-07-15T13:25Z), 15 min after the RPAS image (catalogue ID: 104001007777 EA00; product type: ortho-ready standard 2A). We were on-site at Sarstangen maintaining continuous visual observations of the walruses during and somewhat after capturing the satellite imagery - and group composition and number had not changed from the time of the RPAS-captured image we used. We obtained the same satellite image at three different spatial resolutions: 50 cm (using Maxar Technologies' downsampling algorithm), 30 cm (the raw resolution) and 15 cm (using Maxar Technologies' high-definition algorithm; Maxar Technologies, 2023; [PERSON] et al., 2021; Table 1). For all satellite images, the mean sun azimuth angle was 214.3\({}^{\circ}\), the mean sun elevation angle was 31\({}^{\circ}\) and the off-nadir angle was 14\({}^{\circ}\). All three satellite images were pansharped using the Brovey algorithm and standard deviations stretch, as it rendered the clearest image to discern individual walruses.
### Counting walruses
Walruses hauled out at Sarstangen were counted on the RPAS image and the three satellite images (15, 30 and 50 cm spatial resolution; Table 1) by four different groups of assessors:
* Group 1: five assessors with a high level of expertise in counting wildlife in aerial and, or VHR satellite imagery, with field knowledge (including the field researchers and RPAS operators of the present study);
* Group 2: five assessors with experience in photographic counts of wildlife but with no field knowledge;
* Group 3: nine assessors, without any experience in counting walruses and, or other wildlife in aerial and, or VHR satellite imagery;
* Group 4: 36 assessors, representative of the crowd with mixed levels of experience in counting walruses and, or wildlife in aerial and, or in VHR satellite imagery.
Assessors from Groups 1, 2 and 3 counted walruses in the four images, sequentially and independently, from lowest (50 cm satellite image) to highest spatial resolution (RPAS image). Assessors from Group 4 reviewed one of the four images, assigned to them at random, to replicate what is most likely to happen in citizen science projects, where assessors review some imagery but not all. Overall, each of the four images was reviewed by nine assessors from Group 4 selected at random. All assessors counted walruses following the same protocol (see Data S1), using the open-source software VGG Image Annotator ([PERSON], 2019). Only the walruses hauled out were included in the count. A walrus was considered hauled out, when it was completely on land or grounded in the shallow waters ([PERSON] et al., 2014). All counts per assessor and per image type are available in Data S2.
### Analysis 1: effect of image spatial resolution and level of experience
We tested the effects of spatial resolution of the image and the experience level of assessors on count accuracy by evaluating the variation and bias between assessors. We used the
\begin{table}
\begin{tabular}{l l l l l} Date and Time (UTC, & Date and Time (UTC, & \\ YYYY-MM-DOTH+:mm2) & 2022-07-15T13:10Z & 2022-07-15T13:25Z & 2022-07-15T13:25Z & 2022-07-15T13:25Z \\ Platform type & RPAS & VHR satellite & VHR satellite & VHR satellite \\ Platform model & Maxic 3 & WorldView-3 (HD uplift algorithm) & WorldView-3 & WorldView-3 \\ Spatial resolution & 1.5 cm & 15 cm & 30 cm & 50 cm \\ Image sources: RPAS image © 2023 [PERSON] and [PERSON] (Data 54), Satellite images © 2023 Maar Technologies. RPAS, remotely plotted aircraft system; VHR, very high-resolution. & \\ \end{tabular}
\end{table}
Table 1: RPAS image and WorldView-3 image processed at three different spatial resolutions (e.g., 15, 30 and 50 cm) analyzed in this study.
counts from Group 1, Group 2 and Group 3, which included 74 counts in total. We used a factorial design with two variables 'experience' with three levels (Group 1, Group 2, Group 3) and 'image spatial resolution' with four levels (RPAS, VHR 15, VHR 30, VHR 50) to assess impacts of image resolution and experience. The experimental unit was 'assessor', nested in 'experience' with an unbalanced design since Group 1 and Group 2 had five assessors each and Group 3 comprised nine assessors. Group 1 acted as a control group with accurate counts to model the effects of 'experience', as the assessors from this group had previously obtained a ground-truthed count in the field (the knowledge of the total number of wavlures in the RPAS image), which had a feedback effect when all the subsequent images were counted. The consensus walrus count for the RPAS imagery provided by Group 1 acted as the ground-truthed count.
Based on inspection of the data distribution, we modelled walrus counts in images as log-normal random variables \(Y\sim\text{LN}(\alpha,\sigma^{2})\) with mean \(E(Y)=\mu=\sigma^{a_{1}\sigma^{a}/2}\) and variance \(\text{var}(Y)=\sigma^{a_{2}+\sigma^{2}}\left(\sigma^{a_{1}}-1\right)\). In a linear mixed-effects modelling formulation, we expressed the count of 'assessor' \(k\) from 'experience' group \(i\) of 'image spatial resolution' \(j\) as:
\[\log\left(\mu_{ijk}\right)=\beta_{0}+\beta_{1,i}+\beta_{2,i}+\beta_{3,ij}+ \gamma_{ij}+\alpha_{ki}+\epsilon_{ijk}\]
\[\gamma_{ij} \sim N\left(0,\sigma_{\mathbf{T}}^{2}\right)\] \[a_{ki} \sim N(0,\Psi)\] \[\epsilon_{ijk} \sim N\left(0,\sigma^{2}A_{ii}\right)\]
where \(\beta_{0}\) is the overall mean; \(\beta_{1,i}\) is a fixed-effect for 'experience', with \(i=1,\,\ldots,\,3\); \(\beta_{2,i}\) is a fixed-effect for 'image spatial resolution', with \(j=1,\,\ldots,\,4\); \(\beta_{3,ij}\) is a fixed-effect interaction term; \(\gamma_{ij}\) is a random intercept for 'image spatial resolution' \(j\) within 1 'assessor' \(k\), with \(k=1,\,\ldots,\,K\); \(a_{\omega,i}\) is a random effect for 'assessor' \(k\) nested in 'experience' group \(i\)\(\epsilon_{ijk}\) is a within-group error term; \(A_{ii}\) are positive-definite matrices to model heteroscedasticity (see below); \(\sigma_{\mathbf{T}}^{2}\) is the 'assessor'-specific effects variance; \(\Psi\) is a positive-definite symmetric variance-covariance matrix of grouped between-assessor residuals.
To evaluate differences between experience levels and image spatial resolution levels, we set Group 1 and RPAS as reference terms in the corresponding fixed-effects contrasts matrices,
\[X_{i}=\begin{bmatrix}0&0\\ 1&0\\ 0&1\end{bmatrix},\,\,\,\text{and}\,\,X_{j}=\begin{bmatrix}0&0&0\\ 1&0&0\\ 0&1&0\\ 0&0&1\end{bmatrix}.\]
We tested for heterogeneity in between-assessor variance using specific positive-definite matrix structures of the random effects. We built models with a general symmetric matrix and with a simplified (diagonal only) matrix, with 'experience' and 'image spatial resolution' as grouping variables (\(g_{ij}\)):
\[\Psi^{S}=\begin{bmatrix}\sigma_{g_{1}}^{2}&\sigma_{g_{2,1}}&\sigma_{g_{2,1}} \\ \sigma_{g_{2,1}}&\sigma_{g_{2,1}}^{2}&\sigma_{g_{2,1}}\\ \sigma_{g_{2,1}}&\sigma_{g_{2,1}}&\sigma_{g_{2,1}}^{2}\end{bmatrix},\,\,\, \Psi^{D}=\begin{bmatrix}\sigma_{g_{1}}^{2}&0&0\\ 0&\sigma_{g_{2,1}}^{2}&0\\ 0&0&\sigma_{g_{2,1}}^{2}\end{bmatrix}.\]
For each grouping variable, we compared models with each of these structures and a model with an intercept-only random effect for 'assessor'. Models with \(\Psi^{S}\) evaluated the correlation in residuals between levels of grouping variables, and models with \(\Psi^{D}\) tested the hypothesis that \(\sigma_{g_{1}}^{2}\
eq\sigma_{g_{2}}^{2}\
eq\sigma_{g_{2}}^{2}\) (i.e., uncorrelated between-assessor heterogeneity).
To assess heterogeneity in within-assessor variance (heteroscedasticity), we selected competing variance function models (\(A_{ii}\)) after inspection of patterns in the residuals of the mixed-effects models with better fit. We considered:
* \(\text{var}\left(\epsilon_{ijk}\right)=\sigma^{a}\beta_{g_{ij}}^{2}\rightarrow\text {different variances by factor levels}\) \(g_{i}\)
* \(\text{var}\left(\epsilon_{ijk}\right)=\sigma^{2}\left|\
u_{ijk}\right|^{2} \rightarrow\text{variance as power of a covariate }\left(\
u_{k,ij}\right)\)
* \(\text{var}\left(\epsilon_{ijk}\right)=\sigma^{2}\left|\bar{\sigma}^{n_{ijk}} \rightarrow\text{variance exponential of a covariate }\left(\
u_{k,ij}\right)\right.\)
where \(\delta\) is a vector of variance parameters of the grouping variable, and \(\
u_{k,i}\) is a variance covariate derived from the fitted values of a model which was updated during the fitting process.
We fitted models using maximum-likelihood methods in the nlme package (Pinheiro & Bates, 2000; Pinheiro, Bates, & R Core Team, 2023) in R (R Core Team, 2023). Given the relatively low sample sizes, we used a set of models with reduced parameters and the small sample size Akaike information criterion (AIC\({}_{c}\)) for multi-model selection and inference ([PERSON] & Anderson, 2002). For a given set of models, we obtained \(\Delta_{i}\) as \(\text{AIC}_{ci}-\text{minAIC}_{c}\), where \(\text{minAIC}_{c}\) is the minimum \(\text{AIC}_{c}\) from the model set, to calculate 'Akaike weights' for each model \(i\). These were \(w_{i}=\exp\left(-\frac{1}{2}\Delta_{i}\right)/\sum\limits_{r=1}^{\text{R}}\exp \left(-\frac{1}{2}\Delta_{r}\right)\). For inference, we obtained averaged estimates of parameters of interest as \(\widehat{\theta}=\sum\limits_{r=1}^{R}w_{i}\widehat{\theta}_{r}/\sum\limits_{r=1 }^{R}w_{i}\), where \(\widehat{\theta}_{r}\) is the parameter value estimated with model \(r\). We also assessed model fit using residual plots for heteroscedasticity, normal probability plots and numerical summaries based on approximate confidence intervals of parameters (see Data S3).
To evaluate bias in walrus counts derived from 'image spatial resolution' and 'experience', we used predictions from the best-fit models for each analysis. Predictions were expressed at the counting scale, \(E(Y)\), by exponentiation and using an appropriate bias correction, \(\widehat{\sigma}^{2+\sigma}/2\). This method was expected to perform well because counts were relatively large, without zero values and they had relatively small dispersion ([PERSON] and [PERSON], 2010).
For each level in 'experience' and 'image spatial resolution', we obtained \(\text{bias}\!\left(\widehat{Y}\right)=E_{Y}\!\left(\widehat{Y}\right)-\!Y\) and mean squared error (MSE) as \(E_{Y}\!\left[\left(\widehat{Y}-Y\right)^{2}\right]=\text{var}_{Y}\!\left( \widehat{Y}\right)+\text{bias}^{2}\!\left(\widehat{Y}\right)\), where \(Y\) is the RPAS ground-truthed count. To obtain a robust estimate of \(\text{var}_{Y}\!\left(\widehat{Y}\right)\) we used stratified non-parametric balanced bootstrap resampling ([PERSON] et al., 1986), using 'assessor' within 'experience' group as resampling unit. In each of \(\mathbf{B}\!=\!2000\) bootstrap samples, each assessor in each experience group appeared exactly \(\mathbf{B}\) times in the union of the bootstrap samples, which maintained the natural hierarchy of the data. This method had a slightly better nominal coverage of model parameters by the confidence intervals than a nonparametric residual bootstrap method ([PERSON] et al., 2003) and performed better in simulations (data not presented) due to the simplified random effects structure of our models. At each simulation, model predictions of \(\log\!\left(Y_{i,j}\right)\) were obtained from model-averaged parameter estimates to preserve uncertainty in model selection.
## Analysis 2: effect of the crowd on walrus count accuracy at different spatial resolutions
To generate a skill pool equivalent to crowdsourcing campaigns, where citizen scientists review a portion of the imagery, we combined the counts from Group 2, Group 3 and Group 4 into a group named Crowd. Because this group had a mixture of assessors counting walruses in all four images (14 assessors) and assessors counting walruses in one of the four images (36 assessors), it was an unbalanced design with 50 assessors and 90 counts in total (excluding the same two outliers mentioned in the section above). To model data dependence in the predictors, we retained 'assessor' as a grouping variable.
We expressed the count of 'assessor' \(k\) per 'image spatial resolution' \(j\) as:
\[\log\!\left(\mu_{jk}\right) =\beta_{0}+\beta_{1,j}+\gamma_{kj}+\alpha_{kj}+e_{jk}\] \[\gamma_{kj}\sim N\left(0,\sigma_{\mathbf{\mathrm{T}}}^{2}\right)\]
\[\alpha_{kj} \sim N\!\left(0,\sigma_{\mathbf{\mathrm{a}}}^{2}\right)\] \[\epsilon_{jk} \sim N\!\left(0,\sigma^{2}A_{k}\right)\]
where \(\beta_{0}\) is the overall mean; \(\beta_{1,j}\) is a fixed-effect for 'image spatial resolution', with \(j\!=\!1\), \(\ldots\), \(4\); \(\gamma_{kj}\) is a random intercept for 'image spatial resolution' \(j\) within 'assessor' \(k\), with \(k\!=\!1\), \(\ldots\), \(K\); \(\alpha_{kj}\) is a random intercept for the interaction 'assessor' \(k\) and 'image spatial resolution'; \(e_{jk}\) is a within-group error term; \(A_{ij}\) are positive-definite matrices to model heteroscedasticity (see below); \(\sigma_{\mathbf{\mathrm{T}}}^{2}\) is the assessor-specific effects variance; \(\sigma_{\mathbf{\mathrm{a}}}^{2}\) is the variance of the interaction 'assessor' and 'image spatial resolution'.
We tested for heterogeneity in between-assessor and within-assessor variances, similar to Analysis 1.
We fitted, selected and evaluated the models tested here, in the same manner as in Analysis 1. Inference and bias assessment were also evaluated using the same methods as used for Analysis 1, with the difference that'assessor' was the main resampling unit for the stratified non-parametric balanced bootstrap resampling, though we retained the grouping by 'experience', despite it not being explicitly modelled, to preserve the original data structure in each bootstrap simulation.
## Walrus herd density
We used a semi-automated method to determine the herd density of walruses in the RPAS image using ESRI ArcMap 10.8 (ESRI, 2023). First, the RPAS image was georeferenced to the satellite image (Georeferencing tool in ArcMap). This step was required due to the inherent inaccuracies in the spatial referencing of satellite and RPAS images. One expert placed points in the middle of each individual walrus present in the RPAS image. Then, we constructed a convex hull around each point to draw an outline around the group of walruses (Minimum Bounding Geometry tool with the option of Convex Hull in ArcMap). As this outline included only half of the body of some walruses, we then used the Buffer tool to ensure that all Walruses were included in the outline, using a buffer of \(1.5\,\mathrm{m}\), as the average size of an adult walrus is \(3\,\mathrm{m}\) (\(2.7\,\mathrm{m}\) for females and \(3.2\,\mathrm{m}\) for males; [PERSON], 2018).
The herd density was estimated as the quotient of the number of walruses within the outline divided by the area in \(\mathrm{m}^{2}\) of the outline of the group of walruses.
## Results
### Model selection
For Analysis 1, we tested \(11\) models to investigate the effect of 'image spatial resolution' and 'experience'
when looking at the predicted counts (Fig. 2). Model predictions performed well in terms of precision with appropriate sample size (i.e., Group 3; \(n=9\)) and underperformed otherwise (Group 2; \(n=5\) assessors; Fig. 2). The Crowd showed more variation in the observed counts than any other groups, due in part to its reasonably high sample size (\(n=50\)), which was the highest among all groups (Fig. 2).
When comparing the experience level of the assessors (Group 2 and Group 3), there was less bias and variance for experts (Group 2) for the satellite image with \(30\,\mathrm{cm}\) resolution. For the satellite images with \(50\,\mathrm{cm}\) resolution, both groups showed similar estimated bias and variance, and for the satellite image with \(15\,\mathrm{cm}\) resolution, there was less bias and variance for Group 3 (mixed level of experiences).
### Walrus herd density
The semi-automated perimeter drawn around the walruses (blue full line in Fig. 3) is \(839.40\,\mathrm{m}^{2}\) and includes \(73\) individual walruses. Herd density was thus \(0.09\) walrus/\(\mathrm{m}^{2}\).
## Discussion
To the best of our knowledge, this study is the first to successfully obtain near-simultaneous aerial- and space-borne sensor imagery of a walrus herd resting on shore. The time difference of \(15\,\mathrm{min}\) between the satellite and RPAS imagery and the presence of observers on the ground providing direct observations of the walrus herds during these \(15\,\mathrm{min}\) supported the assumption that no changes in the number of walruses or composition occurred between the image captures. Other studies have tried to obtain satellite imagery captured during aerial surveys and were able to pair them within \(1.5\,\mathrm{h}\)([PERSON] et al., 2023), or \(5-9\,\mathrm{h}\)([PERSON] and [PERSON], 2021). However, the dynamic fluxes in herd attendance limited their inference in validating their interpretation of herd size.
This study demonstrated that VHR satellite imagery can be used to estimate abundance of hauled-out walruses with reasonable accuracy when compared to total counts from on-site RPAS-facilitated images (i.e., total ground truthing). Satellite imagery with a \(30\,\mathrm{cm}\) spatial resolution provided the most accurate results (compared with \(15\,\mathrm{cm}\) and \(50\,\mathrm{cm}\) resolution). This is intuitive with respect to the \(50\,\mathrm{cm}\) resolution because it provides less detail, making it more difficult to be confident in the detection (see also [PERSON] et al., 2019, 2023; [PERSON] et al., 2014). It was a bit more surprising that the \(15\,\mathrm{cm}\) imagery had a lower count accuracy. This is likely because the \(15\,\mathrm{cm}\) imagery is actually only a modified version of the \(30\,\mathrm{cm}\) image using a high-definition algorithm, which may create artefacts that do not match the reality on the ground. Further work exploring the value of such algorithms is needed. A satellite image with a raw resolution of \(15\,\mathrm{cm}\) would likely provide more accurate results. Currently, no
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline Image type & Experience & bias(\(\overline{\gamma}\)) & bias(\(\overline{\gamma}\)) & \(\%\mathrm{bias}\)(\(\overline{\gamma}\)) & \(\mathrm{var}_{\gamma}\)(\(\overline{\gamma}\)) & M5E & \(\sqrt{\mathrm{MSE}}\) \\ \hline RPAS & Group 1 & \(0.00\,(0.00)\) & \(0.00\,(0.00,0.01)\) & \(0.00\,(0.00,0.00)\) & \(0.00\,(0.00)\) \\ VHR 15 & Group 1 & \(-80.0\,(5.96)\) & \(-7.94\,[-12.55,-3.99]\) & \(-10.88\) & \(4.98\,[68.08]\) & \(8.25\,[75.0]\) \\ VHR 30 & Group 1 & \(-5.60\,(5.18)\) & \(-5.23\,[-9.55,-1.72]\) & \(-7.17\,[3.80]\) & \(31.18\,[5.58]\) \\ VHR 50 & Group 1 & \(-5.60\,(4.51)\) & \(-5.29\,[-9.85,-2.49]\) & \(-7.25\,[2.77]\) & \(30.79\,[5.55]\) \\ RPAS & Group 2 & \(0.20\,(0.45)\) & \(0.20\,(0.00,6.0]\) & \(0.28\,[0.03]\) & \(0.07\,[0.26]\) \\ VHR 15 & Group 2 & \(-26.00\,(2.12)\) & \(-25.88\,[-27.33,-24.26]\) & \(-35.45\,[0.61]\) & \(670.22\,[25.89]\) \\ VHR 30 & Group 2 & \(-16.20\,(8.23)\) & \(-16.16\,[-20.79,-9.11]\) & \(-22.14\,[8.94]\) & \(270.07\,[16.43]\) \\ VHR 50 & Group 2 & \(-27.80\,(7.92)\) & \(-28.06\,[-34.20,-21.61]\) & \(-38.44\,[9.57]\) & \(796.87\,[28.23]\) \\ RPAS & Group 3 & \(0.33\,(1.12)\) & \(0.31\,[-0.34,0.89]\) & \(0.42\,[0.12]\) & \(0.22\,[0.47]\) \\ VHR 15 & Group 3 & \(-22.14\,(6.01)\) & \(-22.04\,[-25.91,-17.87]\) & \(-30.19\,[4.38]\) & \(490.13\,[22.14]\) \\ VHR 30 & Group 3 & \(-19.00\,(8.72)\) & \(-19.16\,[-24.48,-14.18]\) & \(-26.25\,[7.17]\) & \(374.30\,[19.35]\) \\ VHR 50 & Group 3 & \(-27.00\,(6.84)\) & \(-27.16\,[-31.14,-23.10]\) & \(-37.21\,[4.15]\) & \(742.05\,[27.24]\) \\ RPAS & Crowd & \(0.13\,(0.76)\) & \(0.12\,[-0.15,0.46]\) & \(0.17\,[0.02]\) & \(0.04\,[0.2]\) \\ VHR 15 & Crowd & \(-25.24\,(5.66)\) & \(-24.92\,[-26.98,-22.85]\) & \(-34.13\,[1.19]\) & \(622.1\,[24.94]\) \\ VHR 30 & Crowd & \(-18.83\,(6.62)\) & \(-18.62\,[-22.28,-15.20]\) & \(-25.50\,[3.10]\) & \(349.69\,[18.7]\) \\ VHR 50 & Crowd & \(-23.04\,(12.47)\) & \(-23.96\,[-28.34,-19.61]\) & \(-32.83\,[5.10]\) & \(579.41\,[24.07]\) \\ \hline \hline \end{tabular} In squared brackets are estimated \(95\%\) bootstrap confidence intervals, and in parentheses are standard deviations for estimated and observed bias respectively.
MSE, mean square error; RPAS, remotely piloted aircraft system; VHR, very high-resolution.
\end{table}
Table 4: Observed \(\mathrm{(bias(\overline{\gamma}))}\) and estimated \(\mathrm{(bias(\overline{\gamma}))}\) bias, mean squared error (MSE) and root mean square error (RMSE) of walrus counts from images from different platforms and resolutions obtained by assessors with different experience levels (first analysis); and by a crowd (second analysis).
* [592] (2024) The Authors. _Remote Sensing in Ecology and Conservation_ published by John Wiley & Sons Ltd on behalf of Zoological Society of London.
Figure 2. Boxplots of walrus counts by image spatial resolution and experience level of the assessors (Analysis 1) and by image spatial resolution and for the Crowd (Analysis 2). The top row provides observations, and the bottom row provides bootstrap predictions from log-linear models in Analyses 1 (GROUP 1-3) and 2 (CROWD). Bows represent 50% of the central data, with limits defined by first (25%) and third (75%) quartiles. The solid lines are median values. Vertical lines are maximum and minimum values without outliers, which are depicted by solid points.
VHR satellites offer such raw spatial resolution, but Albedo is currently developing a constellation of VHR satellites that are designed to capture optical images with a 10 cm resolution. Launch of these satellites is planned for 2024 (Albedo, 2023).
All image assessor groups tested in this study under-counted values in the satellite images, across all spatial resolutions. This was a somewhat surprising result because the images used in this study represent ideal conditions for counting walruses individually. The animals were spread out and the background was light and not structurally complex, which allowed individual walruses to be distinguished easily. There were also not many animals in the images, reducing the risk of observer fatigue and subsequent errors in counting. Furthermore, light conditions were also ideal. Thus, our expectation is that undercounting will be even more pronounced when larger herds are assessed. Walruses are known to gather tightly in densities of 0.63-1.56 walruses/m\({}^{2}\) and in groups of hundreds of animals, or even 1000s or 10s of 1000s in some areas in the Pacific, covering areas of 100 000 m\({}^{2}\)([PERSON] et al., 2017; [PERSON] et al., 2016, 2022; [PERSON] & [PERSON], 2022).
The crowd was less accurate at counting walruses in VHR satellite imagery than experts, as would be expected, and their counts were more variable due to the higher number of counters and the more varied experience levels. Other factors may have played a role in the reduced accuracy, such as the potential for higher level of distraction for members of the public doing counts. However, the higher variation in the observed counts made by the crowd could be modelled, providing more precise mean predictions and a measure of uncertainty representative of citizen science projects. Thus, the crowd counts could be calibrated if some ground-truthed images are included in the model. For larger haul-out groups, a greater increase in bias and variation can be expected, lowering the accuracy. [PERSON] et al. (2020) also saw a reduced accuracy in the crowd counts, with the crowd over-counting animals by misidentifying rocks as Weddell seals.
The density estimated in this study is low compared to many reported densities for walrus haul-out groups ([PERSON] et al., 2017; [PERSON] et al., 2012; [PERSON] et al., 2014). It is likely that group size, temperature, predation risk, topography of the haul-out site, disturbance levels and other factors result in variable densities at haul-out sites. This is an important issue to address when assessing aerial imagery for abundance determination. Models should, where feasible, include a density measure for each group being counted, so that uncertainty can be estimated.
An alternative to citizen scientists' walrus counts in satellite imagery is automated detection. Several studies have been successful in detecting various types of wildlife in VHR satellite imagery ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2023), but more work is needed to provide accurate counts. Convolutional neural networks (CNNs), a type of machine learning is proving to be promising for detecting albatrosses ([PERSON] et al., 2020), whales ([PERSON] et al., 2019; [PERSON] et al., 2023) and seals ([PERSON] et al., 2021). So, it is likely going to be useful for walruses too. CNNs require large training datasets ([PERSON] et al., 2015), which are yet to be produced for walruses.
The results discussed herein are based on one satellite image of a walrus group hauled out on a sandy beach and with low density of walruses. Successful detection and counting of walruses are expected to be affected by the contrast between the walrus and the background environment, which may be influenced by a number of parameters, including geological substrate, light levels, haze and colour of the walruses. Therefore, we recommend repeated studies of haul-out groups with different conditions, including less ideal conditions - such as variable densities of walruses and various substrates (e.g., rocky shores, sandy beaches with large scattered boulders). Here we used RPAS imagery captured nearly simultaneously with the satellite imagery, which allowed us to ground truth estimates from the satellite imagery, but remote cameras installed at known haul-out sites at
Figure 3.: Georeferenced RPAS image with the point annotations (red dot) used to draw a convex hull bounding geometry (black dotted line) and buffered to 1.5 m on the outside to include all walruses (blue full line).
heights that allow total counts of groups could work in a similar manner ([PERSON] et al., 2018), although we anticipate that for larger and tighter haul-out groups, individual walnves will be difficult to distinguish. Therefore, applying the same method as used for aerial surveys, where the outline of the group is digitized and the density of portions of this tight group is estimated from satellite-captured images will be needed to provide counts that are accurate enough to be useful for management purposes ([PERSON] et al., 2022). Additionally, future satellites are expected to have increasingly good resolution.
## Conclusion
Walruses can be counted individually in VHR optical satellite imagery, at least when they gather on shores at relatively low densities. In this study, the highest currently available raw spatial resolution of 30 cm provided the best accuracy; therefore, we recommend that this resolution be selected for assessing abundance until the raw resolution improves for optical satellite imagery. In our study, citizen scientists provided less accurate counts, but the data created in this very cost-effective manner could be calibrated provided some appropriate ground-truth data. Our methods need to be tested further with larger walrus groups on variable substrates.
## Author Contributions
HCC, PTF, KMK, CL, JF, RD conceived, planned and conducted the fieldwork; JF and HCC curated and analysed the data; HCC and JF drafted the manuscript. All authors provided critical feedback and helped shape the research, analysis and the manuscript.
## Acknowledgements
We are thankful to WWF, the Norwegian Polar Institute, the Royal Bank of Canada Tech for Nature Fund, and players of People's Postcode Lottery, who provided the funding needed to facilitate the fieldwork in Vablard. This study represents a contribution to the Ecosystems component of the Wildlife from Space Project at the British Antarctic Survey Polar Science for Planet Earth programme, which is funded by the Natural Environment Research programme. We are grateful to [PERSON], [PERSON] and [PERSON] from the Norwegian Polar Institute in Ny-Alesund who helped keep the project atlogut despite air-company strikes and COVID conditions. We are thankful to the volunteers that counted walnvis in the RPAS or VHR satellite images: [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and 13 anonymous volunteers. Our RPAS flights at Sarstangen were conducted under Permit No. 22/00507-2 from the Governor of Svalbard (RiS number 11906).
## Conflict of Interest
The authors declare no conflicts of interest.
## Data Availability Statement
All the counts per assessor and per image type are provided in a csv format (Data S2).
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## Supporting Information
Additional supporting information may be found online in the Supporting Information section at the end of the article.
**Data S1.** Protocol to count walruses in RPAS and VHR satellite imagery using VGG.
**Data S2.** Counts from all observers for the drone image and all three satellite images.
**Data S3.** Model selection.
**Data S4.** Drone image of walruses hauled out at Sarstangen, Norway, on 15 th July 2022. | wiley | Walruses from space: walrus counts in simultaneous remotely piloted aircraft system versus very high‐resolution satellite imagery | Hannah C. Cubaynes, Jaume Forcada, Kit M. Kovacs, Christian Lydersen, Rod Downie, Peter T. Fretwell | https://doi.org/10.1002/rse2.391 | 2,024 | CC-BY |
wiley/fdada6f0_c799_49b5_8659_9f5b7bcf0101.md | # Earth and Space Science
Warm-Season Drying Across Europe and Its Links to Atmospheric Circulation
[PERSON]
1 Faculty of Environmental Sciences, Czech University of Life Sciences, Prague, Czech Republic, 2 Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czech Republic, 3 Global Change Research Institute of the Czech Academy of Sciences, Brno, Czech Republic, 4 Institute of Meteorology and Climatology, University of Natural Resources and Life Sciences, Vienna, Austria
[PERSON]
1 Faculty of Environmental Sciences, Czech University of Life Sciences, Prague, Czech Republic, 2 Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czech Republic, 3 Global Change Research Institute of the Czech Academy of Sciences, Brno, Czech Republic, 4 Institute of Meteorology and Climatology, University of Natural Resources and Life Sciences, Vienna, Austria
[PERSON]
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[PERSON]
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[PERSON]
4
###### Abstract
We study drying trends across the central latitude strip of Europe (47.5-52.5\"N and 2.5-27.5\"E) during 1980-2019 and their links to atmospheric circulation. Daily differences between potential evapotranspiration and precipitation (PET-P) calculated from the E-OBS data are used to characterize dryness, and atmospheric circulation is represented by circulation types classified using daily sea level pressure patterns from the NCEP/NCAR reanalysis. Circulation types favoring dry conditions in vegetation season (April-September) are identified based on daily PET-P, and their temporal changes, seasonal variations, and links to trends in dryness in individual European regions are analyzed. In the early vegetation season (AMI), drying trends are observed mainly in Western and Central Europe while in the late vegetation season (JAS), they are located predominantly in Eastern Europe. The dry circulation types include all anticyclonic types in all regions, as well as northeast to south (southwest in Eastern Europe) directional types. Trends of the dry circulation types correspond to those of dryness: the largest increase is found during AMJ in Western and Central Europe but during JAS in Eastern Europe. The results show that trends in dryness in the central latitude strip of Europe in the warm half-year were associated with changes in atmospheric circulation, as the largest increases in frequency of dry circulation types occurred in the regions and months affected by pronounced drying. The increasing frequency of anticyclonic types in AMI and reduced inflow of moist air masses from the Atlantic are the key factors supporting intensification of dry conditions in European mid-latitudes.
2023E003434 10.1209/2023E003434 10.1209/2023E003434 10.
of this type have been relatively rare for most other European regions. The reasons include pronounced drying reported for Central and Western Europe, as well as the fact that this is a highly vulnerable area, where increased frequency of heat waves and droughts during the vegetation season are associated with many adverse effects on ecosystem services such as plant productivity (with related strong economic losses in agricultural crop production) despite relatively high average annual precipitation rates ([PERSON] et al., 2019). Increasing trends in drought severity and frequency have been found in several local studies within Central Europe, such as in Germany ([PERSON] & [PERSON], 1999; [PERSON] et al., 2013), the Czech Republic and Slovakia ([PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2009), and Poland ([PERSON] et al., 2022; [PERSON] & [PERSON], 2016; [PERSON] et al., 2022). Drought development in these areas has been confirmed also by studies analyzing droughts in a broader European spatial context ([PERSON] et al., 2023; [PERSON] et al., 2020; [PERSON] et al., 2019; [PERSON] & [PERSON], 2021; [PERSON] et al., 2017, 2020; [PERSON] et al., 2022; [PERSON] et al., 2023; [PERSON] et al., 2017; [PERSON] et al., 2023). These have reported substantial drying especially in the Iberian Peninsula ([PERSON] et al., 2007; [PERSON] et al., 2017, 2020) and France ([PERSON] et al., 2017, 2020). In the Mediterranean area, dry hotspots have been reported mainly from its southeastern part (the Balkans; [PERSON] et al., 2015; [PERSON] et al., 2021) and Italy ([PERSON] et al., 2019; [PERSON], [PERSON], & [PERSON], 2020). In Eastern Europe, the most pronounced drying has been observed in Ukraine ([PERSON] et al., 2017), the Baltic region ([PERSON] et al., 2020), and Hungary ([PERSON] et al., 2022). Northern Europe is categorized as a humid area where most conditions prevail ([PERSON] et al., 2022), but under specific circulation patterns like those in summer 2018, significant droughts occur also in this region (southern Norway, Sweden and Finland; [PERSON] et al., 2020; [PERSON] et al., 2023). Worsening drought conditions in Europe have been reported not only in lowlands but also in mountainous areas, such as in the Alps ([PERSON] et al., 2019; [PERSON] et al., 2022) and the Polish Carpathians ([PERSON] et al., 2021; [PERSON] et al., 2022).
From a seasonal point of view, most studies on drought deal with the vegetation season from April to September ([PERSON] et al., 2021, 2023; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2009), when water availability is critical for agriculture, or the summer months of June-August ([PERSON] & [PERSON], 2016; [PERSON] et al., 2006; [PERSON] et al., 2009; [PERSON] et al., 2022; [PERSON] et al., 2018), when temperatures are highest and amplify evapotranspiration. Only exceptionally is a specific month studied ([PERSON] & [PERSON], 2023). Most studies use data after 1950 to the present ([PERSON] et al., 2015; [PERSON] et al., 2021; [PERSON] et al., 2017; [PERSON] et al., 2022), because longer time series are often unavailable or do not provide the necessary variables. In our analysis, we focused on the period since 1980 characterized by a pronounced change in European climate, with increasing temperature and associated drying.
Drought can be characterized by three main aspects: intensity, duration, and spatial coverage ([PERSON] & [PERSON], 2022). Meteorological, hydrological, and agricultural drought indices have been developed for monitoring and quantifying drought. A drought index usually measures moisture deviation from normal local conditions based on its historical distribution ([PERSON], 2011). Most commonly used are the Standardized Precipitation Index (SPI; [PERSON] et al., 1993), the Standardized Precipitation Evapotranspiration Index (SPEI; [PERSON] et al., 2010), the Palmer Drought Severity Index (PDSI; [PERSON], 1965), the Penman-Monteith method ([PERSON] et al., 1998), as well as precipitation, temperature, or streamflow threshold values ([PERSON] et al., 2007; [PERSON] & [PERSON], 2018; [PERSON] & [PERSON], 2019). Many studies involve a combination of multiple indices ([PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2009). In our analysis, dry and wet conditions were identified based on the imbalance between atmospheric water demand (i.e., potential evapotranspiration and supply (i.e., precipitation). This constitutes a straightforward characterization of drought development also at the daily scale ([PERSON] et al., 2020; [PERSON], 2019).
Atmospheric circulation can be described by circulation types, and many classifications have been developed and applied in relation to drought. There are three basic groups of classifications: subjective (also termed manual), mixed (hybrid), and objective (computer-assisted, automated) ([PERSON] et al., 2008). The subjective methods (e.g., [PERSON], 1952; [PERSON], 1972) were later objectified to mixed or objective classifications, including the Lamb (developed by [PERSON] and [PERSON] (1977)) and Hess-Brezowsky classifications ([PERSON], 2007). Many studies use the objective [PERSON] (Lamb) classification for different regions ([PERSON] et al., 2021; [PERSON] et al., 2009; [PERSON] et al., 2010; [PERSON] et al., 2020; [PERSON] et al., 2014) or the Hess-Brezowsky catalog ([PERSON] et al., 2011; [PERSON], 1999; [PERSON] et al., 2009). The objective Jenkinson classification, a widely used method that was recently applied in a study on circulation-to-drought links in Central Europe ([PERSON] et al., 2020), is modified for individual European regions (see Section 2.2) in the present analysis.
We extend the study of [PERSON] et al. (2020), which focused on the area of the Czech Republic and examined drought trends and their links to circulation for the warm (April-September) and cold (October-March) seasons. The circulation types were divided into anticyclonic, cyclonic, and directional, then subsequently classified into dry and wet. A significant increase of dry and a decrease of wet circulation types was found since the 1950s, coinciding with the observed trends toward drier conditions in both seasons. The record-breaking drought in the 2015-2018 period was also associated with atmospheric circulation favorable for drought ([PERSON] et al., 2020). It remained an open question, however, to what extent these relationships between trends in drought and atmospheric circulation hold true for other European regions.
This study aims to extend knowledge of the relationships between dryness and atmospheric circulation. In contrast to [PERSON] et al. (2020), the analysis is performed on a daily time scale, using differences between potential evapotranspiration and precipitation and circulation types classifications centered for individual regions using a \"moving window\" approach. This concept allows linking rapidly changing atmospheric circulation to dry or wet tendencies in each region separately. We also expand the analysis to a broader spatial scale (from Western to Eastern Europe across the central latitude strip), in order to reveal the extent to which the trends in dryness over the past several decades may have been driven by changing atmospheric circulation. We deal with the vegetation season (April-September), when dryness has the most severe impacts, including negative effects on agriculture, with an emphasis on differences between its early (April-June) and late (July-September) parts.
## 2 Data and Methods
Links between dryness and atmospheric circulation are evaluated using differences between potential evapotranspiration (PET) and precipitation (P), and circulation types (CTs) derived from sea level pressure data.
### Characterizing Dryness
Dryness is characterized by the Climatic Water Balance Index ([PERSON] & [PERSON], 2011), defined as difference between PET and P (calculated from gridded E-OBS 24.0e data; [PERSON] et al., 2018). The same index has recently been used to investigate a rapidity on a daily scale, for example, by [PERSON] et al. (2020) or [PERSON] et al. (2023). PET is defined as hypothetical evapotranspiration with unlimited water access and evaporation needs independent of crop type, crop developmental stage, and management practices. In such a concept, soil factors do not affect PET ([PERSON] et al., 1998; [PERSON] et al., 2020). To calculate PET, we used the Oudin formula:
\[\text{PET}=\frac{0.408\ R_{e}(\text{TG}+5)}{100},\text{ if TG}+5>0,\]
\[\text{PET}=0\text{ otherwise}\]
where PET (mm day\({}^{-1}\)) is potential evapotranspiration, Re (M J m\({}^{-2}\) day\({}^{-1}\)) is the top-of-atmosphere solar radiation calculated on the basis of the time of year and geographical location, and TG (\"C) is mean daily air temperature ([PERSON] et al., 2005). The main advantage of the Oudin formula is that it needs only temperature and radiation data while still showing good results compared to more data-demanding methods ([PERSON] et al., 2017; [PERSON] et al., 2005).
### Vegetation Season, Study Period and Regions
The analysis is carried out for the vegetation season (April-September) divided into two parts: early vegetation season (April-June, AMJ) and late vegetation season (July-September, JAS). The reasons for splitting the vegetation season into two parts are that (a) drought during AMJ has particularly large impacts on vegetation in critical stages of its development ([PERSON] et al., 2009), and (b) trends in dryness and links to circulation may differ between the two parts of the vegetation season. The study period is 1980-2019, for which the trends toward drying are most pronounced ([PERSON] et al., 2022). Changes in the earlier decades of the 20 th century were dominated rather by decadal-scale variability, which makes interpretation of trends less straightforward. Trends in dryness characteristics and frequencies of CTs were estimated by linear regression and the _t_-test was used to evaluate significance of the slope (at p = 0.05).
While the whole of continental Europe is included in maps of the trends in dryness, the study focuses on regions across the central latitude strip of Europe (along the 50\({}^{\circ}\) latitude, Figure 1). The regions correspond to 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) longitude-latitude grid boxes stretching from Western to Eastern Europe, with centers at [5\({}^{\circ}\)E, 50\({}^{\circ}\)N], [10\({}^{\circ}\)E, 50\({}^{\circ}\)N], [15\({}^{\circ}\)E, 50\({}^{\circ}\)N], [20\({}^{\circ}\)E, 50\({}^{\circ}\)N], and [25\({}^{\circ}\)E, 50\({}^{\circ}\)N]. Abbreviations for the regions include a numerical value that represents the center of the region in longitude terms. For example, the region centered at 10\({}^{\circ}\)E is hereafter labeled E10.
### Classification of Circulation Types (CTs)
Atmospheric circulation for the individual regions (Section 2.2) is characterized by circulation types (CTs) derived from circulation indices. The three indices--flow strength, direction, and vorticity ([PERSON] & [PERSON], 1977)--were calculated in a daily time step using the sea level pressure from the NCEP/NCAR reanalysis ([PERSON] et al., 1996). Based on the [PERSON] (1972) catalog, 27 CTs adjusted for each region were derived from the indices ([PERSON] et al., 2009). The detailed way of classifying daily patterns into CTs is described in [PERSON] et al. (2020) for Central Europe (the E15 region in the present analysis), and the procedure was analogous for the other regions under study.
When the absolute value of vorticity was at least five times the strength, strongly anticyclonic (A, if vorticity \(<\)0) or strongly cyclonic (C, if vorticity \(>\)0) types were assigned. If the flow strength was greater than the absolute value of vorticity, that day was classified as one of eight directional types (N, NE, E, SE, S, SW, W, and NW). The remaining days were classified into hybrid types based on their direction and anticyclonic or cyclonic vorticity ([PERSON] et al., 2020). Those CTs were assigned to one of three groups--anticyclonic (A, AN, ANE, AE, ASE, AS, ASW, AW), cyclonic (C, CN, CNE, CE, CSE, CS, CSW, CW, CNW), and directional (N, NE, E, SE, S, SW, W, NW). If the sea level pressure patterns had both flow strength and vorticity below 4, that day remained unclassified (U).
Figure 1: Regions analyzed in the study, centered around 50\({}^{\circ}\)N. Numbers indicate longitude of the center of each box (e.g., E5 represents 5\({}^{\circ}\)E).
## 3 Results
### Spatial Patterns and Within-Season Development of Trends in Dryness
The temporal development of PET, P, and PET\(-\)P in the individual regions for 1980-2019 is shown in Figure 2. A pronounced increase in PET was found in both parts of the vegetation season (driven by increasing temperature) while precipitation trends were relatively weak, with slight decreases (increases) prevailing in AMJ (JAS) (Figure 2). A notable decrease of precipitation in the JAS season was observed in the Eastern European region E25 since 2010, thus enhancing the rise of PET\(-\)P.
Spatial patterns of the PET\(-\)P trends for 1980-2019 are plotted for the whole of continental Europe in Figure 3. Areas with shades of red show a positive (drying) trend, while blue shades represent areas with a negative (wetting) trend. Black outline denotes areas of statistically significant change at p = 0.05. In the early vegetation season (Figure 3 left), a tendency to drying was found especially in the western and central part of Europe. The area of significant positive trends covers almost the whole of regions E5 and E10, and it extends partially to E15. Significant positive trends are found also in Eastern Europe (E25). Outside the studied regions, positive trends are located in the southeastern coastal area of the Baltic Sea and in northern Italy while negative trends occur only scarcely (e.g., in southwest Norway and southeastern Europe). The area of significant positive trends covers 43.0% (420,617 km\({}^{2}\)) of the central latitude strip of Europe, while significant negative trends do not occur in the studied area.
In the late vegetation season (Figure 3 right), the area of significant positive trends covers, in contrast to the AMJ season, only 9.3% (91,350 km\({}^{2}\)) of the central latitude strip. Almost all significant drying trends (within the study regions) are located in E25. Outside the study regions, the area of most pronounced drying occurs mainly in Eastern Europe (Ukraine and Moldova) and to a smaller extent also in other regions (Northern Europe, south-western Europe, and the northern part of the UK). Similarly to as seen for AMJ, significant trends to wetter conditions occur only in small isolated areas outside the study regions.
Figure 2: Mean seasonal values (AMJ\(-\)top, JAS—bottom) of potential evapotranspiration (PET), precipitation (P), and their differences (PET\(-\)P) in each region for 1980–2019. Solid lines show the 11-year moving averages of the mean seasonal values.
The development of trends during the vegetation season can be characterized in more detail when analyzing individual months separately (Figure 4). Within the central latitude strip, a significant drying trend was found in April and June; in May and JAS, by contrast, it is limited to only small isolated areas. In April, the drying trend occurred within large areas in Western and Central Europe (E10, E15) and partly also in Eastern Europe (E25) and was significant in 37.3% (364,821 km\({}^{2}\)) of the central latitude strip. In June, significant drying trends from Western through Central to Eastern Europe covered 36.5% (357,613 km\({}^{2}\)) of the central latitude strip.
Due to different patterns in PET\(-\)P trends for April, May, and June, we analyzed these in more detail using 31-day moving windows (Figure 5). Western (E5, E10) and partly also Central Europe (E15) have pronounced local maxima of the drying trends in April and June. The maximum drying trend appears in June also in the other regions (E20, E25), and a secondary maximum is found at the turn of August/September in E25. Wetting trends are less distinctive and were found mostly at the turn of July/August in Western Europe (E5 and E10), and in May and September for Central and Eastern Europe (E15-E25).
### Characteristics of CTs and Definition of Dry and Wet CTs
This section summarizes basic characteristics of the CTs, including their frequencies, mean PET\(-\)P values, and the definition of dry and wet CTs in individual regions under study. As the frequency of unclassified days (U) was small in all regions and both AMJ and JAS seasons (between 0.8% and 2.9%), they were excluded from further analysis.
All anticyclonic types (Section 2.3) are favorable to drying, meaning that they have positive mean PET\(-\)P values. This applies to all regions (Table 1). The opposite (negative mean PET\(-\)P values) holds true for cyclonic types except for those associated with easterly or southerly flow (CE, CSE, CS, and CSW), which, due to a relatively warm advection, have mean PET\(-\)P values close to zero or slightly positive in some regions (Table 1). That is why the disaggregation of cyclonic CTs into dry and wet (see below) slightly differs between the regions. Directional types have different dry tendencies depending on region: In Western Europe (E5, E10), positive mean PET\(-\)P values are mainly associated with easterly and southerly directions, while the other directional types are characterized by negative values. In Eastern Europe (E20, E25), by contrast, positive mean PET\(-\)P values are found for all directional types except for northerly.
Figure 3: Linear trends in PET\(-\)P for the two seasons (AMJ and JAS) for 1980–2019. The black outline delimits areas where the trends are significant at p = 0.05. The study regions along 50\({}^{\circ}\) latitude are marked by red boxes.
In all regions, the frequency of anticyclonic types (on average 44%) was higher compared to that of cyclonic types (18%). The highest frequencies of anticyclonic types are found between the E10 and E20 regions. The frequencies of directional types ranged between 35% and 40% in all regions, with their lowest values occurring in E10 and E15 (Table 1).
CTs supporting dry conditions (referred to hereinafter as \"dry\"), with positive mean PET\(-\)P differences, were identified for each region. Analogously, \"wet\" CTs were defined as those with negative mean PET\(-\)P values. Because the differences in CTs favorable to dry conditions were minor between AMJ and JAS (Tables S1 and S2 in Supporting Information S1), the definition was based on mean values for the whole vegetation season (April-September, Table 1). After preliminary analyses, we decided not to include CTs with mean PET\(-\)P values close to zero (in the interval between \(-\)0.5 and 0.5 mm/day) into either dry or wet. This concerned only 1 or 2 cyclonic CTs, and 1 to 4 directional CTs depending on region (Table 1). The reason was that these CTs were associated with little-pronounced PET\(-\)P characteristics (compared to the other CTs; note the much larger deviations from 0 for all anticyclonic and most cyclonic CTs) and their inclusion into dry or wet CTs might distort the results in case of directional CTs with higher frequency (e.g., N in E25, 6.6%).
Dry CTs include all anticyclonic types for all regions and directional CTs from the northeast through east to the south (NE, E, SE, S), and in Eastern Europe (E20 and E25) also southwest (SW). Only exceptionally is a cyclonic
Figure 4.— Linear trends in PET\(-\)P in individual months for 1980–2019. The black outline delimits areas where the trends are significant at p = 0.05. The study regions along 50\({}^{\circ}\) latitude are marked by red boxes.
type included within dry CTs (CSE in E10, with mean PET\(-\)P value 1.0 mm/day). Wet CTs, on the other hand, include most cyclonic types together with directional types from the southwest (except for Eastern Europe) to the north.
### Trends of CTs
Trends in the frequencies of anticyclonic (A), cyclonic (C), and directional (DIR) CTs in the individual regions are shown in Table 2. During AMI (upper part of Table 2), a marked increase of anticyclonic types is found in all regions (statistically significant in E5-E20), accompanied by a decrease of cyclonic types (except in E5) that is significant in E25. Trends of directional types are mostly insignificant, except for a pronounced negative trend in E5, which is primarily due to decrease of CTs with the northern component (significant for the NW type, Table S3 in Supporting Information S1). For the late vegetation season, cyclonic types have slightly positive trends in all regions but they are insignificant (lower part of Table 2). These results indicate different changes in CTs between the two parts of the vegetation season: a significant shift toward more anticyclonic circulation in AMJ across the whole central latitude strip but little-pronounced trends, with insignificant but widespread increases in cyclonic types, in JAS (Table 2).
Increased frequencies of anticyclonic CTs at the expense of cyclonic and directional types in AMJ are illustrated in Figure 6 (top). In Central Europe (E15), for example, the mean frequency of anticyclonic CTs was 39.7% in the 2010s compared to 30.8% in the 1980s. Meanwhile, the frequency of cyclonic types declined from 25.6% to 22.6%. In 2015, a season with particularly pronounced drought and heat waves across the central latitude strip of Europe ([PERSON] et al., 2017; [PERSON] et al., 2017), the frequency of anticyclonic CTs exceeded 57% in most regions (except for E25) while cyclonic CTs occurred in less than 10% of days during AMJ. In all regions, differences in frequencies between anticyclonic and cyclonic CTs steadily increased from the 1980s to the 2010s. During JAS (Figure 6, bottom), the trends were relatively weak and insignificant, mainly due to reaching a minimum in the frequency of anticyclonic types (and corresponding maximum in cyclonic and directional types) around 2000, followed by increase (decrease).
### Characteristics of Dry and Wet CTs and Their Trends
Within-season changes in frequencies of dry and wet CTs from April to September are plotted in Figure 7. Dry CTs are found in lower frequencies around May for most regions. At the same time, in this month the maximum frequency of wet CTs occurs, which corresponds also with the development of wetting in this month (Figures 4 and 5). The dry CTs generally occur more frequently in the late rather than early vegetation season, and mainly in Central and Eastern Europe (E15-E25).
Figure 5: Linear trends in PET\(-\)P in 31-day moving windows from April to September for 1980–2019. Red points mark trends significant at p = 0.05.
In the early vegetation season (AMJ), trends in dry CTs are positive in all regions (Table 3 left) and significant at p = 0.05 between E10 and E20. The magnitude of dry CTs' trends in these regions exceeds +2.5%/decade, corresponding to more than +10% increase over the 40 years under study. In the late vegetation season (JAS, Table 3 right), by contrast, a significant drying trend is found only in Eastern Europe (E25) while trends in dry CTs are relatively weak in the other regions.
The increase of dry CTs in the AMJ season in regions E5 to E20 is in line with the increase of anticyclonic types reported in Table 2 and is statistically significant (except for region E5, where the trend in dry CTs is insignificant). These changes in atmospheric circulation supported drying in these regions (Figure 3). Some discrepancy can be found only in E20, where the drying trends were less pronounced, mostly insignificant, and in contrast to a pronounced change toward more anticyclonic (and dry) CTs.
In the JAS season, dry CTs increase significantly only in the E25 region (Table 3). This is associated not with changes in anticyclonic CTs (trend close to zero, Table 2) but with directional CTs favorable for drying (namely E and SE; Table S4 in Supporting Information S1). Unlike in the other regions under study, the trend in Eastern Europe toward a higher frequency of dry CTs agrees with the large drying trends observed in the E25 region (Figure 3).
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline & \multicolumn{2}{c}{E5} & \multicolumn{2}{c}{E10} & \multicolumn{2}{c}{E15} & \multicolumn{2}{c}{E20} & \multicolumn{2}{c}{E25} \\ \cline{2-11} CT & Freq. (\%) & PET-P (mm/d) & Freq.
A statistically significant increase of dry CTs and corresponding decrease of wet CTs during AMJ are analyzed in more detail in Figure 8 (top). The temporal development of dry CTs shows a steady increase with decadal-scale variations in all regions and reaching a maximum in the early 2000s. Analogous (opposite) changes are found for wet CTs. The differences between frequencies of dry and wet CTs during AMJ increased from 16.5% in the 1980s to 25.5% in the 2010s (on average across the regions). The temporal changes in the JAS season (Figure 8 bottom) were characterized by decadal-scale variations rather than long-term trends (except in Eastern Europe, where a significant increase of dry CTs was found).
Subsequently, within-season variations in the trends of frequencies of dry CTs from April to September were analyzed (Figure 9). Increasing trends dominate in Central and Eastern Europe (E15-E25) throughout the vegetation season. These are largest in June, and a secondary maximum occurs at the turn of August/September. In the western part of the studied area (E5, E10), the trends in dry CTs are positive in AMJ only, with maxima in
\begin{table}
\begin{tabular}{l c c c c c c} \hline Region & Trend A (\%/decade) & p-value A (\(-\)) & Trend C (\%/decade) & p-value C (\(-\)) & Trend DIR (\%/decade) & p-value DIR (\(-\)) \\ \hline E5 AMJ & **2.55** & **0.025** & 0.38 & 0.686 & **-2.90** & **0.001** \\ E10 & **2.42** & **0.014** & \(-\)1.02 & 0.301 & \(-\)1.11 & 0.147 \\ E15 & **2.44** & **0.026** & \(-\)1.11 & 0.198 & \(-\)1.20 & 0.167 \\ E20 & **2.60** & **0.021** & \(-\)1.35 & 0.105 & \(-\)1.08 & 0.254 \\ E25 & 1.40 & 0.143 & **-2.09** & **0.031** & 0.70 & 0.406 \\ E5 JAS & \(-\)1.10 & 0.392 & 0.31 & 0.658 & 0.85 & 0.357 \\ E10 & 0.00 & 1.000 & 0.40 & 0.643 & \(-\)0.53 & 0.516 \\ E15 & \(-\)0.42 & 0.738 & 0.48 & 0.573 & \(-\)0.24 & 0.762 \\ E20 & 0.22 & 0.867 & 0.76 & 0.335 & \(-\)1.27 & 0.171 \\ E25 & 0.18 & 0.866 & 0.12 & 0.898 & \(-\)0.52 & 0.541 \\ \hline \end{tabular} _Note._ Bold values show trends significant at p = 0.05.
\end{table}
Table 2: _Linear Trends in Frequencies of Anticyclonic (A), Cyclonic (C), and Directional (DIR) CTs in AMJ (Top) and JAS (Bottom) Seasons for 1980–2019_
Figure 6: Seasonal frequencies of anticyclonic (A), cyclonic (C), and directional (DIR) CTs and their trends in individual regions for 1980–2019. Solid lines show the 11-year moving averages of the seasonal frequencies.
April and June. These results are in good agreement with significant April and June trends toward drier conditions in Western and Central Europe as well as maximum drying occurring in June and at the turn of August/September in Eastern Europe (Figure 5). This suggests close relationships between changes of dry CTs and dryness in the studied regions.
## 4 Discussion
The main goal of the present study was to better understand trends in dryness and their links to atmospheric circulation across the central latitude strip of Europe, that is, the area affected by pronounced recent drying, based on daily circulation-to-dryness links. We adopted--in a relatively innovative application to our knowledge, we are not aware of another study making use and benefit of a similar approach in drought research--the circulation type classification centered on individual \"windows\" across the study area. A different view of dryness--represented by the PET-P index on the daily time scale in our study--is another aspect which adds to existing knowledge. Studies focusing on drought and circulation often use monthly data (e.g., [PERSON] et al., 2020; [PERSON] et al., 2023; [PERSON] et al., 2015, 2022; [PERSON] et al., 2015; [PERSON] et al., 2016), or daily data aggregated to a monthly scale ([PERSON] et al., 2020, 2023; [PERSON] et al., 2019). The daily time scale is crucial in relating drought tendencies to atmospheric circulation patterns, whereas commonly used drought indices such as SPI, SPEI, and PDSI are usually calculated for monthly steps. If high temperatures occur, drought development can accelerate quickly together with heat waves (flash drought), so the daily time step is essential when studying drought dynamics. This is an important aspect in which our analysis differs from most recent drought studies, including those that link dry conditions to atmospheric circulation.
\begin{table}
\begin{tabular}{l c c c c} \hline Region & Trend AM (\%/decade) & p-value AMJ (\(-\)) & Trend JAS (\%/decade) & p-value JAS (\(-\)) \\ \hline E5 & 1.58 & 0.167 & \(-\)1.43 & 0.213 \\ E10 & **2.78** & **0.003** & \(-\)0.34 & 0.750 \\ E15 & **2.79** & **0.008** & 0.67 & 0.536 \\ E20 & **2.60** & **0.011** & 1.07 & 0.357 \\ E25 & 1.63 & 0.094 & **2.28** & **0.043** \\ \hline \end{tabular} Note. Bold values show trends significant at p = 0.05. For the definition of dry CTs, see Section 3.2 and Table 1.
\end{table}
Table 3: Linear Trends in Frequencies of Dry CTs With Their p-Values in AMI (Left) and JAS (Right) for 1980–2019
Figure 7: Within-season frequencies of dry (brown) and wet (cyan) CTs during the vegetation season. Points mark mean frequencies on individual days (for 1980–2019), while solid lines show 31-day moving averages. For the definition of dry and wet CTs, see Section 3.2 and Table 1.
Shift in the Development of Drought During the Vegetation Season Across Europe and Changes in Circulation
We found statistically significant drying trends for 1980-2019 that were spatially varying across the central latitude strip of Europe. In the early vegetation season (AMJ), the trends were significant particularly over western parts of this region. In the late vegetation season (JAS), meanwhile, the drying was recorded
Figure 8: Seasonal (AMJ—top, JAS—bottom) frequencies of dry (brown) and wet (cyan) CTs and their linear trends in individual regions for 1980–2019. Solid lines show 11-year moving averages of the seasonal frequencies.
Figure 9: Within-season variations of trends in frequencies of dry CTs for 1980–2019. Points mark trends estimated for 31-day moving windows centered on a given day, and solid lines show 31-day moving windows of those trends. For the definition of dry CTs, see Section 3.2 and Table 1.
predominantly in the east. Similar spatial variability of drying was noted also by [PERSON] et al. (2023), who focused on the whole of Europe and studied the role of circulation based on high-pressure anomalies for meteorological drought on the monthly time scale.
AMJ drought is an important factor in initiating long-lasting droughts: it poses a major risk for agriculture and, at the same time, affects the vegetation state and its development in the rest of the vegetation season (which is mainly controlled by precipitation in preceding months; [PERSON] et al., 2016). In most studies on drought development, attention is given especially to the summer season ([PERSON] et al., 2020; [PERSON] and [PERSON], 2016; [PERSON] et al., 2018) or to the entire vegetation period ([PERSON] et al., 2021; [PERSON] et al., 2014), but that does not provide intra-seasonal insight into trend variability. Significant drought trends in the early vegetation season in Central Europe were found by [PERSON] et al. (2009), who dealt with station data for the period 1881-2005. In our study's more detailed and updated analysis, we show relatively large variability in drying trends on the monthly scale. While April and June are characterized by significant drying trends over large parts of the domain, almost no regions with drying trends were recorded in May. A similar temporal pattern of drying tendencies was recently reported by [PERSON] et al. (2023) using SPEI. In Eastern Europe, significant changes toward drier conditions were observed in June and August by [PERSON] et al. (2021), who examined spatiotemporal changes of meteorological drought in agricultural areas. In addition, drying tendencies were also found further east, outside the studied regions, in Ukraine and Moldova ([PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2017; [PERSON] et al., 2019). The drying in Eastern Europe during the late vegetation season is related to pronounced warming in late summer within this region and associated warming in the Black Sea region ([PERSON] et al., 2024; [PERSON] & [PERSON], 2018).
Significant increase (decrease) in the frequency of circulation types favorable (unfavorable) to drying was found for AMJ. The increase was widespread across the central latitude strip of Europe and may reflect larger-scale changes in atmospheric circulation. Increased frequency of anticyclonic types may suggest a northward shift of the general circulation, with subtropical highs and ridges becoming increasingly important for Central European climate in late spring and early summer. Some studies have reported decrease of zonal flow in Western, Central, and Eastern Europe (e.g., [PERSON] et al., 2019; [PERSON] et al., 2014), but these did not analyze this phenomenon on monthly and/or seasonal scales. We performed an additional analysis of westerly and easterly CTs (Table 4 and Table S5 in Supporting Information S1) and found significant decrease of the westerly CTs in Central and Eastern Europe and significant increase of easterly CTs in Eastern Europe (Table 4). These trends were more pronounced in JAS than AMJ (Table S5 in Supporting Information S1) and suggest a tendency toward decreasing zonal flow across the central latitude strip of Europe. The reduced inflow of moist (and relatively cooler in the warm half-year) air masses from the Atlantic penetrating into the European interior may be one of the important factors supporting drought intensification, and requires further attention.
The increase of dry circulation types and related drying tendencies in Europe may be associated with several other large-scale factors. One of them is atmospheric blocking ([PERSON] et al., 2015). Atmospheric blocking suppresses zonal flow and strengthens the meridional flow, which is linked to greater presence of tropical air masses in Central Europe ([PERSON] and [PERSON], 2019). The increased frequency of atmospheric blocking over Central Europe is possibly amplified by the weakened Atlantic meridional overturning circulation (AMOC; [PERSON] et al., 2023; [PERSON] et al., 2022). Toward the end of summer and in autumn, the development of drought may be
\begin{table}
\begin{tabular}{l c c c c} \hline Region & Trend W (\%/decade) & p-value W (\(-\)) & Trend E (\%/decade) & p-value E (\(-\)) \\ \hline E5 & 0.97 & 0.563 & \(-\)1.82 & 0.234 \\ E10 & \(-\)2.16 & 0.207 & \(-\)1.37 & 0.411 \\ E15 & \(-\)**4.35** & **0.016** & 1.12 & 0.511 \\ E20 & \(-\)**4.25** & **0.022** & 2.59 & 0.114 \\ E25 & \(-\)**5.31** & **0.004** & **6.52** & **0.001** \\ \hline \end{tabular} _Note._ Westerly CTs include SW, W, NW, ASW, AW, ANW, CSW, CW, and CNW; easterly CTs include NE, E, SE, ASE, AE, ANE, CSE, CE, and CNE. Bold values show trends significant at p = 0.05.
\end{table}
Table 4: Linear Trends in Frequencies of Westerly and Easterly CTs With Their p-Values During the Vegetation Season (April–September) for 1980-2019 related to the North Atlantic Oscillation (NAO; [PERSON] et al., 2015). Droughts' development obviously depends also on the strength and position of the polar jet stream. The stronger and northerly displaced polar jet stream is related to more frequent anticyclonic conditions in European mid-latitudes ([PERSON] et al., 2018), leading to prevailing dry and hot weather in the warm half-year. The drought then goes on and is successively exacerbated. By contrast, weaker and undulated jet stream runs further south and is associated with increased cyclonic activity and weather extremes such as heavy precipitation ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2018). The development of drought and heat waves on the European continent may eventually be influenced by additional climate dynamic drivers such as El Nino-Southern Oscillation (ENSO; [PERSON] et al., 2023), Quasi-Biennial Oscillation (QBO; [PERSON] et al., 2008), Atlantic Multidecadal Oscillation (AMO; [PERSON] et al., 2023), and others ([PERSON] et al., 2023; [PERSON] et al., 2023). Combining global climate dynamics with the CTs and their regional effects remains a task for further studies.
Our study is, as a whole, in good agreement with numerous investigations that have found rising temperatures and radiation together with decreasing air humidity to be the main drivers of the accentuated increase of droughts (especially compound dry-hot events) over large parts of Europe. Underscoring these basic relationships, [PERSON] et al. (2023) reported a statistically significant upward trend in evapotranspiration as a consequence of significantly increasing sunshine duration and air temperature and a decrease in relative humidity during the vegetation season in Poland over 1966-2020. Conditions with little cloud cover, high temperatures, and low relative humidity are typically linked to anticyclonic CTs in the warm half-year. By contrast, a notable increase of water balance deficits (PET\(-\)P) in recent years within the Eastern European area E25 is driven to a great extent by declining precipitation.
The drought situation in the years 2020-2023 corroborated the main findings of our study, as it was marked by regular early summer droughts in Northwestern Europe and drought hotspots in Eastern Europe in late summer ([PERSON] et al., 2023; [PERSON] and [PERSON], 2022; [PERSON] et al., 2023; [PERSON] and [PERSON], 2023; [PERSON] et al., 2023). A comprehensive analysis of the extraordinary, regionally record-breaking drought, heatwaves, and strong rains in the years since 2020 remains a challenge for the future and may lead to deeper understanding of the presented results.
### Links Between Drought Trends and Circulation Types
Good agreement was found between trends in dryness and dry/wet CTs. The substantial drying in the AMJ season across the analyzed domain was associated with increase in the occurrence of dry CTs (statistically significant in E10-E20). In JAS, by contrast, we found a significant increase of dry CTs only in the easternmost (E25) region, which is in accordance with the spatial patterns of drought trends.
While dry (wet) CTs generally consist of anticyclonic (cyclonic) types ([PERSON] et al., 2014; [PERSON] and [PERSON], 1999), directional types were found to have different drying tendencies depending on the region. In Western and Central Europe, drier conditions are mainly associated with easterly and southerly directions, which is in line with studies that have analyzed droughts over Central Europe (e.g., [PERSON] et al., 2022; [PERSON] and [PERSON], 2016; [PERSON] et al., 2020; [PERSON] et al., 2009). In Eastern Europe, by contrast, all directional types (except N) have a dry tendency. This reflects the higher continentality of climate in Eastern Europe, while Western Europe (and partially also Central Europe) is under more pronounced influence of an oceanic climate.
During JAS, the links between trends in dryness and circulation types may be weaker due to a large share of convective precipitation compared to other seasons ([PERSON] and [PERSON], 2013). This is amplified in areas with rugged topography, where local convective processes support the occurrence of precipitation. These heavy precipitation events are, however, not evenly distributed in time and space. Vegetation may then suffer long-term drought with occasional torrential rains ([PERSON] et al., 2019) and greater losses due to direct runoff. This may contribute to the slight discrepancy between an increase in frequencies of dry types not associated with drought trends in regions E15 and E20 in the late vegetation season.
### Choice of the PET\(-\)P Index
In our study, dryness was analyzed through the difference between potential evapotranspiration and precipitation, that is, the Climatic Water Balance Index ([PERSON] and [PERSON], 2011). This index has intuitive interpretation and provides information on drying on the daily time scale, which is essential for its linking to atmospheric circulation patterns. We used PET\(-\)P because the variables required for its calculation are available in E-OBS (although approximation is needed in the case of PET), and the same approach can be applied to many other data sets with daily resolution (while such commonly used drought indices as SPI, SPEI, and PDSI are usually calculated for monthly steps). If extremely high temperature occurs, the development of drought may accelerate along with that of heat waves in a short period (flash droughts; [PERSON] et al., 2024; [PERSON] et al., 2021; [PERSON] and [PERSON], 2023; [PERSON] et al., 2023), so the daily time step is essential when studying drought dynamics.
[PERSON] et al. (2007) questioned the applicability of SPI in monitoring and analyzing droughts because, in such cases, periods without precipitation are the norm and cannot be considered droughts. Furthermore, SPI is often criticized because it does not take into account temperature and related evapotranspiration (i.e., variables relevant to drought; [PERSON] et al., 2010), causing SPI to underestimate drought especially in areas with a strong warming signal ([PERSON] and [PERSON], 2021; [PERSON] et al., 2021). The SPI index includes both precipitation and potential evapotranspiration components but may lead to excessive drying compared to other indicators ([PERSON] et al., 2016) and should be used with caution ([PERSON] et al., 2019). PDSI may be a better choice to characterize atmospheric water demand ([PERSON] et al., 2023), but its main disadvantage is that specific parameters are obtained for areas of the United States, which hinders comparisons among diverse climatic regions ([PERSON] et al., 2021). In PDSI, the data-demanding Penman-Monteith formula is often used to estimate PET ([PERSON] et al., 2010), making the index highly sensitive to imprecision of the data ([PERSON] and [PERSON], 2016; [PERSON] et al., 2012). A general disadvantage of these indices is their built-in imitation of soil moisture memory, which is not desirable when linking day-to-day changes between dryness and circulation types.
We derived potential evapotranspiration using [PERSON]'s formula ([PERSON] et al., 2005) based on temperature and radiation. This method provides better results than does, for example, the Thornthwaite formula based solely on temperature ([PERSON], 1948), which tends to underestimate PET ([PERSON] et al., 2020; [PERSON] and [PERSON], 2004; [PERSON] et al., 2010; [PERSON] et al., 2020). In some cases, better model performance has been reported for more straightforward formulas than for combination formulas like the Penman-Monteith ([PERSON] et al., 2012), the disadvantages of which were mentioned above.
### Relevance of Study Period Lengths and Climatic Seasons
After a preliminary analysis, we decided to focus on the period since 1980, because pronounced multidecadal variability of drought conditions weakens the temporal stability of estimated long-term trends ([PERSON] et al., 2019). Figure S1 in Supporting Information S1 shows for illustration trends in PET-P for the entire available period of the E-OBS data since 1950. The trends are much weaker compared to those in Figure 3 (the scale is kept the same in both figures) and the recent drying is not well represented (the trends are strongly influenced by variability in earlier decades). That is why we preferred to confine the study to a shorter period with a clear climate change signal.
The focus on the 40-year period 1980-2019, which is characterized by pronounced warming in Europe ([PERSON] et al., 2022), allows for better understanding of the links between recent changes in drought and atmospheric circulation in European mid-latitudes, that is, the region with the most pronounced warm-season drying trends in Europe according to the Climatic Water Balance Index (Figure 3). At the same, the period of the last four decades is sufficiently long for estimating trends. The links between dryness and CTs are similar for the whole period of 1950-2019 (Table S6 in Supporting Information S1) as for 1980-2019 (Table 1), and the set of CTs favorable for drying remains almost the same (Table S6 in Supporting Information S1). Using a shorter (e.g., 2000-2019) period for the analysis would result in positive PET\(-\)P trends in JAS (Figure 2), but such time window would not be sufficient for obtaining reliable trend estimates.
The analysis for individual months provided valuable information on intra-seasonal variations in trends. Trends in both PET\(-\)P and dry CTs are relatively sensitive to the selected period of the year. This concerns, for example, June versus August. As visible in Figure 5, the 2 months are quite different and yet they are usually considered as part of the same season ([PERSON] et al., 2020; [PERSON] and [PERSON], 2016; [PERSON] et al., 2006; [PERSON] et al., 2018). It is questionable to what extent climatic seasons (such as JJA) are suitable for analyzing trends. These findings bring a similar view as seen in a study by [PERSON] et al. (2018), who examined the annual cycle of trends in temperature. Generally, we must consider the limitations of trend analysis, which captures only the relationships within the selected temporal and spatial framework and cannot be extended to finer scales without further analysis.
## 5 Conclusions
Our study examined trends in dryness and their links to atmospheric circulation across the central latitude strip of Europe (centered upon 50\"N) during the vegetation season for 1980-2019. In contrast to previous studies, we used the Climatic Water Balance Index (difference between potential evapotranspiration and precipitation) calculated on a daily time scale, in order to link dry or wet tendencies to circulation types (CTs) centered for each region using a \"moving window\" concept. The main results can be summarized as follows:
1. In the early vegetation season (AMJ), significant drying trends are observed mainly in Western and Central Europe, while in the late vegetation season (JAS) they are predominantly found in Eastern Europe. The trends are strongest in April and June, and in Eastern Europe also at the turn of August/September.
2. The anticyclonic CTs have drying tendencies regardless of region. In case of directional CTs, northeast to south (southwest in Eastern Europe) CTs contribute to drying.
3. The trends of the dry CTs correspond to those of dryness: the largest increases in frequencies of dry CTs occur in those regions as well as seasons and months affected by pronounced drying.
4. The increasing frequency of anticyclonic types (during AM) together with reduced inflow of moist air masses from the Atlantic penetrating deeper to the continental regions of Central and Eastern Europe (mainly in JAS) are the key factors supporting drought intensification in European mid-latitudes.
The results show an eastward temporal shift of the regions most affected by drying during the warm half-year and a close link between changes in atmospheric circulation and trends in dryness over the past four decades. Increased frequency of anticyclonic types can be interpreted as a signal of a northward shift of the general circulation, with subtropical highs and ridges becoming increasingly important for the Central European climate above all in late spring and early summer. Although atmospheric circulation is only one factor contributing to the overall drying trends (which are primarily driven by increasing temperatures due to climate change), it affects the spatial and temporal patterns of the trends across Europe in the warm half-year. Therefore, it is important to better understand the circulation-to-drought links also in climate model simulations for present and future climates.
## Data Availability Statement
The E-OBS gridded data set (ECA&D, 2022) used for the drought analysis is freely available from C3S ([[https://doi.org/10.24381/cds.151d3](https://doi.org/10.24381/cds.151d3) ce6]([https://doi.org/10.24381/cds.151d3](https://doi.org/10.24381/cds.151d3) ce6)). The NCEP/NCAR reanalysis (NOAA/NCEP, 2022) used for classification of circulation types can be downloaded for research purposes from NOAA Physical Science Laboratory ([[https://psl.noaa.gov/data/gridded/data.ncep.neanalysis.html](https://psl.noaa.gov/data/gridded/data.ncep.neanalysis.html)]([https://psl.noaa.gov/data/gridded/data.ncep.neanalysis.html](https://psl.noaa.gov/data/gridded/data.ncep.neanalysis.html))). The data sets of circulation types for all regions ([PERSON] et al., 2023) are available on the Mendeley data repository ([[https://doi.org/10.17632/232j5](https://doi.org/10.17632/232j5) bc8 vs.1]([https://doi.org/10.17632/232j5](https://doi.org/10.17632/232j5) bc8 vs.1)).
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wiley/fda98d76_a8e1_4e96_8293_96334fda4a3f.md | # AGU Advances
Research Article
10.1029/2024 AV001197
Paer Review
The peer review history for this article is available as a PPE in the Supporting Information.
Magnetosheath High-Speed Jet Drives Multiple Auroral
Arcs Near Local Noon
Hui-Xuan Qiu
State Key Laboratory of Marine Geology, School of Ocean and Earth Science, Tongji University, Shanghai, China, 2 MNR Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China
[PERSON]
State Key Laboratory of Marine Geology, School of Ocean and Earth Science, Tongji University, Shanghai, China, 2 MNR Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China
Run Shi
State Key Laboratory of Marine Geology, School of Ocean and Earth Science, Tongji University, Shanghai, China, 2 MNR Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China
[PERSON]
State Key Laboratory of Marine Geology, School of Ocean and Earth Science, Tongji University, Shanghai, China, 2 MNR Key Laboratory for Polar Science, Polar Research Institute of China, Shanghai, China
###### Abstract
Magnetosheath High-Speed Jets (HSJs) are transient disturbances characterized by increased dynamic pressure. They can cause various geoeffects, including ultra-low-frequency (ULF) waves and auroras. Theoretically, when ULF waves propagate into the ionosphere as Alfven waves, they can accelerate electrons and generate discrete auroras. However, what types of aurora can be driven by HSJs and what are the underlying mechanisms remain unknown. Using coordinated magnetosheath in situ and ground observations, here, we showed that when a HSJ was identified in the magnetosheath, multiple auroral arcs parallel to the auroral oval were observed near local noon. The electron energy spectrogram of these arcs exhibited \"inverted-V\" structures, indicating the existence of quasi-static parallel electric fields. Concurrently, long-period ULF signals were detected on the ground, suggesting the arrival of Alfven waves. These observations are represented by a kinetic simulation using realistic observational inputs, showing consistency with the theory regarding the generation of the \"inverted-V\" structure by long-period Alfven waves. This study builds a previously unestablished connection among HSJ, ULF wave, and aurora, and provides a mechanism for generation of discrete auroral arcs near local noon, which may reveal the underlying mechanism behind a specific auroral activity commonly observed near local noon as shown in the paper.
Magneticousheath High-Speed Jets (HSJs) are transient irregularities observed between Earth's magnetopause and bow shock. They can cause various geoeffects like ultra-low-frequency (ULF) waves and auroras. However, the specific auroral types driven by HSJs remain elusive. Through coordinated in situ and ground observations, we reveal a novel geoeffect of HSJs--driving multiple discrete auroral arcs near local noon on closed field lines, displaying \"inverted-V\" electron acceleration structures. This challenges the conventional understanding that discrete auroras near local noon predominantly occur on open field lines. Also, our study provides valuable insights into the mechanism and favorable conditions of discrete auroras on closed field lines near local noon. Simultaneously, ground magnetic ULF signals indicate a crucial role of HSJ-induced ULF waves in shaping these \"inverted-V\" arcs. Supported by a kinetic simulation, our observations provide evidence for the recently established electron acceleration mechanism of \"inverted-V\" electrons associated with long-period Alfven waves. Overall, we demonstrate a previously unestablished link between HSJs, ULF waves, and discrete auroral arcs. This groundbreaking connection enhances our understanding of magnetosheath irregularities role in the Earth's magnetosphere-ionosphere coupling system and unveils the mechanisms behind a specific auroral activity commonly observed near local noon.
Footnote †: ENDFOOTNOTE]
et al., 1998; [PERSON] et al., 2008) and a perpendicular size on the order of several \(R_{\rm E}\)([PERSON] et al., 2012; [PERSON] et al., 2012). Under specific upstream conditions, larger-scale HSJs can manifest in the magneto-sheath, reaching up to around 5 \(R_{\rm E}\) (7.2 \(R_{\rm E}\)) in parallel (perpendicular) diameters ([PERSON] et al., 2014; [PERSON] et al., 2022). As HSJs propagate from the bow shock to the magnetopause where magnetic field increases, their speed gradually decreases due to adiabatic breaking effects ([PERSON] et al., 2023), while their perpendicular scales expand ([PERSON] et al., 2020). It has been reported that HSJs with considerable perpendicular sizes significantly impact the magnetopause locally and influence the Earth's magnetosphere-ionosphere coupling system ([PERSON] et al., 2012, 2018; [PERSON] et al., 2019; [PERSON] et al., 2009). Statistical results suggest that the impact rate of HSJs larger than 2 \(R_{\rm E}\) is generally about 3 times per hour ([PERSON] et al., 2016), more frequently than the occurrence rates of other well-known geoeffective phenomena like coronal mass ejections, foreshock transients, and substorms. However, despite widespread acceptance of HSJs' substantial effects on the Earth, these effects are far from fully understood.
When HSJs impact the Earth's magnetopause, their high dynamic pressure pulses can elevate the total pressure acting on the magnetopause ([PERSON] et al., 2019), resulting in local perturbations and deformations of the magnetopause ([PERSON] et al., 2011; [PERSON] et al., 2009). The inward displacement of the magnetopause causes localized magnetospheric compression, and tension in field lines provides restoring forces to counter the boundary displacement ([PERSON] et al., 2009). Consequently, surface waves form on the magnetopause boundary ([PERSON], 1974b; [PERSON] et al., 2009), and various resonant ultra-low-frequency (ULF) waves in the outer magnetosphere are subsequently launched through field line resonance (FLR) ([PERSON] et al., 2019; [PERSON] et al., 2015). In addition, this magnetopause displacement is associated with local perturbations of the closure current system on the magnetopause and between hemispheres ([PERSON] & [PERSON], 2011; [PERSON] et al., 2009), generating fast-mode compressional waves propagating into the magnetosphere ([PERSON] et al., 1984) and Alfven wave pulses along the magnetic field lines ([PERSON] et al., 1954; [PERSON] et al., 2009). These waves arrive at the ionosphere in the way of Alfvenic signals, leading to geomagnetic variations ([PERSON] et al., 2022) and auroral activities ([PERSON] et al., 2018). In short, numerous modes of magnetospheric ULF waves and magnetopause surface waves facilitate HSJs in transferring solar wind power to the Earth. Numbers of observations suggest that the time delay between detected HSJs and the onset of ground-based responses typically spans 1-3 min ([PERSON] et al., 2012; [PERSON] et al., 2021; [PERSON] et al., 2022), consistent with the propagation time of wave signals from the magnetopause to the ground. Moreover, HSJs are capable of initiating magnetopause reconnection in a localized region ([PERSON] et al., 2018), another mechanism to transfer material, energy, and momentum into the magnetosphere and ionosphere.
Davside auroras, directly resulting from the interaction between the solar wind and the Earth's magnetosphere-ionosphere coupling system, can significantly be affected by solar wind variations and magnetosheath irregularities, certainly including HSJs. Multi-instrument observations suggest that HSJs contribute to diffuse auroral enhancements due to increased pitch angle scattering by magnetospheric ULF waves ([PERSON] et al., 2018). It also implied discrete auroral brightenings are potentially influenced by HSJs. In addition, HSJs are proposed to be a driver of \"throat aurora\" through triggering magnetopause reconnection ([PERSON] et al., 2019; [PERSON] et al., 2017; [PERSON] et al., 2022). The throat aurora, different from regular discrete auroral arcs parallel to the auroral oval, is a discrete auroral form extending obliquely from the auroral oval near local noon toward lower latitudes ([PERSON] et al., 2015). Notably, these two auroral activities are carried out through magnetospheric waves-particle interactions and magnetopause reconnection, respectively. It has been suggested that the Alfven waves carrying upward field-aligned currents from the magnetosphere can evolve into a quasi-static parallel electric potential drop ([PERSON], 1983; [PERSON] et al., 2023). The quasi-static parallel electric field and resultant \"inverted-V\" electron acceleration structures are known to contribute to discrete auroral arcs ([PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON], 1960). Therefore, the dynamics of discrete auroral arcs driven by HSJs through such mechanism are highly anticipated. However, previous studies have not shown clear links among HSJs, ULF waves, and auroral activity.
Ground-based auroral observations from all-sky cameras at Yellow River station provide valuable insight into this mechanism. Near magnetic local noon, a distinct auroral phenomenon is frequently observed, as illustrated in Figure 1 and Movies S1 and S2. Initially, we see a discrete auroral spot in red-line emission appeared at high latitudes of the equatorward boundary of the auroral oval, which subsequently moved toward lower latitudes (Figure 1a). As it reached the equatorward boundary, a bright discrete auroral arc emerged, followed by multiple auroral arcs parallel to the auroral oval. Simultaneously, several parallel stripy diffuse auroras at lower latitudeswere observed in green-line emissions (Figure 1b). Although we lack coordinated observations of HSJs in the magnetosheath, we suspect that the equatorward drift of the discrete auroral spot may result from a HSJ moving earthward, and the multiple discrete arcs and stripy diffuse aurora may be driven by the HSJ impacting on the magnetopause. If such speculation can be confirmed by coordinated observations, it will greatly improve our understanding on the geoeffects of HSJs and the underlying mechanisms. More importantly, it will uncover the physical process behind a specific auroral activity that is commonly observed near local noon, as shown in Figure 1.
Figure 1.— Ground-based auroral observations at Yellow River Station on 27 December 2004. (a) Auroral images observed in red (630.0 nm) emission by all-sky camera during 10:10:00 to 10:13:30 UT. The discrete auroral enhancements induced by high-speed jets are indicated by the white arrows overlapping. It moved equatorward from 10:00:00 to 10:12:30 UT. The yellow arrows indicate discrete and multiple auroral arcs parallel to the oval near local noon. (b) Auroral images observed in green (557.7 nm) emission, following the same format as in plot a. Also, the yellow arrows indicate discrete and multiple auroral arcs parallel to the oval near local noon. A continuous time series of this event from 10:09:00 to 10:14:00 UT is available in the Movies S1 and S2.
In this study, we present coordinated observational evidence that a magnetosheath HSJ induced multiple auroral arcs near magnetic local noon, accompanied by clear ground magnetic ULF signals. These observations are consistent with kinetic simulation results using realistic inputs from observations. Thus, we provide a comprehensive framework for how HSJs can drive discrete auroral arcs through ULF waves. These findings significantly advance our understanding of the role played by HSJs in the Earth's magnetosphere-ionosphere coupling system and of the underlying mechanism for discrete auroral arcs near local noon.
## 2 Data and Method
### Data
Magnetosheath observations are from Magnetospheric Multiscale (MMS) mission in particular using the Fluxgate Magnetometer (FGM) and Fast Plasma Investigation (FPI). Solar wind data are obtained from Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, utilizing the FGM and Electrostatic Analyzer (ESA). We employed Geocentric Solar Ecliptic (GSE) coordinate system in these observations. The IMF cone angle (\(\theta\)) was compute using the formula arccos(\(B_{\mathrm{x}}\)/\(B_{\mathrm{total}}\)). Dynamic pressure (\(P_{\mathrm{dyn}}\)) was calculated as \(m_{p}\times n\times\
u^{2}\), where \(m_{p}\) is proton mass, \(n\) is proton number density, and \(v\) is solar wind/ion velocity.
Auroral observations are from Special Sensor Ultraviolet Spectrographic Imager (SSUSI) onboard the Defense Meteorological Satellite Program (DMSP), plotted in magnetic local time (MLT)-geomagnetic latitude (MLT-MLat) coordinate system. The DMSP spacecraft operates at an altitude of about 840 km in polar sun-synchronous orbits with a 101-min orbital period and 98.9\({}^{\circ}\) orbital inclination ([PERSON] et al., 2008). Observations of electron and ion energy spectrograms, differential magnetic field, and density and temperature are obtained from the Special Sensor Precipitating Electron and Ion Spectrometer (SSI/5), Special Sensor Magnetometer (SSM), Special Sensor Ion and Electron Scintillation (SSIES) monitor, respectively.
We also used ground magnetometer data from Ny Alesund (NAL) and Longyearbyen (LYR) stations, with a 10-s resolution. The geographical coordinates (geographical latitude and longitude) of the stations are (78.9\({}^{\circ}\), 11.9\({}^{\circ}\)) and (78.2\({}^{\circ}\), 15.8\({}^{\circ}\)), respectively. These station were chosen due to their proximity to the predicted footprint of the interaction between the HSJ and the magnetopause, as estimated by the magnetopause model ([PERSON] et al., 1998). The footprint was derived from T96 model ([PERSON], 1995; [PERSON] & [PERSON], 1996). Magnetic field data were analyzed in the XYZ coordinates, where the \(X\)-component points north-south direction, \(Y\)-component is along east-west direction, and \(Z\)-direction is vertically down. Magnetic deflections were calculated by subtracting the quiet mean values from observed magnetic field data.
Ground-based auroral images from all-sky camera at Yellow River Station (YRS) were plotted using geographical coordinates. YRS is situated at Ny-Alesund, Svalbard (corrected geomagnetic latitude 76.24\({}^{\circ}\)N, MLT \(\approx\) UT + 3 hr). The optical system at YRS consists of three identical all-sky imagers equipped with band-pass filters at 557.7 (green line), 630.0 (red line), and 427.8 nm, respectively. The red- and green-line observations with a 30-s resolution are used in this paper.
### One-Dimensional Kinetic Model
The 1-D kinetic model used in this study relies on a closed system of equations for distribution functions of hot electrons from magnetosphere and cold electrons from ionosphere, the electrostatic potential, and the parallel magnetic vector potential. Detailed theoretical explanations are available in [PERSON] et al. (2023). This model comprehensively considers electron populations of different temperatures and their associated mode couplings. With an input kinetic Alfven wave at the upper boundary, this model can simulate time variations of electrostatic potential, parallel electric field, electron density, electron distribution function, and electron energy flux. In this study, we employed it to simulate the electron energy flux spectrogram under an incident long-period Alfven wave.
## 3 Results
### Coordinated Observations of High-Speed Jet and Multiple Auroral Arcs
The THEMIS-C satellite positioned upstream in the dust region at \(\sim\)[57.22, 14.99, 1.33] \(R_{\mathrm{E}}\) to measure the solar wind and IMF conditions, as displayed in Figure 2. Our analysis of the solar wind speed data suggested an Figure 2: THEMIS and MMS locations and upstream solar wind conditions. (a) The locations of THEMIS-C and MMS1 satellite in equatorial plane between 07:30:00 and 09:00:00 UT. Dotted and dashed curves represent the bow shock and the magnetopause, respectively. (b) The upstream interplanetary magnetic field (IMF) and solar wind conditions observed by THEMIS-C satellite from 07:30:00 to 09:00:00 UT. The panels (from top to bottom) are IMF in Goecentric Solar Ecliptic coordinates, IMF cone angle \(\theta=\arccos(|B_{\
u}|/B_{\rm total})\), solar wind speed and number density, and dynamic pressure. The gray color indicates the upstream conditions for the observed high-speed jet, considering a \(\sim\)15-min propagation time of solar wind from THEMIS-C to MMS1.
approximate propagation time of 15 min to reach the magnetopause. During this period, the IMF displayed a radial orientation with a cone angle smaller than 40\({}^{\circ}\). Such a radial IMF is conductive to the occurrence of HSJs ([PERSON] et al., 2013). Moreover, the solar wind dynamic pressure remained steady throughout. Therefore, we can rule out the possibility of solar wind dynamic pressure pulse influencing the magnetospheric and ionospheric responses in this event.
During 08:38:00 - 08:45:00 UT on 29 January 2017, the MMS1 satellite was located at \(\sim\)[10.62, \(-\)3.77, 1.89] \(R_{\rm E}\) in the pre-noon region just outside the magnetopause, as depicted in Figure 2a. The distance from its position to the magnetopause boundary was estimated to be \(\sim\)0.45 \(R_{\rm E}\) by using the magnetopause model ([PERSON] et al., 1998). From \(\sim\)08:39:50 to 08:41:40 UT, MMS1 detected a typical magnetosheath HSJ characterized by increased anti-sunward flow velocity and dynamic pressure, as indicated by the dashed vertical lines in Figure 3a. The dynamic pressure in the magnetosheath prior to the HSJ was about 0.5 nPa, ascending to 5 nPa during this event, approximately twice the solar wind dynamic pressure. The anti-sunward velocity increased from nearly zero to \(\sim\)250 km/s. Utilizing the velocity observations, we estimated the parallel size of the HSJ to be \(\sim\)3.83 \(R_{\rm E}\) following the method established in [PERSON] et al. (2016), while the perpendicular size approximated \(\sim\)1.07 \(R_{\rm E}\) using the same approach. However, the determination of the perpendicular scale with single-satellite observations might not be accurate ([PERSON] et al., 2016). Due to a downward velocity component of \(\sim\)50 km/s, the interaction site between this HSJ and the magnetopause laid closer to the subsolar region. Owing to its proximity to the magnetopause and considerable scale size, this HSJ event should impact the magnetopause, eliciting substantial magnetospheric and ionospheric responses.
Figure 3: MMS observation of high-speed jet (HSJ) and coordinated auroral images on 29 January 2017. (a) MMS1 magnetosheath measurements during 08:38:00 to 08:45:00 UT on 29 January 2017. The panels (from top to bottom) are magnetic field in Geocentric Solar Ecliptic coordinates, plasma density, ion velocity, dynamic pressure, ion parallel and perpendicular temperatures, and ion omnidirectional differential energy flux. The HSJ is marked with dashed vertical lines at 08:39:50 UT and 08:41:40 UT. (b) Aurora in the Lyman-Birge-Hopfield short-band (LBHS) band (wavelength of 140–150 nm) observed by the Special Sensor Ultraviolet Spectrographic Imager instrument on board Defense Meteorological Satellite Program F17 satellite from 08:35:38 to 08:53:35 UT is plotted in magnetic local time-geomagnetic latitude coordinates. The black circle represents the approximate footprint of the magnetospheric region near MMS1, mapped by using T96 model ([PERSON], 1995; [PERSON] & [PERSON], 1996). The red squares indicate locations of magnetometer ground stations (From high latitudes to low latitudes: NAL and LYR), and observations at these stations are shown in Figure 4.
Subsequently, we predicted the magnetopause boundary closest to MMS1's position as the interaction site between the HSJ and the magnetopause, and mapped it to the ionosphere along closed field lines using the T96 magnetospheric magnetic field model ([PERSON], 1995; [PERSON] & [PERSON], 1996). The predicted footprint was overlaid onto northern hemispheric auroral observations obtained by the DMSP satellite during the HSJ observations, as shown in Figure 3b. The auroral observations revealed that near the footprint, distinct multiple auroral arcs parallel to the auroral oval were detected at \(\sim\)08:45:30 UT. Similar multiple arcs were observed at the same latitudes within the diskward 3-hr magnetic local time (MLT) region (within a radius of \(\sim\)1,800 km at DMSP's altitude) relative to the predicted footprint from 08:42:00 to 08:43:20 UT. The post-noon arcs were situated within the appropriate region influenced by this HSJ, as previous work has pointed out geomagnetic responses observed within 2,000-km of HSJ's footprint ([PERSON] et al., 2021) and HSJ-induced magnetospheric responses displaying a duskward motion of \(\sim\)2 MLT ([PERSON] et al., 2018). Therefore, the temporal and spatial correlations strongly imply these multiple auroral arcs in both the pre-noon and post-noon sectors were linked with the HSJ.
### Geomagnetic Responses to the High-Speed Jet
During the HSJ observations, the NAL and LYR stations, situated close to the predicted footprint, observed distinct transient geomagnetic pulsations in all three components, as shown in Figure 4. Using a 10% increase in the \(X\) component as a criterion for the onset of magnetic deflection, the time delay spanned from \(\sim\)1 to 3 min. These pulsations exhibited a maximum amplitude and damping time of approximately 80 nT and 780 s, respectively. Moreover, the time-frequency analysis revealed statistically significant signals peaked at \(\sim\)1-2 mHz. It has been reported that magnetosheath HSJs can serve as a source of dayside ground magnetic ULF oscillations by inducing compressional waves and Alfven waves in the magnetosphere ([PERSON] et al., 2019; [PERSON] et al., 2022). Consequently, these geomagnetic pulsations in the ULF band indicated the presence of long-period Alfven waves from the magnetosphere potentially induced by the HSJ observed in Figure 3. If an impacting HSJ is located in the subsolar region, a radial disturbance of magnetic field lines at the magnetopause was expected and should propagate as a poloidal disturbance. Assuming no mode conversion at the ionosphere, this wave would appear as a north-south perturbation (the \(X\) component) in geomagnetic observations. Theoretical insights suggested that an Alfven wave must rotate 90\({}^{\circ}\) when it reaches the ionosphere ([PERSON], 1974; [PERSON] et al., 2005). Therefore, a purely radial disturbance should be observed in the east-west component (the \(Y\) component) of geomagnetic deflections. Since the HSJ event in this study was slightly downward of the subsolar region, both radial and azimuthal disturbances existed, explaining the variations observed in all components. The largest geomagnetic perturbations observed in the north-south component indicate that the magnetic perturbations in the magnetospheric equatorial plane were predominantly toroidal, implying the presence of an FLR. The frequency
Figure 4: Ground magnetometer observations at Ny Alesund and Longyearbyen. (a) The panels (from top to bottom) display geomagnetic deflections observed at the Ny Alesund (NAL) station in the XYZ coordinate system and wavelet dynamic power spectra of the \(X\) (north-south component), \(Y\) (east-west component), and \(Z\) components. Dashed vertical lines delineate the time interval during which the HSJ event was detected by MMS1. (b) Geomagnetic observations at the Longyearbyen (LYR) station, following the same format as in plot a. The geographical coordinates (geographical latitude and longitude) of the stations are provided here, while their positions in magnetic local time-geomagnetic latitude coordinates are represented by red squares in Figure 3b.
detected on the ground tended to decrease with latitude, suggesting that the wave frequency in the equatorial plane decreased with L-shell, consistent with FLR theory ([PERSON] et al., 2019; [PERSON] and [PERSON], 1974a; [PERSON], 1974). Collectively, these observations support that HSJ-induced ULF waves propagated into the ionosphere as long-period Alfven waves and caused significant geomagnetic responses.
### Particle Precipitation Characteristic of Multiple Auroral Arcs
From \(\sim\)08:36:00 to 08:53:30 UT, the DMSP satellite flew at \(\sim\)840-km altitude from the dusk to the dawn region, as indicated by the white line in Figure 5a. It passed over two post-noon auroral arcs between 08:42:00 (B) and 08:43:38 UT (E), with corresponding particle data depicted in Figure 5b. However, its orbit at lower latitudes in the dawn region limited direct observations of the particle precipitation properties of the pre-noon arcs. Notably, the pre- and post-noon auroral arcs showcased analogous two-dimensional morphologies, nearly connected at equivalent latitudes, with a midday auroral gap separating them, suggesting shared particle characteristics.
The post-noon auroral arcs displayed typical \"inverted-V\" structures or \"mono-energetic\" peaks in the electron energy flux spectrogram (Figure 5b), without concurrent ion precipitation, suggesting the existence of quasi-static parallel electric fields. Nevertheless, there were distinctions between these two arcs. The higher-latitude arc, observed between 08:42:00 (B) and 08:42:48 UT (C), exhibited particle characteristics of the boundary plasma sheet (BP) where high-energy electrons from the magnetosphere existed but at lower energies than those from the central plasma sheet (as indicated between \(A\) and \(B\)) ([PERSON] et al., 1991). This suggests that particles from the outer magnetosphere precipitated along closed field lines and were subsequently accelerated by the parallel electric field. On the other hand, the lower-latitude arc, observed between 08:42:48 (C) to 08:43:38 UT (E), displayed particle characteristics of the low-latitude boundary layer (LLBL). This region showed a coexistence of low-energy particles from the magnetosheath and high-energy particles from the magnetosphere. Within this arc, a significant enhancement of the ionospheric magnetic field was observed in a close east-west direction (satellite forward direction), while the variations in the north-south component (poleward direction) were slight. This indicates the presence of an upward field-aligned current within the \"inverted-V\" structure and a downward field-aligned current alongside it. According to the maximum magnetic deflection of \(\sim\)150 nT, the current intensity was estimated to be \(\sim\)1.2 \(\mu\)A/m\({}^{2}\) within an approximate arc width of \(\sim\)100 km.
Based on post-noon observations, we suppose that the multiple auroral arcs in the pre-noon sector, near the predicted footprint and the ground magnetic ULF responses, would also exhibit similar \"inverted-V\" electron accelerations and upward field-aligned currents. It is worth noting that there is a gap between the pre- and post-noon arcs, which may suggest the presence of an odd-mode FLR induced by the HSJ. Previous simulations have shown that the peak intensity of odd-mode FLR induced by upstream dynamic pressure variations can be symmetrically distributed in the pre- and post-noon sectors, with a wave node appearing as a gap at local noon ([PERSON] et al., 2010). Observations have also suggested that this two-dimensional distribution of FLR corresponds to similar auroral morphologies near local noon, but driven by foreshock transients ([PERSON] et al., 2019). Moreover, an impulsive HSJ has been observed to drive FLRs in the outer magnetosphere ([PERSON] et al., 2019). The multiple structure of these arc may be attributed to the spatial distribution of FLRs as well. Previous simulations have indicated that resonance coupling of FLRs induced by a pressure pulse at the magnetopause can occur across several L-shells ([PERSON] and [PERSON], 2022). Therefore, the formation of multiple auroral arcs in this event is potentially linked to FLRs driven by the HSJ.
### Simulation of Precipitation Electrons in Multiple Auroral Arcs
We used a one-dimensional kinetic model ([PERSON] et al., 2023) to simulate the electron energy flux spectrogram at \(\sim\)3,300-km altitude under the incident of long-period Alfven waves carrying upward field-aligned currents from the magnetosphere, with realistic observational parameters in this event. The simulation domain extends from 200 km to 3.2 \(R_{\rm E_{D}}\), encompassing the transition region between the hot plasma from the magnetosphere and the cold plasma from the ionosphere. The boundary conditions of this domain are depicted as follows. At the upper boundary, magnetospheric electrons are at a temperature of 200 eV and a density of \(5\times 10^{5}\) m\({}^{-3}\), while at the lower boundary, ionospheric electrons have a temperature of 0.2 eV and a density of \(2.7\times 10^{11}\) m\({}^{-3}\). In this one-dimensional kinetic mode, a kinetic Alfven wave carrying upward field-aligned currents from the magnetosphere is imposed at the upper boundary as the driver of the system. According to geomagnetic and auroral observations, the parameters of the input kinetic Alfven wave from the magnetosphere were as follows: a period of 30 s and a Figure 5:
perpendicular wavelength of 100 km estimated from the maximal width of these arcs. The reason for approximating the input period from the observed 780 s to 30 s is that when the input Alfven wave period exceed 30 s, the results tend to exhibit quasi-static behavior and will not change much even if the period increases. The amplitude of upward field-aligned currents mapped to the ionosphere was took as 1 \(\mu\)A/m\({}^{2}\). The simulation results are shown in Figure 6.
When this kinetic Alfven wave propagated into the ionosphere, electrons at \(\sim\)3,300-km altitude were accelerated to over 1 keV within tens of seconds, manifesting an \"inverted-V\" spectrogram. This suggests that an incident Alfven wave, with a period of 30 s or more, possesses the capacity to establish a \"U\"-shaped parallel electric field. Consequently, in this event, Alfven waves with longer periods, approaching the observed damping time of geomagnetic pulsations, contributed to the formation of a quasi-static parallel electric field. Furthermore, it has been suggested that if the input kinetic Alfven waves are sufficiently strong and persist long enough, the quasi-static parallel electric field can sustain ([PERSON] et al., 2023). In this study, the HSJ served as a driver, compressing the magnetopause and the magnetosphere to induce ULF waves, most likely FLR. Subsequently, these ULF waves delivered sustained energy to the ionosphere, maintaining the parallel electric field and therefore the long-lasting multiple auroral arcs.
## 4 Discussion
We present evidence that a HSJ led to the formation of multiple discrete auroral arcs near local noon in the boundary plasma sheet or LLBL, which corresponds to closed field lines. The electron energy spectrogram of these arcs displayed \"inverted-V\" structures, suggesting the presence of a quasi-static parallel electric field. In addition, we observed geomagnetic ULF responses associated with this process, indicating that the magnetopause disturbance caused by the HSJ transmitted into the ionosphere as Alfvenic signals. In summary, our findings demonstrate that a HSJ can generate multiple auroral arcs in the closed field line region near local noon through Alfven waves.
These findings have important implications in three key aspects, as outlined below.
1. On the generation of the discrete aurora on closed field lines near local noon
It is widely acknowledged that the discrete aurora near local noon predominantly originates from magnetosheath precipitation characterized by broadband acceleration and is on open field lines ([PERSON], 1997; [PERSON] et al., 2016; [PERSON] et al., 2009). However, the conditions conducive to the formation of the discrete aurora on closed field lines near local noon and the auroral types persist uncertainties. This study provides evidence that multiple discrete auroral arcs, exhibiting quasi-static acceleration on closed field lines near local noon, can be driven by an impacting HSI. Ground-based observations (Figure 1 and Movies S1 and S2) also reveal these discrete auroral arcs in closed field line regions near local noon, particularly at lower latitudes along the equatorward boundary of the discrete auroral oval typically identified as the open-closed field line boundary. These observations are analogous to previous observations of discrete auroral arcs near local noon associated with dynamic pressure variations from foreshock transients ([PERSON] et al., 2019). In summary, we suppose that the discrete auroral particles near local noon are not exclusively from open field line regions but can also originate from closed field line regions under the influence of upstream dynamic pressure disturbances, including magnetosheath HSJs.
2. On the response patterns of the magnetosphere-ionosphere system to HSJs
Upon reaching the magnetopause, magnetosheath HSJs can impact the magnetopause and cause various magnetospheric responses, including transient and localized compressions of the magnetic field, ULF waves, and anisotropies in particle pitch angle distributions ([PERSON] et al., 2018). Consequently, ground magnetic variations
Figure 5: Particle observations of multiple auroral arcs on 29 January 2017. (a) Zoomed-in view of the dayside auroral observation extracted from Figure 3b. The white line represents the trajectory of Defense Meteorological Satellite Program (DMSP) F17 satellite from 08:36:00 to 08:52:30 UT, with the arrow indicating the satellite’s flight direction. (b) Particle precipitation data detected by instruments (SSI, SSM, and SSIES) aboard the DMSP satellite along this trajectory. The panels, from top to bottom, display auroral intensity, differential energy flux spectrograms of electrons and ions ranging from 40 eV to 30 keV, differential magnetic field components in the downward (blue), satellite forward (green), and poleward (red) directions, along with density and temperature. Vertical lines in plot by correspond one-to-one with the black dots in plot a. The “CP”, “BP”, and “LLBL” represent central plasma sheet, boundary plasma sheet, and low-latitude boundary layer, respectively.
and dayside auroral enhancements can be detected at high latitudes subsequent to observed HSJs ([PERSON] et al., 2012; [PERSON] et al., 2018, 2022). However, there is no research determining the specific types of auroral responses induced by HSJs. Our findings provide informative insights into this by revealing that the discrete auroral response to HSJs can manifest as multiple discrete auroral arcs. It is important to note that while HSJs can drive discrete auroral arcs, they may not necessarily generate such arcs and instead drive other auroral forms, such as the throat aurora. In this study, we propose that ULF waves driven by HSJs may be the mechanism behind discrete auroral arcs. Nevertheless, it has been reported that HSJs can trigger magnetopause reconnection under certain conditions ([PERSON] et al., 2018), a potential mechanism for transient auroral responses but not for the discrete arcs parallel to the auroral oval observed in our study. Therefore, different HSJ-induced processes in the magnetopause and the magnetosphere may be the key factors in the pattern of auroral responses.
### 3. On the relationship between ULF wave and \"inverted-V\" electrons
A variety of theories has proposed that long-period waves can yield parallel electric fields ([PERSON], 1996; [PERSON] et al., 1999; [PERSON] et al., 1994), thus accelerating electrons to produce auroral emissions. Based on these theories, simulations showed that auroral arcs associated with ULF waves exhibit precipitated electrons with energies below 1 keV, distinct from discrete \"inverted-V\" arcs ([PERSON] et al., 2021). However, observations ([PERSON] et al., 2017), including those from this study, have suggested correlations between long-period waves (FLR) and \"inverted-V\" electrons accelerated by a quasi-static parallel electric field. This inconsistency between observations and simulations complicates understanding how ULF waves generate \"inverted-V\" electrons. Recently, a one-dimensional kinetic simulation considered the interaction between cold and hot electrons from the ionosphere and magnetosphere, respectively, as well as the wave-mode coupling processes ([PERSON] et al., 2023). This simulation predicts that high-energy \"inverted-V\" electron structures emerges with long-period Alfven waves, consistent with our observations. Consequently, using realistic inputs from observations, we employed this kinetic model to simulate the \"inverted-V\" electron acceleration structures within these multiple auroral arcs, as shown in Figure 6. This result provides valuable insights into the links between ULF waves and the observed high-energy \"inverted-V\" electrons and evidence for the recently established theory of electron acceleration mechanism ([PERSON] et al., 2023).
## 5. Conclusion
We provide compelling evidence that magnetosheath HSJs can drive the formation of multiple auroral arcs parallel to the auroral oval near local noon through ULF waves. The observations established temporal and spatial correlations between the HSJ, multiple auroral arcs, and ULF signals, while simulations reinforced the validity of the underlying mechanism. These findings reveal the previously unconfirmed link between the HSJs, ULF waves, and auroral activity. Also, this study advances the understanding of the interactions between magnetosheath irregularities and the Earth's magnetosphere-ionosphere system and of the mechanism of a specific auroral phenomenon frequently observed near local noon. Moreover, they carry important implications for space weather forecasting and have broader relevance in the study of magnetized celestial bodies.
## Conflict of Interest
There are no conflicts of interest to declare for this study.
## Data Availability Statement
Data from MMS, THEMIS, and ground magnetometers are openly accessible from [[https://lasp.colorado.edu/mms/sdc/public/data/](https://lasp.colorado.edu/mms/sdc/public/data/)]([https://lasp.colorado.edu/mms/sdc/public/data/](https://lasp.colorado.edu/mms/sdc/public/data/)), [[http://themis.ssl.berkeley.edu/data/themis/](http://themis.ssl.berkeley.edu/data/themis/)]([http://themis.ssl.berkeley.edu/data/themis/](http://themis.ssl.berkeley.edu/data/themis/)), and [[https://flux.phys.uit.no/geomag.html](https://flux.phys.uit.no/geomag.html)]([https://flux.phys.uit.no/geomag.html](https://flux.phys.uit.no/geomag.html)),
Figure 6.— Simulated electron energy flux spectrogram. This spectrogram depicts simulated electron energy flux at \(\sim\)3,300-km altitude, obtained from a kinetic simulation detailed in [PERSON] et al. (2023). The simulation domain extends from 200 km to 3.2 \(R_{\rm e}\), encompassing the transition region between hot plasma originating from the magnetosphere and cold plasma from the ionosphere. A kinetic Alfvén wave acts as the driver of this system, carrying upward field-aligned currents. Boundary conditions are specified as follows. At the upper boundary, magnetospheric electrons have a temperature of 200 eV and a density of \(5\times 10^{8}\) m\({}^{-3}\), while at the lower boundary, ionospheric electrons have a temperature of 0.2 eV and a density of \(2.7\times 10^{11}\) m\({}^{-3}\). The incident wave characteristics contain a period of 30 s and a perpendicular wavelength of 100 km. The amplitude of upward field-aligned currents mapped to the ionosphere is set as 1 μAm\({}^{2}\).
respectively. The data from SSUSI, SSJ, SSM and SSISE instruments onboard the DMSP are available from [[https://ssusi.jhuapel.edu/data_retriver](https://ssusi.jhuapel.edu/data_retriver)]([https://ssusi.jhuapel.edu/data_retriver](https://ssusi.jhuapel.edu/data_retriver)) and [[https://ngdc.noaa.gov/eog/download.html](https://ngdc.noaa.gov/eog/download.html)]([https://ngdc.noaa.gov/eog/download.html](https://ngdc.noaa.gov/eog/download.html)). We acknowledge the Polar Research Institute of China (PRIC) for providing all-sky imager (ASI) data at the Yellow River Station (YRS). The ASI observations used in this paper can be obtained from Qiu (2024). MMS and THEMIS data is analyzed and plotted by the Space Physics Environment Data Analysis Software which is downloaded from [[http://themis.ssl.berkeley.edu/software.shtml](http://themis.ssl.berkeley.edu/software.shtml)]([http://themis.ssl.berkeley.edu/software.shtml](http://themis.ssl.berkeley.edu/software.shtml)). The codes for tracing the magnetic field lines are also computed by the SPEDAS software.
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* [PERSON] et al. (2022) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2022). Disviate transient phenomena and their impact on the magnetosphere and ionosphere. _Space Science Reviews_, _218_(5), 40. [[https://doi.org/10.1007/s11214-021-00865-0](https://doi.org/10.1007/s11214-021-00865-0)]([https://doi.org/10.1007/s11214-021-00865-0](https://doi.org/10.1007/s11214-021-00865-0)) | wiley | Magnetosheath High‐Speed Jet Drives Multiple Auroral Arcs Near Local Noon | Hui‐Xuan Qiu, De‐Sheng Han, Run Shi, Jianjun Liu | https://doi.org/10.1029/2024av001197 | 2,024 | CC-BY |
wiley/fda1992c_27db_4c3a_ab48_1fcf77627733.md | [PERSON] et al., 2019). We leverage reprocessed data acquired by the Voyager 2 spacecraft to address these questions, and to determine what data is required from future missions to answer them more fully.
Though there is renewed interest in Uranian satellites due to the possibility of liquid water, fundamental qualities such as the simple-to-complex transition diameters of their crater populations have not been measured since the 1980s ([PERSON], 1989). The simple-to-complex transition is particularly important because it reflects the thermomechanical properties of the impacted surface, providing a line of indirect compositional inference (e.g., [PERSON], 2013; [PERSON] et al., 2018; [PERSON], 1980; [PERSON], 2002; [PERSON] et al., 2021; [PERSON] et al., 2014). Previous studies inferred that Ariel's surface exhibits geologic evidence for periods of widespread resurfacing and high heat flows through the surface relative to expected radiogenic and formation heating. A period of significantly elevated heating could have melted much of the outer ice shell into the ocean. Previous models estimated that radiogenic heating alone would result in low heat flow (\(\sim\)2 mW/m\({}^{2}\)) and limited geologic activity (e.g., [PERSON] and [PERSON], 2022; [PERSON] et al., 2022). However, several features record past high heat flows indicating localized heating and/or an additional heat source (up to \(\sim\)92 mW/m\({}^{2}\)) (e.g., [PERSON] and [PERSON], 2021; [PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2015). [PERSON] et al. (2023) modeled viscous relaxation of Ariel's largest crater and found that heat flows \(>\)30 mW/m\({}^{2}\) are necessary to create the observed topography, higher than radiogenic heating alone could produce. Using models that included tidal heating, [PERSON] et al. (2022) concluded that Ariel could host a residual ocean today.
Miranda also hosts deformed surface features consistent with high historic heat flows. Miranda's surface can generally be categorized into two terrain types: rough, resurfaced areas called coronae, and smoother cratered plains ([PERSON] and [PERSON], 2020). [PERSON] et al. (1997) found that Arden Corona could have been formed by thermally induced upwelling. [PERSON] and [PERSON] (2014) showed that Miranda's coronae may have formed due to convection in the ice shell driven by tidal heating. Previous work has also found high heat flows associated with Arden and Inverness coronae (\(\sim\)31-112 mW/m\({}^{2}\) and \(\sim\)35-140 mW/m\({}^{2}\), respectively) ([PERSON] et al., 2015, 2022b).
The simple-to-complex transition diameter and crater depth-diameter ratios of Ariel and Miranda have only been estimated by [PERSON] (1989). For Ariel, their data set contained 18 craters. Since that work, the imagery and topography have both been reprocessed using modern computational techniques. Advances in GIS technology have also facilitated new studies of Ariel and Miranda's crater populations.
In the past several decades, the simple-to-complex transition has been measured for many icy worlds, including Dione ([PERSON] et al., 2017), Enceladus ([PERSON] et al., 2012), Gandymede ([PERSON] and [PERSON], 2006; [PERSON] et al., 2018), and Callisto ([PERSON] and [PERSON], 2006). This transition diameter depends on surface strength properties, with rocky surfaces having larger transition diameters than icy surfaces. This was used to predict the composition of Ceres ahead of the Dawn mission ([PERSON], 2013), and the prediction was updated using new crater morphology data after the mission ([PERSON] et al., 2016). We build upon this framework to estimate the surface composition and strength properties of Ariel.
Crater-counting studies are also an important tool for determining the age of a surface (e.g., [PERSON] et al., 2024; [PERSON] et al., 2008; [PERSON] et al., 2015; [PERSON] and [PERSON], 2010). Both Ariel and Miranda show signs of geologic activity, but we do not know how recently they may have been active. [PERSON] et al. (2022) estimated the age of different regions on Ariel and Miranda by matching crater counts to impactor production functions from [PERSON] et al. (2003). These production functions have previously been applied to Pluto and Charon to learn about the impactor population of the Kuiper Belt ([PERSON] et al., 2019). We used the same method to determine relative and absolute ages for our study areas on Ariel and Miranda.
In this work, we use newly processed data to estimate the simple-to-complex transition diameter, and infer that Ariel's surface is likely composed primarily of volatile (water?) ices, strengthening the foundation for future studies of the Uranian system. We estimate ages for one region on Ariel and two regions on Miranda, independently verifying results from [PERSON] et al. (2022). We also recommend imaging resolution and spatial coverage for potential future missions that would allow for quantitative hypothesis testing leveraging these morphological methods.
## 2 Methods
### Crater Mapping
We use newly processed imagery and topography from [PERSON] and [PERSON] (2020) to measure craters on Ariel and Miranda. The best resolution of this imagery is \(\sim\)1 km/pixel for Ariel and \(\sim\)250 m/pixel for Miranda ([PERSON] & [PERSON], 2020). On Ariel, the vertical precision of the digital elevation model (DEM) is \(\sim\)0.42 km ([PERSON] & [PERSON], 2020). On Miranda, the vertical precision of the DEM ranges from \(\sim\)0.24 to \(\sim\)1 km ([PERSON] & [PERSON], 2020). We identified two distinct morphological areas on Miranda (Figure 1b). The \"Elsinore\" region on Miranda encompasses Elsinone Corona, while the \"smooth middle\" region is the terrain between coronae. We identified one region on Ariel (Figure 1a), consistent with [PERSON] (1989), which did not divide Ariel into multiple study areas. It should be noted that our study area on Ariel includes chasmata that make up the Pixie Group. [PERSON] and [PERSON] (1991) used fault scarp degradation states, crater density, and cross-cutting relationships of scarps to determine the relative age of the two chasmata groups. They note that the crater population superposed on the scarps of the Pixie group chasmata is similar to that of the crated plains ([PERSON] & [PERSON], 1991). The floors of the chasmata may be younger than the surrounding crated terrains, and future studies should determine how removing them from the study area affects the age results.
We use the Java Mission-planning and Analysis for Remote Sensing (JMARS) crater counting tool in 3-point mode to make crater measurements across all study areas ([PERSON] et al., 2009). We consider only craters with diameters greater than 0.7 km for Miranda's smooth middle, 1 km for Miranda's Elsinore, and 4 km for Ariel, which is equivalent to \(\sim\)3-4 pixels in the reprocessed imagery.
Our study areas were chosen independently of those in previous studies. [PERSON] et al. (1991) conducted a crater counting study on Miranda and found 2 crater populations: fresh and subdued. They then determined the relative size-frequency of both types of craters for Miranda's Uranus-facing side and anti-Uranus side. [PERSON] et al. (2022) used crater density maps along with morphology to categorize different regions. We chose not to use crater density maps as this technique, in principle, may self-select for differences in crater populations and
Figure 1: Regional outlines shown on reprocessed basemaps of Ariel and Miranda ([PERSON] & [PERSON], 2020). (a) We choose a single study region on Ariel (yellow outline) because its surface does not have as distinct morphological differences as seen on Miranda. This region contains chasmata of the Pixie Group which have been studied in previous work and may have young floors ([PERSON] et al., 2022; [PERSON], 1991). (b) Reprocessed Ariel DEM from [PERSON] (2020). (c) We divide Miranda into two study regions, with the red line encompassing a deformed feature called Elsinore Corona and the cyan line encompassing an area of the plains we call the “smooth middle” region. (d) Reprocessed Miranda DEM from [PERSON] and [PERSON] (2020). Images are shown using a cylindrical projection centered at \(-\)40”N, 320”E on Ariel and \(-\)40”N, 280”E on Miranda.
influence the crater statistics, even if the crater distribution is random (e.g., [PERSON] et al., 2015). [PERSON] et al. (2022) used crater counting along with modeled distributions from [PERSON] et al. (2003) to determine ages for Ariel and Miranda. They break their study area on Ariel into two categories based on crater density: \"crated\" and \"tectonic\". On Miranda, their study areas are Elsinore Corona, Inverness Corona, and two categories determined by crater density (\"Crated Dense\", and \"Crated Low\"). They then compared their measured crater distributions to both the Case A and Case B models from [PERSON] et al. (2003). Overall, our study area on Ariel is most similar to the \"Ariel tectonics\" region from [PERSON] et al. (2022). Our Miranda \"smooth middle\" region is most similar to their Miranda \"crated dense\" region, while our study areas for Miranda Elsinore are comparable.
We use relative and cumulative crater size-frequency diagrams (SFDs) to determine the age of a surface, whether resurfacing has occurred, and to learn about the impactor population. Plotting the cumulative SFD for each study area also allows us to determine the relative ages of the surfaces (Figure S2 in Supporting Information S1). An older region will have a higher density of craters because it has had more time to experience impacts. A younger region may have a low density of craters if it has been resurfaced and older craters were erased. We also compared our SFDs to production functions from [PERSON] et al. (2003) to determine how our results compare with a modeled impactor population and estimate absolute ages (Figure S3 in Supporting Information S1). The Supplementary Material presents, in detail, the methods used to produce age estimates.
### Depth-Diameter Ratios and Transition Diameter
We extract topographic profiles of each crater from the digital elevation models of [PERSON] (2020) to determine crater depths and categorize craters as simple or complex. For each crater, we take 4 topographic profiles spanning 1.2 crater radii, with each profile equally spaced about the crater center by a 45\({}^{\circ}\) rotation.
Simple craters are bowl-shaped, while complex craters have additional topographic features (Figure 2). We identify craters as complex when they have an identifiable central peak in the topographic profiles, and as simple when no peak can be identified. [PERSON] et al. (2021) further categorized complex craters on Pluto and Charon by
Figure 2: Diameter-wide E-W topographic profiles of a simple crater on Ariel at \(-17.33^{\circ}\)N, \(357.97^{\circ}\)E (a) and a complex crater at \(-46.76^{\circ}\)N, \(336.88^{\circ}\)E (b) created by concatenating radial profiles 3 and 7. We categorize the blue profile (a) as a simple crater because it lacks an identifiable central peak, while the red profile (b) is categorized as complex because of the central peak. Topographic profiles of each crater are extracted at 45-degree intervals beginning at the crater center and extending to 1.2 crater radii.
morphology (central peaks, scalloped rim, flat floors, and wall terraces), but we did not identify any craters with these additional morphologies in this study. However, higher-resolution images might reveal such features--or provide evidence for their absence. In total, we identified 6 complex craters on Ariel.
Some craters do not have obvious bowl shapes or central peaks, or otherwise lack radial symmetry, and were classified as either uncertain-simple or uncertain-complex (Figure 3). The smallest uncertain-complex crater (Figure 3c) has an apparent peak in one profile, and the other profiles are not clearly bowl-shaped. The possible peak is due to a higher value in only one pixel; the resolution of the DEM is not high enough at this location to confidently classify this crater within the vertical certainty of the data set ([PERSON] & [PERSON], 2020). Finvara (Figure 3d) is a crater with a diameter of \(\sim\)32.56 km, which appears warped because it is at the edge of the Voyager image used to make the mosaic. There is a small central peak visible in some profiles, so we classify Finvara as uncertain-complex. The craters in Figures 3e and 3f are clearly identifiable in the imagery but have inconclusive topography. They are classified as uncertain-simple because they lack identifiable central peaks. The uncertain craters on Ariel are not included in analyses below, but the examples in Figure 3 are pointed out in Figure 5a. The largest crater we identify on Miranda may be complex, but there are several other craters and topographic features overlaid on it that interfere with the profiles. We categorize it as an uncertain-complex crater (Figure 3g).
We use the method detailed in [PERSON] et al. (2017) to determine crater depths. For each profile, we determine 2 depths by subtracting the minimum elevation on the floor from the maximum height on either side of the rim. We then take the average of these depths. We repeat this for all profiles of each crater, and report the mean and standard deviation of the 4 depths. We do not report a depth for every crater because topography is not available (or not available at high-enough resolution) for all locations.
We used depth and diameter measurements to estimate the simple-to-complex transition diameter. At this diameter, more craters have a complex morphology than simple. This statistic is widely used to compare crater populations across planetary bodies (e.g., [PERSON] et al., 2012; [PERSON], 2013; [PERSON] et al., 2016; [PERSON] et al., 2017, 2021; [PERSON], 1989, 2002; [PERSON] et al., 2021). Transition diameter is related to target strength properties and scales inversely with surface gravity ([PERSON], 1980). If complex craters are present, then the surface is not strong enough to maintain the shape of a simple crater of that size. Therefore, a lower transition diameter implies a weaker surface. This weakening may be due to surface composition at the crater location, in addition to factors such as porosity (e.g., [PERSON] et al., 2021), or compositional or mechanical layering (e.g., [PERSON] et al., 2018).
We use two different methods to determine the simple-to-complex transition diameter on Ariel, which are detailed below, following [PERSON] et al. (2021). We exclude uncertain-simple and uncertain-complex craters and craters where topography is not available or is insufficient to resolve the crater. Overall, we included 114 craters in this analysis. We identified only one uncertain-complex crater on Miranda. Therefore, we can only report an upper limit on the simple-to-complex transition diameter for Miranda.
#### 2.2.1 Intercept Method
To use the intercept method, we plot the depth and diameter of all simple and complex craters on Ariel and fit a power law to each data set. Larger craters are expected to be deeper than shallower craters. If a crater is anomalously shallow, it may have experienced alteration, such as viscous relaxation or infilling. One can also compare the slopes of the best-fit lines for simple or complex craters to that of other planetary bodies. The lines are fit with a power law, using
\[d=aD^{\beta}, \tag{1}\]
where \(d\) is crater depth, \(D\) is crater diameter, and \(\alpha\) and \(\beta\) are the fit parameters ([PERSON] et al., 2017).
The point at which the best-fit lines in log-log space for simple and complex craters intersect is taken as the transition diameter. We computed the 95% confidence interval for the slope and \(y\)-intercept for both fits (Figure 4a).
Figure 3:
#### 2.2.2 Morphology Method
The morphology method uses the likelihood of craters over a range of diameters being simple or complex to determine the transition diameter. We plot each crater as a Gaussian distribution and calculate the probability of finding a crater of each size over the full range of observed crater diameters using
\[P(D)=\frac{1}{\sigma\sqrt{2\pi}}\,^{\frac{1}{2}\left(\frac{0-\alpha}{\sigma} \right)^{2}}, \tag{2}\]
where \(P(D)\) is probability of occurrence of the crater diameter, \(D,D_{i}\) is any diameter in the range of counted crater diameters (from 7 to 65 km), and \(\sigma=3\) km, which corresponds to \(\sim\)3 pixels in the imagery. We choose a constant value for \(\sigma\) because smaller craters have larger relative uncertainties in diameter than larger craters because they are closer to the resolution limit.
We sum the probabilities of the simple craters and separately sum the probabilities of the complex craters to create a cumulative likelihood function. As in [PERSON] et al. (2021), we normalize these values to show the fraction of total craters with each morphology at a given diameter. The transition diameter is the diameter at which complex craters account for 50% of the total craters, and maintain at least that fraction for larger diameters. There is no established method for providing an error on this estimate for this application. Another way to report the morphology method transition diameter is the range from the smallest complex crater to the largest simple crater (Figures 3a, 3b, and 4b).
## 3 Results
The power-law exponent (slope of the best-fit line in log-log space), \(\beta\), of the depth-diameter ratio, \(d\)/\(D\), is typically greater for simple craters (steeper slope) than for complex craters ([PERSON], 1980). Later modifications such as floor rebound, rim collapse, and deposition of thick regolith make large craters shallower, leading to a more constant \(d\)/\(D\) slope for complex craters ([PERSON] & Cartwright, 2022; [PERSON], 1974; [PERSON], 1989).
We find that the complex craters have a slightly higher exponent than simple craters (complex \(\beta=1.33\pm 0.457\), simple \(\beta=1.06\pm 0.14\)). However, both of our best-fit lines are within the error bounds for the other category of crater morphology, meaning that the slope data sets are indistinguishable (Figure 4a). This ambiguity likely exists because the resolution of the DEM is insufficient to resolve the smaller, shallower craters ([PERSON] & [PERSON], 2020). These \(d\)/\(D\) ratios can therefore not be used to determine transition diameter, and we cannot report a transition diameter using the intercept method.
Our estimate of \(\beta=1.33\pm 0.457\) for Ariel's complex crater \(d\)/\(D\) slope is not certain enough to constrain Ariel's surface strength. [PERSON] et al. (2021) state that craters appear artificially shallow as the diameter approaches the resolution limit of the DEM, which in turn makes the \(d\)/\(D\) slope steeper. In our case, the vertical resolution for the DEM is \(\sim\)0.42 km, which is similar to the depth of smaller craters. [PERSON] et al. (2021) observed that it is rare to find a complex \(d\)/\(D\) slope above 0.8, and that any inferred slope greater than 0.8 is likely illusory.
Using the morphology method, which does not depend on crater depths, we find a transition diameter of \(\sim\)26 km for Ariel (Figure 4b). This value is the point where the probability curves for simple and complex craters intersect, and complex craters become more likely than simple craters. The uncertainty ranges from the smallest complex crater (\(\sim\)20 km) to the largest simple crater (\(\sim\)24 km). In this case, the largest simple crater is smaller than the
Figure 3: Crater classification of Ariel (a)–(f) and Miranda (g). Some craters are difficult to classify as simple or complex because of the resolution of the data or because their profiles are not radially symmetric. (a) The crater at \(-\)24.084\({}^{\circ}\)N, 340.7816\({}^{\circ}\)E is bowl-shaped and is classified as Ariel’s largest single crater in this study. The diameter is the upper bound on the transition diameter error using the morphology method. (b) The crater centered at \(-\)3.152\({}^{\circ}\)N, 323.384\({}^{\circ}\)E has a central peak at \(\pm\) the smallest complex crater, with a diameter of 20.38 km. (c) The crater at 1.02058\({}^{\circ}\)N, \(-\)35.1773\({}^{\circ}\)E is classified as uncertain-complex because of the apparent central peak in the red topographic profile. It is uncertain because the peak is due to only one pixel and is not visible in every profile. (d) The crater centered at \(-\)14.998\({}^{\circ}\)N, 18.371\({}^{\circ}\)E is distorted because it is located close to the edge of the imagery. (e) The crater centered at \(-\)23.72\({}^{\circ}\)N, 252.16\({}^{\circ}\)E has an uneven rim with profiles that do not exhibit a clear bowl shape or central peaks. (f) The crater centered at \(-\)23.02\({}^{\circ}\)N, 314.94\({}^{\circ}\)E has some profiles that appear relatively flat (blue and yellow) while others show a rough bowl shape (red and orange). (g) The crater centered at \(-\)39.91\({}^{\circ}\)N, 219.48\({}^{\circ}\)E (“Crater B” in [PERSON], 1991) is the largest crater we measure on Miranda. It may be complex, but several other craters and interfering topography overlay the crater, so we classify it as uncertain. This is the only possible complex crater we identify on Miranda.
transition diameter, so only a lower bound is reported. The morphology method is often described as finding the point where complex craters reach 50% probability. In our data, complex craters first reach 50% probability at \(\sim\)21 km, where there is one complex crater and no simple craters. Simple craters again become more likely than complex craters in the next bin size. The transition diameter that we report is the point at which complex craters
Figure 4: We report the simple-to-complex transition diameter using the morphology method but not the intercept method. (a) The transition diameter cannot be confidently determined using the intercept method from current data for Ariel because the slopes for simple and complex crater depth/diameter ratios are indistinguishable due to large uncertainties. Using the intercept method, the simple-complex transition diameter would be the point where the best-fit lines for simple craters (solid green line) intersects the line of best-fit for complex craters (solid pink line). The dashed green and pink lines represent the 95% confidence interval for the slope and \(\gamma\)-intercept of the best-fit lines for simple and complex craters, respectively. For the power law fit to simple craters, \(\alpha=0.058\) and \(\beta=1.06\) (Equation 1). For complex craters, \(\alpha=0.0208\) and \(\beta=1.33\). (b) The morphology method yields a transition diameter on Ariel of 26 km. This is the size at which complex morphology (pink) reaches 50% probability and maintains a higher likelihood than simple craters (green). Another way to determine the transition diameter is to report the range from the smallest complex crater (20 km) to the largest simple crater (24 km). In this case, the largest simple crater is smaller than the transition diameter, so only a lower bound is reported. Each crater is included as a Gaussian distribution with \(\sigma=3\) km.
reach 50% probability _and_ maintain at least 50% probability at all larger diameters. At this point, the probability curves for simple and complex craters intersect in Figure 4b.
Using the most reliable case for each study area (Figure S3 in Supporting Information S1), the absolute age of each region is \(\sim\)1 Gya for Miranda's Elsignore, \(\sim\)3 Gya for Miranda's smooth middle, and \(\sim\)0.4 Gya for Ariel. These estimates are based on the modeled curves that are most closely aligned with our measured curves. For Elsinore Corona, our SFD curve is most aligned with the modeled curve for 1 Gya, though it ranges from \(\sim\)0.5 Gya at larger diameters to \(\sim\)1.5 Gya at smaller diameters. Our SFD curve for Miranda's smooth middle is closely aligned with the modeled curve for 3 Gya, with a dropoff in crater density at larger diameters. Our SFD curve for Ariel is in between the modeled curves for 0.25 Gya and 0.5 Gya, so we report an age of \(\sim\)0.4 Gya. More details about our age estimates can be found in the Supporting Information S1.
## 4 Discussion
### Ariel's Transition Diameter Implies an Icy Composition
Comparing our estimate for Ariel's transition diameter to other bodies is difficult because methods vary widely across the literature (Figure 5). The morphology method yields systematically larger estimates than the intercept method for most bodies, so we can only compare our results to those measured using the same method ([PERSON] et al., 2021). Due to data limitations, we only use the presence of central peaks in our analysis, and therefore compare our results against other measurements of central peak 50% occurrence whenever available. Without an agreed method for estimating error, we cannot quantify how our results compare with others.
Other studies hypothesized that Ariel's surface is primarily composed of water ice, with some rock and ammonia-bearing species (e.g., [PERSON] et al., 2023; [PERSON] et al., 2015, 2020). Observations from JWST and Earth-based telescopes found that CO and CO\({}_{2}\) ice may also be present on Ariel's surface ([PERSON] et al., 2024; [PERSON] et al., 2003). Ariel's bulk density of 1592 \(\pm\) 150 kg/m\({}^{3}\) is slightly less than that of Pluto and Charon ([PERSON] & [PERSON], 2020). Ariel is thus likely composed of a mixture of water ice, silicates, and organics. [PERSON] et al. (2022) used shape data to determine that Ariel is at least partially ice-rock differentiated, to an extent
Figure 5: Transition diameter can reveal the strength of the surface. Our result of \(\sim\)26 km for Ariel is consistent with an icy composition. We report a lower limit on Miranda’s transition diameter of \(\sim\)49 km due to the lack of visible complex craters. The morphology method (a) yields larger transition diameters than the intercept method (b), meaning one can only compare transition diameters that were determined using the same method. However, non-standardized reporting and calculations of formal uncertainties make comparisons difficult. For some bodies, the data resolution is low enough that authors can only report an upper limit on the transition diameter. Pink and green lines represent the best-fits through the data points (not including upper limits) showing the inverse scaling of transition diameter with surface gravity. Table S2 in Supporting Information S1 lists the sources for each point.
that depends on when Ariel formed. An earlier formation (e.g., \(<\)4 Myr after calcium-aluminum-rich inclusion formation) could lead to Ariel being fully differentiated. A later formation could lead to an undifferentiated crust with rock trapped within the icy outer layer. Ariel's bulk density and deformed surface are consistent with a differentiated rocky core and an icy outer layer ([PERSON] et al., 2015).
Our transition diameter estimate for Ariel is consistent with a differentiated body hosting an icy outer layer. Extrapolating from the trend for icy bodies (Figure 5a), we would expect Ariel to have a transition diameter of \(\sim\)16 km if it were primarily icy. Extrapolating from the trend for rocky bodies (Figure 5a), we would expect a transition diameter of \(\sim\)41 km if Ariel had a primarily silicate composition. Our estimate of \(\sim\)26 km is more closely aligned with Ariel's surface being primarily composed of ice rather than silicates.
Transition diameter is related to surface gravity and surface composition. Ariel's surface gravity (0.29 m/s\({}^{2}\)) is most similar to Charon's (0.28 m/s\({}^{2}\)) and Ceres' (0.27 m/s\({}^{2}\)), so these bodies may have similar transition diameters if they have similar surface compositions. [PERSON] et al. (2021) note that Charon's transition diameter (\(\sim\)13.5-16 km) is similar to the result of 15 \(\pm\) 5 km from [PERSON] (1989) for Ariel using the morphology method. [PERSON] et al. (2016) reported a transition diameter on Ceres of \(\sim\)7.5-12 km using the morphology method. Our larger estimate of Ariel's transition diameter might indicate that there is a higher percentage of rock on Ariel than Ceres or Charon. However, with better data, we may be able to confidently identify smaller complex craters and find a lower transition diameter.
We report only a lower limit on Miranda's transition diameter due to the absence of any identifiable complex craters. This may be because of the limitations of the available imagery, or Miranda's surface gravity may be too low to create complex craters. Miranda is also believed to have a thick layer of regolith ([PERSON] et al., 1991), which could mantle craters and hide evidence of central peaks ([PERSON] and [PERSON], 2022). Dione and Tethys have complex craters, though they are roughly twice the radius of Miranda ([PERSON] et al., 2017). Enceladus is similar in size to Miranda, but no complex craters are visible in the available data ([PERSON] et al., 2021). [PERSON] (1989) reported a lower limit on Miranda's transition diameter of \(>\)25 km using a data set of 25 craters. Our largest recorded crater on Miranda is the uncertain complex crater shown in Figure 3g, which has a diameter of \(\sim\)48.76 km. Based on the available data, the transition diameter must therefore be \(\geq\) 49 km since we cannot identify any smaller complex craters. Previous studies found that Miranda's surface is composed primarily of water ice with NH\({}_{3}\) or NH\({}_{4}\)-bearing species ([PERSON] et al., 2022, 2023). Extrapolating from the trend for icy bodies (Figure 5a), we would expect Miranda to have a transition diameter of \(\sim\)46 km if it were primarily icy. Extrapolating from the trend for rocky bodies, we would expect Miranda to have a transition diameter of \(\sim\)85 km if it were primarily rocky. Without a more precise measurement of transition diameter, we are unable to determine if our lower limit of \(\geq\)49 km is more similar to the trend for icy or rocky bodies.
### Ariel and Miranda Experienced Relatively Recent Resurfacing
Our age estimates are slightly younger but generally agree with those of [PERSON] et al. (2022) for similar study areas. [PERSON] et al. (2022) found an age of 1.2 Gya (\(-\)0.8 + 1.9) for Elsinore corona, 3.4 Gya (\(-\)0.9 + 1.1) for Miranda's \"cratered dense\" region, and 0.8 Gya (\(-\)0.5 + 1.8) for Ariel's \"tectonic\" region. Using a different production function, [PERSON] et al. (2024) found an age of 4.26 Gya (\(-\)0.9 + 0.6) for Miranda's \"cratered dense\" region.
Our age estimates indicate that both mooms had geologically active pasts with elevated heat flows and resurfacing. We find that Ariel's surface is generally younger than Miranda's, which is consistent with results for comparable study areas ([PERSON] et al., 2024; [PERSON] et al., 2022). Though not included in this study, Miranda's Inverness Corona may be even younger than our study area on Ariel ([PERSON] et al., 2022). Relatively young ages are consistent with findings that Ariel's chasmata were present during resurfacing events due to past resonances ([PERSON] et al., 2022). Our age estimates for Miranda agree with previous studies that have determined that the cratered plains are older than the coronae, and that the coronae may have formed by resurfacing of the cratered plains ([PERSON] and [PERSON], 2014; [PERSON] et al., 2023; [PERSON] et al., 1997; [PERSON], 1991; [PERSON] and [PERSON], 2020). [PERSON] et al. (2020) found that the past Ariel-Umbriel mean motion resonance led to tidal heating on Miranda. This heating on Miranda could have been higher than \(\sim\)100 mW/m\({}^{2}\), which would have been sufficient to produce Miranda's young coronae ([PERSON] et al., 2020).
### Future Missions Will Enable Improved Studies of Ariel and Miranda
New imagery and topography of Ariel and Miranda would enable researchers to expand studies like this one. The Uranus Orbiter and Probe mission study reports that it will collect global imagery and stereo topography of Uranus' large satellites at resolutions <500 m/pix ([PERSON] et al., 2021). To improve age estimates for the terrains of Ariel, we recommend collecting global imagery with a resolution of \(\sim\)250 m/pixel. This would allow 1 km wide craters to be imaged with \(\sim\)4 pixels across (the limit used to count craters in this study). To improve estimates of the transition diameter, we recommend collecting global imagery with a resolution of \(\sim\)300 m/pixel, which would allow central peaks in uncertain craters to be imaged with \(\sim\)10 pixels across. Central peak heights on icy satellites range from \(\sim\)0.3 to 10 km ([PERSON] et al., 2021). [PERSON] et al. (2017) note that stereo DEMs cannot resolve features smaller than \(\sim\)5 times the resolution of the poorest image in the pair. We therefore recommend future missions to collect topography with a vertical precision of \(\sim\)0.2 km.
For Oberon, Titania, and Umbriel, we recommend future missions collect imagery and topography that is at least comparable to what we currently have for Ariel or Miranda. The best available resolution of imagery for these satellites is \(\sim\)2.9 km/pixel on Titania, \(\sim\)4.3 km/pixel on Umbriel, and \(\sim\)5 km/pixel on Oberon. [PERSON] (1989) reported upper limits for the transition diameter on these three moons (Figure 5a). They recorded only craters wider than 6-8 pixels. Due to the low resolution of the data, most craters of that width are complex. [PERSON] et al. (2024) used reprocessed data to map craters and other features on Titania, and identified a large multi-ring basin. They suggested that the formation of this basin could have erased Titania's large (>30 km) craters through viscous relaxation or tectonic resurfacing. When we obtain data over the rest of Titania's surface, we will be able to determine if this lack of large craters is global. With higher-resolution data, we would be able to identify simple craters and smaller complex craters, which would improve our estimate of transition diameter. If higher-resolution data were available, we could more confidently conduct the measurements in this study for all 5 major Uranian satellites. We may be able to find evidence of elevated heat flow on these moons as well and determine if they experienced tidal heating in association with Ariel or Miranda.
Having imagery for Ariel that is the same quality as that for Miranda would improve our comparisons of their ages. With new data, we can use crater statistics to better compare Ariel and Miranda's bombardment histories to those of other outer solar system bodies such as Pluto and Charon. When we have images of the northern hemispheres of Ariel and Miranda, we can search for differences across more regions. There may be older terrains on Ariel that we have not yet seen, or coronae on Miranda that show evidence of resurfacing more recently than Elsinore. Estimating the age of other parts of these moons may provide more evidence for resurfacing as well as a timeframe for geologic activity.
Future missions could potentially allow us to determine the transition diameter on Miranda as well as improve our estimate for Ariel. We do not currently see any complex craters on Miranda, but we cannot rule out their existence until we have global imagery and topography. Higher-resolution data may reveal other crater morphologies such as flat floors, scalloped rims, or central pits (e.g., [PERSON] et al., 2021; [PERSON] et al., 2021). These additional categories would allow us to determine multiple transition diameters. As transition diameter is related to surface strength, we could potentially use new data sets to estimate the transition diameter across different terrains to determine if there are large-scale heterogeneities in surface composition (e.g., [PERSON] et al., 2018).
A higher-resolution DEM would improve our estimates of transition diameter by allowing us to confidently categorize smaller complex craters and more accurately measure crater depths. The shallow depths of small craters on similar worlds implies that we need a DEM with better vertical precision. On Pluto and Charon, 10 km wide craters have depths of \(\sim\)0.5-2 km ([PERSON] et al., 2021). On Ceres, 1 km wide craters have depths of \(\sim\)0.3 km ([PERSON] et al., 2016). The smallest craters we measured on Ariel (7 km wide) had depths of \(\sim\)0.5 km. However, such estimates may be unreliable because the current DEM has a vertical precision of \(\sim\)0.42 km and is insufficient to use the intercept method. Using improved topography, we could also measure the size of the central peaks in complex craters (e.g., [PERSON] et al., 2021), and compare them to other bodies.
Following these recommendations would allow us to see the Uranian satellites in detail comparable to Pluto, Charon, and Ceres. Similar studies of craters were conducted on Ceres, which was imaged by Dawn with a resolution of \(\sim\)35 m per pixel with additional images of \(\sim\)3.5-8 m per pixel in some regions ([PERSON] et al., 2021). Likewise, New Horizons' imagery and topography vary widely depending on the location. For example, some images of Pluto range from \(\sim\)80 m/pix to \(\sim\)40 km/pix, and images of Charon range from \(\sim\)160 m/pix to \(\sim\)40 km/pix ([PERSON] et al., 2021). The best data from these missions is roughly an order of magnitude better than what is available for Ariel and Miranda. The Dawn and New Horizons missions revolutionized our understanding of other outer solar system worlds, and data from a future mission to the Uranus system will do the same for Ariel and Miranda.
## 5 Conclusions
We used newly processed imagery and topography of Ariel and Miranda to estimate simple-to-complex transition diameter and surface ages. Using the morphology method, we found a transition diameter on Ariel of 26 km, which is consistent with a primarily icy surface. We estimate a lower limit on Miranda's transition diameter of \(\geq\)49 km due to the absence of visible complex craters. We recommend that future missions collect imagery with a resolution of \(\sim\)250 m/pix and topography with a vertical resolution of \(\sim\)0.2 km to improve these studies.
Answering any of the key science questions discussed in this paper requires better imagery and topography. The search for life beyond Earth begins with the search for water, and Ariel and Miranda may be ocean worlds. NASA has already greenstilt missions to ocean worlds Europa and Titan. The NASA Roadmap to Ocean Worlds ([PERSON] et al., 2019) specified that future ice giant missions should prioritize flybys of Ariel and Miranda. Determining which specific processes have shaped their surfaces can help us learn about their geologic and thermal histories ([PERSON] et al., 2021). Higher-resolution imagery and DEMs over more of the surface may reveal unseen examples of flexure or viscous relaxation that can be used to estimate heat flux. New missions will help improve existing crater counts, expand studies to more terrains, and place a timeframe on major resurfacing events. All the measurements made in this paper would be improved by including more study areas and higher-resolution data.
## Data Availability Statement
The crater databases for Ariel and Miranda used in this study are available as JMARS files and an Excel file in the online repository Zenodo ([PERSON], 2024).
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wiley/fd6ee8b8_f23c_45d6_8e48_1d35843310e8.md | Figure 1.— Map of the study site. (a) The Lost City hydrothermal field is located on the southern wall of the Atlantis Massif at the inside corner of the intersection between the Mid-Atlantic Ridge and the Atlantis Transform Fault. Inset shows the location of the LCHF at 30”N. (b) 3D image showing the location of the different vent sites and fluid flow paths indicating the relationship between the vents based on sulfur geochemistry ([PERSON] et al., 2022). Most of the vents at the center of the field comprise the Poseidon structure. Several other vents are located along the eastern wall. Note: thick solid line—first order vent; thin solid line—second order vents; thin dashed lines —third order vents. See text for more details.
fabrics in the serpentinite basement within the 100-m thick detachment shear zone responsible for the exhalation of the massif ([PERSON] et al., 2006; [PERSON] et al., 2005). The serpentinization-influenced vent fluids at Lost City are warm (up to \(\sim\)116\({}^{\circ}\)C), alkaline, and rich in hydrogen, methane, and formate, and show a systematic compositional variability from the central to the more peripheral parts of the field ([PERSON] and [PERSON], 2004; [PERSON] et al., 2022; [PERSON] et al., 2008; [PERSON] et al., 2005; [PERSON] et al., 2010, 2012; [PERSON] et al., 2006, 2008; [PERSON] et al., 2015).
Carbonate-brucite hydrothermal towers with spire- or flange-like morphologies form up to 60 m-high structures when vent fluids and seawater mix ([PERSON] et al., 2003; [PERSON] et al., 2001; [PERSON] et al., 2006). Young, active chimneys consist predominantly of brucite, calcite and aragonite, characterized by low \({}^{87}\)Sr/\({}^{86}\)Sr and trace element contents ([PERSON] et al., 2024; [PERSON] et al., 2003; [PERSON] et al., 2001; [PERSON] et al., 2006). Mineralogical and geochemical changes have been shown to accompany the chimneys during aging ([PERSON] et al., 2006). However, it is unclear whether spatial compositional variability in the vent fluids may have an additional influence on the compositions of the resulting carbonate-brucite structures. In our companion paper, we show that the degree of vent fluid-seawater mixing affects chimney mineralogy such that calcite and brucite precipitate from a vent-fluid rich solution. Aragonite, on the other hand, forms when the fluid has a higher proportion of seawater ([PERSON] et al., 2024). Progressive reaction with seawater during aging of the chimneys when vent fluid flow wanes results in the conversion of aragonite to calcite, dissolution of brucite, and an increase in \({}^{87}\)Sr/\({}^{86}\)Sr and trace element contents ([PERSON] et al., 2006).
The organic compounds and hydrogen in the Lost City vent fluids provide carbon sources and reducing power to a dense community of microbes in the chimneys and subseafloor ([PERSON] et al., 2006, 2022; [PERSON] et al., 2009; [PERSON] and [PERSON], 2020; [PERSON] et al., 2018; [PERSON] et al., 2020). The interior of the chimneys and relatively higher temperature structures are dominated by the methane-cycling Lost City _Methanosarcinales_, while the exterior and lower temperature chimneys are inhabited by a more diverse group of sulfur- and methane-oxidizers, including the filamentous _Eubacteria_ and the methanotrophic _Archaeae_ (ANME-1) ([PERSON] et al., 2006; [PERSON] et al., 2004). The microbial inhabitants of the vent fluids include the hyperthermobile _Thermococcales_ and _Crenarcheota_, and the sulfate-reducing bacteria _Thermodesulfovibrionales_ ([PERSON] et al., 2006, 2022). These microbes represent the subsurface ecosystem at Lost City and share key metabolic strategies with microbes from other serpentinite-hosted systems ([PERSON] et al., 2022), suggesting that biogeochemical processes occurring in those alkaline systems are analogous. For example, the first microbial colonizers of hydrothermal chimneys at the Prony Bay Hydrothermal Field, a shallow coastal serpentinite-hosted system in New Caledonia, have been shown to play an important role in the early formation of the chimney structures ([PERSON] et al., 2017). It is conceivable that a similar process is occurring at Lost City. At present, the role of thick microbial biofilms that populate the chimneys ([PERSON] and [PERSON], 2020) during the construction of the chimneys at Lost City is unclear.
In this study, we document the mineralogy and fabric of hydrothermal chimneys collected from actively venting structures at LCHF, highlighting spatial variabilities within a chimney as well as among chimneys across the field. In addition, we aim to determine whether microbial communities at Lost City play a role in chimney development and to investigate the presence and extent of biologically influenced mineralization. We highlight the importance of brucite during chimney development and show that brucite comprises inorganic mineral membranes that represent flow structures in young, active chimneys. Our results suggest that there may be an important link between brucite mineralization and the incorporation of organic matter in the hydrothermal structures.
## 2 Sampling Sites
Hydrothermal vent structures at Lost City have various morphologies, such as pinnacles and spires, as well as parasitic cone- and flange-structures ([PERSON] et al., 2003; [PERSON] et al., 2001, 2005; [PERSON] et al., 2006). Spires range in size from a few meters up to tens of meters in height, with the most prominent structure _Poseidon_, which is a composite of multiple actively venting structures, rising up to 60 m above the seafloor (Figure 1). Vent structures that comprise Poseidon include Marker 3, Camel Humps, Beehive, Marker 2, Marker C, and Marker 8 (Figures 1 and 2a-2f; Table S1 in Supporting Information S1). [PERSON] et al. (2006) focused on active and inactive samples from the Poseidon structure in order to investigate the mineralogical and geochemical transformation during aging of the chimneys. In this work, we sampled a relatively large number of samples mostly from actively venting structures, including the relatively lower temperature vents away from Poseidon, in order to determine
Figure 2.— Photos of the Lost City event sites investigated. (a) Marker 3 and (b) Camel Humps are sites located near the top of the Poseidon structure. (c) The Bechive structure vents the hottest fluids at the LCHF, but was no longer present during sampling in 2018. (d) Marker 2, Marker C, and (f) Marker 8 are flange vents on the Poseidon structure. Vents along the eastern wall include (g) Calypso, (h) Sombrero, and (i) Marker 6. (j) Carbonate vein along the eastern wall. Vent locations are given in Figure 1. Images courtesy of [PERSON], UofSC/NSF/remotely operated vehicle Jason/2018 © WHOI.
any spatial mineralogical variability within a chimney structure independent of aging. Marker 3 and Camel Humps are two adjacent sites (\(\sim\)several meters apart) near the top of the Poseidon structure, yet the vent fluids have distinct geochemistry and microbial compositions ([PERSON] et al., 2022; [PERSON] et al., 2022). Beehive is a parasitic structure with a morphology resembling a beehive, and was sampled in previous field campaigns ([PERSON] et al., 2003; [PERSON] et al., 2001, 2005; [PERSON] et al., 2006). It vents the hottest fluids (up to 96-116\({}^{\circ}\) C) that are most representative of the first-order, unaltered endmember fluid at Lost City ([PERSON] et al., 2022; [PERSON] et al., 2005). The Beehive structure was missing during sampling in 2018; thus, we collected chimney samples directly at the site where vigorous fluid flow occurs, presumably representing the interior of the previous Beehive structure (Figure 2c). Markers 2, C, and 8 are parasitic flange-like structures growing horizontally from Poseidon and trapping warm vent fluids within the downward facing flanges (Figures 2d-2f). Actively venting chimney structures that we sampled along the steep northeast trending escarpment, referred to as the eastern wall, include the vent structures Calypso, Marker 6, and Sombrero (Figures 1 and 2g-2i). Calypso is a fresh spire that grows directly from the serpentinite wall, while Marker 6 is a small, delicate spire on top of inactive chimney debris. We sampled fresh chimney growth atop a bigger, older structure at the Sombrero site. Although Marker 6 and Sombrero are located away from Poseidon, sulfur geochemistry of the fluids suggests that these structures share a common fluid flow path with Beehive ([PERSON] et al., 2022). In contrast, Calypso has vent fluid compositions with a stronger seawater influence ([PERSON] et al., 2022). A few structures along the eastern wall that did not show evidence of venting at the time of sampling were also sampled. We also sampled carbonate veins or fissure filling deposits west of Marker 8 as well as along the eastern wall (Figures 1 and 2j).
[PERSON] et al. (2022) grouped the vents into four groups based on their sulfur geochemistry, H\({}_{2}\) concentrations, and location within the field. The low sulfide groups, which include Beehive, Camel humps, Marker 6, and Sombrero, are located close to the center of the field and have the lowest sulfide and the highest H\({}_{2}\) and sulfate contents (Figure 1). Sulfide concentrations generally increase with distance from the center of the field in the moderate sulfide (Markers C and 3), high sulfide (Markers 2 and 8), and eastern wall groups (Calypso and veins). At the same time, H\({}_{2}\) and sulfate concentrations increase toward the more peripheral vent groups. This systematic compositional variability is attributed to the progressive sulfate reduction along the different flow paths ([PERSON] et al., 2022; [PERSON] et al., 2005; [PERSON] et al., 2012; [PERSON] et al., 2006). [PERSON] et al. (2022) also suggested that all of the Lost City vent fluids are derived from a primary (first-order) vent fluid with a composition similar to that sampled at Beehive. This first-order vent fluid is then modified to form second- and third-order vents via continued sulfate reduction and incorporation of seawater sulfate (Figure 1).
## 3 Methods
### Sampling
Sampling was carried out in September 2018 during the Return to the Lost City expedition (_RVA Atlantis_ cruise AT42-01) with the remotely operated vehicle (ROV) _Jason_. We sampled sites that had been previously investigated over the course of 20 years of studying Lost City, including Beehive and sites named after field markers (e.g., Marker C) placed in 2003 ([PERSON] et al., 2005), most of which are associated with the Poseidon structure (Figure 1). The structures Sombrero and Calypso, located near the eastern wall, were sampled for the first time in 2018. We collected a total of 37 samples (31 chimneys and 6 carbonate veins) mostly from structures where active venting and non-ambient water temperatures were observed, as well as a few non-venting structures and fissure-filling deposits (Figure 1; see Section 2). Upon recovery, the samples were described macroscopically in terms of texture, color, and the presence of flow structures or layering. Each sample was given a unique ID, which included the _Jason_ dive number, date and time of collection, and sample type (e.g., J.1109.19 Sep.0756 CHIM for a chimney sample collected on 19 September 2018, 07:56 GMT during _Jason_ Dive 1109). For simplicity, we use a shortened version of the sample ID giving the dive number and time of collection (e.g., 1109-0756). The samples were divided onboard amongst the science party members and each of these subsamples was assigned a cruise ID (e.g., sample 1109-0756 is further subdivided into samples with cruise ID LC01349, LC01353, etc.). In some cases, samples show heterogeneities in color, texture, and/or mineralogy. Distinct layers or parts of the samples were sampled and analyzed separately (e.g., LC01349a, LC01349b) for mineralogy and geochemistry. Carbonate minerals were also separated by hand picking under a binocular microscope and were analyzed separately for their stable isotope compositions. The geochemistry of the samples and mineral separates are presented in [PERSON] et al. (2024).
### Analytical Methods
Mineralogy was determined using an X-ray diffractometer with a CuKu\(\alpha\) radiation and a LynxEye detector (Bruker AXS D8 Advance Powder XRD, Bruker Corporation, Billerica, USA) at the Institute of Geochemistry and Petrology, ETH Zurich. We used a scan range of 5-90\({}^{\circ}\) 2\(\theta\) with a step size of 0.02 and scan time of 0.8 s per step. Identification of the minerals was performed using the ICDD Sieve+ (International Center for Diffraction Data, USA) automatic peak search software, which is integrated into the ICDD PDF-2 database. Quantification of the mineral phases was carried out by a full-profile Rietveld refinement method ([PERSON], 1969) using the program Siroquant version 3.0 (Seitronics, Australia), while the calculation of the full-width at half maximum of representative brucite diffraction data was performed using OriginPro ([[https://www.originlab.com/origin](https://www.originlab.com/origin)]([https://www.originlab.com/origin](https://www.originlab.com/origin))).
Thin sections were prepared from resin-impregnated samples for conventional transmitted microscopy using a polarizing microscope (Carl Zeiss Microscopy GmbH, Gottingen, Germany) at ETH Zurich. Fluorescence microscopy was carried out on the same thin sections on a Nikon Eclipse Ci Pol microscope (Nikon Instruments, Inc.) at the Department of Geosciences, University of Fribourg. The samples were excited using blue UV light (472 nm wavelength) combined with a green fluorescence emission filter (520 nm wavelength).
For scanning electron microscopy (SEM), two sets of samples were prepared. The first set was fixed onboard upon collection in 4% paraformaldehyde in 1X phosphate buffered saline solution or 1X glycerol tris-EDTA in 15- or 50-ml falcon tubes. Onshore, these were cut into 2-3 mm-sized pieces, placed inside Eppendor tubes, shock frozen in a liquid nitrogen bath, and freeze-dried for at least 2 hr at ETH Zurich. The second set of samples was not fixed prior to mounting onto the sample holders. Prior to SEM analyses, all samples were coated with Pt-Pd. Microimaging and semi-quantitative elemental analyses were carried out on a FEI Quanta 200F Field Emission Gun - Scanning Electron Microscope (Field Electron and Ion, Co., ThermoFischer Scientific) and an Energy Dispersive X-ray spectrometer (EDAX Octane Super) system at the Scientific Center for Optical and Electron Microscopy (ScopeM, ETH Zurich). Analyses were performed using secondary electron and back-scattered electron detectors at accelerating voltages ranging from 7 to 15 KV.
Micro-X-ray computed tomography (\(\upmu\)X-CT) analyses of samples were performed using the Bruker-SkyScan 2211 \(\upmu\)X-ray CT at the Department of Geosciences, University of Fribourg. Image acquisition was performed using an X-ray source operating at 33-90 kV, 310-600 \(\upmu\)A, and with a step size of 0.2\({}^{\circ}\). Individual shadow images with a pixel resolution of 10-20 \(\upmu\)m and 1.2-6.5 \(\upmu\)m were obtained using a flatpanel and a CCD (charge-coupled device) detector, respectively. During scanning, a 0.5 mm Al-filter was used to reduce beam hardening effects. Shadow images were reconstructed using the Bruker-SkyScan NRecon software (version 1.6.9.18).
Radiocarbon ages of the samples were determined using an elemental analyzer coupled to a Miniscale Carbon Dating system (MICADAS) accelerator mass spectrometer (AMS) equipped with a gas-ion source ([PERSON] et al., 2007) at the Laboratory of Ion Beam Physics, ETH Zurich following the methodology detailed in [PERSON] et al. (2010) and [PERSON] et al. (2010). Carbonate samples were transferred to vacuumisers, flushed with the for 10 min, and reacted with 85% H\({}_{3}\)PO\({}_{4}\) and injected directly into the gas source of the AMS. Standard normalization and blank correction were made with the Nist SRM 4990C standard (Oxalic Acid II) and IAEA C-1 (radiocarbon blank CO\({}_{3}\)), respectively. The precision of the analysis estimated from repeated measurements of IAEA-C2 and coral CSTD during each run is better than \(\pm\)5% on a modern standard. Radiocarbon data are reported as a fraction of modern carbon (F\({}^{14}\)C) and \({}^{14}\)C ages ([PERSON] et al., 2004).
## 4 Results
### Mineralogy and Textures
Descriptions of the samples can be found in Table S2 in Supporting Information S1 and the mineralogy is plotted in Figures 3 and 4 and Figure S1 in Supporting Information S1. Hand specimen photos are in Figure 5; overview micro-CT images and SEM images are shown in Figures 6 and 7 and in Figure S2 in Supporting Information S1. The active chimneys are composed of varying proportions of aragonite, calcite, and brucite, similar to assemblages that have previously been described ([PERSON] et al., 2003; [PERSON] et al., 2001; [PERSON] et al., 2006). The relative proportions of these minerals vary substantially. Bulk samples (Figures 3 and 4) are dominated by brucite and aragonite, with 21 out of 42 having more than 50% brucite and 16 having more than 50% aragonite. Calcite isa minor component in the actively venting chimneys and only 3 bulk samples were observed to contain more than 30% calcite. Two of these are from chimney structures along the eastern wall, and one is from Beehive (Figure 3).
Most of the LCHF chimney samples are heterogenous and friable at the hand specimen scale, showing intricate intermixing between distinctly bright white, fine-grained brucite and cream- to dark cream-colored carbonates that have anastomosing fibrous morphologies often reflecting relict flow structures (Table S2 in Supporting Information S1). Flow textures are preserved either by the direction of crystal growth and/or as mineral channel walls assuming to bound former fluid flow conduits (Figures 5-7; Figure S3 in Supporting Information S1). A few samples exhibit a feathery or quill-like texture produced by acicular arcigantic crystals sharing a common nucleation point (Table S2 in Supporting Information S1; Figure 6a; Figure S3 in Supporting Information S1) with the direction of crystal growth parallel to the direction of fluid flow. This texture may be concealed by abundant fine-grained brucite, giving the sample an overall chalk-like appearance (Figures 5b and 5c).
The majority of the samples appear fibrous in the hand specimen and preserve mineral membrane-bound relict flow paths or fluid conduits (Figures 6b, 6c, and 7a; Figure S4 in Supporting Information S1). The thinnest mineral membranes and the interior of these channel walls are made up of several tens of microns thick brucite upon which later-formed minerals precipitate (Figures 6 and 7a; Figures S3-S5 in Supporting Information S1). The brucite channel walls are made up of individual brucite plates less than 1 um thick forming a reticulated lattice-like texture (Figures S5e and S5f in Supporting Information S1). Aragonite precipitating on the channel walls often forms botryoidal aggregates or fans comprised of acicular crystals that coalesce into crusts/layers
Figure 3: Ternary diagram showing the mineralogy of LCHF chimneys and veins. The samples are composed of variable amounts of brucite, calcite, and aragonite. Subsamples collected from the interior (dark outline) are often brucite-rich, whereas subsamples from the exterior (white infill) are anragonite-rich. Samples from the previously defined low sulfide vent group ([PERSON] et al., 2022) include Beehive and Sombrero and are relatively calcite-rich compared to the samples collected from the moderate sulfide group (Marker C and Marker 3) and from the high sulfide group (Marker 2 and Marker 8). Chimneys from low temperature vents along the eastern wall include Calypso and the carbonate veins and are also calcite-rich. A version of this figure sorted by vent group is found in Figure S1 in Supporting Information S1.
(Figures S4a-S4e in Supporting Information S1), while calcite and brucite occur as globular to botryoidal aggregate textures (Figure 8).
Like the chimneys, the veins are composed of brucite, aragonite, and calcite (Figure 4), whereby brucite is the dominant mineral in almost all the bulk vein samples. In general, the veins have more calcite (25%-34%) and less
Figure 4.— Box plot of the mineralogy of the bulk, interior and exterior parts of the chimneys and veins investigated. The range is bounded by the minimum and maximum abundance for each mineral, while the bottom and top of the box are the first and third quartiles, respectively. The middle line represents the mean mineral abundance.
Figure 5:
aragonite (15%-47%) compared to the chimneys. In contrast to the delicate and highly porous chimneys, the carbonate veins are more lithified and their surfaces are dark gray to dark brown (Figure 5i). However, the interior of the veins still preserves the cream color and fibrous, sinuous textures similar to those of the chimneys (Figure 5j).
### Spatial Variability
The chimneys exhibit textural and mineralogical differences between the interior and exterior parts of the spires. Almost all the subsamples from the interior of the chimney structures (7 out of 8) are composed of 70%-99% of brucite (Figure 4). In the hand specimen, the brucite-rich spire or flange interior is bright white and have a powdery appearance (Figures S6 and S7 in Supporting Information S1). Under the SEM, brucite commonly exhibits botryoidal aggregate textures of individual platy or prismatic crystals that are often associated with calcite (up to 47%) and sometimes with a Mg-silicate phase (Figures 8c and 8d; Figures S6 and S8 in Supporting Information S1). In contrast to the interior, the exterior of the chimneys (\(n=6\)) is primarily anagonite-rich (Figure 4). Structures that are considered to be recently inactive that appear young but where no venting was observed during sampling (\(n=4\)) have more calcite and less brucite than active chimneys (Figure 3). Carbonate
Figure 5: Examples of flow texture preservation at LCHF. (a) Sinuous white mineral surfaces formed by active fluid flow at Marker 3. (b) Hand specimen of sample 1109–1057 from Beehive. As the Beehive structure was no longer present during sampling, this sample was collected from the interior of what used to be the Beehive-like structure, where vigorous active venting was observed. The sample is covered by fine-grained brucite giving it a chalk-like appearance. (c) In places where brucite is dislodged or partially dissolved, the sample has a feathery flow texture formed by the direction of aragonite growth. (d) Sample 1107–174 from Marker 3 showing a fresh spire with sinuous flow structures that have grown on a fine-grained brucite-rich layer. (e) Small piece of a large spire (1107–2314) collected next to the venting flange at Marker 2. (f) Fresh, delicate spire (1108–2002) from Calypso. (g) Detail of white box shown in (f). (h) Bottom of the sample showing sinuous flow texture. (i) Vein or fissure-filling deposit (1110-0838) west of Marker 8. (j) Inside the dark brown weathered crust is a cream-colored interior with a fibrous flow texture.
Figure 6: Overview micro-CT images of flow structures. (a) Flow textures in 1109–1057 from Beehive are preserved by secular aragonite. Rhombohedral calcite (brighter phase) is also present throughout the sample. (b) Fresh spire from Calypso (1108–2002) is composed of interconnected mineral membranes which are made up of brucite and aragonite and bound paleo-fluid flow conditions. (c) In 1107–2314, these mineral channel walls form microcomputments where mineral precipitation is observed. Note that brucite has a lower density than calcium carbonate and appears darker in the micro-CT scan. The detail of the white box can be found in Figure S13 in Supporting Information S1.
veins are also slightly more brucite-rich in the interior while the exterior has slightly more aragonite, although the difference is less pronounced compared to the chimneys (Figure 4). In addition to the spatial differences observed between the interior and exterior of the chimneys, there is a marked difference between the central and the more peripheral sites of the hydrothermal field near the eastern wall (Figure 3). Except for one sample from Beehive and one from Marker 3, samples from the sites at or near Poseidon (Figure 1) have calcite contents that are often less than 10%, whereas many samples from the eastern wall and Calypso (Figure 3) are composed of more than 20% calcite.
### Radiocarbon Ages
The radiocarbon ages of selected active and inactive structures from Lost City are listed in Table 1. Except for two samples, most of the samples from actively venting structures have \({}^{14}\)C ages that are less than \(\sim\)500 years and several samples yielded modern radiocarbon contents (F\({}^{14}\)C \(>\) 1.0), demonstrating that the carbon incorporated into the chimneys is derived from seawater. The \({}^{14}\)C ages of minerals collected from the same sample vary by as much as 3,000 years although there is no systematic difference between aragonite and calcite from the same chimney structure. In general, samples from the low sulfide vent group defined by [PERSON] et al. (2022) (see Section 2) have slightly lower F\({}^{14}\)C values than samples from the moderate and high sulfide groups. The two carbonate veins yielded variable radiocarbon ages. The carbonate vein sampled near the eastern wall has a modern age, whereas the vein located west of Marker 8 has a \({}^{14}\)C age of \(>\)2,000 years. The two inactive chimney
Figure 7: SEM photo mosaic showing the preservation of flow textures in active, inactive, and extinct samples. (a) Active gyre from Calypso (1108–2002) is made up of aragonite-brucite channel walls. Aragonite and brucite-calite aggregates have precipitated on these mineral channel walls. (b) In a recently extinct sample (3651–1231), channel flow structures are preserved. Brucite is still present locally and the sample is made up mostly of aragonite. (c) 3871–1512 is \(\sim\)8,000-year-old sample. Here, channel walls are not clear but can still be recognized by subparallel aragonite crystals. Brucite is absent in this sample. (d) In 3872–1544, an extinct sample, massive and relict flow textures are absent. Brucite is absent and most of the aragonite has been recrystallized to calcite. Approximate ages based on \({}^{14}\)C and/or \({}^{230}\)Th obtained from [PERSON] et al. (2003) and [PERSON] et al. (2011), and this study are also shown. Note: See Figures 4, 5, 510-512 in Supporting Information S1 for more details on these samples.
Figure 8: SEM images highlighting the association of calcite and brentic in young, active chimneys. (a) Calcite (cal) and fine-grained brentic (brc) in sample 1109–1057 from Beehive. (b) Detail of white box in (a). (c, d) In 1109–0743 (Sombrero), brentic occurs as prisms or needles with (c) hexagonal or (d) triangular cross-sections. In both cases, calcite is observed together with brentic. See Figures S6d and S6e in Supporting Information S1 for the general location of these images. (c) Bortyoidal aggregate of brentic plates and subhedral calcite in 1110–0611 (Marker 8). See Figure S7e in Supporting Information S1 for the general location of this image. (f) Detail of white box in (e). (g) Bortyoidal brentic and unusually shaped calcite in 1108–2002 (Calypso). See Figure S5b in Supporting Information S1 for the general location of this image. (h) Detail of the white box in (g).
structures have radiocarbon ages of 8,290 \(\pm\) 92 and 45,471 \(\pm\) 2,418 years, which are less than the \({}^{230}\)Th ages of the same samples (15,989 and 169,516 years, respectively; [PERSON] et al., 2011).
### Inactive Chimney Textures
Inactive vent structures preserve textures similar to active hydrothermal chimneys to a varying degree (Figures 7b and 7c). In a more recently inactive chimney (sample 3651-1231, 585-1,286 years old, [PERSON] et al., 2003; [PERSON] et al., 2011), mineral channel wall structures are still clearly preserved (Figure 7b; Figure S9 in Supporting Information S1). Like in active chimneys, brucite lines the channel walls although evidence of partial brucite dissolution can be observed (Figure S9d in Supporting Information S1), and arquoting needles occur perpendicular to brucite (Figures S9a-S9d in Supporting Information S1). Older inactive chimneys (>10,000 years, [PERSON] et al., 2011) are characterized by the absence of brucite and the transformation of fine needles of aragonite to larger calcite crystals (Figure S10 in Supporting Information S1). In sample 3871-1512, despite the absence of brucite, relief channel walls are still present as linear features formed by supbarallel aragonite needles (Figure 7c; Figure S11 in Supporting Information S1; \({}^{230}\)Th age = 15,989, [PERSON] et al., 2011). In contrast, in an extinct sample (3872-1544, \({}^{230}\)Th age \(\sim\)170,000 years, [PERSON] et al., 2011), the primary mineral textures and channel walls are no longer recognizable (Figure 7d; Figure S12 in Supporting Information S1). In general, with age, the channels of inactive chimneys are progressively filled with increasing number of broken off carbonate crystals and microfossils.
### Microbial Biofilms
The hydrothermal chimneys contain microbial biofilms comprised of cells and extracellular polymeric substances (EPS) of various morphologies and fabrics that range from simple filaments to complex networks of fibers, and
\begin{table}
\begin{tabular}{l l l l l l} \hline Cruise ID & Site & Mineralogy & F\({}^{14}\)C & \({}^{14}\)C age & \({}^{230}\)Th age\({}^{*}\) \\ \hline Low sulfide group & & & & & \\ LC01291 & Beehive & Aragonite & 0.684 \(\pm\) 0.01 & 3,053 \(\pm\) 71 & \\ LC01291 & Beehive & Calcite & 0.957 \(\pm\) 0.01 & 353 \(\pm\) 63 & \\ LC02489 & Sombrero & Aragonite & 0.988 \(\pm\) 0.01 & 94 \(\pm\) 62 & \\ LC02489 & Sombrero & Calcite & 0.975 \(\pm\) 0.01 & 204 \(\pm\) 64 & \\ LC02555 & Marker 6 & Aragonite & 0.944 \(\pm\) 0.01 & 459 \(\pm\) 67 & \\ Moderate sulfide group & & & & & \\ LC01796 & Marker C & Aragonite & 1.030 \(\pm\) 0.01 & \(-\)239 \(\pm\) 64 & \\ LC01796 & Marker C & Calcite & 1.019 \(\pm\) 0.01 & \(-\)149 \(\pm\) 63 & \\ LC00226 & Marker 3 & Aragonite & 1.006 \(\pm\) 0.01 & \(-\)44 \(\pm\) 64 & \\ LC00226 & Marker 3 & Calcite & 0.878 \(\pm\) 0.01 & 1,042 \(\pm\) 66 & \\ High sulfide group & & & & & \\ LC00311 & Marker 2 & Aragonite & 1.018 \(\pm\) 0.01 & \(-\)141 \(\pm\) 64 & \\ LC02604 & Calypso & Bulk chimney & 1.014 \(\pm\) 0.01 & \(-\)111 \(\pm\) 63 & \\ Eastern wall group & & & & & \\ LC01336a & Carbonate vein & Bulk vein & 1.009 \(\pm\) 0.01 & \(-\)75 \(\pm\) 63 & \\ LC01849a & West of Marker 8 & Bulk vein & 0.765 \(\pm\) 0.01 & 2,153 \(\pm\) 69 & \\ Inactive structures & & & & & \\
3651-1231 & Poseidon & Calcite/Aragonite & & 585 \(\pm\) 35\({}^{\circ}\) & 1,286 \(\pm\) 1,278 \\
3871-1512 & Southwest of field & Calcite/Aragonite & 0.356 \(\pm\) 0.00 & 8,290 \(\pm\) 92 & 15,989 \(\pm\) 3,766 \\
3872-1544 & Southwest of field & Calcite & 0.003 \(\pm\) 0.00 & 45,471 \(\pm\) 2,418 & 169,516 \(\pm\) 14,167 \\ \hline \end{tabular} \({}^{*}\)From [PERSON] et al. (2011). \({}^{*}\)From [PERSON] et al. (2003).
\end{table}
Table 1: _Radiocarbon Ages of Chimney and Vein Minerals From Lost City_honeycomb- and parachute-like structures (Table S3 in Supporting Information S1; Figures 9 and 10). EPS is a matrix of various polymers including polysaccharides, proteins, nucleic acids, and lipids produced by microorganisms and serves as their immediate environment ([PERSON], 2010). The presence of biofilms/ EPS is heterogenous even within the same sample and interestingly, they are most commonly associated with brucite. In addition to brucite within the chimney matrix acting as a substrate for biofilms, we observed that individual crystals of brucite may precipitate directly on the microbial filaments or sheets (Figures 9a-9c). In some cases, the microbial filaments seem to influence the growth direction of brucite crystals (Figure 9b). We also observed microbial filaments or worm-like microorganisms that appear to have been partly to fully mineralized by brucite or covered by a Mg-rich thin film (Figures 9d-9h). Microbial biofilms holding together stacks of brucite plates in Marker C were also detected (Figure 9i). In one sample from Sombrero (LC01370B), instead of brucite, microbial biofilms are associated with an Mg-silicate phase of underterminable composition and structure
Figure 9.— Examples of brucite-bifolin association in Marker C. (a) Hexagonal brucite plates on a network of microbial filaments. (b) The basal plane of brucite crystals is oriented parallel to microbial filaments. (c) Brucite crystals that precipitated on a biofilm. (d) Mineralized organism partly buried in bortypoidal brucite. (e) Chains of brucite spheres likely formed from the mineralization of microbial filaments. (f) Putative partly mineralized microorganisms. (g) Putative permeabilized microorganisms enveloped by a Mg-rich biofilm. (h) Putative microbial cell partly buried in an Mg-rich biofilm. (i) Stack of brucite plates associated with a partially preserved matrix of extracellular polymeric substances.
(Figure 10u; Figure S8 in Supporting Information S1). Unfortunately, we were unable to conduct further analyses on this phase.
Interestingly, the intimate relationship of biofilms with these Mg-bearing phases (brucite, Mg silicate) is not observed with arginine or calcite under the SEM. Even in places where biofilms are observed together with aragonite, direct precipitation of anagnonite on the biofilms were not observed and the biofilms are simply draping over or covering anagnonite (Figure 10b). It is important to note, however, that although our observations indicate a close association between brucite precipitation and microbial biofilms/filaments, brucite mostly precipitates in the absence of microbial biofilms and may nucleate upon previously formed minerals (Figures 10c and 10d).
Parachute-like structures, similar to those previously described in _Pseudomonas fluorescens_ isolated from soil ([PERSON] et al., 2009), were observed in some Lost City samples. This structure comprises a canopy of biofilm material that appears to be tethered to the minerals via one or two thin fibers (Figure 10e). Relatively large filamentous tube-like microorganisms greater than 100 um long and about 20 um in diameter were detected in troughs in between adjacent anagnonite spherical aggregates of a sample from Marker C (LC01797A), while the anagnonite themselves are covered by a thick layer of EPS (Figure 10f; Figure S2f in Supporting Information S1). These tube structures may also be completely mineralized by brucite. Although definite identification of these organisms is not possible with the methods used in our study, the morphology of these tubes is similar to the external structures of tube worms ([PERSON] et al., 2011). In samples from Marker C and Marker 6, long filamentous C-rich organisms, about 200 and 1,000 um long, respectively, are present (Figures 10g and 10h; Figure S8 in Supporting Information S1). In Marker 6, this organism is associated with an abundant biofilm characterized by a complex arrangement of fibrillary structures that grade into a semi-organized network of fibers forming honeycomb-like pore spaces (Figure 10i; Figure S8 in Supporting Information S1), which is a common EPS microstructure observed in biofilms and microbial mats in sedimentary environments ([PERSON] et al., 2008; [PERSON] et al., 2007).
Fluorescence microscopy shows that the brucite mineral membranes described above are more fluorescent than the carbonates (Figure 11), with the difference more pronounced in samples associated with biofilms (e.g., Calypso) than in those where no biofilms were observed (e.g., Beehive, Figures S3j-S3k in Supporting Information S1). Interestingly, we observed a rough correlation between brucite fluorescence and crystallinity: fluorescent brucite from Calypso displayed lower crystallinity than that from Beehive (Figure 12). Brucite from Marker C, which is also associated with microbial biofilms (Figure 9), has relatively lower crystallinity (Figure 12). However, we would like to point out that the x-ray diffraction data on which the crystallinity calculations are based are obtained from bulk samples, whereas the occurrence of biofilms and the occurrence of highly fluorescent brucite is only locally observed.
We also observed fluorescent filamentous structures within the channels. These structures are reminiscent of microbial filaments similar to those observed with SEM (Figures 11e and 11f). Micro-CT analyses confirm the presence of these low-density filamentous strands within the chimney conduits (Figure 6b; Figure S13 in Supporting Information S1). These low-density filaments are sometimes associated with a rhombohedral, high-density mineral, which may be calcite based on the form and density (Figure S13 in Supporting Information S1).
## 5 Discussion
### Controls on the Variations in Mineralogy
Our results show clear differences in the mineralogy between the interior and exterior of hydrothermal chimneys and flanges in Lost City. Previous investigations of samples collected across a basal transect of a chimney near Marker H revealed a similar systematic difference in both mineralogy and geochemistry of the interior versus the rim of the sample (Figure S14 in Supporting Information S1) ([PERSON] et al., 2006, 2011; [PERSON], 2016). Although the results of previous studies emphasized the large variability within a single sample ([PERSON] et al., 2006, 2011; [PERSON], 2016), and even alluded that heterogenous precipitation conditions such as variable temperature and pH may result in the observed mineralogical and geochemical heterogeneity ([PERSON], 2011), a mechanistic explanation is lacking.
In our companion paper ([PERSON] et al., 2024), we present geochemical data (6\({}^{13}\)C, 6\({}^{18}\)O, \(\Delta_{47}\), and \({}^{87}\)Sr/\({}^{66}\)Sr) of the Lost City chimneys that constrain the impact of fluid geochemistry on mineralogy and the geochemistry of the precipitating minerals. We suggest that variable mixing ratios between seawater and hydrothermal fluids control fluid geochemistry (e.g., Mg/Ca), and in turn affect the mineralogy and geochemistry of the precipitating minerals. The endmember vent fluids at Lost City are alkaline (pH 9-11), have little to no Mg, and are rich in Ca ([PERSON] et al., 2022; [PERSON] et al., 2005; [PERSON] et al., 2012). Thus, the interiors of the chimneys are bathed in a vent-fluid dominated solution characterized by higher pH and lower Mg/Ca ratios. These conditions promote the precipitation of calcite and brucie. In contrast, agronomic precipitates in the chimney exterior, reflecting an increase in Mg/Ca and decrease in pH resulting from a larger contribution of seawater. We also show that calcite records relatively higher clumped (\(\Delta_{\alpha\beta}\)) and oxygen (8\({}^{18}\)O) isotope temperatures and lower \({}^{87}\)Sr/\({}^{48}\)Sr than aragonite, in concert with its precipitation from a higher temperature vent fluid-rich solution. At lower temperatures, the threshold Mg/Ca ratio for aragonite precipitation is higher, favoring calcite precipitation at a wider range of seawater and hydrothermal fluid mixing ratios ([PERSON] et al., 2024). This may explain why samples from the lower temperature sites such as in Calypso, and some of the carbonate veins have relatively high amounts of calcite (Figure 3; Figures S1e and S1f in Supporting Information S1). In sample 3881-1338, the interior (transect
Figure 10.— Biofilm occurrence in Lost City chimneys. (a) Mg-silicate phase that precipitated on microbial biofilms in Sombrero. (b) In Marker C, biofilm is associated with both aragonite and brucie, but only brucie is observed to precipitate directly on the biofilm. The biofilm covers or drapes over the aragonite. (c, d) Brucite precipitating on earlier formed aragonite in (c) Marker C and (d) Marker 8. (e) Parachute-like structures in Marker 8 consisting of a canopy of biofilm material tethered by a thin fibril structure. (f) Tube like organisms living in between adjacent aragonite spheres in Marker C. (g, h) Long filamentous structures in (g) Marker C and (h) Marker 6. (i) Biofilm in Marker 6 occurs as a network of fibers that in some places form honeycomb-like textures.
no. 2 and 3) is composed of calcite and brucite and has a higher precipitation temperature and lower Mg/Ca than the aragonite-bearing exterior, consistent with our interpretation (Figure S14 and Table S4 in Supporting Information S1).
Multiple lines of evidence point to the existence of primary calcite in the chimneys and veins, including its higher precipitation temperatures ([PERSON] et al., 2024), Mg/Ca ratios that favor calcite over aragonite precipitation, and the close association of calcite and brucite in the chimney interiors (Figure 8). Consistent with this interpretation, primary calcite has lower \({}^{87}\)Sr/\({}^{68}\)Sr ratios relative to aragonite and inactive chimney samples, reflecting the formation from fluids that have relatively less seawater contribution ([PERSON] et al., 2024). Secondary calcite, on the other hand, is formed from the alteration of aragonite and occurs in inactive or extinct samples that have been weathered by seawater ([PERSON] et al., 2006). These older samples often have little to no brucite.
Like the chimneys, the hydrothermal veins are also composed of variable mixtures of aragonite, calcite, and brucite. These hydrothermal veins were formed by hydrothermal fluids flowing in the fracture network in the shallow subsurface of the Atlantis Massif ([PERSON] et al., 2006). The interior of the veins contains similar or slightly more brucite than the exterior (Figures 3 and 4), suggesting a comparable spatial control as in the chimneys, albeit to a lesser degree. In contrast to the fissure deposits collected within the LCHF, carbonate veins recovered from drilling the shallow basement of the Atlantis Massif do not contain brucite ([PERSON]
Figure 11. Conventional and fluorescence microscopy images of sample 1108–2002 from Calypso. (a) The mineral membrane is composed of brucite on which later-formed aragonite may precipitate. (b) Detail of white box on B showing brown laminations in the brucite membrane. (c) Fluorescence microscopy image of a showing that brucite is more fluorescent than aragonite. (d) Fluorescence microscopy image of b showing strong fluorescence in brucite, especially on the brown laminations. (e, f) Fluorescent filamentous material. (g) Channel flow structure bounded by mineral membranes made up of brucite and aragonite. Brucite lines the interior of the channel. Image taken in plane polarized light. (h) Same as g in crossed polarized light. Aragonite exhibits strong birefringence while brucite has low to anomalous interference colors. (i) Fluorescence microscopy image of (g, h). Brucite, which lines the channel, is more fluorescent than aragonite.
et al., 2021). Similar to the chimneys, the \({}^{47}\)Sr/\({}^{68}\)Sr compositions of the veins indicate that they form from a mixture of seawater and hydrothermal fluids ([PERSON] et al., 2024). The veins also contain relatively more calcite than the chimneys (Figure 3; Figures S1e and S1f in Supporting Information S1). \({}^{8}\)I\({}^{8}\)O and \(\Delta_{47}\) data suggest that the veins we investigated in this study are formed at lower temperatures (\(<\)10\({}^{\circ}\)C). As mentioned above, at lower temperatures, the threshold Mg/Ca ratio for magnetic precipitation is higher, favoring calcite precipitation at a wider range of seawater and hydrothermal fluid mixing ratios ([PERSON] et al., 2024). Together, these data highlight the importance of near-surface mixing of seawater in the development of Lost City veins.
### Channel Wall Development
Most of the samples we investigated preserve channel flow structures that are bounded by mineral membranes. These mineral membranes serve as the backbone of the structure of most chimneys and veins and may be preserved as venting wanes and ceases (Figure 7). In young active chimneys, mineral channel walls are made up of brucite, which is stable at relatively higher pH ([PERSON], 2004) and precipitates from solutions dominated by vent fluids (Figure 13a; [PERSON] et al., 2024). The carbonate mineral that precipitates depends on the Mg/Ca of the fluid, which is controlled by the extent of vent fluid-seawater mixing (see Section 5.1). Later renewed influx of vent fluid results in the precipitation of brucite on the previously formed aragonite (Figure 13b).
In mature, yet still active hydrothermal chimneys, earlier formed minerals that comprise the channel walls are fused together to form distinct brucite and aragonite layers (Figure 13c; Figures S4g and S9b in Supporting Information S1), with the original mineral crystal faces unrecognizable. Brucite and carbonate precipitation within the channels continue depending on the nature of the mixed fluid (see Section 5.1). In channels where vent fluid is the dominant component, aggregates of brucite and calcite form (Figures 8 and 13c). Where seawater is dominant, aragonite precipitates perpendicular to the channel walls (Figure 13c; Figures S4a-S4d in Supporting
Figure 12: Crystallinity of brucite in representative Lost City chimney samples. The crystallinity is estimated by performing a Gaussian fit of the X-ray diffraction data and calculating the full-width at half maximum (FWHM) of the brucite (001) peak (FWHM values are shown). Brucite from Beehive is relatively more crystalline (lower FWHM) than those from Calypso and Marker C, where abundant microbial biofilms are observed.
Figure 13:
Information S1). In mature chimneys, channel walls thicken from multiple venting events that form alternating layers of aragonite and brucite (Figure 13c). Minor brucite dissolution may occur locally (Figure S4c in Supporting Information S1). However, brucite precipitation is more prevalent.
Chimney structures become inactive when focused hydrothermal fluid flow wanes. Brucite is unstable at seawater pH and slowly dissolves leaving a chimney composed mostly of carbonates (Figures 13d and 13e; Figures S9-S12 in Supporting Information S1). Mineral channel wall structures are preserved as aragonite and occasional microfossils are found within the channels (Figures 13d and 13e; Figures S9 and S10 in Supporting Information S1). Initial alteration of aragonite to calcite may occur (Figure 13e; Figures S10a-S10d in Supporting Information S1). Prolonged exposure of the chimney to seawater (>5,000 years, Table 1) results in the continued conversion of aragonite to calcite (Figures S10e-S10h in Supporting Information S1). Aragonite channel walls are still recognizable, and the previously formed fluid flow channels are increasingly filled by microcrystalline calcite (Figure S11 in Supporting Information S1). Exitner chimneys are structures that have been inactive and bathed in seawater for more than tens of thousands of years ([PERSON] et al., 2003; [PERSON] et al., 2006). In extinct structures, channels are no longer discernible (Figures 7d and 13f). Aragonite has been completely recrystallized into calcite. The channels are filled by micritic calcite and micro- and nanofossils, producing a massive dense structure (Figures S12 in Supporting Information S1; Figure 7d).
### Biotic and Abiotic Controls on Brucite Precipitation
Brucite is a significant component of young active Lost City chimneys, especially within their vent fluid-bathed interior (Figures 3 and 4). In our companion paper ([PERSON] et al., 2024), we show that mixing between end-member Beehive vent fluids and small amounts of seawater (up to \(\sim\)30 wt %) results in the precipitation of brucite, highlighting that at least for Beehive, most brucite precipitation may occur readily simply inorganically by supersaturation induced by mixing. This is also consistent with the occurrence of brucite in the vent-fluid dominated interior of the chimneys. In addition, our textural investigation suggests an important connection between microbial biofilms and brucite that is not observed with the carbonate minerals (Section 4.5).
One possibility is that the brucite mineral surfaces provide a substrate that is more favorable for the formation of biofilms by the microorganisms than the carbonates, leading to preferential growth of biomass along the brucite channel walls (e.g., [PERSON], 2009). Previous studies highlighting the adsorption of organic matter on brucite mineral surfaces may support this hypothesis. For example, [PERSON] et al. (2017) used in situ atomic force microscopy to directly observe the contribution of brucite surface dissolution to the supersaturation, nucleation, and growth of Mg-organophosphate/pyrophosphate on the brucite (001) surface. Batch adsorption experiments of [PERSON] et al. (2015), on the other hand, revealed that Ca\({}^{2+}\) ions may promote aspartate adsorption on brucite, while Mg\({}^{2+}\) ions may limit this interaction. This observation is highly relevant to our results as the co-occurrence of brucite and organic matter is typically observed in chimney interiors bathed in Ca-rich and Mg-poor vent fluids ([PERSON] et al., 2005; [PERSON] et al., 2015).
In addition, microbial EPS may promote the precipitation of brucite by acting as a physical substrate for mineral nucleation. In general, microbes may play a role in the precipitation of minerals via microbially controlled, microbially induced, and microbially influenced processes, collectively known as organomineralization (see review by [PERSON] et al., 2009; [PERSON], 2022). In microbially controlled mineralization, the microbes play an active role in the mineral precipitation, where the nucleation, growth, morphology, and location of the minerals are directed by microbial activity. On the other hand, in microbially induced mineralization
Figure 13.— Conceptual model of channel wall development in active and inactive chimneys. (a) Initially, chimneys are characterized by brucite mineral membranes that precipitate from a vent-fluid dominated solution. These brucite layers bound fluid flow paths and form an interconnected network of cavities. As more seawater rapidly mixes with the fluids, later formed minerals precipitate on these channel walls, with the mineralogy dictated by the fluid composition (i.e., vent fluid vs. seawater dominated, see [PERSON] et al., 2024 for details). (b) Precipitation of brucite on earlier formed aragonite or continued aragonite precipitation occurs as a result of numerous venting events and mixing with seawater. (c) In mature chimneys, earlier formed minerals fuse together, and the crystal boundaries are no longer clear. Within the channels, extensive precipitation of botryoidal aggregates of minerals occurs. Like in young chimneys, the mineralogy depends on the degree of vent fluid and seawater mixing. Brucite and calcite precipitates from a vent fluid-dominated solution and aragonite from a seawater-dominated fluid. Box shows the approximate area drawn in (a, b). (d) As hydrothermal venting wanes, brucite is no longer stable and starts to dissolve. Only aragonite precipitation from a seawater-dominated fluid occurs. Occaional microfossils are deposited within the channels. (e) In an inactive chimney, most of the brucite is dissolved. The initial alteration of aragonite to calcite may occur within as little as 1,000 years after inactivity. Microfossils continue to be deposited within pore spaces. (f) Continued reaction to seawater results in recrystallization of aragonite to calcite in an extinct chimney. Note: The last two rows represent the corresponding scanning electron images.
processes, microbial activity and its interaction with the environment lead to mineral precipitation. Lastly, microbially influenced mineralization is simply the passive precipitation of minerals on organic matter. Here, the precipitation may result from other external environmental factors and is not a direct result of microbial activities. The presence of living organisms is not required. There is evidence for biologically influenced mineralization at Lost City. Brucite (and Mg silicate) was observed to precipitate directly on microbial filaments, on EPS, as well as on the surfaces of organisms (Figures 9 and 10). Our results suggest that the orientation of the crystal growth of brucite crystals may be influenced by the biofilm (Figure 9b). In some samples, although the presence of EPS is not apparent, EDX analyses indicate small amounts of C despite the absence of CaCO\({}_{3}\) (i.e., little or no Ca detected) (Figure S13 in Supporting Information S1). The higher fluorescence exhibited by brucite relative to the carbonates also points to the presence of fluorescent organic matter in brucite (Figure 11). Antibacterial Mg-rich silicates with similar morphologies as those in the Lost City samples have previously been observed locally in biofilms in evaporites and are interpreted as the result of progressive mineralization of microstructures comprised of EPS ([PERSON] et al., 2010). Brucite biomineralization on hydrothermally derived microbial filaments has also been reported at the Prony Bay hydrothermal field (New Caledonia), especially at the most juvenile hydrothermal chimneys ([PERSON] et al., 2017). These authors hypothesized that the microbes may have been important in the early construction of the chimneys.
In addition to precipitation where organic matter serves as a physical template for mineral nucleation, microbial EPS could also contribute locally to brucite supersaturation by recycling and concentrating seawater Mg. EPS can bind cations (e.g., Ca, Mg) depending on the pH and the functional groups involved ([PERSON] et al., 2007; [PERSON] et al., 2002; [PERSON] et al., 2001). These cations may be released during EPS degradation (due to dehydration, pH changes, organic carbon oxidation), increasing mineral saturation ([PERSON] et al., 2009). Let us take for example, a hypothetical spherical cavity with a 1 mm radius. If the internal surface area of this sphere is covered with a 10 \(\upmu\)m-thick EPS layer, which corresponds to a volume of \(1.26\times 10^{-7}\) L or \(0.126\) mm\({}^{3}\), \(3.14\times 10^{-8}\) mmol of cations may bind to this EPS assuming a cation binding capacity of 0.25 mM ([PERSON] et al., 2007). If these cation binding sites are filled with Mg, and if the cavity has the appropriate pH, more than 27,000 small brucite crystals, about 3 \(\upmu\)m \(\times\) 3 \(\upmu\)m \(\times\) 1 \(\upmu\)m such as those seen in Figure 9a, may precipitate in this cavity. However, future work, including EPS functional group characterization and proton-binding experiments (e.g., [PERSON] et al., 2007; [PERSON] et al., 2002), is necessary to better understand the dynamics of biomineralization at the Lost City chimneys.
At Lost City, the internal structure of hydrothermal chimneys comprises brucite-carbonate mineral membranes forming a network of cavities (see Section 4.1; [PERSON] et al., 2006). These mineral membranes may act as a barrier separating a reduced, electron-rich interior from an oxidized external environment ([PERSON] et al., 2019; [PERSON], 2018). [PERSON] and [PERSON] (2020) discussed the role that Fe-brucite plays as a reactive electron donor that may serve as a metabolic substrate for microbial organisms in serpentinizing environments. Accumulations of microbial lipids were also detected in hydrothermal brucite from the Iberian Margin and at the Chimarera seeps in Turkey ([PERSON] et al., 2015; [PERSON] et al., 2018). Lastly, microbially influenced mineralization on microbial filaments, very similar to that described here, has been reported at the Prony Bay hydrothermal field in New Caledonia ([PERSON] et al., 2017). Clearly, the relationship between organic matter and brucite is a common theme in AHVs. The possibility that the biofilm is not simply a passive substrate for mineral nucleation and the organic ligands may play an active role in the recycling of seawater Mg, at least locally, opens interesting questions regarding the ecological significance of this mineral-microbe interaction. Do microbes draw any advantage through the precipitation of brucite? As described above, future work including EPS characterization and/or mineral precipitation experiments in the presence of Lost City EPS are steps that may help address these unresolved questions.
## 6 Conclusions
In this paper, we describe the mineralogy and textures of hydrothermal chimneys from Lost City and document the intimate association between brucite and microbial biofilms. Flow textures in the chimneys are mostly preserved as brucite-carbonate channel walls that bound paleo-fluid flow paths. Brucite typically precipitates in the interior of the chimneys and in the inner lining of these channels and is locally associated with primary calcite. Aragonite, on the other hand, precipitates on the exterior. In young active chimneys, mineral channel walls are initially composed of brucite, upon which later precipitation of carbonate and/or brucite minerals may occur. These channel walls are preserved to varying degrees in samples from inactive vents. Fluorescence microscopy of these channel walls pointed to the presence of fluorescent organic compounds associated with brucite but not with the carbonate minerals. We suggest that microbial sheaths, filaments, and EPS found within these channels influence the morphology of brucite and serve as substrates for further brucite precipitation or provide a better substrate than calcite for the formation of biofilms. There is also a possibility that microbes may play a more active role in recycling seawater-derived Mg and OH\({}^{-}\) within the chimney cavities and may contribute to brucite precipitation, at least locally. Further work, including characterization of microbial EPS is necessary to test this hypothesis. At Lost City, mineral bound channel walls may create micro-compartments characterized by ideal conditions (temperature, pH), protected from external environmental factors, where microorganisms may live and survive. Indeed, abundant microbes inhabiting these channels may aid brucite mineralization.
## Data Availability Statement
Individual analyses and raw microscopy images are available at the ETH Research Collection (Aquino, 2022).
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* [[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2018)] [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2018). Evidence for archaeal methomogenesis within veins at the onshore serpentinal-hosted Chimera saepts, Turkey. _Chemical Geology_, 483(September 2017), 567-580. [[https://doi.org/10.1016/j.chemgeo.2018.03.027](https://doi.org/10.1016/j.chemgeo.2018.03.027)]([https://doi.org/10.1016/j.chemgeo.2018.03.027](https://doi.org/10.1016/j.chemgeo.2018.03.027)) | wiley | Controls on Mineral Formation in High pH Fluids From the Lost City Hydrothermal Field | Karmina A. Aquino, Gretchen L. Früh‐Green, Stefano M. Bernasconi, Tomaso R. R. Bontognali, Anneleen Foubert, Susan Q. Lang | https://doi.org/10.1029/2023gc011010 | 2,024 | CC-BY |
wiley/fd63947d_e481_4414_bf0e_9e8a94212ccf.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits, distribution and reproduction in any medium medium medium medium, provided the original work is properly.
## 2 Materials and Methods
### Sampling Sites
Samples and oceanographic measurements were collected from three main areas: offshore from Nuuk on the southwest Greenland margin, near Narsaq and Cape Farewell on the south Greenland margin, and the Labrador Sea (Figure S1 in Supporting Information S1). There is a north-south divide in ocean water masses along the southwest Greenland slope, with waters to the south originating in the East Greenland Current (EGC), which flows around Cape Farewell, mixing with Atlantic-sourced waters to form the West Greenland Current (WGC). The WGC flows up the southwest coast of Greenland, receiving GrIS meltwater discharge and terrestrial inputs along its flow path ([PERSON] et al., 2019). Runtorff from the GrIS enters the Labrador Sea via anticyclonic warm-core rings that are shed off the WGC near the northern part of our study area (\(\sim\)65\({}^{\circ}\)N; [PERSON] et al., 2020).
Along most of the WGC, the surface waters are characterized by low macronutrient concentrations in the top 50 m ([PERSON] et al., 2019). In contrast, concentrations of the key micronutrients, such as [dFe] are relatively high, particularly in the surface waters of the continental shelf and slope, corresponding to high meteoric water inputs ([PERSON] et al., 2020). These nutrient observations have been linked with elevated chlorophyll \(a\) (Chl \(a\)) concentrations ([PERSON] et al., 2020), which are consistent with strong biological uptake and the utilization of macronutrients (to produce Chl \(a\)). Despite low [DSi] and low temperatures, there is a surprisingly active diatom community along the southwest Greenland margin ([PERSON] et al., 2019). For example, offshore from Nuuk, the phytoplankton community is dominated (60%-100%) by diatoms ([PERSON] et al., 2010).
### Field Methodology
Hydrographic and water samples were collected on board the _RRS Discovery_ from July-August 2017 (expedition DY081) ([PERSON] et al., 2019). Hydrographic data were obtained from a Sea-Bird SBE 9 plus Conductivity Temperature Depth (CTD) unit including a WET Labs C-Star transmissometer, a Chelsea Technologies Group Aquatracka MKIII fluorometer, and a Bios Spherical QCP Cosine Photosynthetic Active Radiation (PAR) meter. These instruments were attached to a standard stainless steel CTD rosette which housed 24 Niskin bottles. The mixed layer depth (MLD) was defined as the depth of the maximum buoyancy frequency and was comparable to common-used density gradient metrics of MLD ([PERSON] et al., 2017) (Figure S2 in Supporting Information S1). Following the GO-SHIP procedures in [PERSON] et al. (2010), water samples for macronutrient analysis were filtered immediately after Niskin bottle collection through 0.2 \(\upmu\)m Acropak filters into pre-acid cleaned high density polyethylene bottles and were frozen for storage and transport to land. Prior to analysis at Plymouth Marine Laboratory, macronutrient samples were thawed following GO-SHIP nutrient protocols ([PERSON] et al., 2020) in warm water bath for 45 min, followed by equilibration to room temperature for a further 45 min. Samples for stable Si isotope analysis were similarly filtered but stored at ambient temperature without freezing, following GEOTRACES protocol ([PERSON] et al., 2018). Seawater oxygen isotopes were used together with bottle salinity measurements to deconvolve the different freshwater inputs from meteoric water (largely glacial meltwater, mixed with snow melt and non-glacial stream water in this region; [PERSON] et al., 2023; hereafter known as modified meltwater) and sea ice melt using mass balance calculations. Details of this salinity calibration, seawater oxygen isotope analysis, and mass balance calculations have previously been reported ([PERSON] et al., 2019). Suspended particulate matter was collected by filtering a known volume of seawater through polycarbonate filters (0.45 \(\upmu\)m) which were then dried and stored at 4\({}^{\circ}\)C until analysis.
Figure 1: Maps of Arctic surface-water Si data compilation. (a) [DSi], (b) 6\({}^{\mathrm{3}\mathrm{b}}\)DSi, (c) [ASi + BSi], and (d) [ASi + BSi]/[DSi]. Results from this study are compiled with previously published data sets (Table S1 in Supporting Information S1). Values shown are summertime (July–September) data averaged over the top 10 m, which are the average mixed layer depth of the Arctic Ocean for the season. The Arctic maps (50\({}^{\circ}\)N–90\({}^{\circ}\)N, orthographic projection) were drawn using Python 3.9.7 with the Cartopy and Matplotlib packages.
Diatom BSi production, measured as the rate of diatom uptake of nutrient Si, was quantified using additions of the radioisotope \({}^{32}\)Si ([PERSON] et al., 2018). Briefly, samples were collected within the euphotic zone (the bottom of the euphotic zone was defined as 1% irradiance relative to that just below the surface) and spiked with 333 Bq of \({}^{32}\)Si (in the form of silicic acid), before being incubated in surface seawater cooled flow-through incubators on deck, to regulate temperature. A second set of euphotic zone samples were collected, enriched with DSi (+20 uM) to saturate Si uptake, and then spiked with \({}^{32}\)Si before incubations. Light levels at the depth of collection were mimicked during incubations by covering the samples with variable neutral density screening to imitate irradiance levels. The samples were filtered after incubation (1.2 um polycarbonate membranes), and particulate \({}^{32}\)Si activity was quantified using a GM-25 Multicounter (Riso DTU National Laboratory, Denmark) after the samples had aged into secular equilibrium with \({}^{32}\)P. Diatom BSi production was determined from the \({}^{32}\)Si uptake over the incubation period ([PERSON] et al., 2011; Supporting Information S1--Evaluating BSi production). To account for all euphotic-zone diatom BSi production at a station, rates were integrated from the surface to the base of the euphotic zone; this was done for both the ambient DSi and the enriched DSi treatments. An assessment of nutrient DSi limitation of diatom growth can be provided by the percentage ratio of diatom BSi production at ambient condition to diatom BSi production at DSi-enhanced (+20 uM) condition, \(f\rho_{\rm{ambient}}/f\rho_{\rm{enhuned}}\), where values lower than 100% indicate nutrient DSi limitation (i.e., the rate of Si uptake at ambient DSi is lower than DSi is non-limiting, presumably +20 uM).
### Laboratory Methodology
The macronutrients (DSi) were analyzed using techniques as described in [PERSON] (2001), using a SEAL AA3 segmented-flow autoanalyzer. Data quality was ensured using certified nutrient reference materials (KANSO Ltd. Japan). The typical uncertainty of the measurements was between 2% and 3%, and the limits of detection for NO\({}_{3}\) and PO\({}_{4}\) were 0.02 uM. Water-column DSi concentrations did not ever approach the limits of detection (0.02 uM).
The ASi and BSi fractions of the suspended particulate matter were extracted using the standard sequential leaching technique, with 0.2 M NaOH set at 85\({}^{\circ}\)C, and leachates taken every hour for 3 hr ([PERSON] et al., 2015). The concentrations of the extracted ASi + BSi were quantified using standard silicomolybdate chemistry ([PERSON], 1981) and measured on a VMR V-1200 spectrophotometer. Reproducibility of sample ASi + BSi content was based on measurements of duplicate samples, and was typically between 5% and 25%.
Dissolved stable silicon isotopes (8\({}^{30}\)DSi) were measured at the Bristol Isotope Group laboratories, University of Bristol. Given the low [DSi] and salt-water matrix, samples were pre-concentrated using Mg-induced co-precipitation ([PERSON] et al., 2012) prior to purification with cation exchange resin (Biorad AG 50 W-X12) ([PERSON] et al., 2006). Specifically, Si in the samples was co-precipitated with Mg(OH)\({}_{2}\) with 1 M NaOH (Titripur(r) Reag. Ph Eur grade), rinsed three times with 0.001 M NaOH, and redissolved with HCl (lab distilled), before the samples were loaded onto chromatography columns. The yields of the co-precipitation method were >95%, and had no correlation with the \({}^{30}\)Si measurements. Samples were analyzed using a Thermo Scientific(tm) Neptune multi-collector inductively coupled plasma mass spectrometer (MC-ICP-MS), using a dry plasma introduction system (Apex-IR). Standard-sample bracketing (with NBS-28, NIST RMS546), intensity-matched Mg doping and H\({}_{2}\)SO\({}_{4}\) doping were used to correct for internal mass bias and anionic matrix mass bias ([PERSON] et al., 2006; [PERSON] et al., 2011). Samples were measured in duplicates or triplicates, where sample volume allowed, with 2 S. D. ranging from <0.01% to 0.27%. The \({}^{30}\)Si of reference standards were analyzed alongside samples to assess long-term reproducibility. Average measurements of diatomic, LMG-08 (sponge), and ALOHA1000 (Pacific seawater from 1,000 m) are +1.23 \(\pm\) 0.11% (\(n\) = 64), -3.47 \(\pm\) 0.12% (\(n\) = 26), and +1.24 \(\pm\) 0.14% (\(n\) = 52) respectively, which agree with published values ([PERSON] et al., 2017; [PERSON], 2012; [PERSON] et al., 2007). Note that the consensual \({}^{30}\)Si value for ALOHA300 (Pacific seawater from 300 m) has a greater uncertainty and is less well-constrained than that of ALOHA1000 ([PERSON] et al., 2017), and so is not included as a reference material in this study. New seawater \({}^{30}\)DSi measurements from our open ocean station (CTD1, Orphan Knoll, Labrador Sea) are within the range of previously published values from the nearest GEOTRACES stations within the open ocean of the Labrador Sea ([PERSON] et al., 2012; [PERSON] et al., 2022; [PERSON] et al., 2018) (Figure S3 in Supporting Information S1). The \({}^{30}\)Si and \({}^{30}\)Si values of all standards and samples measured during this study plot on a straight line with a gradient of 0.5087 \(\pm\) 0.0020, which lies within the error of kinetic (0.5105) mass-dependent fractionation ([PERSON] et al., 2003). There is also no correlation between the measured \(\delta^{30}\)Si values with mass dependence difference, Mg and blank correction, Mg intensity matching, and Si intensity matching, all of which have R\({}^{2}\) of \(\leq\)0.01 and \(p\) of >0.1.
## 3 Results
The surface waters from south-west Greenland margin and the Labrador Sea have [DSi] ranging from 0.46 to 3.8 \(\mu\)M. These values are some of the lowest [DSi] observed around the Arctic Ocean (Figure 1a). Meanwhile, there is a large regional difference in total concentrations of Si in the reactive particulate silica phases: abiogenic ASi and diatom BSi (hereafter [ASi + BSi]) among the study sites. Off Nuuk, surface water [ASi + BSi] range up to 2.0 \(\mu\)mol/L (Figure 1c), while concentrations at greater depths range up to 4.7 \(\mu\)mol/L. In contrast, [ASi + BSi] observed for the rest of the study area are less than 0.32 \(\mu\)mol/L.
The coastal stations exhibit a wide range of \(\delta^{30}\)Disi, from +0.9% to +2.3%, with one sample measuring \(-\)1.15% (Supporting Information S1--Isotopic compositions of low DSi waters). Above 1 \(\mu\)M [DSi], there is a negative relationship between [DSi] and \(\delta^{30}\)Disi; however, in very low nutrient shallow waters ([DSi]!1 \(\downarrow\)M) this relationship reverses and weakens (Figure 2a). There is a positive relationship between \(\delta^{30}\)Disi and the fraction of meteoric modified meltwater present, and turbidity, although the relationship weakens in waters with lower [DSi] (Figures 2b and 2c). Meanwhile, our open ocean station in the Labrador Sea shows a steeper negative relationship between [DSi] and \(\delta^{30}\)Disi, with \(\delta^{30}\)Disi ranging from +1.5% to +3.7% (Figure 2a).
The measured summertime diatom BSi production integrated over the euphotic zone (at ambient condition, \(f\rho_{\text{ambient}}\)) ranges from \(\sim\)0.02 to 14.4 mmol/m\({}^{2}\)day. The highest \(f\rho_{\text{ambient}}\) is observed on the southwest Greenland margin off Nuuk (Figure 3a). The southwest Greenland \(f\rho_{\text{ambient}}\) are substantially higher than the \(f\rho_{\text{ambient}}\) observed at another Arctic site: Svalbard region (0.27-1.46 mmol/m\({}^{2}\)day), where the surface seawater [DSi] are similarly low (0.26-4.5 \(\mu\)M) ([PERSON] et al., 2018). In contrast, our \(f\rho_{\text{ambient}}\) measurements are relatively modest when compared to the \(f\rho_{\text{ambient}}\) observed at the Bering and Chukchi Seas (0.66-62.9 mmol/m\({}^{2}\)day) ([PERSON] and [PERSON], 2021), where the surface seawater [DSi] are significantly higher (up to 27 \(\mu\)M) than those at our sites (Figure 1a).
Average \(f\rho_{\text{ambient}}\)/\(f\rho_{\text{enhanced}}\) on the southwest Greenland margin off Nuuk is 58 \(\pm\) 6%, which is substantially lower than the average \(f\rho_{\text{ambient}}\)/\(f\rho_{\text{enhanced}}\) on the south Greenland margin off Narsaq/Cape Farewell: 91 \(\pm\) 9%, and those in the Labrador Sea: 86 \(\pm\) 7% (Figure 3b). These results mean that diatoms in the euphotic zone off Nuuk were taking up DSi at only 58% of their maximum uptake rate, indicating a degree of kinetic limitation, but not likely growth limitation (see discussion in [PERSON] et al. (2018)). Furthermore, there was very little quantifiable limitation at Narsaq/Cape Farewell (ratio nearly \(\sim\)100%), and minor limitation in the Labrador Sea.
## 4 Discussion and Conclusions
The southwest Greenland margin stations off Nuuk have the highest [ASi + BSi] (Figure 1b), the highest diatom production (see Results), and some of the lowest \(\delta^{30}\)Disi (Figure 2a) among the Arctic sites that have low surface seawater [DSi] (\(<\)8 \(\mu\)M, Figure 1a). Below we discuss how glacial detritus could provide an explanation for the observations above.
### Detrital ASi on Southwest Greenland Margin
Excluding the low [DSi] seawater samples (\(<\)1 \(\mu\)M) that are potentially influenced by small amounts of DSi derived from organic complexation and reactive metal phases (Supporting Information S11--Isotopic compositions of low DSi waters), the [DSi]-\(\delta^{30}\)Disi trends of the southwest Greenland margin are consistent with biological utilization and isotopic fractionation in waters. We have applied a biological fractionation model ([PERSON] et al., 2004) to our data (Supporting Information S1--Calculation of apparent isotopic fractionation), assuming that diatoms are sourcing DSi from below the MLD. This simple model reveals an overall fractionation (\(\epsilon\)) value of \(-\)0.22 \(\pm\) 0.06% (\(R^{2}\) = 0.52, \(p\) \(<\) 0.01) for an isotopically closed system (Figure S4a in Supporting Information S1), and \(\epsilon\) of \(-\)0.64 \(\pm\) 0.16% (\(R^{2}\) = 0.56, \(p\) \(<\) 0.01) for an isotopically open system (Figure S4b in Supporting Information S1). These apparent fractionation factors are lower than the other Arctic sites--in particular, the \(\epsilon\) estimated at the Fram Strait, situated upstream of our study area, are \(-\)0.6% for a closed system and \(-\)1.1% for an open system ([PERSON] et al., 2022). The lower apparent fractionation factors observed on the southwest Greenland margin reflect the low \(\delta^{30}\)Disi in the near-surface water samples with [DSi] ranging from 1 to 4 \(\upmu\)M (or ln[DSi] from 0 to 1.4 \(\upmu\)M, Figure 2a), when compared to those from the other Arctic sites. This near-surface water isotopic difference between our sites and the other Arctic sites is far larger than the known inter-laboratory analytical uncertainties (0.2%; [PERSON] et al., 2017).
The plausible explanation for the low apparent fractionation along the southwest margin of Greenland is an additional nutrient source consisting of isotopically-light Si, such as the glacially-sourced ASi that readily dissolves in low [DSi] seawater ([PERSON] et al., 2019, 2021). Other potential explanations and model artifacts have also been considered and deemed less likely to account for the observation above Supporting Information S1--Low apparent isotopic fractionation, Figure S5 in Supporting Information S1). We have used a simple isotopic model to test that dissolving glacial detritus (ASi) could be a feasible mechanism that reconciles the low apparent fractionation factor in the study area (Supporting Information S1--Isotopic fractionation model). The model
Figure 2.— Seawater silicon isotope results and correlation plots. Seawater \(8^{\rm{3D}}\)DSi plotted against (a) the natural logarithm of [DSi]; (b) fraction of meteoric water; and (c) turbidity. Results from this study (emphasized with bold black marker outline) are compared with previously published data from the Arctic Ocean (Table S1 in Supporting Information S1). Error bar shows 2.5.D. of long-term replicate \(8^{\rm{3D}}\)DSi measurements of standards. Magenta and blue ovals represent the range of data from fords ([PERSON] et al., 2023) and glacier rivers ([PERSON] et al., 2019) respectively.
suggests that there are several possible combinations of the following variables: (a) relative contribution of ASi dissolution to the bioavailable Si pool, (b) ASi isotope composition, and (c) the isotopic fractionation factor during diatom uptake that could account for the [DSi]-8\({}^{\mathrm{o}}\)DSi observations (Figure S6 in Supporting Information S1). These variables will be further assessed in the next section.
Supporting evidence for the notable presence of glacial ASi along the southwest Greenland margin stems from the exceptional standing stock of ASi + BSi relative to [DSi] (Figure 1d) and to Chl \(a\) (Figure S7a in Supporting Information S1). In fact, the southwest Greenland stations have the second highest [ASi + BSi]/[DSi] observed around the Arctic Ocean (Figure 1d). All these observations suggest a substantial contribution of non-living (detrital) material to the ASi + BSi pool off southwest Greenland. The relative contribution of living diatom BSi and detrital ASi to the ASi + BSi pool can be further estimated from the offset between a computed maximum diatom growth rate at the observed temperature ([PERSON] et al., 2017) and the measured rate of Si uptake by diatoms (Supporting Information S1--Estimation of detrital contribution to the ASi + BSi pool). The estimation above suggests that up to 87 \(\pm\) 11% of the ASi + BSi pool off southwest Greenland is detrital, with the remaining portion being living diatoms. The detritus likely contains a significant portion of glacial ASi (and potentially some detrital/dead diatoms) that is transported by modified meltwater, evident from the elevated [ASi + BSi]/[DSi] at higher meteoric fraction (>0.01) among the southwest Greenland stations (Figure S7b in Supporting Information S1).
### Detrital ASI Sustains Coastal Diatom Production
The supply rate of nutrient Si from the dissolving detrital ASi can be further estimated from the detrital ASi composition calculated above and the glacial ASi dissolution rate inferred from previous experiments ([PERSON] et al., 2017; [PERSON], 1982) (Supporting Information S1--Estimation of detrital contribution to the ASi + BSi pool). Comparing this estimated nutrient supply rate with the diatom BSi production measured using \({}^{32}\)Si tracer suggests that the dissolving detrital ASi could, on average, sustain \(\sim\)50% of diatom production observed at the Nnuk stations. Considering the inferred \(\sim\)50% contribution of dissolving detrital ASi to the nutrient pool utilized by diatoms, the isotopic model developed in the previous section suggests that an open system with ASi isotopic composition of +0.8% and diatom isotopic fractionation factor of \(-\)0.6% would best account for the [DSi]-8\({}^{\mathrm{o}}\)DSi observations at the Nnuk stations (Figure S6 in Supporting Information S1).
Figure 3: Diatom production results. (a) Summertime diatom BSi production integrated from surface ocean to the base of euphotic zone (defined by 1% isolume). (b) Percentage ratio of depth-integrated diatom production at ambient condition to depth-integrated diatom production at DSi-enhanced (+20 μm) condition. The cross and the horizontal line within each bar indicate the mean and median respectively.
The detrital input, most likely containing glacial ASi, may help maintain relatively high levels of diatom production (Figure 3a) on the southwest Greenland margin, and the dissolving detrital ASi can help compensate for lack of BSi dissolution due to low specific rates (driven by the low temperatures) and relatively low DSi in deeper water. [PERSON] et al. (2003) demonstrated that major diatom blooms in many oceanic systems are fueled by \"new\" sources of Si (akin to new nitrogen in the new production paradigm ([PERSON] et al., 2020)). In many parts of the ocean, such as productive upwelling zones and the Southern Ocean ([PERSON], 2014), such new Si would be largely from deep convective mixing; however, in this region of the Arctic and subarctic, the low DSi:NO\({}_{3}\) ratio of the deep water (Figure 8 in Supporting Information S1) brings proportionally more NO\({}_{3}\) into the euphotic zone than DSi (favoring Si to be exhausted first in a diatom bloom). Thus, our finding suggests that regional diatom blooms can also be sustained by a combination of new Si sources to supplement the low DSi:NO\({}_{3}\) in deeper waters. In addition to glacial ASi, non-glacier rivers have been suggested to be another key source of new Si to the Arctic and subarctic oceans ([PERSON] et al., 2012; [PERSON] et al., 2020).
Our results indicate that diatoms on the southwest Greenland margin (off Nuuk) experience greater limitation of nutrient DSi (lower \(f\rho_{\text{ambles}}\)/\(f\rho_{\text{ethanol}}\)) than the other study sites (Figure 3b), despite the elevated supply of detrital ASi. Previous studies have shown that certain diatom groups grow much better with the presence of particulates that slowly release silica ([PERSON] et al., 2003; [PERSON] et al., 2023). Similarly, the abundance of slowly dissolving detrital ASi particles off southwest Greenland likely has promoted growth of these certain diatom groups with such particulate preference, to the extent that this has caused some degree of nutrient DSi limitation in the area. However, this degree of limitation is well within diatoms' capacity to adapt without affecting their growth rate and is a common observation in marine systems ([PERSON] et al., 2018).
### A Silicon Conveyor Belt
New observations from this study reveal a \"conveyor belt\" of detrital ASi sourced from fjord, glacial meltwater, and other terrestrial sources, modifying Si cycling off the Greenland coast. Our data provide, for the first time, strong supporting evidence that Si derived from glaciers and potentially other high-latitude fluvial sources are not entirely buried in fjords, but a significant portion can be transported offshore, dominantly in the form of slowly-dissolving ASi, which is utilized by coastal marine primary producers. Despite the slow dissolution of ASi in low temperature seawater, our data show that sufficient accumulation of the dissolving detrital ASi can support a remarkable level of summertime diatom production, despite some degree of nutrient DSi limitation in such low [DSi] seawater.
Glacial erosion contributes disproportionate amounts of suspended sediments that are transported offshore to pan-Arctic coastal regions, particularly around Greenland ([PERSON] et al., 2012; [PERSON] et al., 2006). Future climate warming is expected to increase the intensities of (sub)glacial weathering, erosion, and the supply of suspended sediments including ASi to the surrounding oceans ([PERSON] et al., 2019; [PERSON] et al., 2017). In the long term, we anticipate large-scale glacier retreat to decrease the transport distance of meltwater and suspended sediments away from the coast, while subsequent exposure of deglaciated watersheds will likely change downstream nutrient transport ([PERSON] et al., 2020). In addition, nutrient supply from other key terrestrial sources, such as the Arctic rivers are also expected to change with climate warming ([PERSON] et al., 2021). Complex changes in the supply of nutrient Si from the different sources above, both spatially and temporally ([PERSON] et al., 2020), will likely shift high-latitude hotspots of diatom production over the spring and summer seasons, with important implications for the distribution of higher trophic levels and pan-Arctic economies that utilize these marine resources. Providing quantitative estimates onto the predictions above will require comprehensive modeling that also considers other key regulators of diatom production such as availability of other nutrients and grazing activities.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The article's main new data: (a) seawater dissolved stable silicon isotope (\(\delta^{30}\)DSi), (b) standing stock of abiogenic and biogenic amorphous solid phases of silica [ASi + BSi], and (c) BSi production (\(\rho\)), are available in Pangaea database, an open data repository which supports the FAIR principles, at [PERSON] et al. (2024). These data, plus (d) integrated BSi production (\(f\)p) and (e) the percentage ratio of BSi production at ambient condition to BSi production at DSi-enhanced (+20 uM) condition (\(f\)p\({}_{\text{ambise}}\)/\(f\)p\({}_{\text{enhanced}}\)), are also available in the Data Set S1. Other seawater data collected from the stations, including: potential temperature, salinity, turbidity, chlorophyll a, \(\delta^{\text{1R}}\)O, [DSi], and [NO\({}_{3}\)] are already available at Hendry (2018).
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wiley/fd35cf37_e274_4bea_8383_83c85611d70c.md | ###### Abstract
The southeastern (SE) Tibetan Plateau (Yunnan) is characterized by low-reliefe uplands that were deeply incised by large rivers. The thermal history of basement rocks in this region remains poorly investigated, while this data is needed to elucidate the complex relationship between tectonics and climate in shaping the surface. To better understand its thermo-tectonic evolution, we carried out apatite fission track thermochronology on 31 samples collected from a large area that covers different tectonic units, including a vertical profile in the middle Mekong River valley; additional zircon LA-ICP-MS U-Pb dating was performed on four basement rocks. Our results confirm that a large portion of Mesozoic crystalline rocks constitute the basement of the SE Tibetan Plateau. Inverse thermal history modeling of fission track data reveal extensive late Oligocene to Miocene rapid basement cooling and exhumation episodes from both inside and outside the active zones (i.e., ductile shear zone and river valley). These thermal events were coincident with the activities of large-scale strike-slip faults that dominate the structural framework. Combined with the published data, we propose that widespread crustal shortening and thickening took place in the SE Tibetan Plateau during the Oligocene- Miocene in the context of a compressive tectonic regime. Low-temperature thermochronological data reveal that both tectonic forcing and climate-driven erosion have played important roles in exhuming the basement rocks in the region. It is also deduced that the present-day relatively low-elevation landscape of the Yunnan area resulted from complex interaction between regional tectonic activity and surficial erosion since the late Oligocene.
2023 TOC007881]Tectonics
## 1 Introduction
Orogenic belts are prominent topographic features on Earth, they are characterized by high elevation and significant tectonic activity. Their evolution results from the interplay between internal (e.g., tectonic shortening, magmatism) and external (e.g., climate variability, river incision) mechanisms, thus providing the best natural laboratory to study the coupling between tectonics, erosion and climate (e.g., [PERSON], 2012; [PERSON], 2009; [PERSON] et al., 2006). The collision between India and Asia at \(\sim\)60-50 Ma ([PERSON] et al., 2014; [PERSON] et al., 2016; [PERSON] et al., 2005; [PERSON] et al., 2010) and the ongoing convergence of the continental plates resulted in the formation of the world's largest orogenic highland, the Tibetan Plateau ([PERSON] et al., 1994; [PERSON] et al., 1992; [PERSON], 1973; [PERSON] et al., 2001), and caused significant crustal shortening and intra-continental deformation within the Eurasian plate as a broader impact ([PERSON] et al., 1989; [PERSON] & [PERSON], 1975; [PERSON], 2006, 2010; [PERSON] & [PERSON], 2000). Understanding the thermo-tectonic evolution of the plateau is critical to explore the regional and even global geodynamics, and paleo-climate change (e.g., [PERSON] et al., 2001; [PERSON] & [PERSON], 1992; [PERSON] et al., 2008; [PERSON] et al., 2001; [PERSON] et al., 2014).
The eastern and southeastern plateau margins exhibit distinct regional structural and morphological characteristics, in which the landscape is characterized by a long-wavelength and low gradient topography (e.g., [PERSON] et al., 2019, 2022; [PERSON] et al., 2003; [PERSON] et al., 2008; [PERSON] et al., 2010; [PERSON] et al., 2015; [PERSON] et al., 2015). Two leading hypotheses are commonly cited to explain the tectonic evolution of these areas. One hypothesis implies material transfer from the orogenic interior to the external regions, channelized within a
## 2 Topographic and Geological Setting of the SE Tibetan Plateau
### Geomorphological Characteristics
The present-day SE Tibetan Plateau (mainly including the Yunnan and western Sichuan and Guizhou Provinces in China) is characterized by a gradual topographic gradient with elevation descending from \(\sim\)4 to 5 km to \(\sim\)1-2 km through a distance of \(\sim\)1,500-1,000 km. Three large rivers, the Salween (Nu), Mekong (Lancang), and Yangtze (Jinsha), originate from the interior Tibetan Plateau, flow parallel southeastward around the eastern Himalayan syntaxis (Namche Barwa) for hundreds of kilometers and then run out of Tibet (Figure 1b). In the so-called Three Rivers region, bedrock gorges up to 3 km deep were created by incision, and steep knick zones are well developed (e.g., [PERSON] et al., 2008; [PERSON] et al., 2020; [PERSON]. [PERSON] et al., 2016; [PERSON] et al., 2021). One key geometric feature of the SE Tibetan Plateau is the occurrence of pervasive high-elevation, low-relief surfaces separated by incised explosions with high relief (i.e., \"negative topography\"), whose genesis has been, however, highly debated (e.g., [PERSON] et al., 2020; [PERSON] et al., 2017; [PERSON] et al., 2015). Some authors proposed that the widespread pre-uplift, low-relief surface initially formed at low elevation, and has been gradually uplifted by the propagation of lower crustal flow since the late Miocene ([PERSON] et al., 2005; [PERSON], 2000; [PERSON] et al., 1997). Others suggested that large-scale crustal blocks were laterally extruded along major strike-slip fault during the middle Cenozoic ([PERSON] et al., 1995; [PERSON] et al., 1982, 2001). Since then the SE TibetanFigure 1.— (a) Overview of Southern Asia within its plate tectonic context with indication of the study area. (b) Simplified topographic map of the eastern and southeastern Tibet Plateau, showing main tectonic units, major faults and large rivers. Red stars denote accelerated explanation events since the Oligocene revealed by published thermochronological or cosmogenic nucidic geochronological data in the region, with black numbers indicating the duration (events marked by single ages imply that the acquired thermochronological ages largely clustered around a certain date, giving less spread in ages): 1 = [PERSON] et al. (2015), 2 = [PERSON] et al. (2009), 3 = [PERSON] et al. (2012), 4 = [PERSON] et al. (2002), 5 = [PERSON] et al. (2015), 6 = [PERSON] et al. (2010), 7 = [PERSON] et al. (2009), 8 = [PERSON] et al. (2007), 9 = [PERSON] et al. (2015), 10 = [PERSON] et al. (2017), 11 = [PERSON] and [PERSON] (2000), 12 = [PERSON] et al. (2005), 13 = [PERSON] et al. (2014), 14 = [PERSON] et al. (2003), 15 = [PERSON] et al. (2016), 16 = [PERSON] et al. (2012), 17 = [PERSON] et al. (2005), 18 = [PERSON] et al. (2016), 19 = [PERSON] et al. (2016), 20 = [PERSON] et al. (1996), 21 = [PERSON] et al. (2019), 22 = [PERSON] and [PERSON] (2011), 23 = [PERSON] et al. (2018), 24 = [PERSON] et al. (2018), 25 = [PERSON], [PERSON], [PERSON], et al. (2020), 26 = [PERSON] et al. (2016), 27 = [PERSON] et al. (2020), 28 = [PERSON] et al. (2021), 29 = [PERSON] et al. (2020), 30 = [PERSON], [PERSON], [PERSON], et al. (2020), 31 = [PERSON] et al. (2021). Red arrows indicate later period strike-slip movements of the shear zones. F, fault; S, shear zone.
Figure 2: (a) Geological map of the SE Tibetan Plateau (Yumnan) based on YBGMR (1990), showing the locations of our four study domains and sampling sites and corresponding apatite fission track ages. ASRR, Aliao Shan-Red River shear zone; CSS, Chongshan shear zone; GLGS, Gaoligong shear zone; JHF, Jinghong fault; LCTF, Lancang thrust fault; MLF, Menglian fault; NTHF, Nanting fault. (b) Simplified map showing main tectonic units of the SE Tibetan Plateau based on [PERSON] and [PERSON] (2012).
Plateau experienced from relief reduction and retreat of the plateau margins by landscape lowering ([PERSON] et al., 2008). This hypothesis was supported by recent stable-isotope paleoaltimetry studies, which indicated that western Yunnan probably has attained its present-day elevation of \(\sim\)2-3 km before the early Miocene ([PERSON] et al., 2014; [PERSON] et al., 2015).
### Main Tectonic Units
Geologically, the SE Tibetan Plateau (Yunnan) consists of several lithospheric fragments, including the Tengchong, Baoshan, Changing-Menglian and Lamping-Simao Units, as well as the Lincang Pluton (Figures 2a and 2b; [PERSON] & [PERSON], 2012). These tectonic units constitute the northern parts of the Sibumasu and Indochina blocks (e.g., [PERSON], 2006; [PERSON] & [PERSON], 2008).
The Tengchong Unit is considered to be a late Paleozoic Gondwana terrane (e.g., [PERSON] et al., 2011), which probably accreted to the SE Eurasia margin in the middle to late Mesozoic ([PERSON] et al., 2016; [PERSON] et al., 2001; [PERSON], 2009). The Precambrian basement of the Tengchong Unit is mainly composed of a Mesoproterozoic high-grade metamorphic complex overlain by early Paleozoic clastic sediments and carbonates ([PERSON], 1990). These rocks were intruded by widespread Mesozoic to Paleogene granitiol photons. The latter are interpreted as the eastward extension of the Gangdese batholith around the eastern Himalayan syntaxis ([PERSON] et al., 2009; [PERSON] et al., 2012). Bounded by the near N-S trending Gaoligong shear zone to the west and Chongshan shear zone to the northeast (e.g., [PERSON] et al., 2017), the Baoshan Unit also has paleontological and stratigraphic affinities to the Gondwana supercontinent ([PERSON], 2002; [PERSON], 2013; [PERSON] et al., 1995; [PERSON], 1998). This terrane consists of Cambrian to Permian low-grade metamorphosed sedimentary strata, which were unconformably covered by Triassic to Jurassic sediments and intruded by Paleozoic to Paleogene granitiolds (YBGMR, 1990).
The Changing-Menglian Unit forms a narrow belt sandwiched between the Baoshan Unit and the Lincang Pluton (Figure 2b). It contains various Precambrian to Permian rocks that were unconformably overlarin by Triassic sediments ([PERSON] & [PERSON], 2012; YBGMR, 1990). This tectonic belt is a source zone representing the closure of a main part of the Paleo-Tethyan Ocean between the Tengchong-Baoshan and Lamping-Simao Units in the late Triassic ([PERSON], [PERSON], et al., 2020; [PERSON] et al., 1995; [PERSON] et al., 2014). The adjacent Lincang Pluton is a giant batholithic complex formed during the late Paleozoic to Triassic ([PERSON] et al., 2018; [PERSON] et al., 2013; [PERSON] et al., 1989). The composition of the pluton predominantly comprises biotite monogramite with minor granodiorite (YBGMR, 1990), which are generally considered to have a continental magmatic arc origin ([PERSON] et al., 2013; [PERSON] et al., 2009; [PERSON] et al., 2012). Located in the west of the Yangtze Craton, the Lamping-Simao Unit is characterized by the occurrence of a thick section of Triassic to Paleogene sedimentary rocks (Figure 2; YBGMR, 1990). This triangular-shaped terrane is thought to be a northern extension of Indochina or the southern continuation of the Qiangtang block, and was assigned to the Cathaysian domain (e.g., Metcalfe, 2013).
### Cenozoic Tectonic Evolution
The Paleo-Mesozoic tectonic framework of the SE Tibetan Plateau was significantly overprinted by intensive intra-continental deformation in the Cenozoic, since the arrival of the India plate at the trench that marked the initial collision with Eurasia around 60-50 Ma ago ([PERSON] et al., 2016; [PERSON], 2019; [PERSON] et al., 2010). The India-Asia collision resulted in \(>\)1,400 km of north-south shortening ([PERSON] & [PERSON], 2000), followed by south-eastward crustal extrusion (Figure 1a; [PERSON] et al., 1982; [PERSON] et al., 2011) and clockwise block rotation ([PERSON] et al., 2017; [PERSON] et al., 2018; [PERSON] et al., 2016) via large-scale strike-slip faults ([PERSON] et al., 1993; [PERSON] et al., 1990; [PERSON] et al., 2010). The upper crustal deformation in the SE Tibetan Plateau was also accompanied by rapid basement exhumation ([PERSON] et al., 2019; [PERSON] et al., 2014; [PERSON], 2011), and fold-and-thrust activity ([PERSON] et al., 2021; [PERSON], 2005; [PERSON] & [PERSON], 1997).
#### 2.3.1 Strike-Slip Fault Activity
Regional-scale strike-slip faults converging toward the eastern Himalayan syntaxis largely controlled the young Cenozoic structures of the SE Tibetan Plateau (Figure 1b). Close to the syntaxis, the Jiali strike-slip fault splays into two major branches as the Parlung and Po-Qu faults respectively, the latter sharply turns southeastward and merges into the Sagainle fault. The sinistral movement of the Jiali fault lasted until the latest Oligocene ([PERSON] et al., 2020), followed by a period of right-lateral shearing during \(\sim\)20-12 Ma ([PERSON] et al., 2003; [PERSON] et al., 2009). The Parlung fault has been proposed to extend southward where it joins the Gaoligong shear zone ([PERSON] et al., 1989). The latter is a \(\sim\)650 km long, narrow N-S trending dextral mylonite belt and represents a discontinuous boundary between the Burma and Indochina blocks ([PERSON] et al., 2018; [PERSON] et al., 2015; [PERSON], 2007; [PERSON] et al., 2012). This shear zone is a Cenozoic transressional deformation zone ([PERSON], 2005; [PERSON] et al., 2012). The dextral strike-slip motion was constrained to have occurred at \(\sim\)28-10 Ma by mica \({}^{\rm 0}\)Ar/\({}^{\rm 99}\)Ar dating ([PERSON] et al., 2009; [PERSON] et al., 2006; [PERSON] et al., 2015; [PERSON] et al., 2012). The nearly N-S-trending Chongshan shear zone is the tectonic boundary between the Baoshan and Lamping-Simao Units (Figures 1b and 2; [PERSON] et al., 2006), and its sinistral ductile deformation has been active since at least \(\sim\)34-32 Ma and terminated by \(\sim\)17-14 Ma, resulting in over 100 km of displacement ([PERSON] et al., 2008; [PERSON] et al., 2010). The Aliao Shand-Red River shear zone extends more than 1,000 km from the SE Tibetan Plateau to the South China Sea (Figure 1), separating the Indochina and South China blocks ([PERSON] et al., 1990). The Indochina block is hypothesized to have extruded for 700 \(\pm\) 200 km southeastward along this regional boundary between \(\sim\)34 and \(\sim\)17 Ma ([PERSON] et al., 1995, 2001; [PERSON], 2003), while reactivation of the reverse right-lateral Red River fault occurred at \(\sim\)10-5 Ma and resulted in \(\sim\)25 km offset ([PERSON] et al., 1993; [PERSON] et al., 2001).
To the south, the NE-SW trending Nantinghe fault extends for more than 200 km (Figures 1b and 2). Its left-lateral motion was inferred to have initiated as early as \(\sim\)20 Ma based on boliotte \({}^{\rm 40}\)Ar/\({}^{\rm 99}\)Ar dating results ([PERSON], [PERSON], [PERSON], et al., 2020), accompanied by estimated displacement ranging from \(\sim\)8 to 21 km ([PERSON] et al., 2014) up to \(\sim\)40-50 km ([PERSON] & [PERSON], 1997). In and around the Tengchong Unit, a series of subordinate strike-slip faults are well developed, such as the Nabang, Yingjiang and Lianghe shear zones (e.g., [PERSON] et al., 2017; [PERSON], [PERSON], [PERSON], et al., 2020). Available thermochronological data cluster between \(\sim\)28 and \(\sim\)11 Ma ([PERSON], [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2015), indicating an Oligocene-Moocene active episode.
#### 2.3.2 Surface Uplit and River Incision
A number of low-temperature thermochronological (apatite and zircon fission track [AFT and ZFT], and apatite and zircon [U-Th]/He [AHe and ZHe] dating) studies have been carried out to constrain the Cenozoic deformation and rock exhumation history of the eastern and SE Tibetan Plateau (Figure 1b), and they show a spatially variable cooling pattern. In eastern Tibet, the majority of data come from the Longmen Shan and surrounding areas on the eastern edge of the Tibetan Plateau. The obtained ZFT, ZHe, AFT and AHe ages are mainly Oligocene to Miocene (\(\sim\)30-5 Ma), and associated age-elevation plots, as well as thermal history modeling, indicate late Cenozoic upper crustal exhumation phases (e.g., [PERSON] et al., 1997; [PERSON] et al., 2009; [PERSON] et al., 2002; [PERSON] et al., 2010; [PERSON] et al., 2013; [PERSON] et al., 2012). It is noted that from the Daocheng granite in the west, [PERSON] et al. (2014) reported Miocene enhanced basement exhumation (\(\sim\)22-15 Ma), representing the uplift of a regional low-relief surface and the onset of river incision.
In the Three Rivers region (northern part of the SE Tibetan Plateau), from two elevation profiles at Degin and Weixi, [PERSON] et al. (2018) recognized two episodes (\(\sim\)60-40 and \(\sim\)20-0 Ma) of rapid exhumation during the Cenozoic, and attributed the second one to the high incision rate of the Mekong river. [PERSON] et al. (2018) also proposed that the Miocene (\(\sim\)17-14 Ma) accelerated exhumation along the Mekong river resulted from an increase in monosonal precipitation and consequential erosion at that time. By comparison, regional exhumation since the late Miocene (\(<\)10 Ma) was interpreted as a result of tectonic uplift related with the northward indentation of the Indian plate ([PERSON] et al., 2016). [PERSON] et al. (2020) studied the thermo-tectonic history of the \(>\)6,000-m-high Kawagebo massif and emphasized that tectonic uplift was required (in addition to fluvial incision) to trigger the rapid Quaternary exhumation there. In the southern part of the SE Tibetan Plateau (Yunnan), the development of fold-and-thrust systems was considered to have controlled regional exhumation and topographic relief generation. This is the case for the early Cenozoic (\(\sim\)50-39 Ma) Ludian-Zhonghejiang belt and the Oligocene-early Miocene (\(\sim\)28-20 Ma) Jian-chuan basin, as revealed by thermochronological and structural data ([PERSON] et al., 2019, 2021; [PERSON] et al., 2017). In addition, along several ductile shear zones, Miocene to Pliocene post-extrusion exhumation was distinguished and thought to be related to climate change or a tectonic transition (e.g., [PERSON] et al., 2020; [PERSON] et al., 2016). While in the downstream Mekong river valley, [PERSON] et al. (2021) recognized mid-Moocene (\(\sim\)17 Ma) fast cooling based on AHe thermochronology, and they suggested it to be linked with (pure) climate-related enhanced river incision.
## 3 Sampling and Methodology
### Sample Information and Setting
In order to have a comprehensive understanding of the upper crustal thermal history of SE Tibet, a total of 31 samples were collected from three main tectonic units, including the Tengchong and Changning-Menglian Units and the Lincang Pluton (Figure 2). These samples are exclusively basement rocks except for one Jurassic sandstone (Y44). Taking into account local geology, basement characteristics, tectonic and structural position, elevation, morphology and geographic locality (e.g., in or away from river valleys), the collected samples were subdivided into four domains (Domains Y-1 to Y-4) for the following discussions. Apatite fission track thermo-chronology was carried out on all the samples, and four granitic samples were dated using zircon U-Pb geochronology to determine their crystallization ages. Detailed locations as well as lithological data are listed in Table 1.
Domain Y-1 contains almost all the representative intrusions exposed in the Tengchong Unit, including a series of subduction-related or intra-plate granitiods from the Jurassic to Paleogene, additional two samples were taken
\begin{table}
\begin{tabular}{l l l l l l} \hline Sample & Lithology & Latitude (‘N) & Longitude (‘E) & Elevation (m) & Crystallization/depositional age1 & Dating method \\ \hline Domain Y-1 & & & & & \\ Y02 & Granite & 24\({}^{\circ}\)45\({}^{\prime}\)35\({}^{\prime}\) & 98\({}^{\circ}\)49\({}^{\prime}\)23\({}^{\prime}\) & 1.654 & Jurassic & AFT \\ Y03 & Granite & 25\({}^{\circ}\)03\({}^{\prime}\)16\({}^{\prime}\) & 98\({}^{\circ}\)21\({}^{\prime}\)08\({}^{\prime}\) & 1.460 & Cretaceous & AFT \\ Y05 & Porphyry & 25\({}^{\circ}\)04\({}^{\prime}\)00\({}^{\prime}\) & 98\({}^{\circ}\)17\({}^{\prime}\)47\({}^{\prime}\) & 1.998 & Paleogene & AFT \\ Y06 & Granite & 25\({}^{\circ}\)08\({}^{\prime}\)39\({}^{\prime}\) & 98\({}^{\circ}\)03\({}^{\prime}\)41\({}^{\prime}\) & 1.754 & Paleogene & AFT \\ Y07 & Granite & 25\({}^{\circ}\)08\({}^{\prime}\)20\({}^{\prime}\) & 98\({}^{\circ}\)03\({}^{\prime}\)00\({}^{\prime}\) & 1.823 & Cretaceous (\(\sim\)136 Ma) & AFT, ZUPb \\ Y08 & Quartz schist & 24\({}^{\circ}\)56\({}^{\prime}\)48\({}^{\prime}\) & 98\({}^{\circ}\)07\({}^{\prime}\)28\({}^{\prime}\) & 1.007 & Early Paleozoic & AFT \\ Y12 & Granite & 24\({}^{\circ}\)32\({}^{\prime}\)41\({}^{\prime}\) & 98\({}^{\circ}\)47\({}^{\prime}\)41\({}^{\prime}\) & 1.794 & Cretaceous & AFT \\ Y13 & Granite & 24\({}^{\circ}\)30\({}^{\prime}\)49\({}^{\prime}\) & 98\({}^{\circ}\)47\({}^{\prime}\)43\({}^{\prime}\) & 2.102 & Cretaceous & AFT \\ Y16 & Graniodiorite & 24\({}^{\circ}\)35\({}^{\prime}\)52\({}^{\prime}\) & 98\({}^{\circ}\)32\({}^{\prime}\)08\({}^{\prime}\) & 1,847 & Triassic & AFT \\ Y17 & Granite & 24\({}^{\circ}\)37\({}^{\prime}\)09\({}^{\prime}\) & 98\({}^{\circ}\)29\({}^{\prime}\)34\({}^{\prime}\) & 1,765 & Cretaceous & AFT \\ Y18 & Granite & 24\({}^{\circ}\)38\({}^{\prime}\)02\({}^{\prime}\) & 98\({}^{\circ}\)27\({}^{\prime}\)12\({}^{\prime}\) & 1,408 & Cretaceous (\(\sim\)117 Ma) & AFT, ZUPb \\ Domain Y-2 & & & & & \\ Y22 & Granite & 24\({}^{\circ}\)57\({}^{\prime}\)49\({}^{\prime}\) & 99\({}^{\circ}\)27\({}^{\prime}\)29\({}^{\prime}\) & 1,087 & Cretaceous & AFT \\ Y26 & Gneiss & 25\({}^{\circ}\)00\({}^{\prime}\)59\({}^{\prime}\) & 99\({}^{\circ}\)37\({}^{\prime}\)38\({}^{\prime}\) & 2,495 & Paleozoic & AFT \\ Y28 & Foliated granite dyke & 24\({}^{\circ}\)57\({}^{\prime}\)55\({}^{\prime}\) & 99\({}^{\circ}\)41\({}^{\prime}\)00\({}^{\prime}\) & 2,366 & Miocene (\(\sim\)20 Ma) & AFT, ZUPb \\ Y29 & Granite & 24\({}^{\circ}\)53\({}^{\prime}\)52\({}^{\prime}\) & 99\({}^{\circ}\)40\({}^{\prime}\)27\({}^{\prime}\) & 1.658 & Jurassic & AFT \\ Y34 & Adamellite & 24\({}^{\circ}\)37\({}^{\prime}\)17\({}^{\prime}\) & 99\({}^{\circ}\)52\({}^{\prime}\)19\({}^{\prime}\) & 2,060 & Jurassic & AFT \\ Y35 & Monzonite & 24\({}^{\circ}\)27\({}^{\prime}\)34\({}^{\prime}\) & 100\({}^{\prime}\)09\({}^{\prime}\)48\({}^{\prime}\) & 1,074 & Triassic & AFT \\ Y36 & Granite & 24\({}^{\circ}\)18\({}^{\prime}\)10\({}^{\prime}\) & 100\({}^{\prime}\)05\({}^{\prime}\)34\({}^{\prime}\) & 1,715 & Triassic & AFT \\ Y37 & Granite & 24\({}^{\circ}\)10\({}^{\prime}\)50\({}^{\prime}\) & 100\({}^{\prime}\)02\({}^{\prime}\)10\({}^{\prime}\) & 1,038 & Triassic (\(\sim\)211 Ma) & AFT, ZUPb \\ Y39 & Orthogenesis & 23\({}^{\circ}\)57\({}^{\prime}\)05\({}^{\prime}\) & 99\({}^{\circ}\)57\({}^{\prime}\)52\({}^{\prime}\) & 1,949 & Paleozoic & AFT \\ Domain Y-3 & & & & & \\ Y43 & Granite & 23\({}^{\circ}\)32\({}^{\prime}\)53\({}^{\prime}\) & 100\({}^{\prime}\)11\({}^{\prime}\)39\({}^{\prime}\) & 845 & Triassic & AFT \\ Y44 & Sandstone & 23\({}^{\circ}\)32\({}^{\prime}\)01\({}^{\prime}\) & 100\({}^{\prime}\)09\({}^{\prime}\)26\({}^{\prime}\) & 1,081 & Jurassic & AFT \\ Y47 & Granite & 23\({}^{\circ}\)30\({}^{\prime}\)57\({}^{\prime}\) & 100\({}^{\prime}\)08\({}^{\prime}\)38\({}^{\prime}\) & 1,223 & Triassic & AFT \\ Y48 & Granite & 23\({}^{\circ}\)33\({}^{\prime}\)29\({}^{\prime}\) & 100\({}^{\prime}\)07\({}^{\prime}\)24\({}^{\prime}\) & 1,361 & Triassic & AFT \\ Y49 & Subvolcanic rock & 23\({}^{\circ}\)34\({}^{\prime}\)31\({}^{\prime}\) & 100\({}^{\prime}\)06\({}^{\prime}\)59\({}^{\prime}\) & 1,511 & Jurassic & AFT \\ Y51 & Granite & 23\({}^{\circ}\)36\({}^{\prime}\) & 100\({}^{\prime}\)05\({}^{\prime}\)32\({}^{\prime}\) & 1,754 & Triassic & AFT \\ Y52 & Quartzcite & 23\({}^{\circ}\)37\({}^{\prime}\)50\({}^{\prime}\) & 100\({}^{\prime}\)00\({}^{\prime}\)35\({}^{\prime}\) & 1,940 & Triassic & AFT \\ Domain Y-4 & & & & & & \\ Y54 & Granite & 23\({}^{\circ}\)03\({}^{\prime}\)48\({}^{\prime}\) & 100\({}^{\prime}\)02\({}^{\prime}\)07\({}^{\prime}\) & 1,898 & Permian & AFT \\ Y55 & Granite & 22\({}^{\circ}\)44\({}^{\prime}\)10\({}^{\prime}\) & 100\({}^{\prime}\)01\({}^{\prime}\)59\({}^{\prime}\) & 1,328 & Permian & AFT \\ Y56 & Diorite & 22\({}^{\circ}\)30 from porphyy (Y05) and quartz schist (Y08) (Figure 2a; Table 1). This domain is a transect across structural fabrics (i.e., several ductile shear zones) and known terrane boundaries within or along the Tengchong Unit (Figure 3a). Domain Y-2 covers the northern Changning-Mengalian Unit where high-grade metamorphic rocks crop out, and the northern segment of the vast Lincang granitic pluton (Figure 2a). Similarly, care was also taken to sample across several major brittle and ductile faults occurring in this transect (Figure 3b). Six samples (Y43-44, 47-49, and 51) from Domain Y-3 comprise a vertical profile near the Lancang River, with altitudes ranging from 845 to 1,754 m with a horizontal distance around 10 km (Figure 2a; Table 1). One adjacent sample (Y52) is also included in this domain. Domain Y-4 refers to the southern part of the Lincang Pluton, four representative samples were collected from the interior of this massif and are less influenced by fault activity or river incision (Figure 2a).
### Zircon LA-ICP-MS U-Pb Dating
The zircon U-Pb system has a high closure temperature (>700\({}^{\circ}\)C, [PERSON] & [PERSON], 2003) and thus is capable of resolving the crystallization age of the igneous rocks. It was applied to four diverse Meso-Cenozoic basement rocks in this study.
The collected samples were crushed with a jaw crusher, grinded with a disc-mill and wet and dry sieved until a suspension-free size fraction between \(\sim\)60 and \(\sim\)250 \(\upmu\)m was obtained. Zircon grains were subsequently separated from these fractions using conventional magnetic and heavy liquid separation techniques and handpicked under a stereo-microscope. Selected zircons were mounted in epoxy resins and polished to approximately half section thickness to expose the grains' interior. To examine the internal texture (e.g., zonation structure) of the zircon grains, cathodoluminescence (CL) imagery of zircons was undertaken at Nanjing Hongchuang Analytical Institute on a Mono CL 3+ Fluorescence Spectrometer.
Zircon grains were analyzed using Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Inferior quality zircons with clear fractures or inclusions and those smaller than the laser beam size were not used. LA-ICP-MS
Figure 3: Geological cross-sections across Domains Y-1 (a) and Y-2 (b) showing contact relationships between different lithological and structural units and sampling sites. Apatite fission track ages for our samples are also indicated. CSS, Chongshan shear zone; GLGS, Gaoligong shear zone; LHS, Lianghe shear zone; NBS, Nabung shear zone; NTIF, Nanting fault; SDS, Sudian shear zone.
analyses were conducted at China Geological Center in Tianjin, using an Agilent 7900s ICP-MS instrument attached to a New Wave 193 um laser ablation system. All zircons were analyzed under a laser beam with a 32 um diameter and a frequency of 5 Hz. Zircon 91500 ([PERSON] et al., 1995) was used as an external standard and analyzed twice for every 10 unknowns. To keep age reproducibility and instrument stability, GEMOC GJ-1 zircon standards ([PERSON] et al., 2004) were analyzed at the beginning and end of each run. The mass fractionation correction and isotopic results were calculated by ICP-MS DataCal ([PERSON] et al., 2008). The results reported here are \({}^{250}\)Pb/\({}^{23}\)U zircon ages (\(<\)1.0 Ga), which are more reliable due to the low content of radiogenic Pb and low uncertainty of common Pb correction. Age calculations and concordia plots were performed using Isoplot R ([PERSON], 2018).
### Apatite Fission Track Analysis
The standard procedure from the fission track laboratory at Ghent University was adopted for the AFT analysis in this study (e.g., [PERSON] & [PERSON], 2002; [PERSON] et al., 2010; [PERSON] et al., 2021, 2022; [PERSON], [PERSON], et al., 2020). Apatite grains were handpicked and mounted in Struers CaldoFix-2 epoxy resin, and sample mounts were grinded and polished (by 6, 3, and 1 um diamond suspension) to expose internal sections. The embedded apatite grains were then etched in 5.5 \(M\) HNO\({}_{3}\) for 20 s at 21\({}^{\circ}\)C ([PERSON] et al., 1999). We made use of the external detector method ([PERSON] et al., 1975), the mounts were hence covered with a 0.025 mm thick mica sheet as external detector (Goodfellow Clear Ruby muscovite), which is kept in place by Scott tape, and stacked into a polyethylene container for irradiation. Thermal neutron irradiation took place in the well-thermalized channel (\(f\)-ratio of 98) X26 at the Belgian Nuclear Research Center in Mod ([PERSON] et al., 2010). Based on dosimetry of IRMM-530 AI-Au foil, a thermal (sub-Cd) fluence rate ratio (Hogdahl convention) of 6.12E10 n/cm\({}^{2}\) s was calculated. This yields and integrated 1-day irradiation flux (7 hr) of 1.54E15 n/cm\({}^{2}\) or up to 2.42E15 n/cm\({}^{2}\) for a 1.5 days (7 + 4 hr) irradiation ([PERSON] et al., 2010). The neutron fluence gradients were documented by evenly spaced IRMM-540 dosimeter glass ([PERSON] et al., 1998). We estimate neutron flux gradients by linear interpolation over the induced track density of the U-doped glasses. After post-irradiation cool-down, the external detectors were punctured at four positions to create mount-mica reference points, after which the micas were removed from the mount. The micas were then etched for 40 min in a 40\({}^{\circ}\)\({}_{\rm w}\) hydrofluoric acid solution at 21\({}^{\circ}\)C. The mounts and mica external detectors were then fixed on standard microscope glasses using transparent nail polish.
Track densities were measured on a fully motorized Nikon Eclipse Ni-E microscope, equipped with a Nikon DS-Ri2 color camera. The microscope and camera are linked to a computer with Nikon NIS Elements Advanced Research software, complemented with an in-house macro-enabled Microsoft Excel sheet (Nikon-_TRACKflow_ \(f\); [PERSON], [PERSON], et al., 2020). Surface track densities were measured on-screen, on images captured using a 100x plan apochromat class objective. The spontaneous track area in the apatite grain and the induced track area in the mica external detector are digitally matched using micro-georeferencing in Nikon-TRACKflow (Helmert transformation and Z-surface interpolation) ([PERSON], [PERSON], et al., 2020) on four coarse and five fine reference points. The digital images are further matched using an image flip and rotation. Where possible, a minimum of 1,000 spontaneous tracks (s.e. \(\approx\)3%) or minimum 20 apatite grains were counted. Ages were calculated and reported as conventional \(\zeta\)-ages ([PERSON], 1990) as well as central ages ([PERSON], 2009) with an overall mean \(\zeta\) value of 317.9 \(\pm\) 3.3 a.cm\({}^{2}\)(Analyst [PERSON]), based on Fish Canyon Tuff and Durango apatite age standards ([PERSON] et al., 2003; [PERSON] et al., 2005).
Confined track lengths and angles to the crystallographic \(c\)-axis were measured using a 100x plan apochromat class objective and a 2\(\times\) secondary optical magnification (Nikon DSC zooming port). Projected tracks were corrected to 3D lengths in TRACKflow using the precise \(z\)- readout of the microscope of the tracks end-points and a correction for the optical media transitions (\(n_{\rm air}\) = 1.0028; \(n_{\rm sp}\) = 1.6455). We aimed at measuring of at least 100 confined tracks for the determination of the length-frequency distribution. Angles to the crystallographic \(c\)-axis were also obtained to quantify annealing anisotropy ([PERSON] et al., 2003; [PERSON] et al., 2007). For samples showing low spontaneous track density and young AFT age (Table 2), a subset of second mounts was subjected to \({}^{250}\)Cf bombardment to generate a higher number of confined tracks ([PERSON] & [PERSON], 1991) at The University of Adelaide. The \({}^{252}\)Cf rig had 1 MBq activity at the time of irradiation, and samples were irradiated for 1 hr each in a vacuum chamber (e.g., [PERSON] et al., 2022). The measurable confined tracks after irradiation are expected to increase by at least four to five times.
### Thermal History Modeling
Thermal histories of the sampled rocks from the SE Tibetan Plateau (Yunnan) were derived by using the QTQ software package (version 5.6.3, [PERSON], 2012). This application performs inverse thermal history modeling based upon the Bayesian transdimensional Markov-Chain Monte-Carlo approach, generating an output with a
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline & & \multicolumn{3}{c}{Spontaneous} & \multicolumn{3}{c}{Induced} & \multicolumn{3}{c}{Dosimeter} & \multicolumn{3}{c}{Track length and \(D_{ps}\)} \\ & No. of & \multicolumn{3}{c}{\(\rho_{s}\) (10\({}^{5}\)} & \multicolumn{3}{c}{\(\rho_{s}\) (10\({}^{5}\)} & \multicolumn{3}{c}{\(\rho_{s}\) (10\({}^{5}\)} & \multicolumn{3}{c}{\(\rho_{s}\) (10\({}^{5}\)} & \multicolumn{3}{c}{\(P_{Q}\)(\({}^{5}\))} & Dispersion & Zeta (\(\zeta\)) age & Central age & \multicolumn{3}{c}{Length} & \multicolumn{1}{c}{\(D_{ps}\)} \\ Sample & grains (\(m\)) & \(N_{s}\) & cm\({}^{-2}\)
range of withheld accepted models with the consideration of a multi-kinetic AFT annealing model ([PERSON] et al., 2007). In addition, the inverse scheme of this software is preferably built to reconstruct the integrated thermal history from an age-elevation profile, when all AFT ages, track length distributions, kinetic parameters and other effective age constraints are taken into account.
In order for QTQ to calculate proposed time-temperature paths, we provided the program with spontaneous and induced track density data, length-frequency distributions and \(D_{\mathrm{par}}\) Thermal history modeling was conducted on 20 samples that generally produced sufficient number (all \(>\)70 and majority \(>\)100) of confined tracks (Table 2). Where reliable ZHe data are available (Lincang River Profile, [PERSON] et al., 2021), we performed the modeling using both the AFT and ZHe results. We did not integrate the AHe results from [PERSON] et al. (2021) and [PERSON] et al. (2018) with our AFT data but treated them separately because the dimensions of apatite grains were not given by these authors. The prior temperature was set at \(70\pm 70\)C, which envelopes the maximum temperature interval as data information could contain. Since all samples are from outcrops, we constrained the present-day temperature to \(15\pm 10\)C. We first ran 10,000 burn-in and 50,000 post-burn to find the appropriate search parameters, after that 200,000 iterations were run as burn-in and post-burn-in iterations.
## 4 Results
### LA-ICP-MS Zircon U-Pb Dating
Zircon U-Pb concordia and weighted mean age diagrams are shown in Figure 4 and isotopic data can be found in Supporting Information S1. Systematic uncertainty ([PERSON] et al., 2016) has been propagated to the weighted mean uncertainty for the group of analyses that defines an average U-Pb age. Samples Y07 and Y18 were taken from the inside the Tengchong Unit. For Y07 at total of 21 analyses yielded comparable ages with an average of \(135.9\pm 3.2\) Ma (MSWD = 3.67), while 19 out of 20 dated zircons from Y18 yielded consistent apparent ages with a mean age of \(117.4\pm 2.7\) Ma (MSWD = 2.68). Granite Y37 is part of the Lincang Pluton, and 21 grains were dated. All of them yielded concordant and consistent ages with a mean \({}^{269}\)Pb\({}^{25}\)U age of \(210.5\pm 4.8\) Ma (MSWD = 2.64). These three concordant ages are interpreted as magmatic crystallization ages due to the clear and concentric oscillatory zoning of the dated zircons and their high Th/U ratios (generally \(>\)0.4) (e.g., [PERSON] et al., 2003). Foliated granite (Y28) was collected from the southern segment of the Chongshan shear zone (Figures 0(b) and 1(a)), 14 dated zircon grains show a wide range of \({}^{209}\)Pb\({}^{25}\)U ages from \(\sim\)1,144 to \(\sim\)20 Ma. Among them, six analyses whose Th/U ratios are comparably low (0.56-0.01) plot together with a concordant age at 20.3 \(\pm\) 0.7 Ma (MSWD = 0.39). Considering that (a) several dated zircons display typical core-min texture with old inherited cores (Nos. 04, 12, and 14; Supporting Information S1); (b) the \(\sim\)20 Ma young results are from either transparent and prismatic zircons, or new growth-zoned rims exhibiting clear oscillatory zoning; and (c) sample Y28 is from a syn-kinematic intrusion developed strictly within the shear zone (Figure 3; [PERSON], 1988; [PERSON], 2006; [PERSON] et al., 2011). It is reasonable to propose that the \(\sim\)20 Ma mean age is a (re-)crystallization age representing the syn-magmatic deformation along the Chongshan shear zone.
### Apatite Fission Track Analysis
All 31 samples from the four domains yield apatite grains that could be satisfactorily analyzed. All samples passed the chi-squared \(P(\chi^{2})\) text with low dispersion, suggesting a single population of grains (Table 2; Supporting Information S2; Galbraith & Green, 1990). New AFT ages are reported as mean zeta-ages \(t(\zeta)\) and they are used in the following discussions, the central age of each sample is also presented.
Eleven samples were collected from Domain Y-1, they generally produce consistent late Oligocene-middle Miocene AFT ages, ranging from \(24.8\pm 1.2\) Ma to \(14.2\pm 0.7\) Ma. Among them, intrusive rocks display various Meso-Cenozoic crystalline ages (Table 1), indicating their different origins and emplacement depths but near coeval regional exhmutation. A total of four samples were found to have \(>\)100 confined tracks with mean track lengths varying between \(\sim\)13.3 and \(\sim\)13.7 \(\upmu\)m, which display narrow distributions (Figure 5). Consequently these samples passed relatively rapidly through the Apatite Partial Annealing Zone (APAZ; \(\sim\)120-60\({}^{o}\)C) and contained tracks that were produced after the latest cooling phase ([PERSON], [PERSON], [PERSON], & [PERSON], 1986; [PERSON], [PERSON], [PERSON], & [PERSON], 1986). Two other samples show insufficient numbers of confined tracks, giving mean values of \(\sim\)13.4 and \(\sim\)12.9 \(\upmu\)m based on limited measurements (Table 2).
Eight samples from Domain Y-2 yield similar Miocene AFT ages that range from \(23.3\pm 1.4\) Ma to \(13.5\pm 1.1\) Ma, while one additional sample Y35 gives an older Eocene (\(\sim\)36 Ma) age. Similar to the age distributions in DomainY-1, comparable AFT ages from this region mainly cluster in the early to middle Miocene crossing several intervening faults (Figure 3). As to the track length data, six samples provided >70 confined tracks, whose mean track length values vary from \(\sim\)13.6 to \(\sim\)12.5 um showing unimodal distributions (Figure 6). Despite \({}^{25}\)CF bombardment increased the number of measurable fission tracks, only 27 confined tracks were found in sample Y39 due to the poor quality of the apatite grains, its mean track length (\(\sim\)12.8 um) is listed for reference only.
Domain Y-3 is represented by an age-elevation profile near the Lancang River (Figure 7), with six sample sites (Y43-44, 47-49, and 51) spanning \(\sim\)900 m of elevation (Table 1), and a set of Miocene AFT ages were obtained from 20.3 \(\pm\) 0.9 to 14.9 \(\pm\) 0.8 Ma (Table 2). It is noted that the AFT central age of the sandstone sample Y44 (18.0 \(\pm\) 1.3 Ma) is significantly younger than its Jurassic depositional age, considering that the chi-squared possibility \(P(\chi^{2})\) of this sample reaches 100% with dispersion of only 0.06% (Table 2), this sample must have been buried deeply enough for the AFT system to have fully reset. The AFT age-elevation diagram shows a clear and positive correlation (Figure 8). A sufficient number of confined tracks were able to be measured from five samples (all \(>\)100), the mean track lengths are \(\sim\)13.8-13.0 um exhibiting clear unimodal and relatively narrow distributions with a dominance of long lengths. These indicate minor track shortening by thermal influence. Although sample
Figure 4: Concordia diagrams of U-Pb analytical results and mean age plots for four representative basement rocks.
Y52 to the west shows an even higher elevation of 1,940 m, it is too far away from the Lancang River (\(\sim\)20 km, Figures 7a and 7b) and was less significantly influenced by river incision, we therefore excluded it from the analysis of the age-elevation profile. This Triassic quartzite exhibits a Miocene AFT age (\(\sim\)18.4 Ma) as well, a total of 100 measured confined tracks gives a mean track length of 13.9 um and a standard deviation of 1.0 um (Figure 8).
Domain Y-4 contains four granite rocks (Y54, 55, 56, and 59) from the interior part of the Lincang Pluton (Figure 2), they show Eocene to Oligocene AFT ages spanning from \(\sim\)48 to \(\sim\)28 Ma (Table 2). The mean track lengths span from \(\sim\)12.6 to \(\sim\)12.1 um (Figure 9), suggesting clear signs of track shortening during the APAZ residence ([PERSON], [PERSON], [PERSON], & [PERSON], 1986; [PERSON], [PERSON], [PERSON], & [PERSON], 1986).
### Thermal History Modeling
Thermal history models were produced for samples with an adequate quantity of confined tracks (\(>\)70). Of the 31 samples analyzed in this study, 20 were found to be suitable for thermal history modeling (majority \(>\)100; Table 2). In this section we present the expected temperature-time paths of all the modeled samples (Figures 5, 6, 8, and 9). These contain features of all the models sampled in the post-burnin sampling and in terms of complexity will generally lie between the maximum likelihood model (more complex) and the maximum posterior model (less complex). Also, the MCMC sampling can be used to calculate the uncertainty for the expected model and so draw meaningful credible intervals (more or less the Bayesian equivalent of confidence intervals). These intervals represent a 95% probability range for a given parameter, calculated so that 2.5% of the parameter values lie below and above the limits defined by the range ([PERSON], 2012). Detailed individual thermal history models for each sample can be found in Supporting Information S3. In our further discussion, we define rates
Figure 5: Expected thermal history models (with the 95% confidence interval in shadow) for four samples (Y02, 06, 07, and 12) from Domain Y-1 (Tengchong Unit) generated in QTQt ([PERSON], 2012) based on apatite fission track data. Confined fission track length distributions for each sample are shown.
Figure 6: Expected thermal history models (with the 95% confidence interval in shadow) for six samples (Y22, 26, 29, 34, 35, and 37) from Domain Y-2 generated in QTQ ([PERSON], 2012) based on apatite fission track data. Confined fission track length distributions for each sample are shown.
Figure 7: (a) Topographic and simplified geological map of the Lancang River valley and the surrounding area with sample locations, based on YBGMR (2000a). Sample apatite fission track ages (red dots; this study) and published AHe ages (yellow dots; [PERSON] et al., 2021) are also indicated. (b) Topographic cross section of transect a-b, showing the SE Tibet morphology incised by the Lancang River in the middle reach. (c) View of the Lancang River valley taken from the eastern flank of the river valley. (d) Field photograph of the steep Lancang thrust fault in the east of the river, generally dipping to the west.
(in our study area's continental collisional zone setting) of \(<\)3, 3-10 and \(>\)10\({}^{\circ}\)C/Ma as slow, moderate and rapid cooling, respectively, based on empirical values (e.g., [PERSON] et al., 2022, 2023).
For Domain Y-1 (Tengchong Unit), two adjacent samples Y06 and Y07 in the west display similar moderate to slightly rapid cooling paths from the mid-Oligocene (\(\sim\)28 Ma) to middle Miocene (\(\sim\)15 Ma). To the east of the Gaoligong shear zone, sample Y12 shows a two-stage thermal history. A rapid cooling phase is predicted to have lasted until the middle Miocene (\(\sim\)12 Ma), when slow cooling gradually brought the rock to ambient present-day surface temperature (Figure 5). Another Miocene AFT age sample Y02 rapidly cooled through the APAZ during the middle Miocene (\(\sim\)18-11 Ma), and the fast cooling is expressed to have continued until the Quaternary (Figure 5).
Thermal history models for Domain Y-2 record various Miocene enhanced cooling events. Sample Y22 rapidly cooled through the APAZ during the early Miocene (\(\sim\)23-20 Ma) and the fast cooling lasted until the middle Miocene
Figure 8.— (a) Integrated thermal history models (with the 95% confidence interval in shadow) for five samples (Y43, 47, 48, 49, and 51) from Lancang River Profile generated in QTQt ([PERSON], 2012) based on apatite fission track (AFT) and published ZHE ([PERSON] et al., 2021) data. The T-t paths of the coldest and hottest samples are indicated by blue and red lines respectively, and the intermediate samples are gray. Confined fission track length distributions for each sample are shown. (b) Individual thermal history models (with the 95% confidence interval in shadow) for the five river profile samples for comparison. (c) AFT (this study) and AHe ([PERSON] et al., 2021) age-elevation plot for the Lancang River Profile. (d) Expected thermal history model for sample Y52 (with the 95% confidence interval in shadow) from Domain Y-3 generated in QTQt ([PERSON], 2012) based on AFT and published ZHE ([PERSON] et al., 2021) data. Confined fission track length distribution for this sample is shown.
(\(\sim\)15 Ma). The thermal history model for Y26 shows a fast cooling pulse between \(\sim\)17 and \(\sim\)10 Ma with a temperature decrease of more than 60\({}^{\circ}\)C (Figure 6). The inverse models predict comparable cooling paths for Y29, 34, and 37, which exhibit entrance into the APAZ in the early Miocene followed by moderate cooling until the Quaternary. As to the Eocene AFT age sample Y35, slow to moderate cooling, thus slower than for others from this domain, is observed and it seemed to have remained in the upper APAZ during \(\sim\)40-30 Ma (Figure 6). However, considering its relatively long mean track length of \(\sim\)13.6 \(\mu\)m, a rapid cooling event is expected to have occurred before \(\sim\)40 Ma.
In the Lancang River vertical profile, five samples (Y43, 47-49, and 51) with sufficient track lengths (all \(>\)100) were used for thermal history modeling. The prior for the paleo-temperature offset between the highest and lowest samples was set to 30\({}^{\circ}\)C/km that stands for the apparent geothermal gradient of the study area (e.g., [PERSON] et al., 2021; [PERSON] et al., 2018). Considering the vertical drop of \(\sim\)900 m, the temperature difference is \(\sim\)27\({}^{\circ}\)C. In addition, we put a roughly constrained temperature condition of 180 \(\pm\) 20\({}^{\circ}\)C at 38 \(\pm\) 3 Ma at the start, based on published ZHe ages located close to our profile ([PERSON] et al., 2021). This will make the cooling paths more completed throughout the APAZ. The integrated modeling results indicate fast cooling since the early Miocene (\(\sim\)22 Ma), lasting until the middle Miocene (\(\sim\)14 Ma) when the rocks cool below \(\sim\)40\({}^{\circ}\)C (Figure 8a). A subsequent re-heating is observed in the models. However, considering that (a) the studied domain was not affected by late Cenozoic extensional tectonics (e.g., [PERSON], 2012; [PERSON] et al., 2022; [PERSON] et al., 2017); (b) the confined track length distributions of samples from this domain all display a distinct unimodal pattern which is not suggestive of overprint by a later thermal event; and (c) the modeled re-heating phase is outside the APAZ temperature window, we consider that this feature does not represent a real geological event. It is hence not further discussed. Then for a comparison, we also compiled the expected models of individual samples from
Figure 9: Expected thermal history models (with the 95% confidence interval in shadow) for four samples (Y54, 55, 56, and 59) from Domain Y-4 (Lincang Pluton) generated in QTOq ([PERSON], 2012) based on apatite fission track data. Confined fission track length distributions for each sample are shown.
the Lancang River Profile (Figure 8b). It is observed that the individual sample modeling results in general fit the integrated ones (Figures 8a and 8b), indicating early to mid-Moocene accelerated rock cooling. Considering that the age-elevation diagram for this profile generally displays a clear and normal linear relationship between AFT age and elevation (Figure 8c), and there is no major intermittent fault in the horizontal tract of the profile (Figure 7a) (the north-trending brittle fault between Y49 and 51 is quite minor and almost invisible in the field), we therefore propose that the Lancang River Profile exhibits a single cooling history and integrated thermal history modeling adequately quantifies that. Located in the westward extension of the vertical profile, single sample Y52 shows a very similar Miocene cooling history to those from the Lancang River valley (Figure 8d; Supporting Information S3). Fast cooling to within the APAZ initiated in the early Miocene (\(\sim\)21 Ma) and lasted until the middle Miocene (\(\sim\)15 Ma), followed by slow cooling that eventually reached the surface temperature.
Regarding the Lincang Pluton of Domain Y-4, all the four analyzed samples display rather slow cooling (\(<\)3\({}^{\circ}\)C/ Ma). This is consistent with their broad length distributions with mean track lengths between \(\sim\)13 and \(\sim\)12 um, typical of track length shortening due to slow cooling through, and long residence in the APAZ ([PERSON], [PERSON], [PERSON], & [PERSON], 1986). The southernmost sample Y59 shows a quasi linear, protracted cooling from the latest Cretaceous to the early Miocene (\(\sim\)20 Ma), with a \(\sim\)30 Ma stay in the APAZ (Figure 9). While the other three granitic rocks (Y54-56) exhibit comparable thermal history models, and slow cooling is observed between \(\sim\)40 and \(\sim\)10 Ma. Although renewed cooling phases are expressed in the models during the late Neogene (Figure 9), these parts are beyond the APAZ and not constrained by the AFT system as such.
## 5 Data Interpretations and Discussion
### Zircon U-Pb Age Interpretations
Generally, our zircon U-Pb dating results are in agreement with published data and demonstrate widespread Mesozoic (crystalline) basements in the SE Tibetan Plateau (Yunnan). With regard to the Tengchong Unit, the magmatic granite (Y18) formed at 117.4 \(\pm\) 2.7 Ma, which is consistent with the granite crystalline age recognized in the nearby Liange region (\(\sim\)115.8 Ma, [PERSON] et al., 2010), suggesting Cretaceous magmatism. Previous geological surveys attributed the well-exposed granidentils in the westernmost Tengchong Unit to the Paleoene according to the lithologic and stratigraphic relationships (Figure 2; YBGMR, 1990, 2000a). However, a crystallization age of 135.9 \(\pm\) 3.2 Ma was obtained for the \"Paleogene\" granite Y07 (Figure 5). Hence, granidentils in this area rather seem to be of Cretaceous than of Paleogene age, and the latter are not so widely distributed as previously considered (YBGMR, 1990, 2000a). In the northern part of the Lincang Pluton, a magmatic event was identified at \(\sim\)210.5 Ma (sample Y37) that is generally in agreement with the published zircon U-Pb data along the pluton ([PERSON] et al., 2018; [PERSON] et al., 2013), thus the intrusion of the Lincang Pluton occurred in the Triassic. Our results confirm that large volumes of igneous rocks were generated during the Mesozoic, which together with the Precambrian basements and Paleo-Mesozoic sediments, constitute the main body of the SE Tibetan Plateau (Figure 2). In some tectonically active belts (i.e., strike-slip shear zones), relatively young syn-tectonic magmatism (\(\sim\)20 Ma, sample Y28) took place as a result of ductile deformation (e.g., [PERSON] et al., 2011; [PERSON] et al., 2020; [PERSON] et al., 2017). It is noteworthy that this sample displays an AFT age of \(\sim\)13.5 Ma, indicative of a more than 500-600\({}^{\circ}\)C cooling within a few million years after formation. We propose that this very rapid cooling (up to \(\sim\)100\({}^{\circ}\)C/Ma) reflects thermal equilibration for a pluton/dyke emplaced at relatively shallow crustal levels. Simple conductive cooling calculations suggest that a pluton/dyke emplaced at depths between \(\sim\)5 and \(\sim\)10 km should thermally equilibrate within \(\sim\)\(\sim\)1 to \(\sim\)4 Ma ([PERSON] et al., 2006; [PERSON] et al., 2019). In addition, fast exhundum and exposure of mylonitrile rocks are very common features of reverse oblique-slip strike-slip faults such as the Chongshan shear zone, implying major transpressive processes characterized by a strong pure shear component during exhundum ([PERSON] et al., 2022; [PERSON], 2016; [PERSON] et al., 2021b).
Thermochronological Interpretations and Mechanisms for Enhanced Miocene Exhundation of SE Tibetan Plateau
Our new low-temperature thermochronological data (i.e., AFT) and inverse thermal history models from the Tengchong and Changing-Menglian Units, as well as the central-north part of the Lincang Pluton reflect wide-spread moderate to rapid cooling during the Miocene (Figures 2, 5, 6, and 8). In the Tengchong Unit, samples Y02 and 12 underwent fast Miocene cooling, and the accelerated cooling episode for samples Y06 and 07 also lasted until the middle Miocene (\(\sim\)15 Ma) (Figure 5). Similar cases also occurred in Domain Y2, where the majority of the samples cooled through the APAZ in the Miocene (Figure 6). Along the Lancang River, the vertical profile constrains rapid early to middle Miocene (\(\sim\)22-14 Ma) cooling as well (Figure 8). It is thus observedthat metamorphic/crystalline basements in SE Tibet (Yunnan) experienced large-scale enhanced cooling and upper crustal exhumation during the Miocene.
One key question is to figure out the mechanisms that drove the pervasive Miocene cooling events. As mentioned above, the geomorphology of the SE Tibetan Plateau is characterized by relatively low-relief upland that is being extensively incised by several large rivers (Figure 1). Based on a set of AHe ages, [PERSON] et al. (2021) and [PERSON] et al. (2018) recognized a rapid middle Miocene (\(\sim\)17-14 Ma) cooling phase both in the upstream and downstream region of the Mekong (Lancang) River, and proposed that the fast exhumation was caused by rapid river incision as a result of intensified precipitation during this period. Our vertical profile in Domain Y-3 is almost identical with the sampling transect in [PERSON] et al. (2021), and the integrated model based on AFT data records an \(\sim\)22-14 Ma exhumation episode, which includes but continued beyond the period of \(\sim\)17 Ma suggested by these authors. Furthermore, the reported AFT ages are in good agreement with the AHe ones from [PERSON] et al. (2021) (Figure 8c). In this region, another sample Y52 which does not belong to the steep vertical profile displays a coincident early-middle Miocene (\(\sim\)21-15 Ma) rapid cooling path compared with the samples from the river flank (Figure 8d). Thus they confirm that the record for a Miocene rapid exhumation along and adjacent to the downstream section of the Lancang River is robust, and this enhanced fast cooling should had commenced by the earliest Miocene (Figure 8a). According to available geological maps (Figure 2; YBGMR, 1990, 2000a), several major faults are developed in Domain Y-3. In the field, these remarkable thrust faults were also recognized. The steep Lancang thrust fault occurs in the east of the sampling site Y43 (Figure 7a), dipping toward the west (Figure 7d), it is close to the Lancang River and serves as the boundary fault between the Lincang Pluton and Lamping-Simao Unit (Figure 2). We propose that tectonic activity of this brittle fault may have played an important role in controlling the Miocene thrusting and exhumation of the central Lincang Pluton.
Near the Changing City, several samples (Y26, 28, and 29) were also collected from the flank of the Lancang River valley (Figure 2a). Among them, samples Y26 and 28 are foliated granitiols taken from the axial zone of the Chongshan shear zone (Figure 3b), thus their exhumation processes may have been influenced by both the activity of the shear zone and river incision. The thermal history model of the sample Y26 recorded moderate middle Miocene cooling (\(\sim\)17-10 Ma) with a cooling rate of \(\sim\)8.6\({}^{\circ}\)CMa (Figure 6). Zircon U-Pb dating for the sample Y28 revealed that the (re-)crystallization of this syn-kinematic granite dyke took place at \(\sim\)20.3 Ma (Figure 4c), together with its Miocene AFT age (\(\sim\)13.5 Ma) implying a very fast cooling after emplacement due to thermal equilibrium, but a convincing cooling path (\(<\)\(\sim\)120\({}^{\circ}\)C) based on AFT analysis cannot be derived due to the lack of adequate number of confined tracks. Sample Y29 is a non-deformed granite and therefore did not suffer intensive ductile shearing, its inverse thermal history modeling curve also indicates a fast Miocene cooling starting in the APAZ at \(\sim\)20 Ma, while the estimated cooling rate (\(\sim\)5.4\({}^{\circ}\)CMa) corresponds to a slower exhumation process compared with Y26 (Figure 6). Is it noted that from a Cretaceous pluton, sample Y22 is \(>\)30 km distant from the Chongshan shear zone and Lancang River (Figures 2a and 3b), yet a relatively moderate cooling phase (\(\sim\)6\({}^{\circ}\)C/ Ma) was recorded between \(\sim\)25 and \(\sim\)15 Ma (Figure 6). Furthermore, in the central and southern Domain Y-2 (Figure 2a), samples Y34 and 37 are also far away from the river valley, but show similar thermal histories to Y29 that is from the western flank of the Lancang River (Figure 6). The Eocene-AFT-age sample Y35 underwent an episode of thermal quiescence since Oligocene, considering that this non-deformed monzonite is not from the axial part of the Nantinghe fault and was probably in a discrete slip plane during deformation, we infer that fault activity here mainly created lateral movement but only limited vertical displacement was produced (Figure 3b). Throughout the above observations and analyses, it can be derived that (a) there was visible difference in exhumation rate between the interior of the ductile shear zone and the area outside during the Miocene. The shallow crust cooling rate inside the Chongshan shear zone was relatively higher than that outside by the comparison between the thermal histories of Y26 and 29; and (b) similar to the case in Domain Y-3, samples which were not influenced by river incision also experienced Miocene rapid cooling phase. As the structural framework of Domain Y-2 is generally characterized by several strike-slip shear zones and large-scale brittle faults (Figure 2; YBGMR, 1983, 1990, 2001), we therefore suggest that brittle fault movements as well as ductile shearing of the strike-slip faults had significant impact on the Miocene upper crustal evolution of the Changing-Menglian Unit and northern Lincang Pluton.
Concerning the samples from Domain Y-1 (Tengchong Unit), the thermal history model for sample Y02 clearly expresses a Miocene accelerated cooling event showing a \(<\)\(\sim\)10 Ma residence within the APAZ (Figure 5). Notwithstanding the cooling curve of another granite (Y12) started high up in the APAZ (Figure 5; Supporting Information S3), its steep slope exhibited for the middle Miocene (\(\sim\)15-13 Ma), predicts the occurrence of a rapid early to middle Miocene cooling episode. Two adjoining samples (Y06 and 07) in the west of this domain displayed a coeval mid-Oligocene to early Miocene moderate to rapid cooling history, suggesting a slightly earlier exhunation event. In addition, considering that all the samples from the Tengchong Unit gave the young late Oligocene-Moocene AFT ages and the obtained mean track lengths are generally \(\sim\)\(\sim\)13 \(\upmu\)m (Table 2), it is reasonable to propose that near contemporaneous exhunation should have prevailed in this area. In and around the Tengchong Unit, several major or subordinate strike-slip shear zones are well exposed, including the Nabang, Sudian, Yingjiang, Lianghe and Gaoligong shear zones from west to east (Figure 3a; [PERSON], 2012; [PERSON] et al., 2015; [PERSON]. [PERSON] et al., 2017). The Cenozoic activities of these \(\sim\)N-S or NE-SW high-strain belts produced a series of intervening gneiss domes, reflecting the formation of anticlines during compression-dominated transpression ([PERSON] et al., 2017). Along these belts, shear strain that involves a pure shear component causes denudation in an obliquety divergent regime with significant vertical movement, exposing deep-seated rocks. This accounts for the more rapid cooling and exhunation of the strongly foliated gneiss Y26 which was taken from the axial part of the Chongshan shear zone (Figures 2 and 3) (i.e., different thermal histories between Y26 and Y29). Further, recent thermochronological study also identified very high \(\sim\)18-11 Ma rock exhunation rates (\(\sim\)1.2 km/Ma) inside the Gaoligong shear zone ([PERSON] et al., 2020). It confirms the Miocene activity of this shear zone and highlights the important role of ductile shear zones in exposing rocks. Therefore, we propose that strike-slip fault movements and the associated contraction were responsible for the Miocene crustal exhunation in the Tengchong Unit.
In the southern Lincang Pluton, models for all the analyzed rocks do not show accelerated cooling pulse but rather display near linear slow cooling during the Paleocene to mid-Neogene (Figure 9), giving \(<\)\(\sim\)2.1\({}^{\circ}\)C/Ma cooling rates that are significantly lower than those from the other three domains. Compared with the central and northern segments of the Lincang Pluton, less ductile shear zones or thrust faults were developed in its southern part, but several strike-slip faults (based on previous field mapping) crossed the region (Figure 2a; YBGMR, 2000b). We infer that the southern Lincang Pluton is a more stable granitic block, faults exposed there are brittle and not deeply rooted, and they were not able to create remarkable regional thrusting to enhance the exhunation process. In addition, strike-slip faults may have moved transversally without dip slip or reverse faulting, and there was no significant vertical displacement to bring about younger thermochronological ages due to deeper exhunation. This is to some extent documented by sample Y56, which is located in the vicinity of a narrow brittle strike-slip fault (the Jinghong fault; Figure 2a), but exhibits an identical thermal history in comparison to those located more distantly from brittle faults (Figure 9). Moreover, the lateral displacement/extrusion (along large-scale shear zones) may have largely accommodated the \(\sim\)E-W shortening under a compressive setting ([PERSON] et al., 1995; [PERSON] et al., 1982; [PERSON] et al., 2022). In this case, this large and rigid pluton in the south (Figures 2 and 10) was more stable and experienced less extensive exhunation during the Cenozoic deformation stage (i.e., India-Asia collision).
In summary, different tectonic units in the southeastern Tibet (Yunnan) recorded widespread late Oligocene to Miocene enhanced basement cooling, and we prefer a tectonic driving force as described above. It is noteworthy that some scholars attributed the middle Miocene rapid cooling phase (\(\sim\)17-14 Ma) along the Lancang River valley to the intensified monsoon precipitation (e.g., [PERSON] et al., 2021; [PERSON] et al., 2018), based on its coincidence with coeval climate optimum records (e.g., [PERSON] et al., 2009; [PERSON] et al., 2001). In addition, environmental indicators (e.g., chemical index of alteration) in Neogene sediments from the South China Sea reveal relatively high mid-Moocene precipitation rates due to strengthening of the East Asian summer monsoon (e.g., [PERSON] et al., 2008). The intensified monsoon precipitation (associated with warm climate and high CO\({}_{2}\)) would have the potential to increase the power of river incision and consequent overburden release ([PERSON] et al., 2013; [PERSON] et al., 2018; [PERSON] et al., 2018). Although our well-constrained integrated modeling results suggest that this cooling pulse should have initiated at \(\sim\)22 Ma (Figure 8), which is several million years earlier than the proposed climate-related event during \(\sim\)17-14 Ma (i.e., middle Miocene climate optimum). Hence, in tandem with tectonic activity, the climate-driven incision would also have contributed to an increase in exhunation rates along the river valley. This is to some extent revealed by relatively higher cooling rates of the Lancang River Profile compared with those of samples from other domains (Figures 5, 6, 8, and 9). On the other hand, it is observed that Miocene enhanced rock cooling was widespread in our study areas. As denudation would not occur without sufficient surface erosion and unroofing, the strengthened surficial erosion during this period therefore exerted a strong influence on the exhunation processes. These considerations are in agreement with a recent hypothesis that climate acts as a great \"equalizer\" of continental-scale erosion in areas with high precipitation, in which younger thermochronological ages and shorter erosional histories were recorded ([PERSON] et al., 2021).
Thus climate change also served as an important driving factor of the Miocene moderate to rapid exhumation in the SE Tibetan Plateau (Yunman).
### Implications for Regional Morpho-Tectonic Evolution
Numerous studies based on structural and paleomagnetic investigations revealed that the SE Tibetan Plateau has been dominated by extrusion tectonics since the late Eocene, and the strike-slip faults/shear zones are considered to accommodate a large component of extrusion of the tectonic units around the eastern Himalayan syntaxis (e.g., [PERSON] et al., 1993, 2001; [PERSON] et al., 2017; [PERSON], 2006; [PERSON] et al., 1982, 1990; [PERSON] et al., 2014).
The newly recognized late Oligocene-Moicene rapid exhumation events broadly coincide with coeval activities of the large-scale fault system in the SE Tibetan Plateau, including the left-lateral shearing along the Ailao Shand-Red River shear zone (\(\sim\)34-17 [PERSON], [PERSON] et al., 1995, 2001; [PERSON] & [PERSON], 2003; [PERSON], [PERSON], [PERSON], et al., 2020), Chongshan shear zone (\(\sim\)34-14 [PERSON], [PERSON] et al., 2008; [PERSON]. [PERSON] et al., 2010) and Nantinghe fault (\(\sim\)20 Ma, [PERSON], [PERSON], [PERSON], et al., 2020), as well as the dextral shearing of the Gaoligong shear zone (\(\sim\)28-10 Ma, [PERSON] et al., 2009; [PERSON] et al., 2006; [PERSON]. [PERSON] et al., 2015; [PERSON] et al., 2012) and Nabang shear zone (\(\sim\)28-20 Ma, [PERSON] et al., 2000; [PERSON] et al., 2006; [PERSON] et al., 2015). Near the eastern Himalayan syntaxis, several near-parallel NE-trending subordinate ductile faults (i.e., the Yingjiang, Sudian and Lianghe shear zones) were also found to have been active during the Oligocene-Moicene (e.g., [PERSON], [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2015). In addition, structurally, shear zones around and in the Tengendong Unit are characterized by intensive transgressional deformation that recorded strain partitioning with simple shear component along these high-strain belts ([PERSON] et al., 2015; [PERSON] et al., 2017). These kinematic data indicate extensive \(\sim\)NW-SE regional compression related with oblique India-Asia convergence during the Oligocene to Miocene (Figure 10). Previous studies suggest that substantial horizontal displacement is usually accompanied by significant vertical strain and exhumation along the large-scale faults and shear zones (e.g., [PERSON] & [PERSON], 2016; [PERSON] et al., 2001; [PERSON], [PERSON], [PERSON], et al., 2020). While our low-temperature thermochronological data reveal that equally moderate to fast shallow crustal cooling also occurred outside the high-strain belts in the SE Tibetan Plateau, indicating that upper crustal shortening and thickening in such a compressive tectonic regime probably affected a considerably large area and resulted in almost simultaneous regional exhumation in the late Oligocene-Moicene.
On the other hand, contrary to the indentation-extrusion model, growing numbers of paleomagnetic and geodetic data suggest that areas adjacent to the eastern Himalayan syntaxis have experienced strong clockwise block rotation along several N-S-trending shear zones ([PERSON] et al., 2014; [PERSON] et al., 2017, 2018; [PERSON] et al., 2001; [PERSON] et al., 2021; [PERSON]. [PERSON] & [PERSON], 1997; [PERSON] et al., 2004). Recently, based on detailed paleo-magnetic data from the Tengchong, Baoshan and Lapping-Simao Units, [PERSON] et al. (2016) proposed that these terranes underwent latitudinal crustal shortening accompanied by eastward extension of the crustal material in the Oligocene; Since the Miocene, their main form of crustal motion was gradually transformed into clockwise rotation, and then the fold and thrusting fault system was less developed as a result. Thermal history models for Domain Y-1, Y-2, and Y-3 reflect that majority of the samples cooled through the APAZ before \(\sim\)10 Ma (Figures 5, 6, and 8), hence our results do not preclude the possibility of the weakening of crustal shortening and thickening in the southeastern edge of the Tibetan Plateau during the Miocene, but such a transformation of crustal motion form probably did not commence prior to the middle Miocene.
Overall, the strongly coupled time between major faults deformation and upper crustal exhumation favors a late Oligocene-Moicene tectonic configuration in which lateral extrusion of the northern Indochina was still ongoing and caused extensive surface uplift of the SE Tibetan Plateau at this time (Figure 10). This model stresses compressive deformation associated with fault movements, and is therefore incompatible with the lower crustal flow model that emphasizes late Miocene passive uplifting by lower crustal flow originated from over-thickened crust of the central Tibet ([PERSON] et al., 2005; [PERSON], 2000; [PERSON] et al., 1997).
It is noteworthy that late Oligocene to Miocene exhumation phases are also widely recognized in the northern part of the SE and eastern Tibetan Plateau (Figure 1b and the references there), suggesting that contemporaneous crustal deformation and denudation were not locally focused but ubiquitous in these tectonically active areas. However, compared with other areas in the eastern and the SE Tibetan Plateau, the majority of the Yunnan (Province) (\(\sim\)22-25 N\({}^{\circ}\)) exhibits distinct lower elevations (generally \(<\)2,500 m, Figure 1b) though it has undergonesimilar intensive basement rocks cooling during the late Cenozoic as revealed by our AFT results, and hence late Oligocene-Moocene exhaustion failed to build a significant mountainous morphology here. We propose that this may partly be due to topography lowering by large river systems (in a wet climate) ([PERSON] et al., 2008), rapid exhunation was accompanied by river incision, leading to accelerating surface erosion. Oligocene-Moocene
Figure 10: Interpretavictive sketch illustrating the Oligocene to Miocene tectonic framework of the SE Tibetan Plateau in the context of the ongoing India-Asia convergence. The \(\sim\)NW-SE directed compression is highlighted (yellow arrows) to trigger southeastward extrusion of continental blocks along large-scale strike-slip faults and the accompanied intensive upper crustal deformation (see details in discussion). F, fault; S, shear zone.
age peaks in the sediment fluxes observed in the marginal seas of Asia has demonstrated that a large amount of bedrock was being eroded and sediment was transported by rivers from southern Asia into the sea during this period ([PERSON], 2006). In addition, a quite warm and humid climate is thought to have prevailed in southern Asia since the Miocene as mentioned above (e.g., [PERSON] et al., 2002, 2008; [PERSON] et al., 2009; [PERSON] et al., 2005), which probably enhanced chemical weathering of the rocks and further accelerated surface erosion. Hence, since the late Oligocene, interlinking driving mechanisms related with tectonic, climatic and surficial erosion processes have actively regulated the intricate topographic evolution of the SE Tibetan Plateau (Yunnan). It would be interesting for future investigations to test whether or not this area was part of a high-elevation plateau (connected with the high-elevation regions to the north).
## 6 Conclusions
This study presents AFT results for 30 crystalline basement rocks and one Jurassic sandstone sample. Additional zircon LA-ICP-MS U-Pb dating was carried out on four crystalline basement rocks as well. These newly obtained data provide new insights into the late Oligocene-Moecene tectonic and topographic evolution of the southeastern Tibet Plateau (Yunnan, China). The following conclusions could be drawn.
1. Our zircon U-Pb dating results confirm that a large section of Mesozoic crystalline basement rocks make up the main body of the SE Tibetan Plateau (Yunnan area). While along the high-strain belts, Miocene (re-)crystallization age represents the timing of the ductile shearing.
2. Oligocene to Miocene AFT ages were widely recognized across different tectonic units, and from both inside and outside the active zones (i.e., ductile shear zone and river valley). Associated thermal history models indicate rapid late Oligocene to Miocene basement exhumation events, which were coincident with coeval activities of large-scale strike-slip faults and attributed to the compressive tectonic regime due to the ongoing India-Asia convergence. We hence provided mechanistic interpretations for the tectonic deformation in the southeastern Tibet Plateau, in contrast with predictions of the lower crustal flow model that implies late Miocene uplift. Meanwhile, mid-Moecene climate-driving erosion also accelerated the basement exhumation.
3. The southern part of the SE Tibetan Plateau (Yunnan) has experienced active tectonics and intense erosion since the late Oligocene. It still remains at relatively low elevations as a low-relief surface as a result of intricate interaction between intense tectonic activity and surface erosion.
## Data Availability Statement
All data presented in this research are available in the Tables and Supporting Information Files. The samples details are given in Table 1. Apatite fission track dating results are presented in Table 2. Zircon geochronology analysis data are available in Supporting Information S1. Detailed inverse thermal history models for each sample are given in Supporting Information S3. All the new data generated in this study are available at [[https://osf.io/ta8r4/](https://osf.io/ta8r4/)]([https://osf.io/ta8r4/](https://osf.io/ta8r4/)).
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## References
* [PERSON] (2017) [PERSON] (2017). QTQ program: January 2017 release (Version 5.6.0) [Software]. Earth. Retrieved from [[http://iearth.edu.au/codes/QTQ/Vermesch](http://iearth.edu.au/codes/QTQ/Vermesch)]([http://iearth.edu.au/codes/QTQ/Vermesch](http://iearth.edu.au/codes/QTQ/Vermesch))[PERSON] (2018). IspolotR: A free and open toolbox for geochronology: September 2018 release (Version 5.3) [Software]. IspolotR. Retrieved from [[http://isoplot.cs.utl.ac.uk/home/index.html](http://isoplot.cs.utl.ac.uk/home/index.html)]([http://isoplot.cs.utl.ac.uk/home/index.html](http://isoplot.cs.utl.ac.uk/home/index.html)) | wiley | New Constraints on the Late Oligocene‐Miocene Thermo‐Tectonic Evolution of the Southeastern Tibetan Plateau From Low‐Temperature Thermochronology | Zhiyuan He, Linglin Zhong, Kai Cao, Wenbo Su, Stijn Glorie, Kanghui Zhong, Chuang Sun, Johan De Grave | https://doi.org/10.1029/2023tc007881 | 2,023 | CC-BY |
wiley/fd5ecdc1_8de9_4627_a3f9_a362daa70f94.md | # Gr Space Physics
Research Article
University of California
C Berkeley, CA 94721-7405
[PERSON]
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
[PERSON]
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
[PERSON]
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
###### Abstract
In the nightside region of Earth's magnetosphere, braking oscillations or buoyancy modes have been associated with the occurrence of low entropy bubbles. These bubbles form in the plasma sheet, particularly during geomagnetically disturbed times, and because of interchange, move rapidly earthward and may eventually come to rest in the inner plasma sheet or inner magnetosphere. Upon arrival, they often exhibit damped oscillations with periods of a few minutes and are associated with Pi2 pulsations. Previously we used the thin filament approximation to compare the frequencies and modes of buoyancy waves using magnetohydrodynamic (MHD) ballooning and classic interchange theory. Interchange oscillations differ from the more general MHD oscillations by assuming constant pressure along a magnetic field line. It was determined that MHD ballooning and interchange modes are similar for plasma sheet field lines but differ for field lines that map to the inner magnetosphere. This suggested that the classic interchange formulation was only valid in the plasma sheet. This paper tests the hypothesis that the agreement between MHD ballooning and classic interchange could be restored inside a bubble. We create a small region of entropy depletion in the magnetotail and compare the buoyancy mode properties. At some locations inside the bubble, the MHD ballooning buoyancy modes resemble interchange modes but with lower frequencies than those of the unperturbed background. Unstable modes are found on the earthward edge of the bubble, while at the tailward edge, MHD ballooning predicts a slow mode wave solution not seen in the pure interchange solution.
202
probably has more structured entropy profiles as a function of position than such models show. While direct measurements of the entropy are not possible, it is possible to estimate the entropy using a technique developed by [PERSON] et al. (2006) which suggests that there is a lot of entropy structure in the tail (e.g., [PERSON] et al., 2011; [PERSON] et al., 2014; [PERSON] et al., 2010). Some global MHD simulations also develop structure in the entropy profile (e.g., [PERSON] et al., 2017; [PERSON] et al., 2011; [PERSON] et al., 2012; [PERSON] et al., 2021; [PERSON] et al., 2015). The motivation of the work presented here is to examine the properties of MHD buoyancy waves in the vicinity of such a localized reduction of the entropy.
The occurrence of plasma flows as they reach their equilibrium location has been associated with magnetohydrodynamic (MHD) buoyancy waves which are a fundamental wave mode of the magnetosphere. A bubble is an entropy-depleted plasma-sheet filament; that is, it has reduced \(pV^{3/3}\) relative to surroundings. The bubble moves Earthward toward its equilibrium position, where its entropy matches that of the local background environment ([PERSON] et al., 2004; [PERSON] & [PERSON], 2007). The bubble often overshoots its equilibrium position and oscillates a few times ([PERSON] & [PERSON], 1999) as buoyancy wave ([PERSON] et al., 2020, 2022; [PERSON] et al., 2012). Buoyancy waves are analogous to neutral-atmospheric gravity waves, in which the buoyant force is gravity rather than magnetic tension. Magnetospheric buoyancy waves are possibly related to Pi2 oscillations ([PERSON] & [PERSON], 2007; [PERSON] et al., 2010; [PERSON] et al., 2020; [PERSON] et al., 2015; [PERSON] et al., 2023).
To better understand the properties of low entropy bubbles, [PERSON] and [PERSON] (1993, 1999) developed an MHD thin filament model to investigate their properties. The thin filament approach represents a highly idealized approximation to the motion of a field line in a plasma sheet background at equilibrium. This total filament pressure \(p\ +\ B^{2}/2\mu_{0}\) balances the background. The thin filament approximation can be expressed as the solution of 1-D MHD equations that can be accurately solved with little dissipation ([PERSON] & [PERSON], 1999). In that work, it was found that a depleted filament overshoots its equilibrium point, where its entropy matches the background value, and undergoes damped oscillations about that location.
In a follow-up study, [PERSON] et al. (2012) derived an approximate formula for the period of the fundamental oscillation frequency of a thin plasma sheet filament for a 2-D force-balanced tail model. They found that in agreement with much previous work on interchange stability (e.g., [PERSON] et al., 1958), for formula predicts that \(\omega^{2}\) is proportional to the entropy gradient and that the system is interchange unstable if the gradient is negative (i.e., \(pV^{5/3}\) decreases away from the Earth). [PERSON] et al. (2013) compared the results from the [PERSON] et al. (2012) equation with periods measured for 20 flow burst braking-oscillation events and found reasonably good agreement. This interchange oscillation formula, although derived for a very simple case, appears to be useful far beyond the constraints assumed in its derivation.
[PERSON] et al. (2020) used an MHD normal mode analysis to determine the buoyancy frequencies and eigenmodes of an oscillating thin filament. The approach was based on a linear approximation and assumed that the perturbations have time dependence of the form \(e^{-i\omega t}\). This leads to a set of eigenvalue equations for the displacement of the fieldline in the parallel \(\left(\xi_{\parallel}\right)\) and perpendicular \(\left(\xi_{x}\right)\) directions ([PERSON] et al., 2020, equations 32 and 33).
\[\frac{\partial^{2}\xi_{\parallel}}{\partial s^{2}}c_{1}(s)+\frac{\partial \xi_{\parallel}}{\partial s}c_{2}(s)+\xi_{\parallel}c_{3}(s)+\frac{\partial \xi_{x}}{\partial s}c_{4}(s)+\xi_{x}c_{5}(s)=-\mu_{0}\rho\omega^{2}\xi_{ \parallel} \tag{1}\]
\[\frac{\partial\xi_{\parallel}}{\partial s}c_{6}(s)+\xi_{\parallel}\ c_{7}(s)+ \frac{\partial^{2}\xi_{x}}{\partial s^{2}}c_{8}(s)+\frac{\partial\xi_{x}}{ \partial s}c_{9}(s)+\xi_{x}c_{10}(s)=-\mu_{0}\rho\omega^{2}\xi_{\epsilon} \tag{2}\]
The coefficients \(c_{1}(s)\) to \(c_{10}(s)\) are a function of the background field ([PERSON] et al., 2020, equations 54-63). Infinite conductance boundary conditions were assumed at the ionospheric footprints. The resulting two coupled equations of motion for the perpendicular and parallel displacements of mass points along the filament were solved as an eigenvalue problem to obtain the associated eigenfrequencies and eigenmodes. This approach differed from other approaches that looked at both poloidal and toroidal Alfven and slow mode waves (e.g., [PERSON] et al., 1989; [PERSON] et al., 2022; [PERSON] et al., 2017) that assumed low plasma beta configurations (\(\beta<1\)) and a dipolar magnetosphere. Many other calculations of ballooning modes using distinct backgrounds and assumptions exist throughout the literature (e.g., [PERSON] et al. (1958), [PERSON] et al. (1989), [PERSON] et al. (1989), [PERSON] et al. (1989), [PERSON] et al. (1991), [PERSON] (1999), [PERSON] et al. (2008), [PERSON] (2004, 2006). The primary purpose of the present paper is to examine the nature of ballooning modes in the presence of an average magnetospheric background modified by the presence of entropy depletions known as bubbles. It uses a more realistic magnetospheric background and a more flexible eigen-analysis than many previous publications, which often assume further simplified backgrounds. For example, the eigenfunctions calculated in the [PERSON] et al. (1991) paper assume the ray-tracing approximation, a short-wavelength version of the WKB approximation ([PERSON], 1975), whereas the present results solve the exact eigenvalue problem and pick out the long wavelength modes. [PERSON] et al. (1991) assumes axisymmetry with a constant rotation equilibrium state (more suitable for an analysis of Jovian magnetospheres), whereas the present results are determined in the noon-midnight meridional plane and do not treat the azimuthal structure of the modes. [PERSON] et al. (1991) includes a gravitational term which is neglected in the present treatment. Another noteworthy difference resulting from the [PERSON] et al. (1991) derivation is that it only allows for real solutions, whereas the thin filament code allows for instability to naturally result because of negative entropy gradients. We could compare our treatment to a variety of other treatments in a similar manner, but the aim of this illustration is to show that the literature often contains eigen-analyses which are non-trivial to compare, as they are more constrained in some dimensions of analysis and less constrained in others.
[PERSON] et al. (2020) used the MHD normal analysis to determine the lowest frequency poloidal modes that were symmetric about the equatorial plane. They found that for field lines that map deep into the plasma sheet (\(\left|x_{\mathrm{e}}\right|>15\,R_{E}\)), these modes were buoyancy modes while field lines that mapped closer to the Earth (inside \(\left|x_{\mathrm{e}}\right|\sim 6\,R_{E}\)) resembled slow mode waves. They also found that the predicted buoyancy frequencies were in surprisingly good agreement with the frequencies predicted by [PERSON] et al. (2012), even though this formula used a much less rigorous approach and was derived for the plasma sheet.
To better understand the relationship between MHD buoyancy modes and interchange in the thin filament model, [PERSON] et al. (2022) looked at pure interchange (PI) modes and compared them to the less constrained MHD normal mode analysis. Using an energy approach like that of [PERSON] et al. (1958), a buoyancy frequency for the interchange modes was derived by assuming that the oscillations are the result of the exchange of two adjacent field lines. The frequency for pure interchange oscillation was obtained as:
\[\omega_{PI}^{2}=\frac{p}{\rho}\frac{\left(\frac{p_{\mathrm{e}}^{\prime}}{p}+ \frac{5}{3}\frac{V_{\mathrm{e}}^{\prime}}{V}\right)\left(\frac{V_{\mathrm{e}} ^{\prime}}{V}-\frac{\left\langle\beta\right\rangle}{2}\frac{p_{\mathrm{e}}^{ \prime}}{p}\right)}{\left(1+\frac{5}{6}\langle\beta\rangle\right)\left(\frac{ \xi_{\perp}(s)^{2}}{\xi_{\perp}(0)^{2}}\!\!\left(1+\frac{\xi_{\parallel}(s)^{ 2}}{\xi_{\parallel}(0)^{2}}\right)\right)} \tag{3}\]
where \(\xi_{\perp}(s)\) and \(\xi_{\parallel}(s)\) are the perpendicular and parallel displacements of mass points with respect to the background field line because of interchange, and \(\rho\) is the mass density. Other variables and conventions are as defined above. The \"e\" subscript indicates that a term is evaluated in the equatorial plane, equivalent to setting \(s=0\) in the displacements. The terms inside the brackets represent the flux tube average of the quantity.
\[\left\langle A\right\rangle\equiv\frac{fA\,\frac{ds}{B}}{f\frac{ds}{B}}. \tag{4}\]
The first parenthetical term in the numerator is the entropy gradient evaluated at the equatorial plane, while the second parenthetical term results from the Alfvenic-timescale pressure re-equilibration of the filament to the local background pressure ([PERSON], 1985). The pressure and flux tube volume are constants for a field line under the interchange approximation, so do not need subscripts. The [PERSON] et al. (2012) formula was compared to the [PERSON] et al. (2020) normal analysis, modified to include zero ionospheric conductance as well as the pure interchange result (Equation 3). They found that tail-like field lines that cross the equatorial plane in the plasma sheet (\(\left|x_{\mathrm{e}}\right|>15\,R_{E}\)) are where the interchange results are most consistent with MHD ballooning normal mode analysis. One requirement for pure interchange is that the resulting pressure perturbation is constant along a field line, which is not generically the case for the more general MHD buoyancy modes.
This paper is a follow-up to the [PERSON] et al. (2022) paper, where we investigate the properties of buoyancy waves inside a low entropy bubble. This was motivated by the realization that while the MHD ballooning and classic interchange treatments deviated from one another for the previously considered average inner magnetosphere. However,13 a more realistic inner magnetosphere is often modified by the presence of low-entropy bubbles which have arrived subsequent to magnetic reconnection further out in the tail during geomagnetically disturbed times. We compare the results from two approaches: (a) the MHD normal mode analysis described in [PERSON] et al. (2020) modified to use zero conductance ionospheric boundary conditions as in [PERSON] et al. (2022); (b) the pure interchange approach described in [PERSON] et al. (2022). A third approach using the [PERSON] et al. (2012) formula was found to have quite good agreement for the frequencies predicted by the two approaches, but for simplicity will not be included in this paper. The results are compared, including the predicted frequencies and associated normal mode and interchange perturbations. The rest of the paper describes the basic approach, including a brief description of the background equilibrium and how the low entropy perturbation was introduced. We show two examples and discuss the results.
## 2 Approach
### Background Model of an Average Magnetosphere
For this study, we started with the same background field model as in [PERSON] et al. (2020, 2022), which consists of a Kp = 2 [PERSON] (1989) model magnetic field and the pressure profile derived by combining a quiet curve from [PERSON] et al. (1987) for \(|x_{\rm r}|<8\,R_{\rm F}\) and [PERSON] et al. (1989) for \(|x_{\rm r}|>8\,R_{\rm F}\). The background field is relaxed to equilibrium in the \(x\)-\(z\) plane using a 2-D, high-resolution version of the friction code ([PERSON] et al., 2003). The density model is taken from the Kp = 2 [PERSON] et al. (2000) model for \(|x_{\rm r}|<8\,R_{\rm F}\) merged smoothly to a [PERSON] and [PERSON] (2003) model for \(|x_{\rm r}|>10\,R_{\rm F}\). The profile for this model along the \(x\)-axis is shown in Figure 1, which includes the pressure, magnetic field, and density model.
### Local Entropy Depletion
To locally reduce the entropy in order to simulate the presence of a bubble, we take the background entropy profile and impose an indentation (local entropy depletion) along the whole field line over some small region in the equatorial plane. This indentation is specified using four control points (\(x_{1},x_{2},x_{3},x_{4}\)) and fitting three bicubic spline curves as illustrated in Figure 2. The spline fits are set between the control points (\(x_{\rm i}-x_{i+1}\)), for \(i=1,2,3\). At the endpoints (\(x_{\rm i}\) and \(x_{\rm k}\)) the value and derivative of \(pV^{5/3}\) is matched to the original unmodified background, ensuring a smooth transition between regions. At the middle control points (\(x_{2}\) and \(x_{3}\)) the value of \(pV^{5/3}\) and its derivative of the fitted curve is specified. In the cases shown below, the derivative is set to zero for simplicity at these locations. By field line tracing from each grid point in the 2D region to the intersection point on the equatorial plane, any grid point that is magnetically connected to this region between the endpoints has its pressure modified to match the specified value of \(pV^{5/3}\). This new configuration is then iterated to approximate force balance as before using a high-resolution version of a 2D friction code ([PERSON] et al., 2003), which results in a change in the entropy profile as the system relaxes to a new equilibrium now containing a localized entropy depletion. This equilibrium-setting process is important for the background to be suitable for linear stability analysis as the use of perturbation theory to perform an eigen-analysis presupposes an equilibrium background. In short, the relaxation procedure is necessary because the indentation procedure does not guarantee the preservation of pressure balance.
Two cases are presented here: Case 1 represents a bubble near the Earth while Case 2 represents a bubble further out in the plasma sheet. For the interested reader, a third case that is further out in the tail is available in the supporting documents. This case results in a larger disruption to the tail configuration and we have less confidence in the equilibrium results for this case. For the two cases shown in the paper, the equilibration process was evolved
Figure 1: Plot of background magnetosphere model used, showing the pressure, \(B_{\rm i}\), density, entropy \(pV^{5/3}\), and flux tube volume \(\
u\) along the tail axis in the equatorial plane as a function of equatorial distance. Note that the plasmaquasae at \(-5\,R_{\rm F}\) is incorporated in the density background. The flux tube volume is computed by integrating \(f\,ds/B\) along the fieldline (s) using the background field.
until the configuration stopped changing, thus approaching an equilibrium. For the third case, the equilibration process never settled down to a static equilibrium. In addition, the reconfiguration for the third case was more drastic both in the bubble and surrounding background.The parameters for the 2 cases used are specified in Table 1. The scale size of the bubble was chosen to approximately match the inferred scale sizes from observations of bursty bulk flows (e.g., [PERSON] et al., 2015; [PERSON] et al., 2019). For example, Figure 2 of [PERSON] et al. (2015) indicate that the average speed of an Earthward moving BBF inside of 10 RE is approximately 100 km/s and lasts about 50 s. This corresponds to an approximate size of 1 RE with a transition region on either side of the bubble adding approximately another 1 RE to the size of the bubble.
Figures 3 and 4 show the resulting configuration before and after equilibration. The before plot includes the indentation but has not been restored to equilibrium, while the after plot shows the preservation of the indentation but is now at equilibrium. In all cases, the tailward portion of the bubble moves slightly earthward as the system relaxes to equilibrium, thus reducing the size of the entropy-depleted region. In Figure 4, which correspond to Case 2 where the average plasma beta is higher, which results in a larger change in the and the resulting depleted region for Case 2 is smaller after equilibration. The relative magnetic field change increases with the placing the bubble tailward. The entropy value at the control points \(x_{2},\text{and}\ x_{3}\) were chosen so as have a slight positive tailward gradient and thus avoid unstable modes in this region, but this does not preclude unstable modes between the control points \(x_{1}\) and \(x_{2}\) at the Earthward end of the bubble. We do not include cases where the bubble was placed further tailward, as it resulted in a dramatic reconfiguration of the tail during the equilibration process and a collapse of the bubble. As can be seen in Figure 1, the background magnetic field had a \(B_{z}\) minimum centered at around \(x_{e}\ =\ -16\ R_{E}\). For the interested reader, a third case further for a bubble further out in the tail is included in the supplemental material.
## 3 Results
### Case 1
The first case is the indentation is the closest to the Earth. Table 2 lists the results on some sampled field lines inside the bubble. The solid line in the top panel of Figure 5 is a plot of the entropy profile for both the unperturbed background (blue) and the indented profile (orange), and the dashed line is the corresponding flux tube volume averaged plasma beta (see Equation 4). Note that the profiles are slightly different even outside the control region because of the equilibration process. Also, the values of the entropy are slightly different from the specified values for the same reason. The second panel of Figure 5 shows the \(z\)-component of the magnetic field and pressure along the \(x\)-axis (in the equatorial plane) for both the background field and the bubble indentation. The third panel of Figure 5 shows the computed buoyancy frequencies for the background field and bubbles using two different techniques, the curves labeled MHD correspond to the normal mode calculation, the curves labeled \"PI\" are from the pure interchange calculation (Equation 3). These frequencies are scaled to the background density profile shown in Figure 1, as described above and in [PERSON] et al. (2020). Since the eigenvalues can in principle be imaginary, both real and imaginary parts are included, where the imaginary components are shown as a dashed line with a shaded background and indicate regions of instability. The change in frequency at around \(x_{e}\ =\ -5\ R_{E}\) corresponds to the plasmapause location in the [PERSON] et al. (2000) model.
Figure 6 shows the modes for the unperturbed background and Figure 7 for the bubble. Note that the displacement at the ionospheric endpoints is small but not zero. For this case, Figure 7 shows that there is an overlap of the MHD normal modes and the pure interchange results at the locations \(x_{e}\ =\ -4.6,\ -4.8,\ -5.0,\ \text{and}\ -5.2\ R_{E}\). In Figure 8 and Table 2 the normalized pressure perturbation from the MHD normal mode analysis as a function of distance \(s\) (\(R_{E}\)) along the field line (from the equator) for the background field is a solid line and a dashed line for Case 1 bubble. The standard deviation
\begin{table}
\begin{tabular}{l l l l l l l} Case & \(x_{1}\) & \(x_{2}\) & \(pV^{\prime 5/3}(x_{2})\) & \(x_{3}\) & \(pV^{\prime 5/3}(x_{3})\) & \(x_{4}\) \\ \hline
1 & \(-4\) & \(-4.5\) & 0.001 & \(-5.5\) & 0.0012 & \(-6\) \\
2 & \(-6\) & \(-6.5\) & 0.008 & \(-7.5\) & 0.01 & \(-8\) \\ \hline \end{tabular} _Note._ Distances are in RE and \(pV^{\prime 5/3}\) in Units of \(nPa\left(\frac{6}{25}\right)^{5.5}\).
\end{table}
Table 1: Specification of Entropy Indentation Geometry for Two Cases
Figure 2: Sketch of the entropy profile along the equatorial plane along with the entropy-depleted region (in blue) showing the control points.
of pressure along the field line (in nPa) for the background and bubble is also shown. For this case, the pressure perturbation at \(x_{v}~{}=~{}-4.6,~{}-4.8,~{}-5.0\) and \(-5.2~{}R_{E}\) is approximately constant along the field line, as can be seen in the reduction in the standard deviation of the pressure perturbation compared to the background. This is consistent with the modes at these locations being pure interchange. All displacements are normalized by the maximum displacement of all the modes ([PERSON] et al., 2020).
The computed frequency at these locations is much lower than the ones obtained in the background case with no bubble, and all two approaches give quite consistent results at these locations. This would imply that the buoyancy
Figure 4: Same format as Figure 3 for Case 2 where the indentation is placed between \(x_{v}~{}=~{}-6~{}R_{E}\) and \(-8~{}R_{E}\).
Figure 3: Top panel shows \(pV^{53}\) in units of \(nPa(\frac{R_{E}}{2})^{53}\) and field line average plasma beta (Equation 4) before and after equilibration for Case 1 where the indentation is placed between \(x_{v}~{}=~{}-4R_{E}\) and \(-6~{}R_{E}\). The bottom panel shows \(B_{z}\) (in nT) and pressure (in nPa).
frequencies inside a low entropy bubble with a small entropy gradient would be small and closer to the values one would expect for the plasmasheet rather than the inner magnetosphere. For \(x_{e}\ =\ -4.2\) and \(-4.4\ R_{E}\) the solution is imaginary, indicating instability. The large value of the frequency tailward of the region of instability (between \(x_{e}\ =\ -5\) and \(-6\ R_{E}\)) is a result of a large negative gradient in \(p\,V^{5/3}\) as its value returns to the background value outside the bubble. The MHD normal modes for \(x_{e}\ =\ -5.5\ R_{E}\) indicate slow mode solutions as the parallel displacement is much larger than the perpendicular displacement. For this location, the MHD normal mode predicts a much lower frequency than the pure interchange.
### Case 2
The results for Case 2 are shown in Figure 9 and summarized in Table 3. The ordinary (unindented) background and the bubble oscillation frequencies are quite different and vary noticeably between \(-6\) and \(-8\ R_{E}\). Note that the eigenvalues are only purely real or imaginary as there is no dissipation in the system. In the case of the ordinary background fields, there are only real eigenvalues, indicating a stable equilibrium with no dissipation. The bottom panel shows the corresponding results for the bubble indentation. For this case, there is a shaded region of imaginary eigenvalues between approximately \(x_{e}\ =\ -6.1\) and \(-6.3\ R_{E}\) where the gradient in \(p\,V^{5/3}\) is positive (decreasing away from the Earth), as the chosen entropy value is set to allow a change in gradient at the earthward edge of the imposed bubble. The large value of the frequency tailward of the region of instability (between \(x_{e}\ =\ -7\) and \(-8\ R_{E}\)) is a result of a large negative gradient in \(p\,V^{5/3}\) as its value returns to the background value outside the bubble. No such increase in frequency is seen in the MHD normal mode result. The reason for the difference can be seen in Figures 10 and 11, which plot the normalized modes for both the pure interchange (solid line) and the MHD normal mode calculation. As before, the normalization is chosen relative to the maximum of all the modes (see [PERSON] et al., 2020 for a discussion of the normalization). Figure 10 is from the background field and Figure 11 for the imposed bubble indentation. In Figure 11, at \(x_{e}\ =\ -7.5\ R_{E}\), which corresponds to the location where there is a jump in the frequency in Figure 9, the parallel displacement for the MHD is larger than the perpendicular displacement, which is what would be expected from an MHD slow mode. These results suggest that to remain compatible with pure interchange assumptions at this location a much higher frequency is needed, while the MHD solution produces a lower frequency but as a slow mode. In other words, the assumptions underlying the pure interchange calculation prevent the slow mode observed in the MHD results from showing up. In addition, as can be seen in Figure 11, at \(x_{e}\ =\ -6.5\ R_{E}\) the pure interchange solution closely resembles the MHD solution, which implies the MHD solution is closer to being a pure interchange mode at this location. This can be confirmed by the pressure perturbation, which is shown in Figure 12, which shows a reduction in the standard deviation of the pressure along the field line from 0.759 to 0.154 nPa. We see similar behavior at \(x_{e}\ =\ -7.2\ R_{E}\). Unstable modes are also shown in Figure 12 at \(x_{e}\ =\ -6.0\) and \(-6.2\ R_{E}\). At the sampling locations
\begin{table}
\begin{tabular}{l c c c c l} \hline Equatorial footprint & Background frequency (Hz) from & Bubble frequency (Hz) from & Background pressure & Bubble pressure standard & \\ location (\(R_{E}\)) & MHD normal mode & MHD normal mode & standard deviation (nPa) & deviation (nPa) & MHD mode \\ \hline \(-6.0\) & 0.0105 & 0.0150 & 0.981 & 0.854 & \\ \(-5.5\) & 0.0107 & 0.0087 & 1.362 & 0.895 & slow mode \\ \(-5.2\) & 0.0109 & 0.0027 & 1.711 & 0.133 & pure interchange \\ \(-5.0\) & 0.0112 & 0.0033 & 2.026 & 0.063 & pure interchange \\ \(-4.8\) & 0.0082 & 0.0025 & 2.427 & 0.092 & pure interchange \\ \(-4.6\) & 0.0057 & 0.0010 & 2.934 & 0.149 & pure interchange \\ \(-4.4\) & 0.0053 & 0.0060i & 3.674 & 0.856 & unstable \\ \(-4.2\) & 0.0050 & 0.0081i & 4.390 & 2.532 & unstable \\ \(-4.0\) & 0.0048 & 0.0035 & 5.428 & 2.225 & \\ \hline \end{tabular} _Note._ Column 1 shows the sampling location in the equatorial plane, the second and third column frequency of the normal mode oscillation from the background and the bubble frequency respectively, with ‘i’ representing imaginary frequencies or instability. The fourth and fifth columns show the standard deviation of the isotropic pressure perturbation for the background and bubble, and the sixth column is the mode produced by the MHD normal mode analysis.
\end{table}
Table 2: Summary of the Results for Case 1\[\text{at}\,x_{e}\ =\ -6.4,\ -6.5\ \text{and}\ -7.2\ R_{E}\ \text{shows a good overlap between the MHD normal mode and pure interchange and the pressure perturbation is approximately constant along the field lines. Outside the bubble region, tailward of \(x_{e}\ =\ -8\ R_{E}\) and earthward of \(x_{e}\ =\ -6\ R_{E}\), the solutions are close to the background field; that is, the frequency curves in the middle and lower panels of Figures 10 and 11 are almost identical. Any difference between them is due to the equilibration of the tail after the bubble indentation was introduced.
Figure 5.— This is the result for Case 1. The solid line in the top panel shows \(p\dot{v}^{2}\) and the dashed line is the field line average plasma beta for both the background and perturbed configuration. The units for \(pV^{55}\) are \(nPa\ (R_{E}/nT)^{5}\). The second panel shows the magnetic field (\(R_{z}\)) in nT and pressure in nPa. The third panel shows the computed frequencies (in Hz) for the unperturbed field using the MHD normal mode (blue), pure interchange (red). The solid lines are for real values, the dashed lines imaginary. In this case, all frequencies are real. The bottom panel shows the computed frequencies for the perturbed background, showing a shaded region of imaginary frequencies between \(x_{e}\ =\ -4.1\) and \(-4.4\ R_{E}\).
Figure 6: Comparison of wave modes from the MHD normal mode (blue line) and classic interchange analysis (red line) for the background field as a function of distance, \(s(R_{E})\), along the field line from the equator. The solid curves represent the perpendicular displacement and the dashed line is the parallel displacement. The associated MHD normal mode frequencies are also shown. All results are normalized to the maximum displacement of the largest mode.
Figure 7: Same format as Figure 6 for the bubble indentation field for Case 1. Note the overlap of the modes for \(\chi_{v}=-4.6,\ -4.8,\ -5.0\ \mathrm{and}\ -5.2\ R_{E}\). Note that for \(\chi_{v}=-4.2\) and \(-4.4\ R_{E}\) the solution is imaginary, indicating instability. The MHD normal modes for \(\chi_{v}=-5.5\ R_{E}\) indicate slow mode solutions, as the parallel displacement is much larger than the perpendicular displacement.
Figure 8: Pressure normalized perturbation from the MHD normal mode analysis as a function of distance s (\(R_{E}\)) along the field line (from the equator) for the background field is a solid line and a dashed line for Case 1 bubble. The standard deviation of pressure along the field line (in Pa) for the background and bubble is also shown. For this case, the pressure perturbation at \(x_{\rm e}=-4.6,\ -4.8,\ -5.0\) and \(-5.2\ R_{E}\) is approximately constant along the field line, as can be seen in the reduction in the standard deviation of the pressure perturbation compared to the background.
## 4 Discussion
The thin filament approximation, while limited in many ways, has proven to be a useful approach to looking at the properties and motion of entropy-depleted field lines in a background medium. The approach follows a one-dimensional field line, neglecting the motion of the field lines transverse to the noon-midnight meridional (\(x\)-\(z\)) plane. However, for the interchange of two field lines to occur, they must move past one another in such a way that both cannot remain in-plane. In addition, the MHD thin filament code neglects feedback from the background and any other filament while this coupling is explicitly included in the interchange derivation. The coupling to the other filaments should be included to properly compare some features of the MHD thin filament model to the classic interchange model. This work is a follow-up to the previous study looking at buoyancy modes where the entropy has been modified relative to the ordinary background to include a bubble, all within the framework of the MHD thin filament approximation ([PERSON], 1999; [PERSON] et al., 2012). After imposing entropy modifications at two locations in the nightside magnetosphere, we used two different approaches to examine the properties and frequencies of buoyancy modes within these entropy-depleted regions. Our methodology (average background, indentation-relaxation, eigen-analysis) presupposes that the bubble can be treated quasi-statically on the timescales of the oscillations. The two approaches used in this study are.
1. MHD normal mode calculation, the basic procedure is described in [PERSON] et al. (2020) except that the ionospheric boundary condition is replaced with a zero conductance, to be consistent with the interchange assumption. The modifications to the boundary conditions are described in [PERSON] et al. (2022).
2. Pure interchange (Equation 3) as described by [PERSON] et al. (2022), used an energy argument to deduce the modes and frequencies that one would expect when the assumptions of the classic interchange theory is applied. This assumption entails that both the background pressure and associated pressure perturbation that arises from interchange is constant along a field line.
Two cases are examined:
Case 1 involves an entropy depletion (bubble) centered at \(x=-7~{}R_{E}\) where it is found that the frequency of the interchange mode is much lower than a typical field line would be than a background field line at that location. Some of field lines resembled pure interchange modes, as shown in Figure 8 and Table 2 for the field line crossing the equatorial plane at \(x_{e}=-6.4\) and \(-6.5~{}R_{E}\), where the pure interchange mode and the MHD normal mode overlap quite closely and the pressure perturbation from the MHD result is approximately constant along the field line. The analysis also reveals the existence of unstable modes between \(x_{e}~{}=-6.4\) to \(-7.2~{}R_{E}\) where the entropy gradient changes sign to decreasing tailward. All two approaches predict a very similar buoyancy frequency with the normal mode and interchange analysis having the closest agreement. The MHD result predicts slow mode waves (\(x_{e}~{}=-7.5~{}R_{E}\) in Figure 8 and Table 2) with lower frequencies, while the pure interchange result predict a larger frequency. Since the MHD result is more general and does not restrict itself to any interchange assumptions, one would expect that this result is likely more physically reasonable. Nevertheless, except for this tailward region of the bubble, it is remarkable how well the two approaches agree, in particular regarding the frequencies.
Case 2 represents a bubble that is further out in the tail and resulted in a small region of unstable modes as in Case 1 and also lower frequencies inside the bubble, however, the modes are less like pure interchange modes than in Case 1. In both cases, we find that the buoyancy frequencies are lower in the bubble, and on the field lines that crosses the equator at \(x_{e}~{}=-6.4,~{}-6.5,~{}\mathrm{and}~{}-7.2~{}R_{E}\) the MHD result resembles pure interchange modes where pressure perturbation is approximately constant along the field line (see Figure 12, Table 3). We also find that on the tailward portion of the bubble, the buoyancy mode results disagree, the MHD normal mode solution finds a lower frequency solution than pure interchange and produces a slow mode wave with motion dominated by the parallel displacements of mass points lining the filament. Nevertheless, it is surprising how well the frequencies arrived at using very different methods agree given that the simplifying assumptions implicit in the MHD thin filament code.
Now, we discuss our implicit interpretation of disagreement between the two methods under consideration (MHD vs. pure interchange). In some sense, the pure interchange approach is a \"more constrained\" approach in virtue of the additional assumption of pressure constancy along a field line. For this reason, we interpret a disagreement between the results of the interchange approach and the MHD approach as a violation of the additional assumptions behind pure interchange. In short, we imply that the ideal MHD is closer to ground truth. However,there is reason to approach such an assumption with caution. It may be that the conditions of the magnetotail are such as to violate MHD while producing kinetic effects that substantiate a pure interchange treatment.
MHD treatments presuppose that interactions between the plasma and electromagnetic fields occurs locally, which requires that the frequencies be much slower than the gyrofrequency and wavelengths much later than gyroradius. However, when the magnetosphere is stressed, the near Earth plasma sheet (NEPS) undergoes
Figure 9.— This shows the results for Case 2, the solid line in the top panel shows \(\rho V^{3}\) and the dashed line is the field line average plasma beta for both the background and perturbed configuration. The units for \(pV^{35}\) are \(nPa\left(\frac{R_{c}}{kT}\right)^{35}\). The second panel shows the magnetic field \(\left(R_{c}\right)\) in nT and pressure in nPa. The third panel shows the computed frequencies (in Hz) for the unperturbed field using the MHD normal mode approach (blue) and pure interchange (red). The solid lines are for real solutions, the dashed lines are imaginary solutions. In this case, all frequencies are real. The bottom panel shows the computed frequencies for the perturbed background, showing a shaded region of imaginary frequencies between \(x_{c}=-6.0\) and \(-6.2\ R_{c}\).
thinning and the local field line curvature increases (e.g., [PERSON] et al., 2004). When the field line curvature becomes comparable to the local gyroradius, the ion orbits become stochastic, undergoing stochastic (non-adiabatic) pitch-angle scattering each time it crosses the equatorial plane ([PERSON], 1989). This violates bounce invariance, since its motion is largely adiabatic away from the equatorial plane, meaning that one should in such cases perform a bounce-averaging. These arguments are considered in great detail in [PERSON] (1994), [PERSON] et al. (1994), where a linear kinetic Vlasov theory for ballooning-interchange modes is developed to capture NEPS dynamics. The paper also provides support for performing flux tube (field line) averaging (bounce averaging and pitch angle averaging) of drift frequencies in cases of high stochasticity, since the individual particles will explore most of the flux tube volume in a small number of bounces.
The main implication of these points is that it may be more realistic in the NEPS to entertain the validity of the interchange assumption over MHD, which allows greater flexibility in the pressure adjustments. In short, where the results of the interchange analysis deviate from the MHD analysis above, it is not obvious that the MHD results are the more trustworthy. Perhaps we should remain open to the question of which conditions are more well-satisfied in the NEPS. For example, we were unable to find any observational data pertaining to slow modes toward the tailward region of flow bursts. Observational data could confirm or refute the presence of these modes near the bubble's tailward edge, in which case some empirical support would be provided for the greater applicability of either the MHD approach or the interchange approach, respectively.
## 5 Conclusion
Using empirically based magnetic field and pressure models, the entropy \(pV^{5/3}\) is generally taken on global scales to be a smooth background function equatorial distance downtail. Additionally, the entropy usually increases tailward. Here, we let the tailward entropy gradient vary substantially in a limited spatial region. We find that if the entropy varies but increases tailward throughout some region, then the buoyancy frequency varies substantially but remains real (indicating a stable configuration). If the entropy gradient decreases tailward in some small region (say, toward the front of the bubble), then the buoyancy frequency becomes imaginary, indicating a region of local instability. If the entropy gradient increases tailward and is not too sharp, then the buoyancy frequency agrees with interchange calculations, even in the inner magnetosphere where previous disagreement was found. Except for some notable locations on the trailing edge of the bubble, the two approaches agree in their prediction of the buoyancy frequencies.
A main result suggested by our findings is that in the presence of bubbles, which frequently show up in the region during geomagnetically disturbed times, such as storms and any substorm expansion phase, the agreement between the MHD and the classic interchange treatments is restored where previous average magnetosphere results showed a disparity in the inner magnetosphere. Our interpretation of these results is that the pure interchange
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline Equatorial footprint & Background frequency (Hz) from & Bubble frequency (Hz) from & Background pressure & Bubble pressure standard & \\ location (\(R_{\rm E}\)) & MHD normal mode & MHD normal mode & standard deviation (nPa) & deviation (nPa) & MHD mode \\ \hline \(-9.0\) & 0.0118 & 0.0150 & 0.289 & 0.272 & \\ \(-8.0\) & 0.0114 & 0.0087 & 0.414 & 0.370 & \\ \(-7.5\) & 0.0112 & 0.0027 & 0.499 & 0.501 & slow mode \\ \(-7.2\) & 0.0110 & 0.0033 & 0.560 & 0.119 & pure interchange \\ \(-6.5\) & 0.0107 & 0.0025 & 0.759 & 0.154 & pure interchange \\ \(-6.4\) & 0.0106 & 0.0010 & 0.792 & 0.217 & pure interchange \\ \(-6.2\) & 0.0106 & 0.0060i & 0.877 & 0.627 & unstable \\ \(-6.0\) & 0.0105 & 0.0081i & 0.981 & 0.578 & unstable \\ \(-5.0\) & 0.0122 & 0.0035 & 2.026 & 2.049 & \\ \hline \hline \end{tabular} _Note._ Column 1 shows the sampling location in the equatorial plane, the second and third column frequency of the normal mode oscillation from the background and the bubble frequency respectively, with ‘i’ representing imaginary frequencies or instability. The fourth and fifth column show the standard deviation of the pressure perturbation for the background and bubble, and the sixth column is the mode produced by the MHD normal mode analysis.
\end{table}
Table 3: Summary of the Results for Case 2 Figure 10: Same format as Figure 6 for Case 2 for the background field.
Figure 11: Same format as Figure 7 for the bubble indentation field for Case 2. Note the overlap of the modes for \(x_{e}=-6.4\), \(-6.5\) and \(-7.2\ R_{E}\). Note that for \(x_{e}=-6.0\) and \(-6.2\ R_{E}\) the solution is imaginary, indicating instability. At \(x_{e}=-7.5\ R_{E}\) we see slow mode waves in the MHD normal mode solution, where motion is dominated by parallel displacement.
Figure 12: Pressure normalized perturbation from the MHD normal mode analysis as a function of distance s (\(R_{E}\)) along the field line (from the equator) for the background field is a solid line and a dashed line for Case 2 bubble. The standard deviation of pressure along the field line (in nPa) for the background and bubble is also shown.
treatment is more reasonable in the inner plasma sheet and inner magnetosphere when the magnetotail is disturbed by the presence of low entropy bubbles, as compared to an average quiet-time magnetosphere.
## Data Availability Statement
The software on which this article is based are available in Toffoletto (2024).
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wiley/fd51f375_48cb_4ef4_bb20_47bfd034a5fe.md | # Geochemistry, Geophysics, Geosystems
[PERSON]
[PERSON]
primary mechanism for strain accommodation throughout the crust (e.g., [PERSON] et al., 2006; [PERSON] et al., 2005; [PERSON] et al., 2019) and mantle lithosphere (e.g., [PERSON] et al., 2010; [PERSON] et al., 2006; [PERSON] et al., 2019). However, problematic in this picture is the low-lying, broadly rifted, and as-yet poorly studied Turkana Depression, separating the elevated Ethiopian and East African plateaus (Figure 1a). Precisely how Cenozoic strain has developed here is uncertain, not least because the Turkana Depression, herein referred to as Turkana, is host to a failed, NW-trending Mesozoic rift system (Figure 1a; e.g., [PERSON] et al., 1987), parts of which were below sea-level in Miocene times ([PERSON] et al., 2015). Geodetic data indicate 40%-100% of present-day strain is localized across faults and eruptive volcanic centers below Lake Turkana, meaning that southern Turkana may be in a state of incipient strain localization at crustal depths ([PERSON] et al., 2020). Whether this pattern is mirrored at mantle lithospheric depths, remains unresolved, including whether or not plate-scale magma-assisted extension is now underway. Strain patterns in northern Turkana and the southwestern Ethiopian plateau are still poorly resolved.
Recent analog experiments and numerical models seeking to understand the evolution of rift linkage between the laterally offset MER and Eastern Rift have treated the Turkana Depression as a relatively simple zone of previously thinned plate between two strong plateaus ([PERSON] et al., 2017; [PERSON] et al., 2019). However, Turkana likely marks a zone of significant material heterogeneity (e.g., [PERSON] et al., 1987; [PERSON] and [PERSON], 1993), rendering these models overly simplistic. Likewise, Cenozoic magmatism and faulting occurred diachronously across the breadth and length of the Depression, suggesting complex plume-lithosphere
Figure 1.— (a) Tectonics of the Cenozoic East African Rift System. The Turkana Depression is shown within the dashed box. Neogene, Paleogene, and Cretaceous rift basins originating from Mesozoic rifting are also shown ([PERSON], 2018; [PERSON], 2018). Triangles are Holocene and Pleistocene volcanic centers (Global Volcanism Program, 2013). (b) The tectonic setting of the Turkana Depression, including the location of major (thick solid lines), minor (thin solid lines), and inferred (dashed lines) Cenozoic faults taken from [PERSON] et al. (2017) and [PERSON] and [PERSON] (1978), and volcanic regions taken from [PERSON] (2017) and [PERSON] (2019). Arrows show plate motion relative to a fixed Nuthan plate in mm/yr ([PERSON] et al., 2020). Earthquakes occurring from January 2019 to September 2020 are shown as circles ([PERSON] et al., 2020).
interactions (e.g., [PERSON] et al., 2019; [PERSON] et al., 2000). For example, the MER adopts its most distributed character in southern Ethiopia which also marks the northernmost limit of Mesozoic extension (Figures 1a and 1b). Whether this broadening is due to inherently different lithosphere in southern Ethiopia or whether complex MER-Eastern Rift linkage kinematics are at play, is unknown. Improved constraints on Turkana's lithospheric seismic structure are thus essential to our understanding of Cenozoic strain development.
Another research question exemplified by the East African Rift (EAR) concerns the cause of Cenozoic flood basalt magmatism (Figure 1a), specifically whether it is related to elevated mantle temperatures resulting from a single or multiple mantle plumes (e.g., [PERSON] et al., 1998; [PERSON] et al., 2000; [PERSON] et al., 2012). The two-plume hypothesis would provide an elegant explanation for the existence of the elevated Ethiopian and East African plateaus and the interconnecting, low-lying nature of the Turkana Depression. However, Turkana's complex history of multiple rifting phases (Figure 1a; e.g., [PERSON], 2018; [PERSON] et al., 1987), allows for the possibility that the plateaus are instead a continuously uplifted region attributed to a single superplume, with the low elevations explained by crust stretched during Mesozoic and Cenozoic times rather than a lack of dynamic support (e.g., [PERSON], [PERSON], & [PERSON], 2006; [PERSON] et al., 1994). Some geochemical and geodynamical modeling studies propose two plumes exist beneath East Africa (e.g., [PERSON] et al., 2006; [PERSON] et al., 2005; [PERSON] et al., 2000). Seismological interpretations, however, remain debated with one or more plumes suggested to impinge beneath East Africa (e.g., [PERSON] et al., 2021; [PERSON] & [PERSON], 2003), most favoring the view that the entire region is underlain by the African Superplume--a broad, steep-sided mantle upwelling rising from the core-mantle boundary ([PERSON] et al., 2002; [PERSON] et al., 2011). The plume head associated with the initial flood magmatism, 45-30 Ma, would have long since dissipated, but multiple remnant plume stems have been proposed (e.g., [PERSON] et al., 2019).
To address these debates, we have produced the first teleseismic \(P\)- and \(S\)-wave relative arrival-time tomography models of the Turkana Depression, using data from the Turkana Rift Arrays Investigating Lithospheric Structure (TRAILS) project, a multi-institutional, US-UK-Ethiopian-Kenyon geophysical experiment designed to fill a critical data gap along the EAR. Body-wave tomography can help constrain upper-mantle structure and offers greater lateral resolution than surface waves, which to-date form the only existing constraints of Turkana's uppermost-mantle structure (e.g., [PERSON], [PERSON], & [PERSON], 2006). At lithospheric depths, we explore whether low wavespeed zones associated with ongoing rifting are focused or broadly distributed. Below the extending African plate, our models illuminate the architecture of mantle upwellings and thus inform East Africa's single-versus-multiple plume debate.
### Tectonic Background
Today, the Turkana Depression (Figure 1b) is a NW-SE-trending, topographically subdued (-0.5 km) region between the uplifted Ethiopian (-2.5 km) and East African (-1.5 km) plateaus (e.g., [PERSON] et al., 1989). The Cenozoic EAR is marked by the approximately ESE-WNW divergence of the Somalian and Nubian plates, and several microlatoplasty, currently extending at 5-7 mm/yr in this area (e.g., [PERSON] et al., 2016). Since -5 Ma, faulting and magmatism have localized to +100-km-wide extensional zones in the MER (80-100 km-wide) north of Turkana, and the Eastern and Western rifts (60-80 km) to the south, traversing the two elevated plateaus (e.g., [PERSON] et al., 1989). Geodetic data show no kinematic connection between the Eastern and Western rifts at the Turkana Depression ([PERSON] et al., 2020), as suggested by [PERSON] (2005). However, Turkana has a unique history, owing to the superposition of EAR-related magmatism and rifting on Mesozoic rift systems (e.g., [PERSON], 2018; [PERSON] & [PERSON], 1994). Faulting, seismicity and Quaternary magmatism (Figure 1b), span a diffuse, 300-km-wide zone that encompasses the earliest known extension south of the Afar Depression (25-30 Ma; e.g., [PERSON] et al., 2000; [PERSON] et al., 1992), and earliest Cenozoic flood basalt magmatism prior to the onset of rifting (40-45 Ma; e.g., [PERSON] & [PERSON], 1980; [PERSON] et al., 1998).
East Africa's pre-rift lithosphere comprises numerous Precambrian terranes, including Archean cratons (e.g., the Tanzania craton) and flanking Proterozoic mobile belts. The main collisional phase, the East African Orogen (700-550 Ma), consisted of a period of protracted island-arc and microcontinent accretion (e.g., [PERSON] et al., 2013). Subsequent deformation and metasomatism in Neoproterozoic mobile belts has meant the EAR developed within these regions (e.g., [PERSON], 2018). However, given their accretionary mode of formation, the mobile belts can themselves encompass ancient lithospheric fragments, detectable by seismic tomography (e.g., [PERSON] et al., 2019).
Turkana's geology is largely concealed by considerable Phanerozoic sedimentary and volcanic strata, meaning its Proterozoic substrate has yet to be explored. Southern Ethiopia is thought to contain a mixture of juvenile Neoproterozoic lithosphere and Precambrian continental crust, a combination typical of an island-arc accretionary setting ([PERSON] et al., 1998). In the same region, Proterozoic ophiolites and sutures mark locations of past subduction (e.g., [PERSON] et al., 2013). Geochemical (e.g., [PERSON], 2019) and petrological studies (e.g., [PERSON] et al., 1997) at Dilo and Mega (Figure 1b), lack any consensus on southern Ethiopia's lithospheric properties, except to note the impact of ancient depletion events, mostly of Proterozoic age. However, older depletion estimates ([PERSON] et al., 2014) and zircon studies ([PERSON] et al., 2012) suggest the presence of Archean lithosphere, termed the \"Southern Ethiopian Shield,\" although its presence is unsubstantiated geophysically.
Thereafter, Turkana has experienced three main distinct rifting phases: during the Cretaceous (130-80 Ma), Paleogene (66-50 Ma), and Miocene-Recent (25-0 Ma; e.g., [PERSON] et al., 2000; [PERSON] et al., 1992). The Mesozoic, mostly magmatic, WNW-ESE-trending Anza and South Sudan rifts (Figure 1a), constitute a failed rift associated with the Central African Rift System (e.g., [PERSON], 2015; [PERSON] and [PERSON], 1992). The Lotkli plains west of Lake Turkana (Figure 1b) experienced faulting and magmatism during the Paleogene, when parts of the Anza graben were reactivated during a poorly understood event (e.g., [PERSON] et al., 1994). Paleogene sequences may mask Mesozoic strata (e.g., [PERSON], 2018).
Cenozoic rifting in southern Turkana developed along the eastern edge of the Archean Tanzania carton \(\sim\)25 Ma, which is stronger than surrounding Pan-African lithosphere. The carton boundary is marked by \(<\)32 Ma carbonatites associated with initial heating and metasomatism at the steep carton edge, localizing magmatism and strain during the initial rifting stages ([PERSON] et al., 2020). Since then, the locus of active faulting migrated eastwards, manifesting in 3-4 sub-parallel NNE-striking half-graben basins (Figure 1b) with dachronous development, contributing to the unusual broadening of the Turkana Depression (e.g., [PERSON] et al., 2000; [PERSON] et al., 1992). Magmatism has also migrated eastward to the Lake Turkana rift basin, and to N-S-trending, largely unfaulted, shield complexes further east of Lake Turkana that have erupted large volumes over the past 3 Ma (Figure 1b; [PERSON], 2016). [PERSON] (2020) interprets dike swarms along the western margin of Lake Turkana as evidence for extension via magma intrusion since 3 Ma. These patterns suggest the linkage between the MER and Eastern Rift may have changed over time as strain migrated eastward, inconsistent with the simultaneous development of strain predicted in numerical models ([PERSON] et al., 2017). Extension and magmatism propagated southward to northern Tanzania between 20 and 5 Ma (e.g., [PERSON], 1986; [PERSON] et al., 2015). In northern Turkana, magmatism and basin formation initiated \(\sim\)18 Ma in two sub-parallel basins, and propagated northward to form the modern MER (e.g., [PERSON] et al., 2000). [PERSON] et al. (2019) suggest the MER is now propagating southward into the Rirba Rift east of Lake Turkana, based on structural and stratigraphic analyses. In contrast to the rest of Turkana, broad shield complexes are absent across the southern MER (Figure 1b).
[PERSON] and [PERSON] (1998) proposed that buoyant plume material impinged on the base of the Turkana lithosphere at 45 Ma, where thinned, base-of-the-lithosphere topography channeled plume material susceptible to melting to surrounding regions. Ethiopian Plateau uplift, often attributed to mantle plumes, is estimated to have commenced 20-30 Ma ([PERSON] et al., 2003) with some studies postulating more rapid Late- Miocene uplift resulting from lithospheric foundering in response to extensive heating of the lithosphere ([PERSON] et al., 2016; [PERSON] et al., 2007). However, more recent drainage analysis argues against rapid uplift relating to lithospheric delamination processes ([PERSON] et al., 2016). East African Plateau uplift is likely to have proceeded Ethiopian Plateau uplift, with some estimates around 14 Ma (e.g., [PERSON] et al., 2010). The Turkana Depression, although low-lying in comparison, was below sea-level prior to the Neogene (e.g., [PERSON] et al., 2015), evidenced by marine whale fossils and sedimentary strata (e.g., [PERSON] and [PERSON], 2011), and is thought to have risen by \(\sim\)600 m concurrently with East African Plateau uplift ([PERSON] et al., 2015).
### Previous Geophysical Studies
Global tomographic studies have imaged a broad (500 km-wide) slow wavespeed structure originating at the core-mantle boundary beneath southern Africa, impinging on the lithosphere below East Africa (e.g., [PERSON] et al., 2008; [PERSON], 2003). Continent-scale ambient noise ([PERSON] et al., 2019), surface-wave (e.g., [PERSON] et al., 2020), body-wave tomography (e.g., [PERSON] et al., 2021; [PERSON] et al., 2001; [PERSON] et al., 2012), and their joint inversion ([PERSON] & [PERSON], 2011) recognize similar features, imaging Turkana as an anomalously slow wavespeed zone. [PERSON] et al. (2019) image several, laterally distinct, slow wavespeed structures along the EAR, suggesting the presence of multiple plume stems linked to the broader African Superplume at depth. Other body-wave tomographic models find that the Superplume splits into two separate upper-mantle structures beneath both Afar and Tanzania (e.g., [PERSON], 2011; [PERSON] et al., 2012). More recently, however, [PERSON] et al. (2020) and [PERSON] et al. (2021) find evidence for two separate whole-mantle plumes: a near-vertical plume beneath the Afar triple junction as well as the African Superplume. The morphology of the latter, as determined from gravity data ([PERSON] et al., 2007) and seismic waveform modeling (e.g., [PERSON] et al., 2002), is characterized best as a sharp-sided thermochemical plume, whereas the plume below Afar is likely a purely thermal upwelling (e.g., [PERSON], 2021).
Regional relative arrival-time tomographic studies provide strong evidence for continuation of the Superplume into the Ethiopian upper mantle (e.g., [PERSON] et al., 2005, 2008; [PERSON], [PERSON], & [PERSON], 2006; [PERSON] et al., 2015). Beneath the East African Plateau, tomography studies reveal a slow wavespeed anomaly in the upper mantle, interpreted as ascending plume material (e.g., [PERSON] & [PERSON], 2013; [PERSON] et al., 2003). Tomography, in conjunction with receiver function studies of the mantle transition zone (e.g., [PERSON], [PERSON], [PERSON], & [PERSON], 2006; [PERSON], 2021; [PERSON] et al., 2000; [PERSON] et al., 2015) that observe near-normal mantle transition zone thicknesses below the MER but thinned in southern Ethiopia, suggest the plume is likely to cross the mantle transition zone below the Turkana Depression, which has been a large data gap prior to this study.
At shallower depths (<100 km), a focused (\(\sim\)150 km-wide) low wavespeed rift-zone is imaged below the MER ([PERSON] et al., 2005, 2008) and Eastern Rift ([PERSON] & [PERSON], 2006; [PERSON] et al., 2019). The Kenya Rift International Seismic Project (e.g., [PERSON] et al., 1994) conducted wide-angle reflection studies to determine variations in crustal thickness and uppermost-mantle structure along the axis of the Eastern Rift, reaching as far north as Lake Turkana (e.g., [PERSON] & The KRISP Teleissemix Working Group, 1994; [PERSON] et al., 1994). Crustal thicknesses of \(\sim\)35 km and \(\sim\)20 km are revealed beneath the East African Plateau and Lake Turkana respectively, the latter ascribed to widespread Mesozoic rifting ([PERSON] et al., 1997). These authors find comparable results to the Rayleigh wave dispersion model of [PERSON], [PERSON], and [PERSON] (2006), where shallow slow wavespeeds, spanning the whole Depression, suggest underlying lithospheric thinning with an average crustal thickness of 25\(\pm\)5 km. Overlapping phases of prolonged rifting have rendered Turkana the area of thinnest continental crust along the EAR excluding Afar, with crustal stretching factors of 1.2-1.6 ([PERSON] & [PERSON], 1994; [PERSON] et al., 1994). [PERSON] et al. (2020) measure higher present-day strain rates in the southern Turkana Depression than the northern MER, but geodetic data are too sparse to evaluate the current localization of strain across the 300-km-wide broadly rifted zone in southern Ethiopia.
## 2 Data and Methods
### The TRAILS Seismograph Network and Teleseismic Dataset
Seismograph deployments in the Turkana Depression and adjoining areas on the MER and Eastern Rift were completely lacking compared to the rest of the EAR until 2019, when the NSF-NERC funded, US-UK-Ethti-opian-Kenyon, TRAILS project began. The TRAILS broadband seismograph network (Figure 1(a)) comprised 34 Guralp CMG-ESP and CMG-3T instruments, capable of responding to periods reaching 60 and 120 s, respectively (see Table S1 in Supporting Information for further station details). Additional data were sourced from permanent GEOFON seismic station LODK (Figure 1(a)). The combined seismic network of 35 seismograph stations spans an area \(\sim\)450 \(\times\) 550 km with an average station spacing of \(\sim\)30-50 km centered on the Turkana Depression (Figure 1(a)).
Waveforms from 2,640 earthquakes of \(\,\mathrm{m}_{\,\mathrm{p}}\geq 5.0\) in the teleseismic epicentral distance range \(30^{\circ}<\Delta<180^{\circ}\) during the period January 2019 to September 2020, were inspected visually for a good signal-to-noise ratio on at least 4 stations. Station-earthquake pairs with \(\Delta\leq 30^{\circ}\) were excluded to avoid non-unique raypstaus caused by mantle-transition-zone-associated triplicates. Ultimately, 607 earthquakes were analyzed for direct P-phases, together with 8 core-diffracted (PDiff) and 70 core (PKP, PKIKP, and PKIKP) phases. Similarly, inspection yielded 205 direct S- and 105 SKS-phase earthquakes (Figures 2b and 2c). To provide greater resolution and improve the uniformity of the data coverage with respect to backazimuth and epicentral distance, further visual inspection of 16,738 lower magnitude earthquakes (\(4.0\leq\,m_{\,\mathrm{p}}<5.0\)) was conducted. This yielded an additional 294 earthquakes for \(P\)-wave analysis and 67 for \(S\)-wave analysis. Earthquake coverage is best from the east and south east (western Pacific subduction zones: 60-130\({}^{\circ}\); Figures 2b and 2c).
Figure 2.— (a) Seismograph stations used in our tomographic analysis. The Turkana Rift Arrays Investigating Lithospheric Structure (TRAILS) stations are shown by the blue triangles (Ethiopian Network; 9A) and the orange inverted triangles (Kenyan Network; Y1). Tectonic features in black are as per Figure 1. (b and c) The backazimuthal and distance distribution of earthquakes used in this study between January 2019 and September 2020. (b) \(\,\mathrm{m}_{\,\mathrm{p}}\geq 4.0\) direct \(P\)-wave (circles) and core phase (crosses and red circles) event epicenters. (c) \(\,\mathrm{m}_{\,\mathrm{p}}\geq 4.0\) direct S-wave (circles) and SKS (crosses and red circles) event epicenters. The concentric circles mark \(30^{\circ}\) intervals in epicentral distance from the center of the network at \(4^{\circ}\) N, \(37^{\circ}\) E (black star). Note that although some earthquakes are located \(\Delta\leq 30^{\circ}\) from the study area on the figure, no individual raypstuhs with \(\Delta\leq 30^{\circ}\) were included to avoid triplicates associated with the mantle transition zone.
### Method of Relative Arrival-Time Determination
Filtered waveforms, using a zero-phase, two-pole, Butterworth bandpass filter with corner frequencies of 0.4 and 2 Hz, and 0.04 and 0.2 Hz for \(P\)- and \(S\)-waves, respectively, were manually picked on the first identifiable coherent peak or trough of body-wave energy across the network. These bandwidths are comparable to previous studies on the EAR (e.g., [PERSON] et al., 2008), but with a higher \(S\)-wave low-pass cutoff than is used in some studies (0.1 Hz: [PERSON] et al., 2005; [PERSON], [PERSON], & [PERSON], 2006). Low-pass filter frequency cut-offs were kept as high as possible to allow for the inclusion of high frequency signals, satisfying the infinite frequency approximation assumed in ray theory which we adopt in our inversions. Direct P- and S-phases were picked on the vertical and tangential component seismograms, respectively; SKS-phases were picked on the radial. Subsequent improvement of manual trace alignment was employed through Multi-Channel Cross-Correlation (MCCC; [PERSON], 1990) allowing for accurate computation of relative arrival-time residuals.
The MCCC procedure windows manual phase picks (3 s for \(P\)-waves; 12 s for \(S\)-waves) to avoid interference from secondary phase arrivals, and searches for the cross-correlation maximum position, \(\tau_{i}^{max}\), between each pair of traces for a single earthquake. These are subsequently used to determine the most appropriate cross-correlation derived relative delay-time, \(\Delta_{i}\), for each station pair for each earthquake:
\[\Delta_{i_{\text{$i_{\text{$i_{\text{$i_{\text{$i_{\text{$i_{\text{$ \text{$\text{$\text{$\text{$}}}$}${$}$}$}}}}}}}}=t_{i}^{r}-t_{i}^{r}-t_{i}^{max}, \tag{1}\]
where \(t_{i}^{r}\) and \(t_{i}^{r}\) are preliminary-picked-arrival estimates for the \(i\)th and \(j\)th traces, respectively. Rays with a mean cross-correlation coefficient <0.85 were rejected. A least-squares minimization procedure is required to optimize relative arrival-time measurements for each station by forcing the mean over all stations to be zero. The standard error of each arrival is also quantified through the MCCC method: relative arrival-times for the \(P\)- and \(S\)-wave dataset have a mean standard deviation of 0.01 and 0.06 s, respectively. Given the trace sampling rate of \(\geq\)0.01 s these errors were considered optimistic, agreeing with comparable studies (e.g., [PERSON] et al., 2001).
Relative arrival-time residuals (\(t_{\text{$\tau_{\text{$\tau_{\text{$\tau_{\text{$\tau_{\text{$\tau_{ \text{$\tau_{\text{$\tau_{\text{$\tau__ \text {$\text{$\tau_ \text{$ $ $ $ $ $ $ $ $ $ $ $ $
except for some rays arriving from the west (225-270\({}^{\circ}\) backazizumuth; Figure 4). Eastern Turkana stations also display large peak-to-peak residual variations (\(\delta_{I_{p}}\) = 2 s; \(\delta_{I_{t}}\) = 5 s). The eastern part of the TRAILS network may thus encompass the eastern edge of the African Superlump. Stations BURE (\(\delta_{I_{p}}\) = 0.52 \(\pm\) 0.21 s), TBIK (\(\delta_{I_{p}}\) = 0.88 \(\pm\) 0.12 s), and KERK (\(\delta_{I_{p}}\) = 0.5 \(\pm\) 0.18 s), located along the length of Lake Turkana, have small peak-to-peak variation (\(\delta_{I_{p}}\) = 1 s; \(\delta_{I_{t}}\) = 4 s) and the largest mean arrival-time residuals, mostly originating from short, eastern, epicentral distance earthquakes. These stations are located in \(>\)3 km-thick sedimentary basins ([PERSON] et al., 2017). Residual trends are more pronounced in the \(S\)-wave dataset (e.g., BURE: \(\delta_{I_{t}}\) = 1.35 \(\pm\) 1.12 s), highlighting \(S\)-wave sensitivity to partial melt. Mean relative arrival-times drop in a NW-SE-trending band across southern Ethiopia, possibly suggesting a break in focused, rift-related low wavespeeds. Stations GAJO (\(\delta_{I_{p}}\) = -0.02 \(\pm\) 0.12 s) and QORK (\(\delta_{I_{p}}\) = 0.0 \(\pm\) 0.16 s), in the central Turkana Depression, have mean relative arrival-time residuals close to zero (i.e., near the regional background mean) and the smallest peak-to-peak variations (\(\delta_{I_{p}}\) = 0.5 s; \(\delta_{I_{t}}\) = 3 s).
Figure 3.— Mean relative arrival-time residuals at each station for (a) \(P\)- and (b) \(S\)-waves. Negative values are relatively early arrivals (faster); positive values are relatively late (slower). Green circles and squares show residuals that lie slightly negative and positive around zero, respectively. Tectonic features in black are as per Figure 1. Triangles are Holocene and Pleistocene volcanic centers (Global volcanism Program, 2013). A selection of seismograph stations, directly referred to in the paper, are labeled. (c and e) Relative arrival-time residual variations as a function of tectonic domain for both the \(P\)- and \(S\)-wave dataset. The colored bars show the proportion of each residual attributed to a certain region. (d and f) Ray coverage as a function of epicentral distance for both the \(P\)- and \(S\)-wave dataset.
### Model Parameterization and Inversion Procedure
We adopt the regularized, least-squares inversion method of [PERSON] et al. (1995) to invert relative arrival-time residuals for mantle velocity perturbations. Source terms and station states were included to account for distant heterogeneity/event mislocations, and unresolvable near-surface structure, respectively. Similar inversion methods have been used by other regional studies along the EAR (e.g., [PERSON] et al., 2008; [PERSON], 2013). Model slowness is parameterized using B-splines under tension ([PERSON], 1981) over a dense grid of 64,800 knots, covering 27 knots between 0-1,000 km in depth, 50 knots between 26-47 E in longitude, and 48 knots between 5'S-14'N in latitude. The central, best resolved, portion of the model is sampled at 25 km intervals at \(\leq\)400 km depth, and 0.1' in latitude/longitude. We extend parameterization, at coarser spacing, beyond the area of interest to create zones where spurious structure can map without being incorporated into the interpreted parts of the model.
Our inversion method utilizes ray theory, which is an infinite-frequency approximation where arrival-times are only influenced by structures along an infinitesimally narrow region. Following [PERSON] et al. (2004), Fresnel zones in our study are of the order \(\sqrt{LL}\) for a wave of wavelength, \(\lambda\), and ray length, \(L\), where \(\lambda\) is determined from the average frequency content of our data (1.2 Hz for \(P\)-waves and 0.12 Hz for \(S\)-waves) and \(L\) represents ray length which in this case we assume to be approximately equal to the depth. In the uppermost, best-resolved, parts of our model, we can thus justify resolution of features no smaller than \(\sim\)20 km and \(\sim\)50 km in the \(P\)- and \(S\)-wave models, respectively.
Figure 4: Backazimuthal variation in arrival-time residuals at four stations (STCK, TELE, MAIK, and MEGE) in each tectonic domain (Lake Turkana, southern Ethiopia, central Turkana, and eastern Turkana) for both the \(P\)- and \(S\)-wave datasets. Residuals are grouped by phase arrival picked in the analysis. The chosen stations are labeled in Figure 3.
Because our inverse problem is under-determined (more unknowns than observations), we regularize through the minimization of a seven-point finite element approximation to the Laplacian operator to penalize model roughness and yield a smooth model that fits the data. A preferred model was chosen by investigating the trade-off between root-mean-square (RMS) residual reduction (data fit) and model roughness (see Figures S2 and S3 in Supporting Information), avoiding models achieving greater residual reduction than justifiable from MCCC-defined data noise levels which we consider, like others, optimistic (e.g., [PERSON] et al., 2012). The chosen models fit 92.27% and 89.07% of the RMS estimated relative-delay times for the \(P\)- and \(S\)-wave models, respectively (see Tables S2 and S3 in Supporting Information). When subtracting the station static terms from the delay times, the RMS relative arrival-time residuals decrease from 0.33 to 0.25 s for \(P\)-waves and from 1.29 to 1.12 s for \(S\)-waves; the resulting residuals reflect more accurately the proportion of delay time anomalies incorporated into the region of the model where we make our interpretations.
## 3 Resolution
To assess resolution, a standard checkerboard analysis was conducted (Figure 5 and Figure S4), using alternating \(\delta V_{ps}=\pm\) 5%, 50 km diameter spherical anomalies, defined by Gaussian functions across their diameter: structures \(<\)50 km are not warranted since they lie below the \(S\)-wave model Fresnel zone. The spherical anomalies were placed at 200 km depth intervals from 100 to 500 km depth, every \(\Gamma^{\circ}\) in latitude/longitude, then inverted using identical model parameterization and regularization to the observed dataset inversion. Travel-times are calculated assuming ray paths through 1D velocity model IASP91. Gaussian residual arrival-time error components with standard deviations 0.03 and 0.1 s were added to theoretical arrival-times for \(P\)- and \(S\)-waves, respectively. The retrieved spheres are laterally distinct, with an amplitude recovery of \(\sim\)50% at \(<\)300 km depth. However, anomalies experience increasing lateral smearing and reduced amplitude recovery (\(\sim\)40%) with depth (Figure 5). To assess vertical smearing further, we place a 150 km diameter sphere at \(4^{\circ}\)N, \(36^{\circ}\)E at 600 km depth, to simulate a large low-velocity mantle-transition-zone anomaly. Some vertical smearing is observed throughout the model, increasing toward the model edges (Figure 5).
Our dataset's ability to retrieve geodynamically plausible structures is tested via several realistic synthetic tests. Models were created to simulate localized rifting, multiple segmented upwellings versus a laterally continuous superplume, and assess smearing between a mantle plume extending up to the mantle transition zone and shallow lateral flow (Figure 6). Gaussian residual time errors were added and the data inverted as with the checkerboard tests. Amplitude recovery in the \(P\)-wave model is \(>\)60% (Figure 6), increasing with depth in central Turkana and decreasing toward the swept. Long-waveible anomalies are inevitably retrieved more easily than steep-gradient, short length-scale structure when regularizing via smoothing: hence the greater amplitude recovery compared to checkerboard tests. Lateral smearing is minimal in both models, however, \(S\)-wave model amplitude recovery (\(\sim\)50%; Figure S5) is lower and smearing more pronounced, than the \(P\)-wave model. The multiple plume model smears upward \(\sim\)100 km (Figure 6; C-C\({}^{\circ}\)). Lateral smearing near the mantle transition zone is minimal. Vertical resolution is limited to \(>\)150-200 km, since features with smaller separation smear and merge, as shown in the synthetic combining shallow low velocities with a deep mantle-transition-zone plume anomaly (Figure 6; A-A). Low wavespeeds along the length of Lake Turkana would be resolved at lithospheric depths, but smear downwards somewhat into deeper features that smear upwards.
## 4 Tomographic Results
The uppermost mantle beneath Turkana is marked by pronounced low wavespeed anomalies (\(\delta V_{p}=-1.5\%\), \(\delta V_{i}=-2.5\%\); Figures 7 and 8), widely distributed across the region that persist to mantle-transition-zone depths. At \(<\)150 km depth, low wavespeeds coincide with recent Pleistocene and Holocene volcanic centers which are themselves broadly distributed throughout Turkana (Figure 1b). Only south of Lake Turkana, along the Suguta Valley do we see evidence for low wavespeeds confined to a relatively narrow, \(\sim\)100-km-wide zone at shallow depths (\(\delta V_{p}=-1.5\%\); \(\delta V_{i}=-3\%\); Figures 7 and 8; B-B\({}^{\circ}\)). The north-south continuity of shallow low wavespeeds is broken at \(\sim\)5\({}^{\circ}\)N by an elongated, narrow, high wavespeed anomaly (\(\delta V_{p}=1.5\%\)), traversing NW-SE in southern Ethiopia to \(<\)200 km depth (Figure 7; 100 km; C-C\({}^{\circ}\), E-E\({}^{\circ}\)). This feature is less
Figure 5.— \(P\)-wave checkerboard resolution tests. Recovery is shown for three depth slices (100, 300, and 500 km) and six cross sections (shown on the 100 km input model depth slice), three of which are a standard checkerboard test and three include an anomalous region in the mantle transition zone. Tectonic features in black are as per Figure 1. White triangles are seismograph stations. Regions with a ray hit count of \(<\)10 are shaded.
Figure 6.— Depth slices and cross sections of synthetic resolution tests showing input anomalies (top row for depth slices and left column for cross sections), the recovered structures using the \(P\)-wave model (bottom row for depth slices and middle column for cross sections), and the \(S\)-wave model (right column for cross sections). The anomalies are defined by Gaussian functions across their widths. Tectonic features in black are as per Figure 1. White triangles are seismograph stations. Regions with a ray hit count of \(<\)10 are shaded.
Figure 7.— P-wave model depth slices and cross sections. Cross section lines are shown on the 75 km slice. Station statics are shown on the 100 km slice. Tectonic features in black are as per Figure 1. White triangles: seismograph stations; Red triangles: volcanic regions; AR, Anza Rift; CBW, Chew Bahir-Weyto Basin; EAP, East African Plateau; EP, Ethiopian Plateau; GP, Gofa Province; KS, Kino Sogo Fault Belt; LB, Lokichar Basin; LI, Lotikippi Basin; LT, Lake Turkana; O, Omo Basin; SB, Segen Basin; SV, Suguta Valley. Areas with low hit count (\(<\)10) are shaded.
Figure 8.— 5-wave model depth slices and cross sections. Cross section lines are shown on the 75 km slice. Station statics are shown on the 100 km slice. Tectonic features in black are as per Figure 1. White triangles: seismograph stations; Red triangles: volcanic regions; AR, Anza Rift; CBW, Chew Bahir-Weyto Basin; EAP, East African Plateau; EP, Ethiopian Plateau; GP, Gofa Province; KS, Kino Sogo Fault Belt; LB, Lokichar Basin; L1, Lotikipi Basin; LT, Lake Turkana; O, Omo Basin; SB, Segen Basin; SV, Suguta Valley. Areas with low hit count (\(<\)10) are shaded.
pronounced in the \(S\)-wave model (Figure 8; 100 km), perhaps due to the lower resolving power of the noisier, longer wavelength \(S\)-wave dataset. High wavespeed anomalies are also present in the Lotikipi basin west of Lake Turkana to \(<\)100 km depth (Figures 7 and 8; 75-100 km). East of Lake Turkana, a pronounced, laterally robust, N-S-trending, high wavespeed (\(\delta V_{p}=1.5\%\)) structure persists sub-vertically to 600 km depth, forming an eastern boundary to the low wavespeeds (Figure 7; A-A). At \(>\)300 km depth, the entire region is underlain by broader low wavespeeds (\(\delta V_{p}=-1.5\%\); \(\delta V_{s}=-3\%\); Figure 7), particularly in the \(S\)-wave model (Figure 8; 500 km). Laterally distinct low wavespeed heterogeneity within the mantle transition zone exists in the \(P\)-wave model (Figure 7; 500-600 km), but resolution of such features is limited outside central Turkana (Figure 5).
## 5 Discussion
### Causes of Seismic Heterogeneity
When interpreting relative arrival-time tomographic models, the \(\delta V_{s,s}=0\%\) contour seldom matches the global zero mean (e.g., Bastow, 2012). Even peak-to-peak amplitude variations will not necessarily document how anomalous the mantle in a region truly is: if phase arrivals across the network are all consistently late or early, that information is lost completely during relative arrival-time calculation (Equation 2). Taking a 0-500 km depth average through global \(P\)- and \(S\)-wave models LLNL-G3 Dv3 ([PERSON] et al., 2012) and SL2013 sv ([PERSON], 2013) below stations where \(\delta t_{p,s}=0\) (stations QORK and BASK for \(P\)- and \(S\)-waves, respectively), \(\delta V_{s,s}=0\%\) in Figures 7 and 8 could be considered to differ from the global mean by \(\delta V_{s}=-1.24\%\) and \(\delta V_{s}=-3.13\%\). These estimates corroborate our absolute arrival-time observations of \(\delta t_{p,lsresiduals \(\langle\frac{\delta t_{L}}{\delta t_{p}}\rangle\) for common earthquake-station pairs as a diagnostic tool for causes of seismic anomalies (e.g., [PERSON] et al., 2005; [PERSON], 2001; [PERSON] et al., 2016). A \(\frac{\delta t_{L}}{\delta t_{p}}\) of 5.38 exists across Turkana (Figure 9a), above the upper bounds of the thermal range (3.6-3.8; e.g., [PERSON] et al., 2003), suggesting the presence of mantle melt as an additional contributor to the seismic anomalies. Similar ratios between \(S\)- and \(P\)-wave absolute arrival-time residuals are also obtained (\(\frac{\delta t_{L}}{\delta t_{p}}\) of 5.18; Figure 9b). [PERSON] et al. (2005) attribute a \(\frac{\delta t_{L}}{\delta t_{p}}\) of \(\sim\)10 to significant fractions of shallow melt beneath the MER; larger ratios than Turkana (Figure 9a), implying that mantle melt, although necessary to explain the low wavespeeds, is likely less focused and voluminous than the MER. However, more melt may be present within the narrow (20-30 km-wide), near-zero elevation, Suguta Valley along the northern Eastern Rift, where high amplitude low wavespeeds (Figure 7; B-P) are highly localized to the rift axis--much like the northern MER. Since arrival-times
Figure 9.— Regression plot of (a) relative and (b) absolute \(S\)-wave versus \(F\)-wave arrival-time residuals for common earthquake-station pairs across all stations in the Turkana Depression. The blue line is a least-squares fit, including Multi-Channel Cross-Correlation derived picking errors, through all common earthquake-station pairs and has a gradient of \(\sim\)5.38 for relative arrival-time residuals and 5.18 for absolute arrival-time residuals. The purple line is the slope in the partial melt affected Main Ethiopian Rift (slope of \(\sim\)10.00; [PERSON] et al., 2005). The red line is the slope in eastern Anatolia (slope of \(\sim\)4.01; [PERSON] et al., 2020), where anomalies are primarily due to temperature and small volumes of mantle melt.
are path-integrated values and \(S\)-waves are generally longer wavelength than \(P\)-waves, these ratios are likely to be underestimates (e.g., [PERSON], 2010).
Several lines of geophysical evidence corroborate our high-temperature and mantle melt hypothesis: early teleseismic studies infer 3%-6% mantle melt (e.g., [PERSON] & The KRISP Teleseismic Working Group, 1994); wide-angle-derived Pn velocities are low (7.5-7.7 km/s; [PERSON] et al., 1994); heat-flow observations are high, peaking at \(>\)90 mWm\({}^{-2}\)([PERSON] et al., 2017); a high conductivity (10\({}^{-1}\)Sm\({}^{-1}\)) anomaly observed via magnetotelluric imaging at 20-100 km depth beneath the northern Eastern Rift is explained best by melt ([PERSON], 1979).
High Velocity Anomaly in Southern Ethiopia: By-Product of Cenozoic magmatism or Pretorozoic-Age (Pan-African) Lithospheric Heterogeneity?
Perhaps the most distinctive feature at 0-200 km depth in the \(P\)-wave model (Figures 7 and 10a), is a NW-SE-trending high wavespeed band (\(\delta V_{r}=1.5\%\)) in the broadly rifted zone of southern Ethiopia, just south of where the MER broadens to three sub-parallel rift basins: Omo, Weyto-Chew Bahir, Segen (Figures 10a and 10b). Synthetic tests (Figure 6) show that high amplitude, \(\sim\)40-km-wide structures can be recovered from the \(P\)-wave inversions. The feature has sharp, near-vertical, anomaly boundaries (Figure 7; C-C), potentially a result of juxtaposed hot/partially molten mantle and a relatively thick, cold, and compositionally distinct lithospheric fragment; purely thermal anomalies are expected to be more laterally diffuse. The more subtle increase in \(\delta V_{r}\) (Figure 8) observed coincident with the high \(P\)-wave band may imply a lithospheric composition to which \(S\)-waves have a lower sensitivity than \(P\)-waves, however, we cannot preclude the possibility that the model differences are due, at least in part, to the larger Fresnel zone (\(\sim\)50 km) and reduced spatial resolution of the \(S\)-wave dataset.
#### 5.2.1 Archean Lithosphere
Although most geochronological studies (e.g., [PERSON] et al., 2004; [PERSON] et al., 2017) suggest the southern Ethiopian mantle lithosphere is Neoproterozoic in age, [PERSON] et al. (2012) and [PERSON] et al. (2014) attribute the presence of abundant 2.5 Ga zircons to Archean lithosphere at depth in the southern Ethiopian Shield. Xenoliths around Mega (Figure 10b) also preserve evidence of ancient Precambrian depletion events, unlike elsewhere in the northern sector of the EAR (e.g., [PERSON] et al., 2011). Iron-depleted, Archean lithosphere is characterized by fast wavespeeds ([PERSON] et al., 2009), affecting \(\delta V_{r}\) more strongly than \(\delta V_{r}\). This contradicts the observation that the high wavespeed band is illuminated best in our \(P\)-wave model (Figures 7 and 8). With the caveat that the lower resolving capabilities and larger Fresnel zone of the \(S\)-wave dataset may at least partly explain the model differences, we suggest that the \(P\)- and \(S\)-wave amplitude recovery, when reviewed in light of the lack of contiguity with other Archean blocks in East Africa, render the Archean lithosphere hypothesis unlikely.
#### 5.2.2 Cenozoic Processes
Alternatively, the high wavespeed band may be a by-product of Cenozoic magmatism. The earliest phase of basaltic magmatism in East Africa (40-45 Ma; e.g., [PERSON], 1980) occurred in SW Ethiopia, potentially depleting the lithosphere of its most easily fusible elements. Melt depletion is generally characterized by increased wavespeeds (e.g., [PERSON], 2003; [PERSON] et al., 2005), with most studies favoring greater increases in \(\delta V_{r}\) than \(\delta V_{r}\)([PERSON], 1997; [PERSON] & [PERSON], 2010), as per our results (Figures 7 and 8). However, melt depletion would have to occur through fractional melting to impact seismic wavepeeds discernibly (e.g., [PERSON] et al., 2008; [PERSON] & [PERSON], 2006). Southern Ethiopia is considered to have experienced relatively low degrees of lithospheric mantle melting ([PERSON], [PERSON], & [PERSON], 2017; [PERSON] & [PERSON], 2002; [PERSON], 2010). Petrological studies at Dilo/Mega (Figure 10b; e.g., [PERSON], [PERSON], & [PERSON], 2017; [PERSON] et al., 2011) instead attest to widespread Cenozoic metasomitism from intruded fertile plume material (e.g., [PERSON] et al., 2012); these would impart seismically slow phases in the lithospheric mantle ([PERSON] et al., 2018) whilst also increasing its temperature. Therefore, the style, location, and spatial extent of magmatism (in 10 Ma at least 30,000 km\({}^{3}\) of magma was widely dispersed across SWEthiopia; Figure 10b; [PERSON] et al., 1993) does not lend itself to the generation of the linear melt depletion zone required to generate our arcuate, high velocity anomaly.
#### 5.2.3 Proterozoic Island-Arc Accretion/Stacked Microcontinents
The elongate nature and sharp vertical anomaly boundaries point to thermochemically distinct lithosphere that is consistent with an arc-accretion process. Southern Ethiopian peridotite xenoliths match Proterozoic mantle closely ([PERSON] et al., 2004) and typically attest to ancient melt depletion of Pan-African age at the latest (e.g., [PERSON] et al., 2011; [PERSON] et al., 2017). Detailed field mapping ([PERSON], 1980; [PERSON] et al., 1976) confirms the presence of an ancient high-grade ultramafic arc complex traversing SW Ethiopia at a similar location and strike to our southern Ethiopian high velocity anomaly (Figures 10a and 10b), however, its true geomorphological extent is masked by Phanerozoic lavas and sediments (Figure 10b; e.g., [PERSON] & [PERSON], 1980; [PERSON], 1994). Several sutures and ophiolitic belts (Figure 10b; e.g., [PERSON] et al., 2013; [PERSON] et al., 2003), dated at 880-690 Ma (e.g., [PERSON] et al., 1992; [PERSON] et al., 2004), reinforce
Figure 10.— (a) P-wave tomography slice at 100 km depth centered on southern Ethiopia. Included on the map are Cenozoic faults (e.g., [PERSON] et al., 2017; [PERSON] & [PERSON], 1978) and Mesozoic basin outlines (e.g., [PERSON], 2018; [PERSON] & [PERSON], 1994), as per Figure 1, seismicity occurring from January 2019 to September 2002 ([PERSON] et al., 2020), and Holocene and Fleistocene volcanoes (Global Volcanism Program, 2013). (b) Surface geology of southern Ethiopia, taken from [PERSON] (1973), [PERSON] et al. (1976), and [PERSON] and [PERSON] (1980). (c) Changes in topography across the high wavespeed band along six parallel cross sections (A–F). The vertical lines in the topographic cross sections are major and minor (solid lines) and inferred (dashed lines) Cenozoic faults. Topography contour lines at 1.5–2 km above sea-level are shown in magenta.
evidence for downward-thrusted ancient oceanic lithosphere. [PERSON] et al. (1998) also established, through zircon dating and isotope geochemistry, that southern Ethiopia comprises a mixture of juvenile Neoproterozoic lithosphere and small volumes of Precambrian continental crust, a combination typical of a Pan-African island-arc setting.
Quaternary lavas in Turkana show remarkable geochemical similarity (e.g., [PERSON] et al., 2006; [PERSON], 2019), except those in southern Ethiopia: [PERSON] (2019) notes that around Mega (Figure 10b), volcanism is unusually mafic. In geochemically distinct southern Ethiopia, xenolith studies (e.g., [PERSON] et al., 1997; [PERSON] et al., 2014) lack any consensus concerning lithospheric composition. Mega lies at the edge of our high wavespeed band, hinting at a possible transition between two lithospheric domains as a cause for our observations: high olivine forsterite (Fo) content in Mega xenoliths is consistent with oceanic peridotite ([PERSON], [PERSON], & [PERSON], 2017), signifying compositional heterogeneity as a cause for the higher wave-speeds. An argument for continental lithosphere has also been made: the 45-35 Ma southern Ethiopian basalts have Na and Fe contents consistent with melting beneath thick continental lithosphere (e.g., [PERSON] & [PERSON], 2002). Either way, the East African Oregon was certainly a period of protracted island-arc and microcontinent accretion involving juvenile Neoproterozoic oceanic crust that formed in and adjacent to the Mozambique ocean (e.g., [PERSON] et al., 2013). Our linear, elongate, high wavespeed band may thus be attributed to a fragment of oceanic or continental lithosphere in the presence of a high-grade ocean arc accretion zone. A relict Proterozoic subduction zone trapped in continental lithosphere potentially forms a rheological feature, strongly affecting the localization and development of subsequent continental tectonics. Such a scenario is not without modern-day analog. Oceanic lithosphere trapped in the uppermost mantle has been proposed in the NW United States: the 55 Ma accretion of the Siletzia microplate during the Cordillerman Orogeny is imaged seismically as a curtain of high wavespeeds to \(\sim\)200 km depth ([PERSON] & [PERSON], 2011). Siletzia appears to be a competent crustal block with a diffuse layer of seismicity close to the Moho ([PERSON] et al., 2020). [PERSON] et al. (2009) also imaged a \(\sim\)100-km-wide high wavespeed band beneath the south-central part of the Gulf of California that is attributed to a 12 Ma slab fragment, trapped at lithospheric depths.
#### 5.2.4 Implications for Mesozoic and Cenozoic Strain Localization
The lack of Quaternary eruptive centers and comparatively thin sequence of Eocene-Oligocene flood basalts coinciding with the Southern Ethiopia high wavespeed band (Figure 10b; [PERSON], 2017) suggest the presence of relatively cold, refractory Proterozoic lithosphere. Intriguingly, the band delimits the northernmost extent of Mesozoic extension in Turkana, and marks an offset in the surface expression of the Mesozoic rift system (Figure 10a). Excluding the zone of continuation of the MER at the center of the high wavespeed band, a marked increase in topography (\(>\)1.5 km) occurs south-to-north (Figure 10c; A-F): abrupt in the west; more subtle in the east (Figure 10c; A-F). These topographic observations support a pre-Mesozoic age for the high wavespeed band, and potentially deem the band a refractory feature governing the northern limit of Mesozoic extension.
A zone of strong lithosphere should exert some control on EAR development too. Intriguingly, Cenozoic rifting lacks focus within and immediately to the north of the high wavespeed zone, where present-day seismicity (Figure 10a) is also diffuse, in contrast to the relatively narrow (\(\sim\)80 km-wide) expression of the MER north of \(\sim\)6.5\({}^{\rm N}\).
Previous analog experiments and numerical models that have attempted to explain the linkage between the MER and Eastern Rift ([PERSON] et al., 2017; [PERSON] et al., 2019) assert the importance of previously thinned lithosphere below Turkana. However, the seismically fast band of refractory lithosphere illuminated in southern Ethiopia by our tomographic models, may have influenced both Mesozoic and present-day strain localization, likely including the complex, broadly rifted, transfer zone between the MER and Eastern Rift within Turkana. The initial conditions in the analog experiments and numerical models therefore require some revision: specifically, a strong zone in southern Ethiopia, not just a simple previously thinned lithosphere in the Turkana Depression between two plateaus, and a diachronous migration and propagation of several \(<\)100-km-wide rift zones.
### The Central Turkana Uppermost Mantle: Ponded Asthenosphere or Melt-Inflitrated Lithosphere?
Below the \(\sim\)80-km-wide central and northern MER to the north of the TRAILS network, the uppermost mantle is characterized by large low wavespeed anomalies at \(<\)200 km depth ([PERSON] et al., 2005, 2008). Similarly focused mantle anomalies also characterize the Eastern Rift ([PERSON] & The KRISP Teleseismic Working Group, 1994; [PERSON] & [PERSON], 2013; [PERSON] & [PERSON], 2006; [PERSON] et al., 2019). Our results corroborate these observations in the south of our study area, beneath the narrow Suguta Valley (Figures 7 and 8; 75-100 km; B-B). In the absence of high-resolution lithospheric thickness measurements, the low wavespeeds could signify concentrated melt intrusions in still-thick lithosphere or a lithospheric thin zone where laterally flowing plume material is ponding. However, the presence of extensive, Pliocene-Recent dikes ([PERSON], 2020) and high present-day strain rates ([PERSON] et al., 2020), mostly focused at the southern end of Lake Turkana, agree with the gradual focusing of magma-assisted rifting to narrower zones.
Turkana's low wavespeed branches at \(\sim\)100 km depth are ponded asthenospheric material beneath broad zones of variably pre-thinned lithosphere, or heavily melt-intruded mantle lithosphere is equivocal. These low mantle wavespeeds are confined to the Eastern Rift, showing no evidence for connection to the Western Rift at the northern end of the East African Plateau.
### The Turkana Sub-Lithospheric Mantle and Transition Zone
Our tomographic models reveal low velocity anomalies (\(\delta V_{p}=-1.5\%\); \(\delta V_{s}=-3\%\)) that persist with depth, at least to the mantle transition zone (Figures 7 and 8; A-A; D-D'), however we cannot preclude the possibility of separate sub-lithospheric and lithospheric low wavespeed anomalies that are merged by vertical smearing (Figures 5 and 6). Absolute arrival-times of \(P\)- and \(S\)-waves recorded by the TRAILS network also attest to significant, deep-seated, low wavespeed mantle structure, particularly from southerly hexazimuth, where \(\delta\mathrm{{}_{t_{\mathrm{obs}}}}\approx 14\)-\(17\) s (Figure 9). Collectively, our observations support the view that African Superlump material dominates sub-lithospheric upper mantle heterogeneity below Turkana.
Despite a lack of coverage below Turkana, several studies (e.g., [PERSON], 2002; [PERSON] et al., 2007) show thermal and compositional complexity in the East African mantle transition zone, consistent with the influence of mantle plumes. Temperature impacts \(\delta V_{p}\) and \(\delta V_{s}\) similarly, however, our \(S\)-wave model depicts more concentrated low wavespeeds at mantle-transition-zone-depths than the \(P\)-wave model (Figures 7 and 8; 500-600 km; A-A'). This discrepancy could be the result of compositional heterogeneity or a hydrated mantle transition zone (e.g., [PERSON] et al., 2011; [PERSON] et al., 2009; [PERSON] et al., 2015), consistent with the near ubiquitous view that the African Superlump is compositionally, not just thermally anomalous ([PERSON] & [PERSON], 2021; [PERSON] et al., 2002; [PERSON] & [PERSON], 2002; [PERSON] et al., 2007).
A fundamental question concerning Turkana is whether or not a lack of dynamic upwelling or lithospheric structure are the main causes for its low-lying nature compared to the surrounding plateaus. Our observations of deep-seated, low velocity material provide no support for the hypothesis that Turkana's low elevation is due to lacking dynamic support. With the caveat that high-resolution crustal and lithospheric thickness measurements are lacking in Turkana, an isostatic response contribution from overlapping Mesozoic and Cenozoic phases of rifting ([PERSON], 2018; [PERSON] et al., 1987), significantly thinning the lithosphere ([PERSON], [PERSON], & [PERSON], 2006; [PERSON] et al., 1994), thus instead likely govern Turkana's low elevations relative to the two plateaus it separates.
## 6 Conclusions
Using data from the recently deployed TRAILS seismograph network of 34 broadband stations, we present the first \(P\)- and \(S\)-wave tomographic models of upper-mantle seismic structure beneath the Turkana Depression.
Relative arrival-time residuals and velocity-constrained temperatures at 100 km depth exceed petrological mantle potential temperature estimates, suggesting the presence of mantle melt, albeit in smaller volumes than below the MER to the north. At \(<\)200 km depth, a NW-SE-trending, \(\sim\)50 km-wide, high wavespeed anomaly (\(\delta V_{p}=1.5\%\)) is interpreted as relatively refractory Proterozoic lithosphere. The coincidence of this high velocity band with the northern limit of the Turkana Depression, and the southerly extent of MER-related fault scarps, implies the band has exerted some control on the spatial extent of Mesozoic and Cenozoic rifting. At lithospheric mantle depths (\(<\)100 km), a single localized low wavespeed zone (\(\delta V_{p}=-1.5\%\); \(\delta V_{s}=-2\%\)) is only present in the southernmost part of our study area where a focused zone of lithospheric extension in the Eastern Rift is illuminated. North of this, within central Turkana, the low wavespeed zone bifurcates to either lithospheric thin-spots that host ponded asthenospheric material or regions of melt-intruuded mantle lithosphere, that merge into a broadly distributed low wavespeed zone in southern Ethiopia. Below mantle lithospheric depths, low velocity anomalies (\(\delta V_{p}=-1.5\%\); \(\delta V_{s}=-3\%\)) provide evidence that dynamic support is continuous below East Africa, not just below the uplifted Ethiopian and East African plateaus. Figure 12 illustrates our main conclusions.
### Data Availability Statement
The TRAILS seismograph networks included in the analysis are 9A (Bastow, 2019) and Y1 (Ebinger, 2018), and were sourced from IRIS DMC ([[https://ds.iris.edu/ds/nodes/dmc](https://ds.iris.edu/ds/nodes/dmc)]([https://ds.iris.edu/ds/nodes/dmc](https://ds.iris.edu/ds/nodes/dmc))). Seismic data for the permanent GeoForschungZentrum ([[http://geofon.gfz-potsdam.de/](http://geofon.gfz-potsdam.de/)]([http://geofon.gfz-potsdam.de/](http://geofon.gfz-potsdam.de/))) LODK station in the Turkana Depression was sourced from ORFEUS ([[https://www.orfeus-eu.org](https://www.orfeus-eu.org)]([https://www.orfeus-eu.org](https://www.orfeus-eu.org))). Seismic Analysis Code (SAC; [PERSON] et al., 2013) and Generic Mapping Tools (GMT; [PERSON], 1998) software were used to process and display seismic data.
Figure 12. Summary diagram illustrating the tectonic and geodynamic processes present in the Turkana Depression. Structural features are shown on the topography map. Cenozoic faults in black are as per Figure 1. Blue and red regions signify high and low wavespeed zones, respectively.
## Acknowledgments
The authors would like to acknowledge collaboration with the University of Narol and Addis Ababa University including their help establishing the TRAL's network. The authors thank the editor [PERSON] and two anonymous reviewers for their insightful comments which helped clarify the manuscript. [PERSON] is funded by an Imperial College Presidents PhD Scholarship [PERSON] and [PERSON] acknowledge support from Natural Environment Research Council grant number NE/S014136/1. C. Higher acknowledges NSFGEO-NER network 18842417.
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wiley/fd34f9a0_08ce_4ca3_8035_cba1c700cc11.md | # IGR Solid Earth
Research Article
10.1029/2024 JB030565
Caprock Genesis in Hydrothermal Systems via Alteration-Controlled Fault Weakening and Impermeabilization [PERSON]
1 Dipartimento di Scienze della Terra, Sapienza Universita di Roma, Roma, Italy, 1 Consiglio Nazionale delle Ricerche, IGAG, Roma, Italy, 1 Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 2 Dipartimento di Geoscienze, Universita degli Studi di Padova, Padua, Italy
[PERSON]
1 Dipartimento di Scienze della Terra, Sapienza Universita di Roma, Roma, Italy, 1 Consiglio Nazionale delle Ricerche, IGAG, Roma, Italy, 1 Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 2 Dipartimento di Geoscienze, Universita degli Studi di Padova, Padua, Italy
[PERSON]
1 Dipartimento di Scienze della Terra, Sapienza Universita di Roma, Roma, Italy, 1 Consiglio Nazionale delle Ricerche, IGAG, Roma, Italy, 1 Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 2 Dipartimento di Geoscienze, Universita degli Studi di Padova, Padua, Italy
[PERSON]
1 Dipartimento di Scienze della Terra, Sapienza Universita di Roma, Roma, Italy, 1 Consiglio Nazionale delle Ricerche, IGAG, Roma, Italy, 1 Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 2 Dipartimento di Geoscienze, Universita degli Studi di Padova, Padua, Italy
[PERSON]
1 Dipartimento di Scienze della Terra, Sapienza Universita di Roma, Roma, Italy, 1 Consiglio Nazionale delle Ricerche, IGAG, Roma, Italy, 1 Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 2 Dipartimento di Geoscienze, Universita degli Studi di Padova, Padua, Italy
###### Abstract
The mechanical and hydraulic behavior of faults in geothermal systems is strongly impacted by fluid-induced alteration. However, the effect of this alteration on fault properties in geothermal reservoirs is under documented. This affects our ability to model the properties of subsurface structures, both in reservoirs and cappCRs, and potential hazards during geothermal exploitation. We investigated fault rocks from the caprock of a fossil hydrothermal system in the Apennines of Italy. We combined field structural observations with mineralogical and microstructural analyses of faults that guided the circulation of hydrothermal fluids and steered the caprock formation. We also performed friction experiments and permeability tests on representative fault rocks. We document fault weakening induced by the effect of hydrolytic alteration leading to the enrichment of clay minerals along the slip surfaces of major faults. Alunite-clay-rich rocks are much weaker (friction coefficient 0.26 \(<\)\(\mu\) \(<\) 0.45) than the unaltered protoolith (trachye, \(\mu\) = 0.55), favoring strain localization. The late-stage enrichment of clays along faults induces a local decrease in permeability of three orders of magnitude (1.62 \(\times\) 10\({}^{-19}\) m\({}^{2}\)) with respect to the surrounding rocks (1.96 \(\times\) 10\({}^{-16}\) m\({}^{2}\)) transforming faults from fluid conuduits into barriers. The efficiency of this process is demonstrated by the cyclic development of fluid overpressure in the altered volcanic rocks, highlighted by chaotic precias and hydrofracture networks. Permeability barriers also enhance the lateral flow of hydrothermal fluids, promoting the lateral growth of the caprock. Velocity-strengthening frictional behavior of alunite-clay-rich rocks suggests that hydrolytic alteration favors stable slip of faults at low temperature.
A natural geothermal system is characterized by the presence of reactive fluids that produce intense alteration of rocks. Circulation of geothermal fluids is controlled by hydraulic conductivity of faults and fractures, which guide the spatial distribution of alteration. Alteration promotes severe changes in the physical and mechanical properties of rocks, controlling subsequent fault reactivation and potential seismic instabilities. We studied a fossil geothermal system in the Apennines, in which we combined field observations with novel laboratory measurements about the strength and permeability of the rocks. We discovered that in volcanic rocks, the alteration first produces clays mixed with sulfates, which are weaker than the original rocks but still permeable. With further alteration and fault activity, clays are concentrated along the faults. By this mechanism, normally porous and permeable fault rocks may evolve into impermeable barriers, forcing the fluid flow toward the outer portions of the altered volume of rocks, laterally expanding the alteration front. Moreover, our experiments suggest that these altered rocks may deform \"quietly\", at least at low temperature. This may imply a reduced risk of earthquakes that could be induced by the movement of fluids in the subsurface, both by natural or anthropic causes.
## 1 Introduction
In hydrothermal systems, the interaction of hot reactive fluids with rocks promotes the formation of alteration domains ([PERSON], 2017; [PERSON], 2013; [PERSON], 2008). These systems are highly dynamic: their structure and mineral composition are the result of the interplay between fault activity and fluid-rock interactions (e.g., [PERSON] et al., 2003; [PERSON] et al., 2011; [PERSON], 1987). Fluid circulation in the Earth's Crust is modulated by faults and fracture systems, in which fluid-rock interactions affect the evolution of mechanical (strength, elastic moduli, etc.) and hydraulic (permeability) properties, serving as conduits or barriers (e.g., [PERSON] et al., 1996; [PERSON], 2010; [PERSON] et al., 2014). This has profound implications for the evaluation of caprock efficiency and for the exploitation of geothermal resources.
For instance, sealing of fractures by mineral precipitation as well as fluid-mediated alteration of pristine rocks represent key processes controlling permeability in geothermal/hydrothermal systems (e.g., [PERSON] et al., 2016; [PERSON] et al., 2021; [PERSON] et al., 1993; [PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] et al., 2012). For some volcanic and hydrothermally altered rocks, fracture sealing and some characterization of physical properties (porosity, density, permeability, ultrasonic velocities, uniaxial strength) have been documented at surface conditions ([PERSON] et al., 2003; [PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] et al., 2012; [PERSON], 1999; [PERSON] et al., 2014). However, there is still a lack of knowledge about the interplay between fault mechanics and fluid-rock interaction processes and the change of physical and mechanical properties of fault rocks at depth in hydrothermal environments. These properties are crucial for the study of permeability evolution and for the efficient and safe exploitation of active geothermal systems. For example, fluid injection into reservoirs can reduce the effective stresses on faults, potentially inducing seismicity (e.g., [PERSON], 2013; [PERSON] & [PERSON], 2013). Optimal injection protocols should be designed on the basis of mechanical models, combining structural data of the reservoir and mechanical properties of hydrothermally altered rocks, which presently are mostly lacking ([PERSON] & [PERSON], 2020). Equally important is the knowledge about the genesis, the structure and permeability of the hydrothermal caprocks that seal high-temperature reservoirs, both in geothermal and active volcanic areas (e.g., [PERSON] et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2016; [PERSON] & [PERSON], 2001; [PERSON] et al., 2024).
To tackle this knowledge gap, we exploit a relevant case-study of a fossil lithocap excellently exposed in the Tuscany-Latium geothermal region of Italy (Figure 1). This regional geothermal field formed in the context of anatectic and mantle-derived magmatism (e.g., [PERSON], 2005) synchronous with backarc extension in the framework of the Apennines subduction system ([PERSON], 2006).
Lithocaps are extensive bodies of hydrothermally altered rocks that are broadly stratabound and that may occasionally have rocks with low permeability. They are located at shallow levels in porphyby and epithermal ore deposits and in active geothermal systems (e.g., [PERSON], 2013). Their formation is related to the circulation of hydrothermal fluids with low pH and high temperature (100\({}^{\circ}\)C-300\({}^{\circ}\)C), promoting metasomatic alteration of the host rock into agrilic or propylitic facies ([PERSON] & [PERSON], 2022). In specific cases, lithocaps may become efficient caprocks of active geothermal systems ([PERSON] & [PERSON], 1967; [PERSON] et al., 2019), a feature important for geo-energy exploitation ([PERSON] et al., 2013). We use the fossil Allumiere lithocap (Figures 0(c) and 0(d); Figure 3) as an exhumed analog to document the structure and permeability of caprocks developed in acid volcanic rocks in active geothermal and volcanic systems.
Combining field structural observations, microstructural analysis, X-Ray Diffraction (XRD) analysis, friction experiments and permeability measurements, we show that the mechanical and hydraulic properties of lithocaps are structurally controlled by the combined effect of alteration and deformation. This progressively transforms large fault zones into barriers to fluid flow, leading to the formation of efficient (low-permeability) and weak (low friction coefficient) caprocks in altered volcanics.
## 2 Geological Background
The study area is located in the Northern Apennines chain, an arc-shaped, NE-verging fold-and-thrust belt, which originated along an eastward retreating subduction zone, in the framework of the convergence between the Adria microplate and the European margin (Figure 0(a)). Since the middle-late Miocene the Thyrremian margin of the Apennine chain has undergone post-orogenic extension and crustal thinning associated with the Tyrrhemian backarc opening ([PERSON] & [PERSON], 1986; Figure 0(b)). Extensional tectonics, associated with a NE-SW tensile stress field, was mainly accommodated by NW-SE and NE-SW-striking structures, with both normal and strike-slip kinematics, roughly synchronous with subduction-related magmatism ([PERSON] & [PERSON], 2009; [PERSON] & [PERSON], 2012; [PERSON], 2005). This led to the development of several ore deposits (e.g., [PERSON], 2011; [PERSON] et al., 2011) and geothermal systems (e.g., [PERSON] et al., 1984, 1994; [PERSON] et al., 2003; [PERSON] et al., 2013).
The study area follows the evolution of the Northern Apennines belt, being characterized by thrusting of a deep water Upper Cretaceous-Oligocene calcareous sedimentary succession (locally named Tolfa Flysch; Figure 0(c)) of Ligurian affinity (i.e., the sedimentary cover of the Tethys Ocean; Figure 0(d)) on top of Mesozoic marine carbonates of the Tuscan domain ([PERSON] et al., 1972). The area was later uplifted and domed by the intrusion of an acidic pluton within the sedimentary succession, associated with the activity of the Tolfa-Cerite volcanic district. K-Ar dating ascribes the extrusion of the Tolfa Dome Complex to 3.5 Ma ([PERSON] et al., 1989), likely guided by a major Figure 1:
NE-striking Pliocene master fault (Tofla fault; [PERSON] et al., 1997; [PERSON], 2006; Figures 1c and 1d). Hydrothermal alteration was promoted by circulation of fluids along two broadly coeval sets of NE- and NW-striking faults and fractures (described in detail in Section 4), dissecting the Pliocene volcanic dome, resulting from the interaction between the regional backarc-related tensional stress field and local doming related to the emplacement of intrusive rocks ([PERSON] et al., 2024). Circulation of hydrothermal fluids with a general acidic composition (pH between 1 and 4) promoted the hydrolytic alteration of felsic volcanic rocks, forming an argillic-rich superficial cover (i.e., the lithocap). Alteration in the Allumiere quarry is considered to be coeval with the activity of major faults cross-cutting the lithocap because secondary mineralization in cavities and along fault planes show acicular and zoned crystals of alunite and natroalunite that typically form under hydrothermal conditions (more details in [PERSON] et al., 2024).
## 3 Materials and Methods
Building on the recent, large scale and mineralogical characterization of the Allumiere lithocap by [PERSON] et al. (2024), we document the structural architecture and mechanical properties of the largest fault zones in this locality. In particular, (a) we present new mesoscale observations of the fault zones, integrated with microstructural details of the fault cores obtained via optical and scanning electronic microscopy; (b) we provide the mineralogical characterization of fault rocks subsequently used to produce experimental fault gouges; (c) we describe and discuss the results of friction and permeability experiments based on these experimental fault gouges.
### Field Work and Sampling
We collected hand-sample rocks from a representative major fault zone (42,1661427; 11,9040874; samples: FC1, FC2, FC3, described below; Figure 5a), which is coeval with alteration.
Although volcanic rocks in the study area suffered a strong imprint of late hydrothermal acid sulfate alteration, we collected a representative sample of the volcanic protolith near the ToIfa village, in the proximity of the Madonna della Rocca Sanctuary (42,152294; 11,942665; sample PL; Figure 1c).
Sample coordinates are referred to WGS 84/UTM zone 32N.
The study of the mineralogy, microstructures, friction and permeability properties of both the protolith and of the altered fault rocks allowed us to investigate the evolution of the mechanical and hydraulic properties of the lithocap rocks during hydrothermal alteration.
### Microstructural and Mineralogical Characterization of Fault Rocks
Microstructural analysis of fault rocks was performed by Scanning Electron Microscopy (SEM) by a Thermo Fisher Scientific Scios 2 microscope housed in the HPHT (High Pressure High Temperature) laboratory of INGV of Rome. The instrument was operated at 10 kV, 0.80 nA and a working distance of 6.9 mm.
Bulk mineralogy of fault rocks was characterized by using X-Ray Diffraction analysis. XRD analyses were performed using a Philips X'Pert PRO X-ray system housed in the Department of Earth Sciences of University of Padova. The instrument was operated at 40 kV and 40 mA using Co radiation. The whole-rock samples were ground and analyzed in the 2-85\({}^{\circ}\) 2\(\theta\) interval with a step size of 0.017\({}^{\circ}\) 2\(\theta\) and a counting time of 100s per step while spinning the sample. Data were collected with variable slit mode to keep the irradiated area on the sample surface constant and converted to fixed slit mode for semiquantitative analysis. Semi-quantitative estimation of mineral phases was performed by calculating peak areas and using mineral intensity factors as calibration constants ([PERSON], 1997) using the Profex-BGMN Doebelin and Kleeberg (2015).
Figure 1: Geological framework of the study area. (a) Simplified geological map of the Northern Apennines (Italy) showing the main, fault systems, principal tectonic units and location of the study area. Modified after [PERSON] et al., 2004; [PERSON] et al., 2020. (b) Schematic crystal cross-section through the Northern Apennines (modified after [PERSON] & [PERSON], 2012) showing the Tyrruhenian backarc rift associated with the Apennines subduction. (c) Simplified geological map of the Allumiere - ToIfa area, presenting the outcropping lithologies in the proximal area of interest (after [PERSON] et al., 1972). The trace of the ToIfa fault is drawn after [PERSON] et al., 1997. The location of the Allumiere quarry is marked by the white star. PL indicates the sampling location of the unaltered trachyte, 4 km SE of the quarry. (d) Schematic cross-section of the study area and interpreted extent of the hydrothermal alteration in the lithocap (orange; modified after [PERSON] et al., 2024).
### Friction and Permeability Experiments
To test the mechanical properties of faulted and altered rocks we performed friction and permeability experiments on rock gouges in the biaxial deformation apparatus \"BRAVA\" housed at the HPHT Lab of INGV Rome ([PERSON] et al., 2014; Figure 2a). To simulate a fault gouge, rocks were crushed with a disk mill and sieved to reach a grain size <250 um. All grains above 250 um were crushed until the whole sample was reduced to the desired grain size. In the case of FC2 and FC3, a mortar and pestle were used to gently disaggregate the natural fault gouges instead of the disk mill.
The samples were deformed in double-direct shear configuration (Figure 2b; [PERSON] et al., 2014). In this setup, two sample layers (\(\sim\)4 mm thick each) were simultaneously sheared at room temperature and water-saturated conditions, under normal stresses (\(\sigma_{w}\)) ranging from 25 to 125 MPa. We first slide the material for 7 mm at the lowest normal stress (\"run-in\" phase) and for 5 mm at each of the following normal stress increments. This amount of slip ensured to reach (near-) steady-state conditions at all investigated \(\sigma_{w}\). After each run-in phase, we performed a velocity-step test to evaluate the velocity dependence of friction in the framework of the Rate-State friction theory (e.g., [PERSON], 1998). We evaluate the parameter (a-b) = \(\Delta\mu_{w}\)/ln(V/V\({}_{0}\)), where \(\Delta\mu_{w}\) is the new steady state friction after a velocity step from V\({}_{0}\) to V. During velocity steps, the slip velocity was increased stepwise from V = 1, to 3, 10, and 30 um/s.
Permeability tests were conducted using an equivalent direct shear configuration (Figure 2c; [PERSON], 2016), but confined in a pressure vessel using oil at the isotropic pressure of 12.5 MPa, isolated by a rubber jacket. In this configuration, we applied a normal stress \(\sigma_{w}\) = 13.5 MPa, and water pore pressure \(P_{p}\) = 5.4 MPa, injected into the sample perpendicular to the gouge layers, via two intensifiers (see [PERSON] et al., 2014 for the details). The chosen normal stress and pore pressure reproduce hydrostatic conditions \(P_{p}\) = 0.4\(\sigma_{w}\), simulating the stress field at a depth of \(\sim\)0.5 km in the lithocap. At these conditions, the sample was deformed at constant velocity of 10 um/s for a total of 7 mm (run-in phase) until near-steady state friction was achieved and was then allowed to relax holding the slip velocity to 0. At this moment, we applied a gradient of pressure across the sample layer of \(\Delta P_{p}\) = 0.5 \(\sigma\) 1 MPa (depending on the sample) until stabilization of the flux of water (Figure 2c). This procedure allows to measure the permeability (\(k\)), calculated using the [PERSON] formula: \(k\) = \(Q\,w_{L}\,\eta_{w}\)/(2 \(\Delta\)\(\Delta P_{P}\)), where w\({}_{\rm L}\) is the total layer thickness (both gouge layers), \(\eta_{w}\) is the viscosity of water, and \(Q\) is the water flux perpendicular to the sample section (\(A\)).
## 4 Fault Architecture in the Allumiere Lithocap and Mineral Alteration
We investigated the fault-controlled agillic alteration of the Tolfa-Allumiere lithocap exposed in an abandoned quarry near the Allumiere village (49.16583; 11.903194; Figure 1c; 3A).
As already mentioned, the unaltered volcanic protolith crops out in the Tolfa town, 4 km SE of the quarry (Figure 1c). Bulk X-ray diffraction analysis of these volcanics, shows the presence of K-feldspar, plagioclase, biotite and cristobalite (Figure 5d). This mineral assemblage is consistent with a volcanic rock of tracb
Figure 2: Experimental setup. (a) Sketch in scale of the double direct shear apparatus BRAVA and double direct shear (DDS) configuration for unconfined (b) and confined (c) experiments. Redrawn from [PERSON] et al. (2023).
composition, in agreement with previous studies in the same area ([PERSON], 2006; [PERSON] et al., 1997; [PERSON] et al., 2024).
Conversely, the lithocap is composed of juxtaposed alteration zones characterized by domains of \"residual quartz\" (reported in red in Figure 3a) embedded in a massive alunite-kaloinite-rich matrix (\"argillic\" and \"advanced agillic\" facies reported in pale yellow and pale green in Figure 3a). Residual quartz domains are competent, dome-shaped bodies consisting of gray and brownish massive and vacuolar silica. The silicified domes are surrounded by the advanced argillic facies (pale yellow; Figure 3a), consisting of whish-reddish rocks very rich in alunite containing minor fractions of kaolinite-quartz-rich rocks with a moderate degree of competence. The advanced argillic facies is surrounded by the argillic facies (pale green; Figure 3a), consisting of yellowish-reddish rocks rich in kaolinite, smectite to illite/smectite mixed layers with alunite-natoalunite and relicts of original volcanic K-feldpars-rich rocks (pale green of Figure 3a). The meso- and micro-structural and mineralogical characteristics of the alteration facies have been extensively documented by [PERSON] et al. (2024).
Figure 3: Architecture of fault zones in Allumiere lithocap. (a) 3D image of the Allumiere quury (Central Italy), showing the distribution of the alteration facies and main faults (modified after [PERSON] et al., 2024). The quury is characterized by a widespread veining, with quartz-rich veins mostly occurring in the lower level of the quury (blue star), and alunite-rich veins more common in the upper levels of the quury (pink star). (b) Stereographic projection (Schmidt net, lower hemisphere projection) measured faults and joints deforming the entire lithocap. Faults are organized in two major systems, with extensional kinematics. Strike-slip faults locally deform the lithocap. Joints are counted with the methods of % per 1% of net area (c) Architecture of major fault zones hosted in the lithocap. Cataclastic deformation and more incoherent rocks are observed around sharp and often striated principal slip surfaces (PSS) marked by reddish or gray horizons.
The structure of the lithocap is strongly shaped by faults and fracture patterns. The bulk of the rock body is pervasively affected by mostly subvertical fractures and minor faults in all the alteration facies (Figure 3b). In addition, major normal and strike-slip faults cross-cut the quarry with NE- and NW-striking orientation (Figure 3b) and are locally identified by sharp contacts between the alteration facies and by the presence of synthetic minor faults (Figure 3c).
Fault zones are characterized by well-developed fault cores, highlighted by cataclasites, chaotic breccias and striated Principal Slip Surfaces (PSS; Figures 4a and 5a).
We note that in the lithocap it is difficult to identify damage zones in a classical sense ([PERSON] et al., 1996). The hydrothermal alteration almost completely obliterated the primary structures of the protolith, which are traditionally used to distinguish fault cores and damage zones. Instead, fragmentation and comminution of pre-existing altered rocks, that is, residual silica and argillic/advanced argillic facies rocks, have been used as a criterion to identify the thickness of fault zones. In more complex structures, fault zones may present strongly silicified centimetric-to-metric isolated blocks embedded in a fine and incompetent matrix with yellowish-whitish appearance (Figures 3c and 4a).
Displacement along major faults is difficult to constrain but it is accommodated along single or multiple PSS constituted by reddish or gray clay-rich (up to more than 70% in volume; [PERSON] et al., 2024) gauges sharply cutting across other fabrics (Figures 4a and 5a). In mining tunnels protected from weathering, we observed well defined slickenlines in clay gouge (e.g., extensional kinematics with downward steps in Figures 4a and 5a).
Figure 4: Evidence of fluid overpressure in the lithocap. (a) Pockets of chaotic breccias associated with major fault surfaces, oriented NW-SE observed in abandoned underground mining tunnels crossing the lithocap. Red lines highlight the slickenlines with dip-slip kinematics. (b) Chaotic breccias are made of angular alunite clasts in a red clay-rich matrix. (c) The lower level of the quarry is characterized by the widespread veining of quartz veins. (d) The upper level of the quarry is characterized by subvertical alunite-rich veins. The Schmidt net shows the attitudes of alunite-rich veins.
Figure 5.— Microstructural and mineralological characterization of the fault zone, sampled for friction experiments. (a) Slip is accommodated along a principal slip surface (PSS) marked by centimetric-thick, well striated red gouge. The gouge has a concentration in clay minerals up to 70% in volume (sample FC3). FC1-FC3 are the rock samples collected across the fault zone for friction experiments. (b) Detail of a quintic-rich foliated catalase (white; FC2) and foliated kaolinite-rich foliated gouge (red; FC3). Note the occurrence of massive aluntic and quartz clats estimated from the wallrock. (c) Mechanical communication (FC2) and clay-concentration with the formation of a kaolinite-rich foliated ultracataclastic (FC3). (d) X-Ray semi-quantitative analysis of the protofl (PL) and of fault rocks collected across the studied fault zone (mineral abbreviations from Whitney & Evans, 2010). Mineral abreviations: Bio: biotite; Crs: cristobalite; KKs: K-feldwer; Plg: plagioclase; Qtz: quartz; Alu: aluntic; Na-alur: natroalunite; Kln: kaolinite; Dck: dickite; Gor: georexiite; Anl: analcime; Off: offretite; Wm: white micas; Mm: montmorillonite.
At the scale of the whole lithocap, there is abundant evidence of the development of cyclic fluid overpressure and hydrofracturing (Figure 4). We document pockets of chaotic breccias ([PERSON] and [PERSON], 2008; Figure 3a), containing angular clasts of massive alunite/natoalunite in a red clay-rich matrix (Figure 4b). The widespread occurrence of these breccias along major faults, rather than along subvertical conduits, and the presence of a kaolinite-rich fluidized matrix indicate that these rocks have formed by episodic faulting and fragmentation of the fault wallrock (e.g., Figure 4a). Moreover, the presence of clasts of massive sulfates (\"advanced agillic\" facies) indicates the late brittle reworking of already intensely altered rocks, close to PSSs.
In the lower levels of the quarry, and in underground tunnels we find widespread occurrence of quartz and alunite veins, typically occurring with a chaotic distribution (Figure 4c). These veins are more evident in massive residual silica domes (Figure 4c).
Toward the top of the Allumiere quarry, hydrofractures are mostly represented by secondary alunite-rich veins, containing alunite and natroalunite precipitated as secondary minerals (Figure 4d, microstructural details in [PERSON] et al., 2024). These fractures have a broad distribution but define a general NW-SE trend (Figure 4d), consistent with the regional NE-SW stretching. They appear to be undeformed with respect to the surrounding rocks but they rarely cut major clay-rich faults, suggesting that they are coeval and likely formed toward the end of the tectonic evolution of the lithocap.
In a transect along a representative fault zone hosted at the contact between agillic facies and advanced agillic facies rocks (Figure 5a), we observe that the degree of alteration and comminution of rocks increases from the outer core zones (FC1, in kaolinite-alunite-quartz rich rocks; Figure 5d) to the alunite-rich rocks (FC2; Figure 5d) to the localized clay-rich red PSS (FC3; Figures 5a and 5d).
XRD data show a marked increase of kaolinite, white micas and other phyllosilicates up to 70-80 wt% in correspondence of the PSS (FC3; Figure 5d).
We carried out microstructural analysis across the principal slip surface, on a sample containing FC2 and FC3 fault rocks (Figures 5a and 5b). At the microscale, we observe the formation of a fault gouge by the mechanical comminution of alunite-rich rocks (FC2, Figure 5c).
The PSS is constituted by a clay-rich foliated gouge containing residual clasts of alunite and quartz entrained from the wallrocks (Figures 5b and 5c). The increase in clay concentration on the PSS (sample FC3; Figure 5d) is aided by the dissolution of fine-grained alunite and natroalunite (Figure 5c), as also indicated from the pervasive development of a foliation and by the survival of large porphyoclasts (Figures 5b and 5c).
## 5 Frictional and Permeability Properties of Altered Fault Rocks
To investigate the mechanical and hydraulic properties of the fault rocks and the evolution of these properties during lithocap formation we performed a suite of friction experiments on rock powders (gouges) obtained from the unaltered volcanic protolith (PL; Figure 5d), and from the fault zone illustrated in Figure 5a: the kaolinite-alunite-quartz rich rocks (FC1; Figure 5d), the alunite-rich (FC2; Figure 5d) and the clay-rich gouge (FC3; Figure 5d).
Curves of evolution of the shear stress with experimental fault slip (Figure 6a), show an initial phase of linear elastic loading, followed by a gentle roll-over and by a phase of \"steady-state\" sliding characterized by stable slip and constant strength of the experimental gouges. This behavior is observed in all tested materials at each normal stress (Figure 6a), with the exception of a slight strain hardening behavior observed in FC3 gouges derived from the PSS.
The sliding shear stress (\(\tau\)) of the gouges was measured at each normal stress and at the end of each run-in phase before the velocity-stepping phase. The shear strength of each sample follows a Coulomb (linear) brittle failure envelope (Figure 6b): \(\tau=\upmu_{\text{n}}+\text{C}\), where C is the cohesion of the rocks, negligible in all samples. Sample PL (unaltered protolith) has a high friction coefficient, \(\upmu=0.55\), a friction coefficient close to [PERSON]'s range (0.6-0.8; [PERSON], 1978; Figure 6c), while the strength of both samples FC1 (kaolinite-alunite-quartz rich rocks) and FC2 (alunite-rich gouge) is lower: \(\upmu=0.45\) (Figure 6c). Sample FC3 (clay-rich gouge) is instead very weak, \(\upmu=0.26\) (Figure 6c).
The permeability of the tested rocks is also affected by the degree of alteration. The clayey FC3 has the lowest permeability (\(k=1.62\times 10^{-19}\) m\({}^{2}\); Figure 6c), three orders of magnitude lower than both the protolith (PL) and the Alu-rich gouges (FC2 \(k>1.6\times 10^{-16}\) m\({}^{2}\); Figure 6c).
All the tested materials show velocity strengthening behavior, that is, positive (a-b), whose values increase with increasing clay content, for example, protolith (PL) and alunite-rich gouges (FC2) versus clay-rich gouges (FC1, FC3). All the tested materials show the tendency to stable slip behavior upon an increase in fault slip velocity (Figure 7). The change in \(b\) values is expressed by the different evolution of friction to steady state values after a velocity step: positive \(b\) values correspond with a peak followed by a gradual decrease (blue curve) while negative \(b\) values correspond with a continuous (monotonic) increase (red curve). The most clay-rich PSS (FC3) show negative \(b\) values instead of positive as in the case of other studied rocks (e.g., FC3 vs. PL; Figure 7e).
## 6 Discussion
### Natural Versus Experimental Deformation
The strength of alunite/natoalunite- and kaolinite-rich rocks, typical of hydrothermal acidic alteration environments, has been poorly documented at crustal stress conditions (e.g., [PERSON] & [PERSON], 2009). Our experiments show that the hydrothermal alteration from trachyte to alunite- and kaolinite-rich rocks leads to a noticeable mechanical weakening of the deforming rocks. This weakening is further enhanced by the precipitation or concentration of clays (up to 70-80 wt%; Figure 5d) along the principal slip zones of natural faults (sample FC3, Figure 6).
Experimentally deformed gouges (Figures 8a and 8b) and naturally deformed fault rocks (Figures 8c and 8d) show similar foliated fabrics in which alunite/natoalunite casts are wrapped by a clay-rich matrix. This fabric is likely the cause of frictional weakness of the experimental samples, which is consistent with previous laboratory measurements on clay-rich gouges (e.g., [PERSON] et al., 2009, 2011; [PERSON] et al., 2010; [PERSON] et al., 2012 and others) and kaolinite in particular (e.g., [PERSON], 2012). In experimental samples, the foliated fabrics are observed only within boundary shears with intense comminution (Figure 8a) and in general the clay-rich foliation
Figure 6: Strength, slip behavior and permeability values of unaltered versus altered rocks. (a) Experimental curves showing the evolution of shear stress versus displacement. Each curve shows the shear strength for each normal stress (25, 50, 75, 100, 125 MPa). For each normal stress step, we measured the steady–state (SS) shear stress and the velocity dependence of friction (VS). (b) Coulomb Criterion envelopes for each rock sample from SS shear stress. The lowest shear stress data (empty circles) come from permeability tests. (c) Coefficient of frictions and permeability values of the unaltered protolith (PL) and of the altered fault rocks (FC1-FC3). Friction coefficient is computed as the slope of the linear best fit from data in panel (b). Permeability data measured with Darcy’s law (see paragraph 3.3).
is less evident (Figure 8b). The greater intensity of clay foliation in natural samples (Figure 8d) is probably modulated by the local concentration of clays along slip surfaces via precipitation from fluids and/or passive concentration (e.g., [PERSON] et al., 2015) via preferential dissolution of sulfates. The dissolution of sulfates may be facilitated by the intense grain size reduction inside the fault that enhances fluid-rock interaction (Figure 5c). Also, in the experimental samples, the natural clay foliation was disrupted by disaggregation and mixing during sample preparation. For this reason, we also infer that the strength measured for FC3 gouges probably represents the upper bound of the possible friction of faults, since intact foliated fabrics are known to be generally weaker than their powdered equivalents ([PERSON] et al., 2009).
As described earlier, we performed experiments on fault gouges, simulating slip along incohesive fault rocks. While it is common to use gouges in friction experiments, they may be less representative of fracturing and slip in cohesive rocks. However, the coefficients of friction derived from Coulomb envelopes, indicate the general strength of the fault rocks with depth. In the Allumiere lithocap, we observe cohesive massive residual silica and faults hosted in poorly cohesive kaolinite- and alunite-rich agillite alteration facies, with the larger faults showing PSS with very high (\(>\)70% vol) concentrations of kaolinite and other clays. PSS in particular are almost cohesionless and very erodible in the field and therefore we assume that experimental gouges well represent the observed structures in the field. Consistently with qualitative Schmidt hammer analysis performed by [PERSON] et al. (2024), all the altered rocks are likely to have negligible or low cohesion, in addition to low friction, with respect to the massive silica and the unaltered volcanics.
Our experiments were carried out at room temperature, whereas slip along the Allumiere faults probably occurred in the presence of pressurized fluids, as suggested by the presence of chaotic preccias and hydraulic fractures (e.g., Figure 4; [PERSON], 2010), and elevated temperatures, potentially between 160\({}^{\circ}\) and 270\({}^{\circ}\)C, by analogy with similar deposits (e.g., [PERSON] et al., 2000). The applicability of our results to rocks under hydrothermal conditions will be, therefore, discussed.
To our knowledge, there is no available data on the strength of alunite-rich rocks and very limited information on friction of kaolinite-rich gouges sheared at elevated temperature conditions (e.g., [PERSON] and [PERSON], 1992). [PERSON] and [PERSON] (1992) showed that wet kaolinite-quartz synthetic gouges (33% quartz, similar to our FC1 sample) presented a small hardening when sheared at elevated (400\({}^{\circ}\)C) temperatures. However, they observed a much higher strength of synthetic quartz/kaolinite mixtures than what we report in our experiments, either
Figure 7: \(a\)–\(b\) values for the unaltered fault gouges (a) and altered rocks (b–d) at different velocity steps (\(v=1\), to 3, 10, and 30 μm/s). (e) The clay-rich gouge (FC3) show negative \(b\) values. (f) The increase in the alteration degree produces an increase in the average (a–b) parameter.
because of the different composition of their gouges (slightly lower phyllosilicates than our FC3) or because of the difference in experimental methods.
An insight into the possible frictional behavior of our kaolinite-rich gouges (FC3 and FC1) at higher temperatures may come from the comparison with other gouges containing different phyllosilicates. In previous studies, gouges retrieved from the slip zone of large phyllosilicate-rich crustal faults such as the San Andreas fault or the Alpine fault show that bulk friction is not dramatically affected by high temperatures (e.g., [PERSON] et al., 2016; [PERSON] et al., 2016), with the possible exception of rocks containing smectite, which has a low temperature of stability ([PERSON] et al., 2014; [PERSON] & [PERSON], 2015). Therefore, it is reasonable to assume that the kaolinite-rich PSS of the Allumiere lithocap are significantly weaker than unaltered or slightly altered surrounding rocks even at elevated temperatures. Either way, the strength of samples constituted mostly by alunite minerals (e.g., FC2-like samples) or very rich in kaolinite (FC3-like) at elevated temperatures are unknown and will be the subject of future investigation.
With regard to the stability of friction and velocity dependent behavior of friction, we observe general velocity strengthening friction in all our samples. Also, the altered rocks of the Allumiere lithocap are more velocity strengthening than the unaltered protoolith (PL). This suggests that the alteration has a stabilizing effect on friction, in addition to rock weakening. The decrease of the \(b\) value in kaolinite-rich altered rocks, and in particular negative \(b\) values along the PSS (FC1 and FC3 in Figures 7e and 7f) is a common feature phyllosilicate rich rocks sheared in friction experiments (e.g., [PERSON] et al., 2016). However, a transition from velocity-strengthening to velocity-weakening friction, is generally observed at temperatures above \(\sim\)150\({}^{\circ}\)C in phyllosilicate-rich rocks (e.g., [PERSON] et al., 2012; [PERSON] et al., 2016; [PERSON] et al., 2016). Therefore, we cannot exclude that at higher temperature, characteristic of the hydrothermal alteration, the faults in the Allumiere caprock experienced unstable, possibly seismic slip, perhaps in the presence of elevated fluid pressures.
Figure 8: Experimentally deformed versus naturally deformed fault gouge microstructures. (a) Boundary shears in the experimental sample are characterized by (b) a foliated fabric with intense communication of alunite/natroolunite clasts. Foliation traces are marked with white dotted lines. (c) Natural ultractalasite are composed of (d) alunite/natroolunite clasts, wrapped in a clay-rich matrix with particularly well-developed foliation. Red dotted lines indicate the traces of boundary shears.
### Alteration Versus Deformation Feedbacks: A Model for Caprock Genesis
At the large scale, the Allumiere caprock is constituted by a body of altered rocks that are weaker than the unaltered volcanics (Figure 6). Among the caprock rocks, the weakest and most impermeable rocks are found in few massive clay-rich rock bodies and along clay-smeared major faults (Figures 5 and 6).
This is illustrated by the presence of several structural-mineralogical domains (Figure 3a) with specific frictional and hydraulic properties (Figures 6 and 7), determined by the presence of alteration minerals (Figure 5d).
Combining structural observations, mineralogical analyses and experiments we propose the following model for the structural and petrophysical evolution of the Allumiere lithocap (Figure 9). Such evolution is controlled by the cyclic brittle deformation and hydrothermal alteration.
Figure 9: Schematic model showing the structural and petrophysical evolution of the caprock of a hydrothermal system.
During initial doming and tectonic extension (Figure 8(a)), deformation of the unaltered protoolith (i.e., tracbyte, sample PL) is accommodated by high-angle fractures and faults that are frictionally strong, as shown by the mechanical data (\(\mu\) = 0.55; Figure 5(c)) and have a high permeability (up to 1.96 \(\times\) 10\({}^{-16}\) m\({}^{2}\); Figure 5(c)). Fautiling and diffuse brittle fracturing promote hydrothermal fluid circulation that causes intense alteration of the protoolith to argillic and advanced argillic rocks (Figure 8(b)). This alteration culminates with the formation of massive alunite-group minerals with minor kaolinite (i.e., advanced argillic alteration; FC2; Figure 5(d)). [PERSON] et al., 2000 proposed a temperature of 100\({}^{\circ}\)C-150\({}^{\circ}\)C for the alunite-kaolinite alteration facies, developed in an acidic to neutral (pH = 3-5) environment, typical of central areas of lithoaps. Since the beginning of this alteration, the lithocap experiences enhanced activity of the altered faults caused by the newly formed mineral phases (e.g., clays and sulfates, FC1-FC2), which are frictionally weaker than the protoolith (Figure 5(b)) and more prone to reactivation. This promotes strain localization and fault growth within the kaolinite-alunite-rich bodies, formed in distal areas from the initial subvertical conduit of fluid ascent, which is now filled by residual silica (Figure 8(b)). During the last stages of extension (Figure 8(c)), since argillic and advanced argillic facies rocks are still permeable (Figure 5(c)), they allow further circulation of acidic fluids promoting preferential dissolution of alunite-group minerals, with the precipitation and passive concentration of clays on PSS of major faults, that is, the evolution from FC1 to FC3-like rocks (Figure 5). Preferential dissolution of alunite-group minerals is favored by dissolution and/or pressure-solution in the presence of acidic (pH < 2) fluids, potentially derived from deep fluid sources ([PERSON] et al., 2024), that increase the solubility of K and Al ([PERSON] et al., 2013). Moreover, the mechanical grain size reduction and fracturing along PSS have the potential to enhance these processes of mobilization. K-Al-rich fluids potentially re-precipitated as secondary alunite-rich veins by filling open fractures in the upper level of the lithocap (Figure 5(d)), in cavities in the massive residual silica and in pre-existing faults ([PERSON] et al., 2024).
The increase in the content of clays, possibly favored by mechanical comminution, leads to the formation of continuous coatings of impermeable material (Figure 5(c)), up to 30 cm thick along major faults (Figure 5(a)). The enrichment of clays along PSSs (FC3) causes a strong decrease of fault permeability, up to three orders of magnitude with respect to the PL and FC1-FC2 facies (Figure 5(c)). Permeability data thus demonstrate a transition of fault behavior from \"conduit\" during the initial stage of alteration, to \"barrier\" (sensu [PERSON] et al., 1996) during the advanced alteration stage associated with the later faulting events. This fluid barrier behavior is corroborated by the occurrence of pockets of chaotic precies associated with major fault surfaces and by by by by bydefractive networks (Figure 4), which are symptomatic of fluid pressure build-up (e.g., [PERSON], 2010) in absence of preferential pathways such as conduit faults or permeable facies. The contrasting mineralogy between quartz veins at the bottom of the caprock and alunite veins at the top (Figure 5(a); Figures 5(c) and 5(d)) may also suggest the occurrence of at least partially isolated hydrological circuits of hydrothermal fluids separated by low permeability fault zones. Quartz-filled hydrofractures may reflect silica-rich fluids from a deeper source trapped below clay-rich fault barriers. Conversely, secondary alunite-rich veins may be the result of pressurized fluids enriched in sulfates dissolved from the same fault zones.
Moreover, the hydraulic preciesa consisting of massive alunite clasts in a clay rich matrix (Figure 5(b)), formed by breakage and remobilization of clay-rich fault cores and alunite-rich wall rocks, may indicate the episodic breaking of fault seals (fault-valve behavior, e.g., [PERSON], 1987).
We infer that the conversion of faults into fluid barriers forces the fluid flow toward the outer portions of the altered volume of rocks (Figure 8(c)), laterally expanding the alteration front and progressively weakening more distal faults. This effect would promote the lateral growth of the lithocap (Figure 8(c)). The presence of weak overpressured faults in the later stages of extension is also corroborated by the activity of several large low-angle normal faults (Figure 0(b)), which imply low frictional strength and are efficient means of tectonic extension ([PERSON], 2011).
Summarizing, the synergetic activity of hydrolytic alteration, slip localization in weak lithologies and clay concentration along faults result in a \"structural\" self-sealing of the lithocap because of hydrological fault barriers, leading to the formation of an efficient caprock.
### Analogies and Potential Implication for Other Active Systems
The structural and petrophysical evolution of the Allumiere lithocap can be used as an analog for the formation of active caprocks in geothermal systems and volcanic systems in the presence of felsic volcanic rocks, such as the M. Amiata geothermal field in the Northern Apennines ([PERSON], 2008), the Yellowstone geothermal system ([PERSON] et al., 2003), and the Campi Flegrei caldera ([PERSON] et al., 2021; [PERSON] et al., 2016). For instance, the shallow caprock of the Campi Flegrei active volcanic system corresponds to a seismic horizon that bends upward in an arch shape underneath the town of Pozzuoli, overlaying the seismically active area ([PERSON] & [PERSON], 2015). Mineralogical analysis of well cores from the superficial rocks (0-2 km of depth) of the Campi Flegrei active volcanic system of Italy show argillization of tuffs, akin to the rocks in the Allumierc lithocap ([PERSON] et al., 1985; [PERSON] et al., 2016; [PERSON] et al., 2015). The argillic alteration documented in the Allumierc-Tofia system may signal the transition from potentially seismic faults to stable zones of localized strain, as suggested by the increasingly velocity-strengthening behavior of the phyllosilicate-rich gouges, at least at low temperature (Figure 7). Earthquake nucleation may still occur in nominally rate-strengthening rocks due to fracturing processes of healed fault materials (e.g., [PERSON] et al., 2014). Earthquake nucleation is thus likely to occur in strongly cemented domains (i.e., residual silica domains; Figure 3a) but is prevented in the altered fault zones due to the presence of phyllosilicates, which promote aseismic creep. On the other hand, the higher temperatures and the increasingly efficient sealing of the altered rocks can promote unstable behavior (e.g., [PERSON] et al., 2016) and local fluid overpressure, respectively. In particular, hydrofracturing when fault seals break (Figure 4) is likely to cause cyclic diffused microseismicity (e.g., [PERSON], 2016).
Episodic seismicity may reveal the breakage of seals as recently suggested in the Campi Flegrei active volcanic systems ([PERSON] et al., 2024) in which this type of altered rocks (i.e., argillic rocks) may constitute the caprock of the hydrothermal system. Our results can be used both to provide suitable mechanical data to refine models for the mitigation of the geological risk (e.g., induced seismicity) in geothermal and volcanic systems (e.g., [PERSON] et al., 2020) and to advance the structural information necessary for the exploration of ore deposits (e.g., [PERSON] et al., 2011; [PERSON] et al., 2024).
Regarding reinjection procedures during geothermal energy exploitation and for the evaluation of seismic hazard, fault activity needs to be modeled taking into account frictional properties of rocks coupled with observations and modeling of poroelastic and thermal stressing effects, injection rates, stress transfer and geological context (e.g., [PERSON] et al., 2024; [PERSON] et al., 2023; [PERSON] et al., 2022). In this context, our field observations and friction tests help to constrain that in the shallow caprocks of hydrothermally altered volcanic systems, major fault display potentially widespread clay-rich cores. The low friction of these fault cores possibly limits the stress accumulation in the most altered zones of the caprock (\"advanced argillic\" facies in ore geology, e.g., [PERSON] et al., 2000) compared to the less altered zones characterized by stronger rocks. In addition, the general velocity-strengthening friction we document in all altered rocks is likely to promote slow/aseismic reactivation of pre-existing faults, at least at low temperature conditions. However, as mentioned in the previous Section, laboratory data should be extrapolated to natural reservoir conditions with care. A more in-depth understanding of the hydro-mechanical coupling of fault rocks (e.g., [PERSON] et al., 2017; [PERSON] et al., 2022) and the effects of temperature on frictional properties of hydrothermal alterations are required.
## 7 Conclusions
Our field observations and laboratory results suggest that the structural evolution of hydrothermal caprocks in acid volcanic systems is strongly affected by the interaction between deformation and chemical alteration along faults. Circulation of acidic fluids (pH \(<\) 2) along faults promotes residual enrichment of clay minerals along principal slip surfaces, promoting fault weakening (friction coefficient evolving from 0.55 to 0.26) and a transition from fault \"conduit\" to \"barrier\" behavior, associated with a decrease of permeability from \(1.96\times 10^{-16}\,\mathrm{m}^{2}\) to \(1.62\times 10^{-19}\,\mathrm{m}^{2}\). The barrier behavior of faults can also guide the lateral growth of alteration, ultimately leading to the formation of an extensive caprock.
The study of the mechanical and hydrological behavior of caprock faults has relevant implications for reinjection procedures during geothermal energy exploitation and for the evaluation of seismic hazard in active volcanic systems. Velocity-strengthening behavior of low permeability fault rocks suggest potential stable slip of faults hosted in argillic rocks, at least at low ambient temperatures. Conversely, domains that suffered minor alteration can still have higher potential for seismic instability and are comparatively much more permeable.
## Data Availability Statement
The data files used in this paper are available at Marchesini (2024).
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wiley/fd14b5ce_94a6_46f5_bc78_083f72dde987.md | # Geochemistry, Geophysics, Geosystems
10.1029/2024 GC011704
Extreme Mantle Heterogeneity Revealed by Geochemical Investigation of In Situ Lavas at the Central Mohns Ridge, Arctic Mid-Ocean Ridges [PERSON]
1 Department of Earth Science, Center for Deep Sea Research, University of Bergen, Bergen, Norway 1
[PERSON]
1 Department of Earth Science, Center for Deep Sea Research, University of Bergen, Bergen, Norway 1
[PERSON]
1 Department of Earth Science, Center for Deep Sea Research, University of Bergen, Bergen, Norway 1
[PERSON]
1 Department of Earth Science, Center for Deep Sea Research, University of Bergen, Bergen, Norway 1
###### Abstract
Mid-ocean ridge basalts reflect the mantle's composition and reveal processes from melting to eruption. The Mohns and Knipovich Ridges have ultraslow spreading rates, low magma budgets and erupted lavas indicating various mantle domains. Here, we use geochemistry and isotope systematics of in situ samples from two axial volcanic ridges (AVRs) to study mantle heterogeneity and melt production. By linking chemical variations to high-resolution bathymetry and age data, we document systematic changes over time in the mantle source of the volcanic sequence. At Mohns Ridge AVR-M10 (72.3\"N), we observed significant variations in chemistry (e.g., (La/Sm)\({}_{\rm N}\) from 0.7 to 2.9) and isotope systematics in basaltic samples from a small area (\(\sim\)1 km\({}^{2}\)), suggesting the emplacement of multiple small-volume lava flows. Pb isotope variations, for example, \({}^{206}\)Pb/\({}^{204}\)Pb (17.91-18.76), are comparable with the observed range along the entire Mohns and Knipovich Ridges. Temporal constraints document that erupted basalts have changed from highly radiogenic Pb compositions to a more depleted signature within 30 ka. To explain the extreme variations in the erupted lavas at the Mohns Ridge, the mantle would need to be highly heterogeneous in composition with effective melt extraction and limited mixing prior to eruption. We use the highly heterogenous mantle underneath the Mohns Ridge to understand the melt extraction processes and mixing of melts and propose a two-stage melting model: continuous generation of enriched melts from a deep and fertile source in the first stage, while depleted melts from a shallower and more refractory mantle occur sporadically and simultaneously with the intermittent ascent of diapirs.
17 JUN 2024 29 OCT 2
Magma chambers are the pooling of melts after segregation in the mantle and are extensively documented in several studies from fast ([PERSON] et al., 2013; [PERSON] et al., 1998) and intermediate spreading ridges ([PERSON] et al., 2006). When melts from different mantle domains and with different histories are mixed in a magma chamber, their original chemical signatures may be suppressed by homogenization. Therefore, the study of small-scale heterogeneities is challenging at fast-spreading ridges where the melts are homogenized in large and long-lived magma chambers ([PERSON] et al., 1996; [PERSON] and [PERSON], 1981; [PERSON] and [PERSON], 1992; [PERSON] and [PERSON], 2009). The occurrence of magma chambers under slow- and ultraslow-spreading ridges is more debated ([PERSON] et al., 2021). However, several studies claim to document that magma chambers also occur in association with these ridges ([PERSON] et al., 2017; [PERSON] et al., 1998, 2006). Nevertheless, the documentation of a magma chamber at the ultraslow-spreading Southwest Indian Ridge occurs in an area with a thicker crust and enhanced melt supply ([PERSON] et al., 2017) and may therefore not be representative of all volcanic segments at ultraslow-spreading ridges.
In this study, we analyze the major and trace element concentrations as well as radiogenic isotope ratios (Sr, Nd, and Pb) of lavas (\(n=75\)) sampled in situ to uncover the magmatic history of individual axial volcanic ridges (AVRs) and gain insights into the melting process and segregation at ultraslow-spreading ridges. We selected two well-developed AVRs, one at the Mohns Ridge (\(72.3^{\circ}\)N) and one at the Knipovich Ridge (\(77.5^{\circ}\)N), to perform a detailed study. The AVR-M10 in the central Mohns Ridge, that hosts the hydrothermally active Aegirs Spring ([PERSON] and [PERSON], 2016), represents a transition in the bathymetry where the rift valley is at its deepest, the crust gets thinner, and large variations in the composition of basalts have been explained by a plume influence from the Iceland--Jara Mypar Plume system ([PERSON], [PERSON], et al., 2016; [PERSON] et al., 1996; [PERSON] et al., 2013). The AVR-K4 is one of the most well-defined AVRs on the Knipovich Ridge and is associated with hydrothermal activity documented during our 2017 AUV mapping campaign. Previous studies have focused on large-scale variations based on dredged samples without visual observations, accurate sampling positions, or detailed observations of the volcanic terrain. Our study goes beyond previous research by providing more detailed spatial information and combining geochemical and isotopic variations from our in situ ROV samples with high-resolution bathymetry (1-2 m). In addition, we build on the age constraints of the volcanic evolution presented in [PERSON] et al. (2023) to study the small-scale spatial and temporal chemical variations from individual spreading segments. We discuss the influence of different mantle domains and how these lead to the heterogeneity recorded in the erupted lavas. Further, we discuss the mantle upwelling and the formation and extraction of melt under ultraslow-spreading ridges.
## 2 Geological Setting
The Mohns and Knipovich Ridges are two of the five first-order ridge segments in the Arctic, now jointly termed the Arctic Mid-Ocean Ridges (AMOR) (e.g., [PERSON] et al., 2010) (Figure 1). The central and northern parts of this ridge system are characterized by ultraslow-spreading rates ([PERSON] et al., 2008), a relatively thin (3-4 km) crust ([PERSON] et al., 2010; [PERSON] et al., 2000), and a deepening rift valley northwards. The Mohns Ridge initiated seafloor spreading approximately 54 Ma, whereas the Knipovich Ridge appeared around 15-20 Myr later ([PERSON] et al., 2008). The spreading direction of both ridges is highly oblique (30-60\({}^{\circ}\)) to the orientation of the rift valley, with Knipovich Ridge being the most extreme. The ridges are separated into multiple spreading cells expressed as en echelon basins and a series of axial volcanic ridges ([PERSON] et al., 1994) occurring approximately every 50 km on the Mohns- and 100 km on the Knipovich Ridge. Volcanic activity is documented throughout the width of the rift valley, with high renewal rates, especially for the AVRs suggested to be steady-state volcanic systems ([PERSON] et al., 2023). The southern part of the Mohns Ridge is strongly affected by the Iceland-Jan Mayen plume leading to enhanced volcanism, seen as a shallow rift valley and closely spaced AVRs, and a geochemical signature indicative of a plume component ([PERSON] et al., 2005; [PERSON], [PERSON], et al., 2016). Previous studies of incompatible trace elements revealed three different geochemical types of lavas suggested to originate from a heterogeneous mantle underneath the Mohns Ridge ([PERSON] et al., 1996). Studies of isotope systematics have further confirmed the heterogeneity and revealed several distinct mantle domains in the area (e.g., [PERSON] et al., 2005; [PERSON] et al., 2017; [PERSON] and [PERSON], 1997). More recent studies of Hf isotopes in basalts have documented highly radiogenic Hf isotopes, indicating a significant contribution from an ancient and ultra-refractory mantle component ([PERSON] et al., 2021), whereas studies of exposed mantle rocks and basalts suggest the presence of a highly depleted and subduction-modified mantle underneath the Mohns Ridge ([PERSON] et al., 2022; [PERSON] et al., 2021).
## 3 Sampling and Analytical Methods
### AUV Bathymetry
The AVR-K4 was mapped in 1-m resolution using a Hugin AUV in 2017 and the central part of AVR-M10 was mapped at 2-m resolution in 2018. Bathymetrical data were collected with a Kongsberg EM2040 multibeam echo sounder using a frequency of 400 kHz. All data were cleaned and processed using NaviModel before the data were gridded and visualized in Fledermaus.
### In Situ Rock Sampling
Our two study areas (Figure 1) were investigated in detail with ROV visual observations and a total of 76 in situ basaltic samples were collected. At the central part of AVR-M10 (study area 1) (Figure 1) at 72.3\({}^{\rm{N}}\), we collected 29 basaltic samples (Figure 2) (19 which contains glass), 11 abyric, and 18 plagioclase phyric. The samples were collected from a variety of volcanic features such as pillow mounds, fissure eruptions, and a lava lake. In the eastern section of the map, a distinct hummock ridge can be observed, known as the \"Aamen\" (catepillar) fissure eruption. A detailed description of the volcanic terrain is given in Stubseid (2024).
Figure 1: Overview of the study area. Bathymetric map of the Mohns and Knipovich Ridges in 75–200 n resolution with two times vertical exaggeration. Data outside the active spreading ridges were downloaded from GEBCO. All AVRs are marked with red outlines and numbered according to their position along the two ridges. The spreading direction, which is similar for both ridges, is marked with white arrows and shows the oblique spreading compared to the orientation of the rift valley. Bathymetry shows a gradual increase in water depth resulting from decreased magmatic activity northwards, and a sudden change in orientation where the Mohns-bend into the Knipovich Ridge. Both study areas are illustrated; 1 is the AVR-M10 in the central Mohns Ridge, whereas 2 is the AVR-K4 at the northern Knipovich Ridge. The inset in the upper left shows all the Arctic spreading segments. Black box is the outline of the main figure. Abbreviations within the inset: KoR = Kolbeinsey Ridge, JM = Jan Mayen, MR = Mohns Ridge, KaR = Knipovich Ridge, GR = Gakkel Ridge.
From the AVR-K4 (study area 2 in Figure 1) at 77.5\"N, 47 samples (Figure 3) of basaltic glass were analyzed. All samples originate from individual pillow mounds or flat-topped circular volcanoes. Aphyric basalts make up the majority of the samples, with only 12 samples displaying varying amounts of plagioclase phenocrysts.
### Major and Trace Element Concentrations
Major element composition was analyzed on hand-picked grains of pure and un-altered basaltic glass by electron microprobe (EMPA) at the University of Oslo on a CAMECA SAX100 instrument fitted with 5 wavelength-dispersive (WDS) spectrometers. An accelerating voltage of 15 kV, a beam current of 10 nA, and a beam size of 10 \(\mu\)m were used. The counting time was 10 s on the peak (and 5 s on each of the 2 background positions). Na and K were analyzed first. Analyses were single-point and between 1 and 3 analyses were conducted on each grain (2-3 grains per sample mounted in epoxy). Calibration standards and X-ray lines used were wollastonite (Si Ka, Ca Ku), Al\({}_{2}\)O\({}_{3}\) (Al K\({}_{2}\)), pyrophanite (Ti K\(\alpha\), Mn K\(\alpha\)), Fe metal (Fe K\(\alpha\)), MgO (Mg K\(\alpha\)) orthoclase (K K\(\alpha\)), albite (Na K\(\alpha\)), Cr\({}_{2}\)O\({}_{3}\) (CrK\(\alpha\)) and NiO (NiK\(\alpha\)). Matrix corrections were performed according to the PAP procedure ([PERSON], 1984) implemented in the CAMECA software.
For samples without any glass, fragments of microcrystalline basalt were used for analysis. We took care to avoid areas with phenocrysts or visible altered areas. A small amount of pulverized (using an agate mortar) rock sample was fluxed using LiB\({}_{\alpha}\)O\({}_{7}\) before the mixture was melted into a small droplet. The droplet was then dissolved in a mixture of HCl, HNO\({}_{3}\), and H\({}_{2}\)O, which kept Si in solution. Major element concentrations were analyzed on a Thermo Absorption (NMR) step were determined by inductively coupled plasma mass spectrometry (ICP-MS) using a Thermo Scientific Element XR at the University of Bergen. Quantification was done by external calibration curves (multi-element standard solutions prepared from certified single-element solutions from Spectrapure) and Sc was used for internal standardization. Quality control was done by USGS CRM BCR2 internal standardization. Quality control was done by USGS CRM BCR2 (Basalt, Columbia River).
### Isotopic Composition of Basalts
For selected basaltic samples, solutions prepared for the trace element analysis were further used for the isotopic characterization of Sr, Nd, and Pb. Prior to dissolution, all hand-picked fragments of glass, or micro-crystalline basaltic groundmass, were leached through acid-washing (3M HCI) and rinsed in an ultrasonic bath prior to analysis to avoid contamination and remove alteration products ([PERSON] et al., 2009; [PERSON], 1991). Separation and concentration of the above-mentioned 3 elements involved 3 consecutive chromatographic separations and followed the procedure as described in [PERSON] et al. (2014). The isotopic analysis of Sr was performed on a Finnigan MAT 262 thermal ionization mass spectrometer (TIMS), whereas the isotopic analysis of Pb and Nd was performed on a Nu Plasma II MC-ICP-MS.
For Pb isotopes, the sample was diluted to 1,000 or 1,200 \(\mu\)l 25 ppb (ug/_l_). The diluted sample was spiked with 6, 25 ppb (ug/_l_) Tl for mass bias correction using a single-element Tl standard (Spectraccan). NIST981 was used as a bracketing standard. For quality control, BCR-2 was included in the entire sample preparation process. The mass
Figure 2: In situ sampling of the AVR-M10. Detailed 2-m resolution AUV bathymetry from the central part of AVR-M10. Two times vertical exaggeration. In situ ROV samples collected from a variety of volcanic features are marked with triangles where black corresponds to aphyric basalts and gray corresponds to plagioclase phyric basalts.
bias correction was done online in the instrument software, assuming natural isotope abundances for the TI standard (\({}^{205}\)Tl/\({}^{203}\)Tl = 2.3880) and an exponential mass bias law. Standard-sample-bracketing was done offline in a spreadsheet using \({}^{208}\)Pb/\({}^{204}\)Pb = 36.7006, \({}^{207}\)Pb/\({}^{204}\)Pb = 15.4891, and \({}^{206}\)Pb/\({}^{208}\)Pb = 16.9356 for NIST981 after [PERSON] et al. (1996). Repeated measurements of the BCR-2 (\(n\) = 18) during 4 analytical runs yielded an average \({}^{206}\)Pb/\({}^{204}\)Pb ratio of 18.7519.
For Nd isotopes, the sample was diluted to 1,000 or 1,200 \(\mu\) 50 ppb (ug/f). For mass bias correction the isotope pair \({}^{146}\)Nd/\({}^{144}\)Nd was used. Correction of \({}^{144}\)Sm overlap on \({}^{144}\)Nd was done by measuring \({}^{147}\)Sm and using the exponential mass bias law. The analysis was done by std-sample-sample-std bracketing using 50 ppb (ug/f) JNdi-1 as the bracketing standard, with \({}^{143}\)Nd/\({}^{144}\)Nd = 0.512115 (GeoReM compilation) and \({}^{145}\)Nd/\({}^{144}\)Nd = 0.348407 ([PERSON] & [PERSON], 2011). For quality control, BCR-2 was included in the entire sample preparation process. The mass bias correction was done online in the instrument software, assuming a true ratio for \({}^{146}\)Nd/\({}^{144}\)Nd of 0.7219 and exponential mass bias law. The bracketing corrections were done offline after the instrumental analysis. Repeated measurements of the BCR-2 (\(n\) = 23) during 4 analytical runs yielded an average \({}^{143}\)Nd/\({}^{144}\)Nd ratio of 0.51263.
Sr isotopic ratios were corrected for mass fractionation using \({}^{88}\)Sr/\({}^{86}\)Sr ratio of 8.375209. Repeated measurements of the SRM 987 Strontium Carbonate standard at the time of analyses yielded an average \({}^{87}\)Sr/\({}^{86}\)Sr ratio of 0.710233 \(\pm\) 9 (2\(e\)) (\(n\) = 10).
## 4 Results
### Major and Trace Element Composition
The AVR-M10 lavas have MgO concentrations from 6.3 to 8.1 wt.% and Mg# from 39.5 to 54.5, and show typical fractionation trends with enrichment in FeO, TiO\({}_{2}\), and Na\({}_{2}\)O and a decrease in CaO and Al\({}_{2}\)O\({}_{3}\) with a decrease in MgO (Figure 4). The samples cluster together in three well-defined groups seen especially well in the FeO, CaO, and Na\({}_{2}\)O plots. Seven samples from the \"Aamen\" fissure eruption (Figure 2) cluster together with a MgO content of around 7.3 wt.% and FeO of \(\sim\)10 wt.%, whereas the one sample from a remnant lava lake is comparable in MgO but lower in FeO (7.8 wt.%). One of the samples from the fissure eruption was higher in SiO\({}_{2}\) than the others (\(\sim\)50.8-53.6 wt.%). Samples from both the \"Aamen\" fissure eruption and the lava lake are highlighted in the following geochemical plots as they represent different volcanic features than all other samples from the hum-mmocky terrain. The three most enriched samples in terms of FeO and TiO belong to the same hummocky mound. Calculations of Na\({}_{8}\) and Fe\({}_{8}\)([PERSON], 1987; [PERSON] et al., 1992) show variations of 2.2-2.5 and 6.2-9.4, respectively.
The samples from the AVR-K4 have MgO of 6.2-7.9 wt.%, Mg# from 44.5 to 55.5, FeO of 7.0-8.9 wt.% and the highest Na\({}_{2}\)O concentrations up to 3.3 wt.%. No internal groups and clusters are observed, and the samples show a similar but slightly vaguer trend than the samples from AVR-M10. The samples show a flatter trend for both FeO and Na\({}_{2}\)O with no well-defined trend in the CaO. The samples yield Na\({}_{8}\) of 2.7-3.1 and Fe\({}_{8}\) of 5.7-8.
The REE patterns for AVR-M10 lavas are highly variable, especially for the LREE, ranging from N-MORB to E-MORB (Figure 5a) with (La/Sm)\({}_{N}\) from 0.7 to 2.9. The only samples with depleted mantle signatures ((La/Sm)\({}_{N}\) \(\sim\) 0.7) are the ones from the \"Aamen\" fissure eruption. All other samples are more or less enriched with (La/Sm)\({}_{N}\) \(\geq\) 1. The extended spider diagram (Figure 5b) shows that all samples follow a similar pattern even though the concentrations vary significantly. All samples show a pronounced negative anomaly for Th and Li, minor negative anomalies for Sr and Ti, and positive anomaly for Ta and Nd. Pb varies from no anomaly to slightly both
Figure 3: Detailed sampling of the AVR-K4 (77.5”N). Detailed 1-m resolution AUV bathymetry from the AVR-K4 illustrates an un-fauleted volcanic terrain dominated by individual humnckcks and flat-topped volcanoes. Two times vertical exaggeration. In situ ROV samples are marked with triangles where black symbols are anyphytic basalts and gray are plagioclase phyric basalts.
positive and negative. The \"Aamen\" fissure eruption forms a distinct group that yields the lowest values in the most incompatible elements. These samples follow the N-MORB pattern for most elements except for some fluid-mobile elements (Cs, Rb, and Ba) that are strongly enriched compared to N-MORB (Figure 5).
All samples from the AVR-K4 cluster together and follow the same enriched REE pattern with (La/Sm)\({}_{\text{N}}\) from 1.1 to 1.4 without any anomalies present (Figure 5a). The extended spider diagram shows identical trends for all samples with negative anomalies for Th and Li, and positive anomaly for Ta.
Figure 4. Major element compositions of analyzed basalts. Major elements of basalts are presented as oxides in bivariate plots, where MgO represents the \(x\)-axis of all sub-plots. Orange stars are samples from the AVR-K4, whereas all blue indicators are from AVR-M10. The lava lake sample from AVR-M10 is highlighted as a blue square and samples from the “Aamen” fissure eruption as blue triangles because they represent samples from distinctly different volcanic features than the surrounding hummocky terrain (stars).
### Isotopic Composition of Sr, Nd, and Pb
All samples from AVR-M10 and 14 samples from AVR-K4 were selected for isotopic analysis of Sr, Nd, and Pb. The samples, consisting of handpicked glass or basaltic groundmass, are unlikely to exhibit any significant alteration effects in the isotope systematics. The AVR-M10 lavas showed an inverse correlation between \({}^{87}\)Sr/\({}^{86}\)Sr and \({}^{206}\)Pb/\({}^{204}\)Pb (Figure 6) and positive correlations between \({}^{207}\)Pb/\({}^{204}\)Pb versus \({}^{206}\)Pb/\({}^{204}\)Pb versus \({}^{206}\)Pb/\({}^{204}\)Pb and \({}^{145}\)Nd/\({}^{144}\)Nd versus \({}^{87}\)Sr/\({}^{66}\)Sr (Figure 6). The samples show an inverse correlation for (La/Sm)\({}_{\rm N}\) versus both \({}^{143}\)Nd/\({}^{144}\)Nd and \({}^{57}\)Sr/\({}^{66}\)Sr and positive correlation for (La/Sm)\({}_{\rm N}\) versus \({}^{206}\)Pb/\({}^{204}\)Pb. All samples yield high \({}^{87}\)Sr/\({}^{66}\)Sr (\(\sim\)0.7032-0.7035) and low \({}^{143}\)Nd/\({}^{144}\)Nd (0.51301-0.51306) (Figure 6). In the Nd/Sr isotopic bivariate plot, we see that the samples cluster together in two well-defined groups, where samples from the \"Aamen\" fissure eruption belong to the high Nd high Sr group and the lava lake sample falls into the low Nd low Sr group. The largest isotopic variations are seen for Pb, especially in \({}^{206}\)Pb/\({}^{204}\)Pb and \({}^{206}\)Pb/\({}^{204}\)Pb ranging from 17.91-18.76 to 37.62-38.73 respectively. The lavas cluster together in several groups based on the Pb isotopes (Figure 6), where the \"Aamen\" fissure eruption defines the least radiogenic samples, and the lava lake is among the most radiogenic. One sample (GS19-ROVS-R13) deviates from the general trend with the most radiogenic \({}^{206}\)Pb/\({}^{204}\)Pb (38.73) and \({}^{207}\)Pb/\({}^{204}\)Pb (15.62).
All analyzed isotopes from the AVR-K4 form well-defined clusters with only minor internal variations. Their isotope ratios display depleted geochemical signatures with less radiogenic \({}^{35}\)Sr/\({}^{66}\)Sr (0.7028-0.7029) (Figure 6) and higher \({}^{145}\)Nd/\({}^{144}\)Nd (0.51314-0.51317) than samples from AVR-M10 (Figure 6). There is a positive correlation between \({}^{87}\)Sr/\({}^{86}\)Sr and \({}^{206}\)Pb/\({}^{204}\)Pb as well as \({}^{207}\)Pb/\({}^{204}\)Pb and \({}^{206}\)Pb/\({}^{204}\)Pb. The variations in Pb isotopes are significantly smaller (\({}^{206}\)Pb/\({}^{204}\)Pb from 18.19 to 18.29) than from AVR-M10.
### Geochemical and Isotopic Variations at AVR-M10
We visually present the significant variations in geochemistry and isotopes across a relatively small area (\(\sim\)1 km\({}^{2}\)) by superimposing the chemical data onto a detailed bathymetry map with a resolution of 2 m (Figure 7a). To provide further information, we present an age column summarizing absolute ages (from Stubseid (2024)) and stratigraphic relationships. Here, all the samples are color-coded based on the observed clustering in the \({}^{207}\)Pb/\({}^{204}\)Pb versus \({}^{206}\)Pb/\({}^{204}\)Pb plot (Figure 7b) and each group is given a number (Gr.1-Gr. 4) based on the age column. A similar clustering, as seen in the Pb-isotopes, is not seen in the Sr and Nd isotopes (Figure 7c) and the samples mix more randomly together. However, samples from groups 1, 3, and 4 stick together at each major Nd/Sr group whereas group 2 samples are mixed between the two groups. In order to establish a basis for comparison between the map, isotopes, and geochemistry, we integrated the Mg# (Figure 7d) to indicate major element concentrations and (La/Sm)\({}_{\rm N}\) (Figure 7e) to showcase the REE patterns.
The lowest part of the volcanic sequence seems to be represented by the group 1 samples that exhibit the most radiogenic Pb, some variations in Sr isotope and in Mg#, and large variations in (La/Sm)\({}_{\rm N}\). In addition to bathymetric observations, two of these samples were previously dated using K/Ar. Sample nr. 1 and 4 yielded ages of 34 \(\pm\) 8 ka and 65 \(\pm\) 10 ka, respectively, whereas the rest of the surface is interpreted to be younger than 25 ka (Stubseid, 2024). One single sample (in red--nr. 25), not included in any group, stands out with the absolute most radiogenic Pb isotopes. In terms of Nd/Sr isotopes, Mg# and (La/Sm)\({}_{\rm N}\), it is comparable with the other samples. Its location on the map suggests that it could represent the very deepest and oldest part of the volcanic surface. The remaining groups comprise samples from a higher (younger) level of the volcanic surface.
Figure 5.— REE and extended trace element diagrams. (a) Rare-earth elements normalized to chondrites (values after [PERSON] and [PERSON] (1995)) show that the AVR-M10 samples vary from N- to E MORB, whereas all samples from the AVR-K4 exhibit a slightly enriched LREE trend. (b) All trace elements normalized to the primitive mantle (values after [PERSON] and [PERSON] (1989)). Samples from AVR-M10 show large variations in concentrations and patterns, whereas similar patterns and concentrations are seen in all AVR-K4 samples. E-, N-, and D-MORB values after [PERSON] et al. (2013).
The temporal relation between each group is well documented by samples 4-7, going from the deepest part of the volcanic sequence toward younger and overlaying lava flows. Group 2 sits on top of group 1 (ref. relations between sample 3, 4, and 5), and exhibits large variations in Nd/Sr isotopes, Mg#, and (La/Sm)\({}_{\rm N}\). This group is stratigraphically overlain by samples from group 3 (ref. samples 2 and 3, and samples 5 and 6). This group, that appears to belong to the same stratigraphic level in the volcanic terrain, cluster well for all chemical parameters (Pb isotopes, Nd/Sr isotopes, Mg#, and (La/Sm)\({}_{\rm N}\)). However, dating of basal sediments next to samples 27 and 28
Figure 6.— Isotopic composition of lavas from both study areas. \({}^{87}\)Sr/\({}^{68}\)Sr versus \({}^{200}\)Pb/\({}^{202}\)Pb illustrate that all AVR-M10 samples are more radiogenic in Sr than AVR-K4 samples. It also shows the large variations in Pb isotopes at AVR-M10 whereas AVR-K4 samples cluster together. \({}^{207}\)Pb/\({}^{202}\)Pb versus \({}^{208}\)Pb/\({}^{202}\)Pb further documents the observed range in Pb isotopes from the AVR-M10. It also illustrates that samples from the “Aamen” fissure eruption reveal the least radiogenic Pb, whereas the lava lake samples are the most radiogenic. One outlier is observed outside the general trend. The AVR-K4 samples cluster together in the middle of the AVR-M10 trend.
Figure 7:
of group 3 indicate minimum eruption ages of 7 and 20 ka, respectively, and shows that samples with identical Pb isotopic compositions have erupted intermittently over several thousand years (Figure 7a). It should be noted that the age relations between samples 6 and 28 are unknown but based on the bathymetric expression sample 28 appears younger.
The youngest samples are those of group 4 with the most radiogenic Sr isotopes, least radiogenic Pb, and low Mg# and (La/Sm)\({}_{\rm{N}}\). Most of these samples (nr. 7, 21-24) belong to the \"Aamen\" fissure eruption consisting of multiple aligned hummocks. Based on ROV observations, this feature is interpreted as the youngest volcanic structure on the AVR surface today (details in Stubseid (2024)). The three remaining samples, nr 8, 9, and 10, belong to a circular mount in the western part of the mapped area that appears older than the \"Aamen\" fissure eruption. These samples are the most fractionated lavas collected from the area, with the lowest Mg# (\(\sim\)40) and CaO, and the highest TiO\({}_{2}\) and Na\({}_{2}\)O.
## 5 Discussion
### Large-Scale Variations Between the Mohns- and Knipovich Ridges
The observed heterogeneity in the Arctic mantle has been explained by a variety of sources, processes, and hypotheses. Ultra-depleted components are described from both basalts ([PERSON] et al., 2021) and peridotites ([PERSON] et al., 2022). Several studies have documented enriched mantle components as the result of fluid enrichment from an ancient subduction zone ([PERSON] et al., 2022; [PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2021). Other enriched components, especially near Jan Mayen, have been explained by the presence of a subcontinental lithospheric mantle (e.g., [PERSON] et al., 2009). Enriched material is also distributed from the Iceland-Jan Mayen plume. However, it is debated whether a separate plume exists underneath the island of Jan Mayen or if the observed plume component extends from Iceland (e.g., [PERSON], [PERSON], et al., 2016).
The geochemical and isotopic signatures of our basalts indicate that there are large differences in the mantle source between the Mohns- and Knipovich Ridges, or that the melting process operates differently at these ridges. Samples from AVR-M10 in the central part of the Mohns Ridge are derived from a heterogeneous mantle source and show similarities to previously published results from the ridge. Their trace element composition, with (La/ Sm)\({}_{\rm{N}}\) \(<\) 1 to \(>\)2, is comparable to the results from [PERSON] et al. (1996) suggesting a heterogeneous mantle and the mixing between depleted and enriched sources. Our documentation of the diverse isotopic composition of the lavas suggests that the chemical and isotopic signatures reflect a heterogeneous mantle source.
Our data is similar to previously published large-scale data from the ridges showing large variations indicative of a complex mixing between multiple mantle components ([PERSON] et al., 2005; [PERSON] et al., 1996). Our samples from the AVR-M10 form a trend between the Gakkel Ridge and Iceland endmembers (Figure 8). Samples show less radiogenic isotope ratios for Sr and Nd compared to Jan Mayen lavas and we therefore suggest that they are not sourced from such a mantle. Only the southernmost basalts from the Mohns Ridge resemble a highly radiogenic Jan Mayen isotope signature (Figure 8) indicative of a subcontinental lithospheric mantle ([PERSON] et al., 2009) or a discrete mantle plume ([PERSON], [PERSON], et al., 2016). Only one of our samples, map ID 25 (Figure 7), exhibits Pb isotopic compositions comparable to those of Jan Mayen basalts. However, this sample deviates from the general Mohns Ridge trend and it is therefore difficult to conclude on a single sample. It is possible that Jan Mayen shares a deep source with Iceland but is affected by metasomatized subcontinental
Figure 7: Detailed overview linking geochemistry and isotopic composition of lavas from the AVR-M10 with high-resolution bathymetry and age relations. (a) 2-m resolution AVR bathymetry of the central part of AVR-M10. In situ lava samples analyzed for isotopic composition are marked as triangles with different colors. The associated number is a simplified sample ID, referred to as “map ID,” corresponding to the numbering of the samples in the master table, [[https://doi.org/10.5281/medo](https://doi.org/10.5281/medo)]([https://doi.org/10.5281/medo](https://doi.org/10.5281/medo)). 13939872. The color of the different samples corresponds to the clustering of Pb isotopes. The age/stratigraphic relationships illustrate the age relationships between given samples where absolute ages have been obtained or relative age relationships confirmed by visual ROV observations. The ages of samples I and I are K/A ages on the basalts. Samples 5 and 6 are stratigraphically younger than 4, whereas the ages from samples 28 and 27 are based on \({}^{14}\)C dating of basal sediments. Sample 21–24, including nr. 7, belong to the only un-faulted and least sedimented volcanic feature. This is confirmed by ROV observations and is therefore interpreted as the youngest volcanic feature. All age estimates are presented in Stubseid (2024). (b) \({}^{207}\)Pb/\({}^{204}\)Pb versus \({}^{206}\)Pb/\({}^{204}\)Pb for the analyzed samples, color-coded based on their different groups and numbered chronologically from old to young. The same colors are used throughout the rest of the figure. (c) \({}^{143}\)Nd/\({}^{244}\)Nd versus \({}^{25}\)Sr/\({}^{25}\)Sr for the same samples with the same colors. The clustering seen in Pb isotopes is not observed here. The samples were separated into two major groups based on their isotopic composition of Sr and Nd. (d) Mg# for all samples as an indicator for the degree of fractionation. Large variations in the degree of fractionation are observed also within the different Pb isotope groups suggesting that samples with similar isotopic composition might not originate from the same eruption. (e) (La/Sm)\({}_{\rm{N}}\) as an indicator for the LREE pattern varying from depleted to enriched. The REE pattern shows large variations within the different isotopic groups.
lithosphere producing a distinct Jan Mayen type signature in close proximity to the island of Jan Mayen. The enriched signatures further north along the Mohns Ridge are more similar to an enriched plume component from Iceland. Therefore, based on the isotopic similarities between our samples and lavas from Iceland, it seems more likely that the studied ridge segment, to a variable extent, is affected by the Iceland Plume. Several studies have suggested that the mantle flow and geochemical signature of the Iceland plume extend at least 1,000 km from its central parts ([PERSON] et al., 2002; [PERSON] et al., 2013) and become incorporated in the MORB mantle as a deep
Figure 8.— Comparison between regional isotope data and samples from this study. Literature data were downloaded from the PetDB Database (www.earthchem.org/ petdb) on 5 March 2024 drawing a polygon including the Reykjanes Ridge, Iceland, Kobbeinsey Ridge, Jan Mayen, Mohns Ridge, Kaipovich Ridge, and Gaskel Ridge and rock classification = basalt, tholeiite and alkali basalt. Additional Jan Mayen data were added from [PERSON], [PERSON], et al. (2016) and [PERSON] et al. (1986), and additional Iceland data were added from [PERSON] et al. (2004) and [PERSON] et al. (2022). All literature data are plotted as circles colored based on the different ridge segments (see details in figure legend). Data from this study are plotted as blue stars (AVR-M10) and orange stars (AVR-K4).
source. The location of AVR-M10, in the middle of the Mohns Ridge, matches the proposed extent of the Iceland Plume with similar Pb isotopes as observed from principle component analysis (e.g., [PERSON] et al., 2013), which could explain some of the enriched components. The enriched component, as well as the magma budget, is decreasing northwards along the ridge, possibly reflecting a gradual dilution of the Iceland Plume.
[PERSON] et al. (1996) documented an enrichment in certain elements (Cs, Ba, Rb, and K) and suggested that these elements were released from a subducting slab producing a \"wet\" mantle underneath the Mohns Ridge. Similarly, [PERSON] et al. (2017) suggested that the Arctic mantle contains dispersed enriched components formed by meta-somstain, presumably at great depths an earlier time. Geochemical investigations of basalts and exposed mantle rocks in the north-eastern part of the Mohns Ridge have further documented the presence of a subduction-modified mantle, which could indicate that the mantle has received fluids from a subducting slab ([PERSON] et al., 2022). The basalts reveal low Nb/U and Ce/Pb and elevated Rb/Nb and Ba/Nb ([PERSON] et al., 2022) and are therefore similar to back-arc basin basalts as defined by [PERSON] et al. (2021). The periodicities have low Al\({}_{2}\)O\({}_{3}\), similar to arc-derived mantle rocks, and the trace element signatures of orthopyroxenes are comparable to those seen in periodites from modern supra-subduction environments ([PERSON] et al., 2022). Along the Gakkel Ridge, [PERSON] et al. (2020) argued for an early Cretaceous subduction-modified mantle with a back-arc basin (BABB) signature ([PERSON] et al., 2021). Our data show several similarities with their evidence for fluid enrichment in the mantle. The Sr isotopic ratio of the AVR-M10 samples is significantly higher than Atlantic/Pacific MORB (Figure 9a) and is similar to Mariana BABB and enriched samples from the Gakkel Ridge. Some of our samples, especially from the \"Aamen\" fissure eruption, are also highly enriched in Cs, Rb, and Ba compared to Th and U (Figure 9b), indicating enrichment of fluid-mobile elements from a water rich flux ([PERSON] et al., 2020; [PERSON] et al., 2021). Several other indicators, such as Ba/Nb versus Rb/Nb, further document that some of the Mohns Ridge lavas show similarities with BABBs ([PERSON] et al., 2021). The \"Aamen\" fissure eruption, with the strongest subduction signature, is also the only sampled volcanic structure on the AVR-M10 with a depleted LREE pattern. This agrees with results from the analysis of upper mantle rocks, sampled directly below gabbro and basalts, from the Mohns Ridge interpreted to be highly depleted and subduction modified ([PERSON] et al., 2022). We, therefore, argue that basalts along the Mohns Ridge are occasionally derived from a depleted and subduction-modified upper mantle.
Samples from the AVR-K4 at 77.5\"N are different from the Mohns Ridge lavas, as they all have a similar chemistry. They show very limited variations in both trace elements and isotopic composition, and the large heterogeneity seen in the central Mohns Ridge is not recorded at individual AVRs in the northern Knipovich Ridge. Samples from the AVR-K4 are more depleted in Sr and Nd isotopes, less thorogenic in Pb (Figure 8), and lack the enriched component observed at the Mohns Ridge. No subduction influence was observed and the Knipovich Ridge lavas were more similar to a normal MORB mantle (Figure 9). Some variations in the isotopic composition are seen in the literature samples, considering the entire Knipovich Ridge (Figure 8). Nevertheless, all of our samples from the same AVR have a similar chemistry. This is surprising compared to the large
Figure 9: A subduction-modified mantle in the Arctic. (a) \({}^{87}\)Sr/\({}^{87}\)Sr versus \({}^{208}\)Pb/\({}^{204}\)Pb show that our samples are more radiogenic in Sr than the Atlantic/Pacific MORB. Radiogenic Sr can be interpreted as enrichment from an ancient subducting slab. Our data are comparable with Mariana BABB and enriched samples from the Gakkel Ridge. (b) Ba/Th versus \({}^{208}\)Pb/\({}^{204}\)Pb illustrates enrichment of the fluid mobile Ba relative to Th as the result of fluid enrichment. Our most enriched samples, from the “Aamen” fissure eruption, have Ba/Th ratios comparable with Mariana BAB and enriched Gakkel Ridge samples. This suggests a subduction-modified mantle under the Mohns Ridge. Literature data from [PERSON] et al. (2020) and references therein.
variations in chemistry observed at the AVR-M10 at the Mohns Ridge. We suggest that these differences reflect variations in the mantle heterogeneities rather than differences in the degree of homogenization. Therefore, lavas at individual AVRs on the Knipovich Ridge seem to be sourced from a more homogeneous and depleted MORB mantle than that observed at the Mohns Ridge. The sudden change in mantle source between the Mohns and Knipovich Ridges suggests that the bend in the ridge geometry (Figure 1) between these two ridges might act as a mantle boundary, similar to the boundaries described from the Gakkel Ridge ([PERSON] et al., 2008; [PERSON] et al., 2003). However, it is not the goal of this paper to unravel the extent and characteristics of the different mantle domains. This will be the focus of a follow-up paper including a larger sample set from the Mohns- and Knipovich Ridge that is currently being analyzed.
### Extreme Pb Heterogeneity in the mantle Underneath the Mohns Ridge
The analyzed basalts from the AVR-M10 reveal extreme heterogeneity resulting from multiple mantle domains: one or more enriched components, a depleted to ultra-depleted component, and a subduction-modified component. The isotopic variations recorded in our samples within \(\sim\)1 km\({}^{2}\), especially for Pb isotopes, are nearly as large as for the entire Mohns- and Knipovich Ridges as a whole (Figure 10). For Sr and Nd isotopes, the variations are not that extreme and the Pb isotopes seem somehow to be decoupled from the other isotopes. However, the variations in the Pb isotopes are two orders of magnitude larger than the analytical uncertainty and are similar to isotopic variation previously reported from the entire Mohns Ridge. Therefore, we argue that the variations in Pb isotopes are real and reflect the heterogeneity in the mantle. The decoupling of Pb versus Sr and Nd isotopes could be explained by non-linear mixing relationships between isotopic compositions of different elements ([PERSON] et al., 2005), and similar decoupling has been observed in Iceland ([PERSON] et al., 2013). Therefore, extreme mantle heterogeneities on local scales might not be recorded in Sr and Nd isotopes alone.
The unique contribution of our study is the scale and time dimension of which these heterogeneities are recorded in spatially associated basalts within a small area (Figure 7). The question that arises is on what scale these heterogeneities occur in the mantle. Is it related to small-scale heterogeneities or does the mantle exhibit large-scale layering? Studies of Os isotope systematics in abysmal periodtites at slow- and ultraslow-spreading ridges have documented that heterogeneities vary from a regional to within-sample centimeter scale ([PERSON] et al., 2004; [PERSON] & [PERSON], 2012; [PERSON] et al., 2009) and there are also presented evidence for higher heterogeneity in the mantle periodtites compared to the associated basalts ([PERSON] et al., 2004; [PERSON] et al., 2006; [PERSON] et al., 2008; [PERSON], 2002; [PERSON] & [PERSON], 2009; [PERSON] et al., 2011). Therefore, it is likely that the mantle is even more heterogeneous than that revealed by the basalts. What we can conclude from our Pb isotope data (Figure 7) is that distinctly different Pb isotopic signatures are recorded in basalt erupted within an area of approximately 1 km\({}^{2}\) during a time span of about 30 ka.
[PERSON] et al. (2021) suggested that compositional variations are more significant on small spatial scales (\(<\)5 km) at off-axis seamounts than what is found on-axis. [PERSON] et al. (2024) document incomplete mixing of isotopically different melts in lower crustal rocks, thus preserving heterogeneities suggested not to be seen in MORBs. A recent study of the Masirah Ophiloitte (Oman) documents synchronous D-MORB and E-MORB magmatism sourced from a heterogeneous mantle, and suggests that such compositional variations could also occur on modern spreading segments ([PERSON] et al., 2024). Our data show large chemical variations within spatially related samples, and we therefore document that extreme heterogeneities can in fact be observed in on-axis basalts at ultraslow-spreading ridges.
### Implications for Volcanic Processes
Our constraints on the spatiotemporal relations of lava flows with different isotopic signatures provide important insights into the volcanic processes at ultraslow-spreading ridges. The exact position of our in situ samples (as opposed to results from dredging) demonstrates that basalts with distinctly different chemistry and isotopic histories have erupted next to, or on top of, other flows. [PERSON] et al. (2023) documented that most AVR surfaces at the Mohns Ridge are younger than 25 ka and that all AVRs have been steady-state volcanic systems, at least for the last 150 ka, with rapid renewal rates. AVRs have been shown to renew 50% of their surface during 18 ka, suggesting a continuous melt supply toward these areas, and that there is a limited chance to expose old lava flows at the AVR surface ([PERSON] et al., 2023). Here, we document extensive variations in the chemistry of erupted lavas formed by individual eruptions during \(\sim\)60 ka. Such an age span, and the exposed bathymetric relief (150200 m), comprise only \(\sim\)1/4 of the total height of the AVR and we therefore only witness parts of the volcanic history. The age estimates from K/Ar dating of samples 1 and 4, and \({}^{14}\)C dating of basal sediments at samples 27 and 28 (Figure 7) document that lavas with near-identical Pb compositions have erupted intermittently during several thousand years. We also observed spatially related lava flows with distinctly different chemistry (Figure 7). Flows that have erupted next to, or on top of, each other reveal different isotopic signatures. Such distinct chemical signatures, combined with bathymmetric observations and age relations, document that this part of the volcanic sequence was formed by several small eruptions from different mantle sources over the last tens of years.
Figure 10.— Isotopic variations along parts of the AMOR. Our data (AVR-M10 at the central Moins Ridge in blue and the AVR-K4 at the Knipovich Ridge in orange) were compared with previously published isotope data downloaded from the PetDB Database (www.earthehem.org/petdb) ([PERSON] et al., 2016; [PERSON] et al., 2005; [PERSON] et al., 2013; [PERSON] et al., 2008; [PERSON], 1997; [PERSON] et al., 1999; [PERSON], 1991). Latitude is the \(x\)-axis of all sub-plots to illustrate the isotopic variations at a spatial scale.
sen, 2005). Therefore, the samples with Fe\({}_{8}\) moving away from the global trend could be the result of such results, and Fe\({}_{8}\) as an indicator of melting depth in this region must be used with care.
Magma chambers are efficiently homogenizing melts at fast-spreading ridges, and only limited heterogeneity is recorded in the erupted lavas ([PERSON] et al., 1996; [PERSON] & [PERSON], 1981; [PERSON] & [PERSON], 1992; [PERSON] & [PERSON], 2009). The heterogeneity recorded in our basalts, however, suggests that as the melts are segregated from the mantle, they ascend and erupt with very limited modification in magma chambers. A similar conclusion has also been reached for basalts at the Gakkel Ridge, where Fe isotopes indicate the absence of homogenization in sub-oceanic magma chambers ([PERSON] et al., 2021).
However, around half of our samples exhibit phenocrysts with varying size and abundance that could stem from fractionation at various levels in the plumbing system. Based on geochemical data, [PERSON] and [PERSON] (2005) argued that the Knipovich Ridge is characterized by thick lithosphere and deep fractionation of magma between segment centers. At segment centers, the mantle upwelling rate and magma production are high enough to intermittently sustain shallow level magma reservoirs that result in eruption of plagioclase ultraphyric basalts. Large internal chemical variations in plagioclase phenocrysts suggest that they stem from small magma reservoirs characterized by a strong degree of undercooling, alternating with periods of magma replenishment.
This suggests that magma mixing, at least to some extent, is a common process at ultraslow spreading ridges. Regarding our isotopic data set, this raises the question of whether our intermediate Pb isotope groups (2 and 3) could result from mixing between the two end-member groups (1 and 4). The Pb isotopes, which form a near-perfect trend between the two endmembers and intermediate groups, can be explained by mixing. However, such a linear trend is not observed for Sr and Nd isotopes, and these isotope systems do not support a simple mixing relationship. Therefore, we argue that the isotopic systematics cannot be explained solely by the mixing of two endmembers in a magma reservoir but rather reflect the melting of different mantle components with diverse isotopic histories. Our data also suggests that during the formation of the volcanic sequence at AVR-M10, the magma chambers were likely ephemeral features limited in size and duration and remained isolated from one another.
Figure 11: Comparison between Fe\({}_{8}\) and Na\({}_{8}\) to estimate melting depth and degree of melting. Background data ([PERSON] et al., 2016; [PERSON] et al., 2013; [PERSON], 2005; [PERSON] et al., 2013; [PERSON] et al., 2008; [PERSON] et al., 2019; [PERSON], 1976; [PERSON] et al., 2002; [PERSON], 1984; [PERSON] et al., 2020; [PERSON] et al., 1999) downloaded from the PeDB Database (www.earthethem.org/petdb). Global trend line after [PERSON] (1987). Samples from the AVR-K4 are higher in Na\({}_{8}\), suggesting lower degrees of melting at the Knipovich Ridge than at the Mohns Ridge. Large variations in Fe\({}_{8}\) could be explained by different melting depths. Samples moving away from the global trend might be the result of low Fe content due to high-pressure fractionation.
### Mantle Upwelling and Melt Extraction
The production of MORBs is the result of partial melting of the mantle over a range of pressures (e.g., [PERSON], 1987). Mantle melting under slow-spreading ridges is suggested to initiate at \(\sim\)100 km depth and progress to around 30 km, resulting in a thick melting column ([PERSON], 1987; [PERSON], 1997; [PERSON], 1995). A heterogenous mantle containing fertile and refractory domains that undergo decompression as it rises below the ridge would be expected to undergo deep initial melting of its fertile components yielding enriched magmas, followed by more shallow melting of the more refractory components generating depleted magmas.
The wide range in trace element and isotopic compositions within a small area at AVR-M10 shows that enriched basalts, potentially derived from deep melting of a fertile source, occur beneath depleted basalts, presumably formed by shallower melting of a refractory source. The enriched basalts could be explained by an enriched Icelandic-Jan Mayen component (low Sr-high Pb), whereas the depleted basalts could stem from a Gakkel-Ridge type component (high Sr-low Pb). The age data show that this transition from an enriched to a depleted source occurred within 30 ka, with the extraction of magmas with intermediate compositions in between (Figure 7). Although the observed order could merely be arbitrary, the temporal evolution observed could be explained by progressive fractional melting of a heterogeneous mantle source composed of fertile and refractory domains.
For a mantle that rises in a continuous steady-state fashion, deep melting of the fertile component should occur contemporaneously with the shallow melting of more refractory components. If the melt is extracted and buoyantly transported upwards primarily by porous flow (e.g., [PERSON], 1979; [PERSON], 1997; [PERSON] & [PERSON], 1991), mixing of the enriched deep magmas with magma formed from a more refractory mantle at shallower levels seems inevitable. Conversely, if the transport of melts from the deep parts of the melt column occurs through channeled flow - either through conduits of focused porous flow or via melt-filled fractures that allow for the chemical isolation of the ascending melts (e.g., [PERSON] et al., 1995; [PERSON] et al., 1995; [PERSON] et al., 2001) - then enriched and depleted melts could be selectively extracted. Through numerical modeling, [PERSON] and [PERSON] (2012) found that fertile mantle heterogeneities can nucleate magmatic channels that transport their melts. These channels then become high-porosity, high-permeability pathways, facilitating rapid magmatic ascent toward the surface. It appears that such mechanisms may allow enriched melts from deep sources to erupt intermittently with depleted melts derived from the shallow, refractory part of the melt column, as observed at the Mohns Ridge.
If the mantle upwells in a discontinuous rather than a steady-state fashion--presumably as discrete mantle diapirs -- melts formed from deep melting of fertile components could potentially be extracted and rise relatively unmodified to the seafloor, followed by melts derived from increasingly refractory domains as the diapir reaches shallower levels (Figure 12). The assumption that the rise of the mantle below spreading ridges may be diapiric and pulsating in nature has been commonly proposed based on studies of ridges and ophiolite complexes ([PERSON] et al., 1988; [PERSON] et al., 2002; [PERSON] et al., 2004; [PERSON] et al., 1988, 2000; [PERSON], 1994). The accretion of oceanic crust at ultraslow spreading ridges is clearly highly three-dimensional, suggesting that mantle flow is focused below the segment centers ([PERSON] et al., 2008; [PERSON] et al., 2003; [PERSON] et al., 2001). It is conceivable that as spreading rates decrease and become ultraslow, the mantle up-flow may become discontinuous and pulsating. [PERSON] et al. (2003) proposed that while thermal conduction is sufficient to inhibit significant peridotite melting, vein melts could still aggregate and trigger local mantle diapirism.
A successful deep electric imaging study was recently conducted across the north-easternmost AVR (AVR-M16) of the Mohns Ridge ([PERSON] et al., 2019). AVR-M16, which hosts the Loki's Castle vent field ([PERSON] et al., 2010), is located 250 km from AVR-M10, the site of this study. The deep electric survey effectively imaged the mantle upwelling beneath AVR-M16, revealing a highly conductive melt-rich region centered at 70 km with conductivity decreasing upwards. Furthermore, a second conductivity maximum appears at around 20 km depth, indicating the presence of a local melt maximum at this level (Figure 12). We suggest that the intermittent eruption of depleted and enriched lava at AVR-M10 may be related to a mantle upwelling pattern similar to that observed below AVR-M16. It seems likely that the enriched basalts could be sourced from the deepest and largest melting region, where the enriched components of the mantle would be expected to undergo melting. The depleted basalts may stem from the shallow melting region, where the residual mantle of the deepest melting region rises and further melts due to continued decompression. Moreover, the two conductivity/melt maxima, one smaller above a larger, result in an hourglass-shaped pattern of the conductivity contours, which intuitivelyappears to be consistent with the diapir rise of partially melted mantle in the upper part of the upwelling system, located above a depth of 50 km (Figure 12).
We therefore further suggest that a steady rise of the mantle, particularly focused on segment centers, results in the melting of fertile components and the formation of enriched melts at depths around 80-60 km. In contrast, buoyancy-driven diapiric rise of partially melted mantle from this primary melting region results in shallow remelting of the refractory mantle components around 20 km. This two-stage model implies a steady formation of deep fertile melts, whereas the depleted melts form irregularly and synchronously with the intermittent rise of diapirs. We have previously documented that the volcanic activity at the AVRs has been robust and developed in a steady-state fashion with a renewal rate of half of the volcanic surface every 18 ka, suggesting that both the magma supply and the mantle upwelling have been steady at these timescales ([PERSON] et al., 2023). Therefore, we conclude that the volcanic evolution at these timescales is primarily controlled by the steady extraction of melts from the deep and robust melting region.
We also propose that as the effective spreading rate decreases, and the effects of conductive cooling propagate deeper, the diapiric rise and second-stage melting of the refractory source may cease, resulting in the eruption of basalt derived solely from melting in the deep melting region. This scenario aligns with the apparent disappearance of N-MORB along the Knipovich Ridge (e.g., [PERSON] & [PERSON], 2005), where the effective spreading rate is reduced by up to 25% compared to the effective spreading rate at the Mohns Ridge.
## 6 Conclusion
Our results document that on-axis lavas can record extreme mantle heterogeneities at ultraslow-spreading ridges. We document large differences in the mantle heterogeneity between the Mohns- and Knipovich Ridges. The AVR-K4 (northern Knipovich Ridge) exposes basalts with very little variations in chemistry (all with a slightly enriched LREE pattern) and isotopic composition. We suggest that these lavas are sourced from a depleted and homogeneous mantle. At the central Mohns Ridge, we document large chemical heterogeneities of spatially associated basalts within a small area of an axial volcanic ridge. The AVR-M10 reveals large variations in chemistry, ranging from D-MORB to E-MORB, and isotopic signature (e.g., \({}^{206}\)Pb/\({}^{204}\)Pb at 17.91-18.76), indicating a heterogeneous mantle. Lavas with similar chemistry have erupted in various locations at the AVR at
Figure 12: Schematic model of the melting process under ultraslow-spreading ridges. (a) A continuous upwelling mantle undergoes decompression with partial melting at different depths of the melt column (black triangle) simultaneously. The melts are rapidly extracted through channels (red lines) enabling melts from a deep fertile source to erupt relatively unmodified. The melts may shortly reside in shallow magma chambers (red blobs with the question mark). (b) Two-stage melting model with a steady mantle upwelling underneath segment centers. Melting of fertile components produces enriched melts at depths around 60–80 km (illustrated by dashed black contour lines in the deep parts). Continued melting lead to the formation of an irregular diapiric rise of partially melted mantle and melting of shallow and refractory mantle components at depths around 20 km (uppermost black dashed contour lines). The shape of the upwelling mantle, and its internal contours, follow the same pattern as observed in the conductivity data presented in [PERSON] et al. (2019).
different times, and lavas with distinctly different compositions have erupted next to, and on top of, each other during some tens of thousands of years. To explain the documented spatiotemporal relations of chemically and isotopically distinct lavas, several small eruptions must have taken place.
We suggest that the observed mantle heterogeneity is reflected through a large-scale layering comprising a deep and fertile plume component extending from Iceland, and a shallower depleted source with a subduction influence (Gakkel-Ridge type). Our temporal constraints document that the melt source has transitioned from a fertile component to a refractory component during 30 ka. We propose a two-stage melting model with continuous melt generation from a deep and fertile component producing enriched melts, whereas depleted melts form episodically and synchronously through diapiric structures and melting of refractory mantle domains at shallower levels. The produced melts are rapidly extracted through melt channels and might erupt directly or shortly reside in small and isolated magma chambers. Therefore, lavas at ultraslow-spreading ridges can retain the heterogeneity of their mantle source due to limited homogenization.
## Data Availability Statement
All geochemical data produced during this study have been uploaded to the Zenodo data repository ([PERSON] et al., 2024) available at [[https://doi.org/10.5281/zenodo.13939872](https://doi.org/10.5281/zenodo.13939872)]([https://doi.org/10.5281/zenodo.13939872](https://doi.org/10.5281/zenodo.13939872)).
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* [PERSON] et al. (2013) [PERSON], [PERSON], & [PERSON] | wiley | Extreme Mantle Heterogeneity Revealed by Geochemical Investigation of In Situ Lavas at the Central Mohns Ridge, Arctic Mid‐Ocean Ridges | Håvard Hallås Stubseid, Anders Bjerga, Leif‐Erik Rydland Pedersen, Rolf Birger Pedersen | https://doi.org/10.1029/2024gc011704 | 2,024 | CC-BY |
wiley/fd040c00_0631_4a27_ab10_f06f509fa67c.md | # Geophysical Research Letters
Research Letter
10.1029/2024 GL112476
[PERSON] and [PERSON] contributed equally to this work
Songleial channels near the grounding zone are able in space but people activity within decades
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**Methodology:** [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON]
**Project administration:** [PERSON]
**Software:** [PERSON], [PERSON]
**Sugglevation:** [PERSON], [PERSON]
**Validation:** [PERSON], [PERSON],
**Visualization:** [PERSON], [PERSON]
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**While subglacial channels are primarily sustained and deepened by meltwater plumes away from the grounding zone, the initial formation of these channels remains subject to multiple hypotheses. Notably, many subglacial channels align with locations where modeled subglacial water passes the grounding zone and leaves the grounded ice sheet ([PERSON] et al., 2017; [PERSON] et al., 2022; [PERSON] et al., 2013; [PERSON] et al., 2016). Here, fresh subglacial water meets ocean water, giving rise to and entraining warmer ocean water, which induces larger localized sub-ice-shelf melt rates. This can lead to the formation of water-filled cavities, sometimes hundreds of meters high, reaching several kilometres landmarks of the continental grounding zone ([PERSON] et al., 2022). High wall-melting rates maintain the cavity by preventing cavity closure through upstream ice advection ([PERSON] et al., 2017). Models coupling ice flow and subglacial channelized drainage produce channels which are increasing in cross-sectional area by an order of magnitude through high-effective pressure upstream of the grounding zone ([PERSON] & [PERSON], 2024). However, even though the principal physical mechanism for this type of channel formation is known, the spatial and temporal dynamics of such subglacial hydrological activities and their interactions with the ocean pose significant challenges for characterization, resulting in a limited understanding of these processes.
In this study, we investigate the temporal dynamics of subglacial channel activity at and upstream of the grounding zone of the Roi Boudouin Ice Shelf (RBIS). We utilize time slices of airborne radar data collected in 2011 and 2019, which provide insight into the internal structure of the ice sheet. Additionally, we analyze morphological structures on the surface of the ice shelf. A comparison of radar repeat flights over the grounded ice sheet around the grounding zone suggests that engalcial features, which we interpret as oversized subglacial channels, have undergone significant temporal changes over an eight-year period. Ice-shelf channels further seawards are an archive for the location of the subglacial water outlet providing evidence for both spatial stability over hundreds of years and temporal logging of the outlet activity.
## 2 Data and Methods
### Radar Data Acquisition and Processing
We used airborne radar data collected with two different radar systems by AWI (Alfred-Wegener-Institut Helmholtz-Zentrum fur Polar- und Meeresforschung, 2016) to map englacial reflections in the vicinity of the grounding zone of East Antarctica's Roi Boudouin Ice Shelf. The radar profiles are oriented orthogonally to ice flow and roughly parallel to the grounding zone and cover both the grounded part of the ice sheet as well as the ice shelf (Figure 1).
In austral summer of 2018/19, we acquired multi-channel ultra-wideband (UWB MCoRDS 5 system) radar data ([PERSON] et al., 2016; [PERSON] et al., 2014) in a frequency range of 150-520 MHz. The radar consisted of an eight-element antenna array mounted on AWTs Polar 6 BT-67 aircraft (Alfred-Wegener-Institut Helmholtz-Zentrum fur Polar- und Meeresforschung, 2016) during the CHIRP DML survey (Channel and Ice Rise Project in DML). Data acquisition consisted of staged linear modulated chirp signals (1 us unamplified, 1 us high-gain and 3 us high-gain) to sound the entire ice column at high resolution ([PERSON] et al., 2023). For radar data processing, we used the Open Polar Radar Toolbox (Open Polar Radar, 2023) and applied pulse compression, synthetic aperture radar (SAR) processing, motion compensation, and array processing ([PERSON] et al., 2021, 2022; [PERSON] et al., 2000; [PERSON] et al., 2014). The data product has a range resolution of \(\sim\)0.35 m and an along-track trace spacing of \(\sim\) 15 m. The UWB data set comprises five profiles, where four are located a few kilometers upstream of the grounding zone with a profile spacing between 1.5 and 3 km. The fifth profile is located \(\sim\) 12 km downstream of the grounding zone on the ice shelf (Figure 1).
In addition, we use radar data acquired in January 2011 with AWTs airborne Electromagnetic Reflection (EMR) system ([PERSON] et al., 1999). These data have been used in previous studies ([PERSON] et al., 2014; [PERSON] et al., 2017), and we use them here to monitor temporal changes that have occurred since. The Aero-EMR operates with a 150 MHz 60 ns burst transmit signal. The recorded radar signals were amplified, band-pass filtered, and passed on to an analog-digital converter. Moreover, the radar data were stacked ten-fold along-track to improve the signal-to-noise ratio. The EMR-60 ns data product has a range resolution of \(\sim\) 5.6 m and an along-track trace spacing of \(\sim\) 60-100 m.
In this study, we considered four radar profiles, which are mostly located at and upstream of the grounding zone and have a profile spacing of \(\sim\) 13 km. The northernmost EMR radar profile overlaps with one of the UWB
Figure 1.— Survey region and overview of radar features. (a) Coastal eastern Dronning Maud Land with radar survey lines with color coding as indicated in the legend. (b) Magnified view on the survey region with ice-flow velocity ([PERSON] et al., 2019) in the background. (c) UWB radargrams from North to South (ice flow from bottom to top), with annotations highlighting distinct englacial features discussed in the text. Numbers on top indicate profile labels for unique identification and are also indicated in (b) The grounding zone ([PERSON] et al., 2017) in (b) is indicated as a white band.
profiles close to the grounding zone. The southernmost EMR profile is located \(\sim\)45 km upstream of the grounding zone (Figure 1). For conversion from time to depth domain for all radar data we used a constant relative dielectric permittivity value of 3.15 for ice, which corresponds to an electromagnetic wave speed of 1.689 10\({}^{8}\) m s\({}^{-1}\).
### Ice Surface Elevation, Bed Topography and Flow Velocity
We used the ice surface elevation, bed topography, and ice surface flow velocity data to explore the englacial features in the radar data, using the ice surface and subglacial topography signatures. Ice surface topography was obtained from the Reference Elevation Model of Antarctica (REMA) digital elevation model (DEM) and resampled to a resolution of 8 m ([PERSON] et al., 2019). Based on the surface DEM we created a hillshade to detect the imprint of subglacial channels in the ice surface. For bed topography, we use BedMachine Antarctica v3 ([PERSON] et al., 2020) with a resolution of 500 m. In addition, we used the Antarctic-wide ice surface flow velocity product from [PERSON] et al. (2019) to calculate the advection time and distance of ice surface features.
### Subglacial Hydrology Modeling
We applied subglacial hydrological modeling in the drainage basin feeding into RBIS to explore the linkage between subglacial water and the features in our RES and remote sensing data. We used the MPI parallel version of the Confirmed-Unconfined Aquifier System model (CUAS-MPI; [PERSON] et al., 2018; [PERSON] et al., 2023), which can represent the physics of a distributed and channelized subglacial hydrological system over a large area and in high temporal resolution. The model uses a single-layer equivalent porous medium approach, which solves a two-dimensional Darcy-type groundwater flow equation, accounting for spatially and temporally evolving hydraulic transmissivity and taking into account both confined and unconfined aquifer conditions ([PERSON] et al., 2018; [PERSON] et al., 2023). The model adopts the classical channel equations ([PERSON], 1976; [PERSON], 1972) as in [PERSON] et al. (2016) and cavity opening ([PERSON], 1987; [PERSON], 1986) as in [PERSON] et al. (2013) to evolve the effective transmissivity. For further details see Supplementary Text S1 in Supporting Information S1.
In addition, we applied the CiDRE (Cordial Drainage Routing Engine) model ([PERSON], 2020) to generate subglacial water propagation pathways and flow accumulation based on the hydropotential ([PERSON], 1972) and subglacial water routing following the methods outlined by [PERSON] and [PERSON] (2010). To account for uncertainties in the input data sets (e.g., ice thickness and ice surface elevation), we follow [PERSON] et al. (2021) and consider the uncertainty estimates of both data sets. The uncertainty limits were based on the information given by the specific data sets and range from \(\pm\)2.4 m in ice surface elevation ([PERSON] et al., 2019) and 10-1,000 m for ice thickness ([PERSON] et al., 2020). We conducted 1,000 calculations of subglacial routing pathways, adding a random error to both input data sets with the uncertainty limits, and stacked the results to provide a comprehensive range of potential water routing pathways.
## 3 Results
### Englacial Channels in Radar Data
Our UWB radar data from 2019 detected strong englacial reflections in the vicinity of the grounding zone at the RBIS (Figure 1). Upstream of the grounding zone they appear as cone-shaped events with pronounced point-like reflections at their apex, which recover systematically along the subglacial channels across individual radar profiles (Figure 1c). At the grounding zone and on the ice shelf, we generally observe broader, step-like event signatures following the reflection of the ice base.
These reflections are observed up to more than 5 km upstream of the grounding zone, within a similar distance (traveltime) range in the radargrams. Therefore, we rule out that these could be off-nadir reflections from seawater-filled channels on the ice shelf or at the grounding zone ([PERSON] et al., 2018), as the radar's beam angle does not permit to detect reflections from such a distance at angles up to three times larger as its beam angle of \(\sim\)21\({}^{\circ}\) in sounding mode ([PERSON] et al., 2022). Moreover, the off-nadir reflections would appear in a much higher range in the nadir-projected signal in the radargrams (approximately at 3 km depth; see Supplementary Text S2 in Supporting Information S1). It is possible that the reflections may consist of a more complex signal that includes off-nadir reflections from the immediate vicinity within a few tens to hundred meters radius ([PERSON] et al., 2014). However, the recurring signal along the radar profiles at similar locations and similar range suggests that this is an englacial reflector on the grounded part of the ice sheet, extending parallel to the flow direction.
Based on their spatial positioning and geometrical attributes within the radargrams, we categorize these reflections into coherent features designated as subglacial channels (CH1-CH5). Three of these subglacial channels (CH3-CH5) were reported in previous surveys ([PERSON] et al., 2017). We consider two possible configurations for these channels that could produce the observed reflections: (a) they are water-filled cavities, several hundred meters high and a few tens to hundreds of meters wide, similar to those observed by [PERSON] et al. (2022); [PERSON] et al. (2023); [PERSON] (2023) at the Kamb Ice Stream and potentially filled with sedimentary material ([PERSON] et al., 2017); (b) they are smaller subglacial channels that have a vertical crevasse on their upper side ([PERSON] et al., 2012).
The UWB profile at the grounding zone from 2019 overlaps with an EMR profile acquired in 2011 (Figure 2). A detailed comparison shows that the size and shape of some of these cavities have changed close to the limits of the radar resolution. Two additional smaller channel signatures between CH4 and CH5 are evident in the 2011 EMR profile but not visible in the 2019 UWB profile. Most importantly, CH2 is completely absent in the 2011 EMR profile (Figures 2c and 2d). In the UWB data, the cavity of CH2 is vertically incised by about 190 m with respect to the surrounding ice-sheet bed reflection.
The subglacial channels exhibit variations in both spatial extent and radar backscattering characteristics. On the grounded part near the grounding zone, some channels (CH3-5 in profile 20190106_01_004) exhibit gaps in the basal reflection. Further upstream, however, a continuous basal reflection is observed, which could be explained by the channels becoming narrower and the radar return additionally being influenced by side reflections. The westernmost channel (CH1) appears solely at the grounding zone and on the ice shelf and has the lowest height above the surrounding ice-sheet base. Channels CH3, CH4, and CH5 are distinctly observable on the shelf and extend up to approximately 10 km upstream of the grounding zone in our UWB data set. The height of CH4 exhibits a gradual increase with advection across the grounding zone, whereas CH3 and CH5 remain above 200 m height (Supplementary Figure S2 in Supporting Information S1). For these three channels, we also observe an increase in return power with decreasing distance toward the grounding zone. CH2 is clearly visible in the two northernmost profiles (at the grounding zone and on the ice shelf). Its radar signature upstream of the grounding zone is less distinct and weaker compared to the other channels, therefore we speculate if the reflection could present the tip of a vertical crevasse ([PERSON] et al., 2012) above a smaller subglacial conduit. Furthermore, CH2 is the only channel identifiable in the southernmost radar profile.
In addition to radar reflections from the subglacial channels, a distinct layer-like englacial reflector is located at the eastern edge of the profiles. This reflection does not follow the bed topography and does not exhibit a resemblance to the signatures of CH1-5. Instead, it resembles the shape of an anticline, with a wavelength of \(\sim\) 5 km and an elevation of roughly \(\sim\) 300 m and could be an indication of large-scale englacial folding providing insights into the mechanical properties of the ice ([PERSON] et al., 2024). However, this reflection is not apparent in the radar profile on the ice shelf.
### Channel Imprint on the Ice-Sheff Surface
Downstream of the grounding zone, we observe typically elongated surface troughs on the ice shelf in alignment with the flow direction, which coincide with the locations of identified subglacial channels in the radar data. These troughs start at the grounding zone for CH1, CH3, CH4, and CH5 and some of these surface features exhibit deviations from flowlines discussed elsewhere ([PERSON] et al., 2024; [PERSON] et al., 2020). However, CH2 presents a different pattern: its surface depression is nearly absent up to approximately 10 km downstream of the grounding zone (Figure 2e). Moreover, the location where the surface trough becomes clearly visible corresponds to a deeper, topographically confined elliptical depression. This depression was investigated previously and tentatively interpreted as an englacial lake ([PERSON] et al., 2017), advected from the grounding zone area (Supplementary Figure S3 in Supporting Information S1) where surface melting frequently occurs ([PERSON] et al., 2017).
### Subglacial Hydrology Modeling
The CUAS-MPI simulations (Supplementary Figures S4 a-S4d in Supporting Information S1) lead to a small band close to the grounding zone with low effective pressure (\(N=p_{\rm ice}-p_{\rm water}\approx 0\) MPa) that is primarily caused by the applied ocean boundary condition. In this band, the high effective transmissivity (\(T_{\rm eff}\) > 1 m\({}^{2}\) s\({}^{-1}\)) would allow for efficient water transport. Since the water input into the model originates from geothermal heat flux and basal friction, this input increases downstream due to faster ice flow and is largest in an area of thick ice that is grounded well below sea level (see \(-500\) m bed elevation contour in Supplementary Figure S4 in Supporting Information S1). High water input in addition to high effective transmissivity then leads to high subglacial water flux toward the grounding zone that concentrates in the regions where we observe subglacial channels (Figure 3a). Considering solely the gradient of the hydropotential (which does not provide information on flow rates and water flow in channels), we note that at CH1, CH2, and CH3, the subglacial water precisely converges toward the detected channels (Figure 3b).
Figure 2: Temporal changes of englacial features near the grounding zone. (a) EMR Profile acquired in 2011 (profile 20113139), (b) UWB Profile acquired in 2019 (profile 20190106_01_004). Magnified views on englacial features at CH2 in the EMR and UWB profile are shown in (c) and (d). (e) Map view of ice-shelf surface features at locations where channels were detected in the radar data. The grounding zone ([PERSON] et al., 2017) in (e) is indicated as a white band.
## 4 Discussion
### Temporal Dynamics of Subglacial Channel Activity
Our radar data documents five subglacial channels on the grounded ice sheet, intruding into the ice sheet and laterally extending into the Roi Baudoin Ice Shelf. Based on the available information, we cannot definitively determine whether the observed features are (a) completely water-filled cavities ([PERSON] et al., 2023; [PERSON] et al., 2022) potentially filled with sediment ([PERSON] et al., 2017), (b) smaller subglacial channels with vertical crevasses ([PERSON] et al., 2012), or a combination of these possibilities. However, the combination of our radar observations, subglacial hydrological modeling, and features on the ice shelf, we consider it most likely that these are cavities probably filled with ocean water mixed with subglacial outflow.
The increase in size of the incision with decreasing distance to the grounding line remains consistent with observations at the grounding zone of the Kamb Ice Stream ([PERSON] et al., 2022). Nonetheless, we note that the ice dynamic and topographic environment at the grounding zone of the Kamb Ice Stream is different from the setting at RBIS. However, so far little is known about temporal changes in subglacial channel activity. The geometry of the ice directly above the channels does not present a coherent pattern, as it appears as a mix of ridges, valleys, or flat topography (Figure 1c). Given our limited knowledge of the force balance within the channels and the fact that the channels seem relatively narrow (a few tens to hundreds of meters and thinning upstream), combined with the likelihood of a temporally varying water supply system and interactions with the ocean, a valley in the ice surface above the channels should not necessarily be expected.
Broadly speaking the locations of CH3-5 have remained stable in the time interval (2011-2019) given by our repeat radar transects, although some changes in the geometry of the ice-shelf cavity are evident. The stable locations are in line with the ice-shelf channel lineations further seawards, which appear near parallel to ice-shelf flow lines for hundreds of years of ice advection. CH2 (which was not evident in the 2011 EMR radar transect) has a distinctly different pattern in this regard because the corresponding ice-shelf channel extends far in the ice shelf but is disconnected to the contemporary grounding zone. This distance gap corresponds to approximately 60 years of ice advection.
We define \"activity\" in the sense that subglacial water is transported from the ice-sheet interior toward the grounding zone, creating Rothlisberger channels in a high-pressure system ([PERSON], 1972), potentially also combined with Nye channels ([PERSON], 1957), where it interacts with ocean water that primarily deepens and sustains the subglacial channel, and causes basal melting of the ice shelf in the direction of ice flow ([PERSON] et al., 2013;
Figure 3: Overview of subglacial hydrological modeling, overlaid by the location (colored dots) of the channels in the radargrams (compare Figure 1b). (a) Subglacial water flux magnitude from CUAS-MPI. The white arrows indicate the direction of ice flow. (b) Magnified view of the survey region showing subglacial water routing (number of upstream cells) based on the hydrothermal gradient. The grounding zone ([PERSON] et al., 2017) is indicated as a white band.
[PERSON] et al., 2016; [PERSON] & [PERSON], 2008). As soon as the combination of the water pressure, flux, and the contribution of ocean water can no longer maintain the subglacial channels open, the basal melting on the underside of the ice shelf also ceases, and with it, the basal channel signature at the ice shelf's surface ([PERSON] et al., 2016).
Based on the radar and ice surface features associated with CH2 (Figure 2), we hypothesize the following temporal evolution scenario (summarized in Figure 4). (a) Subglacial channel CH2 was active many hundreds of years prior to \(\sim\) 1960 C.E. based on the current flow field and the trough extent on the ice shelf. Considering that we observe a clear ice surface trough up to a distance of \(\sim\) 5-10 km from the grounding zone along ice flow, the advection time corresponds to approximately 60 years with the present-day flow field. (b) The channel was deactivated around 1960 (60 years before the ice surface DEM date). We hypothesize that a substantial change of the subglacial characteristics caused a lowering at the ice surface and infill of supglacial meltwater in a circular depression at the ice-shelf surface (Figure 2e). (c) As we observe no englacial reflection in our 2011 EMR data (Figure 2c), we suggest that the subglacial channel at CH2 remained inactive at least until 2011, that is, water flow and ocean water intrusion were too low to result in sufficiently high melt rates to cause incision of the channel into the ice-sheet base. (d) Between 2011 and 2019, the inland channel system of CH2 was reactivated, which we infer from characteristic englacial reflection in the 2019 UWB data (Figure 2d).
### Potential Channel De- and Re-Activation Mechanisms
Our observations suggest that the subglacial hydrological system influences the subglacial channel location, and combined with direct interaction with the ocean, acts as the driving force behind the subglacial channels both on the grounded side as well as at the ice-shelf base. This is supported by our subglacial hydrological modeling and observations at other Antarctic grounding zones ([PERSON] et al., 2016; [PERSON] et al., 2022) and general modeling approaches ([PERSON] & [PERSON], 2024). The system controls the location and melt rates at the ice underside on the
Figure 4: Sketch of the temporal evolution of subglacial channel activity at CH2 based on ice-surface and radar-feature interpretation.
grounded channel as well as the melt rates of the plume. We consider two fundamental mechanisms that can lead to episodic changes in subglacial water supply at the same location:
If the subglacial hydrological system further upstream could predominantly be characterized as a distributed system, small changes in ice sheet geometry (top and base) will cause a shift in subglacial water flow. The water supply would thus follow the gradient of the hydropential, which is most sensitive to gradients of the ice surface elevation. Possible explanations for changes in ice surface on timescales of less than 100 years could include changes in spatial snow accumulation patterns, changes in drainage geometry, or intense basal melting, resulting in relative lowering or raising of the ice surface or erosional and depositional sedimentary processes at the ice-sheet base. However, a mere relocation of water flow in the order required to make the ice-shelf imprints of CH2 disappear would have likely required another outlet feature to appear in the nearby environment.
Another possibility that could induce changes in channel activity is spatially fixed but temporary changes in water supply due to the filling and draining of subglacial lakes. Active subglacial lakes in this region have not been identified so far, but a large number of subglacial lakes and their network likely remain undiscovered ([PERSON] et al., 2021), with recent discoveries also made in this Antarctic sector ([PERSON] et al., 2024). The filling and draining of a subglacial lake would modulate melt rates and could thus explain the cessation and reactivation of subglacial channels at the same location.
The shutdown of subglacial channels near the grounding zone suggests a rapid and extensive change in the steady-state interaction between subglacial and ocean water. This could potentially have been caused by a subglacial flood ([PERSON] et al., 2016), resulting in extreme local melting and subsequent cessation of subglacial water supply. The consequences of such floods have recently been documented in a channel cavity on the Kamb ice stream ([PERSON] et al., 2016; [PERSON] et al., 2022). Especially in the context of the reactivation of the CH2 system, we consider substantial activity of a subglacial lake as reservoir for the subglacial water supply on time scales of decades instead of an overall shift in the subglacial hydrological system as more plausible.
### Significance for the Antarctic Ice-Shelf System
The flow of substantial volumes of freshwater from subglacial hydrological channels into ice-shelf cavities has been demonstrated to play a crucial role in basal melting of ice shelves at the grounding zone ([PERSON] et al., 2022; [PERSON] et al., 2020). Subglacial water flux from the inland alone cannot create and sustain the observed hundred-meters high subglacial channels observed here. Nonetheless, we find strong indications, that it impacts the initiation and evolution of basal channels, in turn affecting ice-shelf stability, and the occurrence of calving events ([PERSON] et al., 2018). Moreover, subglacial channels imprint changes in ocean and atmospheric foreions at the ice-shelf surface ([PERSON] et al., 2024; [PERSON] et al., 2020). Our observation of the transient behavior of channels upstream of and at the grounding zone over timescales of decades makes it even more challenging to project their impact on Antarctica's ice-shelf systems in the future and their contribution to the vulnerability to grounding zone retreat ([PERSON] et al., 2024; [PERSON] and [PERSON], 2024; [PERSON] et al., 2024). It highlights the need for fully coupled ice-sheet-hydrology simulations as (re-activation of channels can trigger ocean plumes at the grounding zone, and their deactivation can also cease or weaken the interaction with the ocean. Such processes thus also influence ice-shelf thinning and thickening and the interaction of the ice shelf with pinning points ([PERSON] et al., 2017; [PERSON] et al., 2022).
## 5 Conclusions
Subglacial signatures from repeated radar measurements and morphological features on the ice-shelf surface near the grounding zone between the West Ragnhild Glacier and Roi Baudouin Ice Shelf in East Antarctica reveal temporal changes in the subglacial hydrological system. We inferred that subglacial channels can shut down and reactivate at the same location around the grounding zones within decades, indicating an interaction between subglacial water supply and ocean water intrusion undergoing episodic phases of activity and shut down. These are potentially more likely linked to the filling and draining of subglacial lakes than the relocation of water routing due to ice-sheet geometry changes, as well as changes in ocean plumes, although we do not have evidence which process prevails and causes the temporal change. Variability on such short timescales has not been observed in this region before, providing new insights into the transient nature of the subglacial system around the grounding zone of the Antarctic Ice Sheet, which profoundly affects ice-shelf-ocean processes. A better understanding of these temporal changes in the hydrological system incorporating lake drainage mechanisms is necessary to understand the associated physical mechanisms better, yet at the same time presents significant challenges for simulating such processes and thus increases uncertainties in future predictions of processes related to subglacial hydrology.
## Data Availability Statement
Radar data products from the AWI UWB CHIRP survey in the 2018/19 season ([PERSON] et al., 2023) and from the AWI EMR survey in the 2010/11 season ([PERSON] et al., 2024) are available on the PANGAEA data repository. The CUAS simulation output is available at Zenodo (Kleiner & Humbert, 2024). The REMA ice surface DEM ([PERSON] et al., 2022) is available from the U.S. Polar Geospatial Center. BedMachine Antarctica (Version 3; [PERSON] et al., 2020) and ice surface flow velocities from [PERSON] et al. (2019) are available at the National Snow and Ice Data Center. CUAS-MPI is available at [[https://github.com/tudasc/CUAS-MPI](https://github.com/tudasc/CUAS-MPI)]([https://github.com/tudasc/CUAS-MPI](https://github.com/tudasc/CUAS-MPI)).
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wiley/fcfd1257_a7af_420f_81dc_31fcda57d3cc.md | # Variations in Physiology and Genomic Function of _Prochlorococcus_ Across the Eastern Indian Ocean
Siyu Jiang
Armosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan, \"Department of Ocean Sciences, Tokyo University of Marine Science and Technology, Tokyo, Japan, \"Department of Ocean Science, Hong Kong University of Science and Technology, Hong Kong, Hong Kong, \"Graduate School of Agricultural and Life Sciences, The University of Tokyo, Tokyo, Japan, \"Center for Mathematical Science and Advanced Technology, JAMSTEC, Yokohama, Japan, \"Collaborative Research Institute for Innovative Microbiology, The University of Tokyo, Tokyo, Japan, \"Research Center for Oceanography - National Research and Innovation Agency, Jakarta, Indonesia
[PERSON]
###### Abstract
The widespread distribution of _Prochlorococcus_ can be attributed to the extensive genetic diversity that allows them to adapt to various oligotrophic environments. We investigated the adaptation of _Prochlorococcus_ to nutrient environments in the surface eastern Indian Ocean (EIO, 16.5\"N to 20\"S, 88\"E) in November 2018. The growth rate of the _Prochlorococcus_ population and its response to macronutrient enrichments (NH\({}_{4}^{+}\) and PO\({}_{4}\)\({}^{3-}\)) and the abundance of functional gene modules related to nutrient utilization were examined by on-deck incubation experiments and metagenomic analysis, respectively. Although the dissolved inorganic nitrogen was depleted (\(\sim\)58 nM) and the _Prochlorococcus_ populations were dominated by the high-light-adapted II ecology, _Prochlorococcus_ populations showed distinct physiological patterns, especially the response to macronutrient enrichments, indicating their adaptation to local nutrient environments. At the northernmost station in the Bay of Bengal, the significant increase in growth rate with macronutrient enrichments and the highest abundance of the phosphate starvation response two-component regulatory system module indicated adaptation to phosphorus-limited environments. In the southern EIO, the insignificant increase in growth rate with macronutrient enrichment and higher abundance of the iron complex transport system module suggested adaptation to iron-limited environments. However, genomic characteristics are not always associated with physiological characteristics. The abundance of the nitrate/nitrite transport system module was higher in the southern EIO, where the growth of _Prochlorococcus_ relies on regenerated nitrogen sources as revealed by incubation experiments. These results reflected the complexity of _Prochlorococcus_ adaptation especially in chronically oligotrophic environments, which was better revealed by combining physiological and genomic analyses.
Published in: 10.1029/2023 JC019898
1
## 1 Introduction
The widespread distribution of _Prochlorococcus_ can be attributed to the extensive genetic diversity that allows them to adapt to various oligotrophic environments. We investigated the adaptation of _Prochlorococcus_ to nutrient environments in the surface eastern Indian Ocean (EIO, 16.5\"N to 20\"S, 88\"E) in November 2018. The growth rate of the _Prochlorococcus_ population and its response to macronutrient enrichments (NH\({}_{4}^{+}\) and PO\({}_{4}\)\({}^{3-}\)) and the abundance of functional gene modules related to nutrient utilization were examined by on-deck incubation experiments and metagenomic analysis, respectively. Although the dissolved inorganic nitrogen was depleted (\(\sim\)58 nM) and the _Prochlorococcus_ populations were dominated by the high-light-adapted II ecology, _Prochlorococcus_ populations showed distinct physiological patterns, especially the response to macronutrient enrichments, indicating their adaptation to local nutrient environments. At the northernmost station in the Bay of Bengal, the significant increase in growth rate with macronutrient enrichments and the highest abundance of the phosphate starvation response two-component regulatory system module indicated adaptation to phosphorus-limited environments. In the southern EIO, the insignificant increase in growth rate with macronutrient enrichment and higher abundance of the iron complex transport system module suggested adaptation to iron-limited environments. However, genomic characteristics are not always associated with physiological characteristics. The abundance of the nitrate/nitrite transport system module was higher in the southern EIO, where the growth of _Prochlorococcus_ relies on regenerated nitrogen sources as revealed by incubation experiments. These results reflected the complexity of _Prochlorococcus_ adaptation especially in chronically oligotrophic environments, which was better revealed by combining physiological and genomic analyses.
Plain Language Summary _Prochlorococcus_ are the smallest but most abundant photosynthetic organisms on Earth. Their widespread distribution (40\"N to 40\"S) and dominance in global subtropical and tropical phytoplankton communities could be attributed to the extensive genetic diversity that allows them to adapt to various environments. Although the adaptation of _Prochlorococcus_ to nutrient environments could be reflected by variation in the genome, this method sometimes masks the complexity of _Prochlorococcus_ adaptation. In this study, we combined incubation experiments with metagenomic analysis to better understand _Prochlorococcus_ adaptation in the eastern Indian Ocean, which is consistently nutrient-depleted but has subtle variations in nutrient environments. The results showed that the _Prochlorococcus_ population had three distinct physiological patterns in the study area. In particular, the distinct response to the additional nutrients in incubation experiments indicated their specific adaptations to local nutrient environments. Furthermore, by considering the physiological characteristics with the spatially varied abundance of functional genes related to nutrient acquisition, it was revealed that _Prochlorococcus_ growth was limited by different nutrients (nitrogen, phosphorus or iron) across the study area. Our results suggested the complexity of _Prochlorococcus_ adaptation to oligotrophic environments, which can be elucidated by considering both physiological and genomic characteristics.
characteristics. We expected that the combination of on-check incubation experiments, metagenomic analysis and detailed measurements of nutrient conditions (NO\({}_{3}\)\({}^{-}\), NO\({}_{2}\)\({}^{-}\), NH\({}_{4}\)\({}^{+}\), urea, PO\({}_{4}\)\({}^{-}\), and dissolved iron (dFe)) would reveal the adaptation of the _Prochlorococcus_ population to oligotrophic environments with different nutrient conditions in the EIO.
## 2 Materials and Methods
### Study Area and Sampling
This study was conducted along a meridional transect in the EIO in November 2018 (88\({}^{\circ}\)E, 16.5\({}^{\circ}\)N to 20\({}^{\circ}\)S, Figure 1). The hydrographic properties, including temperature, salinity, and density, were measured by an SBE 911 plus conductivity-temperature-depth (CTD) system (Sea-Bird Electronics), which was reported in [PERSON] et al. (2022). The surface seawater (10 m) used for determining environmental parameters, conducting metagenome analysis and performing incubation experiments was collected using acid-cleaned Niskin-X bottles (General Oceanics) equipped with the CTD system.
### Environmental Parameters
The distribution of temperature, salinity, and density along the transect was obtained directly by the CTD system. The concentrations of NO\({}_{3}\)-, NO\({}_{2}\)-, NH\({}_{4}\)+, and PO\({}_{4}\)\({}^{-}\) were measured by sensitive liquid waveguide spectrophotometry as described in [PERSON] et al. (2022), with detection limits of 3, 2, 4, and 3 nM, respectively.
Figure 1: Map of station locations with surface currents during the cruise. Incubation experiments (white circle) were conducted except at station 2 (black circle). The stations were divided into the Bay of Bengal (BoB), equator, southern or SISG (Southern Indian subtropical gyre) stations. The white arrows indicate the current system and an anticyclonic eddy observed at station 7 (SEC: South Equatorial current). The OSCAR sea surface velocity data was obtained from the NOAA Coastwatch server (coastwatch.pfleg.noaa.gov/erdap/).
Samples used for analyzing the urea-derived nitrogen (urea-N) were filtered through a precombusted GF/F filter (GE Healthcare UK Ltd.) and collected as filtrate into acid clean polypropylene bottles. The concentration of urea-N was measured using the highly sensitive liquid waveguide spectrophotometry method as described in [PERSON] et al. (2020). The detection limit of urea-N was 5 nM.
Samples for dFe were collected by using Teflon-coated Niskin-X samplers deployed onto the CTD-CMS system ([PERSON] et al., 2023) and preconcentrated in a clean room to avoid any contamination. The concentration of dFe was determined from the preconcentrated samples by high-resolution inductively coupled plasma-mass spectrometry (HR-ICP-MS, Thermo Element XR) following the protocol described in [PERSON] et al. (2016). The detection limit of dFe was 0.009 nM.
### Phytoplankton Community
The chlorophyll \(a\) (Chl \(a\)) concentration representing the phytoplankton biomass was measured onboard by a fluorometer (10-AU-005; Turner Designs, San Jose, CA, USA) with a non-acidification method ([PERSON] et al., 2022; [PERSON], 1994). To further determine the contribution of _Prochlorococcus_ to the community Chl \(a\), an additional 2-4 L of seawater was collected by filtering through 25-mm-diameter Whatman GF/F filters (GE Healthcare Life Sciences, Pittsburgh, PA, USA). The concentrations of Chl \(a\) and divinyl chlorophyll \(a\) (Dv, the marker pigment of _Prochlorococcus_) were analyzed by a high-performance liquid chromatography (HPLC) system (Shimadzu, Tokyo, Japan) as described in [PERSON] et al. (2021).
The abundance and characteristics of _Prochlorococcus_ cells were determined by flow cytometry (FCM). Seawater (1.8 mL) was fixed with buffered paraformaldehyde (final concentration of 0.5%) and analyzed by a Becton-Dickinson FACSCalibur cytometer with yellow-green fluorescent beads (diameter = 1 \(\upmu\)m, Polysciences) as the internal standard ([PERSON] et al., 2022). The cell size represented by the equivalent spherical diameter (ESD) was calculated according to the equation ESD = 3.48 \(\times\) SS\({}^{\text{3.46}}\), in which SS is the geometric mean of the side scattering signal normalized by the internal standard ([PERSON] et al., 2011). The cellular Chl \(a\) content was represented by the geometric mean of the normalized red fluorescence intensity (FL3).
### Incubation Experiments
To determine the growth rate of _Prochlorococcus_ and its response to macronutrient enrichment, a series of 24-hr dilution experiments were conducted with surface seawater (10 m). This is a commonly used technique, in which the natural seawater was diluted with seawater that filtered through acid-cleaned 0.2 \(\upmu\)m filter capsules (Pall Corporation, New York, NY, USA) on several different proportions ([PERSON] & Hassett, 1982). This method allows us to measure phytoplankton growth and grazing mortality rates separately, rather than measuring a net growth rate. The experimental setup and rate estimation were described in [PERSON] et al. (2022). In brief, we used four dilution treatments (\(D_{i}\) (dilution factor) = 0.2, 0.5, 0.8, and 1, which means there were 80%, 50%, 20%, and 0% particle-free seawater in treatments), with duplicated incubation bottles (2.4 L) for each treatment. To reveal the response of _Prochlorococcus_ to additional macronutrients, ammonium and phosphate were enriched in these incubation bottles (final concentrations of 0.5 \(\upmu\)M NH\({}_{4}\)Cl and 0.03 \(\upmu\)M KH\({}_{2}\)PO\({}_{4}\)). Additionally, another two incubation bottles (\(D_{i}\) = 1) were prepared as controls without macronutrient enrichment. All these bottles were gently mixed, covered with a neutral-density filter with 50% light transmission, and incubated for 24 hr in an on-deck incubator with running surface seawater. Seawater was collected for FCM and HPLC analysis before incubation as the initial samples, and from each bottle after incubation. All carboys, tubes, filter capsules and incubation bottles used for experiments were acid-cleaned and rinsed with distilled water and seawater 3-4 times before using.
In this study, we differentiated _Prochlorococcus_ from other phytoplankton by both FCM and its marker pigment Dv determined by HPLC analysis. The _Prochlorococcus_ division rate and Dv production rate were calculated from variations in cell abundances and pigment concentrations before and after incubation experiments, respectively. In details, the _Prochlorococcus_ net growth rate (\(k_{s}\)) in each dilution treatment could be described by \(k_{s}=\ln\) (\(C/[D_{i}\times C_{0}]\)), where \(C_{0}\) is the initial _Prochlorococcus_ cell abundance or Dv concentration, and \(C_{i}\) are those after incubation. By fitting \(k_{i}\) and \(D_{i}\) to a linear regression, the instantaneous _Prochlorococcus_ gross growth rate with macronutrient enrichment (\(\mu_{u}\)) and the mortality rate (\(m\)) were obtained by the \(y\)-axis intercept and regression slope. Further, the _Prochlorococcus_ gross growth rate without macronutrient enrichment (\(\mu_{0}\)) was calculated by \(\mu_{0}=m+k_{\text{corr}}\) where \(k_{\text{corr}}\) was the _Prochlorococcus_ net growth rate in the control bottles without macronutrient enrichment. With these measurements, the response of _Prochlorococcus_ cellular characteristics (cell size and cellular Chl \(a\) content) and growth rates (cell division rate and Dv production rate) to macronutrient enrichment was determined by comparing the results derived from bottles incubated with and without macronutrient enrichment.
### Metagenomic Analysis
The seawater for metagenomic analysis (6-7 L, 10 m layer) was sequentially filtered through a 3.0-\(\upmu\)m-pore-size Nuclepore filter (47-mm-diameter, Whatman, Clifton, NJ, USA) and a 0.22-\(\upmu\)m-pore-size Sterivex filter unit (Millipore, Bedford, MA, USA). The filters were subsequently stored at \(-80\)degC until further processing in the lab. Samples of the Sterivex cartridge filters were used for the analysis, as free-living _Prochlorococcus_ cells are dominant according to FCM analysis (Figure S1 in Supporting Information S1). DNA extraction was carried out with the MagAttract PowerWater DNA/RNA Kit (QIAGEN) according to the manufacturer's instructions. Extracted DNA was fragmented (400 bp) using the Covaris ME220 (Covaris LLC., MA, USA), and the MGLEasy Universal DNA Library Prep Set was used to prepare sequencing libraries. Shotgun sequencing of metagenome samples was performed using the DNBSEQ-G400 platform (2 x 200 bp) (MGI Tech Co., Ltd., Shenzhen, China; the number of paired reads of each sample is shown in Table S1 in Supporting Information S1).
The assembly of metagenomic shotgun sequences was performed by MEGAHIT v1.2.9 ([PERSON] et al., 2015). Searches of the RefSeq database (34,740 bacterial and 764 archeal genomes) for nucleotide sequence identities of the assembled contigs were performed using BLASTN v2.6.0+ with subsequent comparison of the nucleotide sequences showing significant homology (<1e\(-\)50 of e-value) to annotate taxonomic information.
Metagenome shotgun reads were mapped to the taxonomically annotated contigs by BWA mem v0.7.15 ([PERSON], 2013), and those mapped reads were joined by FLASH v1.2.11 ([PERSON] & [PERSON], 2011). The reads mapped to the contigs derived from _Prochlorococcus_ were listed and extracted. ORFs with over 30 amino acids extracted by getorf in the EMBOSS v6.6.0.0 package were randomly sampled up to 3 million sequences for Genomic(tm) analysis.
To analyze the ecotype composition, one million reads were used to search the _Prochlorococcus_ sequences of the 16S rRNA gene and the _rpoC1_ gene, a highly variable phylogenetic marker gene. The _Prochlorococcus_ sequences of the 16S rRNA gene listed in [PERSON] et al. (2013) were used as reference sequences. The homology search was performed by blast of BLAST (v2.6.0) ([PERSON] et al., 2009) against these reference sequences, and hits with more than 97% identity were counted. The reference sequences of _rpoC1_ were collected by the following procedures. First, the _Prochlorococcus_ genomes listed in [PERSON] et al. (2014) and [PERSON] et al. (2018) were collected. Then, gene prediction was performed with PRODIGAL (v2.6.3) ([PERSON] et al., 2010), and the orthologous genes of _rpoC1_ were extracted from among the single-copy genes assigned by Orthofinder (v2.5.4) ([PERSON] & [PERSON], 2019). The homology search was performed by blastx against the reference amino acid sequences of _rpoC1_, and hits with \(>\)90% identity and \(>\)50 amino acids of alignment length were counted. The sequence reads that hit multiple ecotypes with the same score were removed from the count for both analyses.
Additionally, the patterns of metabolic and physiological potential of _Prochlorococcus_ at stations 1, 3, 4, and 5 and stations 7 to 10 were investigated using the Genomapier(tm) (formerly MAPLE) system ver. 2.3.2 ([PERSON] et al., 2018; [PERSON] et al., 2016). The multi-FASTA file consisting of 3 million amino acid (AA) sequences over 30 AAs in length mapped to the known _Prochlorococcus_ genomes at each station were subjected to metagenomic analysis using Genomapier(tm). Genes were mapped to 814 functional modules defined by KEGG (pathways, 310; complexes, 298; functional sets, 167; and signatures, 49), and the module completion ratio (MCR) was calculated according to a Boolean algebra-like equation described previously ([PERSON] et al., 2012). The module structure and the outline of Genomapier system are shown in Figures S3 and S4 in Supporting Information S1, and a user's guide in Supporting Information S1. Additionally, this system automatically calculates module abundance when the modules are completed by the metagenomic sequences. To compare the module abundances across metagenomic samples, it is necessary to normalize each sample because the number of cells used to construct the metagenome is different. In this study, we normalized the module abundance to the number of ribosomal proteins (i.e., abundance/ribosomal protein \(\equiv\) abundance/cell), since the ribosome is basically composed of the same number of ribosomal proteins regardless of the species. Further, to reveal the spatial variation in module abundances,the abundance ratio of each module at each station was calculated by dividing the module abundance by the minimum abundance among all stations. According to the rarefaction curve of KO types (KEGG orthologous gene ID) assigned to _Prochlorococcus_ reads, the number of KO types reached a plateau and was similar among all stations, indicating a similar gene repertoire at each station (Figure S2 in Supporting Information S1). In a previous study using the Genomaple system, there were only few abundance ratios higher than two in the data set collected from the Sargasso Sea ([PERSON] et al., 2016), we thus considered the abundance ratio higher than two could indicate there is a difference in functional properties among stations. The results obtained from the Genomaple system are available in Supporting Information S1, including the module completion ratio (MCR), \(Q\)-value (indicator of working probability of each module), and module abundances. Additionally, our sequencing data was submitted to the National Center for Biotechnology Information (NCBI) Sequence Read Archive (SRA) (2023) database (accession number PRJNA938607).
### Statistical Analysis
To better reveal the variations in _Prochlorococcus_ physiology across the EIO, nonmetric multidimensional scaling (NMDS, using Bray-Curtis distance) was applied to the physiological results (cell size, cellular Chl \(a\) content, _Prochlorococcus_ cell division rate and Dv production rate, summarized in Table S2 in Supporting Information S1) by using the package \"vegan\" (version 2.6-2, [PERSON] et al., 2022) in the R program (R 3.6.0, R Core Team, 2020). The environmental vectors (temperature, salinity, concentrations of NO3-, NO2-, NH4+, PO4-, urea-N and dFe at 10 m depth, summarized in Table 1) were also fit to the NMDS ordination by the function \"envfit\" in the \"vegan\" package to show the correlation between environmental variables and ordination.
Furthermore, Pearson's product-moment correlation tests were performed to examine the correlation between the nutrient concentration and the abundance of related functional modules. The correlations between concentrations of NO3- and NO2- with the nitrate/nitrite transport system module, urea-N with the urea transport system module, NO3- with the module for assimilatory nitrate reduction, PO4- with the phosphate transport system module, PO4- with the phosphate starvation response two-component regulatory system module, and dFe with the iron (III) transport system module were examined. The correlations between _Prochlorococcus_ cell division and Dv production rates with the abundance of functional modules which showed spatial variations were also examined by Pearson's product-moment correlation tests. All statistical analyses were performed using the R program (R 3.6.3, R Core Team, 2020).
## 3 Results
### Environmental Conditions
The study stations were divided into three groups according to geographical location (the stations in the Bay of Bengal (BoB, stations 1-4), equatorial station (5) and southern stations (7-10), Figure 1). The BoB stations showed higher surface temperatures and lower surface salinities and densities than the equatorial station (Figure 2), which was affected by the eastward surface current Wyrtki Jet ([PERSON] et al., 2022). Because of the existence of this current, the mixed layer depth (MLD, determined by a difference of 0.125 sigma-theta with respect to the sea surface) at station 5 was the deepest (93 m) among all stations (Table 1). At the southern station 7, a cyclonic eddy was observed with the uplift of both the thermocline and pycncoline (Figures 2a and 2c). The occurrence of this cyclonic eddy was also demonstrated by the negative sea level anomaly (SLA) and sea surface current ([PERSON] et al., 2022). In contrast, the other three southern stations (8-10) showed southward decreases in surface temperature and increases in salinity and density (Figure 2). Additionally, these three stations were located south of the South Equatorial Current (SEC) within the SISG, where the water column was relatively stable with no obvious variation in density in the top 100 m (contours in Figure 2c) ([PERSON] et al., 2022). We thus further referred to stations 8-10 as the SISG stations.
At the depth (10 m) where the incubation experiments were conducted, dissolved inorganic nitrogen (DIN, sum of NO3-, NO2-, and NH4+), PO4- and urea-N all showed low concentrations (27 \(\pm\) 18 nM (mainly contributed by NH4+), 84 \(\pm\) 49 nM and 113 \(\pm\) 81 nM, respectively, Table 1). The PO4- concentration increased southward from the BoB stations and reached the highest value at the equatorial station (168 nM). There was also spatial variation in urea-N concentrations. In the surface layer (10 m, Table 1), the concentration decreased from station 1 (281 nM) to station 4 (91 nM) in the BoB but increased from station 7 (46 nM) to station 10 (111 nM) in the southern stations. In the vertical distribution, some higher urea-N concentrations (\(>\)200 nM) were observed in the upper 100 m at the BoB and equatorial stations but not at any SISG stations (Figure 3c). Similarly, the depth of the DIN nutricline (the shallowest depth of DIN exceeded 100 nM) at SISG stations 8-10 was 80-125 m, while it was 30-40 m at stations 1-7 (Figures 3a and 3b, Table 1).
The dFE concentrations in the 10 m layer were \(\leq\)0.1 nM except at northernmost station 1 (0.400 nM) and southernmost station 10 (0.140 nM) (Table 1, [PERSON] et al., 2023). Similar to urea-N, the vertical distribution of dFE showed higher subsurface concentrations except at the SISG stations (Figure 3d).
The phytoplankton biomass at the 10 m layer also showed geographical variations, with higher Chl \(a\) concentrations appearing near the equator (\(>\)200 mg L\({}^{-1}\) at stations 4 and 5, Table 1). In contrast, low values were observed at the southern stations (\(<\)100 ng L\({}^{-1}\) at stations 8-10). The southernmost station (10) showed the lowest value of 52 ng L\({}^{-1}\). In terms of the vertical distribution, the subsurface chlorophyll maximum (SCM) layer was deeper at SISG stations 8-10 with a lower Chl \(a\) concentration (\(\sim\)367 ng L\({}^{-1}\), \(\geq\)100 m), while it was shallower but had a higher concentration at stations 1-7 (387-771 ng L\({}^{-1}\), 40-60 m) (Table 1). Although the community Chl \(a\) showed spatial variation in the surface layer, the contribution of _Prochlorococcus_ (Dv) to the community Chl \(a\) was consistently higher than 50% (Table 1, Figure 4), with the highest proportion at station 4 (73%), indicating the predominance of _Prochlorococcus_ in the phytoplankton community throughout the study area. The _Prochlorococcus_ abundance determined by FCM generally decreased southward, from the highest value of \(217\times 10^{3}\) cells mL\({}^{-1}\) at station 1 to \(100\times 10^{3}\) cells mL\({}^{-1}\) at station 10 (Table 1).
Figure 2.— Vertical distributions of temperature (a), salinity (b), density (c), and the temperature–salinity diagram in the top 200 m (d). The contour in (c) indicates the density variation (6d) per meter. The stations were divided by colors in (d) (yellow for stations in the Bay of Bengal (BoB, stations 1–4), red for equatorial station 5, and blue for southern stations (7–10)).
Figure 3: Vertical distributions (nM) of dissolved inorganic nitrogen (DIN, sum of NO\({}^{+}\), NO\({}_{2}\) and NH\({}_{4}^{+}\)) (a), PO\({}_{4}\)\({}^{3-}\) (b), urea-derived nitrogen (c), and dissolved iron (dFe, d). Blanks in (a) and (b) indicate where the concentrations exceeded the upper detection limit of 1,000 nM.
### Prochlorococcus Cellular Characteristics
The _Prochlorococcus_ ESD derived from SSC showed spatial variation in the surface EIO (Figure 5a, Table S2 in Supporting Information S1). The largest cell size was observed at station 4 (0.60 mm), while the smallest cell size was observed at stations 8 and 10 (0.44 \(\upmu\)m). When converted to cell volume, the cells at station 4 were approximately 2.5 times larger than those at stations 8 and 10. The cellular Chl \(a\) represented by the geometric mean of FL3 suggested a similar pattern, with higher values in the BoB and at the equator (stations 1-5, 0.116 \(\pm\) 0.025) and lower values at the southern stations (0.054 \(\pm\) 0.011) (Figure 5b, Table S2 in Supporting Information S1). Especially at stations 3-5, the geometric FL3 showed a value higher than 0.11.
### Prochlorococcus Growth Status
The cell division and pigment (Dv) production rates determined by incubation experiments represented the _Prochlorococcus_ growth status (Table S2 in Supporting Information S1 and Figure 6). The division rates were higher than 0.8 d\({}^{-1}\) at stations 3-5 and up to 0.41 d\({}^{-1}\) at other stations (Figure 6a). The Dv production rate, which is the pigment production rate of all _Prochlorococcus_ cells rather than that at the cellular level, showed a different distribution pattern (Figure 6b). A production rate higher than 0.9 d\({}^{-1}\) was observed at southern stations 7-10. In contrast, lower production rates were found at the BoB and equatorial stations (stations 1-5, \(<\)0.6 d\({}^{-1}\)).
### Response of _Prochlorococcus_ to Macronutrient Enrichment
The response of _Prochlorococcus_ to macronutrient enrichment was examined by comparing cellular characteristics (cell size (ESD), cellular Chl \(a\) (FL3)) and growth status (division rate and Dv production rate) between those incubated with and without macronutrient enrichment (Figures 6 and 7, Table S2 in Supporting Information S1).
In terms of cellular characteristics, _Prochlorococcus_ cells incubated with enriched macronutrients were larger than those incubated without
Figure 4: Contribution of _Prochlorococcus_ (divinyl chlorophyll \(a\)) to the phytoplankton community chlorophyll \(a\).
Figure 5: Equivalent spherical diameter (a) and geometric mean of normalized red fluorescence (b) of _Prochlorococcus_ cells.
macronutrients (paired _t_-test, \(p\) < 0.05) (Figure 7a). However, _Prochlorococcus_ cells were larger than before incubation even without enriched macronutrients at stations 1, 7, 9 and 10. The cellular Chl \(a\) showed a similar pattern, in which the cells had higher FL3 with enriched macronutrients than without (paired _t_-test, \(p\) < 0.05) (Figure 7b). Similar to the cell size, _Prochlorococcus_ cells had a higher FL3 than before incubation even without macronutrient enrichment, except at stations 3-5.
In terms of the growth status (Figure 6), the division rate at station 1 was the lowest (0.16 d\({}^{-1}\)) and was increased by 1.93 times (0.31 d\({}^{-1}\)) with the enriched macronutrients. At stations 3-5, where the division rates were higher than 0.8 d\({}^{-1}\), the division rates only slightly increased or decreased with macronutrient enrichment. In contrast, the division rates at southern stations 7-10 (0.35 \(\pm\) 0.05 d\({}^{-1}\)) decreased by half (0.16 \(\pm\) 0.06 d\({}^{-1}\)) with macronutrient enrichment. On the other hand, the Dv production rate showed a different pattern with the division rate. At southern stations 7-10, where the Dv production rates were higher than 0.9 d\({}^{-1}\) (1.17 \(\pm\) 0.24 d\({}^{-1}\)), the production rates were not significantly affected by macronutrients (1.24 \(\pm\) 0.16 d\({}^{-1}\) with macronutrient enrichment, paired _t_-test, \(p\) = 0.45). In contrast, the Dv production rates at stations 1-5 were increased at least two-fold with macronutrient enrichment.
### Prochlorococcus Ecotype Composition
The _Prochlorococcus_ ecotype composition derived from the 16S rRNA and _rpoC1_ genes is shown in Figure 8. Although there were some spatial variations in ecotype composition, the surface EIO was predominated by the HLII subtype (>80% for both methods). The proportion of LL ecotypes was \(\sim\)19% and \(\sim\)13% according to the 16S rRNA and _rpoC1_ genes, respectively. In particular, a higher proportion of the LL ecotype was observed at equatorial station 5 (17% and 13% for 16S rRNA and _rpoC1_, respectively).
### Abundance of Functional Modules Related to Nutrient Utilization
The relative abundance ratio of functional modules related to nutrient utilization (nitrogen, phosphorus and iron, Figures S3 and S4 in Supporting Information S1) is shown in Figures 9-11. The shadow indicates a ratio of 2, which represents a difference in functional properties among stations. In terms of nitrogen (Figure 9), the related modules showed spatial variation in abundance, except for the urea transport system. The abundance ratio of the urea transport system module at all stations was lower than 2, indicating no obvious difference among stations (Figure 9d). The assimilatory nitrogen reduction module had the lowest abundance at station 1 but was especially abundant at stations 7 and 9 (14.9 and 16.0, Figure 9a). Similarly, the NiT/TauT family transport system module also had the lowest abundance at station 1, and the abundance showed a southward increasing trend (Figure 9c). The nitrate/nitrite transport system module showed higher abundances at stations 9 and 10 (8.5 and 10.8), while at stations 1 and 5, the abundance was low or undetectable (Figure 9b).
The relative abundance ratio of modules related to phosphorus utilization is shown in Figure 10. Although the phosphate starvation response two-component regulatory system module showed spatial variation in abundance (Figure 10a), both the phosphate transport system and phosphonate transport system modules had similar abundances among stations (no value higher than 2, Figures 10b and 10c). In particular, the relative abundance of the phosphate starvation response two-component regulatory system module decreased southward, except for a low abundance at station 5 (4.6).
There were two modules related to iron utilization determined in this study (Figure 11). One was the iron (III) transport system module, showing a similar abundance among stations (Figure 11a). The other was the iron complex transport system module, showing a southward increasing abundance with an extremely high value at the southernmost station 10 (47.0) but was not detectable at station 1 (Figure 11b).
Figure 6: _Prochlorococcus_ cell division (a) and divinyl chlorophyll \(a\) (Dv) production rates (b) incubated with and without macronutrient enrichments.
## 4 Discussion
### Prochlorococcus Physiology as an Adaptation to Local Nutrient Environments
One objective of this study was to investigate whether the _Prochlorococcus_ population exhibits varied physiology as an adaptation to oligotrophic environments with different nutrient conditions. Although the DIN concentration was at the nanomolar level throughout the surface EIO (Table 1 and Figure 3), the spatial variation in surface Chl \(a\) (S2-298 ng L\({}^{-1}\), Table 1) indicated that the phytoplankton community was experiencing different nutrient conditions before our arrival. For instance, the high levels of Chl \(a\) at stations 4 and 5 (>200 ng L\({}^{-1}\), Table 1), which were not typical for oligotrophic waters, could be a result of nutrient enrichment induced by regional physical events ([PERSON] et al., 2022). In contrast, stations 8-10 were located within the SISG, where the hydrographic properties are relatively stable as less affected by physical events compared to BoB and equatorial stations. The low surface Chl \(a\) (<100 ng L\({}^{-1}\)) and deeper DIN nutricline (\(\geq\)80 m) and SCM layer (\(\geq\)100 m) at these stations collectively indicated that it was a typical environment of oligotrophic gyres (Table 1). Therefore, the study area, which was consistently oligotrophic but with subtle variations in nutrient conditions, may induce variations in the physiology of the _Prochlorococcus_ population as an adaptation to local nutrient environments.
According to the NMDS analysis based on all the physiological results obtained from the incubation experiments (Table S2 in Supporting Information S1), stations were distinguished into 3 clusters with totally distinct physiological patterns (Figure 12).
Stations 3-5 showed higher division rates (>0.8 d\({}^{-1}\)) than other stations (\(\sim\)0.41 d\({}^{-1}\)), which were not significantly affected by macronutrient enrichment (Figure 6a). This result was consistent with previous studies reporting that the division of _Prochlorococcus_ was not limited by nutrient availability and could reach the maximal rate of one doubling per day (0.69 d\({}^{-1}\)), even in oligotrophic environments ([PERSON] et al., 1997; [PERSON] et al., 1995).
Figure 7: Equivalent spherical diameter (a) and geometric mean of normalized red fluorescence (b) of _Prochlorococcus_ in the initial samples and those incubated with and without macronutrient enrichments.
At southern stations 7-10, _Prochlorococcus_ physiology was completely different from that at other stations. The Dv production rate was higher (1.17 \(\pm\) 0.24 d\({}^{-1}\)) than that at other stations (\(\sim\)0.58 d\({}^{-1}\)) and was not significantly increased with the enriched macronutrients (1.24 \(\pm\) 0.16 d\({}^{-1}\), Figure 6b). This result indicated that the _Prochlorococcus_ cells could maintain several photosynthesis related components and have a relatively high pigment production rate even in a low-nutrient environment (DN of 22 \(\pm\) 19 nM, urea-N of 70 \(\pm\) 29 nM, and PO\({}_{4}\)\({}^{-2}\) of 89 \(\pm\) 27 nM at the southern stations, Table 1). The high Dv production rate and its weak response to the enriched macronutrients suggested that there was almost no nitrogen and/or phosphorus limitation on pigment production or that _Prochlorococcus_ did not prefer the enriched ammonium and phosphate. Although in contrast to the BoB and equatorial stations, this result was consistent with that observed in the central North Pacific, where the Dv production rate was high and was not affected by the enriched ammonium and phosphate ([PERSON] et al., 2021). We thus consider it might be common for _Prochlorococcus_ inhabiting chronically oligotrophic environments with rare nutrient supply events to gain the ability to utilize other forms of nutrients, such as dissolved organic nitrogen (DON, such as urea and amino acids, etc.) to meet the requirements for pigment production ([PERSON] et al., 2017; [PERSON] et al., 2003; [PERSON] & [PERSON], 2005).
Another enigmatic result at stations 7-10 was that the _Prochlorococcus_ division rate decreased by approximately half (0.35 \(\pm\) 0.05 to 0.16 \(\pm\) 0.06 d\({}^{-1}\), Figure 6a) when the macronutrients were enriched, while the cell volume increased by 23% (Figure 7a). Moreover, the enriched macronutrients were not used for pigment production, since the Dv production rate was similar with and without enrichment (Figure 6b). Therefore, when high levels of NH\({}_{4}\)\({}^{+}\) and PO\({}_{4}\)\({}^{-3}\) were available, increasing the cell size took priority over cell division and pigment production for _Prochlorococcus_. These results possibly indicated luxury nutrient uptake by _Prochlorococcus_, that is, storing nutrients within biomass rather than being used immediately for growth ([PERSON], [PERSON], et al., 2019). It is well known that microalgae can take up the pulsed phosphorus supply and store it as polyphosphate rather than utilizing it for immediate growth ([PERSON], [PERSON], et al., 2019). In particular, the enhanced biosynthesis of inorganic polyphosphate was observed during the slow cell division phase for green microalgae ([PERSON], [PERSON], et al., 2019), which supports the possibility that the decreased cell division of
Figure 8: _Prochlorococcus_ ecotype composition revealed by 16S rRNA (a) and marker gene _rpoC1_ (b).
_Prochlorococcus_ observed in our study was a result of luxury nutrient uptake. Although luxury nutrient uptake has not yet been reported for _Prochlororococcus_, our results suggested that _Prochlororococcus_ in oligotrophic environments could deal with the pulsed nutrient supply by temporarily increasing cell size (or cell quota of that nutrient for storage) as an adaptation to nutrient scarcity. Future experiments with longer incubation periods and cell stoichiometry analyses are needed to reveal this mechanism of phytoplankton inhabiting chronically oligotrophic environments.
### Prochlororococcus Ecotype Composition
The metagenomic analysis included the _Prochlororococcus_ ecotype composition (Figure 8) and the relative abundance ratio of functional modules related to nutrient utilization (Figures 9-11). In the case of ecotype composition, both the 16S rRNA and _rpoC1_ genes revealed the predominance of the HLII ecotype (>80%) in the surface EIO (Figure 8). This result was consistent with previous studies in this area ([PERSON] et al., 2006; [PERSON] et al., 2020), implying the adaptation of surface _Prochlorococcus_ to the HL environment. Additionally, both methods showed a slightly higher proportion of LL ecotypes at equatorial station 5 (17% and 13% compared with the mean value of 8% and 3%, Figure 8), where the MLD was the deepest (93 m compared with the mean value of 34 m) because of the occurrence of the Wyrtki Jet (Figure 1). Our results suggested that the mixing induced by physical events could transport LL ecotypes from the subsurface layer to the surface, thus altering the surface ecotype composition. This result was also consistent with a previous study determining the surface _Prochlororococcus_ ecotype composition in southern subtropical gyres, which showed that the proportion of HL ecotypes was higher where the water column was stratified with a shallower MLD, while LL ecotypes dominated where the MLD was deeper ([PERSON] et al., 2006).
The adaptation of _Prochlororococcus_ to temperature could also be inferred from the ecotype composition. HLI ecotypes can tolerate a lower temperature than HLII ecotypes ([PERSON] et al., 2006). [PERSON] et al. (2020) also reported that the proportion of HLI ecotypes increased southward in the surface southern EIO with decreasing
Figure 9: Relative abundance ratio of functional modules related to nitrogen utilization (also see Figure S3 in Supporting Information S1) detected in _Prochlorococcus_ populations. (a) Assimilatory nitrate reduction. (b) Nitrate/nitrite transport system. (c) NitT/TauT family transport system. (d) Urea transport system. The shadow indicates the relative abundance ratio of 2.
temperature. Similarly, we observed the highest HLI ecotype proportion at the southernmost station (10) (4% and 9% for 16S rRNA and _rpoC1_, respectively, Figure 8), where the temperature was the lowest (24.0\({}^{\rm{c}}\)C vs. \(>\)27\({}^{\rm{c}}\)C at other stations, Table 1).
In contrast to light and temperature, adaptation to nutrient availability is difficult to infer from ecotype differentiation, which is defined mainly by phylogenetic relationships ([PERSON] et al., 2016; [PERSON], [PERSON], et al., 2009). It has been extensively reported that the adaptation of _Prochlorococcus_ to nitrogen, phosphorus and trace metals is related to flexible genes located in hypervariable genomic islands and is subject to commonly occurring phage-mediated horizontal gene transfer (HGT) ([PERSON] et al., 2015; [PERSON] et al., 2006; [PERSON] et al., 2007; [PERSON], [PERSON], & [PERSON], 2009; [PERSON], [PERSON], & [PERSON], 2009; [PERSON] et al., 2011). This is in contrast to light adaptation, which is a basic and deeply divergent trait involving many interacting proteins and thus is considered not easily changed ([PERSON] et al., 2005). Therefore, adaptation to nutrient availability generally reflects local environmental selective pressure rather than following the ribotype-defined phylogeny as light and temperature do ([PERSON] et al., 2015; [PERSON], [PERSON], & [PERSON], 2009; [PERSON] et al., 2010). In the following section, we will discuss the adaptation of _Prochlorococcus_ to local nutrient conditions according to the relative abundance ratio of functional modules related to nutrient utilization and its association with physiological characteristics obtained from incubation experiments.
### _Prochlorococcus_ Functional Modules and Their Association With Physiological Characteristics
In the case of modules related to nitrogen utilization, all modules except the urea transport system module showed consistent spatial variations, with the lowest abundance at BoB station 1 (the nitrate/nitrite transport system module was not detectible at this station, Figure 9). In particular, we observed a negative correlation between the concentration of NO\({}_{3}\) + NO\({}_{2}\)\({}^{-}\) and the abundance of nitrate/nitrite transport system module (Figure S5a in Supporting Information S1, \(p\) < 0.05), indicating an increasing abundance of transport genes with decreasing NO\({}_{3}\)\({}^{-}\) + NO\({}_{2}\)\({}^{-}\) concentrations. Moreover, the occurrence of a higher abundance of nitrate/nitrite transport or assimilation genes in environments with lower nitrate/nitrite concentrations was consistent with previous observations. [PERSON], [PERSON], and [PERSON] (2009) reported that nitrate assimilation genes were present in most _Prochlorococcus_ in the Indian Ocean, where the nitrate concentration was low. Similarly, [PERSON] et al. (2016) observed that approximately 20%-50% of _Prochlorococcus_ HLII cells in subtropical Atlantic and Pacific oceans possessed the nitrate reductase gene when the water was stratified and the inorganic nitrogen concentration was low. Therefore, it might be advantageous for _Prochlorococcus_ cells to reserve the potential to access the whole pool of nitrogen in the low DIN environment while to have a small genome in a high DIN environment ([PERSON], [PERSON], & [PERSON], 2009). Additionally, _Prochlorococcus_ has a large pangenome ([PERSON] et al., 2007), in which only limited core genes were shared by all _Prochlorococcus_ cells. It could also be advantageous for the population to reserve the specific flexible genes functional for utilizing certain nutrients in some cells to expand the potential of nutrient utilization or niches of the whole population in a low DIN environment. On the other hand, the abundance of the urea transport system module did not vary spatially (Figure 9d), although the physiological characteristics of _Prochlorococcus_ differed across stations, indicating that urea utilization might be an essential function for _Prochlorococcus_([PERSON] et al., 2009; [PERSON] et al., 2017). Previous studies that showed _Prochlorococcus_ could grow well on urea, sometimes better than on ammonium, also supports this possibility ([PERSON] et al., 2007; [PERSON] et al., 2017).
Figure 10: Relative abundance ratio of functional modules related to phosphorus utilization (also see Figure S4 in Supporting Information S1) detected in _Prochlorococcus_ populations. (a) Phosphate stratum response two-component regulatory system. (b) Phosphate transport system. (c) Phosphate transport system. The shadow indicates the relative abundance ratio of 2.
For phosphorus, variability in _Prochlorococcus_ gene content was also related to phosphorus availability in local environments ([PERSON] et al., 2006; [PERSON] et al., 2009). It has been reported that _Prochlorococcus_ cells inhabiting low phosphorus environments (phosphate concentration <100 nM) contained a variety of genes related to phosphorus utilization, while in environments with high phosphate concentrations (>100 nM), these genes were less abundant ([PERSON] et al., 2009). In this study, although the phosphate concentration varied from 16 to 168 nM (Table 1), the abundance of modules related to the phosphorus transport system showed no obvious variation across stations (Figures 10b and 10c). In contrast, the abundance of the phosphate starvation response two-component regulatory system module was negatively correlated with the phosphate concentration (Figure S5e in Supporting Information S1, \(p<0.05\)) and decreased southward (Figure 10a). The high abundance at the BoB stations indicated that the _Prochlorococcus_ population adapted to the low phosphate availability in terms of gene content.
Similarly, the adaptation of _Prochlorococcus_ to iron was also associated with the iron availability of the local environment. [PERSON] et al. (2010) reported that two _Prochlorococcus_ cln inhabiting iron-depleted environments adapted to low iron availability by reducing the iron requirement through the loss of several iron-containing proteins. Furthermore, [PERSON] et al. (2011) reported that the genes expressed differentially in response to iron stress were mostly flexible genes located in labile genomic regions and were affected by HGT. In our results, the abundance of the iron (III) transport system module was similar among stations (Figure 11a), while the abundance of the iron complex transport system module generally increased southward (Figure 11b). This result suggested that the _Prochlorococcus_ in the southern stations might adapt to iron-limited environments by also utilizing other iron sources such as the iron complex to meet the requirement. Similarly, a previous study revealed iron limitation in SISO by determining the satellite-based fluorescence quantum yield ([PERSON] et al., 2009). The iron limitation in the SISO might be because its location is far away from continents with limited iron supply from sediment and atmospheric deposition. In this case, the low division rate of _Prochlorococcus_ in southern stations could also be a result of iron limitation as observed in the eastern equatorial Pacific where the division rate was significantly limited by iron ([PERSON] and [PERSON], 2000), or it is a result of co-limitation by iron and other nutrient elements (e.g., nitrogen and iron).
Our study provided both the physiological and genetic characteristics of the _Prochlorococcus_ population in the EIO. Considering these results collectively allows us to generate an association between physiological and genetic characteristics and further reveal the nutrient limitation of _Prochlorococcus_ growth in the study area. For instance, the _Prochlorococcus_ population at BoB station 1 was unique in both physiological and genetic characteristics. For physiological characteristics, _Prochlorococcus_ at this station showed the lowest cell division rate and Dv production rate which were increased by at least 1.9 times with the enriched macronutrients (Figure 6), indicating that there was either nitrogen and/or phosphorus limitation. According to the [DIN]: PO\({}_{4}\)\({}^{-2}\) ratio (1.31) being lower than the Redfield ratio of 16, _Prochlorococcus_ growth could be nitrogen limited, as a previous study suggested in this area ([PERSON] et al., 2019). However, considering that _Prochlorococcus_ can actively acquire and grow well on urea ([PERSON] et al., 2007; [PERSON] et al., 2002; [PERSON] et al., 2017), it is also necessary to take urea utilization into consideration. We then calculated the [DIN + urea-N]: PO\({}_{4}\)\({}^{-1}\) ratio; the result of 18.88 was slightly higher than the Redfield ratio, indicating the possibility of phosphorus limitation on _Prochlorococcus_ growth (Table 1). The highest abundance of the phosphate starvation response two-component regulatory system module at this station (Figure 10a) could be an adaptation to phosphorus limitation. Similarly, [PERSON] et al. (2021), who linked the two-component response regulator _phoBR_ to phosphorus stress, also reported the adaptation of _Prochlorococcus_ to phosphorus stress in the BoB.
However, using genomic variation as an indicator sometimes masks the complexity of _Prochlorococcus_ adaptation to nutrient environments, especially those inhabiting chronically oligotrophic environments. According to [PERSON] et al. (2021), the southern EIO was a region with nitrogen stress because of the higher gene abundance
Figure 11.— Relative abundance ratio of functional modules related to iron utilization (also see Figure S4 in Supporting Information S1) detected in _Prochlorococcus_ populations. (a) Iron (III) transport system. (b) Iron complex transport system. The shadow indicates the relative abundance ratio of 2.
-plate starvation response two-component regulatory system module suggested adaptation to phosphorus-limited environments (Figure 10a). We thus consider it possible that the _Prochlorococcus_ population was co-limited by nitrogen and phosphorus. Alternatively, the population was composed of _Prochlorococcus_ clades/strains that were limited by different nutrients or showed different physiological characteristics, as previously reported that even the closely related ecotype could have different physiological characteristics in cell division and carbon assimilation ([PERSON] & [PERSON], 2019). Further studies combining incubation experiments with more detailed genetic analysis, that is, also collecting samples after incubation to reveal the response in transcriptomic expression, will be helpful to provide clear evidence of how different the physiology of coexisting clades/strains is and how it affects the population-level physiology.
## 5 Conclusions
Considering the capability of utilizing various nutrient sources, the adaptation of _Prochlorococcus_, especially those inhabiting chronically oligotrophic environments, is difficult to be determined solely by genomic variation and needs to be further studied. By combining on-deck incubation experiments with metagenomic analysis, this study generated an association between _Prochlorococcus_ physiological and genetic characteristics and investigated the adaptation of _Prochlorococcus_ to oligotrophic environments with different nutrient conditions. Although the surface EIO was consistently oligotrophic and the _Prochlorococcus_ population was dominated by the HLII ecology throughout, the results obtained from incubation experiments showed that _Prochlorococcus_ populations had distinct physiological characteristics as adaptations to different local environments. Moreover, the nutrient limitation and adaptation of _Prochlorococcus_ to local nutrient environments can be revealed by collectively considering the physiological and genomic characteristics. At BoB station 1, the significant increase in growth rate with macronutrient enrichment and the highest abundance of the phosphate starvation response two-component regulatory system module indicated the adaptation of the _Prochlorococcus_ population to phosphorus-limited environments. In contrast, the situation was relatively complicated in the southern EIO.
Figure 12: Similarity of _Prochlorococcus_ physiological characteristics at study stations determined by nonmetric multidimensional scaling analysis with the environmental vectors (temperature (Temp), salinity (Sal), concentrations of NO\({}_{3}\)\({}^{-}\), NO\({}_{3}\)\({}^{-}\), NH\({}_{4}\)\({}^{+}\), PO\({}_{4}\)\({}^{-}\), urea and dissolved iron (dFe)). Only the salinity showed a significant correlation with the ordination (\(p<0.01\)). The numbers next to the symbols indicate the study stations. Note that stations 3–5 and 7–10 were clustered very well, which meant that these data points could not be differentiated in the figure.
The low cell division rate, insignificant response of pigment production rate to the enriched ammonium and phosphate, and the higher abundance of the iron complex transport system module collectively suggested that _Prochlorococcus_ growth was limited by iron availability and that _Prochlorococcus_ possibly adapted to utilize various iron sources to meet the requirements. However, there are also some genomic characteristics not associated with physiological characteristics. On one hand, the abundance of nitrate/nitrite transport system module was higher in the southern EIO, with very low nitrate and nitrite concentrations (<8 nM) but high pigment production rates (>0.9 \(4^{-1}\)). On the other hand, the nitrogen isotopic compositions of _Prochlorococcus_'s marker pigment DV was consistently low throughout the cruise, indicating utilization of regenerated nitrogen rather than nitrate and nitrite ([PERSON] et al., 2022). _Prochlorococcus_ population might adapt to the low nitrogen environment by utilizing various nitrogen sources while still possessing some nitrate/nitrite related genes to reserve the potential to access the whole pool of nitrogen. Future studies conducting experiments with longer incubation periods, combining with stoichiometry analyses of isolated _Prochlorococcus_ cells and the marker pigment DV, or transcriptomic analysis would be helpful to solve these inconsistences. In summary, our results revealed the complexity of _Prochlorococcus_ adaptation especially in chronically oligotrophic environments and raised the importance of improving the understanding of the association of genetic to physiological characteristics. We thus recommend further studies considering both physiological and genomic analyses to better elucidate _Prochlorococcus_ adaptation to nutrient environments.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Our sequencing data was submitted to the National Center for Biotechnology Information (NCBI) Sequence Read Archive (SRA) (2023) database (accession number PRINA938607).
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wiley/fce79b16_859a_4ae3_9251_55fab0fabaa6.md | # IGR Solid Earth
Research Article
10.1029/2024 JB029642
###### Abstract
The high sensitivity of \(V_{p}\)/\(V_{S}\) to the presence of melt makes images of \(V_{p}\)/\(V_{S}\) structure particularly useful in magmatic systems, but detailed three-dimensional models of \(V_{p}\)/\(V_{S}\) structure in magmatic systems are often restricted to the upper crust where there is a concentration of seismic sources used for imaging. \(P\)-\(S\) tomography is a new technique that has been used to image three-dimensional crustal-scale variations in \(V_{p}\)/\(V_{S}\) in regions with limited seismic instrumentation. We apply the \(Ps\)-\(P\) tomography technique to a well-constrained, independently imaged magmatic setting, Mount St. Helens, to outline the efficacy and limitations of this imaging approach. Our \(Ps\)-\(P\) tomography model reveals previously imaged high \(V_{p}\)/\(V_{S}\) upper crustal magma reservoirs beneath active volcanic systems at Mount St. Helens, Mount Adams and the Indian Heaven Volcanic Field and low \(V_{p}\)/\(V_{S}\) anomalies associated with crystallized plutons. Our model also provides new \(V_{p}\)/\(V_{S}\) constraints in the lower crust that reveal a high \(V_{p}\)/\(V_{S}\) anomaly connecting the Mount St. Helens and Mount Adams reservoirs and a low \(V_{p}\)/\(V_{S}\) anomaly associated with lower crustal cumulates or mafic accreted terranes. Decimation tests further show that first order \(V_{p}\)/\(V_{S}\) structure is recoverable using as few as four recording seismometers. These images resemble those of independent, higher resolution images from traditional techniques, highlighting the utility of \(Ps\)-\(P\) tomography for imaging three-dimensional variations of \(V_{p}\)/\(V_{S}\) throughout the crust, including in data-poor settings or with arrays not designed for structural seismic investigations, such as many volcano monitoring networks.
We use \(Ps\)-\(P\) tomography to image the relative \(V_{p}\)/\(V_{S}\) crustal structure in the region surrounding Mount St. Helens, Washington state, USA.
\(P\)-\(P\) tomography model is correlated with previously imaged structure around the volcano, highlighting the accuracy of the technique
\(P\)-\(P\) tomography reveals \(V_{p}\)/\(V_{S}\) structure throughout the crust and is shown to be effective with as few as four available seismic stations
[1][PERSON]
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come from \(V_{P}\), \(V_{S}\) and resistivity imaging; to date there are no independent constraints on lower crustal \(V_{P}\)/\(V_{S}\) due to the limited depth distribution of local seismicity required for local earthquake tomography ([PERSON] et al., 2020) and poor \(S\)-wave coverage in the lower crust from explosions ([PERSON] et al., 2016), which would provide critically important details for understanding how the deep crustal magmatic system links to the upper-to-mid crust.
Collectively, the wealth and diversity of geophysical images produced in recent decades provides an increasingly clear and consistent perspective on the magmatic and seismic crustal structure of the MSH region. The cumulative picture of the magma plumbing system throughout the crust is an ideal framework with which to compare new imaging results in this study and to validate the accuracy and efficacy of new imaging techniques. In this study, we apply \(Ps\)-\(P\) tomography ([PERSON] et al., 2020) to image the subsurface of the MSH system and compare the results to the previously imaged structure from each of these geophysical imaging techniques, illustrating the reliability of \(Ps\)-\(P\) tomography results and providing complementary constraints on our understanding of the magmatic system structure.
## 2 Methods
### Receiver Functions and Adaptive Common Conversion Point Stacking
The input data for \(Ps\)-\(P\) tomography are derived from computed receiver functions. Receiver functions highlight velocity discontinuities below a station by isolating converted body wave phases such as those generated by the Moho discontinuity through the deconvolution of seismogram components ([PERSON], 1979). Data used for \(P\)-wave receiver functions are from the broadband portion of the iMUSH network, consisting of 70 three component broadband stations. Receiver functions used for this study are from Delphi, Thomas, and Levander, (2021). In their procedure, compiled event data include telesismic earthquakes occurring from October 2014 to August 2016 at epicentral distances of 30-95\({}^{\circ}\) with magnitudes \(M>5.5\) (Figure S1a in Supporting Information S1). Events were uniformly processed, with each seismogram demeaned, detrended, tapered, rotated into the Z-R-T domain, and bandpass filtered between 0.05 and 4 Hz. Data were then visually inspected to ensure a clear \(P\)-wave arrival for each event. For events that showed a clear \(P\)-wave arrival, 1.2 and 2.4 Hz (2.8 and 5.0 Gaussian factor, respectively) \(P\)-wave receiver functions were computed by deconvolving the vertical from the radial seismogram using the iterative deconvolution technique ([PERSON] and [PERSON], 1999), which was terminated at either 800 iterations or when there was a misfit improvement of <0.001 between iterations. The resulting \(P\)-wave radial
Figure 1: _Study region._ (left) Regional map of the Cascadia subduction zone. The yellow triangle indicates Mount St. Helens. The white box corners indicate the region of all additional maps herein. Red triangles are all other Holocene aged volcanoes ([PERSON] et al., 2010). Solid black lines indicate plate boundaries; the North American (NA), Juan de Fuca (JdF) and Gorda plates are labeled. White lines are state boundaries in the United States. (middle) Topographic map of the study area indicating Mount St. Helens and nearby Holocene aged volcanoes including Mount Adams, Mount Rainier, the Indian Heaven Volcanic Field (HWF) and West Crater (WC). (right) Map of the iMUSH seismic deployment. Black triangles are broadband stations used for this study. White circles are short period stations used for the active source imaging studies discussed herein ([PERSON] et al., 2016, 2019). Dashed red lines indicate the profiles for cross sections presented in later figures.
receiver functions were then visually inspected using the FuncLab package ([PERSON] & [PERSON], 2012; [PERSON], 2018), resulting in a total of 7,920 \(P\)-wave receiver functions out of 23,178 possible event-station pairs.
Common conversion point (CCP) stacking ([PERSON] & [PERSON], 1997) was then performed with the 2.4 Hz receiver functions to create a high resolution 3D model of velocity discontinuities. CCP stacking is performed by creating a spatial grid throughout a study area, converting waveforms from \(Ps\) time to depth using a velocity model and mapping the rays to their appropriate locations at depth. The time segments that fall within a given grid are then averaged to reproduce the discontinuity structure at that location. We modify this approach by allowing grids to adapt their spatial dimensions to ray density (adaptive CCP, or ACCP, stacking; [PERSON] et al., 2015). The ACCP volume in this study differs from [PERSON], [PERSON], and [PERSON], (2021) in the frequency content of the receiver functions and parameterization of the grid. In this study, the grid spacing is 0.05\({}^{\circ}\) (as opposed to 0.1\({}^{\circ}\) in the prior study) with a bin height of 0.5 km and a minimum bin width of 0.1\({}^{\circ}\) (as opposed to 0.2\({}^{\circ}\) in the prior study). If \(<\)10 receiver functions are traced through a given bin, the bin width dilates in steps of 0.1\({}^{\circ}\) until it includes at least 10 receiver functions or until a maximum bin width of 0.4\({}^{\circ}\) is reached (as opposed to 1\({}^{\circ}\)). We use a simplified 1D layer-over-halfspace velocity model for MSH after [PERSON] et al. (1999) to ray trace and convert receiver functions to depth. This model consists of a 38 km thick crust with \(V_{P}=6.6\) km/s over a mantle with \(V_{P}=8.01\) km/s. Both layers have a \(V_{P}\)/\(V_{S}\) of 1.78. In extreme cases with a high degree (\(>\)30%) of partial melting ([PERSON] et al., 2010), this starting model may be an oversimplification that does not account for significant alterations to predicted ray paths, but in most cases such deviations are negligible at the scale of our study area.
### \(Ps\)-\(P\) Tomography: Determining a Starting Model
\(Ps\)-\(P\) delay times are minimally sensitive to absolute crustal velocity and velocity gradients within the crust ([PERSON] et al., 1995) so a detailed regional velocity model for the crust is not required for \(Ps\)-\(P\) tomography ([PERSON] et al., 2020). Instead, broad estimates of average crustal \(V_{P}\), average crustal \(V_{P}\)/\(V_{S}\) and depth to Moho variations are the minimum requirements for initial time to depth conversion of \(Ps\)-\(P\) phases and ray tracing. Starting \(V_{P}\) was determined by averaging the straight path travel time of \(P\) waves from crustal earthquakes within the study region (roughly \(\sim\)150 km radius around MSH). Direct \(P\) and \(S\) phase arrival times from all \(M>1\) earthquakes occurring shallower than 45 km depth over a 10 year period from 2012 to 2021 within the region of our model domain and with both \(P\) and \(S\) picks from at least five unique recording stations were downloaded from the USGS ANSS Comprehensive Earthquake Catalog (U. S. Geological Survey, 2017). This depth range was chosen to roughly isolate crustal earthquakes. A linear regression of earthquake-station distance versus direct \(P\) travel time was performed, resulting in an average crustal \(V_{P}\) of 6.4 km/s (Figure 2a). This velocity is an indirect reflection of the velocity models used for locating local earthquakes, providing an independent source of starting velocity. Starting \(V_{P}\)/\(V_{S}\) was determined using the same regional \(P\) and \(S\) pick data set. For each earthquake with sufficient picks, a Wadati diagram was used to estimate the crustal \(V_{P}\)/\(V_{S}\). The average among all regional crustal earthquakes of 1.74 is used as our starting \(V_{P}\)/\(V_{S}\) (Figure 2b). This starting \(V_{P}\)/\(V_{S}\) value is used solely for estimating Moho pierce
Figure 2: _Starting model determination_. (a) Linear travel distance versus travel time for regional crustal earthquake \(P\) phases used for calculating a starting \(V_{P}\) of 6.4 km/s. (b) Histogram of \(V_{P}\)/\(V_{S}\) measurements for individual regional crustal earthquakes used for calculating an initial \(V_{P}\)/\(V_{S}\) of 1.74. The red curve is a normal fit to the histogram. (c) Map of Moho pierce points predicted from measured \(Ps\)-\(P\) delay times and the initial crustal velocity model that are spatially averaged to determine a starting Moho model. Pierce points generally shallow to the east, consistent with independent Moho models ([PERSON], [PERSON], & [PERSON], 2021; [PERSON] et al., 2019). Additional symbols are as in Figure 1.
points for measured _Ps-P_ delay times and not for inversion. These values are comparable to those expected for average continental crust ([PERSON], 1996). Mantle values from the _ak135_ average velocity model ([PERSON] et al., 1995) are used for teleseismic ray tracing. This procedure is used to provide a geophysically relevant starting velocity for the inversion, but we note that the specific values chosen have a minimal effect on the resultant tomography model and do not tangibly affect model interpretation.
_Ps-P_ delay times are sensitive to variations in crustal thickness with a steep tradeoff with average \(V_{P}\)/\(V_{S}\)([PERSON] et al., 1990) rather than absolute crustal velocities and velocity gradients. To isolate the impact of 3D variations in \(V_{P}\)/\(V_{S}\) on _Ps-P_ delay times, we must first account for this tradeoff by removing the potential effect of regional variations in crustal thickness through an optimal Moho model. An optimal Moho model is approximated by converting _Ps-P_ delay times to depth to estimate individual Moho pierce points for each analyzed receiver function and averaging the scattered pierce points in a 0.2\({}^{\circ}\) grid over the entire model domain (Figure 2c). Pierce points were determined by computing the depth to Moho with our starting crustal velocities and the _P45s_ phase (_Ps_ phase generated at 45 km depth) ray parameter (to roughly approximate average Moho depth in our study area) and projecting along the event backazimuth. Empty grid nodes within the model domain are filled using an existing regional Moho model ([PERSON], [PERSON], & [PERSON], 2021). This Moho surface is interpolated using a cubic B-spline function ([PERSON] et al., 2006) during ray tracing and travel time determination. In regions where the Moho is poorly constrained, such as in the MSH forearc ([PERSON] et al., 2019), the resulting model equates to an empirical best estimate of Moho geometry from _Ps-P_ measurements and does not necessarily represent the true Moho geometry. The effects of such uncertainty are explored in our discussion of model resolution. Our optimized Moho model (Figure S2 in Supporting Information S1) is broadly consistent with prior models of crustal thickness that thicken to the west from Adams to MSH ([PERSON], [PERSON], & [PERSON], 2021; [PERSON] et al., 2019). This model, which we use for our final inversion, effectively maximizes the role of crustal thickness variations in fitting measured variations in _Ps-P_ delay times. Finally, given a starting Moho geometry and our initial crustal \(V_{P}\) of 6.4 km/s, a starting uniform crustal \(V_{S}\) is chosen in order to minimize _Ps-P_ delay time misfit (Figure S3 in Supporting Information S1), resulting in an average crustal \(V_{S}\) of 3.7 km/s, also comparable to that expected for average continental crust ([PERSON], 1996).
### _Ps-P_ Tomography: Picking and Quality Control
_Ps-P_ delay times were measured using the visually inspected subset of 1.2 Hz radial receiver functions as previously described. A critical characteristic of picked _Ps-P_ delay times is that they represent conversions from a single, laterally contiguous seismic discontinuity; our picking procedure, including the use of lower frequency receiver functions, is designed to ensure this characteristic while maintaining efficiency for processing of such a large data set. For each individual station, the Moho-generated _Ps-P_ phase was assumed to be the highest positive receiver function value within a manually selected time window (Figure 3). Use of a consistent time window for all receiver functions at a given station increases the likelihood that all picked phases represent _Ps_ phases generated at the same discontinuity. Time windows were selected for a station in order to maximize the number of receiver functions with a maximum peak that is confidently inferred as the Moho-generated _Ps-P_ phase and to minimize the number of receiver functions with a maximum peak that could be interpreted as a different phase. Phase picks were visually inspected on backazimuth-sorted record sections to ensure that a consistent phase was picked while allowing for variability in delay time due to diverse ray parameters and backazimuthally dependent variability in delay time that could be due to Moho dip ([PERSON] & [PERSON], 2000), anisotropy and/or heterogeneous velocity structure. Picks that appeared to be inconsistent with the majority-picked phase, were relatively low amplitude or otherwise displayed phase ambiguity were excluded from the final data set for _Ps-P_ tomography.
As a final step to ensure our picked _Ps-P_ phases were generated at the contiguous Moho discontinuity, predicted Moho pierce points were calculated for each phase pick and visually inspected on ACCP stacks (Figure 3). If a picked phase does not approximate a contiguous discontinuity with other picked phases, the picking procedure for that station is repeated with a different time window. This procedure is performed iteratively until agreement is reached. In some cases (e.g., Figure 3, left), phase identification remains ambiguous due to some combination of a weak Moho conversion, interference from phase multiples, high seismic attenuation and strong structural heterogeneity. In such cases, our procedure maximizes the probability that phase picks occur along a contiguous surface, regardless of the converter's nature. As such, when there is not a clear Moho phase and/or there is phase ambiguity, data are retained. However, the possibility of proximal incongrurous phases being picked on adjacent stations introduces unmodeled error into the inversion that requires caution when interpreting proximal structure.
Representative examples of the picking and quality control procedure showing a station with easily identifiable Moho-generated _Ps-P_ phases (MI10, \(\sim\)5 s) and a station with an ambiguous Moho-generated phase (MJ03, \(\sim\)6-7 s) are illustrated in Figure 3. Following quality control, 6,064 of the 7,920 receiver functions used for ACCP stacking yielded picks that were retained for _Ps-P_ tomography (Figure S4 in Supporting Information S1).
### _Ps-P_ Tomographic Inversion
A fundamental assumption for _Ps-P_ tomography is that variations in _Ps-P_ delay times that are not accounted for by variations in Moho geometry (residual delay times) are instead accounted for by velocity heterogeneity in the crust that can be represented by 3D variations in \(V_{\pi}\)/\(V_{S}\) structure ([PERSON] et al., 2020). Variations in \(V_{\pi}\)/\(V_{S}\) are modeled by solving for the \(V_{S}\) structure required to best fit _Ps-P_ delay times in the case of a fixed \(V_{\pi}\). Thus, _Ps-P_ tomography is a local isotropic \(V_{S}\) tomography inversion solved exclusively in the crust and adjacent nodes that serves as a proxy for relative variations in \(V_{\pi}\)/\(V_{S}\) (Figure 4; [PERSON] et al., 2020). Here this is done with an iterative, damped least squares inversion ([PERSON], 1944; [PERSON], 1963). No spatial smoothing is included in the inversion, as it is not necessary with the broad grid cells used in our parameterization of the model. Teleseismic \(P\) and _Ps_ converted phase predicted travel times and ray paths are computed using the 3D wavefront tracking code, _fm3d_([PERSON] et al., 2006; [PERSON] et al., 2006) by subtracting the predicted \(P\) travel time from the predicted _Ps
Figure 3: _Quality control procedure._ (top) Receiver functions sorted by backzaimuth for two representative stations including one with an ambiguous, inconsistent Moho-generated _Ps-P_ phase (MJ03; left) and one with an unambiguous, consistent phase (MI10, right). Positive amplitudes are filled in as red and negative amplitudes are filled in as blue. Excluded receiver functions are gray. Selected time window for each station is marked with the gray shaded region and the maximum positive amplitude used as our picked _Ps-P_ phases are marked by the black (included) and gray (excluded) bars. Note the broader time window used for MJ03 to account for greater phase uncertainty, (bottom) Predicted piece points for picked _Ps-P_ phases (gray circles) for each of the receiver functions above projected onto an adjacent cross section (cross section B) through our ACCP volume reflect the relative ambiguity of the identified phases. The pierce points straddle multiple diffuse positive arrivals at station MJ03, whereas all cluster around a strong, contiguous positive arrival at station MJ10. Yellow triangles shown at the surface and in the insets show the location of the station used for each test. Dashed lines demarcate the horizon interpreted as the Moho; this is not directly related to our a priori Moho model. Solid black line is the Juan de Fuca (JdF) slab surface ([PERSON] et al., 2012) for reference; the plotted slab surface is not interpreted from the ACCP stacks. Other symbols and abbreviations are as in prior figures. Trace profile can be found in Figure 1.
travel time, with inversion sensitivity limited to the crustal portion of the _Ps_ path (Figure 4). Crustal \(S\) ray paths, including Moho pierce points, are reassessed at each iteration in response to the 3D crustal _Vs_ field using _fm3d_ while crustal \(P\) paths do not change in accordance with the fixed _V\({}_{P}\)_ (Figure S5 in Supporting Information S1). Because _V\({}_{P}\)_ tends to covary with _Vs_ in real Earth materials, leaving crustal \(P\) paths constant has the effect of damping computed variations in _V\({}_{P}\)V\({}_{S}\)_([PERSON] et al., 2020). Forward modeling utilizes a cubic B-spline function representation of the velocity model ([PERSON] et al., 2006) and the input Moho model. Travel time residual data are computed by subtracting the predicted \(P\) travel times from the predicted _Ps_ travel times (_t\({}_{P_{s}P}\)_) and comparing the differences to measured delay times. Travel times are considered to be sensitive to velocities at model nodes directly adjacent to the crustal \(S\) ray path as a function of distance to the ray path ([PERSON] et al., 2020); thus, frequency-dependent sensitivity kernels are not explicitly considered, but the broad region of sensitivity surrounding each ray path as expected from the first Fresnel zone is instead implicitly accounted for by broad node spacing. In order to limit the influence of outlier residuals, delay time residuals greater than \(\pm\)1 s are excluded from the inversion, though those data may be reincorporated in subsequent iterations if the residuals are reduced by updated velocity models.
Overall, _Ps-P_ tomography in this study follows the same procedure that is outlined in detail in our prior study at Mount Cleveland Volcano, Alaska ([PERSON] et al., 2020), with differences limited exclusively to the input data and the starting parameterization. The model domain is similarly parameterized as regular gridded nodes separated by 10 km in the North-South and East-West directions with layers spaced 10 km apart from 10 km above sea level to 60 km below sea level. This node spacing is chosen to balance minimizing node spacing with maximizing uniformity in resolution (as evaluated by the diagonal values of the model resolution matrix \(R\) prior to inversion, Figure S6 in Supporting Information S1). Here, the model domain is centered on the MSH edifice and extends \(\sim\)100 km in each cardinal direction with all initial sampling within the 90 km nodes.
### _Ps-P_ Tomography Model Selection
The final model chosen for presentation is the product of two parameter choices made using traditional L-curve analysis of the tradeoff between data fit and model size (magnitude of model heterogeneity). First, the damping factor is selected by evaluating the tradeoff between the variance of the data misfit vector and the L2 norm of the model after a single tomographic iteration (Figure S7a in Supporting Information S1). We select a damping parameter value of 50 because smaller damping values result in much larger model fluctuations without substantially improving initial data fit (Figure S7a in Supporting Information S1). Second, we choose to iterate two times, as additional iterations require a significant increase in model size without substantial improvement in data fit (Figure S7b in Supporting Information S1) or increase in the number of data meeting the residual threshold for inclusion (Figure S7c in Supporting Information S1). Notably, the interpretive significance of these choices is negligible because the feature of the resulting tomography models most sensitive to differences in damping strength and number of iterations is the amplitude of velocity perturbations and our model can only be interpreted as relative variations in _V\({}_{P}\)V\({}_{S}\)_. The first order structure of the tomography model, including shape and dimension of imaged anomalies, is generated with a single iteration, regardless of parameter choice (Figure S8 in Supporting Information S1).
Our particular choice in model results in a reduction of data misfit variance of \(\sim\)39% among data included in the final model prior to inversion (\(\sim\)29% of all data; Figure S4 in Supporting Information S1). This is in addition to the effect of optimizing the a priori Moho geometry rather than assuming a uniform (flat) Moho geometry, which results in a reduction of data misfit variance among the same data by \(\sim\)25% (\(\sim\)21%; Figure S4 in Supporting Information S1). The combined effect of optimizing a priori Moho geometry and inverting for crustal velocity heterogeneity is a reduction of data misfit variance of \(\sim\)54% (\(\sim\)44%; Figure S4 in Supporting Information S1).
Figure 4: _Ps-P tomography method._ Cartoon depicting the _Ps-P_ tomography method, in which _Ps-P_ delay times (_t\({}_{P_{s}P}\)_) measured at the surface (seisnographs; open triangles) are used to calculate residuals that are inverted along the crustal \(S\) paths (black dashed lines) given an a priori assumed Moho surface (solid black line) and crustal _V\({}_{P}\)_ structure. _Ps-P_ delay times depend on lateral variations in crustal thickness (_h_) and 3D _V\({}_{P}\)V\({}_{S}\)_ heterogeneity.
tion S1), it is likely the former, which is consistent with a broadly serpentinized mantle wedge in the Cascadia forearc and/or a high velocity lower crust associated with the accreted Siletzia terrane as seen in other data sets (e.g., [PERSON] et al., 2003).
### _Ps-P_ Tomography Model Resolution
The first order controls on scale of resolution in _Ps-P_ tomography come from the sampling sensitivity of converted _Ps_ waves and our model parameterization. Wave sensitivity can be estimated by the Fresnel zone radius of converted \(S\) waves in the crust. The maximum Fresnel zone radius expected in this study is \(\sim\)9 km, calculated following the approach of [PERSON] et al. (2017) derived from [PERSON] (1995) and using a receiver function corner frequency of 1.2 Hz, a maximum study area Moho depth of 50 km and the starting crustal _V\({}_{S}\)_ of 3.7 km/s. Comparably, the tomography model is parameterized at 10 km node spacing, setting a lower limit on resolution scale. This is intentionally coarse resolution relative to more traditional local tomography studies in order to
Figure 5: _Adaptive common conversion point (ACCP) stacks._ Cross sections through the ACCP volume along profiles (a-c). Other symbols and abbreviations are as in prior figures. Trace profiles can be found in Figure 1.
account for the broader sensitivities of teleseismic converted phases compared to local earthquake phases as well as to prioritize the accuracy of long wavelength observations over finer resolution of anomaly shape and size. Additionally, coarse (10 km) model parameterization ensures sufficient, and relatively uniform crossing ray coverage throughout the study area given the station spacing; this is expressed by consistency in the spatial distribution of the diagonal values of the model resolution matrix \(\mathbf{R}\) (Figure S6 in Supporting Information S1).
The 3D structure of tomographic resolution can also be used to inform interpretation of the resulting tomography model; this can be evaluated through examination of the resolution kernels (columns of the \(\mathbf{R}\) matrix) of each model parameter. Two representative examples of resolution kernels for the first inversion iteration, one in the upper crust and near the center of the model domain and one in the lower crust and away from the center, are displayed in Figure S9 of the Supporting Information S1. Akin to a \"spike test,\" \"point spread function\" or \"Backus-Gilbert Kernel,\" each kernel represents the model sensitivity to perturbations of a given model parameter (e.g., how individual model perturbations may influence estimated structure elsewhere in the model). These illustrate the combined effect of model parameterization, forward problem formulation and data distribution on model resolution. Both kernels display limited lateral spread outside of the node's explicit sensitivity (1 node dimension), implying a high degree of lateral resolution within our chosen model parameterization. Spread in the vertical direction beyond a single node is also visible for both kernels, a result of the near vertical incidence of incoming teleseismic waves in the crust (Figure S5 in Supporting Information S1). This suggests that each model parameter is sensitive to velocity structure within a wide depth range, otherwise known as vertical smearing. Notably, such recovery remains depth-dependent, supporting resolvability between upper crustal and lower crustal structure. While here we discuss \(\mathbf{R}\) for the first inversion iteration because the first order structure of the resulting tomography is generated after one iteration, we note that \(\mathbf{R}\) for subsequent iterations (Figure S8 in Supporting Information S1) illustrates that model updates are increasingly poorly resolved for low velocity zones compared to high velocity zones due to predicted ray bending (e.g., [PERSON] et al., 2020).
It is important to also qualitatively evaluate how model resolution impacts the likelihood of recovery of true structure in the inversion through synthetic anomaly recovery tests because of nonlinearity in the inverse problem. Synthetic data are generated by solving the forward model through a known velocity structure and are inverted using the same inverse procedure as described in Section 2; the recovered model can be directly compared to that used to generate the synthetic data. Two synthetic anomaly recovery tests with checkerboard velocity patterns are shown in Figure 6 and Figure S10 in Supporting Information S1. In each, checkers are defined as two nodes wide in each dimension and alternate between high and low \(V_{S}\) relative to the starting crustal velocity. These consist of a
Figure 6: _Checkerboard synthetic tests_. Cross sections through two checkerboard synthetic model recovery tests including a single layer of two node cubic checkers (left) and two layered checkers (right). Both input anomalies (top) and recovered structure (bottom) are shown. Dashed black lines outline the region of the model domain with at least 10 independent ray hits. Velocity structure is contoured at \(\pm 10\%\)i\(V_{S}\). Solid black lines are topography and the a priori Mobo model. Vertical smearing is dominant when there is a single layer of checkers (left) whereas high amplitude depth dependent heterogeneity is only recovered when it is present in the true model (right).
include (a) a Moho of uniform depth that does not attempt to account for lateral variations in _Ps-P_ delay times through variations in crustal thickness, (b) a regional Moho model derived explicitly from ACCP imaging ([PERSON], [PERSON], & [PERSON], 2021) and (c) the Moho model from this study that is optimized to maximally account for measured _Ps-P_ delay times prior to inversion for velocity heterogeneity. In each inversion, starting crustal \(V_{S}\) is chosen to minimize initial misfit. To first order, these tests reveal nearly identical crustal structure regardless of which Moho model is used. Minor variations in velocity can be observed in the upper crust (e.g., X = 30 km), though such variations are exceeded by the anomaly amplitude. More significant variations in velocity can be observed in the lowermost crust, including some polarity reversals where anomalies are weak (e.g., X = \(-\)40 km). These occur where lateral Moho depth gradients are most different between Moho models, suggesting that uncertainty in lowermost crustal velocity can be increased when a priori Moho uncertainty is high, as is the case throughout the western region of the study area. Overall, these tests indicate that recovery of first order velocity structure in _Ps-P_ tomography is insensitive to the chosen a priori Moho geometry, but that there is some sensitivity among anomaly amplitudes, particularly in the lowermost crust.
### _Ps-P_ Tomography Model
Our final _Ps-P_ tomography model is shown in both depth section and cross section in Figure 8 and Figure S11 in Supporting Information S1. The model is presented here as relative perturbations in \(V_{S}\) (%d\(V_{S}\)) because _Ps-P_ tomography is a local \(V_{S}\) tomography inversion. However, input data for the inversion are more sensitive to variations in \(V_{\
u}\)/\(V_{S}\) and are minimally sensitive to \(V_{S}\) independently, so relative perturbations in \(V_{S}\) should be seen as a proxy for relative variations in \(V_{\
u}\)/\(V_{S}\) in which low \(V_{S}\) (red) corresponds to relatively high \(V_{\
u}\)/\(V_{S}\) and high \(V_{S}\) (blue) corresponds to relatively low \(V_{\
u}\)/\(V_{S}\) (e.g., Figure S11 in Supporting Information S1). Overall, the model
Figure 7: _Sensitivity to Moho geometry._ Cross sections through inversion results using three end member a priori Moho geometries, including (top) the data-optimized Moho model, (middle) the regional Moho model from [PERSON], [PERSON], and [PERSON] (2021) and [PERSON], [PERSON], and [PERSON] (2021) and (bottom) a uniform Moho with no topography (flat). Note similar first order structure across all three models indicating that the inversion has only minor sensitivity to chosen Moho geometry. Sensitivity to Moho geometry is largely restricted to anomaly amplitudes in the lowermost crust. Symbols and abbreviations are as in prior figures.
reveals significant lateral heterogeneity across the study region, broadly consistent with prior \(V_{\
u}\mathcal{N}_{S}\) tomography ([PERSON] et al., 2019; [PERSON] et al., 2020). Observed structures range in lateral dimension from \(\sim\)10 km (1 model node) to \(\sim\)40 km, whereas heterogeneity can be characterized broadly as upper crustal or mid-to-lower crustal in the vertical dimension due to non-negligible vertical smearing. Interestingly, upper crustal and mid-to-lower crustal structure appears to be broadly anti-correlated. Checkerboard tests reveal this character only when vertically oriented opposite polarity pairs are included as input, suggesting that this is a robust observation that reflects true structure.
In the upper crust (e.g., 10 km depth slice, Figure 8) the model ranges from \(\sim\)\(\pm\)27%d\(V_{S}\). At these depths, regions of relatively low \(V_{S}\) are seen directly below each of the Holocene aged volcanic centers ([PERSON] et al., 2010) including MSH (anomaly A1), Adams (A2), HIVF (A3) and West Crater (A4), with each reaching peak amplitudes \(<\)\(-\)10%d\(V_{S}\) in addition to other discrete anomalies. Beneath MSH, low \(V_{S}\) extends to \(\sim\)10 km depth (A1), with a peak amplitude of \(\sim\)\(-\)14%d\(V_{S}\) near the surface. The lowest \(V_{S}\) is seen below Adams, extending from the surface to \(\sim\)10 km depth with peak amplitudes exceeding \(-\)25%d\(V_{S}\)(A2). This anomaly also stretches \(\sim\)35 km to the southwest to beneath the HIVF, where amplitudes reach \(\sim\)\(-\)18%d\(V_{S}\)(A3). The relative contiguity of the low \(V_{S}\) structures varies, with at least two larger regions of low \(V_{S}\) including the Adams to HIVF anomaly and another west of MSH (A5) along with several low \(V_{S}\) zones limited to \(\sim\)2 (10 km) nodes in dimension. These regions of low \(V_{S}\) are separated by regions of relatively high \(V_{S}\) including one large, somewhat contiguous structure stretching from south of MSH to the northeast between MSH and Adams (A6) and a more localized feature \(\sim\)15 km to the NW of MSH office (A7).
Figure 8: _P\({}_{S}\)-P tomography model._ Depth sections and cross sections through the final _P\({}_{S}\)-P_ tomography volume, displayed as perturbations in 5%d\(V_{g}\) (top) Depth sections at 10 and 30 km depth. (top right) Station map with cross section profiles in red. (bottom) Vertical cross sections through the tomography model at the noted profiles. Anomalies referenced in the text are labeled. Velocity structure is contoured at \(\pm\)10%d\(V_{S}\) Symbols and abbreviations are as in prior figures.
In the mid-to-lower crust (e.g., 30 km depth slice, Figure 8) model amplitudes are significantly weaker, ranging from \(\sim\)\(\pm\)20%\(dV_{S}\) at 30 km depth (though amplitudes are higher in the lowermost crust). Lower recovered amplitudes in the lower crust in checkerboard synthetic tests suggest this could be due in part to reduced resolution at these depths. However, amplitudes in the lowermost crust (\(\sim\)40 km depth) are comparable to the high amplitudes in the upper crust, suggesting lower amplitudes in the mid-to-lower crust may also indicate lower \(V_{\
u}\)/\(V_{S}\) heterogeneity at these depths (e.g., [PERSON] et al., 2020). In the lower crust, Holocene aged volcanic centers correlate with regions of relatively high \(V_{S}\), with the largest lower crustal light \(V_{S}\) body beneath Adams (\(\sim\)20%d\(V_{S}\)) extending from \(\sim\)30 km depth to the Moho and from Adams to \(\sim\)25 km to the southwest toward the IHVF (A8). The strongest lower crustal low \(V_{S}\) anomaly is located between MSH and Adams from \(\sim\)30 km depth to the Moho with peak amplitudes exceeding \(-\)30%d\(V_{S}\) (A9). This anomaly is among a roughly south-north oriented discontinuous string of low \(V_{S}\) anomalies in the lower crust separating the two stratovolcanoes. Relatively low recovered amplitudes in the lower crust of low \(V_{S}\) input anomalies in checkerboard synthetic tests suggest that these observations of high amplitude low \(V_{S}\) (high \(V_{\
u}\)/\(V_{S}\)) structures in the lower crust are indicative of relatively strong and/or robust true high \(V_{\
u}\)/\(V_{S}\) structures.
## 4 Discussion
### Validation of Imaged Crustal Velocity Structure
To validate the success of the _Ps-P_ tomography method at Mount St. Helens, we directly compare our tomography model to imaged structure using established techniques. As previously noted, our model of \(V_{S}\) perturbations can be more aptly interpreted as a model of relative variations in \(V_{\
u}\)/\(V_{S}\), making prior \(V_{\
u}\)/\(V_{S}\) tomography models most directly comparable. For simplicity in comparison to other geophysical imaging results, we assume an expected first order correlation between regions of high \(V_{\
u}\)/\(V_{S}\) in our tomography model with low \(V_{\
u}\), low \(V_{S}\) and high conductivity. This assumption does not always hold, as the composition of solid-melt systems also exerts a control on velocity (e.g., [PERSON], [PERSON], & [PERSON], 2021; [PERSON] et al., 2022), but is reasonable to first order in magmatic systems where the frequent presence of partial melt displays such correlation. This is illustrated by the concurrent high \(V_{\
u}\)/\(V_{S}\) (e.g., [PERSON] et al., 2016), low \(V_{\
u}\) and \(V_{S}\) (e.g., [PERSON] et al., 2020) and high conductivity (e.g., [PERSON] et al., 2009) anomalies seen in the upper crust beneath MSH and the surrounding concurrent low \(V_{\
u}\)/\(V_{S}\) (e.g., [PERSON] et al., 2020), high \(V_{\
u}\) (e.g., [PERSON], 1989), high \(V_{S}\) (e.g., [PERSON] & Shen, 2017) and high resistivity (e.g., [PERSON] et al., 2018) anomalies observed in prior studies. Consistent with these observations, we observe a high \(V_{\
u}\)/\(V_{S}\) anomaly in the upper crust beneath MSH (anomaly A1) and low \(V_{\
u}\)/\(V_{S}\) anomalies both to the northwest (A7) and northeast (A6) of MSH. Likewise, we observe upper crustal high \(V_{\
u}\)/\(V_{S}\) anomalies coincident with high \(V_{\
u}\)/\(V_{S}\), low velocity, high conductivity structures previously imaged beneath IHVF (A3) and Mount Adams (A2).
We also observe a high \(V_{\
u}\)/\(V_{S}\) anomaly in the lower crust (A9) that is coincident with a prominent low velocity (e.g., [PERSON] & Shen, 2017; [PERSON] et al., 2023), high conductivity ([PERSON] et al., 2018) anomaly attributed to partial melting and a possible magma pathway sourcing MSH and a low \(V_{\
u}\)/\(V_{S}\) anomaly (A10) coincident with high lower crustal velocities beneath MSH interpreted as either an ultramafic cumulate zone related to the magmatic system or accreted Siletzia crust (e.g., [PERSON] et al., 2019; [PERSON] et al., 2016).
These observations collectively illustrate that our _Ps-P_ tomography model faithfully identifies the location of each of the most prominent and consequential structures identified with established geophysical imaging techniques. We further inspect the fidelity of our model with respect to the results of high resolution tomography models by directly comparing velocity structure to recent 2D tomography models (Figure 9) derived from active source imaging techniques ([PERSON] et al., 2016). The active source component of iMUSH consists of a contemporaneous and spatially overlapping, but distinct seismic deployment from the broadband sensors used for this study such that the comparative active source models are constructed using completely independent data in addition to independent techniques. As _Ps-P_ tomography models serve as a proxy for variations in \(V_{\
u}\)/\(V_{S}\), it is most appropriate to compare our model to other \(V_{\
u}\)/\(V_{S}\) models (Figure 9, second panel). However, technical limitations in the active source studies restrict \(V_{\
u}\)/\(V_{S}\) tomography images to the upper crust ([PERSON] et al., 2016, 2019), so we also compare our images to the \(V_{\
u}\) tomography from the same study (Figure 9, third panel) which provides high resolution structural constraints on lower crustal velocity structure. We also provide direct comparisons of our tomography model to a 3D active source \(V_{\
u}\)/\(V_{S}\) tomography model (Figure S12 in SupportingInformation S1), but choose to focus on the 2D images here because resolution in the 2D study is closer to the relatively low resolution of \(P_{S}\)-\(P\) tomography.
Direct comparison of our tomography model to independent active source tomography models reveals some important observations. First, the first order upper crustal structure is consistent with that in the active source \(V_{P}\)/\(V_{S}\) tomography (Figure 9, bottom panel), highlighting the fidelity of the \(P_{S}\)-\(P\) tomography technique to retrieving known \(V_{P}\)/\(V_{S}\) structure. This is most clearly seen along the Y line, where alternating high amplitude low and high \(V_{P}\)/\(V_{S}\) anomalies line up along the cross section. This correlation breaks down slightly in the northwest (X distance \(<-20\) km) of the profile, which we attribute to higher uncertainties associated with inconsistent Mohogenerated \(P_{S}\) arrivals in the forearc (e.g., Figure 3, left). The uncertainty associated with the assumption that a consistent \(P_{S}\)-\(P\) horizon is picked on each receiver function is directly dependent on the strength, clarity and contiguity of the Moho conversion. Our ACCP stacks confirm prior observations ([PERSON] et al., 2016; [PERSON] et al., 2021; [PERSON] et al., 2019) that this conversion is weak beneath the Cascadia forearc to the west of MSH, leading to enhanced uncertainty in this part of the model. Along the X line, \(V_{P}\)/\(V_{S}\) heterogeneity is reduced, but there is still a clear correlation between higher \(V_{P}\)/\(V_{S}\) to the southwest of MSH and lower \(V_{P}\)/\(V_{S}\) to the northeast with high \(V_{P}\)/\(V_{S}\) directly below MSH.
In the lower crust, where direct comparisons of \(V_{P}\)/\(V_{S}\) are not available from other techniques, we can compare our results with imaged \(V_{P}\) structure. Here, we observe an alternating pattern of low and high \(V_{P}\)/\(V_{S}\) coincident with high (Figure 9, gray shaded regions) and low \(V_{P}\) anomalies in the lower crust that are roughly anticorrelated with upper crustal structure, including a broad low \(V_{P}\)/\(V_{S}\), high \(V_{P}\) structure in the lower crust beneath MSH. This illustrates that the \(P_{S}\)-\(P\) tomography technique can provide accurate first order constraints on lower crustal \(V_{P}\)/\(V_{S}\) where constraints are otherwise limited or nonexistent using traditional imaging techniques.
Second, these comparisons place additional constraints on the sensitivities of our tomography inversion. Interpretation of the tomography model is largely limited to average \(V_{P}\)/\(V_{S}\) variations between the upper and lower
Figure 9.— _Model comparisons_. Comparison of our final \(P_{S}\)-\(P\) tomography model (top row) with active source tomography models along vertical cross section X (left) and Y (right), 2D \(V_{P}\)/\(V_{S}\) (second panel) and \(V_{P}\) (third panel) tomography models ([PERSON] et al., 2016). (bottom) Same as the top row (\(P_{S}\)-\(P\) tomography model) except with overlays of low/high \(V_{P}\)/\(V_{S}\) in the upper crust (shaded blue \(<1.6\), shaded red \(>1.95\)) and \(V_{P}\)??
crust. For example, [PERSON] et al. (2016) image relatively low \(V_{\mu}\)/\(\mathcal{N}_{S}\) in the shallowest crust above the 4-13 km depth upper crustal MSH magma reservoir (Figure 9). This structure is largely invisible to our _Ps-P_ tomography, which displays high \(V_{\mu}\)/\(\mathcal{N}_{S}\) from \(\sim\)15 km depth to the surface. Instead, shallow low \(V_{\mu}\)/\(\mathcal{N}_{S}\) structure is likely reflected in the relatively low amplitude of the observed high \(V_{\mu}\)/\(\mathcal{N}_{S}\) anomaly (A1) compared to surrounding structure. Thus, while _Ps-P_ tomography faithfully recovers first order structure, the resulting model should be considered primarily as a means of accurately capturing strong or broad variations in \(V_{\mu}\)/\(\mathcal{N}_{S}\), such as those associated with magma storage and partial melting.
### _Ps-P_ Tomography Utility
Mount St. Helens exemplifies the comprehensive crustal imaging that can be produced with extensive geophysical instrumentation, but most settings, including the vast majority of volcanic regions, do not and/or cannot host such infrastructure due to logistical challenges associated with physical access, subaerial exposure and available resources. One such example is Mount Cleveland volcano in the central Aleutian arc, at which limited instrumentation and array aperture has precluded any robust seismic imaging below the shallowest crust ([PERSON] et al., 2021) using traditional imaging techniques. Detailed receiver function analysis ([PERSON] et al., 2020) and _Ps-P_ tomography ([PERSON] et al., 2020) were used at Mount Cleveland volcano using a limited duration seismic network of 11 instruments, showing that contrary to other techniques, _Ps-P_ tomography does not require extensive instrumentation to image the crust. This raises the question of instrumentation requirements for successful implementation of the technique.
Here we test the bounds of array aperture requirements for _Ps-P_ tomography by inverting subsets of the iMUSH broadband network and directly comparing the results to the tomography model produced with the full iMUSH broadband network (Figure 10). We decimate our data set to roughly reflect the spatial scales and instrumentation levels typical of remote volcanoes, such as Mount Cleveland volcano. We test radii of \(\sim\)25 km (20 stations), \(\sim\)18 km (11 stations) and \(\sim\)10 km (four stations) surrounding the central volcanic orifice to test the lower bound for obtaining robust and accurate structure beneath a volcano. Arrays of fewer seismic stations were not considered because fewer would not allow for cross sampling in three dimensions. The array utilized for each test has an average station spacing of \(\sim\)10 km. Each inversion uses the same parameters (damping parameter, number of iterations, node geometry) and a priori velocity model (Moho geometry, \(V_{\mu}\)) with the exception of starting \(V_{S}\) in order to facilitate the most direct comparison possible. The starting \(V_{S}\) for each inversion was determined using the same optimization procedure, resulting in a best fit starting velocity of 3.75 km/s for the \(\sim\)18 km radius test and 3.70 km/s for all other inversions.
Differences between each decimated model are apparent (Figure 10). First, each subsequent decimation reduces the lateral area of sufficient ray coverage, coincident with the spatial coverage of the included stations (dashed lines, Figure 10). Second, the amplitude and dimensions of some structures varies across models, with the upper crustal high \(V_{\mu}\)/\(\mathcal{N}_{S}\) zone beneath MSH (A1 in Figure 8) appearing larger and slower (higher \(V_{\mu}\)/\(\mathcal{N}_{S}\)) in tests with 20 and 11 stations due to a lack of crossing ray coverage beneath anomaly A5 constraining its depth and amplitude. Another example includes a lower velocity (higher \(V_{\mu}\)/\(\mathcal{N}_{S}\)) on average in the lowermost crust beneath MSH (A10) when only four stations are used due to reduced ray coverage of that region from further stations. However, while amplitude differences are observed, first order structure beneath MSH (and the surrounding region when covered) remains consistent regardless of the lateral scope or quantity of stations employed. Importantly, in all tests, including that with only four stations used, a high \(V_{\mu}\)/\(\mathcal{N}_{S}\) zone
Figure 10: _Station decimation tests._ Cross sections through inversion results using data from different subsets of seismic stations including (top) all stations, (second panel) 20 of the nearest stations to Mount St. Helens (\(\sim\)25 km radius), (third panel) 11 of the nearest stations (\(\sim\)18 km radius) and (bottom) four of the nearest stations (\(\sim\)10 km radius). Note the relative size of the sampled areas and the similarity in first order structure where models overlap, indicating the high fidelity of the model with minimal data where there is ray coverage. Yellow triangles in the insets show the stations used for each test relative to the entire network (black triangles). Symbols and abbreviations are as in prior figures.
in the upper crust directly below MSH is recovered; this is underlain by a mid-to-lower crust that is broadly lower \(V_{\rho}/V_{S}\). Notably, the higher \(V_{\rho}/V_{S}\) seen in the lowermost crust beneath MSH when only four stations are used is consistent within uncertainties resulting from an unconstrained Moho geometry, though this could feasibly be misinterpreted as a high \(V_{\rho}/V_{S}\) lowermost crust without thorough consideration of resolution and uncertainty.
The _Ps-P_ tomography station decimation tests we perform illustrate that first order crustal-scale constraints on \(V_{\rho}/V_{S}\) structure are achievable with limited instrumentation, including down to a minimum of only four recording seismometers. At MSH, a high \(V_{\rho}/V_{S}\) zone that may be interpreted as a magma reservoir would be constrained to the upper crust without strong evidence for mid or lower crustal storage, independent of additional seismic velocity constraints. This has implications for a wide variety of applications in regions with limited resources and/or accessibility, including in volcanic systems worldwide. An understanding of subsurface magmatic structure is critical for understanding magmatic processes at individual active volcanoes ([PERSON] et al., 2022; [PERSON] et al., 2023), but estimates of crustal magma storage depth are lacking at hundreds of global systems due to a dearth of seismic infrastructure (e.g., [PERSON] et al., 2020). Among those volcanoes, many have overlying seismic networks of \(\sim\)-10 recording seismometers; these are networks designed for seismic monitoring, but generally insufficient for use with traditional tomographic techniques (e. g., [PERSON] and [PERSON], 2021), though some recent studies have utilized these small networks for constraining shallow crustal ([PERSON] et al., 2023) and deep crustal ([PERSON] et al., 2020) magmatic structure. While all seismic imaging techniques, including _Ps-P_ tomography, benefit from increased instrumentation, _Ps-P_ tomography may be used with existing volcano monitoring networks to provide first order estimates of magma storage in situ without the need for imaging-intended instrumentation. The instrumentation threshold indicated by these tests may also influence the design of future seismic campaigns, suggesting that more individual sites could be imaged using similar or fewer resources. We note that receiver functions used for this technique are single-station measurements and thus do not require contemporaneously operating stations. Thus, spatial sampling for _Ps-P_ tomography may be enhanced by the periodic relocation of a monitoring scale network without compromising monitoring objectives in cases where network growth is inhibited.
## 5 Conclusions
_Ps-P_ tomography ([PERSON] et al., 2020) is a relatively new seismic imaging technique that utilizes Moho-generated _Ps-P_ delay times derived from computed receiver functions to provide 3D crustal-scale images of relative variations in \(V_{\rho}/V_{S}\). We directly compare our _Ps-P_ tomography model of the Mount St. Helens region to independent \(V_{\rho}\), \(V_{S}\) and upper crustal \(V_{\rho}/V_{S}\) tomography models to show that _Ps-P_ tomography faithfully recovers first order structure imaged with traditional imaging techniques. ACCP stacks produced in complement to _Ps-P_ tomography show variability in Moho depth and character, with a Moho that shallows to the east across the region and is relatively weak and incoherent in the forexure. Our _Ps-P_ tomography recovers structures consistently seen in other tomographic models of the area, such as high \(V_{\rho}/V_{S}\) structures in the shallow crust beneath recently active volcanic centers including MSH, Mount Adams and the Indian Heaven Volcanic Field as well as low \(V_{\rho}/V_{S}\) zones coincident with surface exposed crystallized plutons. In the lower crust our model reveals a high \(V_{\rho}/V_{S}\) structure between MSH and Mount Adams coincident with a region of high conductivity that is likely to contain some partial melting as well as low \(V_{\rho}/V_{S}\) directly beneath each of the recently active volcanic centers that may represent cumulates or mafic accreted terminates. Finally, we test the technique against a variety of theoretical instrumentation levels to show that _Ps-P_ tomography can successfully recover first order velocity structure throughout the crust with minimal seismic infrastructure (at least four stations). While _Ps-P_ tomography is a relatively low resolution imaging technique, these analyses show that it is a viable technique for imaging the entire crust, including the commonly inaccessible lower crust, in any crustal setting with at least \"small-\(N\)\" seismic infrastructure. The validation of _Ps-P_ tomography illustrated here shows that the technique may be useful in identifying first order structures at a coarse scale using existing seismic arrays that were not originally designed for structural investigation (e.g., volcanic monitoring networks) as well as in unexplored localities in cases where resources may be limited, where accessibility and subaerial exposure is challenging and/or where breadth of coverage is prioritized over resolution.
## Data Availability Statement
The tomography model in this study, called _MSH1\(S\)2023_, will be made available online at the IRIS Earth Model Collaboration (IRIS DMC, 2011). The data used for this study are publicly available and can be downloaded from the IRIS Data Management Center under the network code XD ([PERSON], 2014).
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wiley/fcd31a0f_9bb3_481d_9fe8_41f4a10f7ee2.md | # Earth and Space Science
Alongshore Variable Accretional and Erosional Coastal
Foredune Dynamics at Event to Interannual Timescales [PERSON]
1C Coastal and Hyrauntics Laboratory - Field Research Facility, U.S. Army Engineer Research and Development Center, Duck, NC, USA 1
[PERSON]
1C Coastal and Hyrauntics Laboratory - Field Research Facility, U.S. Army Engineer Research and Development Center, Duck, NC, USA 1
[PERSON]
1C Coastal and Hyrauntics Laboratory - Field Research Facility, U.S. Army Engineer Research and Development Center, Duck, NC, USA 1
[PERSON]
1C Coastal and Hyrauntics Laboratory - Field Research Facility, U.S. Army Engineer Research and Development Center, Duck, NC, USA 1
[PERSON]
1C Coastal and Hyrauntics Laboratory - Field Research Facility, U.S. Army Engineer Research and Development Center, Duck, NC, USA 1
###### Abstract
Natural and constructed dunes are increasingly being utilized to buffer flooding impacts from storms and rising sea levels along sandy coastlines. However, a lack of data at the appropriate spatial and temporal resolution often precludes isolating the total magnitude, specific timing, and alongshore variability of volumetric coastal dune changes resulting from both wave and wind-driven processes. Here mobile terrestrial lidar data from 46 collections along a 6.5 km stretch of sandy beach and dunes in Duck, NC, USA are used to assess the magnitude and drivers of alongshore variable dune responses between 2012 and 2020. Despite numerous major storm events which impacted the dunes over this time period, the dunes grew volumetrically both in nonvished and un-nonvished sections of the study site. Growth of the dunes was seasonally and spatially variable with the largest total growth recorded in the Fall, coinciding with a period of frequent windy storms but also the highest total water levels, and along the regions with the lowest gradient \(\beta_{back}\). The vertical accretion patterns of these wind-blown sediments are shown to vary depending on the dune management style, specifically, if dunes were not managed, sand fenced, or artificially constructed. Dune erosion also occurred episodically within the study period, with the steepest sloped beach sections likely to be the most impacted during individual storm events.
10.1029/2022 EA002447
1
## 1 Introduction
Foredunes are common landforms on many sandy beaches that develop from the complex interplay of marine, aeolian, ecological, and anthropogenic processes. The magnitude of accretional inputs to coastal dunes is dependent on wind properties (e.g., [PERSON], 2003; [PERSON], 1990), sediment availability ([PERSON] et al., 2014), the influence of beach morphology on fetch lengths and moisture patterns ([PERSON] et al., 2009; [PERSON] et al., 2018; [PERSON], 1994), dune grass properties (e.g., [PERSON], 1981; [PERSON] et al., 2020; [PERSON] et al., 2012), and feedbacks of the dune morphology on the local wind field (e.g., [PERSON], 2019; [PERSON] et al., 2013). Foredune landforms develop slowly from these aeolian inputs, with typical forendue growth rates of under \(\sim\)15 m/m/yr during accretional conditions along much of the world's beaches (e.g., [PERSON] et al., 2019; [PERSON] et al., 2018; [PERSON] et al., 2020; [PERSON] et al., 2012; [PERSON] et al., 2010; [PERSON] et al., 2019). Wave-driven sediment transport may cause a wider range of potential impacts, with some mild storm events being a positive source of sediment supply to the forendue (e.g., [PERSON] et al., 2018) whereas overwash and inundation events ([PERSON], 2000) commonly destroy entire dune systems (e.g., [PERSON], 2008; [PERSON] et al., 2011). During collisional events, corresponding to periods when the total water level (TWL) exceeds the dune toe, an erosional scarp feature is often formed (e.g., [PERSON] et al., 2020; [PERSON] et al., 2007). Although the elevation and duration of the TWL relative to the dune toe are the primary drivers of the magnitude of dune erosion (e.g., [PERSON] et al., 2004; [PERSON] & [PERSON], 2012), morphologic feedbacks and biotic factors (e.g., [PERSON] et al., 2015) are also known to influence the scale of dune impacts during storms. These morphologic effects include the role of nearshore sandbars and beach morphology influencing wave setup, incident swash, and infragragravity swash contributions to wave runup (e.g., [PERSON] et al., 2019; [PERSON] et al., 2013), controls of the pre-storm dune face slope on dune erodibility (e.g., [PERSON] et al., 2015), and the trajectory of the dune toe in response to wave collision (e.g., [PERSON] et al., 2017). As these morphologic and environmental conditions can be highly site specific, there can be considerable alongshore variability in dune accretion and erosion over regional scales ([PERSON] et al., 2022; [PERSON] et al., 2014).
There are increasing efforts to construct dunes on low-lying beach systems around the world for added resilience from storm and sea level rise-related flooding hazards (e.g., [PERSON] et al., 2015; [PERSON] et al., 2018). These constructed dunes are designed to serve similar functions to natural dunes, with their primary purpose ofserving as a local topographic high to limit overtopping and water-related hazards to low-lying, beach-adjacent infrastructure. There are, however, notable differences in both the protective and ecosystem services that natural vs. artificial dunes provide (e.g., [PERSON] & [PERSON], 2020). For example, built dunes are often planted with sparse, regularly spaced sprags that can take numerous years to develop. This is in contrast to the dense vegetation that is characteristic of many natural dune systems that is known to be effective at trapping wind-blown sands ([PERSON], 1981, 1989; [PERSON] et al., 2015), having important implications for subsequent sediment deposition patterns. Sand fences are widely used to aid in the trapping of sand and stabilization of coastal foredunes ([PERSON] & [PERSON], 2009) on both constructed, as well as non-built, dunes. [PERSON] et al. (2020) found that the placement of sand fences near the base of the dune resulted in a wider, but less tall, dune complex relative to nearby un-fenced dunes. The details of fence orientation and location additionally play a critical role in determining where and how much sediment is trapped on dunes (e.g., [PERSON] & [PERSON], 2011; [PERSON] et al., 1991; [PERSON] et al., 2001).
Dune construction is often associated with beach nonuishment. Wind-blown fluxes to the dunes have additionally been observed to increase immediately following beach nonuishment placement (e.g., [PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2018). This increase in aeolian transport to the dune is presumably related to either (a) an increased beach fetch on wide, recently constructed beaches, resulting in more frequent saturated transport over the backshore, and/or (b) a larger fraction of fines (relative to the native beach sands) on the beach immediately following beach nonuishment that have a lower threshold velocity for the initiation of wind-blown sand transport ([PERSON], 1937). Though these are hypotheses, limited studies have documented these altered aeolian transport dynamics (e.g., [PERSON], 2000) on nonuished vs. natural beach systems.
Despite these ecological and morphodynamic processes that are recognized as having an effect on sediment transport and bed elevation change in beach-dune systems, few research studies have explored how natural vs. managed dunes differ in their behavior--likely in part due to the complicated three-dimensional (3D) evolution of these features across a wide range of timescales (days to years). Studies that characterize alongshore variable 3D dune evolution are typically completed using airborne lidar data. These data cover large geographic extents, but for the purposes of most sites are too temporally coarse (e.g., \(>\)1 yr sampling intervals) to attribute dynamics to discrete storm events. Root mean square surveying errors for airborne lidar data are generally thought to be \(\sim\)0.05-0.3 m, with errors increasing on sloped and vegetated terrains (e.g., [PERSON] et al., 2018; [PERSON], 2004). These data often provide sufficient accuracy and resolution for measuring storm-driven erosional patterns in coastal systems, but may be in the noise for measuring the comparatively smaller magnitude accretional processes. Many beach monitoring programs also collect cross-shore transect-based data on monthly to seasonal scale that provides valuable insights into subaerial coastal morphology change. However, transect-based analyses suffer from not being able to characterize the full topographic complexity of coastal dune systems. Over the past decade, the use of structure-from-motion reconstructions of topography using unmanned aerial vehicles (UAV) has become common across coastal and non-coastal areas ([PERSON] et al., 2019; [PERSON] et al., 2019). However, there remain issues with the detection of the bed surface in (a) heavily vegetated regions which may limit the detection of small-scale aeolian deposition signals within dunes and (b) scalability issues with using UAV systems over large regions due to ground control and line of sight constraints which limits their use generally to the sub-kilometer scale ([PERSON], [PERSON], [PERSON], & [PERSON], 2019; [PERSON] et al., 2019).
Terrestrial laser scanning is also increasingly being utilized to provide 3D insights into coastal landform evolution (e.g., [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON], 2019; [PERSON] et al., 2017; [PERSON] et al., 2017). Tripod-based applications are limited in the geographic domain of surveying, although lidar scanners can also be mounted on vehicles to extend the scales of data collection ([PERSON] et al., 2018; [PERSON] et al., 2013). These mobile terrestrial lidar (MTL) applications have the benefit of being able to cover regional spatial domains with high accuracy, although do have field of view limitations that limits their ability to resolve deposition landward of the dune crest for MTL systems being driven on the beach.
In this study, we present 3D MTL measurements collected along a 6.5 km stretch of coastline in Duck, NC, USA that included a segment with nourished beaches and dunes. Using this data, we quantitatively detail alongshore variability in dune erosion and growth rates in order to decouple the relative morphologic and anthropogenic factors that contribute to the resistance of these features. In this manuscript, Section 2 gives an overview of the field site and the MTL data collection program. Data collected at timescales of days to months apart over a multiyear period are used to quantify the timing, magnitude, and spatial distribution of bed elevation changesand corresponding volume changes to dunes. The results of these collective morphology data, in the context of environmental and anthropogenic influences, is provided in Section 3. Discussion of the data and the drivers of alongshore and temporally variable dune processes are given in Section 4. Conclusions are provided in Section 5.
## 2 Field Data Collection and Methods
### Field Site
The Outer Banks is a barrier island chain off of the North Carolina (United States) coast. These islands typically experience numerous collisional events per year from hurricanes or remnants of hurricanes, tropical storms, and extratropical events (e.g., [PERSON] et al., 2001). The influence from these storms is commonly non-uniform, with morphologically controlled hotspot beach and dune erosion preferentially threatening certain sites with uncharacteristic offshore ([PERSON] et al., 2006) or inner surf zone bathymetry ([PERSON] et al., 2021). These morphologic behaviors have been well documented on the northern Outer Banks, especially via a long-term monitoring program at the U.S. Army Engineer Research and Development Center (ERDC) Field Research Facility (FRF) in Duck, NC ([PERSON] and [PERSON], 2019; [PERSON] et al., 1988). Data from the FRF shows a highly 3D beach topography throughout the region that evolves on daily timescales associated with beach cusp evolution ([PERSON] and [PERSON], 2019), intermittent storm-driven beach and dune erosion ([PERSON], [PERSON], et al., 2019), and prevalent sand mobilization from wind-driven processes that contributes to dune growth ([PERSON], [PERSON], et al., 2020). This study focuses on a 6.5 km stretch of beach within the town of Duck (Figure 1), including the FRF property
Figure 1: Overview map of the study site location (panels (a-b)), including the alongshore extents of the six zones used in this analysis (panel (a)). Additionally, a pictures of (panel (c)) the CLARIS lidar platform and (panel (d)) a representative section of beach and dune from Zone 2 are shown. Pictures of scrap development at roughly the same location within Zone 3 are shown on 20 September 2019 following Hurricane Dorian (panel (e)), on 18 November 2019 coinciding with a Nor’Easter even (panel (f)), and 7 December 2020 shortly after dune collision from the swells of Hurricane Teddy (panel (g)).
(Zone 2 in Figure 1a). The 1 km stretch of coast at the FRF is unique for the region in that, other than access ramps for vehicles, there is no management of the beach or dune system since their construction by the Civilian Conservation Corps in the 1930s ([PERSON] et al., 1984). This includes no sand fencing along this 1 km coastal stretch, as noted in Table 1.
Because there is a negative background erosion rate in the Outer Banks ([PERSON] and [PERSON], 2019) that is about \(-\)1 m/yr in Duck ([PERSON] et al., 2017), in part due to long-term net longshore transport rates to the south ([PERSON] and [PERSON], 1989), many local communities have adopted a policy of active beach and dune noninstrument (e.g., [PERSON] and [PERSON], 2012). In the Summer of 2017, the town of Duck, NC placed about 1 million m\({}^{3}\) of dredged sediments along a \(\sim\)2.5 km stretch of coastline in order to expand useable beach for recreational purposes, buffer impacts of storms, and mitigate long-term erosion trends ([PERSON], 2017). The initial nourished design template included a wide, flat upper beach and a constructed dune. Sediment for the nourishment was sourced from two offshore borrow sources. The dune was planted with _Ammophila brevifoliauta_ and sand fences were installed in numerous rows within the constructed dune complex. Although the zone of placement of sand within the Town of Duck was limited to 2.5 km, the remainder of the town's coastline, other than the FRF, have installed sand fencing to aid in the trapping of wind-blown sand (Table 1). It is also common for used Christmas trees to be placed and grasses to be planted near the base of the dune throughout managed portions of the study site to aid in additional sand trapping.
### Environmental Forcings
Numerous meteorological and oceanographic instruments are located at the FRF which provide the necessary context for observed morphologic changes within the study bounds. A tide gauge located at end of the FRF pier was used to generate a time series of still water levels (SWL, Figure 2). Wind speeds and directions were collected at a meteorological station also located at the end of the pier at 20 m elevation. Wave heights, periods, and directions were derived from a waverider buoy located in approximately 17 m water depth offshore the study site. Any temporal gaps in the wave time series were supplemented with data from a wave buoy located further offshore Duck in 26 m water depth. To determine the occurrence of wave collision with the dunes, wave runup and TWLs were estimated from the available data. The eight empirically based models for 2% wave runup exceedance level (\(R_{220}\)) included within [PERSON] et al. (2020) were averaged to generate an hourly record of wave runup. The hourly TWL was calculated as the average \(R_{22\text{ }}\) plus the measured SWL from the FRF pier. An example TWL time series assuming a beach slope (\(\beta_{head}\)) of 0.1 m/m (the average regional \(\beta_{head}\)) is shown in Figure 2i. Any reference to TWLs at site-specific locations throughout the manuscript utilizes locally measured (spatially variable) \(\beta_{head}\) in the wave runup calculations. Note that all vertical references to water levels and bed elevation herein are provided in the NAVD88 datum, where mean high water (MHW) is approximately 0.4 m.
### Morphology Data
#### 2.3.1 Coastal Lidar and Radar Imaging System (CLARIS)
The CLARIS is a custom-built mobile surveying platform for coastal environments (Figure 1c). Detailed topographic data has been collected with CLARIS along the Outer Banks study site since 2012. The current iteration of the CLARIS platform, which has been operational since 2017, is built onto a four-wheel drive passenger van.
\begin{table}
\begin{tabular}{l l c} \hline Region & Management type & Y range (m) \\ \hline Zone 1 & Partially managed—sand fences & \(-\)1,200 to 0 \\ Zone 2 & Unmanned/natural & 0–1,000 \\ Zone 3 & Constructed—beach and dune nourishment, sand fences & 1,000–2,100 \\ Zone 4 & Constructed—beach and dune nourishment, sand fences & 2,100–3,300 \\ Zone 5 & Partially managed—sand fences & 3,300–4,300 \\ Zone 6 & Partially managed—sand fences & 4,300–5,300 \\ \hline \end{tabular}
\end{table}
Table 1: Management Type by RegionThe unit includes a Riegl VZ-2000 lidar scanner which continuously scans to collect high-resolution 3D point clouds of terrain and other objects. The CLARIS system also includes an IX-Blue ATLAS-C inertial navigation system (INS) with an integrated inertial measurement unit, wheel-mounted distance measurement instrument, and global navigation satellite system antennas to allow for precise orientation of the lidar-derived point clouds in real-world space. Previous iterations of CLARIS (<2017) were mounted on different vehicle platforms but included similar instrumentation and data quality, as outlined in [PERSON] and [PERSON] (2017).
Figure 2.— Time series of (a) significant wave height, (c) peak wave period, (e) still water level, (g) total water level (TWL) using \(\beta_{\text{trans}}\) of 0.1 m/m, and (i) wind speed. Red dots represent time periods where the estimated average TWL exceeded 3 m, which approximates the regional dune toe elevation as derived from Beuzen (2019). Monthly average values for each environmental variable are also shown in panels (b, d, f, h, and j) as black lines. The average direction of winds when \(u_{\text{e}}\) exceeds 8 m/s (approximate threshold velocity for aeolian transport, panel (n)) and waves when significant wave heights exceed 3 m (panel (f)) are also shown as orange lines.
. These CLARIS data cover the beach and dune face in high detail and are therefore used to quantify dune evolution in time and space. Based on typical driving speeds (\(\sim\)10 km/hr) and height of the vehicle (\(\sim\)2.5 m), data density is roughly 100 pts/m\({}^{2}\) between overlapping famescans within about 50 m of the van. An analysis of the scanner performance with these settings for resolving beach and dune topography is described in [PERSON], [PERSON], et al. (2020). Mean vertical errors using gridded CLARIS outputs relative to RTK GPS measurements are typically \(<\)0.05 m, making the data from this system suitable to resolve both recreational and erosional processes within coastal dunes in locations with sufficient point density. The CLARIS system does have line of sight limitations and cannot measure bed elevation changes near or past the dune crest. Thus, bed elevation change associated with jettation events and other thin layer deposition past the froedune crest (e.g., [PERSON], 2016; [PERSON] et al., 2013) are not captured by CLARIS.
#### 2.3.2 Collection Time Periods
At least quarterly (four times per year) CLARIS scans are collected in Duck. These surveys are supplemented by occasional pre- and post-storm surveys, usually coinciding with hurricane events that hit the Outer Banks. Between 2012 and 2020, 46 CLARIS surveys were completed which include at least a portion of the 6.5 km study site. The only beach noniurishment that has occurred within this study time period and within the area of interest was in Summer 2017. For the purposes of this work, we consider the pre-nourishment time period to be from 6 November 2012 to 23 February 2017. It is of note that this initial survey for which detailed 3D morphology data from CLARIS along the whole study site is available is timed shortly after Hurricane Sandy, which made landfall along the US East Coast in October 2012 and which caused considerable beach and dune impacts along the Outer Banks ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2014). Within Duck, these impacts included vertical lowering the beach face by over 1 m and significant scarping and erosion of the dune face \(\sim\) 8-12 m landmark relative to the pre-storm profile that included significant damage to ocean-front homes and infrastructure in certain regions. Unfortunately, pre-Sandy CLARIS data was not available along the entire length of the study site, so the impacts from this storm are not directly considered in this study.
The post-nourishment time period is considered as 21 November 2017-10 September 2020, with the start of this time period occurring shortly after beach fill placement and corresponding to a CLARIS survey that had data for the entire area of interest. Detailed analysis is completed on interannual trends, particularly related to differences in dune dynamics within the pre- and post-nourishment time periods, from these CLARIS data. Additionally, with these high temporal frequency data, we also focus on analysis of dune impacts at the storm time scale for select events and on the seasonality of dune growth to determine when, where, and why dunes are growing.
Multiple major storm events have impacted the beaches and dunes in Duck between 2012 and 2020. A collection of pre-/post-storm CLARIS surveys where data for the Duck study area were collected are investigated further. Hurricane Jose passed offshore of the Outer Banks in September 2017, immediately following the beach noniurishment. Significant wave heights (\(H_{s}\)) reached up to 4.2 m on 19 September 2017 and had peak wave periods (\(T_{p}\)) between \(\sim\)11 and 13 s for the duration of the event (Table 2 and Figure 2). For a \(\beta_{\text{road}}\) of 0.1 m/m, it estimated that the maximum TUL reached up to 4.4 m and exceeded the 3 m contour level over 4 high tides for a total duration of 24 hr. Based on the spatially variable pre-storm beach slopes, 94% of locations in the alongshore were expected to have TWLs that resulted in collisional impacts during Hurricane Jose. These high TWLs were caused in part by non-tidal residuals (NTR), calculated as the difference between the astronomical predicted tide and measured SWL, of up 0.85 m that coincided also with a spring tide. CLARIS data was collected on 18 September 2017 before the storm and 22 September 2017 immediately following the storm.
Two years later, Hurricane Dorian made landfall in the southern Outer Banks on Hatteras Island (\(\sim\)100 km south of Duck) on 6 September 2019. This is a recent storm of record for the area with peak \(H_{s}\) of 4.4 m at the 17 m wave gauge and over 6 m as measured at other FRF wave gauges, although the storm passed by the Duck region within a matter of hours. The highest \(H_{s}\) did not coincide with the maximum SWL (that included an NTR of up to 1.19 m), resulting in a maximum estimated TWL of only 3.7 m. There were 7 total hours during this event where swash may have been in the collision regime based on the empirically estimated TWLs using a beach slope of
\begin{table}
\begin{tabular}{l c c c c c} \hline & & & Max & Max \\ Storm name & Time period & Max (m) & Max & SWL & TWL \\ \hline Hurricane Jose & September 2017 & 4.2 & 14.8 & 1.29 & 4.39 \\ Hurricane Dorian & September 2019 & 4.4\({}^{a}\) & 11.3 & 1.40 & 3.66 \\
2019 Nor Easter & November 2019 & 4.7 & 14.0 & 1.21 & 4.38 \\ Hurricane Teddy & September 2020 & 3.9 & 17.7 & 1.21 & 4.45 \\ \hline \multicolumn{6}{l}{\({}^{\ast}\)Other FRF wave gauges showed peak \(H_{s}\) exceeding 6 m during this short-lived, energetic hurricane event.} \\ \end{tabular}
\end{table}
Table 2: Peak Environmental Characteristics of Storms Events With Detailed Pre-/ Post-Storm CLARIS Data0.1 m/m. Overall, 97% of the Duck dunes were expected to be in the collision regime at some point during Hurricane Dorian based on the spatially variable pre-storm \(\beta_{back}\). CLARIS surveys were collected on 4 September 2019 and 10 September 2019 to characterize the impacts of Hurricane Dorian.
Whereas, hurricanes traveling from the Gulf of Mexico or South Atlantic often pass by the Outer Banks relatively quickly, there can be far-field wave events and other storm systems that can result in sustained higher than normal wave energy over multiple tidal cycles across the U.S. East Coast. For example, Hurricane Teddy never made landfall in the continental U.S., but did slowly cross the Atlantic and resulted in long-period waves that reached the beaches of the Outer Banks. The event had maximum \(H_{s}\), \(T_{p}\), NTR, and TWLs of 4.0 m, 20 s, 0.54, and 4.5 m, respectively. There were 66 hr over about 10 high tides, coinciding with spring tide conditions, during which the TWL may have reached the 3 m contour and 10 hr where the predicted TWL exceeded 4 m assuming a beach slope of 0.1 m/m. The entire stretch of the study site was predicted to be in the collision regime at some point during Hurricane Teddy. CLARIS data was collected on 10 September 2020 and 25 September 2020 to characterize impacts primarily related to Hurricane Teddy.
Nor'Easters also commonly impact the region. CLARIS data was collected on 14 November 2019 and 19 November 2019, during which interval \(H_{s}\) reached up to 4.8 m. Positive NTRs, up to 0.79 m, occurred coincident with the elevated wave energy. Empirically estimated TWLs suggested that the dune toe was impacted 45 total hours during this period, with maximum TWLs of 4.4 m (assuming a beach slope of 0.1 m/m) contributing to these collision impacts. During this Nor'Easter it is estimated that 100% of the dunes in the study site experienced dune collision during this event based on the pre-storm \(\beta_{back}\) measurements from CLARIS.
There were other local and far-field events that resulted in predicted collisional dune impacts in this period from 2012 to 2020, as shown by the red dots in Figure 2i. However, as closely spaced pre-/post-storm morphology data is not available for most of these other impactful events.
### Morphology Data Processing
For this study, the raw lidar returns data from CLARIS were filtered to determine the bare-earth bed elevation using standard Riegler terrain filters within the RiScan Pro software. Data was rotated into a local coordinate system that is oriented according to a regional shoreline angle (69.97\({}^{\circ}\) represents shore-normal) where \(y=0\) m falls within the FRF property. The filtered data is gridded onto a 0.25 m grid in both the cross-shore and long-shore directions for the entire 6.5 km stretch of coast to generate a regional digital elevation model (DEM) for each data collection (e.g., Figure 3). A secondary filter is further applied on each gridded DEM to remove cells with sparse data points near the dune crest where vegetation can limit accurate detection of the bed (e.g., [PERSON], [PERSON], et al., 2020). Errant returns are additionally removed from the gridded surface using a cross-shore Gaussian smoother.
These processing approaches result in high detail elevation grids, although there are still potential errors associated with the definition of the bed. Potential source errors from individual surveys include imperfect positioning information (e.g., RTK GPS, and IMU uncertainty) or vegetation sources, which can typically be treated as having randomly distributed uncertainty for individual points. Therefore, while no rigorous error propagation has been completed here due to the scale of the data, these errors are further minimized within this analysis by focusing on spatially averaged products and \(\sim\)interannual trends (to be described). These potential sources of error are nonetheless important to consider when interpreting these topographic data and resultant outputs.
Useable data usually extends \(\sim\)1 m or less below the dune crest for CLARIS scans following the filtering steps. Dune volumes (\(V_{done}\)) are calculated from the total cross-sectional area between 3 and 8 m elevation. This upper limit encapsulates the region approximately up to the dune crest. In some locations, the dune crest height does not exceed 8 m, in which case volumes would represent the volume up to the highest point of useable CLARIS data. For data cells close to the dune crest where data was not available in a particular survey, a no-change condition from the previous survey is assumed for that cell. The 3 m elevation is chosen based on the approximate average dune toe elevation calculated from all of the available data using pybeach ([PERSON], 2019). This implementation of pybeach utilizes a pre-compiled machine learning algorithm that uses Random Forest classification and which was pre-trained on profiles and manually selected dune toe elevations and locations from similar, sandy coastal dune systems. The change in dune volume (\(\Delta V_{done}\)) above this 3 m dune toe represents the volumetric change in the total measured dune volume over a fixed time interval, such as within storm events. The rate of change in dune volume (\(dV_{\text{data}}\)/_dt_) is also reported based on end-point values of \(V_{\text{data}}\) in order to normalize the data and allow for intercomparison between different zones and time periods.
Although CLARIS is usually driven at low tide and includes data at and below MHW for the majority of scans, during stormy periods higher TWLs limit the dry, driveable beach. Thus the 1 m elevation is chosen as the lower limit for calculating beach parameters based on broader availability of CLARIS data over time and space. Beach volumes (\(V_{\text{bank}}\)) are measured as the total volume between 1 and 3 m elevations within each cross-shore transect of data within the DEM region for each of the 44 dates. For any time period or location where CLARIS did not successfully collect data down to 1 m, the local \(V_{\text{bank}}\) was not calculated. Similarly to \(V_{\text{data}}\), \(V_{\text{bank}}\) is calculated from the 0.25 x 0.25 m gridded data and, consistent with typical conventions, are reported as volume changes per meter extent of shoreline in the alongshore. Similarly to the dune region, \(\Delta V_{\text{bench}}\) and \(dV_{\text{bank}}\)/_dt_ are also calculated from these data. The cross-shore distance of the seaward-most 1 m (\(x_{\text{tar}}\)) and 3 m (\(x_{\text{tar}}\)) bed locations was recorded to determine \(\beta_{\text{break}}\). This end-point slope neglects intermediate details of the beach profile, such as berms and other curvature, although is common approach used to define general geometric attributes of the beach. Because the exact location of dune crest is poorly defined with the CLARIS data due to line of sight limitations and given that the crest of the dune is not above 8 m at all sites (e.g., Figures 3b-3l), a dune slope is not calculated.
All relevant volumetric and geometric metrics that were computed for the beach and the dune for each 0.25 m in the alongshore for each of the 46 surveys are then averaged in 5 m alongshore bins for subsequent analysis. The binning step serves to reduce highly local (e.g., single cross-shore transect) variability in measured morphological changes, including around sand fences and dune walkway cut-throughs, to allow for improved understanding of the causation of observed morphologic changes. For the purpose of further quantifying general regional behavior and implications of differing management styles on dune evolution, the data is further subset and averaged into six alongshore zones that are each approximately 1 km in length (Table 1) for portions of the analysis.
Figure 3.— A 3D gridded representation of topographic change in the post-nourishment time period (21 November 2017 to 10 September 2020) where the vertical elevation represents the 21 November 2017 topography and the solid black line shows the location of the 3 m contour. The extents of each of the six zones are shown by the colored polygons. Dashed black lines show the locations of transects shown in panels (b–l). These example cross-shore profiles show topographic change from selection locations throughout the study site for the entire period of record from 6 November 2012 (blue) to 25 September 2020 (red). The nourishment, which included the construction or expansion of dunes at the profiles shown in panels (e–i), occurred in summer 2017.
To isolate the seasonal aeolian contribution to dune growth, the gridded morphostrigraphic approach of [PERSON] et al. (2018) was utilized. The timing and vertical locations of net aeolian deposition was recorded independently for each cross-shore transect in the alongshore from the 0.25 m DEM. Using this method erosional periods are ignored in order to isolate dune growth mechanisms, which are primarily driven by wind-driven sediment fluxes. From the cross-shore transects, volume changes are calculated per 0.01 m vertical elevation within the dune using this morphostrigraphic method and summed to determine the location and timing of net accretional inputs to the dune (\(\Delta V_{\textit{dune,accretional}}\)), with the corresponding annual rates of dune growth expressed as \(dV_{\textit{dune,accretional}}\)/\(dt\). The method is calculated on all of the available data, except that net changes associated with the dune construction corresponding to bed elevation changes between surveys from 14 July 2017 and 18 September 2017 were removed to isolate only natural dune growth processes. For the purposes of the seasonal investigation, Fall is considered the period from September to November, winter is December to February, Spring is March to May, and Summer is June to August.
## 3 Field Observations
### Interannual Timescale: 2012-2020
#### 3.1.1 Beach Evolution
Representative cross-shore transect profiles from the dune crest to the water line for each of the 46 CLARIS surveys are shown in Figure 3 across the length of the study site. The beach topography is temporally and spatially variable, with a vertical envelope of variability of up to \(\sim\)2 m on the beach in some locations (Figure 3). The zone-averaged \(\Delta V_{\textit{hunch}}\) within each zone (Figure 4c) typically varied by only \(\pm\)10 m\({}^{3}\)/m between subsequent surveys in the pre-nourishment time period. However, there is alongshore variability in \(\Delta V_{\textit{hunch}}\) within this time period as shown in Figure 5g. For example, \(\Delta V_{\textit{hunch}}\) within Zone 4 ranged from 3 to 30 m\({}^{3}\)/m of growth within the pre-nourishment time period, as extracted from the 5 m binned alongshore data.
The construction of the beach nonwithstanding resulted in a large, rapid increase in \(V_{\textit{hunch}}\) (\(>\)50 m\({}^{3}\)/m) within Zones 3 and 4 (Figure 4c). Following construction, the beach in this noninvariant region steadily lost volume at \(\sim\) monthly scales up to the end of 2020. Despite these sediment losses, \(V_{\textit{hunch}}\) at the end of the post-nourishment period still exceeded the average pre-nourishment \(V_{\textit{hunch}}\) in Zones 3 and 4\(-\)indicating that some of the nonwished sands were retained within the subaerial portion of the system \(\sim\)3 yr after nonwishment. Similar trends were observed with \(\beta_{\textit{hunch}}\) within the nonwishment region (Figure 4e). Mild beach slopes (\(\beta_{\textit{hunch}}\)\(<\) 0.05 m/m) were measured immediately post-nourishment, with slopes gradually steepening to similar \(\beta_{\textit{hunch}}\) from before beach nonwishment (\(\beta_{\textit{hunch}}\)\(\sim\) 0.1 m/m).
As sediment was lost from the nonwishment zone immediately following the nonwishment construction, average beach volumes within Zones 1, 2, and 5 increased throughout 2017 and 2018 (Figure 4c). Beach slopes shallowed in all zones except zone 2 from the start to end of 2017 (Figures 4e and 4f). Zones 1, 2, and 5 all had the highest recorded \(V_{\textit{hunch}}\) in the year following nonwishment, relative to the rest of the record. However, these volume gains were relatively short-lived, with beach volumes returning to the pre-nourishment beach volume by the end of 2019 (Figures 4c and 4d) in Zones 1, 2, and 5. There were not consistent increases in \(V_{\textit{hunch}}\) in Zone 6 in this post-nourishment time period.
#### 3.1.2 Dune Evolution
On average, the coastal foredunes in the region have been both vertically aggrading and prograding (Figure 3) during the study time period. Over the 2012-2017, pre-nourishment time period, the dunes accreted (\(\Delta V_{\textit{dune}}\)\(>\) 0) along 91% of the study area overall (Figure 5a). In the years after the nonwishment, the portion of accreting dunes decreased to 83% of the study area. Zone 2 had both the largest recorded negative \(\Delta V_{\textit{dune}}\) and lowest proportion of accretional area (68%) of anywhere in the study site during the pre-nourishment time period. Over this time period, the dunes in Zone 2 lost an average of 1.2 m\({}^{3}\)/m and was the only zone with a negative average \(\Delta V_{\textit{dune}}\). This erosional trend reversed in the post-nourishment time period within Zone 2. In the period from late 2017 to 2020, there was an average 8.1 m\({}^{3}\)/m net dune growth, with 83% of the Zone 2 dunes being accretional over this time period.
The proportion of dunes that were erosionally increased in Zone 1 between before (90% accretional, 10% erosional) and after (56% accretional, 44% erosional) the nonwishment (Figures 5a and 5b). Similarly, in Zone 3 the proportion of erosional area increased from before (86\(\%\) accretional, 14\(\%\) erosional) to after (68\(\%\) accretional, 32\(\%\) erosional) nonurishment. In Zones 4, 5, and 6 the dunes were accretional in \(>\)95\(\%\) of region both before and after nonrishment. Annually normalized beach and dune growth rates are shown in Figures 6a-6f. The zone-averaged annual \(dV_{\textit{same}}/dt\) only decreased in Zones 1 and 6 in the post-nourishment time period. The change in \(dV_{\textit{same}}/dt\), either positive or negative, only exceeded 3 m\({}^{2}\)/m/yr in Zone 2. \(dV_{\textit{same}}/dt\) was similar (\(\pm\)2 m\({}^{2}\)/m/yr) before and after nonrishment in Zones 1, 2, 5, and 6. Annualized average beach volume losses were much higher in the post-nourishment time period in Zones 3 and 4 associated with beach fill re-equilibration.
The isolation of net accretional conditions using the morphost stratigraphic approach indicates that there have been alongshore variable accretion patterns across the freedue face throughout the study region. The annual dune accretion rate was 2.9 m\({}^{3}\)/m/yr on average within Duck (Table 3) when removing volume changes associated from anthropogenic point of sediment by ignoring net changes to \(V_{\textit{same}}\) during the construction period. The highest annual average \(dV_{\textit{same},\textit{normal}}/dt\) occurred in Zones 4 and 5 and lowest rates in Zones 1 and 2. The distribution of where wind-blown sediments were deposited in the dune also varied spatially within the study site (Figure 7). The morphost stratigraphic analysis indicates that a larger proportion of accreted sediments within regions that are actively managed are deposited at high dune elevations (\(>\)6 m; Figure 7a) relative to their unmanaged counterparts. Overall 40.2\(\%\) of observed dune accretion was noted above 6 m in the partially managed dune sections (Zones 1, 5, and 6), 34.6\(\%\) in the constructed dune region (Zones 3 and 4), and only 23.0\(\%\) in the unmanaged zone (Zone 2). Conversely, 37.7\(\%\), 38.7\(\%\), a 48.0\(\%\) of total sediment gains are located below 5 m for the same zones, respectively.
Figure 4.— Time series of zone-averaged dune volume change (panel (a)), beach volume change (panel (c)), and beach slope (panel (e)) throughout the period of interest. The gray shaded region represents the nonrishment time period in Zones 3 and 4. Net annual volumetric (and beach slope) changes are shown in panels (b and d) (panel (f)).
#### 3.1.3 Beach and Dune Interaction
The CLARIS data shows that dune growth rates have the potential to be higher on lower-sloping (more dissipative) beaches sections (Figure 8), although there is considerable scatter in these trends. For example, Zone 4 generally had among the lowest \(\beta_{bench}\) (avg \(\beta_{bench}\) = 0.086 m/m) and the highest average dune accretion rates (\(dV_{dane,accision}/dt\) = 3.2 m\({}^{2}\)/m). While similar average \(\beta_{bench}\) existed across the entire study period in Zone 2 as in Zone 4, Zone 2 had much lower net dune accretion rates (\(dV_{dane,accision}/dt\) = 1.6 m\({}^{2}\)/m). Conversely, Zone 2 had similar lower net dune accretion rates to Zone 1, although Zone 1 had much higher \(\beta_{bench}\) (avg \(\beta_{bench}\) = 0.107 m/m). The data points in Figure 8 show tight clustering within each zone.
When considering collisional impacts according to the framework of [PERSON] (2000) and for calculating dune volume changes, a definition of the dune toe is necessary. The 3 m elevation contour used throughout this work represents the regional average from the entire data set derived using Beuzen (2019), however, there is considerable spatio-temporal variability in this metric. Figure 9a shows that the time-averaged predicted dune toe elevation using pybeach in Zone 3 is the lowest among all regions at 2.65 m elevation. The highest zone-averaged dune toe is located in Zones 1 and 5 with 3.06 and 3.10 m, respectively. When applying the temporally averaged \(\beta_{bench}\) at
Figure 5: Dune (panel (a–f) and beach (panels (g–l)) volume changes from the pre-/post-nourishment time periods and for specific storm events. Additionally, pre-storm beach slopes are shown in panels (m–p).
each 5 m alongshore location with the composite wave runup predictions for the full environmental time series (as shown in Figure 2), this local variability in the dune toe elevation results in predicted dune collision occurring on average 1.3% of the time and up to 2.0% of the time throughout the year at the most vulnerable locations (lowest dune toe and steepest \(\beta_{\text{bac}}\)) within Zone 3 (Figure 9b). Conversely, collision was estimated at only 0.2% of the time at the least vulnerable portion of Zone 5. On average, Zones 1, 2, 4, 5, and 6 had zone-averaged collision frequencies of 0.9%, 0.7%, 0.9%, 0.5%, and 0.7% of the time, respectively. Within some individual zones (e.g., Zones 1, 2, and 6), there is a weak (\(R^{2}\leq 0.4\)) but statistically significant relationship between the estimated time in the collision regime and the net \(\Delta V_{\text{danc}}\). The time in the collision regime explains more variance in \(\Delta V_{\text{danc}}\) than the average dune toe elevation alone (not shown) for the majority of the zones, indicating that the duration of dune collision is likely an important factor to consider in regionally variable dune responses across timescales.
### Event to Seasonal Timescale
#### 3.2.1 Seasonal Patterns in Dune Accretion
Trends in beach and dune evolution were highly variable in time, in part dependent on seasonality in environmental forcings. Although dunes can grow any time of the year when wind speeds exceed the threshold velocity, the morphostriagraphic analysis shows that dune volume gains were not equally distributed throughout the year (Figure 7). The largest rates of accretion occurred in Fall within all zones (Table 3), constituting between 31% and 47% (depending on the zone) to the total annual dune growth in this season. Despite Spring including some of the most energetic wind speeds (Figure 21), there was comparatively lower \(dV_{\text{danc,accreted}}/dt\) in this season for all zones. Summer was the period with the lowest average volumetric change to the dunes.
Vertical aeolian deposition patterns also do vary seasonally, with the unmanaged coastal extent especially differing in Summer and Fall relative to the other managed coastal extents (Figures 7b-7e). Specifically, there is more
Figure 6: End-point annual beach and dune volume change rates for the pre-nourishment (black) and post-nourishment (red) time periods (panels (a–f)) and end-point beach and dune volume changes rates for each example storm event (panels (g–j)) for each zone. Dots represent the regional average value, with bars representing values \(\pm 1\) standard deviation.
\begin{table}
\begin{tabular}{l c c c c c} \hline Region & Total & Fall & Winter & Spring & Summer \\ \hline Zone 1 & 1.7 & 0.8 & 0.3 & 0.3 & 0.2 \\ Zone 2 & 2.1 & 0.8 & 0.5 & 0.3 & 0.2 \\ Zone 3 & 3.0 & 1.4 & 0.5 & 0.4 & 0.3 \\ Zone 4 & 4.3 & 1.4 & 1.1 & 0.8 & 0.6 \\ Zone 5 & 3.9 & 1.2 & 1.2 & 0.8 & 0.5 \\ Zone 6 & 2.5 & 0.8 & 0.8 & 0.6 & 0.2 \\ All & 2.9 & 1.0 & 0.7 & 0.5 & 0.3 \\ \hline \end{tabular}
\end{table}
Table 3: Average volumetric Dune Accretion Rate per Season and Year, in m*/m*/yr, for Each Zonerelative sediment gain to the lowest elevation dune segments (<4 m) on unmanaged dune sections, relative to their constructed or managed counterparts in these seasons.
#### 3.2.2 Storm-Driven Dune Response
#### 3.2.2.1 Hurricane Jose
Shortly following nonrishment construction, Hurricane Jose impacted the Outer Banks. This event led to along-shore variable \(\Delta V_{\text{head}}\), with zones of both beach growth and beach erosion observed during this event (Figure 5i). On average there was a mean \(\Delta V_{\text{head}}\) of \(-1.3\) m\({}^{3}\)/m during the storm across all zones, although some data gaps within the nonrishment zone existed due to incomplete coverage to the 1 m contour. Zone 2 had the highest volume losses to the beach compartment during Hurricane Jose. However, while there was 3.2 m\({}^{3}\)/m lost on average from the beach during Jose in Zone 2 (Figure 6g), the northern-most part of this zone immediately adjacent to the nonrishment gained up to 14 m\({}^{3}\)/m during the storm (Figure 5i).
There was similarly wide variability in dune impacts during the storm (Figure 5c). The mean zone-averaged \(\Delta V_{\text{dune}}\) during Hurricane Jose was \(\sim\)0 m\({}^{3}\)/m. Zones 2, 5, and 6 all had mean negative \(\Delta V_{\text{dune}}\) throughout the storm. Both Zones 2 and 6 had locations where dune erosion was \(-5\) m\({}^{3}\)/m or greater. In Zones 5 and 6, these volume losses were related to erosion near the base of the dune (Figures 10q and 10u), whereas in Zone 2 this is attributed primarily to net erosion of the dune face between 4 and 7 m (Figure 10e). There were positive mean \(\Delta V_{\text{dune}}\) in Zones 1, 3, and 4. In Zone 3, the nonrished section that had the most dune erosion over the post-nonrishment period (Figure 5b), none of the variance (\(R^{5}\)) in \(\Delta V_{\text{dune}}\) was explained by \(\beta_{\text{head}}\) during Hurricane Jose (Figure 11a).
#### 3.2.2 Hurricane Dorian
Beach volume losses were widespread during Hurricane Dorian, with 97% of the study area having a negative \(\Delta V_{\text{head}}\) and 38% of the region having more than \(-10\) m\({}^{3}\)/m of \(\Delta V_{\text{head}}\). The average volume of sediment lost from \(V_{\text{head}}\) was 8.7 m\({}^{3}\)/m across all zones. Dune erosion was similarly geographically widespread (71% of the region with \(\Delta V_{\text{dune}}<0\)), although with less magnitude than \(\Delta V_{\text{head}}\). The average \(\Delta V_{\text{dune}}\) was \(-0.8\) m\({}^{3}\)/m. Up to 4.7 m\({}^{3}\)/m of
Figure 8: Net annual accretional volume gains from plotted against average \(\beta_{\text{head}}\).
Figure 7: Normalized patterns in the vertical distribution of accreted sediments for each set of dune management types, including those that are partially managed (Zones 1, 5, and 6), recently constructed and actively managed (Zones 3 and 4), and unmanaged (Zone 2), using the morphost stratigraphic approach for (a) all months, (b), Fall, (c) Winter, (d) Spring, and (e) Summer.
sediment was lost from the dune, with this most extreme value located in Zone 3. In Zones 3-6, there was erosion close to the dune toe elevation as measured between the pre- and post-storm CLARIS surveys (Figure 10). Minor (\(\sim\)1 m) vertical dune scarps were noted in Zone 3 s shown in Figure 1e. While this energetic storm did cause dune erosion in many locations with Duck, there were sediment gains to the dunes, on average, in both Zones 1 and 2 during this event (Figure 6h). There were minimal volumetric changes to the dune near the 3 m base of the dune in Zones 1 and 2, although deposition was observed between 4 and 6 m elevation (Figures 10b and 10f). \(\beta_{bench}\) is a statistically significant variable that explains over 40% of the variance in \(\Delta V_{dave}\) in Zones 4 and 5, although explains 20% or less of the variance in the remaining zones (Figure 11b).
#### 3.2.2.3 Nor'Easter
The Nor'Easter event which impacted the Outer Banks in November 2019 eroded 92% of the beaches within the study domain. An average of 6.2 m\({}^{3}\)/m was lost from \(V_{bacula}\) during this time period. An average of 2.2 m\({}^{3}\)/m was also lost from the dune throughout the entire study site between 14 November 2019 and 19 November 2019. 88% of the dunes in this region were erosional, with Zones 3 and 4 having the highest volumetric losses of the dune of any region during this storm (up to \(\sim\)8 m\({}^{3}\)/m). Volumetric erosion between 3 and 4 m elevations was noted, on average, within all six zones (Figures 10c, 10g, 10k, 10o, 10o, and 10w). Zone-averaged volume changes at other elevation bins were close to zero within all six zones.
#### 3.2.2.4 Hurricane Teddy
The volumetric beach erosion from the far-field waves of Hurricane Teddy was among the largest of any of the studied storm events, with 95% of the study domain experiencing beach erosion with an average loss of \(-\)8.3 m\({}^{3}\)/m during the storm. There were more alongshore variable impacts to the dunes associated with the waves from Hurricane Teddy. There was a zone-averaged loss of \(-\)0.5 m\({}^{3}\)/m from the dunes. In Zones 1 and 6, the dunes on average gained volume during the event (Figure 6j), primarily between 3 and 4 m elevations (Figures 10d and 10x), whereas Zone 3 had the highest volume losses averaging \(-\)4.4 m\({}^{3}\)/m within that single zone. Field evidence from Zone 2 indicates that TWLs did reach the dune during Hurricane Teddy and contributed to regions of both new dune scarping and zones with wrack deposition within the vegetated portion of the dune (not shown) where no discernible erosion could be observed. Overall, 56% of the dunes in the entire study site were erosional, whereas 44% of the dunes accreted during this time period. Dune erosion within Zones 2-5 were mostly limited to the lower portion of the dune (\(<\)5 m). During swells from Teddy, \(\beta_{bench}\) explained 69% of the variance in \(\Delta V_{dave}\) in Zone 3--suggesting that \(\beta_{bench}\) was important for controlling where dunes were most impacted (Figure 11d).
Figure 9: (a) Alongshore variable mean dune toe elevation derived from Beuzen (2019) and (b) the frequency of total water levels exceeding the dune toe at each alongshore extent, utilizing the local mean \(\beta_{bench}\) as input. Panel (c) shows the time in the collision regime vs. total dune volume changes across the entire study time period.
Figure 10: Vertical volumetric changes in 1 m vertical segments for Hurricane Jose (column 1), Hurricane Dorian (column 2), a 2019 Nor’Easter event (column 3), and Hurricane Teddy (column 4) for zones 1 (panels (a–d)), 2 (panels (e–h)), 3 (panels (i–l)), 4 (panels (m–p)), 5 (panels (q–t)), and 6 (panels (u–x)). Dots represent the regional average value for each elevation bin, with bars representing values \(\pm 1\) standard deviation.
## 4 Discussion
### Field Insights Into Dune Morphodynamics
#### 4.1.1 Morphologic Controls
Consistent with previous observations of beach-dune interaction ([PERSON] & [PERSON], 2008; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2013), there is some dependency of dune volume losses on pre-storm \(\beta_{\text{beach}}\) shown by the CLRARIS data (Figure 11) in many circumstances. The relative importance of \(\beta_{\text{beach}}\) on \(\Delta V_{\text{dune}}\) varies widely between zones and different storms, with many locations where zero or very low variance in \(\Delta V_{\text{dune}}\) explained by \(\beta_{\text{beach}}\). This observation suggests that while locations with steeper \(\beta_{\text{beach}}\) can be more susceptible to wave runup (e.g., [PERSON] et al., 2006) and resulting erosion during discrete events, there are likely additional environmental, morphologic, and/or ecological factors at play that influence or control the scale of these potential erosional volumes. For example, the most negative \(\Delta V_{\text{dune}}\) often co-occur with the zones of most negative \(\Delta V_{\text{beach}}\) (Figures 6h and 6j) indicating a possible further coupling between the evolution beach and dune system. Similarly to [PERSON] et al. (2022), this may suggest that details of the beach morphology beyond \(\beta_{\text{beach}}\), such as the pre-storm backshore volume, are additionally important for explaining spatio-temporal variability in \(\Delta V_{\text{dune}}\).
shown in Figure 9a. Since this region with the regionally lowest dune toes coincides with the region that required expensive beach and dune nonurishment, better understanding of the causation and implications of this potential geologic control on dune toe variability in the context of dune vulnerability is critically important.
### Environmental Controls
Data from storm timescale indicated that the largest dune erosion events can be associated with multiple-day moderate Nor'Easters, rather than the largest TWL events (Figures 5c-5f). While this is consistent with the important role of wave duration from laboratory studies (e.g., [PERSON] & [PERSON], 2012), field efforts (e.g., [PERSON] & [PERSON], 2018), and model results (e.g., [PERSON] et al., 2019), the literature on this topic is heavily skewed toward documentation for hurricanes and extreme wave events vs. lower peak wave conditions, but longer duration, events such as Nor'Easters. However, it is important to note that in the period of interest there have been no hurricane events that have resulted in overwash or inundation regime impacts, as defined by [PERSON] (2000), within this specific region. These more extreme regime classifications would generally be expected to have more catastrophic dune impacts than those in the collision regime. Similarly, pre-/post-morphology data which could be attributed to only a single event was only available for a subset of collisional events, all coinciding with the post-nonurishment time period.
Erosion during storms documented by CLARIS was almost always isolated to the regions under 5 m (Figure 10), consistent with the highest predicted TWLs between 2012 and 2020 (Figure 2d). However, the data also show that, simultaneous to erosion of the lower portion of the dune, the dunes have consistently been gaining volume in the \(\sim\)decade period of interest in this study. Moreover, some of this wind-driven growth of the upper portion of the dune (>5 m) is shown to occur simultaneously (e.g., during the same event) to wave-driven dune erosion during the investigated storm events (e.g., Figures 10b and 10v). This suggests that aeolian processes may mask some erosional signatures even at the storm timescale in pre and post-storm volume change calculations. This further indicates the importance and complexity of wind-wave-surge sequencing on coastal foredune evolution (e.g., [PERSON] & [PERSON], 2018) and the need for frequent surveying to de-couple the relative contributions of wave and wind processes on dune evolution. For example, limited survey data available before 2013 limits a complete quantitative understanding of dune recovery following Hurricane Sandy. Although, the dunes were generally accretive throughout the pre-nourishment time period, in the 5 yr post-sandy the dunes in the vicinity of Zones 2 and 3 regained less than \(\sim\)50% of the original dune face position based on the data that is available. This indicates both the slow timescale of dune recovery relative to storm-driven erosion that is likely further slowed by the multitude of collisional events that happen per year in the Outer Banks.
Interestingly, the largest dune accretion events occur in the Fall months within most zones (Figure 7 and Table 2), coinciding with the period of highest TWL conditions but not necessarily the highest average wind conditions (Figure 2l). Since wind-blown sediment fluxes scale with wind speed (Bagnold, 1937), time-averaged wind speeds are less relevant for predicting wind-blown fluxes relative to the maximum conditions that have some landward-directed component. Both hurricanes and Nor'Easters, which can have high sustained wind speeds, are common during this Fall period. Additionally, the average wind direction for speeds exceeding 8 m/s (representative of storm conditions) is strongly from the north with an onshore, cross-shore component during both September and October (Figure 2n) that promotes sediment flux from the beach to the dune. Conversely, the Spring, which has highest mean wind velocities, has no hurricane events and instead has winds that are more typically from the south and with a mean offshore directed component.
### Anthropogenic Controls
#### 4.3.1 Vertical Distributions of Deposited Sediments
All of the sites saw more volumetric sediment gains at elevations below 6 m than above, although more sediment was deposited at these higher elevations (>6 m) in the managed coastal sections relative to the unmanaged coastal stretch. Nearly 50% of net accreted sediments were observed below 5 m in Zone 2 indicating that there is preferential deposition lower on the dune in this natural region. The cause for these depositional patterns is likely in part related to the location of vegetation and sand fencing which are crucial for producing wind-blown sediment transport gradients. The dune nonurishment region initially included regular spacing of sprips _Ammophila brevigulata_, with additional _Unicola paniculata_ planted near the dune crest ([PERSON], 2017), with similar vegetation present in the other partially managed coastal sections as well. Conversely, there is a wider range of species present at the unmanaged FRF site including _Panicum amarum_, _Sparting patens_, _Solidago sempervirens_, _Erigeron canadensis_, and _Smilax bona-nav_ (e.g., [PERSON], 1976; [PERSON] & Zinnert, 2022). Quadrat surveys of dune grass vegetation on the dune face in portions of the study site, as presented in [PERSON] (2022), showed that the total living cover was about twice as high in Zone 2 than Zone 3 and that the species richness was higher in Zone 2 than Zone 3. As different species trap sediment in different magnitudes and styles (e.g., [PERSON] et al., 2021), variable species composition on the dune may contribute to these management-style dependent dune face deposition patterns. This behavior, at least within the nonwithstanding site, may also be related to the lack of well established vegetation following sprigging immediately following construction. Limited vegetation density which would allow sediment bypassing more readily than established, more densely spaced plants.
Sand fencing also plays a critical role for causing sediment transport gradients and therefore influences the spatial distribution of deposited sediments across the dune face. Within Zones 3 and 4 in Duck, 10-foot length sand fences were regularly placed (approximately 2-3 m apart in the longshore) at a 45\({}^{\circ}\) angle relative to the coastline in multiple rows across the dune face along with dune construction. Sand fences have been placed throughout Zones 1, 5, and 6, although in a less regular arrangement since dunes in those site were not constructed and therefore had variable topography in the alongshore. Zone 2 has never had sand fences installed. Interestingly, if sand fences are partially responsible for the vertical distribution of deposited dune face sediments, allocating sediment toward the upper part of the dune would generally serve to increase the height of the dune as opposed to dune widening as has been observed along other fenced dune regions (e.g., [PERSON] et al., 2020). Observations from Duck supports widespread observations that the details of vegetation, sand fencing, and other obstructions on the dune (e.g., Christmas trees) can modify the deposition patterns within the dune and its subsequent shape, and therefore likely have important implications for the future resilience of that dune system to later storm-driven erosion.
#### 4.3.1.1 Drivers of Increased Sediment Flux to Dune
The exact details of how management factors individually alter the accretion and erosion trends is as of yet unclear, although interestingly the only zone that did not have a positive mean \(dV_{\text{head}}/dt\) or \(dV_{\text{dam}}/dt\) (Figure 6) in the pre-nonwithstanding time period (2012-2017) was Zone 2--the only beach section that had no active management. Instead Zone 2 had slightly negative (\(\sim\)\(-\)1 m\({}^{3}\)/m/yr) mean \(\Delta V_{\text{dam}}\) and \(\Delta V_{\text{head}}\), with large local variability, in this pre-nonwithstanding period. These trends in Zone 2, relative to the observations from adjacent sections of coast, would suggest that natural settings with no beach or dune management are overall more dynamic, perhaps arising in part due to the lack of efforts to stabilize the dune morphology through fencing, grass planting campaigns, the use of Christmas trees, and, in certain circumstances, sand placement that is present in the other regions.
Dunes in the beach nonrishment section naturally accreted following the nonrishment at rates that exceeded the pre-nonrishment time period (Figures 4 and 6). The largest annual increases in \(\Delta V_{\text{dam}}\) in the nonrished section (Zones 3 and 4) coincided with the years immediately following sand placement in 2017 (Figures 4a-4b and 6c-6d). This is consistent with observations from a nearby nonrishment in 2011 in Nags Head where data suggests that there was higher than normal aeolian activity in the year immediately following beach fill construction ([PERSON] et al., 2018). Similarly to the explanations for alongshore variability in sediment to the dune (Section 4.1.1), two mechanisms exist that may contribute to post-nonrishment rises in aeolian contributions to dune growth. First, there is a grain size dependence on the threshold velocity (\(u_{t}\)) for wind-blown sand--with smaller grains being capable of being transported under lower wind speeds. Repeat beach grab data from the FRF indicate that the average median grain size (\(D_{\text{so}}\)) for the region is approximately 0.34 mm. Using Bagnold (1937), the \(u_{t}\) for sands of this size are 7.6 m/s (at 20 m elevation, consistent with the height of the FRF anemometer). Winds that include some onshore wind component are expected to be able to mobilize this median grain size 15.4% of the time at Duck for the study time period (e.g., utilizing the environmental time series shown in Figure 2k) and transport some of the sediments toward the dune. Because aeolian transport rates scale non-linearly with increases in wind speed above the threshold velocity--substantial rates of transport associated with very energetic winds would occur less frequently. The Duck beach nonrishment included sediment sourced from two borrow sites, one with a \(D_{\text{so}}\) of 0.28 mm (\(u_{t}\) = 6.8 m/s) and one of 0.36 mm (\(u_{t}\) = 7.8 m/s) (CPE, 2017). Additionally, it is noted that there is some fraction of shell hash and coarse material also present in the constructed beach/dune system. For the smaller borrow-sourced \(D_{\text{so}}\), \(u_{t}\) would be exceeded for winds with an onshore component 19.2% of the time, whereas median sands from the coarser borrow site are only mobilized 14.5% of the time. This introduction of slightly finer sediments into the system can explain both in an increase in the number of accretional events per year and the net magnitude of volumetric dune growth immediately following nonurishment. Zones that were immediately adjacent to the beach nonurishment also saw an increase in dune growth rates in the post-nourishment time period.
Beach width can similarly contribute to increased aeolian activity on beach nonurishment sites. There is a minimum distance that it takes for sediment to reach a saturated concentration, referred to as a critical fetch length that determines whether unsaturated or saturated transport occurs prior to the dune. This length scale has been shown to vary widely based on site and environmental characteristics, generally being in the range of tens to hundreds of meters (e.g., [PERSON], 2003; [PERSON] et al., 2008; [PERSON], 2010). Assuming a critical fetch length of 20 m (50 m) and utilizing the environmental time series in Figure 2, the resultant occurrence of expected saturated transport before the base of the dune (3 m) would be 13.9% (10.1%), 9.8% (3.3%), and 5.0% (1.5%) for the period from 2012 to 2020 for \(\beta_{break}\) of 0.05, 0.1, 0.15 m/m, respectively. In this example, \(\beta_{break}\) of 0.05 m/m is representative of the beach conditions shortly after notrainment (Figure 4e), whereas the average regional \(\beta_{break}\) is about 0.1 m/m. Independent of other variables (e.g., grain size variation), saturated transport to the base of the dune is likely to occur 1.42 and 3.1 times more often on the recently nonurished beach section (0.05 m/m) relative to Duck beaches with slopes of 0.1 and 0.15 m/m, respectively, based on these slopes and fetch constraints.
After the initial \(\sim\)1 yr following the beach fill construction, the data show a reduction in annual \(\Delta V_{\textit{thea}}\) in Zone 3 between 2018 and 2019 (Figure 4b). This trend is similar to observations at Nags Head from [PERSON] et al. (2018) where aeolian fluxes reduced after the first year following nonurishment. In Duck, this trend occurred despite there being more sediment on the beach (high \(V_{break}\)) relative to the pre-nourishment period (Figure 4c). While there was more overall sediment within the 1-3 m elevation contours in this timeframe in Zones 3 and 4, there was a gradual loss in \(\Delta V_{break}\) and a steeping in \(\beta_{break}\) following equilibration of the nonurishment (Figure 4e). This increase in \(\beta_{break}\) in the years following nonurishment, associated with the landward retreat of the 1 m contour, would serve to (a) decrease fetch lengths undershore winds and decrease the occurrence of saturated wind-blown transport to the dunes and (b) increase wave runup and therefore increase the occurrence of dune collision/erosion. Simultaneous to sediment losses from Zones 3 and 4 due to the diffusion of the nonurishment, the opposite effect happened on beaches adjacent to the nonurishment as \(\Delta V_{break}\) increased that may have also modified \(\beta_{break}\) and contributed to increases in \(\Delta V_{share}\).
### Conceptual Model for Managed and Unmanaged Dune Evolution
From the study findings, we propose conceptual diagrams in Figure 12 which synthesize the relationships between environmental forcings and the various morphodynamic feedbacks of the dune and beach in time and space on unmanaged, managed, and down-drift nearby unmanaged coastlines yielded from the field data. While the same physical processes apply independent of whether a system is allowed to naturally evolve or is anthropogenically modified, the time evolution of the system is heavily dependent on management actions (e.g., [PERSON] et al., 2020; [PERSON] & [PERSON], 2011). Upon the occurrence of a beach nonurishment (Time 3 in Figures 12a-12d) sediment is typically rapidly lost from the beach-berm system. Assuming a beach slope definition from the dune toe to the shoreline, the beach slopes are instantaneously reduced due to this equilibration of the beach fill placement (Figure 12d). Between times 3 and 4 in Figure 12, if large wind events occur (Figure 12b) it would be expected that aeolian transport rates and corresponding net transport to the dune would be larger on a constructed beach system relative to the same environmental forcings applied to a natural area due to these various fetch and sediment supply effects (e.g., [PERSON] et al., 2018). The data suggest that aeolian activity is enhanced not just at dunes behind the beach nonurishment, but also at adjacent stretches of coast. This is likely to happen especially in regions with large rates of longshore subaqueous sediment transport and/or strongly oblique winds, such as is common in the Outer Banks.
Over time the \(\beta_{break}\) as measured from the dune toe to the shoreline, within the constructed region may be expected to gradually increases after the initial placement, reflected by equilibration, sediment losses to the nearshore, sediment losses to the dune, and longshore transport gradients. As the \(\beta_{break}\) increases and the beach width decreases, the magnitude of net dune growth during windy periods decreases (e.g., [PERSON] et al., 2018) and the frequency of dune collision from waves increases. A wave event (Figure 12a) that caused no erosion to the dune in the constructed zone at Time 5 may be expected to have much more substantial impacts at a later time after the nonirishment (Figure 12c). Thus while the net dune growth in a constructed region may be higher between Times 3 and 4, the natural system has the possibility to have relatively higher (or similar) net dune growth between Times 3 and 7 in this simplified framework due to time evolution of the time evolution beach characteristics.
These trends are also influenced by the actual morphology of the dune system. In the case of the constructed dune system, at least as seen in this present study, there is persistent scarping and retreat during storms at the base of the constructed dune (Figure 12i). However, the same constructed dune grew volumetrically throughout the study
Figure 12.— Conceptual schematic of beach and dune changes along natural and constructed dune systems, as well as coastal stretches downdrift of constructed regions. Synthetic time series of waves (panel (a)), winds (panel (b)), dune volumes (panel (c)), and beach slopes (panel (d)) are shown, with the solid lines representing mean responses and shaded regions representing the range (where relevant). Panel (c) shows the total range of possible beach slopes on constructed beaches (red), relative to unmanaged (black) and downdrift (blue) beaches. Various times of references (1–7) are noted by vertical lines on the panels and are described in the text. A general overview of factors that change with time from the start o the beach nonjustment from Time 3 to Time 7 are shown in panel (f). A corresponding conceptual schematic of representative cross-shore bed elevation changes relative to the location of vegetation and sand fencing on unmanaged (panel (g)), partially managed (panel (h)), and recently constructed (panel (i)) dunes are also shown. Dotted lines indicate deviations from the initial bed at interannual scale.
period as the bulk of those accumulated sediments were located on the upper portion of the dune face. A trend of overall dune face steepening between the crest and toe is noted along constructed dune systems in this scenario (Figure 12i). Conversely, in this study time periods sediment along natural dune systems was preferentially accumulated lower on the lower dune face relative to the managed regions likely, as schematized in Figures 12g-12i, due to both sediment trapping by vegetation low on the dune face and/or possible contributions of marine deposition within the lower portion of the dune complex (e.g., [PERSON] et al., 2019) (e.g., Hurricane Teddy).
Consistent with a wide range of other studies ([PERSON], 2010; [PERSON] et al., 2022; [PERSON], 1988), the data here collectively indicate that beach morphology has numerous important feedbacks on transport dynamics that contribute to the ability for the dune system to accrete and/or erode. However, other physical, ecological, morphologic, and environmental factors likewise modify these transport dynamics which contributes to the broad potential trajectories of coastal geomorphic evolution (e.g., Time 7 in Figure 12).
## 5 Conclusions
Coastal foredune evolution is highly three-dimensional resulting from the complex interplay between marine, aeolian, ecological, and anthropogenic processes. On interannual timescales the dunes throughout the study site are growing despite being in the collision regime numerous times per year. Dunes on sections of coast with the lowest \(\beta_{\text{break}}\) generally grow at the highest rates, whereas net volumetric dune growth is lowest on steeper beach sections. This is due in part because these steeper sections are prone to more dune collision during storms due to slope effects on wave runup. Beach nonurishment alters the local morphology of the beach which correspondingly alters aeolian transport rates and dune erosion through slope and fetch effects. Increases in \(\Delta V_{\text{dane}}\) were found in the post-nourishment time period behind the beach nonurishment zone resulting from reduced frequency from dune collision during storms and enhanced aeolian transport associated with larger beach widths. The distribution of deposited sediments within the dune were also shown to vary between unmanaged and managed sections of coast. Specifically, a larger portion of aeolian deposition occurs at lower elevations (<5 m) on unmanaged beach sections relative to those that have been managed resulting from differences in spatial patterns in vegetation type and density, sand fencing, and/or the shape of the dune between these various stretches of coast. The collective data indicate that beach and dune management alter both the magnitude and form of dune evolution, having important implications for the resilience of dunes to future impacts and the protective services they provide to infrastructure immediately landward of the dune. Specifically, vegetation and sand fencing are both independently important for trapping patterns of wind-blown sands and thus may be used to design more resilient dunes at the storm timescale. However, regionally variable sediment supply effects due to background erosion, grain size controls on beach slope, and anthropogenic additions of sediment predominantly control the magnitude of dune volume growth or erosion and therefore have a relatively more important influence on dictating the long-term trajectory of these features.
## Data Availability Statement
All environmental data used in this work can be accessed through the FRF THREDDS server at https://chldtredds. erdc.dren.mil/. Specifically, the 17 m bulk wave statistics data can be found at [[https://chldtata.erdc.dren.mil/](https://chldtata.erdc.dren.mil/)]([https://chldtata.erdc.dren.mil/](https://chldtata.erdc.dren.mil/)) thredds/catalog/gtrf/oceanography/waves/waverider-17m/catalog.html, with data gaps provided at a 26 m buoy as described in the text that can be found at [[https://chldtata.erdc.dren.mil/thredds/catalog/gtrf/oceanography/waves/](https://chldtata.erdc.dren.mil/thredds/catalog/gtrf/oceanography/waves/)]([https://chldtata.erdc.dren.mil/thredds/catalog/gtrf/oceanography/waves/](https://chldtata.erdc.dren.mil/thredds/catalog/gtrf/oceanography/waves/)) waverider-26m/catalog.html. SWL and wind data are also available on the THREDDS server from the oceanography and meteorology folders, respectively. Data can be downloaded as netcdf files from the THREDDS server with no registration required. All CLARIS data collected by ERDC for Duck and the broader Outer Banks for the time period of interest can be found through the Geospatial Research and Data Management System (GRiD) at: [[https://grid.nga.mil/grid/](https://grid.nga.mil/grid/)]([https://grid.nga.mil/grid/](https://grid.nga.mil/grid/)). Registration is required to access GRiD, but is publicly accessible and instantly available following registration. Data can be searched geographically for the area of interest within the Outer Banks, with data listed by date of survey and listed as being collected by \"USACE.\"
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wiley/fc8d5831_0aae_4875_8817_bfba9970cf29.md | # GeoHealth
Research Article
10.1029/2021 GH000519
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 4 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
4 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA, 4 Center of Excellence in Environmental Toxicology, University of Pennsylvania, Philadelphia, PA, USA
[PERSON]
1 Department of Chemistry, Haverford College, Haverford, PA, USA, 2 Now at University of California, Los Angeles, CA, USA, 3 Department of Earth and Environmental Science, UniversitySince the Consumer Product Safety Act of 1977, later amended by the Consumer Product Safety Improvement Act of 2008, United States (U.S.) legislation has decreased lead concentration in paints and similar coatings so that it must not exceed 90 ppm (WHO, 2020). In general, however, 1978 is understood as the year in which lead-based paint was banned for residential use (Centers for Disease Control and Prevention CDC, 2020). Similarly, there have been active efforts at the local levels to curtail childhood lead poisoning ([PERSON] et al., 2017; IARC, 2006). In recent years, the Philadelphia Department of Public Health has reported an increase in the number of children screened alongside a decrease in the number of screened children with elevated blood lead levels (EBLLs). Despite this progress, however, significant numbers of children continue to be burdened by lead exposures. In 2018, the City of Philadelphia reported 1,434 newly identified children with blood lead levels (BLLs) at 5-9 \(\mu\)g/dL and 433 children with BLLs greater than 10 mg/dL (Philadelphia Department of Public Health, 2018). However, due to the CDC recently redefining the blood lead reference value from 5 to 3.5 \(\mu\)g/dL or greater (CDC, 2021, 2021), we expect the number of identified children with EBLLs to increase.
The majority of the City of Philadelphia is considered at risk for lead hazards from lead paint but the issue of childhood lead poisoning is highly racist and classist ([PERSON] and [PERSON], 2007). In five zip codes within low-income communities of color in North and West Philadelphia, one in 15 children screened has EBLLs (PCCY, 2018). Another study found that children in parts of North Philadelphia, where the population is predominantly Black, were 2-2.5 times more likely to be lead poisoned than in the City of Philadelphia as a whole ([PERSON] et al., 2002). These studies highlight the disproportionate burden from pollutants seen in environmental justice communities, defined by the Pennsylvania Department of Environmental Protection (PA-DEP) as having \(\geq\)20% of the population below the poverty level and/or \(\geq\) 30% minority population, as is the case in parts of North Philadelphia (PA-DEP, 2021; [PERSON] and [PERSON], 2019). At the national level, Black children experience 2.8 times higher odds of having BLLs \(>\) 5 \(\mu\)g/dL even when compared to low-income white and Latine populations, along with a greater likelihood of being exposed to lead ([PERSON] et al., 2020). In fact, according to [PERSON] et al. (2020), being Black is the second strongest predictor for EBLLs aside from housing built in 1950. A combination of historically racist redlining, poor housing quality, environmental racism, current inequitable enforcement of regulations, and poor healthcare access have compounded to create the current disparity in childhood lead poisoning ([PERSON] and [PERSON], 2007; [PERSON] et al., 2020).
Considering historic and current lead and lead-contaminated dust production in Philadelphia, there are five major sources or processes that can continue to generate and disperse lead particles or that persist as lead residues in the environment. The five major lead sources (Figure S1 in the Supporting Information S1) are historic smellers, leaded gasoline, lead paint, demolitions, and lead pipes. Leaded gasoline was widely used in the U.S. starting in the 1920s until, as for paint, legislation mandated a significant decrease in lead concentration in 1978; however, during its use, it created large amounts of ambient lead (IARC, 2006), which is persistent and can still contribute significantly to the lead burden in cities ([PERSON] et al., 2021)[PERSON] Lead paint was both produced and used extensively in homes and on roads within Philadelphia from the late 1800s until 1978 ([PERSON] et al., 2017; [PERSON] and [PERSON], 1998). Previous work has found high correlations between housing code violations, old property, and lead hazards within the home due to chipping lead paint and lead-contaminated dust ([PERSON] et al.[PERSON] 2017; HUD, 2002; [PERSON] et al., 2015; [PERSON] and [PERSON], 2006). Research completed in Philadelphia identified floor dust at household entryways as an important indicator of lead exposure in children ([PERSON] et al., 2019). Studies have also found an increase in lead-contaminated dust and lead-in-soil near demolition and smeller sites ([PERSON] et al., 2003; [PERSON], 2019; [PERSON] et al., 2015; [PERSON] et al., 2007; [PERSON] and [PERSON], 1995; [PERSON], 2015; West Chester University, 2015)[PERSON] There is also evidence of significant lead-contaminated dust accumulation on ceilings and roofs that, when disturbed during demolition, could resuspued hazardous lead-contaminated particles into the air, nearby homes, streets, and soils ([PERSON] and [PERSON], 2005)[PERSON] Regarding lead drinking water pipes, also known as lead service lines, most cities in the U.S. stopped the production of such pipes in 1920, but Philadelphia was one of the few cities that continued installing and preserving lead pipes until 1950 ([PERSON], 2008). For this reason, it is believed that housing units built before 1950 are more likely to have lead pipes, and therefore produce lead hazards.
With the exception of the lead pipes, the major sources of lead generate and disperse lead-containing particles in air from where they settle and accumulate in soil or on other surfaces (e.g., roads, floors), either directly or subsequent to chemical and physical alteration. Because lead strongly adsorbs onto soil, it is a persistent environmental pollutant, which creates an ongoing risk of exposure, particularly in soils that have not been remediated([PERSON] et al., 2017; [PERSON], 2015; West Chester University, 2015). Soil is therefore the primary outdoor environmental medium to sample and analyze to identify lead presence and risk ([PERSON] and [PERSON], 1998)[PERSON]
The approach in this study was developed with the goal of addressing existing health disparities in childhood lead poisoning. In order to do so, this work begins by investigating which lead sources continue to be lead-risk factors in Philadelphia. Second, we verify which lead-risk factors have the greatest impact on childhood lead poisoning in Philadelphia. Third, we determine which census tracts are at the highest risk for childhood lead poisoning, and identify sites for future soil sampling and analysis. In addition to lead sources and demographic data, evidence of lead such as lead-in-soil data, EBLLs, and brownfield/land recycled sites are considered for lead-risk analysis. This study improves understanding of lead sources and spatial risk of poisoning in Philadelphia so that public health policy can provide comprehensive solutions aimed at preventing childhood lead poisoning, especially for at-risk populations.
## 2 Materials and Methods
### Study Area
The study area, broadly defined as West, North, and Upper North Philadelphia, was based on the results of a previous investigation, which analyzed lead risk at the zip code level within Philadelphia ([PERSON] et al., 2021). Lead risk at the zip code level was determined by mapping various lead-risk factors, including owner-occupied units, renter-occupied units, units built before 1980, demolitions, minority population (defined as racial and ethnic minorities within the United States), Black population, children in poverty, median income, EBLLs in children, number of smellers, and lead-in-soil data ([PERSON] et al., 2021). A housing unit, as defined by the Census Bureau, is a house, an apartment, a group of rooms, or a single room intended to serve as a living quarter. Demolitions, as defined by OpenDataPhilly (2021), are all types of demolitions that are legally occurring throughout the city. The zip codes with the highest risk, that is, a high number of simultaneous lead-risk factors, as identified by [PERSON] et al. (2021) were zip codes 19121, 19125, 19132, 19133, 19134, 19138, 19140, 19141, 19143, and 19144 (Figure S2 in the Supporting Information S1; see also [PERSON] et al., 2021). Zip codes 19134 and 19125, however, were omitted from being a part of the area investigated here due to significant remediation work and research carried out in this region.
For the study presented here, we evaluated ninety-four census tracts (Figure S3 in the Supporting Information S1), all of which are located within each of the high-lead-risk zip codes (Table S1 and Figure S3 in the Supporting Information S1). Census tracts 9800, 9801, 9805, and 9809, also located in the high-lead-risk zip codes, were removed from the analysis as no data were found for these census tracts for various lead-risk factors analyzed. Census tracts 71 and 172 are represented as a single census tract instead of two separate census tracts (e.g., 71.01 and 71.02 designated as 71) in the following analysis and maps, because data were represented in both forms across the sources of data, likely due to data being from different years and therefore census tract borders changing.
### Lead-Risk Assessment
Thirteen lead-risk factors (Table 1) were evaluated to determine lead-exposure risk within the region of study. The considered lead-risk factors fall into three categories: (a) evidence of lead or lead exposure; (b) potential sources of lead; and (c) demographic risk factors as established by the CDC (CDC, 2019). Although lead exposure from
\begin{table}
\begin{tabular}{l c} \hline Lead-risk categories & Lead-risk factors \\ \hline Evidence of Lead or Lead Exposure & Elevated lead-in-Soil Data, EBLLs in Children, Brownfield/Land Recycled sites \\ Potential Lead Sources & Housing Code Violations, Critical Housing Code Violations, Lead Violations, \\ Demolitions, Demolitions due to a Housing Code Violation, Properties Built Before 1980, Properties Built Before 1950, Smellers and manufacturing sites \\ Demographics previously associated with Lead-risk Factors & Low Income; Minority Population \\ \hline \end{tabular}
\end{table}
Table 1: Lead-Risk Categories and the Corresponding Lead-Risk Factors Explored in This Studyall sources is cumulative, exposure sources vary for individuals. Our study is not designed to explore the relative contribution of lead exposure to individuals. Our grouping of risk factors is not intended to imply parity in their relative contribution, but rather represents a quantification of cumulative sources that combine to increase the risk of lead exposure.
Despite the CDC's recently lowered blood lead reference of 3.5 \(\mu\)g/dL, this research reports and analyzes lead risk using the previous reference level of 5 \(\mu\)g/dL due to the availability of data at the time. Due to a lack of information regarding the location of lead pipes in Philadelphia, housing built before 1950 is used here as an indicator of the presence of lead pipes within a home. Because of conflicting results, renter-occupied units were not included as a lead-risk factor in our assessment of the lead risk, as described in Section 4.1 of this paper. However, the renter- and owner-occupied housing data were analyzed since renter-occupied housing units are typically regarded as a lead-risk factor (CDC, 2019). Although leaded gasoline was identified as a lead source in Philadelphia considering the thousands of renter ions of lead estimated to have been deposited in Philadelphia soils, no data were found to analyze at the census tract level, and therefore our research did not include this lead source in its analysis. Critical housing code violations are factors that either accelerate paint deterioration or are linked to or produce lead-paint hazards. Housing code violations labeled as critical housing code violations in this research are: lack of rental property license, lacking or poor debris removal, hazards due to poor plumbing system, poor ventilation, partial collapse of roof/wall, deterioration of roof/wall, or presence of cracked walls, and hazards due to unsafe interior or presence of lead. A lack of rental property license is linked to higher likelihood of lead hazards within the home (HUD, 2002). Meanwhile, poor ventilation and leaks from the plumbing system accelerate the deterioration of paint, whereas deterioration, cracking, and collapsing of walls produce lead paint chips and debris. For each census tract, the median lead-in-soil concentration was calculated. Then census tracts at highest risk for lead were identified by ranking census tracts, within each lead-risk factor, from highest to lowest risk. Lastly, for simplicity smelter and manufacturing sites where lead smelting was also performed will be solely referred to as smelters for the remainder of the paper.
### Data Collection
Data for the 13 considered lead-risk factors (Table 1) were collected from various sources. Blood lead levels, demolition, and housing code violation data are collected by the City of Philadelphia and were retrieved from OpenDataPhilly (OpenDataPhilly, 2021). Lead-risk factors such as children in poverty, age of property, median income, and minority population were collected by the U.S Census Bureau and taken from the 2015-2019 American Community Survey (U.S. Census Bureau, 2020). Because the American Community Survey only provides housing data by 10-year increments, this research will be evaluating homes built before 1980, instead of 1978, to assess the likely presence of lead paint. The soil data were collected by the U.S. Environmental Protection Agency (U.S. EPA) and through the University of Pennsylvania's Academically Based Community Service (ABCS) Course on Lead and by graduate and undergraduate students working through The Community Engagement Core of Penn Medicines Center of Excellence in Environmental Toxicology (CEET). Many of the soil samples were collected by residents, as organized by the EPA, the ATSDR, universities, and farmer/gardner groups, who generally collected five samples from the top 0-15 cm of soil in their yards, and recorded the nearest intersection for the sake of identity protection. Lead concentrations were then determined using portable X-ray fluorescence (XRF) spectrometers which included: Innov-X 4000 SL; NITON XL792 YW; Innov-X Delta; Olympus Delta Professional with 40 kV Tube and SDD detector custom configured with modes for soil; Thermo Fisher Scientific XL 3t 600. In the case of the ABCS course and CEET sampling, soils were collected primarily by students between 2015 and 2020, where students were instructed to collect 5 samples from the top \(\sim\)1.5 cm of soil. Again, portable XRF spectrometers were used to determine the lead concentration. Smelter and manufacturing site data were retrieved from both the EPA's Superfund Program Database and the paper Discovering Unrecognized Lead-Smelting Sites by Historical Methods ([PERSON] et al., 2001; U.S. EPA, 2016). Brownfield and land recycled sites were taken from the PA-DEP website (PA-DEP, 2021a, 2021b)
### Mapping and Statistical Analysis
Maps produced in this analysis used the geographic entity codes and coordination values for Philadelphia census tracts as taken from the U.S. Census Bureau's (2020) Philadelphia census tract level shapefile. The lead-risk factors were then mapped on top of the shapefiles using RStudio Version 1.3.1093 (R Core Team, 2013). Whiteareas within the maps are census tracts that were omitted (e.g., 9800, 9801, 9805, and 9809) or had inconsistencies in labeling within the data set. Gray areas within the maps are census tracts where data were unavailable for the specific factor mapped. A statistical online resource, \"Social Science Statistics\", was used for the Spearman correlation analysis within this study (Social Science Statistics, 2018). All correlations discussed in this research are statistically significant (\(\mu<0.05\)). Statistically non-significant correlations are available in the data repository ([PERSON] et al., 2021).
## 3 Results
### Demographic Lead-Risk Factors
Demographic lead-risk factors are community characteristics that, when present within a region, indicate a higher likelihood that the community is at risk for lead poisoning. The demographic lead-risk factors evaluated in this study are based on the CDC's designated at-risk populations for childhood lead poisoning (CDC, 2019) and include low-income households and communities of color, especially non-Latine Black communities. In addition, although renter-occupied units were not included as a lead-risk factor for the census tract level lead-risk assessment, we still investigated the renter- and owner-occupied housing data, because according to the CDC (CDC, 2019), renter-occupied housing units are typically regarded as a lead-risk factor.
#### 3.1.1 Renter- and Owner-Occupied Housing Units
Approximately half of the census tracts (5094) evaluated within this study had nearly equal representation of owner-occupied and renter-occupied housing units within their populations (Figure 1a). Sixteen of the evaluated census tracts (161, 171, 235, 248, 263.02, 264, 265, 266, 267, 270, 277, 280, 281, 288, 289, and 389) had more than half of housing units owner-occupied (Figure S4 in the Supporting Information S1), whereas the remaining twenty-eight census tracts (69, 77, 78, 79, 86.01, 139, 140, 147, 148, 153, 163, 164, 165, 166, 170, 173, 176.02, 199, 201.01, 206, 239, 240, 241, 242, 245, 246, 268, and 287) had more than half of housing units renter-occupied.
Figure 1: (a) Map illustrating the percentage of renter-occupied units across the census tracts analyzed; (b) Comparison of Spearman correlation coefficients for renter-occupied and owner-occupied units across various lead-risk factors. The inset shows a map of Philadelphia with all the high-risk zip codes, that is, the region of focus in this study, highlighted in gray. Because the inset outlines zip codes rather than census tracts, the map and the inset do not perfectly align.
#### 3.1.2 Black and Minority Population
A majority of the census tracts (76/94) evaluated were majority Black communities (Figure S5 in the Supporting Information S1). In two of the ninety-four census tracts (67 and 77), the majority of the population belongs to a non-Black minority (Figure S6 in the Supporting Information S1). The remaining sixteen census tracts (67, 77, 161, 162, 163, 164, 175, 176.01, 176.02, 195.01, 197, 198, 199, 206, 235, 236, 287, 288, 288, 383, and 389) have a white majority and are located along the border between North Philadelphia and the River Wards (see Figure S3 in the Supporting Information S1), a section of Philadelphia that is undergoing gentrification ([PERSON], 2016; Lubrano & Gammage, 2019).
#### 3.1.3 Median Income
A majority of the census tracts (62/92) for which median income data were available are below the U.S poverty line, which is defined as a median family income of S26,200/year for a family of four (Figure S7 in the Supporting Information S1) (U.S. Census Bureau, 2021). Thirty-one of those census tracts had median incomes below $20,000/year, and five of those census tracts (148, 151.01 164, 176.01, and 241) are considered in deep poverty, that is, with a median family income of $13,100/year for a family of four (U.S. Census Bureau, 2021). Only four census tracts (235, 236, 264, 270) have median incomes greater than $40,000/year, with two of these census tracts above $67,000/year (235 and 236). Three of the four census tracts with median incomes greater than $40,000/year are among the census tracts with more than half of housing units owner-occupied (Figure S4 in the Supporting Information S1). The two census tracts with exceptionally high median incomes (235 and 236) also have a majority white population (Figure S6 in the Supporting Information S1).
### Properties Built Before 1980 and 1950
A majority (61/94) of the census tracts evaluated have 90% of housing units built before 1980 (Figure S8 in the Supporting Information S1). In two of the census tracts (248 and 264), 100% of housing units were built before 1980. Within these 61 census tracts, there are 113,597 pre-1980 housing units, which thus could pose a risk for lead hazards. Only four census tracts have less than 63% of housing units built before 1980, and these neighboring tracts are located along the border between North Philadelphia and Lower North Philadelphia.
Of the census tracts studied, only two census tracts (389 and 289) had more than 30% of housing units built before 1950 (Figure S9 in the Supporting Information S1). Fourteen census tracts (69, 70, 171, 200, 263.02, 264, 265, 276, 280, 281, 282, 288, 289, and 389) had at least 20% of housing units built before 1950.
### Housing Code Violations
Between 2007 and 2020, the City of Philadelphia reported 499,435 housing code violations across the census tracts analyzed in this study. A majority of these census tracts are clustered in North Philadelphia (Figures S10 and S11 in the Supporting Information S1), primarily the Strawberry Mansion area (see Figure S3 in the Supporting Information S1). Of the housing code violations reported, 6085 (1%) are critical housing code violations (Figure S12 in the Supporting Information S1). Twenty-eight of these 6085 critical housing code violations, spread across 21 census tracts (65, 72, 74, 80, 82, 83, 164, 165, 169, 175, 176, 197, 198, 199, 200, 201, 240, 243, 282, 283, and 284; Figure S12 in the Supporting Information S1), are lead-hazard violations. Licenses and Inspections (L&I), Philadelphia's department responsible for the safety and livability of housing units, has had a long history of poor regulation and inefficiency due to chronic understiffing and inadequate funding to meet public demand for essential services (Howell & Lazzara, 2014; [PERSON], 2019). One survey of Philadelphia tenants and landlords even indicated there were loopholes to building and development regulations that allow landlords to evade Philadelphia housing standards ([PERSON] & Lazzara, 2014). For this reason, lead-hazard violations are likely underrepresented. Sixteen census tracts (71, 74, 137, 149, 151, 152, 164, 165, 167, 168, 169, 172, 175, 201, 265) had over 100 critical housing code violations (Figure S12 in the Supporting Information S1), whereas seven (71, 137, 152, 161, 169.01, 169.02, and 172) had more than 10,000 housing code violations within the 13-year time period reported.
### Demolitions
Between 2007 and 2020, the City of Philadelphia reported 5233 demolitions within the region studied in this research, and 3792 (73%) of those demolitions were due to housing code violations. Of the 94 census tracts analyzed, only one census tract (267) had no demolitions within the timeframe. Sixteen census tracts (169.02, 167.01, 169.01, 168, 137, 165, 149, 152, 172.01, 138, 161, 153, 175, 164, 174, and 151.01) had 100 or more demolitions (Figure S13 in the Supporting Information S1). Three of the census tracts (169.02, 167.01, and 169.01) had over 200 demolitions, with 90% of the demolitions as a result of housing code violations; these three tracts are geographically located alongside each other in the Strawberry Mansion area (Figure S14 in the Supporting Information S1).
### Historic Smelters
Of the 42 historic smelters known to date within Philadelphia, six are in the region of study ([PERSON] et al., 2001; U.S. EPA, 2016; West Chester University, 2015). The six smelters are within 5 census tracts (139, 152, 161, 173, and 241), with census tract 161 having two smelters. Four of the historic smelters are secondary smelters: A. Perez & Son Division of Abrams Metal Co. Lead Smelter, Jos. Rosenthal's Sons Smelter, American Alloys Co.; and Electric Storage Battery. The other two, an unnamed smelter within census tract 161 and American Alloys Co., were likely primary smelters, although not confirmed in the smelter source materials ([PERSON] et al., 2001; U.S. EPA, 2016).
### Soil Samples
Within the region of interest, there are 570 lead-in-soil data points documented (Figures S15 and S16 in the Supporting Information S1), of which 155 (27%) soil-sampling points record hazardous soil lead levels, as defined by the EPA for bare residential soils where children play, that is, with lead contents of 400 ppm or greater ([PERSON] & Farago, 1995). Some soil-sampling points exhibit extremely high lead contents, with values ranging from 1000 to 5341 ppm. A majority of the lead-in-soil data are concentrated within 10 census tracts (71, 72, 73, 74, 78, 79, 80, 202, 239, and 244) in West Philadelphia, where a total of 381 (67%) data points are located (Figure S15 in the Supporting Information S1). For census tract 74 alone, there are 86 soil data points. For 34 of the 94 census tracts (36%), there are no soil data available at all, indicating a significant gap within the data set (Figure S16 in the Supporting Information S1).
### Brownfield and Land Recycled Sites
Within the region of study, there were no brownfield sites documented. However, there were 23 land recycled sites within 20 census tracts (71.01, 73, 74, 78, 80, 137.01, 139, 148, 161, 163, 165, 166, 169.01, 170, 171, 175, 176.01, 203, 240, and 287; Figure S17 in the Supporting Information S1). These sites were cleaned up between 2003 and 2020. In nine of the census tracts, the contaminant identified was leaded gasoline, indicating residuals from leaded gasoline as a lead-hazard source within Philadelphia. The remaining fourteen land recycled sites had contaminants generically labeled as \"lead contaminants\".
Twenty-one of the 23 land recycled sites had lead-contaminated soil, eight of those sites had lead-contaminated groundwater, whereas two sites solely had lead-contaminated groundwater. A majority of the land recycled sites are located in census tracts with none to very low concentrations of hazardous soil lead levels (Figure S18 in the Supporting Information S1). In three of the land recycled sites (78, 166, and 175), activities on and use of the sites were limited due to severe contamination even after the clean-up.
### Elevated Blood Lead Levels
In 2015, a total of 70,750 children were screened for lead in blood within the census tracts analyzed here. Of the screened children, 4059 (6%) were reported to have EBLLs, that is, a BLL \(\geq\)5 Hg/dL. However, the number of children screened ranged greatly among the studied census tracts, with some census tracts reporting only 30 children screened, whereas others reported 685. Sixteen census tracts (77, 86, 148, 153, 162, 166, 200, 204, 205, 206, 241, 248, 264, 269, 270, 287, and 389) screened less than 50% of children 0-5 years old. The percentage ofscreened children with EBLLs ranges among census tracts from 3.4% to 17.6%, with census tract 200 having the highest percentage. Thirty-one census tracts (200, 283, 204, 169.01, 166, 203, 169.02, 151.01, 202, 238, 167.01, 149, 245, 201.01, 172.01, 247, 242, 173, 172.02, 284, 171, 168, 74, 244, 174, 246, 72, 138, 252, 282, and 281) had 10% or more children screened with EBLLs (Figure S19 in the Supporting Information S1).
### Census Tracts With the Highest Lead Risk
The census tracts with the highest evidence of lead risk are 175 and 172, which are also environmental justice areas. These two census tracts were ranked high risk in eight of the thirteen lead-risk factors evaluated (Figure S20 in the Supporting Information S1). It is important to note that the census tracts most frequently appearing as high risk are concentrated within the Strawberry Mansion area (Figure S3 in the Supporting Information S1), especially if including the census tracts considered high risk in seven of the 13 lead risk factor variables (Figure S20 in the Supporting Information S1).
## 4 Discussion
### Risks of Lead Poisoning Associated With Owner-Occupied Housing
The CDC states that a high percentage of renter-occupied units within a community is a lead-risk indicator (CDC, 2019). This relationship exists because rental units, especially low-income housing, tend to have more health code and housing code violations than owner-occupied homes ([PERSON] and [PERSON], 2014; [PERSON] and [PERSON], 2002; [PERSON], 2019). This issue can be compounded by a lack of sociopolitical capital within low-income neighborhoods ([PERSON] et al., 2018). In comparison, homeowners, in most cities, are in a higher income class and therefore are monetarily in a better position to preserve their homes.
Philadelphia, however, has had a historically high homeownership rate due to housing policy in the nineteenth and early twentieth centuries, which promoted the building of affordable rowhomes ([PERSON], 2019). This policy resulted in a large mass of old housing stock so that 88% of housing in Philadelphia was built before 1980. The impact of this housing policy is visible in Figure 0(a), where in many census tracts, approximately half of the housing units are owner-occupied, despite only four census tracts having median incomes greater than $40,000/year (Figure S7 in the Supporting Information S1). Significantly, eight of the fourteen census tracts (171, 263.02, 265, 280, 281, 288, 289, and 389) with at least 20% of housing built before 1950 (Figure S9 in the Supporting Information S1) also coincide with the 16 census tracts with more than 50% of the housing units owner-occupied (Figure S4 in the Supporting Information S1). These findings suggest a high risk of lead pipes within owner-occupied housing units. Owner-occupied housing and properties built before 1980 show the highest correlation among the lead-risk factors evaluated in this research (\(R=0.79\); Figure 0(b) and Table S2 in the Supporting Information S1) and present a nearly identical risk of EBLLs in contrast to what has previously been reported in other cities. This result documents a unique housing lead-risk situation in Philadelphia.
This unique situation is most evident when comparing the correlation values between renter-occupied and owner-occupied housing units to lead-risk factors (Figure 0(b) and Table S2 in the Supporting Information S1). Census tracts with a high percentage of owner-occupied units have higher likelihoods of also having a higher percentage of pre-1950 buildings and minority populations than census tracts with many renter-occupied units (Figure 1). Older buildings and minority populations are both lead-risk factors established by the CDC, which are typically associated with renter-occupied housing (CDC, 2019). There is also a slightly higher correlation between owner-occupied units and other lead-risk factors, such as housing code violations, than there are with renter-occupied units (Figure 0(b)).
Housing code violations within areas with a high percentage of owner-occupied units are likely underrepresented since the City of Philadelphia requires rental properties to be inspected for a rental property license, but this level of regulation and inspection does not exist for owner-occupied housing. Based on these results, Philadelphia's lead policy and support should be reimagined to increase both attention and resources to homeowners alongside current efforts to support renters. Specifically, census tracts 171, 263.02, 265, 280, 281, 288, 289, and 389 should be further supported as they simultaneously have a larger homeowner population and a higher number of old housing units.
### Demolitions as a Critical Risk Factor for Childhood Lead Poisoning
Demolitions affect mostly buildings constructed before 1980 which likely contain lead paint. Therefore, demolitions are a risk indicator of EBLLs in children, likely due to the release of lead-contaminated dust from paint (Figure 2). Lead-contaminated dust from demolitions that has settled on streets, that is, road dust, or soil can be tracked or blown into nearby homes, posing a threat for the residents, especially children ([PERSON] et al., 2003; [PERSON] et al., 2007). Therefore, demolition sites and their radius of impact, defined as the 122-m radial range where risk of lead exposure due to demolitions is possible (e.g., Lauer, 2019), were mapped alongside EBLLs. Our analysis revealed that demolition points and radius of impact overlap in part with census tracts where many children have EBLLs, marked by the orange colors (Figure 2). It is of note that there exist some areas with a low percentage of children with EBLLs yet a high number of demolitions, but the association between demolitions and EBLLs is further validated by the relatively strong correlation between demolitions and the percent of children with EBLLs (\(R=0.55\); Table S2 in the Supporting Information S1) and more clearly visible when demolitions are superimposed onto a map displaying the absolute number of children with EBLLs (Figure S21 in the Supporting Information S1). In addition, census tracts, within Figure 2, with a low percentage of children with EBLLs yet a high number of demolitions also overlap with census tracts that have the lowest percentage of properties built before 1980 (Figure S8 in the Supporting Information S1) and have fewer housing code violations (Figure S10 in the Supporting Information S1) compared to those with a high percentage of children with EBLLs and a high number of demolitions. Our result is critical considering previous studies found that exposure to multiple demolitions within a residential block was associated with a significant increase in BLLs within children and with cumulative increases in inhalation of ambient lead ([PERSON] et al., 2003; [PERSON] et al., 2007). Thus, our study in combination with previous evidence (Figure 2), supports a clear link between EBLLs and the demolition of old buildings, especially in North Philadelphia (Figure S22 in the Supporting Information S1). The data, therefore, establish that the demolitions of buildings built prior to 1980 within West and North Philadelphia are a critical risk factor for childhood lead poisoning.
Given the findings in this investigation, demolitions in Philadelphia need further regulation to minimize the risk of lead-contaminated dust exposure. To be effective, however, such regulations must be enforced, which requires inspections for compliance. The \"East Baltimore Protocol\" is a strict protocol for demolition, which mandates, among other procedures, wetting the structure before and during demolition, along with wetting debris before
Figure 2: (a) Map presenting the percent of children with EBLLs by census tract, as collected in 2015 by the City of Philadelphia; (b) Map displaying each housing unit demolished (red dot) from 2007 to 2020 and each demolished unit’s 122-m radius of impact (red circle) superimposed onto the EBLL map shown in (a). The EBLL legend applies to both maps.
covering and transporting it. This protocol was found to generate 56 times less lead-contaminated dust in nearby areas during demolition as well as during debris removal, due to stricter regulation compared to dry demolition ([PERSON], 2019). Philadelphia's demolition standard, however, does not require wetting of the structure before or during demolition, but merely recommends applying water or an approved dust suppressant to minimize dust. These recommendations at most reduce lead-contaminated dust production by 2.6 times ([PERSON], 2019). The City of Philadelphia should therefore make demolition requirements more stringent, for example, by applying those contained in the \"East Baltimore Protocol\". Following this protocol is more time-consuming and therefore more costly. However, its significant reduction in lead-contaminated dust generation, combined with the evidence from our study, demonstrates its necessity in Philadelphia. Nevertheless, even when following the \"East Baltimore Protocol\", the danger of lead-contaminated dust is present. For this reason, it is important to prioritize the maintenance and rehabilitation of buildings within Philadelphia, instead of demolition. It has been shown that rehabilitation and preservation of buildings improve economic, social, and emotional outcomes of residents, whereas demolitions often accelerate gentrification and the displacement of marginalized communities ([PERSON], 2019). Further analysis should compare the lead risk associated with the East Baltimore Protocol versus rehabilitation of structures for those residents who continue to live within the building and surrounding area.
### Lead Paint and Demolitions Are Critical Lead-Source Emissions for Childhood Lead Poisoning
Housing code violations and demolitions were found to be correlated in this study (\(R=0.74\), Table S2 in the Supporting Information S1). Considering that housing code violations are associated with paint deterioration and the existence of other lead-paint hazards, a higher number of housing code violations increases the likelihood of lead hazards present in a home (HUD, 2002). Since housing code violations also correlate with demolitions, it is likely that demolitions in Philadelphia are releasing and redistributing lead-contaminated dust. Lead-contaminated dust accumulation on ceilings and roofs is especially relevant in older and poorly maintained housing as lead-contaminated particles have settled during earlier, more industrial periods and were able to enter and remain within cracks and crevices of the structures ([PERSON], 2005). Therefore, a high number of housing code violations would indicate a higher risk of lead-contaminated dust from ceilings and roofs. The high correlation value between census tracts with a high percentage of children who have EBBLs and census tracts with a high number of housing code violations (\(R=0.68\); Figure S23 and S24 in the Supporting Information S1) corroborates the conclusion that demolition of units with housing code violations produce lead-contaminated dust hazards. Based on the correlation values there appears to be a compelling relationship between housing code violations, demolitions, and the number of children with EBLLs. This relationship strongly suggests that a major cause of EBLLs in West and North Philadelphia is the ingestion of lead-paint dust and other forms of lead-contaminated dust in housing, in agreement with City reports and prior studies ([PERSON] et al., 2017; Philadelphia Department of Public Health, 2018; [PERSON] & [PERSON], 2006). Therefore, these two lead-risk factors are shown together in Figures 3 and S25 to identify the areas of highest lead risk due to lead paint and dust. Census tracts with the highest lead risk due to lead paint deterioration and dust are: 65, 74, 85, 137, 138, 140, 149, 151.01, 152, 153, 164, 165, 167.01, 168, 169.01, 169.01, 169.02, 173, 174, 175, 201.01, 202 (deep purple in Figure 3). Many of these census tracts border each other, creating a large section in North Philadelphia that is at high risk of lead poisoning due to contaminated dust from lead paint and other sources, such as soil ([PERSON] et al., 2017). Given that contaminated dusts from lead paint and other sources, such as soil, are regarded as a major source of childhood lead poisoning, housing within these census tracts, and especially this section of North Philadelphia, needs to be investigated for lead hazards and remediated as soon as possible to decrease childhood lead poisoning (see also [PERSON] et al., 2007; [PERSON], 2006). This would require redirection of funding,
Figure 3: A bivariate map that presents census tracts where demolitions and housing code violations are the most prevalent, illustrated by the deep purple color. Census tracts with a high number of demolitions are represented by increasingly darker pink, whereas census tracts with a high number of housing code violations are represented by increasingly darker blues. Census tracts with few demolitions and housing code violations are represented by a light laverder.
greater staffing and more stringent regulation efforts on the part of L&I to inspect renter-occupied and in addition owner-occupied housing (HUD, 2002).
### Low-Income Housing is at Greater Risk for Housing Code Violations and Demolitions
Median income is negatively correlated with demolitions (\(R=-0.65\), Table S2 in the Supporting Information S1). This correlation suggests that lower-income communities are more likely to be at risk of lead exposure through the demolition of buildings. Our finding is in line with demolition practices generally, as substandard housing within U.S. cities is demolished at higher rates than other housing units ([PERSON] et al., 2007). Within Philadelphia's Department of L&I, the demolition of housing units with hazards is standard practice; due to a lack of funding, when a housing unit exhibits hazards, L&I tends to demolish the building instead of repairing it, because, if at a later date the building is responsible for an injury and/or health impact, the liability would be costly ([PERSON], 2019). Median income is also negatively correlated with demolitions due to housing code violations (\(R=-0.65\); Table S2 in the Supporting Information S1). These results suggest that demolitions occur at higher rates within low-income communities because units are more likely to have housing code violations. Therefore, our results indicate that low-income housing is more likely to have housing code violations, which are associated with increased risk of childhood lead poisoning, and result in demolitions, which in turn elevate the risk of lead poisoning. This is an example of environmental injustice where low-income communities of color experience the disparity of elevated lead exposure in part due to L&I practice of enhanced demolition.
### Racial Disparities in Housing Standards and Risk of Lead Exposure
Predominantly Black communities are correlated with EBLLs, housing code violations, and properties built before both 1980 and 1990 (\(R=0.53\), 0.50, 0.66, and 0.54, respectively; see Table S2 and Figures S26, S27, S28, and S29 in the Supporting Information S1). These findings point to significant racial disparities in housing standards and risk of exposure to lead. Our results indicate that Black children are at the highest risk for lead poisoning within West and North Philadelphia. These results are consistent with the CDC's conclusion that non-Latine Black children and communities are at highest risk for lead poisoning and the associated social impacts (CDC, 2019). For this reason, greater support needs to be provided for schools and health facilities in predominantly Black neighborhoods within Philadelphia. These efforts should be done in addition to primary prevention of lead poisoning by providing financial support toward household rehabilitation and inspection for low-income and lower-middle-class Black families in Philadelphia.
### Potential Relationship Between Historical Smelters and Childhood Lead Poisoning
Due to poor regulation, lack of health-informed policy, and economic interests, the emissions from U.S. smelters were not monitored or restricted in the early nineteen hundreds, limiting our ability to evaluate past deposition and present lead impact due to lead's persistence in soil from smeller fallout ([PERSON], 2015). Smelter emissions can travel large distances from the site of smelting, creating a significant radius of impact, which must be considered when evaluating soil lead levels near smelter sites ([PERSON] & [PERSON], 1995). Based on a literature review that compiled soil studies around smelters, the greatest distance from a smelter with hazardous soil lead levels, as defined by the EPA at 400 ppm, is 500 m ([PERSON] & [PERSON], 1995).
Historic smeller sites along with their 500-m radius of impact were superimposed onto a map displaying Philadelphia's 2015 reported data on children's EBLLs by census tract (Figure 4a) (OpenDataPhilly, 2021). Since there are only six smelters in the studied area and only limited Pb-in-soil data are available for these locations, it is difficult to reach sound conclusions regarding the contribution of lead-in-soil from smelters. The available data for the soils close to these smelters, however, suggest that further data should be collected. From the data available we could not identify a relationship between smelters and children's EBLLs within the census tracts analyzed. Only two smelters have a radius of impact that seems to overlap with census tracts in which more than 10% of children have EBLLs. This may mean that historical smelters are not as critical a lead-risk factor to consider when evaluating areas of high lead risk in Philadelphia, but additional data are required to support this preliminary conclusion. Notably, the majority of the 42 known former smelters in Philadelphia were located in the Riverwards (see Figure S3 in the Supporting Information S1) rather than in North and West Philadelphia (see [PERSON] et al., 2021). Despite the paucity of lead-in-soil data points, hazardous soil lead levels were observedwithin the smelters' radius of impact in each of the smelter-hosting census tracts, for which soil data were available (Figure 4b).
None of the brownfield and land recycled sites in the Philadelphia areas studied here are co-located with historical smelter locations, although three sites do appear within the radii of impact. Based on this finding, it seems that these smelter sites have not been remediated and are likely to have lead contamination, especially considering the immobility of lead within soil. Previous studies within the Kensington neighborhood of Philadelphia reported that soil lead levels were significantly higher near historical smelters than at Philadelphia locations where no smelters previously existed ([PERSON] et al., 2015). It may be that other, more local forms of remediation, which are not documented, have been completed, such as gardens; however, since this is unverified there is a need for greater sampling of soil within these smelter-hosting census tracts and their radii of impact.
### Increased Efforts to Sample Soil Are Needed in North Philadelphia
The emissions from lead sources evaluated in this study primarily settle on soil. Lead-contaminated dust and paint may also settle on roads, porches, and inside homes, but these sites are often inaccessible for sampling. Bodies of water may also be a final sink for lead particulates, but they are not relevant in the area examined in our study. As such, soil becomes the most accessible and relevant environmental medium to investigate for the identification of sites with a high lead risk in need of preventive action. Previous studies have even used soil-Pb data to predict spatial variation in BLLs ([PERSON] et al., 2016) and reported that the resuspension of lead-in-soil explains the spikes in BLLs during the summer season ([PERSON] et al., 2017; [PERSON] et al., 2013). Despite resounding evidence for the existence of a relationship between BLLs and soil-Pb levels ([PERSON] et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2016; [PERSON] et al., 2013), we did not find a statistically significant relationship between EBLLs and lead-in-soil concentrations (\(R=-0.24393;p=0.067; see data repository) within the region of study. However, a previous study within Philadelphia identified a significant positive relationship between BLLs and soil-Pb levels ([PERSON] et al., 2017), suggesting that our research may not have included sufficient soil data. Therefore, our research revealed a need for greater future sampling of soils within the area of study. Within this area, some census tracts were more densely sampled than others (primarily within West Philadelphia), making it difficult to compare lead risk from soil between these regions of Philadelphia and its association with
Figure 4: (a) Map displaying the sites of the six historic smellers in the study area (red dots) and each site’s 500-m radius of impact (red circles); (b) soil data for each census tract that hosts a former smelter, along with sampling points specifically within the smelter’s radius of impact. bdl = below detection limit.
reported EBLLs. Despite the limited amount of soil data in most census tracts (Figure S15 in the Supporting Information S1), only 22 of the ninety-four (23%) census tracts evaluated do not contain sites with lead-in-soil values \(\geq\) 400 ppm. Some of the samples are at exceedingly hazardous soil lead levels; in the most extreme case, the soil lead levels are up to 13 times the EPA hazard threshold of 400 ppm (Figure S16 in the Supporting Information S1). Although the majority of the hazardous soil data points were within West Philadelphia, where most of the sampling occurred, there are a few outside of this part of town, which suggests that more samples need to be collected from North Philadelphia.
Furthermore, recognizing that a child's EBLL is a reflection of recent cumulative exposure to lead from multiple sources, lead-in-soil data are a useful lead-risk indicator for one important source of exposure in need of preventative action ([PERSON] et al., 2017). Therefore, any effort to effectively reduce BLLs must include soil remediation. Also, despite the federal reference level for hazardous soils being at 400 ppm for bare soils in play areas, various states have lowered the lead-in-soil threshold in response to concerns that the 400 ppm value was established through a risk assessment process using 10 ug/dL, the then current blood lead level that the CDC considered safe. Since 2012, the CDC has considered no amount of lead in blood to be safe, and since last year, has lowered the blood lead reference level to 3.5 ug/dL (CDC, 2021, 2021). The EPA has not yet incorporated this important understanding of low-level lead risk into its threshold for lead-in-soil.
Evidence of historic smelters and significant numbers of demolitions with associated emission of lead-contaminated dust in North Philadelphia further highlight a great need for soil sampling in this area. This is especially pressing when considering that previous work in Philadelphia identified floor dust at household entryways as a critical risk factor for childhood lead poisoning ([PERSON] et al., 2019). A few significant open-land areas, which existed as green space when the smelters were likely active and continue to be green spaces with no evidence of remediation, include: a large public park and church within the radius of impact of the Cadman, A.W. MFG. CO. 2 Lead Smelter in census tract 241 (Figure S30 in the Supporting Information S1); several schools within the radius of impact of the A. Perez & Son Division of Abrams Metal Co. Lead Smelter, American Alloys Co. and another unnamed smeller in census tracts 139 and 161 (Figures S30 and S31 in the Supporting Information S1); and significant open-land in the form of residential laws within census tract 139 (Figure S30 in the Supporting Information S1), which being private property are less likely to be sampled and remediated ([PERSON] et al., 2007). Open-land areas around smelters are especially important for remediation, as previous research has found remediating soil proximate to smelters with lead concentration >500 ppm resulted in a 2.5 ug/dL reduction in BLLs among children 3 years old and younger ([PERSON] et al., 2003).
### Limitations and Future Directions
There are several limitations to this study, however, including missing lead sources such as census tract-level data on highly frequented roads, along which leaded gasoline emissions from mobile sources would have accumulated, and locations of existing lead service lines. The PA-DEP's Land Recycling Program reports include only those Brownfield sites that have been identified for clean-up so that they can be re-used. There are likely numerous other contaminant sites that are not included in these reports because they are not commercially viable. There is also a gap in the availability of soil data within North Philadelphia that needs to be closed in order to better understand the risk within that region. Certain data are also highly underrepresented due to limitations within L&I, including data on housing code violations, and especially lead violations. For these reasons, this study can only present conclusions based on the available data, and therefore does not provide a complete representation of the cumulative lead risk within the studied area of Philadelphia. Moreover, despite this study investigating lead risk in Philadelphia at the smallest geographic unit done to date, it is limited by the representation of data at the census tract level. In one study, census blocks rather than census tracts were found to better predict BLLs and other health effects, as health outcomes are more closely associated with an individual's immediate environment than with larger geographic areas ([PERSON] et al., 2010). This emphasizes the importance of further work identifying lead risk, along with other health risks, at a neighborhood level. Remediation and prevention efforts should also take into account the considerable role of the proximate environment on lead risk and health outcomes. In previous studies, significant decreases in lead contamination and BLLs were reported at the neighborhood level when remediation efforts targeted both high-risk homes and surrounding homes ([PERSON] et al., 2017; [PERSON] et al., 2016).
Another point illuminated by the data used here was the disparity in BLL screening of children. Despite having the greatest proportion of children with EBLLs relative to the total number of children screened, census tract 200 is one of the 16 census tracts with less than 50% of children screened, and it does not emerge as one of the highest lead-risk census tracts (Figure S20 in the Supporting Information S1). This result may indicate a need to increase screening across all census tracts, or point to a lead source that was not evaluated in this study but impacts census tract 200 and others in the region, for example, lead drinking water pipes or historic leaded gasoline emissions. Our research identified fourteen census tracts in which 25% of the housing units were built before 1950, including census tract 200. These census tracts should be prioritized for an investigation of lead pipes by the Philadelphia Water Department, followed by replacement of the identified lead service lines. Considering the CDC's recent decision to lower the blood lead reference value from 5 \(\mu\)g/dL to 3.5 \(\mu\)g/dL, significant efforts must be made to increase screening for children across Philadelphia, but especially in the identified high-risk census tracts. These efforts would require increased access to on-site testing, education across stakeholders (i.e., parents, physicians, local public health organizations), and greater collaboration with local health providers and community organizations. Efforts to increase both BLL screening and soil sampling can be done effectively and efficiently through community engagement, which improves community capacity and lowers the risk of adverse health outcomes ([PERSON], 2018; [PERSON] et al., 2015). A reevaluation of lead-risk factors among children with reported EBLLs using the new 3.5 \(\mu\)g/dL blood lead reference level would further improve our understanding of lead risk in Philadelphia.
A historical analysis could be used to investigate the legacy of leaded gasoline emissions in Philadelphia, which could be achieved by identifying and mapping roads that were heavily trafficked during the timeframe of leaded gasoline use, and by determining the lead isotopic composition of soils adjacent to these roads, which may carry a unique gasoline isotopic signature (see, for example, [PERSON] et al., 2021), and thus would help in spatially analyzing the potential emission dispersion of gasoline-derived lead. This information would help in further prioritizing remediation and preventative action. It is especially important to investigate leaded gasoline considering that nearly equal amounts of lead in gross-tonnage were used in white lead pigment as was in leaded gasoline before the mandated decrease in their lead contents ([PERSON] & [PERSON], 1998).
## 5 Conclusions
Lead paint, housing code violations, demolitions, and owner-occupied housing continue to be lead-risk factors in Philadelphia. A significant finding of our research is that the lead risk is highly correlated with owner-occupied housing in Philadelphia due to high homeownership in low-income areas. This association should be further investigated in other cities, as its implications for policy and prevention of lead poisoning are critical. Furthermore, this research identified that demolitions are strongly associated with EBLLs in children, pointing to lead-contaminated dusts released during the demolition process as an important source, suggesting that dusts from lead paint play an important role in lead poisoning. Lead-contaminated dust from demolition activity warrants additional regulatory mitigation and greater code enforcement, as it impacts low-income communities of color, that is, environmental justice communities, considerably more than higher-income white communities in Philadelphia. Census tracts 175 and 172, which were identified as having the highest risk for childhood lead poisoning, should have resources directed to them in order to increase efforts to remediate homes, test and support children within these areas. The 16 census tracts with less than 50% of children screened for EBLLs should receive targeted screening programs by the Philadelphia Department of Public Health.
It is important to note that the census tracts most frequently appearing as high risk are concentrated within the Strawberry Mansion area, especially when including the census tracts considered high risk in regard to seven of the thirteen lead-risk factors (Figure S20 in the Supporting Information S1). Support to identified high-risk communities should include holistic lead-hazard screening and remediation for all lead sources ([PERSON] et al., 2016) as it is the most effective approach to decreasing childhood lead poisoning. The Federal Department of Housing and Urban Development uses an average per-unit cost of $12,000 (HUD, 2018). Given the high costs of holistic screening and remediation, prioritization of high-risk neighborhoods is the most financially feasible way of beginning to address the issue. This research consolidates lead risk at the census tract-level for this purpose. In addition, this research identified open-land space around former shelter sites that the EPA and the City should sample and remediate if necessary. Our results provide insights for public health policy moving forward, especially for the City of Philadelphia's Department of Public Health, Department of License's and Inspection, and City Council.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Datasets and script used to map data for this research are available at The Environmental Data Initiative ([PERSON] et al., 2021). The lead-risk factor data used for the lead-risk analysis and mapping in the study are all available at The Environmental Data Initiative which is released to the public domain under Creative Commons CCO 1.0. Version 1.3.1093 of RStudio was used for mapping data into visuals.
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wiley/fc8665f6_2c0a_4a2e_9383_87be6b06afd6.md | # IGR Atmospheres
Research Article
10.1029/2024 JD041078
1
Estimating the Electric Fields Driving Lightning Dart
Leader Development With BIMAP-3D Observations
[PERSON]
1 Electromagnetic Sciences & Cognitive Space Applications, Los Alamos National Laboratory, Los Alamos, NM, USA, 12 Langmuir Laboratory for Atmospheric Research, New Mexico Institute of Mining and Technology, Socorro, NM, USA2
[PERSON]
Electromagnetic Sciences & Cognitive Space Applications, Los Alamos National Laboratory, Los Alamos, NM, USA, 1
[PERSON]
1 Electromagnetic Sciences & Cognitive Space Applications, Los Alamos National Laboratory, Los Alamos, NM, USA, 1
[PERSON]
1 Electromagnetic Sciences & Cognitive Space Applications, Los Alamos National Laboratory, Los Alamos, NM, USA, 1
Footnote 1: [[https://a.open](https://a.open)]([https://a.open](https://a.open)) access article under the terms of the Creative Commons Arithmetic-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.
###### Abstract
In this paper, a numerical dart leader model has been implemented to understand the leader's development and the corresponding electric field changes observed by the 3D broadband mapping and polarization (BIMAP-3D) system. The model assumes the extending leader channel is equipotential and has a linear charge distribution induced by an ambient electric field. The charge distribution induced by the ambient field can be used to model the electric field change at the ground. We then find the ambient electric field which best fits the field change measurements at the two BIMAP stations. The estimated ambient electric field decreases in the direction of dart leader propagation. Our observations and modeling results are consistent with our earlier hypothesis that dart leader speed is proportional to the electric field at the leader tip. The model also supports our earlier analysis that leader speed variations near branch junctions were due to previous charge deposits near the junctions. The modeled tip electric field is generally lower than the breakdown field unless the pre-dart-leader channel has a significant temperature of \(\sim\) 3,000 K. This is consistent with the fact that dart leaders typically do not form new branches into the virgin air. Furthermore, the tip field is generally close to the negative streamer stability field at ambient temperatures, explaining the nature of the narrow and well-defined channel structure. In addition to the charge distribution and the ambient and tip electric field, the development of the channel potential and current distribution are also presented.
A dart leader is a discharge process that occurs at the later stage of a lightning flash. It retraces the path established by earlier discharges and propagates at a high speeds of 1%-10% the speed of light. Recently, we developed a system called BIMAP-3D that can map lightning radio sources in 3D with high time resolution. We also measured the electric field at the ground caused by lightning discharges. In this paper, we modeled a 3D mapped dart leader as a perfectly conducting wire. A conducting wire placed in an external electric field disturbs the field around it. We used our wire dart leader model to find an electric field in the cloud so that the modeled disturbance matched the electric fields we measured at the ground. The estimated cloud field decreases in the direction of dart leader propagation. Our model suggests that the speed of a dart leader is closely related to electric field at the dart leader tip. The modeled electric field at the dart leader tip is also too low to form a new discharge path through the air, explaining why they follow previously established paths.
qualitative descriptions of the induced charge distribution. [PERSON] and [PERSON] (1993, 1998) expanded upon [PERSON]'s initial work with numerical modeling of equipotential lightning channels. The model of [PERSON] (1960) has historically been referred to as the bidirectional leader model, but we will instead refer to it as the equipotential leader model, since the equipotential assumption is the most significant difference between this model and other non-physics-based leader models. A number of studies have used measured field changes to model simple charge configurations along leader channels without considering leader conductivity ([PERSON] et al., 2022; [PERSON] et al., 2013; [PERSON] et al., 2020; [PERSON] et al., 2023; [PERSON] et al., 2015; [PERSON] et al., 2011). By contrast, relatively few studies have attempted to compare the equipotential model to observed electric field changes associated with lightning ([PERSON] & [PERSON], 1993; [PERSON], 2014; [PERSON] & [PERSON], 2015), and these studies have been somewhat limited by lack of knowledge of the extent or location of the leader channel.
The BIMAP-3D system has the capability to map out very high frequency (VHF) radio sources along lightning channels in 3D over time ([PERSON] et al., 2023) and simultaneously measures the electric field changes with a fast antenna at each of the two BIMAP stations. If we assume the active and continuous dart leader channel sections with recent VHF activity are at equipotential and choose some reasonable channel radius, the only remaining unknown in the model is the cloud electric field distribution along the channel. The cloud electric field can then be estimated through standard nonlinear inverse problem techniques as described in Section 3.
This approach to indirectly measure the ambient electric field is similar in concept to the work reported by [PERSON] (2020), but our use of time resolved leader lengths and field changes allows the estimated ambient field along the leader channel to be spatially resolved. This additional information leads to a number of insights on the physical conditions of the developing channel.
As a note on terminology, in our previous papers ([PERSON] et al., 2021, 2023b), we have discussed the use of the terms \"K-leader,\" \"dart leader,\" and \"recoil leader\" to refer to what is fundamentally the same phenomenon. Following some recent discussion and consensus within at least part of the lightning community ([PERSON] et al., 2023b, 2024; [PERSON] et al., 2023; [PERSON] et al., 2023), we now choose to use the term dart leader exclusively to refer to this phenomenon, as we previously suggested in [PERSON] et al. (2021). To avoid confusion about whether a dart leader is followed by a return stroke, we suggest that dart leaders may be further classified as in-cloud (IC) dart leaders or cloud-to-ground (CG) dart leaders whenever the distinction is relevant, as we suggested in [PERSON] et al. (2021).
Following this terminology convention, in this paper, we apply the equipotential model to IC dart leaders to understand the electric fields and other conditions that drive the leader's development. This work builds on recently reported observations of dart leaders ([PERSON] et al., 2023b) and serves as a more rigorous test of some of our hypotheses on the dart leader propagation physics. When applying the methodology discussed in Section 3, the model results are consistent with our hypothesis that dart leader speed is proportional to the leader tip electric field, as we first suggested in [PERSON] et al. (2021). We demonstrate that an ambient field which starts relatively high and decreases along the channel results in a tip field that matches the observed speed trends of initial acceleration and gradual deceleration. We also confirm that the branch junction speed variations can be explained by charge deposits near the primary channel. Our results also provide possible explanations to some other observed dart leader properties, such as their well-defined and narrow channel width in VHF and the fact that they typically do not exit the preconditioned channel structure to propagate through virgin air.
## 2 Instrumentation
In this paper, we make use of lightning observations from the BIMAP-3D system ([PERSON] et al., 2023) that has been deployed at Los Alamos National Laboratory (LANL) since 2021. It consists of two stations, each with four VHF antennas arranged in a Y configuration. The two stations are 11.5 km apart. Lightning data from each station is first processed separately to form a 2D lightning map and then is combined and reprocessed to produce a 3D lighting map. Based on observations of dart leader channel widths, the random uncertainty of BIMAP-3D can be better than 10 m in easting, northing, and altitude in ideal conditions ([PERSON] et al., 2023). Systematic biases in the absolute location have not been evaluated, but the 3D results produced by the triangulation and DTOA location techniques typically differ by less than 30-50 m, and this gives an estimate of the absolute location error. For lightning channels several kilometers away, a location bias of 50 m is negligible for this study.
BIMAP-3D also has a fast electric field change antenna or fast antenna (FA) at each station. The relative positions of the two stations are shown later in Figure 3. We are using fast antennas previously developed for the Los Alamos Sferics Array (LASA) ([PERSON] et al., 2002) to measure vertical electric fields at the ground. The fast antenna at station 1 (FA01) has a highpass time constant of 1 ms, and the fast antenna at station 2 (FA02) has a time constant of 0.2 ms. For a first order high-pass filter, the low frequency content can be reliably recovered by de-dropping (deconvolution) ([PERSON] et al., 2016; [PERSON] et al., 2006) as long as the low frequency signal is sufficiently above the noise level, the direct current (DC) offset for \"zero-level\" of the signal is reliably known, and the signal does not saturate. For both FA01 and FA02, the low frequency content can be recovered down to the 60 Hz noise from nearby power infrastructure. There is no explicit low-pass filter in the fast antennas, but above 20 MHz there is essentially no signal. In this study, we are interested in the electrostatic field change associated with the dart leaders, so we digitally lowpass the signals at 25 kHz. The flash being analyzed occurs close enough that the measured field change is essentially all electrostatic. The field change signals we are analyzing are thus more in the slow antenna regime ([PERSON], 2010, p. 8). We also de-droop the field change for each dart leader separately, making use of the fact that there is essentially no field change in the interval between dart leaders for this flash. In addition to recovering the low frequency content, de-drooping corrects for any differences caused by the different time constants between the two fast antennas. Figure S1 in Supporting Information S1 compares the raw and de-drooped signals for both FA01 and FA02 for one dart leader.
In [PERSON] et al. (2023b), we found a relative calibration between FA01 and FA02 by comparing peak amplitudes for distant return strokes. This relative calibration was sufficient for qualitative modeling analysis. For quantitative modeling in this paper, we need an absolute calibration for each fast antenna. To achieve this we used 48 hr of National Lightning Detection Network (NLDN) peak current data for strikes within 100 km of our stations that were captured by either of our stations. We restricted the NLDN data set to strikes that were at least 15 km away from both stations and with reported peak currents between 0 and \(-\)50 kA. With these restrictions, we found 263 strikes for FA01 and 87 strikes for FA02. To compare NLDN peak currents to our field change measurements, we used the empirical relation from [PERSON] et al. (2014) (first reported by [PERSON] et al. (1992) based on results from [PERSON] et al. (1989)) given in Equation 1
\[I=0.0037 ED-1.5 \tag{1}\]
where \(I\) is the peak current in kA, \(E\) is the peak field change in \(V/m\), and \(D\) is the distance to the stroke in km. Based on this equation, we derived calibration factors for our fast antennas based on each NLDN strike with units of \(\left[\frac{V}{m}\right]\) per digital count. After finding the calibration factor for each match between the NLDN and our fast antennas and removing any obvious outliers, we found the average calibration factor for each station. The calibration factors were \(4\,\pm\,2\) mV/(m-count) for FA01 and \(2\,\pm\,1\) mV/(m-count) for FA02. In each case the 1\(\sigma\) uncertainties are about 50% of the calibration value. This is a significant source of uncertainty for all the quantities calculated in this paper.
## 3 Methods
### The Equipotential Leader Model
Following the approach of [PERSON] (1998), we consider a leader as a long cylinder with effective capacitive radius \(r_{C}\). If the cylindrical channel is placed in an ambient potential distribution \(\Phi_{amb}(s)\) and a linear charge distribution \(\lambda(s)\) is placed along the channel, then the new potential along the channel \(\Phi(s)\) will be given by
\[\Phi(s)=\Phi_{amb}(s)+\frac{1}{4\pi r_{0}}\int_{s_{a}}^{s_{b}}\frac{\lambda \left(s^{\prime}\right)ds^{\prime}}{\sqrt{\left(s-s^{\prime}\right)^{2}+r_{C}^ {2}}} \tag{2}\]
where \(s\) is the coordinate along the length of the channel. \(s_{a}\) and \(s_{b}\) are the ends of the channel.
For an assumed equipotential channel, we have \(\Phi(s)\ =\ \Phi_{\alpha_{\alpha}}\ =\ const.\) For \(s_{a}\leq s\leq s_{b}\), we further assume that the leader has no net charge, since the transfer of charge between the leader and the cloud should be negligible at dart leader timescales. Under these assumptions, the channel potential must be given by the average value ([PERSON] et al., 1995):
\[\Phi_{\alpha_{\alpha}}=\frac{1}{s_{b}-s_{a}}\int_{\alpha_{\alpha}}^{n_{b}}\Phi_ {\alpha_{\alpha}\beta}(s)ds \tag{3}\]
We then wish to find the charge distribution \(\lambda(s)\), which satisfies this condition. To evaluate this numerically with the method of moments technique, we discretize the leader channel into \(N\) segments of length \(\Delta s\), where each segment has a uniform charge density \(\lambda_{i}\). We then linearize Equation 2 as ([PERSON] and [PERSON], 2015):
\[[\Phi_{i}]=[\Phi_{\alpha_{\alpha_{i}}}]+[K_{i_{\lambda}}][\lambda_{j}] \tag{4}\]
where \(\Phi_{i}\) is the net potential at \(s_{i}\), \(\Phi_{\alpha_{\alpha_{i}}j}\) is the ambient potential at \(s_{i}\), and \([K_{i_{\lambda}}][\lambda_{j}]\) gives the approximate potential at \(s_{i}\) due to the linear charge density \(\lambda_{j}\) at every location \(s_{j}\) along the channel. \(\Phi_{i}\), \(\Phi_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_{ \alpha_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_{\alpha_ \alpha_{\alpha__{\alpha___ \alpha_ \alpha_ \alpha_ \alpha_{\alpha__ \alpha_ \alpha_{\alpha__ \alpha__ \alpha_{\alpha__ \alpha__ \alpha__ \alpha__ \alpha__ \alpha__ \alpha__{\alpha__ \alpha__{\alpha__ \alpha__{\alpha__ \alpha_{\alpha___ \alpha_{\alpha___\alpha__ \alpha_{\alpha___\alpha__ \alpha__{\alpha___\alpha__ \alpha__{\alpha___\alpha__{\alpha____ \alpha__\alpha__{\alpha____\alpha___a__a
Calculation of the electric field at the leader tip \(E_{\text{tip}}\) is somewhat nuanced because of uncertainty about the effective channel radius \(r_{C}\), so we will discuss this separately in Section 3.2.
The leader tip potential drop \(\Delta\Phi_{\text{tip}}\) can also be calculated, it is simply defined as
\[\Delta\Phi_{\text{tip}}=\Phi_{\text{clu}}-\Phi_{\text{amb}}(\text{s}_{\text{tip}}) \tag{8}\]
This is the difference between the channel potential and the ambient potential that would exist at the tip if there was no leader present. Our \(\Delta\Phi_{\text{tip}}\) is similar to the definition of \(\Delta U_{g}^{*}\) in [PERSON] and [PERSON] (2011) or \(\Delta U_{t}\) in [PERSON] and [PERSON] (2000) (Equation 4.3 and other uses throughout). The potential drop \(\Delta\Phi_{\text{tip}}\) is generally proportional to the tip field \(E_{\text{tip}}\) but has the advantage that it does not depend on the tip geometry. Nevertheless, we will include \(E_{\text{tip}}\) estimates despite the much larger uncertainty because many other papers on leader and streamer propagation consider average electric fields over some distance rather than potential difference at a single point.
_EXAMPLE_: As an example of the model calculations, Figure 2 shows the leader potential and charge distribution for a negative leader with \(r_{C}=1\) m growing in a uniform ambient field \(E_{\text{amb}}=100\) kV/m, following the atmospheric electricity sign convention \(E=\
abla\Phi\). The channel segment length is \(\Delta s=50\) m. In this example, the positive tip of the leader stays stationary and the model values are plotted when the negative tip has reached distances of 500, 1,000, 1,500, and 2,000 m. In Figure 2a, the potential is uniform within the channel, but the value of \(\Phi_{clu}\) increases as the negative leader tip extends through the uniform field. In a uniform field \(\Phi_{clu}\) is equal to the potential at the middle of the channel. Beyond the ends of the leader, the potential quickly returns to the ambient potential as marked in black.
Figure 2b shows how the charge distribution changes as the leader propagates. In a uniform field, the leader has equal amounts of positive and negative charge at the tips, tapering off to zero at the middle of the leader channel. As the leader propagates the symmetry of the charge distribution remains, but the magnitude of the charge at either end increases. Since only one tip is propagating in our example, the zero charge point also moves. In a uniform field, the zero charge point is always halfway along the leader. For an equipotential channel, the induced charge \(\lambda(s)\) at each point is proportional to the difference between the channel potential \(\Phi_{clu}\) and the ambient
Figure 2: Examples calculations of the leader potential and charge distribution for various leader lengths in a uniform ambient field \(E_{\text{amb}}=100\) kV/m, following the atmospheric electricity sign convention \(E=\
abla\Phi\). Plots show the potential along the leader channel (a) and the induced charge distribution (b).
potential at that point \(\Phi_{\rm amb}(s)\), \(\lambda(s)\propto\Phi_{\rm c,in}-\Phi_{\rm amb}(s)\) as pointed out originally by [PERSON] (1960). So, the point on the leader with zero charge is the point where \(\Phi_{\rm c,in}-\Phi_{\rm amb}(s)=0\), at the middle of the channel in this case. There is a slight enhancement to the charge density \(\lambda(s)\) at the tips of the leader beyond the value expected by a \(\lambda(s)\propto\Phi_{\rm c,in}-\Phi_{\rm amb}(s)\) relation (Figure 2b, the change in slope near the tips). This charge enhancement at the tips is related to the change in capacitance per unit length at the tips of a cylinder ([PERSON], 2000).
### Leader Tip Electric Field
Having estimated the ambient field and associated charge density along the channel, we also wish to estimate the electric field at the leader tip. Each segment of the leader is a uniformly charged cylinder of length \(\Delta s\), radius \(r_{\rm C}\), with a linear charge density \(\lambda_{i}\). The electric field along the s-axis from each cylindrical segment is given by
\[E_{i}(s)=\frac{\lambda_{i}}{2\pi r_{\rm C}^{2}\epsilon_{0}}\bigg{[}\sqrt{r_{ \rm C}^{2}+s^{2}}\ +\Delta s-\sqrt{r_{\rm C}^{2}+(\Delta s+s)^{2}}\ \bigg{]} \tag{9}\]
where in this case \(s=0\) is defined as the propagating end of the cylinder, and the equation is only valid ahead of the cylinder in the direction of propagation (\(s\geq 0\)). A derivation of Equation 9 is provided in Appendix A.
Equation 9 demonstrates that the field for each segment drops off very quickly over distances on the order of \(r_{\rm C}\). Thus, the field at the tip of the leader can be approximated as due to just the final segment as long as \(\Delta s\gg r_{\rm C}\). This field is highest right at the edge of the cylinder, so for \(s=0\)
\[E_{\rm tip}(0)=\frac{\lambda_{\rm tip}}{2\pi r_{\rm C}^{2}\epsilon_{0}}\bigg{[} r_{\rm C}+\Delta s-\sqrt{r_{\rm C}^{2}+(\Delta s)^{2}}\ \bigg{]} \tag{10}\]
Without further knowledge, the effective capacitive radius \(r_{\rm C}\) for a dart leader channel could plausibly be anywhere from 1 mm (estimated dart leader conductive radius ([PERSON], 1998)) to 100 m (streamer zone length at 10 km altitude observed by [PERSON] et al. (2014)). Thus, this \(1/r_{\rm C}\) dependence appears to pose a significant challenge in extracting any useful information about the magnitude of the tip field.
However, the electric field at a single point in a highly nonuniform field is not really useful in any case. More relevant to a discussion about streamer or breakdown activity at the tip would be the average field at the tip over some distance \(d\)
\[\overline{E_{\rm tip}}(d)=\frac{1}{d}\!\int_{0}^{d}\frac{\lambda_{\rm tip}}{ 2\pi r_{\rm C}^{2}\epsilon_{0}}\bigg{[}\sqrt{r_{\rm C}^{2}+s^{2}}\ +\Delta s-\sqrt{r_{\rm C}^{2}+(\Delta s+s)^{2}}\ \bigg{]}ds \tag{12}\]
which evaluates to
Figure 3: A plot of the path of the IC dart leader, labeled K-5, over time relative to the two fast antennas. Panels are: altitude versus time (a), altitude versus casting (b), northing versus causing (c), and northing versus altitude (d). The points of K-5 are colored by time. The measured field change versus time at each station is also included (e), and the locations of the two fast antennas are marked in panels (b)–(d). The location of K-5 relative to the surrounding flash structure can be seen in Figure 3 of [PERSON] et al. (2023b).
\[\overline{E_{\text{tip}}}(d) =\frac{\lambda_{\text{tip}}}{4\pi e_{0}d}\left[\ln\left(\frac{\sqrt{r_{ C}^{2}+d^{2}}\ +d}{r_{C}}\right)\right.\] (A) \[\left.+\ln\left(\sqrt{r_{C}^{2}+\Delta s^{2}}\ +\Delta s\right)\right.\] (B) \[\left.-\ln\left(\sqrt{r_{C}^{2}+\left(\Delta s+d\right)^{2}\ + \Delta s+d}\right)\right.\] (C) \[\left.-\frac{\Delta s+d}{r_{C}^{2}}\sqrt{r_{C}^{2}+\left(\Delta s +d\right)^{2}}\right.\] (D) \[\left.+\frac{d}{r_{C}^{2}}\sqrt{r_{C}^{2}+d^{2}}\right.\] (E) \[\left.+\frac{\Delta s}{r_{C}^{2}}\sqrt{r_{C}^{2}+\Delta s^{2}} \right.\] (F) \[\left.+\frac{2d\Delta s}{r_{C}^{2}}\right]\] (G)
where we have labeled each term (A, B, C, etc.). This integral was evaluated using Wolfram Alpha (Wolfram Research Inc, 2024).
Assuming \(\Delta s\gg d\!>\!r_{C}\) then \((B)\ +\ (C)\approx 0\). Applying the binomial approximation for \(\frac{\tilde{c}}{\left(\Delta s+d\right)^{2}}\!<\!1\), \(\frac{\tilde{c}}{\tilde{c}}\!<\!1\), and \(\frac{r_{C}^{2}}{\left(\Delta s\right)^{2}}\!<\!1\) to terms \((D)\), \((E)\), and \((F)\), respectively, yields \((D)\ +\ (E)\ +\ (F)\ +\ (G)\approx\frac{1}{4}\). So, we are left with
\[\overline{E_{\text{tip}}}(d)\approx\frac{\lambda_{\text{tip}}}{4\pi e_{0}d} \left[\ln\left(\frac{\sqrt{r_{C}^{2}+d^{2}}\ +d}{r_{C}}\right)+\frac{1}{4}\right] \tag{14}\]
If we choose \(d\ =\ 1\) m then the difference in tip fields between \(r_{C}\ =\ 0.001\) m and \(r_{C}\ =\ 1\) m is about a factor of 7. This is still rather large, but at least gives an estimate of the tip field within about an order of magnitude, even across three orders of magnitude in radius. We do not use this approximation in the actual model calculations of \(E_{\text{tip}}\), but it is useful for demonstrating the logarithmic dependency on \(r_{C}\).
Additionally, the channel radius \(r_{C}\) is the effective radius of the cover charge initially deposited by streamers at the leader tip and any subsequent changes to the cover charge by later corona or streamers ([PERSON] & [PERSON], 2000, chapter 2.4). The radius \(r_{C}\) should then approximately correspond to the radius at which the radial electric field is equal to the streamer stability field. Assuming the axial and radial fields are the same order of magnitude, one should expect \(\overline{E_{\text{tip}}}(r_{C})\) to be close to the value of the streamer stability field. If this condition is met then we can be more confident that we have chosen \(r_{C}\) correctly and our calculated \(E_{\text{tip}}\) values are essentially correct. A more sophisticated model would allow \(r_{C}\) to vary so that the radial field was always equal to the streamer stability field for each segment (e.g., [PERSON] et al. (2009)), but for now a simpler model with fixed \(r_{C}\) is used.
We note that \(E_{\text{tip}}\) as discussed in this section is essentially the \"vacuum solution\" field as defined by [PERSON] and [PERSON] (2011), we are not accounting for streamers forming ahead of the conductive leader tip. Streamers ahead of the tip would reduce the field at the tip by spreading the potential drop \(\Delta\Phi_{\text{tip}}\) over a larger distance. Under typical approximations, this would result in a constant \(E_{\text{tip}}\) equal to the streamer stability field \(E_{\text{sr}}\), which extends for a distance \(L\ =\ \Delta\Phi_{\text{tip}}/(2E_{\text{sr}})\) ([PERSON], 2000, p. 69).
For \(E_{\text{tip}}\), in this paper, we will report the values calculated from Equation 13 over a distance of \(d\ =\ 1\) m.
### Ambient Electric Field Estimation
For any ambient electric field distribution, we can calculate the charge distribution along the channel with Equation 6. If we can map the channel path parameter \(s_{i}\) to 3D coordinates \((x_{i},y_{i},z_{i})\) in the sky, we can then calculate the vertical electrostatic field at a point \((X,Y,Z_{grad})\) on the ground (where \(Z_{grad}\) is the altitude of the ground above sea level) due to the charge distribution \(\lambda_{i}\) as:
\[E_{z}(X,Y,Z_{grad})=\sum_{i=1}^{N}\frac{\lambda_{i}\Delta s}{2\pi\epsilon_{0}} \frac{z_{i}-Z_{grad}}{\left(x_{i}-X\right)^{2}+\left(y_{i}-Y\right)^{2}+\left(z _{i}-Z_{grad}\right)^{2}\right]^{\
icefrac{{1}}{{2}}}} \tag{15}\]
where the ground is treated as an ideal infinite conducting plane. Since the lightning channel is far from our field measurement locations, each segment of the channel can be approximated as a point charge. This calculation can be done for each time step \(t_{k}\) corresponding to a leader extension by \(\Delta s\), to give the vertical field on the ground as a function of time, \(E_{z}(X,Y,Z_{grad},t_{k})\).
Typically for a lightning flash, the ambient electric field \(E_{amb}(s)\) is not known, but the vertical electric field at the ground \(E_{z}(t)\) can be measured with an electric field change antenna. The extent of the conducting channel at any point in time can also be inferred from 3D lightning interferometer data. An initial guess can then be made for the ambient field \(E_{amb}(s)\). For a conductive channel with endpoints at \(s_{s}\left(t_{k}\right)\) and \(s_{b}\left(t_{k}\right)\), the charge distribution \(\lambda_{i}(t_{k})\) induced by the guess \(E_{amb}(s)\) can be calculated from Equation 6. The corresponding field change at the ground \(E_{z}(t_{k})\) can be calculated from Equation 15. The goodness of fit between the measured and modeled field changes can then be evaluated as
\[\chi^{2}=\sum_{t_{k}}\frac{(E_{amb}(t_{k})-E_{abs}(t_{k}))^{2}}{\sigma_{k}^{2 }} \tag{16}\]
where \(E_{amb}(t_{k})\) and \(E_{abs}(t_{k})\) are the modeled and observed fields, respectively, at time \(t_{k}\), and \(\sigma_{k}\) is the estimated uncertainty in the observed field.
We can then find the ambient electric field \(E_{amb}(s)\) which minimizes the \(\chi^{2}\) value iteratively using a nonlinear optimization technique such as the Levenberg-Marquardt algorithm ([PERSON], 1944; [PERSON], 1963). The field on the ground does not depend strongly on each individual point \(E_{amb}(s_{k})\), so in order to limit the number of degrees of freedom, we assume \(E_{amb}(s)\) takes the form of a polynomial of order \(n\) rather than individually fitting each value of \(E_{amb}(s_{k})\). Figure S2 in Supporting Information S1 shows the extreme case of polynomial order \(n=50\) in order to illustrate the results when allowing a large number of degrees of freedom. We also include a penalty in the \(\chi^{2}\) value for solutions where \(E_{\text{tip}}\) changes signs, since a real leader should stop propagating if this condition ever occurred. This penalty is chosen to be large enough to suppress sign changes in \(E_{\text{tip}}\) but small enough that it does not upset the convergence of the solution or lead to significantly increased errors in Equation 16.
### Model Implementation
Dart leader K-5 from [PERSON] et al. (2023b) was chosen to implement the model since this is a relatively simple IC dart leader. Figure 3 shows the known information for K-5, including the full 3D extent of the leader channel over time relative to the two fast antennas (FA01 and FA02) along with the electric field change versus time at the ground at these locations. This is the known information from which we want to estimate the unknown ambient electric field along the channel.
The leader path is simplified by smoothing the measured VHF source locations with a rolling average of the location over \(\pm 20\,\mu\)s. Equally spaced and consecutive points \(\Delta s=50\) m apart are selected to serve as the discrete leader segments in the model. The model includes a fixed channel radius of \(r_{C}=1\) m to account for charge being transported radially outward from the thin (i.e., \(\sim\)1 mm, ([PERSON], 1998)) conducting core into the corona sheath/ cover charge. To first order the capacitance of a long thin cylinder of length \(L\) and radius \(r_{C}\) is given by ([PERSON], 2000):
\[C=\frac{2\pi\epsilon_{0}L}{\ln(L/\tau_{C})} \tag{17}\]The dependence of the estimated background field on the channel radius is thus weak, changing the modeled radius from 1 mm to 1 m only increases the capacitance by a factor of 2 for a \(L=1\) km channel. The validity of the \(r_{C}=1\) m assumption in terms of the effect on the estimated tip electric field will be evaluated at the end of Section 4.1.
The channel of K-5 is obviously not perfectly straight. Since the axial field produced by each cylindrical segment (Equation 9) drops off quickly over distances on the order of \(r_{C}\ll\Delta s\), only the nearest segments should contribute significantly to the potential at each point along the leader channel. Thus, we assume that Equation 2 is still valid for the potential along a real tortuous leader channel as long the channel is approximately straight over distances of a few times \(\Delta s\).
The potential of each leader segment also depends on the fields from the other segments and the image charge of each segment in the ground plane below. The electric field produced by each segment or image charge falls off as approximately \(1/R^{2}\). However, the distance from one channel segment to the nearest segment is just 25 m, whereas the distance to any ground image is \(\sim\)10 km, since the dart leaders occur about 5 km above the ground in this flash. The field contribution of the nearest channel segments is thus approximately \(\left(10^{4}\right)^{2}/25^{2}\sim 10^{5}\) times stronger than the contribution of the closest image charge, and we can safely ignore the effect of image charges on the leader potential for leaders far from the ground.
We also assume that the dart leader channel starts with a conductive length of 100 m at \(t=0\) in order to have some initial tip field and field change. Rather than skipping the first 100 m of dart leader development, we use the 3D map of the full flash to find a path along the same branch for 100 m in the direction opposite to the dart leader tip propagation. Negative values of channel distance \(s\) correspond to this \"backward\" direction along the branch. The negative dart leader tip starts at \(s=0\) at time \(t=0\).
## 4 Results
### Estimated Cloud and Tip Fields
All electric fields in plots use the atmospheric electricity sign convention, that is, for the ambient cloud E-field and tip E-field a positive E-field will accelerate electrons in the direction of leader propagation \(\hat{s}\). Since the behavior of the negatively charged dart leader tip is the subject of interest, this sign convention makes the plots easier to interpret.
Figure 4 shows the modeled field change (a and b) and estimated ambient field (c), where the ambient field is estimated using polynomials of various degrees \(n\). The constant field (\(n=0\)) is clearly a worse fit to the measured field changes than the higher polynomial degrees, which all result in similar field changes. All the modeled field changes seem to only fit the slow components of the measured field change up to about 5 kHz. This is true even if we drastically increase the allowed degrees of freedom (\(n=50\) is shown in Figure S2 in Supporting Information S1). This suggests that the higher frequency components of the field change (above \(\sim\)5 kHz) are not associated with the general extension of the leader but some other process which is not captured by our model. Since the higher frequency components do not seem to match between the two stations, they may also be local interference at each station.
The \(n>0\) polynomial ambient fields (Figure 4c) generally decrease in the direction of dart leader extension as predicted in [PERSON] et al. (2023b) based on dart leader speed trends. [PERSON] (1992) also predicted electric fields which decrease along dart leader channels based on the way charge gets left behind as the channel decays, although this behavior has not been fully modeled. Since the \(n=3\) and \(n=4\) polynomials add extra oscillations and rapid changes in field strength without improving the fit to the fast antenna measurements (Figures 4a and 4b), we will specifically consider the \(n=2\) case for the rest of our analysis. The same conclusions could be drawn from the \(n=1\) case since the ambient fields are similar.
The ambient field values, which are mostly below 15 kV/m, are low compared to typical thunderstorm fields, which are often measured to reach 50-100 kV/m ([PERSON] et al., 2001; [PERSON] & [PERSON], 2008; [PERSON] et al., 2007, 2015). This is expected since the preceding leader, return stroke, and other discharge activities would have zeroed out the field along the channel, and the ambient field estimated here therefore represents the recovery of the field along the channel as charge deposited in the corona sheath continues to diffuse radially outward between strokes. The estimated ambient field is thus only the ambient field at the location of the dart leader channel for the duration of dart leader propagation. We cannot directly infer the ambient field at any other location or time.
The sign change of the field in Figure 4c (\(E_{\mathrm{amb}}<0\)) is somewhat surprising, but the charge redistribution during a lightning flash is complex, and it is possible dart leaders from other branches transported excess negative charge onto this branch while this branch was otherwise decayed and nonconducting.
Figure 4d shows the modeled leader tip field \(E_{\mathrm{tip}}\) (solid, left axis) and tip potential drop \(\Delta\Phi_{\mathrm{tip}}\) (dashed, right axis) versus time. The \(n=3\) and \(n=4\) cases were omitted to make the plot less cluttered. The curves for \(E_{\mathrm{tip}}\) and \(\Delta\Phi_{\mathrm{tip}}\) for a particular \(n\) value are nearly identical up to a scaling factor. In Figure 4d \(|\Delta\Phi_{\mathrm{tip}}|\) is plotted instead of \(\Delta\Phi_{\mathrm{tip}}\) for comparison with \(E_{\mathrm{tip}}\) and easier interpretation. The \(n=1\) and \(n=2\) cases have an initial increase and gradual decreases of the tip field and potential drop, which is well correlated with the measured speed versus time of K-5 (Figure 4e), supporting our claim in [PERSON] et al. (2023b) that the leader speed is generally proportional to the leader tip field. With the current polynomial field approach, the model is incapable of catching small details such as the speed dip at 200 \(\mu\)s.
We include the \(n=0\) case in Figure 4d to demonstrate that in a uniform field the leader tip field and potential drop will increase indefinitely. The change in tip field with a change in length \(\frac{d}{dt}[E_{\mathrm{tip}}]\) is actually constant in a uniform field, but the slope \(\frac{d}{dt}[E_{\mathrm{tip}}]\) of the \(n=0\) curve is not constant in Figure 4d because we are using a nonconstant leader speed \(\left(\frac{d}{dt}[E_{\mathrm{tip}}]\right)=\frac{d}{dt}[E_{\mathrm{tip}}]\)\(\frac{d}{dt}\)).
We may wish to compare our modeled tip fields to various field thresholds for traditional breakdown or streamer propagation. The conventional breakdown and streamer stability electric field thresholds in air are traditionally defined at sea level and room temperature, and they scale with air number density (\(N_{air}\)) ([PERSON] et al., 2019). The relative density compared to sea level and room temperature is \(\delta=N_{air}(h,T)/N_{air}(h=0\ \mathrm{km},T=300\ \mathrm{K})\), which can be approximated as
\[\delta(h,T)\approx\frac{300}{T}e^{-t/10.4} \tag{18}\]
Figure 4: A plot of the modeled field change compared to the measured ground electric field change versus time (a and b), the estimated ambient cloud electric field versus channel distance (c), the estimated leader tip electric field \(E_{\mathrm{tip}}\) versus time (d, left axis), and tip potential drop \(\Delta\Phi_{\mathrm{tip}}\) versus time (d, right axis) for various degrees \(n\) of polynomial ambient fields. We plot \(|\Delta\Phi_{\mathrm{tip}}|\) so the curves are not inverted compared to \(E_{\mathrm{tip}}\). The measured leader speed versus time (e) is included for comparison.
where \(h\) is the height above sea level in kilometers and \(T\) is the temperature in Kelvin. The exponential term is a standard atmospheric approximation ([PERSON], 2010, p. 23) though [PERSON] calculates the density scale height assuming an isothermal atmosphere, and we include the temperature lapse rate as
\[H_{0}=\frac{1}{\frac{GM}{RT_{0}}-\frac{L}{T_{0}}}\approx\,10.4\,\,\,\mathrm{km} \tag{19}\]
where \(g=9.8\,\,\mathrm{m/s^{2}}\) is the gravitational acceleration at earth's surface, \(M=0.029\,\,\mathrm{kg/mol}\) is the molar mass of dry air, \(R=8.314\,\,\mathrm{J/mol}\) K is the universal gas constant, \(T_{0}=288.15\,\,\mathrm{K}\) is the sea level standard temperature, and \(L=0.0065\,\,\mathrm{K/m}\) is the temperature lapse rate (using relevant standard atmosphere values from [PERSON] et al. (1985)). The temperature term in Equation 18 is derived from the ideal gas law, which can be rewritten as \(N_{air}=p/k_{B}T\), where \(p\) is the pressure and \(k_{B}\) is [PERSON]'s constant. So at equal pressures, the gas number density is inversely proportional to the temperature.
Applying the altitude density scaling, at the altitude of \(\sim\)7 km above sea level, the breakdown field is expected to be \(E_{\mathrm{A0}}\cdot\delta\approx 1500\,\,\mathrm{kV/m}\), where \(E_{\mathrm{A0}}=3000\,\,\mathrm{kV/m}\) at sea level. From Figure 4d, we see that the modeled tip fields are much lower than the breakdown threshold especially at the beginning of propagation. This is surprising since this threshold should be the tip field required for leader propagation. However, since dart leaders propagate through preconditioned channels, the temperature may still be high from the previous lightning processes. If we assume a pre-dart-leader temperature of \(T=3,000\,\,\mathrm{K}\)([PERSON], 1968), we get \(E_{\mathrm{A0}}\cdot\delta\approx 150\,\,\mathrm{kV/m}\), which is close to the modeled leader tip fields at the start of propagation (Figure 4d). Thus, a dart leader could only propagate with the modeled initial tip field in a channel with \(T\)\(\gtrsim\)3,000 K, and a relatively high pre-dart-leader channel temperature (\(\sim\)3,000 K) may be required for dart leaders to initiate. The fact that the tip field never reaches the breakdown field for ambient air at 7 km may also explain why dart leaders typically do not form new branches and instead follow the existing flash structure. The range of tip field values we found are generally in agreement with the range of tip fields measured with Pockels sensors by [PERSON] et al. (2002) in triggered lightning strikes, although their measurements were made near sea level. The tip potential drop estimates in Figure 4d are also in reasonable agreement with the \"typical value\" of 15 MV given for dart leaders in Rakov and Uman (2003) Table 1.1.
The fact that the estimated leader tip field is initially lower than even the nominal streamer stability fields in virgin air (\(E_{\mathrm{A0}}\cdot\delta\) in the range of 500-750 kV/m at 7 km ([PERSON] & [PERSON], 1997; [PERSON] et al., 2008; [PERSON] & [PERSON], 2014) may also explain the observation that the width of dart leader channels resolved in VHF is much narrower than those of stepped leaders ([PERSON] et al., 2023a; [PERSON] et al., 2021; [PERSON] et al., 2023). The fact that negative leaders are detected much more readily than positive leaders in VHF suggests that the observed VHF predominantly comes from negative streamers. The axial field at the leader tip (\(E_{\mathrm{tip}}\)) should also be the highest electric field at any point on the leader. So if \(E_{\mathrm{tip}}\) is below the negative streamer stability threshold in virgin air, there should be no negative streamers anywhere on the leader except within the \"warm\" (\(\sim\)1,000 K) preconditioned channel core with a radius on the order of centimeters ([PERSON] & [PERSON], 1968), where the air density is lower. Recalling that \(E_{\mathrm{tip}}\) is the average field over 1 m, if \(E_{\mathrm{tip}}\) is approximately equal to the virgin air stability field, and if the radial electric field near the tip is approximately equal to \(E_{\mathrm{tip}}\), then we may expect streamers out to a radius of about 1 m. This is in contrast to negative stepped leaders where \(E_{\mathrm{tip}}\) is expected to be close to the breakdown field, and the streamer zone may have a radius of 10-100 m ([PERSON] et al., 2014; [PERSON] & [PERSON], 2013; [PERSON] et al., 2023).
In fact, our streamer zone estimates agree very well with the high speed video observations of [PERSON] and [PERSON] (2013). While they observed a radial streamer/corona zone of 10-20 m on a descending negative stepped leader, a later dart leader in the same channel had no visible radial streamer zone, although there is some faint uniform luminosity which may be corona. Instead of a wide radial streamer zone, the dart leader exhibited a long forward streamer zone confined to the preconditioned channel, extending \(\sim\)20-40 m ahead of the leader tip. This long forward streamer zone is expected. If the air density in the preconditioned channel is \(\sim\)4/10 th the ambient density, then the forward streamer zone within the preconditioned channel should be about 10 times longer than the radial streamer zone.
### Speed, Tip Field, and Tip Current
Figure 5 shows a direct comparison between the measured leader speed, the modeled tip field, and square root of the modeled tip current versus time for the \(n\,=\,2\) case (Figure 4). In the Figure, we have normalized each variable to a maximum value of 1 to remove any constants of proportionality. It is clear that the speed and tip fields are closely correlated except for the speed dip at 200 \(\mu\)s and a small variation at the end. We do note that the correlation is not as strong for other orders \(n\) of the polynomial ambient field, and the correlation is also somewhat sensitive to how the errors are weighted in Equation 16 and model parameters. In fact, due to the ill-posed nature of the inverse problem, there are essentially infinitely many ambient fields, which could reproduce the measured field changes. Among these infinite solutions, there are many possible ambient fields, which result in \(E_{\rm tip}\) curves that do not match the leader speed, although many are physically unreasonable. Although we cannot therefore definitively conclude that the leader speed is proportional to the tip field as guessed by [PERSON] et al. (2021, 2023b), we can at least claim that the observed field changes are consistent with a relationship of \(v\propto E_{\rm tip}^{2}\) for an equi-potential leader.
If we frame the speed/field relationship as the leader mobility, \(v\,=\,\mu E\), then we get a value of \(\mu\,=\,15\) m\({}^{2}\)/Vs for this particular dart leader. As shown in Figure 4d, the curves for \(E_{\rm tip}\) and \(\Delta\Phi_{\rm tip}\) are essentially identical up to a scaling factor, so the dependence of the speed can be expressed in terms of either the tip field or potential drop. If we model the tip speed as \(v\,=\,\eta\Delta\Phi_{\rm tip}\) we get a value of about \(\eta\,=\,2\) m/Vs.
Since there is a fair amount of uncertainty in the correlation between tip field and speed, we cannot completely rule out other power law relations such as the \(v\,=\,a\Delta\Phi_{\rm tip}^{1/2}\) relation suggested by [PERSON] and [PERSON] (2000) Equation 4.2. We note that the value of \(a\,=\,15\) m\(\big{/}\big{(}\)sV\({}^{1/2}\big{)}\) suggested by [PERSON] and [PERSON] (2000) gives a speed two orders of magnitude too low even if we assume the relationship can be adjusted as \(v\,=\,a\sqrt{\frac{\Omega_{m}}{\delta}}\) for a 3,000 K pre-dart-leader channel at 7 km altitude, where \(\delta\) is defined in Equation 18. Regardless of the form of the relation, our results do suggest that the tip electric field or potential drop appears to be one of the main factors for the dart leader speed.
The square root of the tip current is also very well correlated with the speed in Figure 5, but this should not be surprising. If we rewrite Equation 7 we can see that
\[I_{\rm tip}(t_{k})=-\Delta s\,\frac{\lambda_{\rm tip}(t_{k})-\lambda_{\rm tip}( t_{k-1})}{t_{k}-t_{k-1}}=-\frac{\Delta s}{\Delta t}\lambda_{\rm tip}(t_{k}) \tag{20}\]
Figure 5: A plot of the normalized values of speed, tip field, and the square root of current versus time for the \(n\,=\,2\) fit.
where \(\Delta s/\Delta t\) is just the speed of the leader, and we are making use of the fact that \(\lambda_{j}(t_{k-1})\ =0\) for the advancing leader tip. This would suggest that \(I_{ip}\propto v\), but we must further consider that from Equation 13\(\lambda_{ip}\propto E_{ip}\), so we must have \(I_{ip}\propto vE_{ip}\). We have also just established that \(v\propto E_{ip}\), so therefore \(I_{ip}\propto v^{2}\propto E^{2}\) is exactly the form we should expect. This result also generally agrees with numerical modeling of the streamer to leader transition by [PERSON] and [PERSON] (2013), and empirical relations suggested by [PERSON] et al. (2008) and [PERSON] (1997) (p. 213) based on laboratory spark experiments.
### Other Model Results
Figure 6 shows the modeled potential, charge density, and current distributions along the leader colored by time again for the \(n\ =2\) model. Each curve in Figure 6 is a snapshot of conditions along the entire plotted distance at a particular time indicated by the color.
Ahead of the negative leader tip at any point in time, the charge and current are zero, and the potential quickly returns to the ambient potential as the leader tip field falls off as approximately \(1/R^{2}\). The ambient potential for most of the channel (\(s>50\) m) can be seen as the darkest blue curve. The position of the propagating negative leader tip at each time step (each colored curve) is indicated by the sharp increase in the respective curves in all three panels of Figure 6. We also remind the reader that as a fundamental model assumption the potential is uniform within the channel, so the channel extent is indicated by horizontal lines in Figure 6a. Some distance past the positive tip of the leader (in the \(-s\) direction) is also included to show the return to ambient conditions on that end.
Figure 6a shows that the potential along the active part of the channel is always a horizontal line due to the equipotential assumption, and the overall channel potential is increasing over time as the leader grows in length. If we consider the dart leader as transporting negative charge while leaving relatively stationary positive charge behind, then this increase in channel potential over time corresponds to an overall decrease in potential energy as expected. We can also see that the charge distribution (Figure 6) essentially satisfies \(\lambda(s)\propto\Phi_{chu}\ -\ \Phi_{amb}(s)\) away from the tips.
The amount of charge at the negative leader tip in Figure 6b does increase initially as in our simple dipole model in [PERSON] et al. (2023b), but then the charge at the tip decreases somewhat as the leader progresses. However, there is a larger deposit of charge behind the tip (negative charge from \(1000<s<3500\)), which remains present to the end of leader propagation. The charge density at the positive tip also increases continually as the leader progresses, although the increase is fastest at the beginning. The combined effects of the increasing positive tip charge,
Figure 6: Plot of the potential distribution (a), charge density distribution (b), and current distribution (c) along the leader channel, colored by time, for the \(n\ =2\) polynomial ambient field. In all three plots, the sharp increase at the leading edge indicates the leader tip position at that time.
decreasing negative tip charge, and remaining negative charge along much of the channel may be the cause of the nearly constant tip charge in our previous dipole model as the leader slowed to a stop ([PERSON] et al., 2023b). The scale of the charge density at tens of \(\mu\)C/m is much smaller than typical charge density estimates of about 1 mC/m, but these estimates are typically for stepped leaders in virgin air, where the ambient fields (and thus charge density) are much higher.
The current in Figure 6c is highest right at the negative tip. For a more realistic channel with some finite conductivity, we would expect this peak to follow a little behind the leader tip as the charge density at the tip takes some finite time to build. An example of this lagging, current peak is presented by [PERSON] and [PERSON] (2015) (their Figure 5c). The amount the current peak lags behind the propagating tip depends on how fast the leader propagates relative to the timescale at which the new leader segment approaches equipotential with the rest of the channel. The current then drops off toward the stationary positive tip of the leader since the potential is not changing as much at that end. The peak current magnitude is about 800 A, which is in reasonable agreement with the \"typical\" dart leader current of 1 kA given in [PERSON] and [PERSON] (2003) Table 1.
## 5 Discussion
### Validity of the Equipotential Assumption
Our modeling results assume a perfect equipotential channel; therefore, the conclusions we draw about dart leader propagation are only valid if real dart leader channels are approximately equipotential. In this section, we put forward three arguments that dart leader channels are approximately equipotential, and that our modeling results are therefore valid.
First, a channel with finite conductivity \(\sigma_{R}\) will approach an equipotential over time, so the key question is how the timescale at which the channel reaches equipotential compares to the timescale of the leader propagation.
For a channel of length L with conductivity \(\sigma_{R}\) and conductive/resistive radius \(r_{R}\), the total channel resistance is given by
\[R=\frac{L}{\sigma_{R}\sigma_{R}^{2}} \tag{21}\]
We can then estimate the timescale at which the leader approaches equipotential as \(\tau\approx RC/10\) (see Appendix B for a derivation). Writing the equation out fully combining Equations 17 and 21, we have
\[\tau\approx\frac{1}{10}\frac{2\pi\varepsilon_{0}L}{\ln(L/r_{C})}\frac{L}{ \sigma_{R}\pi r_{R}^{2}} \tag{22}\]
This time constant is derived assuming a channel of fixed length \(L\) suddenly becomes conductive in a uniform field, which does not really match the conditions of an extending channel in a nonuniform field, but it is still useful to consider the results of this simple approximation.
High speed spectroscopy observations of dart leaders suggest that they reach temperatures of \(\sim\) 20 kK ([PERSON] et al., 2017; [PERSON], 1975), which corresponds to equilibrium conductivity \(\sigma_{R}\) of about 10 kS/m ([PERSON] et al., 2017; [PERSON], 1963). The conductive radius \(r_{R}\) of a dart leader channel is estimated to be about 1-4 mm ([PERSON], 1998), and for a well-developed dart leader, it is likely to be closer to 4 mm. The channel for leader K-5 is about 3,500 m long by the end of its propagation, so with \(r_{R}\) = 4 mm and \(\sigma_{R}\) = 10 kS/m we get a time constant of \(\tau\) = 10 \(\mu\)s. Since 10 \(\mu\)s is short compared to the propagation timescale of dart leaders (100-1,000 \(\mu\)s), the dart leader channel should be close to equipotential.
As a second argument, \(\tau\) is also an estimate of how long it should take the field change to stop after propagation ceases. Any significant current in the channel will lead to a changing field at the ground. Ohm's Law \(j=\sigma E\) suggests that the current will only drop if either the field or conductivity drop. The channel conductivity is kept high by current heating the channel, so we should not expect the conductivity to drop while there is still significant current on the channel. Thus, for a hot plasma channel, the current will only stop when the field along the channel drops to essentially zero. Therefore, the channel must be close to an equipotential when the field on the ground has stopped changing and \(\tau\) must also be low enough to allow the channel to reach equipotential by this time. Since the measured fields in Figures 4a and 4b have essentially stopped changing even before the leader has stopped propagating, we can assume that the leader is in fact close to an equipotential.
Finally, we consider the nonlinear resistance of a plasma channel. A plasma channel with some applied current will quickly reach equilibrium between ohmic heating and heat losses. Laboratory experiments performed by [PERSON] et al. (2006) suggest this happens on a timescale around 1-10 \(\mu\)s. The associated resistance will cause the current in the channel to be somewhat less than the ideal equipotential current, and the channel will take longer to reach the equipotential charge distribution. Therefore, there will be some remaining potential gradient (\(\
abla\Phi_{obs}\)) along the channel while it is still extending.
Laboratory experiments give us some idea of the magnitude of \(\
abla\Phi_{obs}\). In a free burning arc experiment [PERSON] et al. (2006) found a nearly constant potential gradient of 2.5 kV/m across the channel while the applied current decreased from 2300 to 600 A. Similarly, [PERSON] (1962) suggested that for currents above 100 A the channel reaches a steady state potential gradient of 1 kV/m; although based on other experiments, [PERSON] and [PERSON] (2014) argued that for long lightning channels the potential gradient should continue to decrease as current increases beyond 100 A. Any of these potential gradients are small enough that they should not significantly change our results. To verify this, we model dart leader K-5 while including the worst-case-scenario of a constant potential gradient of 2.5 kV/m from [PERSON] et al. (2006). If the potential gradient were lower than 2.5 kV/m, the channel would be closer to an ideal equipotential and therefore closer to the model results we have already presented.
To model the constant potential gradient, we set the channel potential gradient \(\
abla\Phi_{obs}\) to be equal to the constant gradient \(\
abla\Phi_{convex}\) as long as the resulting \(\Phi_{obs}(s)\) is between \(\Phi_{max}(s)\) and the ideal equipotential value at each point. Otherwise, the channel remains at \(\Phi_{obs}(s)=\Phi_{min}(s)\). In keeping with our second argument for the equipotential model, we allow \(\
abla\Phi_{obs}\) to approach zero as the leader slows to a stop. Based on Figure 11 of [PERSON] et al. (2006), we drop \(\
abla\Phi_{obs}\) to zero linearly over about 350 \(\mu\)s.
Figures in the format of Figures 4 and 6 are included in Supporting Information S1 for \(\
abla\Phi_{center}=2.5\) kV/m (Figures S3 and S4 in Supporting Information S1). We show the \(n=1\) ambient field because the \(n=2\) case has convergence issues when including the potential gradient. The results shown in Figures S3 and S4 in Supporting Information S1 are very similar to the ideal equipotential results. Therefore, the results of our equipotential modeling are a good approximation of the true leader properties even if a real leader has some internal potential gradient. This is true as soon as the channel has reached equilibrium between ohmic heating and heat losses, which seems to occur within 1-10 \(\mu\)s ([PERSON] et al., 2006).
### Branch Junctions
In [PERSON] et al. (2023b), we hypothesized that the rapid speed variations as dart leaders passed branch junctions may be caused by charge deposits near those junctions. If the two branches were previously conductive at different times, they may be at very different potentials, and a significant amount of charge would be deposited at the transition from one potential to the other. The negative dart leader tip would be repelled by a negative charge deposit near the junction, so that the dart leader might decelerate while approaching the junction and accelerate after passing it.
It is clear from the results in Section 4 that rapid variations in the ambient field are not resolved based purely on fitting to the measured field changes at the ground. In order to test our branch junction hypothesis explicitly, we need to modify our approach. Since the results in Section 4.2 do suggest a correlation between the tip field \(E_{\text{tip}}\) and the leader speed, we add this as another constraint using our assumed relationship of \(v=\mu E_{\text{tip}}\), leading to a \(\chi^{2}\) value
\[\chi^{2}_{speed}=\sum_{\alpha}\frac{\left(\mu E_{\text{tip}}(t_{\alpha})-v_{ obs}(t_{\alpha})\right)^{2}}{\sigma_{speed}^{2}} \tag{23}\]
We also add a term to the ambient field, which corresponds to the charge configuration in Figure 7. For a branch junction at location \(s_{junc}\) with a point charge \(q_{junc}\) at a distance \(h_{junc}\) along the perpendicular second branch, the resulting electric field on the leader channel is \[E_{junc}(s)=\frac{q_{junc}}{4\pi\epsilon_{0}}\frac{s-s_{junc}}{\left[(s-s_{junc})^{ 2}+h_{junc}^{2}\right]^{3/2}} \tag{24}\]
where we are treating the channel as perfectly straight for simplicity and calculating the \(\overrightarrow{E}_{junc}\cdot\hat{s}\) component of the field.
To avoid having the junction charge significantly modify the field fit away from the junction, we find the fitting parameters in two stages. First, \(h_{junc}\) and \(q_{junc}\) are fit using the Levenberg-Marquardt algorithm, while using an assumed value of \(s_{junc}=1.675\) m since this is where the change in speed is observed along the channel. The same \(n=2\) ambient field previously found in Section 4 is used as the background field. The value of \(\mu=15\) m\({}^{2}\)/(Vs) from Section 4.2 is also used so that the proportionality between the speed and tip field remains the same. The time range of Equation 23 is limited to \(t=100\,\mu\)s to \(t=260\,\mu\)s, since this is the range of the dip in the observed speed (Figure 4). This way we are fitting the dip specifically without trying to optimize the fit for other times. For the fast antenna field change fit, we continue to use full time range. The combined goodness of fit parameter is then \(\chi^{2}_{\rm{ste}}=\chi^{2}_{F01}\,+\,\chi^{2}_{F022}\,+\,\alpha^{2}_{\rm{ speed}}\) where \(\alpha\) is a weighting term, which we adjusted manually to achieve a reasonable balance between fitting the field change and the speed.
After finding a reasonable fit for the junction point charge parameters, we then refit the background field with a 2 nd order polynomial in order to find a better fit with both terms present. This process could be repeated iteratively, alternating between junction charge and background field fits, but we found one iteration was enough in this case. It may also be possible to fit the junction charge and background field both at the same time, but due to issue with convergence to the optimal result and the need for human judgment in weighting the \(\chi^{2}\) values, the two stage approach was more tractable.
Figure 8: Equipotential model results when adding the junction charge term to the \(n=2\) ambient field from Section 4. In the same format as Figure 4, the plot shows the measured and fit field change versus time for FA01 (a) and FA02 (b), the ambient field versus channel distance (c) including the background 2 nd order polynomial field, the junction charge field, and the sum of these two components. The leader tip field versus time (d, left axis) and tip potential drop versus time (d, right axis) is shown along with the measured and modeled leader speed versus time (e).
Figure 7: A diagram showing the configuration of the branch junction charge as hypothesized by [PERSON] et al. (2023) The junction between branches is located at a point \(s_{junc}\). A charge \(q_{junc}\) is located a perpendicular distance \(h_{junc}\) away from the junction point along the second branch.
The results from this process are shown in Figure 8. Figures 8a and 8b show essentially the same field change at the ground as the \(n=2\) results in Figures 4a and 4b. The ambient field in Figure 8 includes the 2 nd order polynomial background field, the junction charge field from Equation 24 and the sum of the two field terms. The best fit values are \(h_{junc}=265\) m and \(q_{junc}=-92\) mC. The tip field and tip potential drop versus time in Figure 8d show a pronounced dip around the location of the dip in speed in Figure 8e. We further include the modeled \(v\,=\,\mu E\) in Figure 8e, in general there is now an excellent agreement with the measured leader speed for the whole leader duration.
We note that there is no branch visible in the BIMAP-3D sources at the \(s_{junc}=1675\) m location of the simulated charge, even when we include all VHF sources from the full recorded flash. There are multiple small side branches within a few hundred meters of this location that appear in VHF either before or after K-5, and possibly the speed variation we observe is due to the combined influence of these multiple side branches. It is also possible that some previous leader activity deposited charge directly along the channel without the need for a branch junction. Ultimately, our modeling, in conjunction with the observation of speed variations, suggests the presence of some excess charge along the channel, although the source of this charge is not clear in this case. Either way, we have at least demonstrated that our hypothesis from [PERSON] et al. (2023b) is generally viable. We have reinforced our conclusion from Section 4.2 that, using the equipotential model, a leader speed relationship of \(v\,=\,\mu E_{\text{tip}}\) is consistent with both our observations of field changes at the ground and the observed leader speed. Further, under the equipotential model, it is possible for a charge deposit a relatively short distance from the primary channel to cause \(E_{\text{tip}}\) to exhibit a rapid drop and recovery, such as the branch junction speed changes reported in [PERSON] et al. (2023b), without significantly changing the field change measured at the ground.
### Bidirectional Development
High speed camera observations of dart leaders initiating outside of clouds indicate that the bright channel initially extends bidirectionally, but the extension in the positive tip direction quickly halts once it reaches the previously observed end of the preconditioned channel ([PERSON] et al., 2024; [PERSON], 2016). Unfortunately, this extension in the positive direction is not observed in VHF by BIMAP-3D.
We have performed some tests assuming the positive tip extends at the same speed as the negative tip until it reaches the end of the branch as observed in earlier VHF. Plots showing the K-5 results when including this bidirectional development are included in Supporting Information S1 (Figures S5 and S6) in the style of Figures 4 and 6. The estimated ambient field is somewhat lower in magnitude when including bidirectional development but still generally decreases in the direction of propagation. The modeled negative tip field is slightly lower, peaking at about 500 kV/m rather than 800 kV/m, but it is still generally correlated with the leader speed. Thus, the inclusion of this bidirectional development does not significantly change any of our conclusions. The most significant change is that the current is high at both leader tips while they are propagating with a more uniform current through the middle of the channel. After the positive tip reaches the inferred end of the branch and stops propagating, the current distribution is similar to the distribution shown in Figure 6.
### Other Dart Leaders
We also estimated ambient fields and tip fields for several other IC dart leaders from the same flash analyzed by [PERSON] et al. (2023b). Figures for these are included in Supporting Information S1 (Figures S7-S16) to avoid an excessive number of figures in the main text. The path each dart leader follows can be seen in the figures of [PERSON] et al. (2023b) or the figures and animations in Supporting Information S1 for that paper ([PERSON] et al., 2023a).
In most cases shown in Supporting Information S1, we were able to find ambient fields such that the modeled leader fit both the measured field changes, while also having a tip field which was generally correlated with the leader speed. In all these valid cases, the estimated cloud field generally decreases along the channel length similar to Figure 4c. The highest field values are also similarly low, less than about 10-15 kV/m.
In general, the modeled leader tip fields seem to explain the major trends in increasing or decreasing average leader speed, while failing to capture the more complex speed variations of some leaders. These generally support our conclusion that the observed leader speed trends can be explained as \(v\,\propto\,E_{\text{tip}}\) for an equipotential leader, especially considering we are estimating the ambient field with only a few degrees of freedom, so we cannot expect to match complicated variations in speed.
For the empirical relation \(v=\mu E_{\text{tip}}\), we find \(\mu\) values ranging between 10 and 30 m\({}^{2}\)/Vs. For the relation \(v=\eta\Delta\Phi_{\text{tip}}\), we find \(\eta\) values ranging between 1 and 4 m/Vs. Since our uncertainties are large and the quality of fit varies for each leader, we cannot say whether the differences in these values among different dart leaders are caused by random uncertainty or if they reflect something more fundamental such as the temperature of the pre-dart-leader channel in each case.
In a few cases (the full K-8 and K-13, Figures S12 and S16 in Supporting Information S1, respectively), we were not able to match the measured field changes from both stations. These cases indicate that it is possible for a dart leader to have a more complicated field change even if the observed development in VHF seems fairly simple. Comparing the field change timing (Figures S12 and S16 in Supporting Information S1) to the leader development ([PERSON] et al., 2023), for both K-8 Full and K-13, the shift toward a positive field change at FA02 occurs close to the time that those dart leaders reach junction J1. This strongly indicates that the more complicated field changes are caused by VHF invisible development into the other branch at J1. These cases are included to show that while our equipotential model constrained by the BIMAP-3D observations works in most cases, there are some exceptions.
## 6 Summary and Conclusions
In this paper, we have modeled dart leaders with a contemporary version of the equipotential leader model first proposed by [PERSON] (1960). Using the observed 3D dart leader development and ground electric field changes, along with the equipotential model, we then applied standard inverse problem techniques to estimate the ambient field in the cloud. The equipotential model then also provided some insights into the development of the channel, including the channel potential, charge density, and current along with the electric field at the leader tip. Due to the integral nature of the electrostatic field change at the ground in Equation 15, there are essentially an infinite number of ambient field solutions, which will fit the observed field changes even when constrained by the path and speed of leader development as observed by BIMAP-3D. Solving for this ambient field is thus an \"ill-posed\" inverse problem. The modeled dart leader channel properties are therefore not definitive but are at least consistent with our observations. The fact that our modeled results seem to explain more general observed properties of dart leaders, and the fact that we obtained most of these model results using only simple linear or quadratic ambient fields lend further credibility to our claims.
The following conclusions, listed according to their corresponding section within this paper, are consistent with our observations:
Section 4.1
1. A physically plausible ambient field \(E_{\text{amb}}\) that matches VHF observations of channel development and electric field changes at the ground can be found.
2. The estimated ambient field along the dart leader channel is generally low less than 15 kV/m (\(0.01E_{\text{iso}}\delta\) at 7 km) and decreasing in the direction of dart leader propagation.
3. The modeled \(E_{\text{tip}}\) and \(\Delta\Phi_{\text{tip}}\) are essentially proportional to each other.
4. \(E_{\text{tip}}\) is generally less than the normal breakdown threshold at 7 km and ambient temperature. This possibly explains why dart leaders are typically confined to preconditioned channels.
5. The modeled \(E_{\text{tip}}\) values are close to the negative streamer stability field in ambient air \(E_{\text{iso}}\cdot\delta\), suggesting that negative streamers should only extend a few meters radially outward from the channel in agreement with VHF observations of narrow dart leader channels ([PERSON] et al., 2023; [PERSON] et al., 2021; [PERSON] et al., 2023).
Section 4.2
1. \(E_{\text{tip}}\) and \(\Delta\Phi_{\text{tip}}\) are correlated with the observed leader propagation speed.
2. The square root of the current at the leader tip is also correlated with leader speed, this is expected since the model equations yield \(I_{tip}\propto v\cdot E_{\text{tip}}\) and our model results show \(E_{\text{tip}}\propto v\).
Section 4.3
1. The equipotential model allows the calculation of the potential of the leader channel as well as the charge and current distributions, all resolved in time and space.
Section 5.11. The equipotential model is a good approximation of the true leader properties. Section 5.2
2. A charge deposit near the channel can produce tip field variations, which could explain the speed variations we observed associated with branch junctions by [PERSON] et al. (2023b). Section 5.4
3. Similar results to the above conclusions can be obtained for several other dart leaders from the same flash.
4. For the empirical relation \(v=\mu E_{\text{tip}}\), we find typical values of 10\(<\)\(\mu\)\(<\)30 m\({}^{2}\)/Vs.
5. For the empirical relation \(v=\eta_{\Delta}\Phi_{\text{tip}}\), we find typical values of 1\(<\)\(\eta\)\(<\)4 m/Vs.
6. In a few cases, the model cannot fit the observed field changes at both stations simultaneously, we suggest these cases may correspond to VHF invisible development along other branches in the flash structure.
In addition to specific insights we have gained into dart leader development, we hope this paper ultimately serves as a proof of concept for a method to combine observations and physics-based modeling in order to improve our understanding of lightning processes in general.
## Appendix A Cylinder Tip Field Derivation
The electric field produced by any uniform volume of charge is given by
\[\overrightarrow{E}=\frac{1}{4\pi\epsilon_{0}}\iiint\frac{\rho}{R^{3}} \overrightarrow{R}dV \tag{10}\]
Consider a uniformly charged cylinder and the electric field produced along the \(\hat{z}\) axis. By symmetry, the electric field will only be in the \(\hat{z}\) direction, so we can replace \(\overrightarrow{R}\) with \(\overrightarrow{R}:\hat{z}=z\). We will also have \(R=\sqrt{r^{\prime 2}+\frac{z}{z}}\), and the volume element becomes \(dV=r^{\prime}d\phi dr^{\prime}dz\). So we have
\[E_{\text{cyl}}(z)=\frac{1}{4\pi\epsilon_{0}}\iiint\frac{\rho z^{\prime}}{(r^ {\prime 2}+z^{2})^{\chi/2}}d\phi dr^{\prime}dz=\frac{1}{2\epsilon_{0}}\iiint \frac{\rho z^{\prime}}{(r^{\prime 2}+z^{2})^{\chi/2}}dr^{\prime}dz \tag{11}\]
where the integral over \(\phi\) is trivial since there is no \(\phi\) dependence. The term in the integral should be recognizable as the electric field on the axis of a ring of uniform charge with radius \(r^{\prime}\) for a total charge \(\rho r^{\prime}\) (with appropriate units for \(\rho\)).
If the cylinder of charge has radius \(r\), then the integral over \(r^{\prime}\) is
\[E_{\text{cyl}}(z)=\frac{1}{2\epsilon_{0}}\iiint\frac{\rho z^{\prime}}{0} \frac{\rho z^{\prime}}{(r^{\prime 2}+z^{2})^{\chi/2}}dr^{\prime}dz=\frac{1}{2 \epsilon_{0}}\int\left[-\frac{\rho z}{\sqrt{r^{\prime 2}+z^{2}}}\right]\int_{0}^{r}dz \tag{12}\]
which evaluates to
\[E_{\text{cyl}}(z)=\frac{\rho}{2\epsilon_{0}}\int\left(1-\frac{z}{\sqrt{r^{2} +z^{2}}}\right)dz \tag{13}\]
where this equation without the integral should be recognizable as the electric field on the axis of a uniformly charged disk, where \(\rho\) would be a surface charge density instead of a volume density.
To find the field from the full cylinder, we then integrate over uniformly charged disks at location \(z^{\prime}\), so we substitute \(z\to z-z^{\prime}\) and integrate over \(z^{\prime}\). For a cylinder that extends from \(z^{\prime}=-L\) to \(z^{\prime}=0\) the integral is then \[E_{cy}(z)=\frac{\rho}{2\epsilon_{0}}\int_{-L}^{0}\left(1-\frac{\left(z-z^{\prime} \right)}{\sqrt{r^{2}+\left(z-z^{\prime}\right)^{2}}}\right)dz^{\prime}=\frac{ \rho}{2\epsilon_{0}}\left[z^{\prime}+\sqrt{r^{2}+\left(z-z^{\prime}\right)^{2} }\right]\bigg{|}_{-L}^{0} \tag{10}\]
which evaluates to
\[E_{cy}(z)=\frac{\rho}{2\epsilon_{0}}\left[\sqrt{r^{2}+z^{2}}+L-\sqrt{r^{2}+ \left(z+L\right)^{2}}\right] \tag{11}\]
This is the same as Equation 9 in the main text if we substitute \(z\to s\), \(L\rightarrow\Delta s\), and \(\rho\rightarrow\lambda/\left(2\pi r^{2}\right)\).
## Appendix B Time Constant Derivation
To first order, the self-capacitance \(C_{int}\) of a long cylindrical leader channel is given by Equation 17. The total resistance \(R_{tot}\) of the channel is then given by Equation 21. If we split this leader channel into N discrete segments, then each segment has capacitance \(C_{tot}/N\) and resistance \(R_{tot}/N\). We note that the capacitance \(C_{tot}/N\) is not between the channel and some hypothetical coaxial shell but rather the self-capacitance between each cylindrical segment of length \(L/N\) and every other segment of the channel.
If the leader is initially nonconductive in a uniform electric field and then suddenly becomes conductive, this is analogous to being driven by equal and opposite voltages at the two ends and then having the voltage supplies suddenly disconnected. We set the potential at the center of the leader to 0 for convenience, since the channel will approach the central potential in a uniform field (Equation 3).
First, we consider the simple case of N = 2 segments. We then have an electrical circuit with two capacitors of value \(C=C_{tot}/2\) separated by a resistor of value \(R=R_{tot}/2\) as shown in Figure 11. If this circuit is driven by equal and opposite voltages \(+V\) and \(-V\) (analogous to a leader channel in a uniform field), then by symmetry the voltage must always be 0 in the middle of the resistor, and the circuit in Figure 11 is equivalent to the circuit in Figure 11 (up to the sign of the voltage). The circuit in Figure 11 is a regular RC circuit, so we can immediately see that the time constant is \(\tau=\left(R_{tot}/4\right)\left(C_{tot}/2\right)=R_{tot}C_{tot}/8\). For N = 2 our choice of \(R=R_{tot}/2\) is somewhat contrived, but as N gets larger the difference between \(R_{tot}\) and \(R_{tot}(N-1)/N\) becomes negligibly small.
We then consider the N = 4 case, shown in Figure 11. Again by symmetry, we can see that the voltage at the center of the middle resistor must always be zero, and thus the discharging circuit is equivalent to Figure 11. After applying [PERSON]'s node law for this circuit and substituting the relevant terms in voltage and \(\frac{dV}{d}\), we get a system of ordinary differential equations
\[\frac{dV_{1}}{dt}=\frac{16}{R_{tot}C_{tot}}(-V_{1}+V_{2}) \tag{12}\]
\[\frac{dV_{2}}{dt}=\frac{16}{R_{tot}C_{tot}}(V_{1}-3V_{2}) \tag{13}\]
where \(V_{1}\) and \(V_{2}\) are indicated in Figure 11.
This system of differential equations can be reframed as an eigenvalue problem by writing the system as
\[\frac{d}{dt}\begin{bmatrix}V_{1}\\ V_{2}\end{bmatrix}=\frac{16}{R_{tot}C_{tot}}\begin{bmatrix}-1&1\\ 1&-3\end{bmatrix}\begin{bmatrix}V_{1}\\ V_{2}\end{bmatrix} \tag{14}\]
which has a solution of the form
\[\overline{V}=\overline{X}\epsilon^{\mu} \tag{15}\]where \(\overrightarrow{X}\) is an eigenvector and \(\lambda\) is the corresponding eigenvalue of the matrix in Equation 11. The system of capacitors will then have two time constants corresponding to the eigenvalues \(\tau=1/\lambda\). In this case, the eigenvalues and corresponding eigenvectors are
\[\lambda=\frac{16}{R_{\text{tot}}C_{\text{tot}}}(\pm\sqrt{2}-2);\quad \overrightarrow{X}=\begin{bmatrix}1\pm\sqrt{2}\\ 1\end{bmatrix} \tag{12}\]
The full solution will be a linear combination of solutions of the form given in Equation 10 for the two eigenvalue/eigenvector pairs, but for our purposes, we are interested only in the time constants \(\tau=1/\lambda\). Since we are trying to estimate an upper bound for the timescale at which a leader channel reaches equipotential, we are interested in the long run behavior (\(t\,\rightarrow\,\infty\)). The faster time constant term will decay more quickly, leaving the slower time constant term to dominate in the long run. This time constant is
\[\tau=\frac{R_{\text{tot}}C_{\text{tot}}}{16(2-\sqrt{2})}\approx\frac{R_{\text{ tot}}C_{\text{tot}}}{9.37} \tag{13}\]
Checking higher orders of N with numerical simulations, we find that the decay time remains within the range
\[\frac{R_{\text{tot}}C_{\text{tot}}}{8}<\tau<\frac{R_{\text{tot}}C_{\text{tot} }}{10} \tag{14}\]
We thus suggest \(\tau=\,RC/10\) as a convenient rule of thumb for the timescale at which a lightning channel becomes an equipotential. Strictly speaking this approximation is only valid for a stationary channel, which suddenly develops in a uniform field, but it may still be a useful reference for a more realistic model of leader development.
## Data Availability Statement
The 3D mapping and field change data used for this paper has previously been made available online ([PERSON] et al., 2023). All data files are in text format with headers that describe each data column. A PDF is included, which describes the included files and gives examples of the headers and column format.
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wiley/fca81546_e2a2_47f6_8088_9850b710ddfb.md | # Earth and Space Science
Evolution of Five Reanalysis Products With Radiosonde Observations Over the Central Taklimakan Desert During Summer
[PERSON]
1 State Key Laboratory of Severe Weather (LAsW), Chinese Academy of Meteorological Sciences, Beijing, China, 1
[PERSON]
1 State Key Laboratory of Severe Weather (LAsW), Chinese Academy of Meteorological Sciences, Beijing, China, 1
[PERSON]
2
[PERSON]
3
[PERSON]
1 State Key Laboratory of Severe Weather (LAsW), Chinese Academy of Meteorological Sciences, Beijing, China, 1
[PERSON]
2
[PERSON]
1 State Key Laboratory of Severe Weather (LAsW), Chinese Academy of Meteorological Sciences, Beijing, China, 1
[PERSON]
1 State Key Laboratory of Severe Weather (LAsW), Chinese Academy of Meteorological Sciences, Beijing, China, 1
###### Abstract
To provide guidance for the use of reanalysis data in the Central Taklimakan Desert (CTD), five reanalysis products are evaluated based on the radiosonde data obtained from two field experiments during summer for the first time in the CTD, including the European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis version 5 (ERA5), ECMWF Reanalysis-Interim (ERA-Interim), Japanese 55-years Reanalysis (JRA55), Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA2), and the National Centers for Environmental Prediction-Department of Energy Reanalysis version 2 (NCEP2). The results show that reanalysis temperature (\(T\)), specific humidity (\(Q\)), geopotential height (GPH), and wind field (\(U\) and \(V\) components) are consistent with the radiosonde observations in terms of the vertical distribution. In general, ERA5 has the best performance in the CTD during the study period, followed closely by ERA-Interim. However, NCEP2 produces the largest error. The errors of all the reanalysis data show significant diurnal variations, and the diurnal variations differ from each other. Moreover, the results indicate that the reanalysis datasets have the largest deviation at 850 hPa (near the ground), which means that in the desert region complex interactions may exist between the land surface and the atmosphere. Therefore, more attention should be paid to the description of complex interactions between land and atmosphere over the moving-sand desert region in the numerical models.
2021
Evolution of Five Reanalysis Products With Radiosonde Observations Over the Central Taklimakan Desert During Summer
13 APR 2021
19 FEB 2021
Evolution of Five Reanalysis Products With Radiosonde Observations Over the Central Taklimakan Desert During Summer
13 APR 2021
## 1 Introduction
The Taklimakan Desert (TD) is located in the Eurasian continent in the mid-latitude region of the Northern Hemisphere ([PERSON] et al., 2016). As the second-largest desert in the world, it occupies the central part of the Tarim Basin, with a total area of \(\sim\)337,600 km\({}^{2}\), and the average elevation is about 1.1 km. TD is flanked by high mountain ranges, the Pamirs to the west, Tianshan Mountain to the north, and Kunlun Mountain to the south. Due to the special topography, the easterty wind is dominant in the lower troposphere ([PERSON] et al., 2016). As shown in Figure 1, TD is covered by moving sand that can spread hundreds of kilometers, causing inconvenient transportation ([PERSON] et al., 2001). Besides, due to the dry climate, the frequency of sand storms have been increased in this region in the last decades ([PERSON] et al., 2017; [PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON] et al., 2007), it brings danger to the habitants ([PERSON] et al., 2017). More than this, as the main dust source in East Asia ([PERSON] et al., 2001; [PERSON] et al., 2003), TD has a great influence on global weather and climate. Since the dust particles in TD can be transported to North America and other regions, it affects the radiation budget and hydrological cycle there ([PERSON] et al., 2016; [PERSON] et al., 2017).
At present, as shown in Figure 1, there is only one conventional surface station available (shown as a black dot) in the Central Taklimakan Desert (CTD) due to the harsh natural conditions (e.g., moving-sand, sandstorm), which is far below the requirement to understand the characteristics of weather and climate over this region. Consequently, atmospheric reanalysis data has been widely used for weather, climate, and environmental studies in this area as the substitute for observational data (e.g., [PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2019). However, there exist many uncertainties of the reanalysis data because only a few observational data in this region are assimilated into the reanalysis products ([PERSON] et al., 2004). Besides, although satellite observations have been widely used in the reanalysis data with the development of data assimilation techniques, many uncertainties may be contained in the reanalysis data due to the shortcomings of satellite data in the desert area ([PERSON] & [PERSON], 2009). Furthermore, uncertainties may also be causedby data assimilation technique and predictive model ([PERSON] et al., 1996; [PERSON] et al., 2014). In view of these inherent uncertainties, it is highly imperative to assess the reanalysis data before weather, climate, and environmental studies ([PERSON] et al., 2011; [PERSON] et al., 2019; [PERSON] et al., 2014).
Several previous studies have shown that reanalysis datasets have multiple degrees of errors for meteorological variables, especially in regions with harsh environmental conditions and insufficient observation data. For instance, based on the comparison of observations at weather stations and reanalysis data (MERRA, NCEP/NCAR-1, CFSR, ERA-40, ERA-Interim, and GLDAS), [PERSON] and [PERSON] (2012) pointed out that CFSR has the best overall performance over the Tibetan Plateau, while NCEP/NCAR-1 ranks at the last place. By evaluating reanalysis temperature and precipitation amount of the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) (R1) and NCEP-Department of Energy (NCEP-DOE) (R2) based on the surface weather observations, R1 and R2 are found to perform worst for precipitation amount than temperature over the Western Himalayas by [PERSON] et al. (2017). Besides, they found that R1 and R2 perform better for temperature on stations at higher elevations than at lower elevations. Also, [PERSON] et al. (2010) used both surface weather stations and radiosonde observations to verify the performance of the reanalysis products of ECMWF Reanalysis-40 years (ERA-40) and NCEP-NCAR in the Antarctic and found that both products capture the intraseasonal variability of temperature and pressure during winter over the Antarctic.
The quality of reanalysis data in the CTD given by the global model remains uncleardute to the less observational data available there. In this study, the radiosonde data obtained from two experimental field observations in the CTD is used to evaluate the performance of five widely used reanalysis products, including the
Figure 1.— Spatial distribution of observational stations, surface classifications (shaded in colors), and elevation (contours) over the Taklimakan Desert and its surrounding areas. Operational radiosonde and surface stations are marked with black circles and asterisks, respectively. Circles with crosses denote sites where both radiosonde and surface observations are available. The black dot represents the radiosonde site (83.63\({}^{\circ}\)E, 39.04\({}^{\circ}\)N, 1.099.3 m) in the central Taklimakan Desert. The closest four grid points, which are used to interpolate to the radiosonde site by the bilinear interpolation method, surrounding the radiosonde site from ERASA, ERA-Interim, JRAS5, MERRA2, and NCEP2, are denoted with respective boxes of red, green, blue, black, and purple lines.
European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis version 5 (ERA5), ECMWF Reanalysis-Interim (ERA-Interim), the Japanese 55-years Reanalysis (JRA55), the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA2), and the National Centers for Environmental Prediction-Department of Energy Reanalysis version 2 (NCEP2). This study aims to lift the veil on the accuracy of the reanalysis data of CTD, and might provide a guidance to increase the accuracy of numerical model forecasts in this region where only sparse observations are available due to the complicated underlying boundary conditions.
The remainder of this paper is organized as follows. Section 2 gives an overview of the observations and reanalysis datasets, as well as a brief description of the research method. Section 3 provides detailed results of verification, and the Taylor diagrams are applied to compare the reanalysis data in Section 4. A comparison of diurnal variations among the five reanalysis products is given in Section 5. Finally, summary and discussion are stated in Section 6.
## 2 Data and Method
### Observations and Reanalysis Datasets
Tazhong station (83.63\({}^{\circ}\)E, 39.04\({}^{\circ}\)N, 1,099.3 m) marked with a black dot in Figure 1 is located in the CTD. The radiosonde data were collected at the Tazhong station during the periods from June 25 to July 3, 2015, and the entire July in 2016, using the global positioning system (GPS) based radiosonde. During the balloon ascending, a digital radiosonde equipped with a GPS and a receiver at the ground was set up to receive and record the data. The ground receiving system (CFL-GNSS-JS) was developed by Beijing Changfeng Microelectronics Technology Company, which has been widely used in China. Four times high-resolution vertical profiles of meteorological variables were obtained every day at 0000, 0600, 1200, and 1800 UTC. One of the advantages of the radiosonde measurement is the high vertical resolution, which is achieved by high frequency (1-s per data set) data acquisition during the balloon ascending. In other words, the vertical resolution of radiosonde data is \(\sim\)5-8 m (e.g., [PERSON] et al., 2016; [PERSON] et al., 2018).
In this study, the instantaneous meteorological variables temperature (\(T\)), specific humidity (\(Q\)), geopotential height (GPH), zonal wind (\(U\)), and meridional wind (\(V\)) at the specific levels (i.e., 850, 800, 750, 700, 650, 600, 550, 500, 450, 400, 350, 300, 250, 200, 150, and 100 hPa) are selected to evaluate reanalysis products.
It should be noted that the radiosonde data used in this study was not assimilated into any of the reanalysis data. ERA5, ERA-Interim, JRA55, MERRA2, and NCEP2 are chosen to be compared with radiosonde data since they are new-generation reanalysis products. There are a variety of differences in these reanalysis data sets, in terms of temporal and spatial resolution, selected data assimilation schemes, physical parameterizations, numerical schemes, and so on ([PERSON] et al., 2012). All the reanalysis data from 850 hPa to 100 hPa with interval of 50 hPa are evaluated, except for NCEP2 with 850, 700, 600, 500, 400, 300, 250, 200, 150, and 100 hPa levels available. Corresponding to the 4-times daily radiosonde data, the instantaneous values of the reanalysis datasets with intervals of 6 h are evaluated. The specifications of the reanalysis datasets used in this study are listed in Table 1.
### Methods
In order to compare the reanalysis data on linear grids with the radiosonde data at the observational site, the reanalysis data are interpolated to the radiosonde site at the same time and same pressure levels, using the bilinear interpolation method. The closest four model grid points used to interpolate for all reanalysis are marked in Figure 1. It is worth noting that there is no obvious terrain in the CTD, while it is common that the height of sand-dunes are from several meters to tens of meters. Except the NCEP2 has a lower horizontal resolution, there are quite small differences between the observational site and the model terrain (Table 1). The statistical quantities error (\(D\)), mean error (ME), root mean square error (RMSE), correlation coefficient (\(R\)), and standard deviation (STD) are used to evaluate the performance of the chosen reanalysis datasets. An error of reanalysis data set (\(D_{i}\)) is defined as the difference between the reanalysis and the observation, which is given by \[D_{i}=F_{i}-O_{i} \tag{1}\]
\(F_{i}\) and \(O_{i}\) stand for the meteorological element of reanalysis products and observations at each time, respectively. ME, RMSE, \(R\), and STD are calculated by the following formulas, which are
\[ME=\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}D_{i} \tag{2}\]
\[RMSE=\sqrt{\frac{\underset{i=1}{\overset{N}{\sum}}D_{i}^{2}}{N}} \tag{3}\]
\[R=\frac{\frac{\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}\Big{(}F_{i}-\overline {F}\Big{)}\big{(}O_{i}-\overline{O}\Big{)}}{\sqrt{N\underset{i=1}{\overset{N}{ \sum}}\Big{(}F_{i}-\overline{F}\Big{)}^{2}}\sqrt{\frac{1}{N}\underset{i=1}{ \overset{N}{\sum}}\big{(}O_{i}-\overline{O}\Big{)}^{2}}} \tag{4}\]
\[STD=\sqrt{\frac{\underset{N=1}{\overset{N}{\sum}}\Big{(}D_{i}-ME\Big{)}^{2}} {N-1}} \tag{5}\]
where \(N\) (\(=158\)) is the total number of the observations in this study, and \(\overline{F}\) and \(\overline{O}\) stand for the average value of meteorological element of the reanalysis products and observations respectively.
## 3 Overall Root Mean Square Errors (RMSEs) and Mean Errors (MEs)
The vertical profiles of the RMSE for each reanalysis product verifying against radiosonde observations are given in Figure 2. It is obvious that the largest RMSE of \(T\) occurs at 850 hPa level which is near the ground in the CTD. At this level, ERAs has the smallest RMSE, followed by MERRA2. While NCEP2 shows the largest
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline \multicolumn{1}{c}{Reanalysis} & \multicolumn{1}{c}{Center} & \multicolumn{1}{c}{Horizontal resolution} & \multicolumn{1}{c}{Vertical levels} & \multicolumn{1}{c}{Terrain} & \multicolumn{1}{c}{Reference} \\ \hline ERA5 & ECMWF\({}^{\text{a}}\) & Model native: N320(T,639) \(\sim\)31 km Data & Model native:137 (hybrid \(\alpha\)-p) & 1,113.56 m & (Hersbach \& \\ & & files: 0.15\({}^{\text{a}}\)\(\times\) 0.15\({}^{\text{a}}\) & Data files: 37 & & & \\ ERA-Interim & ECMWF\({}^{\text{a}}\) & Model native: N128(T,255) \(\sim\)79 km Data & Model native60 (hybrid \(\alpha\)-p) & 1,096.07 m & ([PERSON] et al., 2011) & \\ & & files: 0.75\({}^{\text{a}}\)\(\times\) 0.75\({}^{\text{a}}\) & Data files: 37 & & & \\ JRA55 & JMA\({}^{\text{b}}\) & Model native: N160(T,319) \(\sim\)55 km Data & Model native60 (hybrid \(\alpha\)-p) & 1,103.36 m & ([PERSON] \& \\ & & files\({}^{\text{c}}\): 1.25\({}^{\text{a}}\)\(\times\) 1.25\({}^{\text{a}}\) & Data files: 37 & & & \\ MERRA2 & NASA GMAO\({}^{\text{a}}\) & Model native: 0.5\({}^{\text{a}}\)\(\times\) 0.625\({}^{\text{a}}\) Data files\({}^{\text{d}}\): & Model native:72 (hybrid \(\sigma\)-p) & 1,111.22 m & (Gelaro \& \\ & & 0.5\({}^{\text{a}}\)\(\times\) 0.625\({}^{\text{a}}\) & Data files\({}^{\text{d}}\): 42 & & & \\ NCEP2 & NOAA/NCEP \& DOE AMP- & Model native: F47(T62) \(\sim\) 1.875\({}^{\text{a}}\) Data files: & Model native:28 (\(\sigma\)) Data & 1,743.20 m & ([PERSON], 2001) & \\ & II project\({}^{\text{c}}\) & & files: 17 & & & \\ \hline \hline \end{tabular}
* Approximate longitude grid spacing is reported in degrees for models with regular Gaussian grids (Fn) and in kilometers for models with reduced Gaussian grids (Nn). Wavenumber truncations for models with Gaussian grids are shown in parentheses. Terrain refers to the topography height above the sea level, which is obtained from the four closest grid points surrounding the radiosonde site using the bilinear interpolation method.
* “European Center for Medium-Range Weather Forecasts.\({}^{\text{b}}\)Japanese Meteorological Agency.”National Aeronautics and Space Administration Global Modeling and Assimilation Office. \"National Oceanic and Atmospheric Administration/National Center for Environmental Prediction and the Department of Energy Atmospheric Model Intercomparison Project.”As for JRA55, data can be access from [[http://doi.org/10.5065/DeHHBH41](http://doi.org/10.5065/DeHHBH41)]([http://doi.org/10.5065/DeHHBH41](http://doi.org/10.5065/DeHHBH41)).”As for MERRA2, inst6_3 days_ana.
* No data collection were used in this work. ([[https://doi.org/10.5067/A756](https://doi.org/10.5067/A756) XP56 XZWS]([https://doi.org/10.5067/A756](https://doi.org/10.5067/A756) XP56 XZWS)).
\end{table}
Table 1: Specifications of the Reanalysis DatasetsRMSE which is about twice as large as that of ERA5. The RMSEs of \(Q\) decrease with increasing height and approach to zero near 200 hPa. It should be noted that the low RMSE values in upper levels result from very low values of \(Q\). As a matter of fact, the reanalysis datasets show a weaker capability to capture variations of \(Q\) at the upper troposphere, it can be inferred from the smaller correlation coefficients shown in Figure 3. The secondary maximum RMSE of \(Q\) appears at around 600 hPa with a temperature near 0\({}^{\circ}\)C, while the one of \(T\) occurs at 300 hPa level. The RMSEs peak of \(T\) at lower (upper) levels is related to the complicated interactions with land (tropopause). The RMSEs peak value of \(Q\) appears at the bottom with the same reason as for \(T\), while the second RMSEs peak of \(Q\) may result from the complicated cloud microphysical processes near 0\({}^{\circ}\)C. The vertical distributions of GPH show the same results as \(T\). For the vertical distributions of \(U\)/\(V\) wind field, it is different from the distribution of \(T\), its peak value appears at three levels (850 hPa, 600-500 hPa and 300 hPa) respectively. More specifically, for \(U\), the largest RMSE for ERA5, MERRA2, and MERRA2. The RMSEs peak value of \(Q\) appears at the bottom with the same reason as for \(T\), while the second RMSEs peak of \(Q\) may result from the complicated cloud microphysical processes near 0\({}^{\circ}\)C. The vertical distributions of GPH show the same results as \(T\). For the vertical distributions of \(U\)/\(V\) wind field, it is different from the distribution of \(T\), its peak value appears at three levels (850
JRA55 appear at 300 hPa not 850 hPa. Compared with others, ERA5 performs the best for \(U/V\) winds near the ground, and NCEP2 displays the largest RMSE.
Broadly speaking, the RMSEs of \(T\), Q, GPH, \(U\), and \(V\) decrease with increasing height, with the largest value of RMSE occurred near the ground, which means that in the desert region complicated interactions may exist between the land and the atmosphere, whereas the models might lack a full description of the mechanisms involving thermal and dynamical processes near the ground ([PERSON] et al., 2018). Except for \(Q\), which has very small values at the levels above 150 hPa, RMSEs of other variables increase rapidly at those levels. Around 300 hPa, \(T\), \(U\), and \(V\) have their secondary largest RMSE. The large RMSEs at 300 hPa might be related to the interactions between the troposphere and the stratosphere ([PERSON] and [PERSON], 2012).
Regarding to the vertical distributions of RMSE of different reanalysis, ERA5 has the smallest RMSE, while NCEP2 has the largest one with an exception of \(Q\). Thus, with an overview, ERA5 has the best performance ability over the CTD during the study period, followed closely by ERA-Interim. With respect to the
Figure 3: Same as Figure 2 but for correlation coefficient (\(R\)).
correlation coefficient (Figure 3), \(T\) has the highest \(R\) among the variables. Except for NCEP2, \(T\) has high \(R\) with values over 0.90 below 600 hPa. For ERA5, \(R\) of \(T\) is larger than 0.90 except for the one at 500 hPa level. Compared with other meteorological variables, \(Q\) has the worst performance in terms of \(R\), especially above 300 hPa levels. It is found out that the reanalysis products show good performances in \(T\), while it has low qualities in \(Q\). The results are in highly agreement with the results given by [PERSON] and [PERSON] (2013) over the Tibetan Plateau. On the other hand, the values of \(R\) of GPH are lower than 0.50 below 700 hPa in all the products, implying complicated interactions between land and atmosphere occur in the lower levels near the ground. Interestingly, \(U\) wind shows the lowest \(R\) near the ground, while \(V\) shows the lowest one at 700 hPa. This might be related to the dominant easterly wind in the lower levels due to the topography.
In terms of MEs (Figure 4), an atmospheric variable can be overestimated or underestimated with irregular patterns among the reanalysis products. In general, ERA5 has the lowest ME, followed closely by ERA-In-term. At 850 hPa level, \(T\) is underestimated in JRA55 and NCEP2, while it is overestimated in ERA5, ERA-Interim, and MERRA2. It is worth noting that the \(T\) cold bias near the ground of NCEP2 is likely to
Figure 4.— Same as Figure 2 but for mean error (ME).
be related to the large terrain difference between model and observation (Table 1) due to the coarse horizontal resolution of NCEP2. \(Q\) is overestimated by NCEP2, while underestimated by others at most levels. Besides, it should be emphasized that ERA5 has much less ME near the ground (850 hPa) compared to others. Concerning MEs of GPH, large errors occur at 850 hPa and 100 hPa in ERA5, JRA55, and MERRA2. Besides, GPH is overestimated at lower layers while underestimated at upper layers by ERA5, JRA55, and MERRA2. For the MEs of GPH in ERA-Interim, it is almost positive at all the levels except for 100 hPa. For NCEP2, it has positive MEs for GPH at each level, and its largest ME appears at 850 hPa. MEs of _U_(\(V\)) are underestimated at the upper level of 250 hPa in all the products except for V wind in MERRA2. In the lower levels below 500 hPa, the NCEP2 has negative MEs of _U_(\(V\)), while the other reanalysis products mostly have positive values.
There exist great differences among the reanalysis products. The great differences among the reanalysis products may be caused by several reasons (e.g., [PERSON] et al., 2014; [PERSON] et al., 2017; [PERSON] et al., 2008; [PERSON] & [PERSON], 2012), one of which is the different model resolution. ERA5 has the finest horizontal and vertical resolution, and thus gives the best capture capability. The result is consistent with [PERSON] et al. (2002) that decreasing the grid spacing to \(\sim\)10 km or less normally produces more realistic mesoscale structures, with particular benefits for orographically and diurmally driven flows. Besides, [PERSON] and [PERSON] (2012) pointed out that various numbers and types of observations assimilated in those reanalysis products is another reason for the difference. In addition, some of the differences are led by the data assimilation and numerical model systems. For instance, [PERSON] (1993) cumulus scheme is utilized in ERA-Interim, while an updated version of the Tiedtke scheme with some modifications is applied in ERA5 ([PERSON] et al., 2017).
## 4 Comparisons Among the Reanalysis Datasets
Figure 5 shows the comparisons of [PERSON] diagrams ([PERSON], 2001), which derived from the \(R\) and STD of \(T\), \(Q\), GPH, \(U\), and \(V\). In general, ERA5 (green dots) is the closest to the \"OBS\" compared with others datasets, which means that ERA5 has the highest \(R\) and the smallest RMSE. In the contrast, NCEP2 lies the furthest from the \"OBS,\" with relatively poor performance. Besides, ERA5 captures the variations (STD) better than other datasets, especially in the distribution of \(T\). For instance, similar STDs as the observations can be viewed at 400 and 150 hPa.
Regarding to the variables, all reanalysis models performed well in the \(T\) field and its variations (Figure 4(a)). However, obvious differences are visible in \(Q\) (Figure 4(b)). The reanalyzes show reasonable patterns in GPH, while all products show larger variations than the observations. The results are consistent with the vertical distribution of RMSE, \(R\), and ME in Figures 2-4. As an alternative to observation data, ERA5 is most suitable compared to the other reanalysis products, followed closely by ERA-Interim. Moreover, the variable \(T\) has the highest credibility.
## 5 Diurnal Variations of RMSEs and MEs
Figure 6 shows the diurnal variation of the RMSEs for \(T\), \(Q\), GPH, \(U\), and \(V\) in each of the reanalysis products. The RMSEs of all the meteorological elements show significant diurnal variation. Concretely speaking, ERA5 has the smallest diurnal variation, compared with other reanalysis products. Taking \(T\) as an example, the diurnal variation of ERA5 is imaparent, and the peaks of RMSEs of other reanalysis datasets appear at lower levels, in which ERA-Interim and NCEP2 have peaks of RMSEs at 0000 local standard time (LST, UTC + 6), and JRA55 and MERRA2 occurring at 1200 LST. Obviously, the RMSEs diurnal variation for \(Q\) appears below 400 hPa. However, a slight diurnal variation can be seen in upper levels due to the low RMSEs. Note again that the low RMSEs result from very small values of \(Q\) by taking \(R\) into account, not the good performance of RMSEs (Figure 2(b)). The peaks of \(Q\) occur at 0000 LST of ERA5, ERA-Interim, and MERRA2, while those of JRA55 and NCEP2 occur at 1800 LST and 1200 LST respectively. All reanalysis products have large RMSEs for GPH at 1200 LST. The errors may be related to the strong radiation in the middle of the day, which makes the atmospheric boundary layer in an unstable state and thus affects the results of the reanalysis ([PERSON], 1988). For \(U\) wind, large RMSEs occur at 0000 LST or 0600 LST, although the peaks appear at different levels. For instance, ERA5 has the largest RMSEs at 300 hPa, while NCEP2
## References
* (1)
Figure 5.— Taylor diagrams of (a) temperature (T, \({}^{\circ}\)C), (b) specific humidity (\(Q\), g kg\({}^{-1}\)), (c) geopotential height (GPH, gpm), (d) zonal wind (\(U\), m s\({}^{-1}\)), and (e) meridional wind (\(V\), m s\({}^{-1}\)) for ERA5 (dots), ERA-Interim (triangles), JRA55 (rhombuses), MERRA2 (hexagrams), and NCEP2 (stars) over the central Taklimakan Desert based on data during the study period (from June 25 to July 3, 2015, and the whole July of 2016). \"OBS\" stands for reference point. The numbers denote pressure levels in vertical from 850 hPa (1) to 100 hPa (10).
Figure 6.— Durinal variations of root mean square error (RMSE) of (a1–e1) temperature (\(T\), \({}^{\circ}\)C), (a2–e2) specific humidity (\(Q\), g kg\({}^{-1}\)), (a3–e3) geopotential height (GPH, gpm), (a4–e4) zonal wind (\(U\), m s\({}^{-1}\)), and (a5–e5) meridional wind (\(V\), m s\({}^{-1}\)) with the respective reanalysis products of ERA5, ERA-Interim, IRAS5, MERRA2, and NCEP2 at isobaric levels.
has a peak at 850 hPa with a value of 6.75 m s\({}^{-1}\). As for \(V\), except for ERA5, all the peaks of other reanalysis products occur at 0000 LST on 850 hPa.
The diurnal variation of ME is shown in Figure 7. Note that the levels and time of the ME peaks are consistent with that of the RMSE peaks, indicating that the diurnal variation of RMSE is greatly dependent on the
Figure 7.— Same as Figure 6 but for mean error (ME).
diurnal variation of ME. In view of the ME variations, irregular errors (overestimate or underestimate) of atmospheric variables are shown in the reanalysis products, indicating that the accuracy of reanalysis may be influenced by different factors. It is worth noting that the GPH of all the products are overestimated at 0000, 0600, and 1200 LST on almost all levels except for JRA55 and MERRA2.
Both RMSEs and MEs show significant diurnal variations in all variables, and the diurnal variation of RMSE is greatly dependent on the diurnal variation of ME. In summary, ERA5 has the smallest variation, while NCEP2 shows the most significant diurnal variation. Moreover, the large errors of GPH near the surface in the middle of the day (1200 LST) suggest that all the reanalysis models are insufficient to simulate the boundary layer processes with strong turbulence over CTD ([PERSON], [PERSON], et al., 2019). Therefore, more attention should be paid to investigate the characteristics in the boundary layer over CTD and to improve the boundary layer parameterization scheme of reanalysis models ([PERSON] et al., 2011).
## 6 Conclusions and Discussions
The radiosonde observational datasets (including \(T\), RH, Q, GPH, \(U\), and \(V\)) from the two field experiments carried out at Tzazhong station in CTD were utilized to evaluate the performance of five reanalysis products, including ERA5, ERA-Interim, JRA55, MERRA2, and NCEP2. By comparison, in terms of RMSE, the accuracy of ERA5 stands in the first place, followed by ERA-Interim, JRA55, MERRA2, while NCEP2 has the largest RMSE. The same results can also be detected from the comparisons in Taylor diagrams (Figure 5). ERA5 (NCEP2) has the finest (coarsest) horizontal and vertical resolution, suggesting that the model resolution plays a significant influence on the quality of the reanalysis data.
Concerned with meteorological variables, the reanalysis products provide the highest credibility of the \(T\) field in CTD. However, all the reanalysis products show large errors (RMSE and ME) on the low level of 850 hPa (near the ground). The same pattern can be found in the vertical distributions of \(Q\), GPH, and wind field, which means that in the desert region complex interactions may exist between the land surface and the atmosphere. To some extent, that also means the land-atmosphere processes were not well represented in these reanalysis model systems. In view of this, developing an appropriate representation approach by taking desert surface characteristics into account in future reanalysis works should be considered. Besides, the RMSEs of \(T\), \(Q\), GPH, \(U\), and \(V\) decrease with the increasing height. The second-largest errors of \(T\), \(U\), and \(V\) occur at the higher levels of 300 hPa, indicating that the interactions between the troposphere and stratosphere have a strong influence on the accuracy of the reanalysis products. Particularly, the secondary maximum RMSE of \(Q\) occurs at the lower level at 600 hPa, which may result from the complicated cold cloud microphysical processes near 0\({}^{\circ}\)C. RMSEs and MEs show obvious diurnal variations in the meteorological variables. By comparison, ERA5 with the highest resolution shows the smallest variation, while NCEP2 has the most significant diurnal variation. The large error near the ground of GPH in the middle of the day (1200 LST) means that the reanalysis models lack sufficient capacity to describe the boundary layer processes with strong turbulence in CTD.
Finally, we would like to mention several limitations of this statistical study. The observations were obtained in summer (June and July), thus the results only indicate the performance of these reanalysis data during summer. We infer that the largest error near the ground is related to the complicated underlying surface of the desert and interactions between the ground and the atmosphere. Detailed comparisons among the land models used in the reanalysis systems might give some clues to explain the differences between the reanalysis datasets. However, it is a challenge to launch a comparison among the land models. The shortcoming should be kept in mind in the future comprehensive observations and further studies are required. Last but not the least, although there are large differences among the reanalysis products, it is troublesome to determine what is the main factor resulting in the differences because it could be due to model configuration (e.g., resolution), model framework (e.g., physical parameterizations), assimilation system, computational techniques, etc. Nevertheless, this study proves the performance of the most widely used reanalysis products in the context of an evaluation of the observations in summer of CTD. The results may be helpful for the reanalysis data application and might provide a guide for launching comprehensive field experiments for atmospheric sciences researches in this region.
## Data Availability Statement
The ERA5 and ERA-Interim were provided by the ECMWF at ([[https://apps.cemwf.int/data-catalogues/era5/7](https://apps.cemwf.int/data-catalogues/era5/7) type=an&class=ea&stream=operf&expver=1]([https://apps.cemwf.int/data-catalogues/era5/7](https://apps.cemwf.int/data-catalogues/era5/7) type=an&class=ea&stream=operf&expver=1)) and ([[https://apps.cemwf.int/datasets/data/interim-full-daily/levtype=pl/](https://apps.cemwf.int/datasets/data/interim-full-daily/levtype=pl/)]([https://apps.cemwf.int/datasets/data/interim-full-daily/levtype=pl/](https://apps.cemwf.int/datasets/data/interim-full-daily/levtype=pl/))), respectively. The JRA55 was obtained from Japanese Meteorological Agency (JMA) and is available at ([[http://doi.org/10.5065/D6](http://doi.org/10.5065/D6) HIH6H41]([http://doi.org/10.5065/D6](http://doi.org/10.5065/D6) HIH6H41)). The MERRA2 are provided by the Goddard Earth Sciences Data and Information Services Center (GES DISC) ([[https://doi.org/10.5067/A7S6](https://doi.org/10.5067/A7S6) XP56V-ZWS]([https://doi.org/10.5067/A7S6](https://doi.org/10.5067/A7S6) XP56V-ZWS)). And the NCEP2 was obtained from National Oceanic and Atmospheric Administration (NOAA) Physical Sciences Laboratory (PSL) at ([[https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html](https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html)]([https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html](https://psl.noaa.gov/data/gridded/data.ncep.reanalysis2.html))). Selected radiosonde data archiving for supporting this paper is underway and can be found online ([[https://doi.org/10.5281/zenodo.4549921](https://doi.org/10.5281/zenodo.4549921)]([https://doi.org/10.5281/zenodo.4549921](https://doi.org/10.5281/zenodo.4549921))).
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wiley/fc5a9d39_3469_4f33_9df4_7dfb3a1fff0b.md | # Geophysical Research Letters
Research Letter
H.-10.1029/2023 GL107310
Lessons From Transient Simulations of the Last Deglaciation
With CLIMBER-X: GLAC1D Versus PaleoMist
[PERSON]
1 Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremenhaven, Germany, 2 Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany, 3 Postdam Institute for Climate Impact Research, Potsdam, Germany
[PERSON]
1 Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremenhaven, Germany, 2 Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany, 3 Postdam Institute for Climate Impact Research, Potsdam, Germany
[PERSON]
1 Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremenhaven, Germany, 2 Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany, 3 Postdam Institute for Climate Impact Research, Potsdam, Germany
[PERSON]
1 Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremenhaven, Germany, 2 Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany, 3 Postdam Institute for Climate Impact Research, Potsdam, Germany
[PERSON]
1 Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremenhaven, Germany, 2 Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany, 3 Postdam Institute for Climate Impact Research, Potsdam, Germany
###### Abstract
The last deglaciation experienced the retreat of massive ice sheets and a transition from the cold Last Glacial Maximum to the warmer Holocene. Key simulation challenges for this period include the timing and extent of ice sheet decay and underwater input into the oceans. Here, major uncertainties and forcing factors for the last deglaciation are evaluated. Two sets of transient simulations are performed based on the novel ice-sheet reconstruction PaleoMist and the more established GLAC1D. The simulations reveal that the proximity of the Atlantic meridional overturning circulation (AMOC) to a bifurcation point, where it can switch between on- and off-modes, is primarily determined by the interplay of greenhouse gas concentrations, orbital forcing and freshwater forcing. The PaleoMist simulation qualitatively replicates the Bulling-Allerod (BA)/Younger Dryas (YD) sequence: a warming in Greenland and Antarctica during the BA, followed by a cooling northern North Atlantic and an Antarctic warming during the YD.
The last deglaciation, spanning roughly 20,000 to 10,000 years ago, marked a period of Earth's history characterized by the retreat of massive ice sheets that had covered large parts of the planet. During this phase, a drastic transition occurred from the cold Last Glacial Maximum to the warmer and more stable climate of the Holocene. A main challenge for simulating the last deglaciation is the timing and amplitude of the ice sheet decay and the amount of meltwater that enters into the oceans. Using two different reconstructions of ice sheets, we employ an efficient climate model to explore changes at the end of the last ice age. Our comparison shows notable differences in the timing and amplitude of abrupt climate events in the simulations using two different ice-sheet reconstructions. Furthermore, we investigate the effects of factors such as greenhouse gases and Earth's orbital changes on the large-scale ocean currents with respect to underlying ice sheets. Ultimately, our study sheds light on how different elements of the Earth's system shape the termination of the last ice age, enriching our understanding of Earth's climate history and guiding further deglaciation scenarios.
2023
Accepted 16 AU 2024
## 1 Introduction
During the last deglaciation, 20-10 kyr before the present (BP), all climate variables encountered large-scale changes. From a cold Last Glacial Maximum (LGM), the climate state transited to the warm interglacial state. This transition was triggered by changes in insolation and geochemical processes ([PERSON], 2015). Furthermore, greenhouse gas (GHG) concentrations rose by 80-100 ppm ([PERSON] et al., 2001; [PERSON] et al., 2005; [PERSON] et al., 2013) and ice sheets melted, and positive feedbacks occurred ([PERSON] et al., 2012). As a result, the atmospheric and oceanic circulation experienced significant changes (e.g., [PERSON] and [PERSON], 2017; [PERSON] et al., 2023), and the global mean sea level rose by about 100-130 m (e.g., [PERSON] et al., 2021; [PERSON] et al., 2014). However, these changes did not happen steadily; some abrupt events, pronounced in Greenland ice records, such as the warming during the Bulling-Allerod (BA; [PERSON] et al., 2002; [PERSON] et al., 2003) or the cooling during the Younger Dryas (YD; [PERSON] et al., 2007) occurred during the last deglaciation.
Modellers are striving to simulate the last deglaciation to improve our understanding of climate change mechanisms and enhance model accuracy. Accurate simulations allow scientists to refine their models, leading to better future climate predictions. This periods' major changes in ice sheets, ocean circulation, and CO\({}_{2}\) levels are crucial for understanding the climate system. Insights from these simulations inform Earth's climate sensitivity, regional responses, and strategies for mitigating climate change effects. Several studies highlight different facets of glacial-interglacial climate, including the last deglaciation, by employing model simulations with prescribed icesheet changes (e.g., [PERSON], 2011; [PERSON], 2007; [PERSON] et al., 2009; [PERSON] et al., 2022; [PERSON] et al., 2014, 2017) or more complicated simulations done by coupled ice sheet-climate modeling (e.g., [PERSON] et al., 2013; [PERSON] & [PERSON], 2011; [PERSON] et al., 2015). [PERSON] and [PERSON] (2011) and [PERSON] et al. (2013) emphasized that orbital changes primarily drive glacial-interglacial cycles. [PERSON] et al. (2021) showed that an abrupt transition from warm interstadial to cold stadial states could be initiated directly by precession and obliquity changes. [PERSON] et al. (2015) suggested that orbital forcing is the main driver of the reduction of North American ice sheets, while GHG forcing accounts for 30% contribution as the second driver. GHG, particularly CO\({}_{2}\), are essential for the amplitude of the cycles and result in complete delgaciation ([PERSON] et al., 2013; [PERSON] et al., 2005; [PERSON] & [PERSON], 2011; [PERSON] et al., 2014). Prescribing ICE-4G ice sheets ([PERSON], 1994), [PERSON] et al. (2009) indicated that orbital forcing and atmospheric CO\({}_{2}\) increase initiate the warming around Antarctica without direct triggers from the Northern Hemisphere.
Previous studies showed that a primary source of uncertainty in the glacial-interglacial simulations is the ice sheet evolution, which has a decisive influence on the timing and occurrence of climate events (e.g., [PERSON] et al., 2020; [PERSON] et al., 2022; [PERSON] et al., 2014; [PERSON] et al., 2014). Ice sheet heights are important for simulating the atmospheric ([PERSON], 2000; [PERSON] et al., 2014) and oceanic circulation ([PERSON] et al., 2018; [PERSON] et al., 2014; [PERSON] et al., 2014). [PERSON] et al. (2022) and [PERSON] et al. (2023) follow the protocol of the Intercomparison Project Phase four (PMIP4; [PERSON] et al., 2017) for transient simulation of the last deglaciation ([PERSON] et al., 2016), and compare the effect of the ICE-6G ([PERSON] et al., 2014; [PERSON] et al., 2015) and GLAC1D ([PERSON] et al., 2014; [PERSON] et al., 2012) ice sheet reconstructions. Consistent with the control of the ocean circulation by ice sheet height ([PERSON] et al., 2014), [PERSON] et al. (2022) indicate that topography differences lead to changes in the jet stream's magnitude, the atmospheric circulation, and river directions in the last deglaciation. [PERSON] et al. (2023) employ an Earth system model of intermediate complexity (EMIC) and show that changes in bathymetry lead to a cooling in the deglaciation simulations. In addition, the use of evolving ice sheets implies changes in freshwater flux into the ocean, affecting the Atlantic meridional overturning circulation (AMOC) ([PERSON] et al., 2010; [PERSON] et al., 2004; [PERSON] et al., 2007). The deglacial AMOC strongly depends on the timing and magnitude of freshwater forcing at high latitudes of the North Atlantic or Arctic, where deep water forms (e.g., [PERSON] et al., 2020; [PERSON] et al., 2010; [PERSON], 2009; [PERSON] et al., 2006). When the freshwater shifts over a critical value, called bifurcation point ([PERSON] & [PERSON], 2004), the AMOC can shift or fluctuate between modes (e.g., [PERSON] et al., 2022; [PERSON] et al., 2018; [PERSON], 1999; [PERSON] et al., 2022; [PERSON] et al., 2017). Accordingly, AMOC instability can lead to abrupt climate changes during the last deglaciation (e.g., [PERSON] et al., 2002; [PERSON], 2007; [PERSON], 2000). [PERSON] et al. (2012) conduct sensitivity simulations with the ICE-5G ([PERSON], 2004) reconstruction and investigate different combinations of GHG, orbital, and ice sheet forcing. They suggest that ice sheet reconstructions provide limited constraints on the timing, volume, and location of the freshwater discharges associated with melting ice sheets.
Due to uncertainty in ice-sheet evolution and the meltwater derived from them, transient simulations of the last deglaciation (e.g., [PERSON] et al., 2023; [PERSON] et al., 2022; [PERSON] et al., 2014) show discrepancies in terms of global mean surface temperature (GMST) and AMOC strength compared to the proxy-based reconstructions (e.g., [PERSON] et al., 2013; [PERSON] et al., 2004; [PERSON] et al., 2021; [PERSON] et al., 2012), particularly during the BA and YD. Hence, the PMIP4 protocol prescribes two reconstructions, GLAC1D and ICE-6G, as boundary conditions for ice-sheet evolution. However, the freshwater derived from these reconstructions is not sufficiently accurate to replicate GMST and AMOC comparable to the proxies (e.g., [PERSON] et al., 2023). These reconstructions are calculated by inverse modeling and exhibit notable uncertainties, attributed mainly to the viscosity model employed for the solid Earth. This paper presents transient simulations of the last deglaciation with an EMIC, CLIMBER-X ([PERSON] et al., 2022). EMICs are well-suited for long-term climate system integrations ([PERSON] et al., 2002) and are capable of simulating deglaciation ([PERSON] et al., 2009; [PERSON] et al., 2005; [PERSON] & [PERSON], 2011; [PERSON] et al., 2014). To address the uncertainty caused by ice-sheet reconstruction, we employ a new ice-sheet reconstruction, PaleoMist ([PERSON] et al., 2021), that is used for the first time as an ice-sheet boundary condition for the last deglaciation. PaleoMist reconstructs the ice sheets using different methodologies and prescribes the different freshwater schemes in the last deglaciation simulation. We primarily aim to evaluate the deglacial climate as simulated by CLIMBER-X with PaleoMist by comparing it with the GLAC1D simulation. Moreover, we examine the role of the other two foreings prescribed by the PMIP4 protocol, GHG and orbital, during the last termination with respect to the underlying ice sheets and by isolating the effects of orbital, GHG, and ice sheets.
## 2 Method
### Model
CLIMBER-X, the version of [PERSON] et al. (2022), employs several sub-models to simulate various climate components. It employs the semi-empirical statistical-dynamical atmosphere model (SESAM; [PERSON] et al., 2022), the 3-D frictional-geostrophic ocean model GOLDSTEIN ([PERSON] et al., 1998; [PERSON] and [PERSON], 2002; [PERSON] and [PERSON], 2005), the thermodynamic sea ice model (SISIM; [PERSON] et al., 2022), and the land surface model PALADYN ([PERSON] and [PERSON], 2016). CLIMBER-X's horizontal resolution is set to \(5^{\circ}\times 5^{\circ}\) for all components. The model is designed to capture the mean climatological state and can simulate at a speed approximately 100-1,000 times faster than full general circulation models when using comparable computational resources ([PERSON] et al., 2022).
### Choice of Ice Sheet Reconstruction
PaleoMist and GLAC1D use different methodologies to reconstruct the past ice sheets. GLAC1D creates the Greenland Ice Sheet based on an ice sheet modeling exercise that was tuned to fit Holocene sea level observations ([PERSON] and [PERSON], 2002). Antarctica and North American ice sheets are based on an ensemble average of several thousand ice sheet model simulations that scored favorably in fitting constraints such as Holocene sea level changes and present-day uplift rates ([PERSON] et al., 2014; [PERSON] et al., 2012). Conversely, PaleoMist calculates the ice sheet using the ICESHEET program ([PERSON] et al., 2016), which assumes perfectly plastic, steady-state conditions for the ice sheet (i.e., the lateral shear stresses are ignored, and the ice surface is not dynamically changing). Employing the model SELEN ([PERSON] and [PERSON], 2007), changes in sea level and Earth's deformation are computed using a time series of ice sheet changes. Finally, the sea level change is added to modern topography and the ice sheet thickness to produce a paleo-topography reconstruction ([PERSON] et al., 2021). Due to the above differences, the sea level increases linearly in PaleoMist while showing variation in GLAC1D, particularly during BA and YD (see Figure S1 in Supporting Information S1).
While the differences in methodologies between PaleoMist and GLAC1D are significant, it is essential to address the criticisms and responses surrounding PaleoMist as a novel reconstruction to understand their broader implications fully. [PERSON] et al. (2022) criticize that PaleoMist is based only on near-field constraints, resulting in discrepancy with previous studies (e.g., [PERSON] and [PERSON], 2014) in the estimation of the relative sea level. To reply to [PERSON] et al. (2022), [PERSON] et al. (2022) reason that by relying on near-field constraints, PaleoMist would be independent of deep-sea foraminifera and avoid sea-level proxies with high uncertainties. Moreover, [PERSON] et al. (2022) question in using spherically symmetric Earth structures to represent far-field sea level. Therefore, [PERSON] et al. (2021) utilize non-ice sheet proxies not as absolute constraints but to test PaleoMist qualitatively. This debate highlights the complexities and potential uncertainties in ice sheet reconstruction methodologies, underscoring the need for a cautious interpretation of sea-level data and the importance of considering multiple approaches for a comprehensive understanding of ice sheet roles in the simulation of the last deglaciation.
### Experimental Design
We conduct two sets of transient deglaciation simulations, Exp_GLAC1D and Exp_PaleoMist, each consisting of five simulations: full-fored (GLAC1D_full and PaleoMist_full), with constant ice sheet reconstruction (GLAC1D_fixICE and PaleoMist_fixICE), with constant GHG (GLAC1D_fixOrbit and PaleoMist_fixOrbit), and pre-industrial (PI) simulation (GLAC1D_PI and PaleoMist_PI; Table S1 in Supporting Information S1). In both experiments, GHG concentrations and orbital parameters are prescribed by [PERSON] et al. (2017) and [PERSON] et al. (2004), respectively. In addition, the GLAC1D reconstruction ([PERSON] et al., 2014; [PERSON] et al., 2012; [PERSON] and [PERSON], 2002) is used for ice sheets, bathymetry, and land-sea mask in Exp_GLAC1D, while Exp_PaleoMist employs the PaleoMist reconstruction ([PERSON] et al., 2021). Except for PI simulations, full-fored simulations are integrated from 25 kyr BP with pre-industrial equilibrium and then switch to LGM boundary conditions. The model is subsequently run until the year 6.5 kyr BP. We prescribe time-varying topography, bathymetry, greenhouse gases(GHG; CO\({}_{2}\), N\({}_{2}\)O, CH\({}_{d}\)), and orbital parameters into the full-forced simulations. The GHG and orbital parameters forcing field is updated yearly, while topography, bathymetry, and ice sheet distribution are changed every 100 years. In the model, the freshwater (FW) flux to the ocean is computed from a combination of precipitation-evaporation, sea ice fluxes, and land runoff. Additionally, the prescribed changes in ice thickness are converted into a liquid water flux that is routed into the ocean following the steepest surface gradient.
The sensitivity simulations begin with boundary conditions from 22 kyrs BP, and throughout the simulation, the corresponding forcing remains constant at the 22 kyrs BP level, while the other forcing factors vary over time. We prescribe the LGM values recommended in the PMIP4 protocol ([PERSON] et al., 2017). This means that in simulations with constant GHG forcing, CO\({}_{2}\), N\({}_{2}\)O, and CH\({}_{4}\) were set to 190 ppm, 200 ppb, and 375 ppb, respectively. Similarly, eccentricity, obliquity, and perihelion are kept constant in simulations with constant orbital forcing at 0.018994, 22.949\({}^{\circ}\), and 114.42\({}^{\circ}\), respectively. This configuration is intentionally designed to determine the distinct role of individual forcing factors. Finally, we define PI as the year 1850 and follow PMIP4 instructions for applying GHG and orbital forcings in the PI simulations.
## 3 Results and Discussion
### Sensitivity Simulations to Different Forcings
In Figure 1, the left panels show the deglacial dynamics for Exp_GLAC1D, whereas the right panels are for Exp_PaleoMist. We perform sensitivity forcing experiments, maintaining different deglacial forcing components at LGM levels. In scenarios with fixed ice sheets and bathymetry (blue lines in Figure 1), North Atlantic FW forcing (\(\geq\)30\({}^{\circ}\) N, including freshwater in the Arctic Ocean) remains near LGM levels. Consequently, North Atlantic SSS and AMOC show minor changes. However, in Exp_GLAC1D, FW forcing slightly exceeds Exp_PaleoMist in average by approximately 0.05 Sv, resulting in a weaker early Holocene AMOC. GLAC1D_fixcke and PaleoMist_fixcke simulations underestimate the last deglacial warming, yielding an early Holocene GMST approximately 2.5\({}^{\circ}\)C warmer than LGM. This result aligns with the anticipated consequences of constant FW forcing and albedo effects. Furthermore, these simulations do not replicate the abrupt events during the last deglacial, possibly due to constant ice sheet heights during the simulations. [PERSON] et al. (2014) indicate that changes in northern hemisphere ice sheet height can trigger rapid climate shifts.
In simulations with constant GHG forcing (red lines in Figure 1), FW forcing is higher than in full-forced simulations due to more precipitation occurring in the fixCHG simulations (see Figures S2, S3, and S4 in Supporting Information S1). This is notable in Exp_PaleoMist during YD and early Holocene (Figure 1b). When FW exceeds approximately 0.24 Sv during the simulations, AMOC transitions to off-mode. This transition aligns with HS1 culmination in Exp_GLAC1D (Figure 1e) and YD onset in Exp_PaleoMist (Figure 1). This supports [PERSON] et al. (2017) results, suggesting atmospheric CO\({}_{2}\) changes critically impact the timing of AMOC transitions. Nonetheless, abrupt declines in FW within GLAC1D_fixGHG lead to sudden AMOC strengthening, subsequently resulting in a rapid increase in GMST. Furthermore, the GMST increases only by approximately 3\({}^{\circ}\)C during deglacialiation in simulations featuring constant GHG forcing. This underscores the significant role played by transient GHG concentrations in driving the last deglacial process.
There is a conspicuous FW forcing in GLAC1D_fixOrbit and PaleoMist_fixOrbit (green lines in Figure 1). Ice sheets' contribution to FW forcing remains unchanged across full-forced, constant GHG and orbital simulations. However, there are substantial variations in precipitation patterns, global mean precipitation, and evaporation between these simulations and the full-forced ones (see Figures S2, S3, and S4 in Supporting Information S1).
GLAC1D_fixOrbit and PaleoMist_fixOrbit depict higher precipitation in the Northern Hemisphere, leading to increased FW in the North Atlantic. Furthermore, AMOC transitions to an off-mode state at comparable times (as shown in Figures 1e and 1f) as in simulations with constant GHG forcing. This finding aligns with the outcomes of a study by [PERSON] et al. (2021), which demonstrated that precession and obliquity play influential roles in shaping hydroclimate in glacial-interglacial cycles. GHG and orbital forcings influence FW fluxes by changing precipitation patterns, with a sustaining effect on the AMOC. Moreover, the GLAC1D_fixOrbit and PaleoMist_fixOrbit simulations effectively replicate the increase of approximately 5\({}^{\circ}\)C in GMST during the last deglacial. This underscores the significant impact of GHG and ice sheets on the simulation of global temperatures during this period, although such forcing also affects the dynamics of AMOC.
### Full-Forced Simulations: GLAC1D Versus PaleoMist
After analyzing the effects of different forcing mechanisms individually in the previous subsection, we now proceed to evaluate the climate during the last deglaciation. In this subsection, we compare the GLAC1D simulation with the PaleoMist simulation to understand the differences and similarities between these simulations and the implications of ice sheet choice in modeling the deglaciation climate. In full-forced simulations (black lines in Figure 1), North Atlantic SSS (Figures 1c and 1d) is anti-correlated with North Atlantic FW forcing
Figure 1: North Atlantic FW, North Atlantic SSS, AMOC at 26”N, and GMST for Exp_GLAC1D (a),(c),(c),(c),(c), and for Exp_PaleoMist (b),(d),(f), and (h). We define LGM as 22–19 kyr BP, Heinrich Stadial 1 (HS1) as 19–14.7 kyr BP, BA as 14.7–13 kyr BP, and YD as 13–11.6 kyr BP. North Atlantic index for SSS is defined as an average over 50”N–70”N and 45”W–0”W. The blue background represents LGM, BA, and early Holocene, while the white background represents HS1 and YD. Note that the vertical axes differ for Exp_GLAC1D and Exp_Paleomist except for GMST panels (g) and (h). North Atlantic FW flux encompasses precipitation-evaporation, sea ice fluxes, land runoff, and liquid water flux melted from ice sheets.
(Figures 1a and 1b) and reduced by about one psu during the simulations. This reduction is attributable to the freshwater contributions resulting from ice sheet melting ([PERSON], 2002; [PERSON] et al., 2012). North Atlantic SSS differs from 1 to 5 psu between GLAC1D_full and PaleoMist_full during various temporal segments (Figures 1c and 1d). GLAC1D_full is less saline over the Atlantic and more saline at the surface of the other oceans (see Figure S5 in Supporting Information S1). During BA, due to the shutdown of AMOC in Exp_GLAC1D (Figure 1e), the northward transport of warm and saline water is disrupted, producing pronounced differences (exceeding 5 psu in North Atlantic) relative to Exp_PaleoMist (Figures 1c and 1d). During YD, GLAC1D_full simulates more saline surface water near Greenland, where deep water forms in the North Atlantic (Figures 1c and 1d). This phenomenon is potentially linked to the stronger AMOC in GLAC1D_full compared to PaleoMist_full (Figures 1e and 1f).
The glacial sea surface temperature anomaly (ASST) relative to PI period is almost identical over the northern hemisphere in GLAC1D_full and PaleoMist_full (see Figure S7 in Supporting Information S1). The global ASST during LGM (average over 22-19 kyr BP) is \(-2.18\) and \(-2.15^{\circ}\)C for GLAC1D_full and PaleoMist_full, respectively. These results are around \(1^{\circ}\)C warmer than cooling \(3.14\pm 0.29^{\circ}\)C reconstructed by [PERSON] et al. (2020). During the Northern Hemisphere winter, PaleoMist_full and GLAC1D_full are consistent with MARGO (MARGO, 2009) over the Southern Ocean western Atlantic. In the Southern Ocean eastern Atlantic, PaleoMist_full shows more cooling than GLAC1D_full and aligns better with MARGO. However, in the Southern Ocean western Pacific, MARGO indicates colder temperatures than our simulations (Table S2 in Supporting Information S1).
The simulated global cooling during the LGM (average over interval 22-19 ka BP), relative to PI, amounts to \(6.12^{\circ}\)C in PaleoMist_full and \(5.9^{\circ}\)C in GLAC1D_full. These results are in agreement with the data assimilation-based estimate of \(6.05\pm 0.43^{\circ}\)C by [PERSON] et al. (2020), the data assimilation-based estimate of \(6.75\pm 0.48^{\circ}\)C by [PERSON] et al. (2021), and the model-based estimate of \(6.2^{\circ}\)C in [PERSON] et al. (2022). However, [PERSON] et al. (2022) reconstructed a smaller GMST anomaly (LGM-PI) of \(4.5\pm 0.9^{\circ}\)C. PaleoMist_full depicts a colder LGM (GMST) (by approximately \(0.5^{\circ}\)C) than GLAC1D_full due to higher ice sheet altitudes. This \(0.5^{\circ}\)C difference is more than the difference between the \(6.12\) and \(5.9^{\circ}\)C anomalies because of the difference in GLAC1D_PI and PaleoMist_PI temperatures.
[PERSON] et al. (2024), a multi-model intercomparison study of the early part of the last deglaciation (20-15 ka BP), show that strong AMOC leads to regional warming in Greenland and the North Atlantic. At the same time, disruptions due to meltwater input can cause significant cooling. The AMOC state at the end of LGM is significant in determining the sensitivity of models to FW forcing during HS1. Models with a stronger and deeper AMOC are less sensitive to FW inputs compared to those with a weaker and shallower AMOC. In alignment with [PERSON] et al. (2024), GLAC1D_full and PaleoMist_full show warming by 15 ka BP and a strong correlation between GMST and AMOC (Figures 1g and 1h).
During BA, GLAC1D_full oceans are warmer than PI in most regions (see Figure S7 in Supporting Information S1) due to an abrupt AMOC shift (Figure 1e), leading to an abrupt increased temperature at the end of BA. The main differences between full forced simulations occur during BA due to significant FW flux differences (see Figure S8 in Supporting Information S1) and very different AMOC (Figures 1e and 1f). GLAC1D includes significant ice volume loss during BA in the North Atlantic, associated with the major meltwater pulse MWP-1A ([PERSON], 2005), resulting in substantial FW influx (Figure 1a). GLAC1D loses \(0.225\times 10^{7}\)\(km^{3}\) ice more than PaleoMist during BA. This configuration imparts a diminished AMOC in GLAC1D_full (Figure 1e), correspondingly inducing lower SSS in the North Atlantic relative to PaleoMist_full.
The AMOC alterations are often proposed as a main factor in abrupt climate shifts during the last deglaciation (e.g., [PERSON] et al., 2002; [PERSON] and [PERSON], 2007; [PERSON] and [PERSON], 2000; [PERSON] et al., 2024). AMOC strengthening during the BA compared to HS1 is observed in reconstructions ([PERSON] et al., 2004; [PERSON] et al., 2018) and modeling studies (e.g., [PERSON] et al., 2009). In GLAC1D_full, AMOC increases at the end of HS1 but experiences an off-mode transition at the onset of the BA period, followed by a substantial resurgence at the end of the BA (Figure 1e). The sudden reduction in AMOC during BA is common in the transient simulations prescribing GLAC1D (e.g., [PERSON], 2002; [PERSON] et al., 2012) (see Figure S9 in Supporting Information S1). In PaleoMist_full, AMOC has an abrupt increase and reduction at the end of HS1. It increases considerably at the onset of BA and is almost stable by the end of BA (Figure 1f). In both simulations, the abrupt strengthening of AMOC occurs before BA. As shown in Figure 1 for different simulations, the timing of the abrupt changes in the AMOC depends on the FW flux. [PERSON] and [PERSON] (2019) suggested that the gradual increase in atmospheric CO2 during HS1 may cause a weakening of stratification of the North Atlantic, which results in an abrupt rise in the AMOC during the BA transition. In contrast to BA, [PERSON] et al. (2004) indicated AMOC was weak during YD. In GLAC1D_full, AMOC after the overshoot decreases gradually during YD, while in PaleoMist_full, it experiences variations and an abrupt reduction (Figures 1e and 1f). Furthermore, a YD-like event for AMOC is observed in PaleoMist_full in the early Holocene at 10 ka BP due to an increase in FW influx. This maximum FW occurs in the early Holocene because of the time resolution of the PaleoMist reconstruction, which is 2,500 years. At 10 ka BP, ice sheets suddenly decrease, resulting in the North Atlantic FW growth.
When comparing the evolution of North Atlantic SST in the simulations with a corresponding marine climate record ([PERSON] et al., 2012), PaleoMist_full simulation reflects the warming and cooling patterns over the North Atlantic during BA and YD periods. In contrast, the GLAC1D_full simulation suggests cooling during the BA, followed by a sudden increase and decrease, and relatively stable temperature during YD (Figures 2a-2c).
For the BA/YD sequence in GMST, the [PERSON] and [PERSON] reconstructions show a \"warming-cooling-warming\" sequence in global mean surface temperature (GMST; Figure 2d). In GLAC1D_full, the transition from BA to YD is also seen, following AMOC pattern (Figures 1e and 1g). If the abrupt reduction and overshoot during BA are ignored, GLAC1D_full shows a \"warming-cooling-warming\" sequence, but this sequence is late with respect to the reconstructions (Figure 2d). Moreover, the warming of the BA in GLAC1D_full matches neither NGRIP nor DomeC temperature records (Figures 2a and 2b). Comparing Buttes_GLAC1D and GLAC1D_full, AMOC shifts to the weak mode simultaneously at the onset of BA in both simulations. Still, the timing and magnitude of overshoot of AMOC at the onset of YD is mostly a model-dependent feature, and consequently, the GMST trajectory is different in GLAC1D_full (see Figure S9 in Supporting Information S1).
Conversely, GMST within the PaleoMist_full scenario follows mainly GHGs (Figure 1h), with some shorter variations (\(\approx\)0.25\({}^{\circ}\)C) at the onset of the BA (warming-cooling-warming) occurred much earlier than reconstructions (Figure 2d). Moreover, there is a minor short-term cooling (\(\approx\)0.1\({}^{\circ}\)C) during the YD, which is not comparable with the reconstruction cooling. Generally, a \"warming-stable-warming\" sequence from \(-\)15 to \(-\)12.5\({}^{\circ}\)kyr BP is observed in PaleoMist_full for GMST and temperatures in DomeC and NGRIP locations (Figures 2b and 2d).
Finally, Figures 3d-3g indicate surface temperature anomalies between the BA and HS1 and between YD and BA for both PaleoMist_full and GLAC1D_full. PaleoMist_full shows a pronounced warming between the BA and HS1 and a moderate cooling between YD and BA in the northern North Atlantic. The opposite is found for GLAC1D_full with cooling between the BA and HS1 and warming between YD and BA. The deglacial meltwater and its influence on AMOC after the timing of the two-step character \"cold-warm-cold-warm\" during the termination: For PaleoMist_full, the HS1-stadial comes along with a weaker AMOC and a stronger AMOC during BA (Figures 3a and 3b), in contrast to GLAC1D_full. The PaleoMist simulations replicate, at least qualitatively, the BA/YD sequence with respect to reconstructions: a warming in Greenland and Antarctica in the BA, a cooling northern North Atlantic, and a warming in Antarctica in the YD.
## 4 Conclusions
This study pioneers the use of the PaleoMist ice sheet reconstruction ([PERSON] et al., 2021) to simulate the last deglication, contrasted with the more traditional GLAC1D reconstruction ([PERSON] et al., 2014; [PERSON] et al., 2012). In both PaleoMist and GLAC1D simulations, LGM temperatures and southern ocean Atlantic SSTs are consistent with data assimilation-based estimates of [PERSON] et al. (2020) and MARGO (2009), respectively.
Variations in sea level pressure, wind patterns, and surface temperatures, especially during the BA warm period, illustrate the different behavior of GLAC1D and PaleoMist. These differences are attributed to the varying configurations, extents, and topographies of the ice sheets, affecting the atmosphere-ocean circulation. We show that the PaleoMist simulation outperforms GLAC1D in capturing the pronounced warming in the northern North Atlantic, which is a main characteristic of BA ([PERSON] et al., 2014). In agreement with previous studies (e.g., [PERSON] et al., 2012; [PERSON] et al., 2023; [PERSON] et al., 2022), we find that the timing and magnitude of climate events during the termination are affected by the ice sheet reconstruction. PaleoMist shows greater glacial ice sheet heights, particularly in the Northern Hemisphere, while GLAC1D has a substantial ice sheet volume loss, causing an off-mode in the AMOC during the BA. The strong fluctuations in deglacial meltwater in GLAC1 Dlead to abrupt changes in global mean temperature and fail to capture the BA/YD transition sequence. The freshwater derived from PaleoMist does not induce an off-mode AMOC during the BA but a pronounced warming in the North Atlantic realm. The YD cooling in the PaleoMist simulation seems to be underestimated for this area, especially over Greenland, where most likely a pronounced overshoot dynamics is relevant ([PERSON] &
Figure 2: (a) Evolution of temperature at MSRIP (Greenland), DomCC (Antarctica), and SST at North Atlantic (NA87-22; [PERSON] et al., 2001), (b) Evolution of temperature at MSRIP, DomC, and SST at North Atlantic in PaleoMist,full, (c) Evolution of temperature at MSRIP, DomC, and SST at North Atlantic in GALC1D_full, and (d) GMST anomaly from the early Holocene (defined as 11.5–6.5 s Bx) for GLAC1D_full, PaleoMist,full, [PERSON] et al. (2012), and [PERSON] et al. (2021). Data for MSRIP, DomC, and NA87-22 in (a) are from [PERSON] et al. (2012). North Atlantic index for SST in (b) and (c) is defined as an average over 50”N–70”N and 45”W–0”W. Discrepancies between [PERSON] et al. (2012) and [PERSON] et al. (2021) reconstructions are due to utilizing different observation data sets, background states, and methods. Note that there are different vertical axes for different variables.
Figure 3: AMOC stream function for GLAC1D_full and PaleoMist_full during HS1, BA, and YD (a), (c), and (e). Near-surface temperature (2m temperature) anomalies between BA and HS1 and between YD and BA for PaleoMist_full (d) and (f) and GLAC1d_full (e) and (g), indicating the differences in the regional temperature signatures. The shown variables are averaged over the defined intervals.
[PERSON], 2003; [PERSON] et al., 2020; [PERSON] et al., 2017). The exact timing of the BA/YD sequence with respect to [PERSON] et al. (2012) and data assimilation-based [PERSON] et al. (2021) reconstructions is a subject of further investigation. Besides model uncertainties, we cannot exclude dating uncertainties of marine sediment cores due to changes in reservoir ages (e.g., [PERSON] et al., 2017; [PERSON] et al., 2020).
Assessing the contributions of ice sheets, GHGs, and orbital forcing to warming during the last deglaciation, we demonstrate the significant role played by both GHGs and orbital forcing in regulating the freshwater flux into the North Atlantic, consequently affecting SSS and ocean circulation, consistent with (e.g., [PERSON] et al., 2012; [PERSON], 2011). The timing of deglacial transitions is particularly influenced by the magnitude of freshwater fluxes associated with the retreat of Northern Hemisphere ice sheets ([PERSON] & [PERSON], 2009; [PERSON] & [PERSON], 2003, 2007). As an extreme case, [PERSON] et al. (2009) proposed that BA warming is controlled by the cessation of freshwater input, highlighting the significant role of deglacial freshwater in the abrupt recovery of AMOC. However, this freshwater history would be inconsistent with paleo-sea level proxies and both ice sheet reconstructions used here. We indicate that GHGs and orbital forcing influence the precipitation patterns, affecting the proximity of the AMOC to its bifurcation point between the on- and off-mode states. A significant reduction in freshwater input can lead to a shift in AMOC to a more stable mode. Our experiments could be further developed as a way to better assess the history of ice sheet evolution. Climate-ice sheet models combined with data assimilation could be suitable for estimating the ice sheets and deglacial meltwater.
The dynamics of the last termination include a reduction in the height of the ice sheets and an increase in GHG concentrations to achieve appropriate warming. The direct effect of orbital forcing on global mean surface temperature is relatively small. This will be different in a fully interactive Earth system model including ice sheets (e.g., [PERSON], 2017; [PERSON] et al., 2019), then the glacial termination is triggered by orbital forcing. Simulations with prescribed ice sheets cannot resemble the full dynamics of the termination as in such simulations, the deglacial freshwater flux acts as a forcing rather than a response to AMOC changes ([PERSON], 2000). As a logical next step, transient simulation of the last deglaciation with fully interactive ice sheets will explore the climate and biogeochemical feedback in the system. Single forcing experiments are deemed to be important in evaluating the phase-space and instabilities in the system.
## Data Availability Statement
The source code of CLIMBER-X (Version V2) and the instructions to install and run the model are available through [PERSON] et al. (2022). The output of simulations used for the analysis and figures is archived on Zenodo ([[https://doi.org/10.5281/zenodo.10159104](https://doi.org/10.5281/zenodo.10159104)]([https://doi.org/10.5281/zenodo.10159104](https://doi.org/10.5281/zenodo.10159104)), [PERSON], 2023).
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wiley/fc67acb4_1dcf_4055_bd68_d6658bd03f63.md | function as a significant nitrogen reservoir within the cell, releasing nitrogen for other cellular processes through degradation under nitrogen-limiting conditions or starvation ([PERSON], 1992; [PERSON] et al., 1994; [PERSON] & [PERSON], 1980). Structurally, PBSs are composed of a central allophyocyanin (APC) core, a series of rods, and associated linkers ([PERSON] et al., 2007). The rods, containing phycocyanin (PC), or a combination of PC and phycoerythrin (PE), bind various phycobilin chromophores with distinct light-absorbing wavelengths, such as phycocyanobilin (PCB), phycerythrobilin (PEB), and phycourobilin (PUB) ([PERSON] et al., 2013; [PERSON] et al., 2017; [PERSON] et al., 2007).
_Synechococcus_ are categorized into three main pigment types (PTs) based on the pigment composition present on the PBS rods. Pigment type 1 (PT 1), which only contain PC and are characterized by only the red light absorbing PCB on the rods, are mainly found in estuary and coastal regions where red light dominates. Pigment type 2 (PT 2) contain PC and phycoverhrini I (PE-I), having both PCB and the green-light-absorbing PEB attached on the rods; they are mainly distributed in coastal, shelf and mesotrophic waters. Pigment type 3 (PT 3) contain PC, PE-I and PE-II, with rods comprised of PCB, PEB and blue light absorbing PUB. PT 3 are further divided into several subtypes according to the fluorescence excitation ratio at 495 and 545 nm (PUB to PE ratio): 3a (<0.6), 3b (0.6-1.6), 3c (>1.6) and 3d (variable PUB to PEB ratio) (Everroad & Wood, 2012; [PERSON] et al., 2018; [PERSON] et al., 2014; [PERSON] et al., 2007). PT 3d, also known as type IV chromatic acclimating strains (CA4), can adjust their PUB/PEB ratio to optimize green or blue light absorption. This group can be further categorized into PT 3 dA and PT 3 dB, each characterized by distinct configurations (CA4-A and CA4-B) in terms of gene content, order, and genomic context ([PERSON] et al., 2018; [PERSON] et al., 2013). While both PT 3 dA and PT 3 dB can enhance PUB to PEB ratio under blue light and reduce it under green light, they exhibit similar yet distinct regulatory mechanisms ([PERSON] et al., 2021). In addition, one strain RCC 307 with medium PUB was identified as PT 3 eAW with weak ability to perform chromatic acclimation ([PERSON] et al., 2013; [PERSON] et al., 2007). The newly described PT 3f possess unique gene content and organization of the PBS genomic region ([PERSON] et al., 2017; [PERSON] et al., 2018).
_Synechococcus_ are highly phylogenetically diverse. Based on various gene markers, _Synechococcus_ cluster five is divided into three subclusters (S5.1, S5.2 and S5.3) and composed of more than 20 phylogenetically lineages that exhibit different physiological characteristics and ecological niches ([PERSON] & [PERSON], 2012; [PERSON] et al., 2016; [PERSON] et al., 2019; [PERSON] et al., 2008). Among various phylogenetic clades, clade I to IV and CRD 1 are generally most abundant and widely distributed in global ocean ([PERSON] & [PERSON], 2012; [PERSON] et al., 2016). Clade I and IV generally co-occur in cold and nutrients rich waters while clade II and III co-dominate in warm oligotrophic waters in tropical and subtropical region ([PERSON] & [PERSON], 2012; [PERSON] et al., 2016; [PERSON] et al., 2019; [PERSON] et al., 2008). Clade CRD 1 were initially found in upwelling of Costa Rica Dome and are widely distributed in iron deplete region ([PERSON] et al., 2016; [PERSON] et al., 2022; [PERSON] et al., 2005; [PERSON] et al., 2016). It was reported that _Synechococcus_ core genomes possess different evolution history with PBS rods genes ([PERSON] et al., 2021; [PERSON] et al., 2007). Consequently, one given phylogenetic clade may possess different PTs and one given PT could be found in various phylogenetic clades.
Mesoscale eddies are ubiquitous oceanic circulations which could last days to months temporally and have diameters of 50 to 200 km spatially with cores reaching as deep as 2,000 m ([PERSON] et al., 2011; [PERSON] & [PERSON], 2009). Satellite data revealed tremendous number of mesoscale eddies in the global ocean ([PERSON] & [PERSON], 2009), and they serve as one of key drivers of phytoplankton community. Three kinds of mesoscale eddies were recognized till now: cyclonic eddies (CEs), anticyclonic eddies (ACEs), and mode-water eddies (MEs) ([PERSON] et al., 1999, 2007). Mesoscale eddies play important roles in both regional and global biogeochemical cycles by enhancing vertical and horizontal mixing of water masses. The strong mixing in the mesoscale eddies greatly change the concentration or property of various oceanic tracers, including temperature, salinity, nutrients, dissolved oxygen, and dissolved organic/inorganic carbon ([PERSON], 2009; [PERSON], 1997). Consequently, both chemical and physical changes will greatly influence the biomass, primary production, and community structure of phytoplankton. Previous studies estimated that mesoscale eddies supplied 20% to 40% of nutrients requirements of phytoplankton ([PERSON] & [PERSON], 2000; [PERSON] et al., 2003; [PERSON], 1998) and the nutrients input induced 20% to 50% new production ([PERSON], 1988; [PERSON], 2003; [PERSON], 1998).
South China Sea is the largest marginal sea in the western Pacific Ocean and mesoscale eddies formed frequently. An average of \(32.8\pm 3.4\) eddies were observed annually by satellite, with the average diameters ranging from 46.5 to 223.5 km ([PERSON], 2011; [PERSON] et al., 2010). It was estimated that mesoscale eddies influenced a mean area of 160-170 km\({}^{2}\), covering about 9.8% of the SCS area with water deeper than 1,000 m ([PERSON] et al., 2010). Mesoscale eddies occur frequently in both northern and western South China Sea (SCS) ([PERSON] et al., 2021; [PERSON] et al., 2003; [PERSON] et al., 2010). During southwesterly monsoon in western SCS, strong wind together with an eastward jet from Mekong River generates eddy dipoles almost annually ([PERSON] et al., 2021; [PERSON] et al., 2006; [PERSON] et al., 1999), with one CE in the north and one ACE in the south near 10\({}^{\prime}\)N. The eastward jet intrudes the two eddies and forms the sandwich structure. The eddy dipoles are usually formed in late June to August and disappeared totally in October or November ([PERSON] et al., 2010).
Previous studies reported that the abundance and biomass of _Synechococcus_ which are one of major components of phytoplankton community in SCS changed dramatically in the eddy ([PERSON] et al., 2021; [PERSON] et al., 2016). However, how the physical and chemical property of mesoscale eddies affect pigment type composition and phylogenetic diversity of _Synechococcus_ via vertical mixing is still not investigated. In this study, we investigated the abundance, pigment type composition and phylogenetic diversity of _Synechococcus_ in mesoscale eddies in western South China Sea in summer, 2018, aiming to get better understanding of the distribution of different pigment types and phylogenetic clades in mesoscale eddies and its environmental drivers.
## 2 Materials and Methods
### Study Area and Sampling
We collected samples from 16 stations during a cruise investigating the dipole eddies in western South China Sea (8-16\({}^{\circ}\)N, 110-114\({}^{\circ}\)E) from 18 August to 21 September 2018 on board R/V Shiyan3 (Figure 1). The sea surface anomalies in sampling area were based on data from Global Ocean Gridded \(L\) 4 Sea Surface Heights and Derived Variables Nrt ([[https://doi.org/10.48670/moi-00149](https://doi.org/10.48670/moi-00149)]([https://doi.org/10.48670/moi-00149](https://doi.org/10.48670/moi-00149))). Temperature and salinity profiles were obtained by a conductivity-depth-temperature (CTD) instrument (SBE 9/11 plus, Sea-Bird Electronics, Washington, USA). Water samples were collected with 12L Niskin bottles equipped with CTD from 3 to 7 depths within 200 m. DNA samples were collected by filtering 2L of seawater with 0.22 \(\mu\)m PC membranes (Millipore, Eschborn, Germany) under low pressure. Chlorophyll \(a\) (Chl _a_) samples were collected by filtering 1L of seawater onto GF/F filters (Whatman, UK). For _Synechococcus_ abundance measurement using flow cytometry (FCM), 1.8 ml water samples were fixed with paraformaldehyde (1% final concentration) after pre-filtering with 20 \(\mu\)m (pore size) mesh. All the DNA, Chl \(a\) and FCM samples were frozen quickly in liquid nitrogen and stored in \(-80^{\circ}\)C in laboratory until further analysis. For nutrients concentration measurement, 100 ml water samples were filtered with acid-cleaned 0.45 \(\mu\)m acetate cellulose filters and stored at \(-20^{\circ}\)C until further analysis.
### DNA Extraction, PCR, Sequencing, and Phylogenetic Analysis
DNA was extracted using the modified phenol-chloroform protocol of [PERSON] et al. (2000). The DNA was precipitated overnight in \(-20^{\circ}\)C with isopropanol instead of ammonium acetate-ethanol. The extracted DNA was stored at \(-20^{\circ}\)C until further analysis. The amplification of rpoC1 gene was performed using nested-polymerase chain reaction (PCR) approach following [PERSON] et al. (2006) and [PERSON] et al. (2015). The first round of PCR was conducted using the primer rpoC1-C and rpoC1-N5 and the PCR products were used as templates for the second-round PCR with the barcoded primers rpoC1-39F and rpoC1-462R ([PERSON] et al., 2006; [PERSON] et al., 2015). The PCR reactions were performed with triplicates and the PCR products were sequenced by Novogene company (Beijing, China) using Illumina platform. To identify pigment type, PCR reactions of cpeBA operon were performed following [PERSON] et al. (2006) and [PERSON] et al. (2017) with primer SynB3 FW and Syn A1R. The PCR products were sequenced using a Pachio system by Novogene Corporation Inc (Beijing, China).
The sequence data was analyzed using Qime2 ([PERSON] et al., 2019). Paired-end sequences without primer sequence were demultiplexed using denux command and the sequences were then quality filtered, merged and deregplicated using the DADA2 workflow ([PERSON] et al., 2016) to determine amplicon sequence variants (ASVs). For classification of phylogenetic clade using rpoC1 gene, the taxonomy of ASVs was assigned using the database of reference sequence provided by [PERSON] et al. (2019). To identify PTs using the cpeBA operon, we compiled a database containing sequences from PT 2A, PT 3B, PT 3a, PT 3c, PT 3 dA, PT 3 dB, PT 3 eA, and PT 3f, sourced from both isolated strains and field surveys in previous studies ([PERSON] et al., 2017, 2018; [PERSON] et al., 2022). Subsequently, a native Bayes classifier was trained using databases of rpoC1 and the cpeBA operon, respectively. The classifier was then used to classify ASV sequences with detailed taxonomic information. The cpeBA sequence database can be accessed at [[https://github.com/xzhangdm/SCS_Eddy_2018.git](https://github.com/xzhangdm/SCS_Eddy_2018.git)]([https://github.com/xzhangdm/SCS_Eddy_2018.git](https://github.com/xzhangdm/SCS_Eddy_2018.git)).
### Nutrients Concentration, Chl \(a\) Concentration, and _Synechococcus_ Abundance Measurement
The concentration of dissolved inorganic nitrogen (DIN) including nitrate (NO\({}_{3}^{-}\)), nitrite (NO\({}_{2}^{-}\)), ammonium (NH\({}_{4}^{+}\)), phosphate (PO\({}_{4}^{-}\)) and dissolved silicate (DSi) were measured with an AA3 Auto-Analyzer (Bran + Luebbe GmbH, Germany) according to the JGOFS protocols ([PERSON] et al., 1996). The detection limit for nitrate, nitrite, ammonium, phosphate and Disi were 0.015, 0.0.003, 0.04, 0.024 and 0.03 uM, respectively. For Chl \(a\) concentration measurement, the samples were extracted in 90% acetone for 24 hr in \(-20^{\circ}\)C in dark. The Chl \(a\) concentration was measured following [PERSON] (1994) by a Turner Designs Trilogy Laboratory Fluorometer (Turner Designs, USA) using CHL-A NA configuration. The abundance of _Synechococcus_ was analyzed using a BectonDickinson FACSCalibur flow cytometer equipped with a 488 nm laser ([PERSON] et al., 2014). Ten microliters of yellow-green fluorescent beads (1 um, Polysciences, Warrington, PA, USA) were added to each sample as an internal standard.
### Statistical Analysis
The following statistical analysis were conducted using \(R\) software (version 4.2.2) (R Core Team, 2022). Spearman ranking analysis was used to investigate the correlations between environmental factors and relative
Figure 1: Sea level anomalies and sampling stations in the research area of the southwestern South China Sea in summer, 2018. Cyclonic and anticyclonic features are shown in blue and red, respectively. Map of the sea surface anomalies was based on data from Global Ocean Gridded \(L\) 4 Sea Surface Heights and Derived Variables Nrt ([[https://doi.org/10.48670/moi-00149](https://doi.org/10.48670/moi-00149)]([https://doi.org/10.48670/moi-00149](https://doi.org/10.48670/moi-00149))).
abundance of different PTs and dominant phylogenetic clades. Nonmetric multidimensional scaling (NMDS) plots were plotted using \"ggplot\" package to reveal the relationship between the _Synechococcus_ communities based on the Bray-Curtis dissimilarity ([PERSON], 2010).
## 3 Results
### Hydrographic Conditions
The eddy dipoles were observed during the cruise in western South China Sea in summer 2018, based on sea level anomaly (SLA) (Figure 1). One CE was present between 11 and 13\"N while an ACE was observed between 8 and 11\"N. The maximum SLA of ACE reached to 13.2 cm compared with surrounding waters while the CE exhibited a negative SLA of 25.4 cm. Dipole eddy induced completely heterogenous profile of temperature and salinity in CE, ACE and surrounding waters (Figure 2). No significant difference of temperature and salinity was observed between the surface water of eddies and surrounding waters. However, remarkable difference of temperature and salinity between CE and ACE were observed from 25 m to the bottom of euphotic layer, evidenced by the dome structure of isotherm and isohaline in CE and depression in ACE (Figures 1(a) and 1(b)).
Nutrients concentration showed completely distinct vertical profiles in CE and ACE (Figure 2). In ACE, DIN, inorganic phosphate and DSi were almost depleted in surface water. The concentrations of DIN, inorganic phosphate and DSi kept almost constant in the upper 100 m and increased gradually with depth in lower euphotic layers. In CE, the concentration of DIN (Figure 1(e)), phosphate (Figure 1(f)) and DSi (Figure 1(g)) showed no significant difference from surface to 25 m but increased gradually from 25 m to the bottom of euphotic layer. In almost all the depths, dissolved inorganic nutrients concentration was significantly higher in CE than that in ACE, indicating the pumping effects of upwelling. The distribution pattern of CH \(a\) concentration was distinct in CE and ACE (Figure 1(d)). The deep chlorophyll maximum layer (DCM), which was estimated using the fluorescence profiles, was remarkably shallower (\(\sim\)40 m) in CE than ACE (\(\sim\)80 m). CE also displayed higher Chl \(a\) concentration in DCM (0.942 \(\mu\)g L\({}^{-1}\) on average) than ACE (0.367 \(\mu\)g L\({}^{-1}\) on average) (Figure 1(d)).
### Abundance and Distribution of _Synechococcus_
Significantly high abundance of _Synechococcus_ was observed in the upper euphotic layers (surface and 25 m) in CE, with maximum abundance of more than \(8\times 10^{4}\) cells ml\({}^{-1}\). Clear dome structure of _Synechococcus_ abundance was observed in sampling area and _Synechococcus_ were much more abundant in CE than in ACE, reflecting higher nutrient supply from the subsurface water in CE (Figure 1(c)).
### Chromatic Acclimating _Synechococcus_ Dominated _Synechococcus_ Community in Mesoscale Eddies
In this study, both PT 2 and PT 3 _Synechococcus_, including 7 subtypes (PT 2A, PT 2B, PT 3a, PT 3c/3 dB, PT 3 dA, PT 3 eA, PT 3f), were detected (Figure 3). The pigment type composition showed no recognizable difference in surface water between CE and ACE; however, a remarkable difference of pigment type composition was observed between CE and ACE in 25 m and depths below. Chromatic acclimating _Synechococcus_ dominated the communities in both CE and ACE except the surface waters. Clear niche segregation between two typical chromatic acclimators (i.e., PT 3 dA and PT 3c/3 dB) was observed. PT 3 dA dominated in CE, consisting about 69.2% of total pigment types in 25 m and below layers in average. In 25 and 100 m of station C3, PT 3 dA were almost the solo pigment type, contributing more than 95% to the community. In contrast, PT 3 dA were rarely observed in ACE. Unlike PT 3 dA, PT 3c/3 dB distributed widely in both CE and ACE, but they were much more abundant in ACE than in CE. The share of PT 3c/3 dB ranged from 12.6% to 67% in ACE, with average relative abundance of 40.3% in the whole column, compared with just 13.4% in CE. Additionally, PT 3 eA, which may possess ability of weak chromatic acclimation, also contributed a small proportion of the _Synechococcus_ community in both CE (7.4% in average) and ACE (8.4% in average). On average, the total relative abundance of chromatic acclimators including PT 3 dA, PT 3c/3 dB and PT 3 eA was 70.3% and 50.6% in CE and ACE, respectively, indicating they are the most dominant pigment types of _Synechococcus_ in mesoscale eddies where vertical mixing is more vigorous.
PT 3a were detected in every sample with significant percentage in our results, with the average proportion of 22.1% and 33.6% in CE and ACE, respectively. The relative abundance of PT 3a were higher in surface water than in 25 m and layers below in CE while no such pattern was observed in ACE. PT 2A, PT 2B and PT 3f were minor pigment types in this study. PT 2A were widely distributed in both CE and ACE while PT 2B were detected only at surface water of S65 and S66. The seldom reported PT 3f were mainly observed in ACE and almost absent in CE.
### Phylogenetic Composition and Diversity of _Synechococcus_
Since PT 3 dA and PT 3c/3 dB dominated CE and ACE, respectively, we further investigated the dominant phylogenetic clades of _Synechococcus_ in sampling stations (Figure 4, Figure S1 in Supporting Information S1). In the surface water of CE, clade II and CRD 1 were the most dominant clades, whereas clade III and II dominated in the surface water of ACE. Clade UC-A, an oligotrophic clade that is rarely reported shared a fair proportion in the surface of both types of eddies (Figure 4). From 25 m depth to the bottom of the euphotic layer in CE, it was completely dominated by CRD 1 (40.7% on average). Other common clades included clade I, II, XV and XVI. In contrast, no single clade dominated in the water column of ACE below 25 m, with clade III and II each accounted 20.9%, and 17.5%, respectively. The rarely reported clade PAC2, ENV 1 and UC-A also contributed 7.5%, 6.1%
Figure 2: Vertical distribution of temperature, salinity, _Synechococcus_ abundance, dissolved inorganic nitrogen, phosphate (PO\({}_{\lambda}\)), silicate (DSi) concentration. Sampling depth was from the surface to 200 m depth in each station located in CE and ACE.
Figure 3: Composition of _Synechococcus_ pigment types at different depths and sampling sites in CE and ACE.
and 4.7% to the community below 25 m, respectively. A significant proportion of S5.3 _Synechococcus_ was also recorded in the subsurface water of both CE and ACE.
NMDS analysis also indicated that both pigment types and phylogenetic clades composition were distinct in CE and ACE except limited number of surface water samples (Figure S2 in Supporting Information S1). Different pigment types and phylogenetic clades demonstrated distinct preference of environmental conditions (Figure 5, Figure S3 in Supporting Information S1). For instance, PT 3c/3 dB together with PT 3f showed complete opposite selection of environmental conditions to PT 3 dA, with the former dominating in warm waters (positively correlated with temperature) while the latter thriving in cooler and nutrient rich waters (characteristics of upwelling associated with CE). The same differentiation can be found in phylogenetic clades. For example, clade CRD 1, I, XV, XVI and ENV 1 displayed positive relationship with nutrients concentration but negative relationship with temperature. In contrast, clade II, III, WPC1, PAC1, PAC2, UC-A prefer relative warm and nutrients-deplete waters (Figure 5, Figure S3 in Supporting Information S1).
## 4 Discussion
### Different Ecological Niches for the Two Chromatic Acclimators
The ambient light spectrum could significantly influence the pigment type composition and hence plays key role in shaping the community structure of _Synechococcus_. However, little is known about the vertical distribution of various pigment types in euphotic layers of open waters. To our knowledge, this is the first study investigating the vertical profile of pigment type composition in mesoscale eddies. By modifying pigment composition in PBS, chromatic acclimators possess great adaptive advantage over _Synechococcus_ with a fixed pigmentation, especially in waters where vertical mixing is relative strong and the ambient light spectrum changes dynamically. Our results, for the first time, suggested chromatic acclimators were the most abundant and dominant PTs in upwelling and downwelling mixing waters of mesoscale eddies (Figures 3 and 6).
The two typical chromatic acclimators shared one common ancestor ([PERSON] et al., 2013), however, the cause for the differentiation of the two related but different chromatic acclimating pigment types are not well known. It was reported that the phycobilin lyase and lyase-isomerase pairs play key roles in chromatic acclimation of _Synechococcus_([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2019, [PERSON], [PERSON], et al., 2019). PT 3 dA
Figure 4: Average abundance of different phylogenetic clades in CE and ACE. \(A\), surface water in CE; \(B\), surface water in ACE. C, 25 to 200 m in CE; \(D\), 25 to 200 m in ACE.
Figure 5: Redundancy analysis between _Synechococcus_ PT, clades and environmental factors. _Synechococcus_ PT and clades (in the box) closer to the environmental factors (pointed by arrows) indicate more positive correlations, while opposite to the arrow direction indicating negative effects. The first two axis (RDA1 and 2) with the highest explanation to the community variations were shown. Temp, temperature; Sal, salinity; DIN, dissolved inorganic nitrogen; PO\({}_{\rm{e}}\), phosphate; DSi, silicate.
and PT 3 dB exhibit distinct members of the MpcQWYZ phycobilin lyase enzyme family and a genomic island exhibiting two unique configurations (CA4-A and CA4-B versions) ([PERSON] et al., 2021; [PERSON] et al., 2013). The CA4-A genomic island includes the mpEZ gene responsible for encoding the phycobilin lyase-isomerase MpcZ. Similarly, the CA4-B version encompasses the mpEW gene encoding phycobilin lyase MpcW ([PERSON], 2017; [PERSON] et al., 2021; [PERSON] et al., 2013; [PERSON], [PERSON], et al., 2019; [PERSON] et al., 2012). Additionally, apart from the genes within the genomic island, PT 3 dA and PT 3 dB also contain mpEY and mpEQ genes encoding lyase-isomerase MpcQ, respectively, as indicated by [PERSON] et al. (2021). During chromatic acclimation process of PT 3 dA, the PEB lyase MpcY attaches PEB at C83 residue of the phycoverthrin-II \(\alpha\)-subunit (MpcA) in green light, while lyase-isomerase MpcZ acts on the same site, binding and isomerizing PEB into PUB in blue light ([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2019). For PT 3 dB, the lyase MpcW and lyase-isomerase MpcQ acts on MpcA-C83 as the same role with MpcY and MpcZ of PT 3 dA, respectively ([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2019). PT 3 dA strain dramatically increases the transcript levels of mpEZ in blue light to raise PUB content while the mpEY is expressed without significant change in both light colors ([PERSON], [PERSON], et al., 2019). For PT 3 dB, gene mpEW is up regulated in green light to increase PEB content while mpEQ is not significantly differentially regulated between green light and blue light ([PERSON] et al., 2021). One hypothesis is that PT 3 dA were originally green light specialist but obtained the ability to use blue light more efficiently while PT 3 dB were initially blue light specialist but evolved to utilize green light more efficiently ([PERSON] et al., 2021; [PERSON], [PERSON], et al., 2019, [PERSON], [PERSON], et al., 2019). Our results indicated that PT 3 dA proliferated significantly in upwelling of CE where the dominant light possibly changed from blue to green as the water move upward from lower to upper euphotic layers, while PT 3 dB dominated in downwelling of ACE where the light spectrum might switch from green light in upper euphotic layers to blue light in lower euphotic layers.
The chromatic acclimating _Synechococcus_ requires approximately six generations, equivalent to several days, to adjust their PUB/PEB ratio in response to the prevailing ambient light color ([PERSON] et al., 2006; [PERSON], 2001; [PERSON] et al., 2012). Previous study suggested that the vertical transport of water in the upwelling zone aligned
Figure 6: Distribution of different pigment types in CE and ACE. Number of elliptical dots represent the abundance of _Synechococcus_ which is higher in upper euphotic layers in CE than that in ACE. Each color of dots represents one detected pigment type in this study. The lengths of arrows with different colors on the left represent the penetrating depths of different visible light in open ocean. The upward and downward directions of arrows on the boundary of CE and ACE represent upwelling and downwelling while the blue color and red color represent CE and ACE.
with this chromatic acclimation process ([PERSON] et al., 2021). It was estimated that eddies with maximum SLA >0.5 cm possess a vertical velocity of up to 50 m day\({}^{-1}\), while weak eddies (maximum SLA <0.2 cm) have a vertical velocity of up to 15 m day\({}^{-1}\)([PERSON] et al., 2018). The maximum SLA of the mesoscale eddies in this study was 0.254 cm, suggesting that it will take several days for the water being transported from the bottom of euphotic layer to the surface. The time scale of the vertical water movement and the duration of the chromatic acclimation process matched each other, providing a perfect environment favoring chromatic acclimators over _Synechococcus_ with fixed pigmentation.
In addition, another possible chromatic acclimator PT 3 eA could not be ignored in mesoscale eddies. The rarely reported PT 3 eA were initially described based on one medium PUB strain RCC307 (S5.3) isolated from Mediterranean Sea and identified as PT 3b ([PERSON] et al., 2007). [PERSON] et al. (2013) later suggested its weak ability of chromatic acclimation as it possessed a CA4-A gene island and named it as PT 3 eA to distinguish it from typical chromatic acclimators. Currently whether PT 3 eA (RCC 307) are independent pigment subtype is still an issue worthing further investigation and previous studies described RCC 307 with various names including PT 3b ([PERSON] et al., 2007; [PERSON] et al., 2018), PT 3e ([PERSON] et al., 2014), PT 3 eA ([PERSON], 2017; [PERSON] et al., 2013; [PERSON] et al., 2022), PT 3 dA ([PERSON] et al., 2022; [PERSON], 2017; [PERSON] et al., 2021; [PERSON] et al., 2018), and asterisk-highlighted PT 3b, 3e or 3 dA due to its uniqueness ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2018). However, PT 3 eA are most possibly different from typical CA4-A. Clear divergence between RCC 307 and PT 3 dA were revealed based on analysis of mpeBA and cpeBA operon ([PERSON] et al., 2021, 2022; [PERSON] et al., 2022). Moreover, RCC 307 closely related strains were widely distributed and abundant in Eastern Indian Ocean, SCS and surrounding waters based on previous studies ([PERSON] et al., 2022; [PERSON] et al., 2022). In this study, PT 3 eA could be detected in all the samples, with the maximum relative abundance reaching 19.6% and 41.9% in CE and ACE, respectively. Together, the three chromatic acclimators are better adapted to the dynamically varied light spectrum due to vertical mixing and they play key roles in biogeochemical and ecological processes in mesoscale eddies.
In addition to light, temperature might be another important environmental factor determining the distribution of _Synechococcus_ community structure in the water column. Previous studies indicated the PT 3 dA were largely predominated in the _Synechococcus_ community in subpolar region while PT 3 dB were abundant in relatively warm waters ([PERSON] et al., 2018; [PERSON] et al., 2017). Our results showed that PT 3 dA dominated in cold waters below 25 m in CE while the share of PT 3c/3 dB were abundant and even dominated in the warm downwelling waters of ACE, as well as the surface water of CE, which agreed well with previous studies ([PERSON] et al., 2018; [PERSON] et al., 2017). RDA and Spearman analysis showed PT 3 dA displayed negative correlation with temperature while PT 3c/3 dB were positively correlated with temperature, indicating their distinct thermal niches (Figure 5, Figure S3 in Supporting Information S1).
Based on our Spearman analysis (Figure S4 in Supporting Information S1), the most possible contributor of PT 3 dA and PT 3c/3 dB were upwelling associated clade CRD 1 and warm water adapted clade II/III, respectively. We observed completely different dominant phylogenetic clades in surface water and subsurface water. Warm water adapted clade H dominated surface water of CE while typical upwelling and cold water adapted clade CRD 1 dominated in \(\sim\)25 m (Figure 4, Figure S1 in Supporting Information S1). The average temperature changed from \(\sim\)29\({}^{\circ}\)C in surface water to \(\sim\)21\({}^{\circ}\)C in 25 m in CE. The large temperature difference, together with the high similarity in both pigment type and phylogenetic composition among all surface water samples (Figure S2 in Supporting Information S1), indicated that the upwelling in CE did not reach the sea surface.
### Nutrients Pumping in CE Induces High _Synechococcus_ Abundance and Reshapes Their Distribution
Mesoscale eddies are widely recognized as a dynamic system delivering nutrients into euphotic zone and enhancing new production as well as organic carbon export ([PERSON], 1997; [PERSON] et al., 2010; [PERSON] et al., 2013, 2023). Cyclonic eddies enhance nutrients supply via upwelling from depth ([PERSON] et al., 2007) and induce 20% to 50% of the new production ([PERSON], 1988; [PERSON], 2003; [PERSON], 1998), while the biological process in ACE is much more complex. In the dipole eddies in western South China Sea, [PERSON] et al. (2021) quantified the vertical nitrate fluxes to the base of the euphotic zone in the same cruise and found that the turbulent nitrate flux at the base of the euphotic zone of CE was significantly higher than that of ACE and the new production in CE was mainly supported by upwelling. [PERSON] et al. (2016) reported a 2.6 times increase of total Chl \(a\) biomass in CE compared with areas outside of the eddy in western South China Sea, mainly due to the contribution of the enhanced productivity in upper mixed layer as the result of nutrient pumping ([PERSON] et al., 2016). Our results showed that the CE and ACE generated clear upwelling and downwelling respectively in our sampling area, which greatly reshaped the distribution pattern of not only _Synechococcus_ but also the whole phytoplankton (Figures 2 and 6). Biomass of phytoplankton including _Synechococcus_ was greatly promoted by nutrients pump in upper euphotic layers in CE based on our Chl \(a\) data. We observed high _Synechococcus_ abundance at \(\sim\)25 m of CE (Figure 2), which was induced by upwelling nutrients pump. Although nutrients input could stimulate the growth of various clades, changes in the light and temperature may play key roles in determining the niche differentiation within the euphotic layer and between CE and ACE. Nutrients pump, relatively cold water and the capability of chromatic acclimation (PT 3 dA) may have helped clade CRD 1 to hold a great advantage over other clades and proliferate rapidly in CE.
## 5 Conclusion
In this study, we investigated the pigment type and phylogenetic and composition of _Synechococcus_ in a cyclonic eddy (CE, cold eddy) and an anticyclonic eddy (ACE, warm eddy) located in western South China Sea in summer, 2018. We observed remarkable enhancement of _Synechococcus_ abundance in upper euphotic layers of CE resulted from the nutrients pumping. Highly diverse pigment types and phylogenetic clades were detected. Chromatic acclimating _Synechococcus_ including PT 3 dA, PT 3c/3 dB and PT 3 eA dominated in mesoscale eddies, indicating their great advantage over _Synechococcus_ with a fixed pigmentation in vertical mixing water column where ambient light spectrum changes dynamically. We also observed evident niche segregation of both pigment types and phylogenetic clades in CE and ACE, resulted from different physical and chemical properties of mesoscale eddies including ambient light and temperature. PT 3 dA dominated in CE while PT 3c/3 dB were abundant in ACE. The typical upwelling associated clade CRD 1 were dominant in CE while warm water adapted clade II and III dominated in ACE. Our results indicated that the most possible contributor of PT 3 dA and PT 3c/ 3 dB were upwelling associated clade CRD 1 and warm water adapted clade II/III, respectively. This study, for the first time, revealed the key role of chromatic acclimating _Synechococcus_ in mesoscale eddies, the typical vertical mixing system.
## Conflict of Interest
The authors declare that the research was conducted without any commercial or financial relationships that could be construed as a potential conflict of interest.
## Data Availability Statement
All rpoC1 gene and cpeBA operon sequences used in this study were deposited in the National Center for Biotechnology Information Sequence Read Archive under accession number: PRJNA1036140. The other data can be accessed at [[https://github.com/xzhangdm/SCS_Eddy_2018.git](https://github.com/xzhangdm/SCS_Eddy_2018.git)]([https://github.com/xzhangdm/SCS_Eddy_2018.git](https://github.com/xzhangdm/SCS_Eddy_2018.git)).
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wiley/fc264175_ad6c_4f75_a056_bd48db1e5a3f.md | ## Water Resources Research
### Writing - review & editing
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON]
### Writing - review & editing
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON]
### Proof of the - review & editing
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], 2001), simulating lateral subsidies of water and nutrients that influence spatial variation in vegetation productivity ([PERSON] et al., 2001; [PERSON] et al., 2022).
In this study, we parameterized and applied a RHESSys model to understand the response of a Mountain Ash water supply catchment to the pressures of the Millennium Drought. We examined the spatial and temporal shifts in ecohydrologic states, processes, and feedbacks that determined partitioning between green (evapotranspiration, noting that most evaporation was interception-driven) and blue (storage and streamflow) water use during the drought. We also outlined and tested two hypotheses to explain post-drought water partitioning, which showed persisting higher green and lower blue water use relative to the pre-drought case. The two hypotheses were (a) that higher post-drought green water use was associated with rising evaporative demand, independent of the drought itself, and (b) that changes in vegetation growth and/or nutrient cycling induced by the drought had a persisting influence on the post-drought period, increasing green water use. As well as offering novel explanations for the well-known streamflow dynamics that have puzzled researchers studying catchments in this region, we demonstrated that the RHESSys model can successfully represent nonstationary conditions where behavior is influenced by feedbacks between ecological and hydrological processes.
## 2 Data and Methods
### Walshes Creek Catchment
Walshes Creek catchment is located in the Yarra Ranges National Park east of Melbourne (Figure 0(a)) and has an area of 55 km\({}^{2}\). Elevations in the catchment range from 400 to 1,000 m above sea level. The soil textures ([PERSON] et al., 2015) are relatively uniform across the catchment, with most areas dominated by clay or clay loam (Figure 0(c)). Its runoff feeds directly into the Upper Yarra Reservoir, which forms an important part of the Melbourne and Yarra Ranges water supply system. Walshes Creek catchment is characterized by Mountain Ash forests that have been heavily protected for over 100 years in order to preserve water quality. The response of these forested catchments to climate variability and change has important implications for the region's water security.
The climate at Walshes Creek catchment is temperate with average annual precipitation of 1,300 mm and a water year starting in March. Around 20% of rainfall is typically converted to runoff and we estimate an aridity index ([PERSON], 1948) around 1.0, which indicates that ET is substantially limited by both water and energy. The distribution of Topographic Wetness Index (TWI), a measure of how much upstream area converges to a given point ([PERSON] et al., 1995), is shown in Figure 0(b). We define upland areas where TWI \(<\) 6, riparian areas where TWI \(>\) 9 and mallogue areas where \(6<\) TWI \(<\) 9. Based on fire maps provided by the Victorian Department of Sustainability and Environment, it appears that Walshes Creek has not burned since the January 1939 wildfire event, although neighboring catchments were impacted in 2009. Therefore, we estimate the forest age as at least 80 years (noting that we do not know whether the 1939 fire was stand replacing in this area). The catchment is one of the Australian Bureau of Meteorology's (BoM) Hydrologic Reference Stations and has quality-controlled streamflow data spanning 18/05/1979 to 28/02/2019.
### RHESSys Model Description
We selected the modeling platform RHESSys ([PERSON] and [PERSON], 2004) for this analysis because it simulates the key processes that influence catchment response to climate variability, such as dynamic vegetation growth, subsurface storage, nutrient cycling, and lateral water/nutrient subsidy effects. It has been successfully applied in many studies of environmental change ([PERSON] et al., 1996; [PERSON] et al., 2016; [PERSON] et al., 2018; [PERSON] et al., 2020; [PERSON] et al., 2009). The parameters that are typically calibrated in RHESSys are associated with soil hydraulic properties, which are expected to remain relatively stable at decadal timescales. Therefore, in an idealized case, the calibrated parameters should be stationary (although we recognize that calibration can mask uncertainties in other aspects of the simulation). This makes RHESSys more suitable for assessments of catchments under change than simpler models whose calibrated parameters effectively account for a wide range of dynamic and static catchment attributes, leading to non-stationarity when they are applied in conditions different to the calibration period ([PERSON] et al., 2014; [PERSON] et al., 2016; [PERSON] et al., 2011; [PERSON], [PERSON], & [PERSON], 2018; [PERSON] et al., 2019; [PERSON] et al., 2010; [PERSON] et al., 2014). Previous work has shown that detailed, process-based models are more transferable between different climate conditions than simpler models ([PERSON] and [PERSON], 2020; [PERSON] et al., 2019), which supports the notion that more complex process representation can help modelers capture changing catchment dynamics.
Figure 1: Walshes Creek catchment (a) location relative to Melbourne and the Upper Yarra Reservoir, (b) digital elevation map, (c) aspect map, (d) Topographic Wetness Index categories used to define upslope, midslope, and riparian areas, and (e) soil texture classes.
The RHESSys model is described in detail in [PERSON] (2004), although the code has since been substantially updated and we use the version described in [PERSON] et al. (2019). At a minimum, the user must specify daily precipitation, maximum temperature and minimum temperature. RHESSys follows the approach of MTN-Clm ([PERSON] et al., 1987) to estimate daily values for required climate variables that are not input by the user, such as incident direct and diffuse radiation which are simulated based on solar geometry and atmospheric transmissivity. Solar geometry, skyview factors, and temperature are adjusted based on terrain.
The vertical soil profile is simulated across two layers (saturated and unsaturated), with additional stores to account for water detention in the soil surface, leaf litter, and canopy, as well as snowpack. Infiltration is calculated based on [PERSON]'s infiltration equation ([PERSON], 1957). Soil depth is user specified, and in this study, we also fixed a constant root depth. Evaporranspiration rates in the model are calculated using the Penman-Monteith formulation ([PERSON], 1965), with a modified [PERSON] (1976) method to model leaf conductance as a function of plant type, soil moisture, temperature, vapor pressure deficit, photosynthetically active radiation, and atmospheric carbon dioxide. Photosynthesis rates are simulated using a modified [PERSON] et al. (1980) approach that uses the rate of transpiration, atmospheric carbon dioxide, PAR, and N availability. Carbon allocation to canopy components is dynamically adjusted based on water and nutrient limitations. Therefore, RHESSys accounts for climatic controls on vegetation growth and water use.
Lateral hydrologic and solute fluxes through the landscape are simulated explicitly until water reaches the stream network ([PERSON] et al., 1994), after which they are assumed to reach the outlet within one (daily) timestep. Water and solutes exiting a conceptual deeper groundwater store are routed through the riparian zone, contributing to riparian ecosystem subsidy ([PERSON] et al., 2019). The lateral flux of water and dissolved nutrients downslope in the shallow subsurface saturated zone, along with seepage from the deeper groundwater store into the riparian area, is the basis for subsidy to lower slope and riparian ecosystems. RHESSys requires a large number of parameters, most of which are typically set a priori based on available literature. Parameters that are usually calibrated control vertical and horizontal hydraulic conductivity, as well as water transfer from the saturated soil zone to the conceptual groundwater store.
### RHESSys Model Set-Up and Calibration
We developed the model of Walshes Creek catchment using Shuttle Radar Topography Mission (SRTM) elevation data ([PERSON] and [PERSON], 2013) downloaded from the USGS Earth Explorer website and soil type information from the Soil and Landscape Grid of Australia ([PERSON] et al., 2014a, 2014b, 2014c). For model setup, we used the GIS2 RHESSys scripts ([[https://github.com/faurenceelin/GIS2](https://github.com/faurenceelin/GIS2) RHESSys]([https://github.com/faurenceelin/GIS2](https://github.com/faurenceelin/GIS2) RHESSys)) with a grid resolution of 60 m (selected to maximize resolution but maintain manageable computational cost). Based on aerial imagery at the site, we assumed similar species occurrence throughout the watershed, with a Mountain Ash observatory and a tall shrub undersorty. Typical shrubs recorded in the nearest Ausploits surveys near Heavelville (about 35 km west of Walshes Creek) with a similar burn history include _Pomaderis aspera and Acacia melanovalon_ ([PERSON] et al., 2015). The parameters characterizing the overstory and understory vegetation were sourced from literature where available, with references detailed in Table S1 in Supporting Information S1. Where parameter estimates were not available (35% of parameters for Mountain Ash and 69% for understory), we used a combination of default values and expert judgment to model plausible vegetation behavior. We fixed the overstory root depth at 4.5 m and understory root depth at 0.65 m to maintain consistency with field measurements from a Mountain Ash forest ([PERSON], 1975a). In the absence of soil surveys, we set soil texture specific parameters (Figure 1e) using default values but increased the effective soil depth to 15 m based on measurements from a similar site where depth to bedrock ranged from 5 to 20 m ([PERSON] and [PERSON], 1980).
Climate input data for the RHESSys model was obtained from the Australian Water Availability Project (AWAP, also known as Australian Gridded Climate Data, AGCD) using the R package _AWAPer_([PERSON] et al., 2020). We used daily catchment-averaged rainfall, maximum temperature, and minimum temperature as climate inputs to the model, together with linearly increasing atmospheric carbon dioxide (CO\({}_{2}\)) from 340 ppm in 1980 to 410 ppm in 2019. RHESSys requires direct and diffuse shortwave radiation to be specified separately to facilitate the topographic radiation correction, but AWAP only provides total incoming solar radiation. Additionally, measured data are unavailable before 1990 and a climatology is used in AWAP, which may not be appropriate given known global trends in solar radiation ([PERSON] et al., 2005). Therefore, we used AWAP radiation data as a reference to calibrate parameters used by RHESSys's internal shortwave radiation generating scheme, which is based on [PERSON] et al. (1987).
A first-pass model calibration was undertaken in static mode (no vegetation growth) to approximate hydrologic parameters, with simulated streamflow benchmarked against daily streamflow data (Melbourne Water Corporation, 2020) downloaded from the BoM Hydrologic Reference Station website. Note that this calibration used data over the decade starting 1990, but we later adopted a different calibration period that did not include part of the Millennium Drought (see below). The initial hydrologic parameters were used for the first phase of model spin-up (in dynamic mode) to build approximate soil C and nitrogen (N) pools, with the historical climate series repeated until these pools were stable (less than 5% change per decade). To determine the final set of hydrologic parameters, the spun-up model was recalibrated for 10 years from 1985 to 1994 inclusive, this time in dynamic mode. The first year was excluded from benchmarking to minimize the impact of initial soil moisture, with the remaining 9 years used to calculate performance statistics. 2000 parameter sets were randomly generated between default bounds using the R _stats_ package and applied in RHESsys, after which we judged the better performing simulations to be acceptable. We considered performance in terms of both Nash-Sutcliffe Efficiency (NSE) (Nash & Sutcliffe, 1970) and Kling-Gupta Efficiency (KGE) ([PERSON] et al., 2009), ultimately adopting the parameter set that maximized daily KGE at 0.82. We then completed an additional spin-up phase, which ended when the overstory and undersorty LAI were relatively stable and no longer appeared to be adapting to the altered hydrologic regime. Note that the trees did not reach their maximum height (set at 100 m based on Ashton (1975a)) within this time and continued to gain carbon throughout the final simulation. We consider this appropriate because Mountain Ash are unlikely to reach their maximum height within 80 years (the current estimated age of the forest). Age dynamics in Mountain Ash forests are complex and depend on several processes that are not captured in the current version of RHESsys (e.g., self-thinning of the overstory ([PERSON] et al., 2022), succession in the understory). The spin-up period was therefore concluded based on our evaluation of the model output rather than aiming for total equilibrium or matching the simulation time to true forest age.
The final model was applied over a study period spanning 01/01/1980 to 28/02/2019, with minimal performance degradation (daily KGE = 0.8 over the full study period). Vegetation growth was validated against the satellite-derived Copernicus Leaf Area Index (LAI) product described by [PERSON] et al. (2019) with 1 km spatial resolution and 10-day temporal resolution, with post-processing based on [PERSON] et al. (2022). We defined the Millennium Drought period as 01/01/1998 to 31/12/2009. Average rainfall was 12% lower during the drought than earlier in our study period and average temperature was about 0.5 degC higher (Figure 2). In the post-drought period, average rainfall nearly recovered to pre-drought levels (4% lower than pre-drough), but temperatures climbed to 0.6 degC above the pre-drought case.
### Model Performance
When applied over the full study period, the model showed robust hydrologic performance with a KGE of 0.77 at the annual timescale and 0.8 at the daily timescale (Figure 3). The streamflow simulation was also relatively accurate
Figure 2: Average annual rainfall and temperature (by water year) shown before, during, and after the Millennium Drought. Dashed lines indicate average values over the three periods. The \(x\)-axis labels (in this and subsequent time series plots) show time in years.
Figure 3: Model performance in terms of (a) annual streamflow, (b) daily streamflow, (c) 365-day moving average of runoff ratio, and (d) LAI.
during and after the Millennium Drought (daily KGE = 0.71 for both periods as opposed to 0.81 pre-drought), despite having been calibrated using pre-drought data only. This is important because hydrologic models often perform poorly when transitioning into climatic periods that are substantially different to the calibration period, an issue that has been recognized specifically in the context of the Millennium drought ([PERSON] et al., 2020). The simulation largely captured the reduction in runoff ratio experienced at Walshes Creek catchment during the drought (Figure 3c), although runoff was overestimated during the drought-ending wet years (2010-2012) and slightly underestimated during the transition into drought (1998). Together, these issues suggest that the model may have underestimated the buffering effect of catchment storage during transition into and out of drought.
The model also showed good performance in simulating ecological processes in the catchment (Figure 3d). The Copernicus remotely sensed watershed-average LAI product agreed well with the total LAI magnitude and seasonality in RHESsys. The model showed slightly higher seasonal variability, which may relate to the assumption that there are specific periods of leaf growth and leaf fall that do not overlap. The approximately equal split between overstory and understory LAI on average is appropriate for a Mountain Ash forest of this age, based on measurements taken at the nearby Maroondah catchments ([PERSON] et al., 1998). The simulated ET had higher seasonal and interannual variability than the Derived Optimal Linear Combination Evaportranspiration (DOLCE) or the Global Land Evaporation Amsterdam Model (GLEAM) data extracted over the same area (Figure S1 in Supporting Information S1), which could be due to the remotely sensed products' larger spatial scale. The average ET in RHESsys was slightly lower than GLEAM but higher than DOLCE.
## 3 Catchment Behavior Before, During and After the Millennium Drought
Given the model was able to reproduce ecohydrologic dynamics, including transitions into and out of drought (notably conditions it was not calibrated for), we judged that it could be applied to examine water partitioning changes over the study period. As shown in Figure 3c, there was a substantial drop in the runoff ratio over the drought period. In absolute terms, our simulation showed that streamflow (blue water), and to a lesser extent evaporation (green water), declined during the drought, but transpiration (green water) remained almost consistent with pre-drought levels (Figure 4a). This suggests that the vegetation was able to access the same amount of water in total despite a large (12%) decrease in rainfall. It follows that the fraction of rainfall that was transpired increased during the drought (Figure 4b), while the evaporated fraction remained constant. Therefore, runoff declined disproportionately relative to the rainfall decrease.
The seasonal timing of any LAI and/or transpiration changes could have hydrologic implications for Walshes Creek catchment given the strong seasonal patterns in streamflow (Figure 5c), but we did not see evidence of ecohydrologic responses specific to time-of-year. In fact, mean catchment LAI decreased slightly during the drought in every month of the year compared to the pre-drought case (by an average of 3.5%), then recovered post-drought (Figure 5a). Transpiration was maintained during the drought across all seasons, indicating a year-round increase in transpiration per unit LAI (Figure 5b). The seasonal patterns of streamflow modeled before, during and after the drought compare well with observations (Figure S2 in Supporting Information S1).
The model indicated that spatial patterns of vegetation growth and green water use could help explain the change in water partitioning (Figure 6). The modeled pre-drought LAI across the catchment was spatially variable, with the highest values in certain midslope areas and the lowest values in upslope areas (Figure 6a1 and Figure S3 in Supporting Information S1). The differences in pre-drought LAI were associated with a tradeoff between water/N availability (influenced by downslope subsidy) and radiation (influenced by terrain slope and aspect). The largest LAI decreases during the drought were modeled in the midslope areas with highest initial growth (Figure 6a2), with smaller decreases further upslope. However, LAI did not change in the riparian area, which displayed resilience to prolonged drought. This suggests that water subsidies were enough to maintain the LAI in the riparian area despite loss of local rainfall, which is in line with patterns simulated under drying future climate scenarios in [PERSON] et al. (2022). After the drought, LAI in the upslope and midslope areas mostly recovered, while the riparian zone had higher LAI than pre-drought (Figure 6a3). Our results are broadly consistent with remotely sensed NDVI based on LANDSAT 8 top-of-atmosphere reflectance ([PERSON] et al., 2009), which shows an increase in the ratio of riparian NDVI to non-riparian NDVI during the drought with an additional increase after the drought (Figure S4 in Supporting Information S1). Shifts in the relationship between TWI and LAI are further demonstrated in Figure S3 in Supporting Information S1, which shows a change in the shape of the LAIgradient around the midslope to riparian transition during the drought. This change in LAI gradient was largely maintained in the post-drought period.
Prior to the drought, the riparian area contributed 10.8% of annual ET across 9.6% of the catchment area (Figure 6b1). During the drought, ET decreased everywhere except the riparian zone where it increased (Figure 6b2), leading the riparian zone to contribute 11.3% of catchment ET. This change in spatial partitioning can help explain why catchment-wide transpiration was maintained despite a decrease in LAI; the relatively high-transpiration riparian zone utilized more water during the drought than pre-drought. Interestingly, ET in the post-drought period was higher than pre-drought throughout the entire catchment, and particularly in the riparian zone (Figure 6b3). This suggests longer term changes in the catchment related either to vegetation response to the drought and/or differences in post-drought climate (relative to pre-drought). The spatial patterns in ET shifts both during and after the drought were associated with differences in transpiration as opposed to evaporation (Figure S5 in Supporting Information S1). During the drought, there were increases in saturation deficit depth (Figure 6c2) that did not completely recover to pre-drought levels in the post-drought period (Figure 6c3). Higher ET despite a larger saturation deficit depth post-drought (relative to pre-drought) indicates an overall shift in partitioning towards green, as opposed to blue, water use.
## 4 Hypothesis Testing to Explain Change in Ecohydrologic Partitioning
Section 3 describes a shift in catchment water partitioning during the Millennium Drought, with higher fractional green water use (at the expense of blue water) under dry conditions. However, it is not clear why this partitioning
Figure 4: Two-year moving average of (a) flow, transpiration and evaporation and (b) proportion of rainfall converted to flow, transpiration and evaporation. Average values before, during and after the Millennium Drought are shown as dotted lines.
change was partially maintained in the wetter post-drought period. This section outlines two possible hypotheses for the heightened transpiration as a fraction of rainfall post-drought, either of which could explain the apparent nonstationarity in the model results. We then describe two model experiments that were set up to test the plausibility of each hypothesis for explaining post-drought vegetation growth and ET.
### A Hypothesis Based on Rising Evaporative Demand
One potential explanation for the ecohydrologic response outlined in Figure 6 is that changes in climate variables other than rainfall impacted simulated growth during and after the drought. Vapor pressure deficit (VPD) impacts evaporative demand and was higher during and after the drought than pre-drought (Figure 7). While RHESSys simulates stomatal closure in response to high VPD, this may not fully compensate for the positive effect of VPD on evaporative demand, leading to an overall increase in potential ET ([PERSON], 1965). This could help explain the increase
Figure 5: Seasonal, basin-wide averages of simulated (a) LAI, (b) transpiration, and (c) streamflow during the pre-drought, drought, and post-drought periods.
Figure 6: Spatial plots of simulated mean (a) LAI, (b) annual ET, and (c) saturation deficit depth (SDD), which is the depth of the water table. Variables are shown as (1) average pre-drought values as a baseline, (2) drought average minus pre-drought average, and (3) post-drought average minus pre-drought average.
Figure 7: Two-year moving average of modeled daily mean vapor pressure deficit that may have contributed to the simulated ecohydrologic response during and after the drought.
in modeled ET in the relatively water-rich riparian area during the drought despite decreases in the more water-limited upslope areas. High average VPD over the post-drought period (relative to pre-drought) is consistent with findings that evaporative demand increased from the mid-1990s to 2016 due to rising VPD ([PERSON], [PERSON], et al., 2018), and that relative humidity has been declining ([PERSON] et al., 2021) in the region. Note that the model-generated shortwave radiation in RHESsys (which uses day-night temperature difference to estimate atmospheric transmissivity and is therefore influenced by temperature trends) was also higher post-drought than pre-drought, which is not consistent with the AWAP data at Walshes Creek that shows high radiation during the drought followed by a return to pre-drought levels. This may have led the model to overestimate the post-drought evaporative demand to some extent. Warmer temperatures enhance the rate of nutrient cycling in RHESsys ([PERSON], 1994), so post-drought warming could also have impacted vegetation growth and ET via increased N availability.
### A Hypothesis Based on Ecological Response to Drought
An alternative (or perhaps complementary) explanation for the increase in ET shown in Figure 6b3 is that there were changes in vegetation growth and/or nutrient cycling during the drought that persisted post-drought, enhancing water uptake. This hypothesis is consistent with the model results, which show higher mineralized N during the drought compared to pre-drought, with a further increase post-drought (Figure 8a). During the drought, available N increased due to high temperatures accelerating decomposition ([PERSON] & [PERSON], 1994) while low soil moisture had a smaller negative influence on decomposition. Vegetation N uptake reduced during the drought because upland and midslope growth was suppressed by water limitation, and the low rainfall reduced the potential for N flushing. These factors contributed to N accumulation during the drought that enhanced post-drought N availability (Figure 8b). Downslope accumulation of this additional N due to flushing (particularly during the wet period from 2010-2012) could explain the particularly strong riparian vegetation growth post-drought. On average, mineralized N availability was 9.1% higher post-drought relative to pre-drought and N uptake by the vegetation was 3.7% higher. Simulated photosynthesis was limited by N across 38% of grid cells on average over our study period, supporting the notion that N played an important role in vegetation dynamics. Therefore, enhanced post-drought productivity due to persisting effects of higher N availability may have contributed to the modeled behavior shown in Figure 6.
The decomposition scheme in RHESsys ([PERSON] et al., 1996) is known to have low sensitivity to moisture limitation compared to an alternative scheme from Biome-BGC ([PERSON] et al., 2005), and uncertainty is highest under hot and dry conditions ([PERSON] et al., 2022). In addition, N redistribution in both the vertical and horizontal
Figure 8: 365-day moving average of simulated (a) mineralized N and (b) N uptake.
directions is sensitive to parameters that describe exponential decay rates of soil N and hydraulic conductivity ([PERSON] et al., 2020). Because N observations were not available to inform these aspects of the model set-up, we acknowledge high uncertainty around N dynamics in our simulation.
### RHESSys Experiments to Attribute Altered Water Partitioning After Drought
Having formed two plausible hypotheses for the spatially and temporally varying responses of ET in the RHESSys model, we tested the contributions to post-drought behavior via the following two ecohydrologic experiments:
* Hypothesis/experiment 1 (rising evaporative demand): Run the model for the pre-drought period immediately followed by the post-drought period (i.e., removing the drought and any concurrent changes in vegetation growth and nutrient cycling from the simulation). If altered post-drought climate explains the post-drought response in Figures 5(a)-5(c), we will see similar behavior.
* Hypothesis/experiment 2 (ecological response to drought): Run the model for the pre-drought period, then the drought period, then the pre-drought period (i.e., removing the potential contribution of post-drought climate). If carry-over effects of the drought explain the post-drought ecohydrologic response in Figures 5(a)-5(c), we will see similar behavior.
Interestingly, the experiments showed that neither hypothesis in isolation fully explained the changes shown in Figure 6. If the period of drought was removed from the simulation (following hypothesis 1), post-drought LAI declined in non-riparian areas, indicating that high VPD after the drought increased water stress and reduced growth (Figure 8(a)). The riparian areas showed increased growth, indicating that N limitation was relatively more important than water limitation there. As such, enhanced N cycling under warmer post-drought conditions impacted growth in the riparian zone more than increased water demand. Time series of basin-wide LAI, mineralized N and potential ET for experiment 1 are shown in Figure S6 in Supporting Information S1, indicating that average productivity decreased slightly due to water stress despite higher N availability.
Removing the effects of post-drought climate (following hypothesis 2) gave basin-wide LAI increases in the post-drought period relative to pre-drought, suggesting that ecosystem dynamics during the drought enhanced subsequent growth (Figure 8(a)). This positive effect on growth was strongest in the riparian area, since N (as opposed to water) availability had a relatively larger impact there. Basin-wide ecological shifts over time in experiment 2 are shown in Figure S7 in Supporting Information S1. The combination of both post-drought climate and drought-associated ecological changes explains the LAI response in Figure 5(a), which shows trend magnitudes in between those of the two synthetic experiments (substantial increases in the riparian area with little change midslope and upslope).
The processes posed by both hypotheses contributed to the post-drought enhancement of ET that was strongest in the riparian zone (Figure 5(b)) compared to Figure 8(b), but the trends were larger in experiment 1. However, we note that vegetation interactions and differing timescales mean that the experiments can indicate, but not precisely quantify, the effects in the original simulation. The ET changes contributed to larger saturation deficit depths in both experiments (Figure 8(c)), which also aligns with the original post-drought simulation (Figure 5(c)). Overall, our results suggest that both altered post-drought climate and ecological dynamics during the drought were factors in shifting the post-drought green/blue water partitioning relative to pre-drought.
## 5 Discussion
The ecohydrologic modeling presented in this study showed that changing spatial patterns of water partitioning could contribute to an increase in the proportion of green water consumption in a Mountain Ash catchment under severe drought (Figure 6). This response was facilitated by lateral water subsidies to the riparian zone that allowed transpiration to increase under higher water demand. Enhanced N mineralization and reduced upslope uptake (leading to larger N subsidies) also played a role in maintaining riparian growth during the drought. Persisting high VPD and N availability after the drought led to higher modeled transpiration post-drought relative to pre-drought despite slightly lower average rainfall. While we do not have detailed ground observations of vegetation before, during and after the drought to support these conclusions, the model's skill in reproducing both streamflow at the catchment outlet (Figure 3, Figure S2 in Supporting Information S1) and remotely sensed LAI (Figure 5(d)) suggests that our conclusions are plausible. Additionally, fine-scale remotely sensed NDVI at the site shows increased riparian growth relative to the rest of the catchment during and after the drought (Figure S4 in Supporting Information S1). Our results are consistent with literature that has shown the resilience of the riparian zone to drought ([PERSON], 2018) and increased partitioning of available water to ET during dry periods ([PERSON] et al., 2021) in other catchments. There is also observational evidence that Mountain Ash stand
Figure 9.— Difference relative to pre-drought (a) average LAI, (b) annual average ET, and (c) average saturation deficit depth (SDD) for (1) experiment 1 with the drought period removed (i.e., no vegetation response to drought) and (2) experiment 2 with the pre-drought climate repeated after the drought (i.e., no altered post-drought climate).
transpiration tends to increase under warming given sufficient water availability as increased evaporative demand overwhelms the effects of water-saving stomatal closure ([PERSON] et al., 2010). Using the Community Atmosphere Biosphere Land Exchange model (CABLE) at a coarser resolution of 5 km, [PERSON] et al. (2020) simulated no loss of hydraulic conductance across Victorian wet sclerophyll forests during the Millennium Drought. Our results support their conclusions, noting that transpiration may have changed at smaller scales such that decreases in upslope areas were compensated by increases in riparian areas.
A recent study using remotely sensed data demonstrated increased upslope water use during drought in the Southern Appalachian Mountains (USA), which reduced downslope subsidies such that lowland ET decreased ([PERSON] et al., 2022). These results contrast with the reductions in ET we simulated in upslope areas in the Walshes Creek catchment, likely because energy (as opposed to water) limitation was more prevalent across the [PERSON] et al. (2022) study region. However, for Walshes Creek we also concluded that reductions in downslope water subsidies can strongly affect locations that are accustomed to receiving them (hence the reduction in midslope LAI in Figure 62), although the drought was not severe enough to induce substantial water limitation in our simulated riparian zone. The contrasting results of our study with [PERSON] et al. (2022) highlight the importance of local and regional factors in determining hydrologic response to drought.
Our simulation results showed that ET was higher and the water table was lower in the post-drought period than the pre-drought period, suggesting a shift towards green and away from blue water use. This aligns with the conclusions of [PERSON] et al. (2021) that enhanced ET prevented recovery of catchment runoff ratios post-drought, although they were discussing catchments for which the effect was larger. We attributed the shift partly to altered post-drought climate, since continued warming led to higher VPD (hence higher potential ET) and enhanced N mineralization (hence higher riparian LAI) relative to pre-drought. Additionally, N mineralization increased and uptake decreased during the drought, leading to carry-over effects in the post-drought period. Growth in the riparian area benefited especially from greater N stores across the catchment, since reduced upland growth during the drought led to decreased local N consumption and therefore more potential for downslope transport. Our results highlight the complex combination of factors that can lead to altered hydrologic response under climate variability and change. The shift from blue to green water use both during and after the drought have important implications for Melbourne's water supply, particularly since the latest IPCC report projects rainfall could decline by up to 16% (5 th percentile of RCP8.5 projections) and average temperature could increase by 4.8\({}^{\circ}\)C (95 th percentile of RCP8.5 projections) in this region by 2100 (IPCC, 2022).
This study has also demonstrated that the RHESSys model can be successfully applied in a Mountain Ash catchment, including under climate variability for which it was not calibrated. To our knowledge, this is the first published application of RHESSys for an Australian ecosystem, and may open the door to future advances like those achieved with RHESSys in the US, Europe and Asia ([PERSON] et al., 2016; [PERSON] et al., 2019; [PERSON] et al., 2017; [PERSON] et al., 2007; [PERSON] et al., 2018; [PERSON] et al., 2022; [PERSON] et al., 2009; [PERSON] et al., 2007). Some data processing tools for RHESSys setup have already been adapted to work with Australian data sets ([PERSON] and [PERSON], 2015) and the model's potential role in addressing nationally important research topics such as changing fire risk has been highlighted recently ([PERSON] et al., 2022). The catchment we simulated was relatively humid (aridity index \(\sim\)1), but many Australian eucalypt forests are more water-limited and accurately accounting for electrophysiological processes may be even more important for simulating hydrologic behavior ([PERSON] et al., 2016). While we consider that eeohydrologic behavior was largely well-represented, we identified two aspects of the model that could be improved in the future, especially for applications in eucalypt forests. First, it would be useful to include the phosphorous cycle in RHESSys, since growth in many Australian ecosystems is highly dependent on phosphorous availability ([PERSON], 1962; [PERSON] et al., 2015; [PERSON] et al., 1997). Second, the ability to simulate coincident leaf growth and fall, rather than requiring two non-overlapping periods, would make the simulation more realistic for eucalypt-dominated forests ([PERSON] et al., 2016).
A limitation of this study is that RHESSys is currently unable to fully represent the effects of decreased subsurface flow connectivity under drying (although hydraulic conductivity of the soil does decrease with water content, potentially forming low transport regions). Connectivity changes have been put forward as a potential driver of reduced runoff ratios during and after the drought ([PERSON] et al., 2015). Our results suggest that the observed streamflow dynamics in Walshes Creek can be mostly explained through ecological and climate shifts alone, without the need to assume major changes in groundwater connectivity. However, the simplified groundwater dynamics in RHESSys could explain why streamflow was overestimated in the very wet years immediately following the drought (Figure 3). Future work could use a more detailed groundwater model such as PARFLOW-CLM ([PERSON] and [PERSON], 2008) to test the potential contribution of altered groundwater behavior to observed streamflow dynamics.
The version of RHESSys we applied does not automatically simulate vegetation mortality due to water stress (although mortality events can be prescribed). To our knowledge, the Millennium Drought did not lead to significant tree mortality in Victorian Mountain Ash forests, but the later 2017-2019 Drought was associated with water stress mortality in other eucalypt forests ([PERSON] et al., 2020, 2022). Therefore, we believe that it would be valuable for future research to examine drought mortality in ecohydrologic modeling of eucalypt-dominated catchments under severe drought. Vegetation mortality based on depletion of non-structural carbon stores under drought stress has been implemented in an alternative version of RHESSys ([PERSON] et al., 2013), but at this stage the model has only been applied in North American pine forests. Advances in understanding and simulating (a) the effects of stress on C allocation ([PERSON] et al., 2018); (b) the implications of moisture availability for decomposition and N cycling, and (c) CO\({}_{\text{g}}\) effects on growth and ET will be important for better quantifying catchment response to climate variability and change. [PERSON] and [PERSON] (2019) used RHESSys to demonstrate the importance of soil water holding capacity and root depth/density for forest response to thinning fuel treatments; future work could test the sensitivity of the drought response we modeled to these properties.
Previous work on catchment response during and after the Millennium Drought ([PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2015, 2016) has often focused on the different responses of catchments across southeast Australia. Some catchments experienced much larger shifts in their rainfall-runoff relationships than others, and post-drought streamflow recovery was highly variable. It is possible that the mechanisms we identified for Walsheres Creek also apply for other catchments to various degrees, but we cannot confirm this based on our simulations of one ecosystem type. Using an ecohydrologic model with sufficient process detail to represent ecohydrologic behavior under change (such as RHESSys) in catchments with different climate, terrain and vegetation could help untangle the reasons for the observed heterogeneity in catchment responses, and this is a promising avenue for future research.
## 6 Conclusions
The RHESSys modeling undertaken in this study has demonstrated that a large decrease in streamflow (relative to the decrease in rainfall) during the Millennium Drought in Walshees Creek was likely caused by the ecosystem consuming a higher fraction of rainfall as transpiration. Notably, the absolute value of mean catchment-wide transpiration was almost maintained during the drought despite lower LAI on average. In water-limited upper and midslope areas, the combination of reduced rainfall and increased evaporative demand reduced vegetation LAI, driving declines in ET. However, the riparian area continued to receive enough water via subsidy to maintain LAI at pre-drought levels. Furthermore, in these water-rich areas the increased evaporative demand led to higher ET during the drought than in the pre-drought period. The contrasting responses across space helped the forest to maintain its overall transpiration rate so that the rainfall deficit was almost entirely expressed through stream-flow reduction. Model experiments showed that a combination of post-drought warming and drought-induced increases in mineralized N led to persistent changes in water partitioning post-drought, specifically slightly higher green water consumption relative to blue water. While these outcomes are based on a modeling exercise and not confirmed directly through observations of transpiration and mineralized N in the catchment, the high agreement between modeled and observed streamflow, including during the transitions into and out of drought, suggest that the simulated mechanisms are likely to be realistic. Overall, our results demonstrate the value of detailed ecohydrologic modeling for generating hypotheses around complex catchment response to change.
## Data Availability Statement
SRTM data ([PERSON], 2013) for this study were downloaded from the USGS Earth Explorer website ([[https://earthexplorer.uses.gov/](https://earthexplorer.uses.gov/)]([https://earthexplorer.uses.gov/](https://earthexplorer.uses.gov/))). Soil classes were calculated based on silt/clay/sand fractions from the Soil and Landscape Grid of Australia ([PERSON] et al., 2014, 2014, 2014) obtained through [[https://shiny.esoil.io/Apps/SLGAViewer/](https://shiny.esoil.io/Apps/SLGAViewer/)]([https://shiny.esoil.io/Apps/SLGAViewer/](https://shiny.esoil.io/Apps/SLGAViewer/)). Streamflow data for Walshees Creek (Melbourne Water Corporation, 2020) were sourced from [[http://www.bom.gov.au/water/hrs/#id=229661A](http://www.bom.gov.au/water/hrs/#id=229661A)]([http://www.bom.gov.au/water/hrs/#id=229661A](http://www.bom.gov.au/water/hrs/#id=229661A)). Fire maps were downloaded from the Forest Fire Management Victoria website ([[https://www.ffm.vic.gov.au/history-and-incidents/past-bushfires/past-bushfire-maps](https://www.ffm.vic.gov.au/history-and-incidents/past-bushfires/past-bushfire-maps)]([https://www.ffm.vic.gov.au/history-and-incidents/past-bushfires/past-bushfire-maps](https://www.ffm.vic.gov.au/history-and-incidents/past-bushfires/past-bushfire-maps))).
The GIS2 RHESSys scripts developed by [PERSON] ([[https://github.com/laurencelin/GIS2](https://github.com/laurencelin/GIS2) RHESSys]([https://github.com/laurencelin/GIS2](https://github.com/laurencelin/GIS2) RHESSys)) were used for model setup. LANDSAT data (U.S. Geological Survey, 2013) were downloaded using Google Earth Engine using the command _ee_ImageCollection_(\"_LANDSAT/LCO8/C01/1T_TOA_\"). RHESSys default parameters are available at [[https://github.com/RHESSys/RHESSys/wiki/Parameter-Definition-Files](https://github.com/RHESSys/RHESSys/wiki/Parameter-Definition-Files)]([https://github.com/RHESSys/RHESSys/wiki/Parameter-Definition-Files](https://github.com/RHESSys/RHESSys/wiki/Parameter-Definition-Files)). The Walishes Creek RHESSys model prepared for this study is available on Zenodo, see [PERSON] et al. (2023).
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wiley/fc29eb29_2184_4875_858c_a6e6859210bd.md | # Mesoscale Surface Wind-SST Coupling in a High-Resolution CESM Over the KE and ARC Regions
[PERSON]
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 International Laboratory for High-Resolution Earth System Model and Prediction (HESP), Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
[PERSON]
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 International Laboratory for High-Resolution Earth System Model and Prediction (HESP), Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 International Laboratory for High-Resolution Earth System Model and Prediction (HESP), Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 International Laboratory for High-Resolution Earth System Model and Prediction (HESP), Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 College of Ocean and Atmospheric Sciences, Ocean University of China, Qingdao, China
Zhijia Tang
1 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese Academy of Sciences, Beijing, China, 1 Laboratory for Ocean and Climate Dynamics, Pilot National Laboratory for Marine Science and Technology, Qingdao, China, 1 Center for Excellence in Quaternary Science and Global Change, Chinese Academy of Sciences, Xi'an, China, 1 Key Laboratory of Physical Oceanography, Ministry of Education, Institute for Advanced Ocean Study, Frontiers Science Center for Deep Ocean Multispheres and Earth System (DOMES), Ocean University of China, Qingdao, China, 1 University of Chinese Academy of Sciences, Qingdao, China, 1 University of Chinese AcademyPacific associated with tropical instability waves ([PERSON] et al., 2001; [PERSON] et al., 2001; [PERSON] et al., 2003; [PERSON] et al., 2019; [PERSON], 2014; [PERSON] & [PERSON], 2008), and the western coast of South America ([PERSON] et al., 2020, 2021). At mesoscales, wind stress perturbations correlate well with SST perturbations ([PERSON] & [PERSON], 2005; [PERSON] et al., 2012). The response of the surface wind to SST perturbations leads to mesoscale perturbations in the corresponding wind stress curl and divergence fields that are respectively linearly related to the crosswind and downwind SST gradient perturbations ([PERSON] et al., 2001; [PERSON] & [PERSON], 2005; [PERSON] et al., 2003; [PERSON] & [PERSON], 2006). It is demonstrated that the mesoscale eddies can potentially affect atmospheric storm tracks through baroclinic instability processes ([PERSON] et al., 2015, 2017; [PERSON] et al., 2018). The response of surface wind to mesoscale SST perturbations is, in turn, capable of having negative feedback onto SST ([PERSON] et al., 2017). Besides, the interactions between the oceanic mesoscale eddies and the atmosphere have been demonstrated to strengthen the Kuroshio Extension jet by enhancing the eddy dissipation, with the underlying mechanisms illustrated ([PERSON] et al., 2016).
The prevailing mechanisms by which mesoscale SST perturbations influence the overlying atmosphere include the pressure adjustment (PA) mechanism ([PERSON], 1987) and the downward momentum transport (DMT) mechanism ([PERSON] et al., 1989). As for the DMT mechanism, when air passes from warm to cold water regions, the responded SST perturbations enhance the vertical stability of the atmosphere, leading to a decrease in downward momentum transport. So, when the DMT mechanism plays a dominant role in the atmospheric response, there is a decrease (increase) in wind speed over cold (warm) SST perturbations, leading to wind convergence upstream and divergence downstream over the cold SST perturbations regions, which presents a dipole pattern ([PERSON] et al., 2015). On the other hand, when the atmospheric adjustment time is sufficiently long, which allows for vertical mixing to take place within the atmospheric boundary layer (PBL), the heat is transported upward to modify the air temperature; this acts to adjust surface level pressure (SLP) gradients with its responded pattern being well matched to the SST gradients ([PERSON] et al., 2016). This is referred to as the PA mechanism with which the adjustment of surface wind is closely related to SLP perturbations, and a monopole response pattern of SLP perturbations is expected to occur. As a result, surface wind divergence and SLP perturbations are distributed directly above the centers of SST perturbations ([PERSON] et al., 2013).
Most case studies hold the view of these two popular mechanisms. Previous studies have indicated that the atmospheric responses to mesoscale SST perturbations can be involved in different mechanisms that are dependant on various background conditions. For example, it was proposed that the PA mechanism plays a more important role under weak wind conditions, while the DMT mechanism exerts a dominant effect under strong wind conditions ([PERSON] et al., 2015; [PERSON] et al., 2019). In addition, [PERSON] (2007) proposed a mechanism that is quite different from the prevailing DMT and PA mechanisms. His study is focused on the midlatitude regions where under strong wind conditions, the surface wind is accelerated primarily due to the momentum provided by an increase in the along-front winds. Besides, he found that in low latitude regions with weak wind, the DMT and PA mechanisms both exert a dominant effect on the momentum budget. [PERSON] and [PERSON] (2011) suggested that the PA mechanism plays a pronounced role over areas with strong SST fronts, such as ARC and KE. However, [PERSON] et al. (2015) showed that the oceanic eddies affect the overlying atmosphere by the DMT mechanism over the south Atlantic and ARC regions. The DMT mechanism is also proven dominant in the KE region ([PERSON] et al., 2016; [PERSON] et al., 2013), while [PERSON] and [PERSON] (2015) proposed that the PA mechanism is more important there. Clearly, the mechanisms for the atmospheric responses to mesoscale SST perturbations are case dependent and regionally dependent, which is still controversial. Besides, whether the mechanisms are seasonally dependent remains to be seen in different regions of the world ocean. Therefore, it is imperative to comprehend the mechanisms for mesoscale air-sea interactions through theoretical inference, diagnostic analyses, and model simulations.
Currently, high-resolution and long-term satellite observations are still lacking for adequately determining the atmospheric state at mesoscales and small scales, which makes it difficult to ascertain to what extent the PA and DMT mechanisms could explain the atmospheric responses in specific regions. Most studies on this aspect are based on numerical simulations using coupled models which provide a powerful tool for the understanding of mesoscale ocean-atmosphere interaction mechanisms. However, the relationship between mesoscale wind stress and SST perturbations strongly depends on model's resolution; in coarse resolution models, the positive correlations cannot be adequately captured, but negative correlations emerge instead ([PERSON] et al., 2010). As the model resolution is increased, significant positive correlations appear especially in eddy-resolving models, but the strength of the coupling is still weaker than that observed ([PERSON] et al., 2010; [PERSON] & [PERSON], 2006).
Aside from the importance of model resolution, other primary factors that limit the accurate simulations of mesoscale air-sea coupling strength exist, such as the parameterization of vertical turbulence in the atmospheric boundary layer ([PERSON] & [PERSON], 2010; [PERSON] et al., 2009; [PERSON], 2007). [PERSON] et al. (2018) found that the magnitude of wind speed is also an important factor that causes the intermodel difference in the intensity of mesoscale air-sea interaction. Given the studies mentioned above, models with different resolution and vertical mixing parameterization exhibit different representations of mesoscale air-sea interactions, implying that the simulated characteristics and underlying mechanisms for atmospheric responses to mesoscale SST perturbations can be model dependent.
Recently, the International Laboratory for High-Resolution Earth System Prediction (iHESP) releases an unparalleled set of multi-century high-resolution climate simulations, using a high-resolution Community Earth System Model (CESM-HR). Good performance of the CESM-HR has been demonstrated, including simulations of mean climate state and interannual variability ([PERSON] et al., 2020). As one of the main research themes of iHESP is to understand climate variability and predictability on various space-time scales, it is necessary to quantify and assess the oceanic role in inducing atmospheric perturbations and their interactions at mesoscales and small scales. As evident, the model is capable of representing extreme events such as tropical cyclones and extreme rainfall. In addition, the mesoscale heat flux responses to SST are also well depicted; but the representations of the mesoscale air-sea interactions are still not well known, especially in association with momentum flux such as surface wind stress response to SST perturbations. In this study, the extent to which the CESM-HR can simulate the response of surface wind to mesoscale SST perturbations is assessed. To understand the performance in representing mesoscale air-sea interactions in the CESM-HR, physical insight into the mechanisms for mesoscale couplings is clearly needed. As mentioned above, previous investigations based on coupled models indicate that the mesoscale air-sea interactions can operate through the PA and DMT mechanisms, whose relative dominances in atmospheric responses can be regionally dependent. Here, the CESM-HR products are used for such investigations. Some specific questions can be addressed, such as whether the mechanisms for atmospheric responses can be changed with seasons and regions. Section 2 introduces the data and methods used. In Section 3, the CESM-HR products are used to quantify the mesoscale air-sea coupling strength, which is then compared with that observed. Mesoscale perturbation fields in PBL are calculated to explore the dominant mechanisms for the atmospheric responses over different regions during winter and summer seasons. Conclusion and the discussion of possible reasons for the underestimated mesoscale coupling strength in CESM-HR are presented in Section 4.
## 2 Data and Methods
### Satellite Observations and CESM-HR Products
Two datasets of satellite observations are used in our study: wind speed from Quick Scatterometer (QuikScat, version 4) and SST from the Advanced Microwave Scanning Radiometer (AMSR-E, version 7). The AMSR-E was on NASA's EOS Aqua spacecraft, launched on 4 May 2002, and operated until 4 October 2011. The QuikScat was launched in June 1999 and stopped rotating in November 2009. Correspondingly, data during the overlapped period from January 2003 to December 2008 are utilized. The SST and wind vector fields are monthly averaged states with a resolution of 0.25\({}^{\circ}\). The wind stress (\(\tau\)) was calculated from the wind speed at 10 m above the sea surface using the bulk formulation (\(\tau_{x}\), \(\tau_{y}\)) = \(\rho_{a}C_{p}\sqrt{u^{2}+v^{2}}(u,v)\), where \(\rho_{a}\) is the air density; \(C_{p}\) is the drag coefficient; \(u\) and \(v\) are zonal and meridional wind components, respectively (Large & Pond, 1981, 1982).
The CESM-HR simulated datasets are used in our study. The detailed description of CESM-HR can be found in [PERSON] et al. (2020); here, we only highlight the aspects of relevance to this study. The atmospheric component of CESM-HR is the fifth version of the Community Atmospheric Model (CAM5) with a resolution of 0.25\({}^{\circ}\) and the oceanic component is the second version of the Parallel Ocean Program (POP2) with a resolution of 0.1\({}^{\circ}\). There are 62 vertical levels in the ocean with a maximum depth of 6.000 m, and 42 levels in the atmosphere with a top layer at 3 hPa. The iHESP released the data set of the first 317-year preinitial control (PI-CTRL) simulation in June 2020. The model output data used in this study are monthly averaged states with a resolution of 0.1\({}^{\circ}\) grid and during the model year from 327 to 338. Note that the overall performances of this model in historical climate simulation and future climate projection have been analyzed thoroughly in [PERSON] et al. (2020), and it is evident that the biases in ocean temperature, salinity, and related fields have been reduced in the CESM-HR simulations compared to the corresponding coarse resolution CESM simulations. In particular, the oceanic mixed layer depth that can have impacts on the persistence of SST anomalies is in much better agreement with Argo-based observations.
### Calculation of Mesoscale Perturbations and Coupling Coefficients
The mesoscale perturbation fields for variables of interest here are extracted using a high-pass filter called Loess (locally weighted regression) ([PERSON] & [PERSON], 1988). Following the work by [PERSON] and [PERSON] (2006), the filter cutoff lengths of 10\({}^{\circ}\) latitude and 30\({}^{\circ}\) longitude are employed to obtain smoothed fields; then, perturbations are obtained by subtracting the smoothed fields from the origin fields. In the following, we will analyze the relationships of wind stress divergence and curl with the downwind and crosswind SST gradient fields. The later fields are calculated through the formula presented in [PERSON] and [PERSON] (2006). The SST and wind stress perturbations are computed first, then are the SST gradient, divergence and curl fields, respectively.
To quantify the intensity of mesoscale air-sea coupling, we compute the coupling coefficient (\(\alpha\)) for mesoscale SST and wind stress perturbations, with \(\alpha\) being positive for their positive correlation. The larger the \(\alpha\), the stronger the coupling strength. For each grid point, the regression coefficient of the high-pass filtered wind stress onto SST is employed as \(\alpha\). When evaluating the coupling strength over an area such as KE and ARC, we divide the SST perturbations from \(-3.3\) to \(3.3^{\circ}\)C into 22 compartments with \(0.3^{\circ}\)C intervals in which the wind stress perturbations that fall into the corresponding SST perturbations are found. The median of SST and wind stress perturbations in each interval are calculated, and then the latter can be linearly fitted to the former. Therefore, the linear regression coeffcient is used to represent the regional coupling intensity (\(\alpha\)).
### Eddy Identification and Composite Analyses
To more convincingly demonstrate the atmospheric responses to SST perturbations, an eddy composite analysis is performed. The flow vector geometry-based eddy detection method is utilized to obtain the eddy centers and shapes ([PERSON] et al., 2010), which are derived through four constraints; the velocity vectors are derived from SST fields ([PERSON] et al., 2011). The averaged distance between the shape edge in each direction and the eddy center is taken as the eddy radius \(R\). The compositing domain is taken in a circular area of \(2R\) surrounding the eddy center. For each eddy, perturbation fields are interpolated onto a common grid which is scaled by \(R\) with a grid spacing of \(R/10\). Then the perturbation fields are averaged for cyclones (CEs) and anticyclones (AEs), respectively.
## 3 Results
### Characteristics of Mesoscale Air-Sea Coupling
A global view of the mesoscale SST and wind stress perturbations is illustrated in Figure 1 for the extracted fields from CESM-HR products and satellite observations by Loess high-pass filter. Pronounced mesoscale perturbations are seen in the extratropical oceans, including KE and ARC, where ocean mesoscale eddies are pronouncedly active in association with prominent oceanic fronts. The magnitude and spatial scales of SST perturbations and SST-induced wind stress perturbations for the CESM-HR (Figures 0(b) and 0(d)) are comparable to those for satellite observations (Figures 0(a) and 0(c)). It is evident that wind stress perturbations coincide well with SST perturbations, with correspondence of low (high) wind stress perturbations over cool (warm) SST perturbations both for the CESM-HR and satellite observations. Note that the perturbations are calculated from monthly averaged fields during boreal winter (November to February) of the model years for the CESM-HR and the actual years for observations, and some discrepancies exist in their spatial distributions. For example, the magnitude of the perturbations for the CESM-HR is larger than that observed.
Considering the close relationship between SST and wind stress perturbations at mesoscales, their temporal correlation is calculated and is shown in Figure 2. A significant positive correlation emerges globally, especially over areas with pronounced mesoscale perturbations mentioned above. The correlation is negative in the Indo-Pacific warm pool region and is mostly not significant because the related physics might be different from that in the KE and ARC regions. Particularly during the boreal summer, SST changes over this region are mainly generated by wind and cloudiness anomalies in the overlying atmosphere, so there exists a negative correlation between SST and wind stress ([PERSON] & [PERSON], 2013). [PERSON] et al. (2010) compared the simulations of CCSM with different resolutions and found that the correlation between SST and wind stress perturbations is negative in coarse coupled models but turns to be positive when the resolution increases. By comparing their results from the CCSM simulation with the CESM-HR, both of which have the same resolution, we found that the regions with positivecorrelation coefficients for the CESM-HR are more widely distributed, such as the northwestern Pacific and the eastern tropical Pacific, which is more consistent with what is observed. This suggests that the CESM-HR has a good representation for the positive correlation between mesoscale wind stress and SST perturbations.
To quantify the response of wind stress to mesoscale SST perturbations, coupling coefficients (\(\alpha\)) are calculated and shown in Figure 3. Although the overall magnitude of \(\alpha\) for the CESM-HR is significantly smaller than that observed, the spatial patterns of \(\alpha\) are similar, with high coupling strength in the KE and ARC regions. The regression analysis has been carried out by the method described above for KE (145\({}^{\circ}\)\(-\)180\({}^{\circ}\)E, 32\({}^{\circ}\)\(-\)45\({}^{\circ}\)N) and ARC (10\({}^{\circ}\)\(-\)180\({}^{\circ}\)E, 36\({}^{\circ}\)\(-\)50\({}^{\circ}\)S) regions, whose results are shown in Figures 3c and 3d. The slope represents the coupling strength; so, the steeper the slope, the stronger the coupling. Note that the coupling strength in the CESM-HR (red line) is weaker than that in the observations (blue line) by a factor of 1.28-1.92. In this manner, the coupling strength between the wind stress divergence (curl) perturbations and downward (crosswind) SST gradient perturbations for the CESM-HR is calculated and shown in Table 1, which is substantially smaller than that observed by a factor of 1.74-3.08. Although the coupling coefficients simulated by the CESM-HR are much smaller than those observed, especially in the response of the wind divergence and curl to the SST gradient perturbations, their positive correlations are well depicted. The strength of the wind stress response to mesoscale SST perturbations attains more than half of that observed, by nearly 80% especially in the ARC region. This indicates that the CESM-HR can capture the atmospheric responses to mesoscale SST perturbations to large extent.
Dividing the coupling coefficients for the CESM-HR by those for observations, we can obtain a ratio that represents the ability of the CESM-HR to capture the mesoscale coupling strength. A global view of the ratio is displayed in Figure 4a; values over most regions are less than 100%, indicating the coupling strength simulated by the CESM-HR is weaker than that observed. Compared with the climatological wind speed in Figure 4b, we find that the ratio tends to be large in the regions where there exists high background wind mostly. This is consistent with the similar study by [PERSON] et al. (2018) who found that there exists a positive correlation between coupling strength and wind speed among different models. So, it is speculated
Figure 1.— High-pass filtered sea surface temperature (SST, upper panels) and wind stress amplitude (low panels) for (a and c) AMSR-E and QuikScat satellite observations and for (b and d) CESM-HR. All calculations were carried out using monthly averaged data in boreal winter (November to February).
Figure 2.— Temporal correlation of high-pass filtered sea surface temperature with wind stress amplitude. The colored areas indicate where the correlation is significant at the 95% significant level. (a) AMSR-E and QuikScat satellite observations and (b) CESM-HR.
that the differences in coupling strength between different regions can be associated with the relative dominance of mechanisms for atmospheric response to mesoscale SST perturbations. As mentioned in the introduction, the PA and DMT mechanisms can be of different importance under different background wind.
To further understand this, \(\alpha\) and climatological wind speed at 10 m are calculated in the KE and ARC regions, which is shown in Figure 5. Seasonal variations are clearly revealed in Figure 5, with strong coupling strength in winter but weak in summer. This result is consistent with previous studies ([PERSON], 2012; [PERSON], 2005), indicating that the CESM-HR can well capture the seasonal variability of the mesoscale coupling strength. The strongest coupling strength emerges over the KE region during November to February, while it emerges over the ARC region during May to August, because the boreal winter is opposite to that of austr. In the following, winter is referred to the time when computations are performed in November to February over the KE region but in May to August over the ARC region, respectively. Likewise, summer is referred to the time when computations are performed in May to August over the KE region but in November to February over the ARC region, respectively. Given the disparity in coupling strength between the two seasons, the coupling strength in winter and summer is calculated separately for the two regions. As shown in Table 2, the value of \(\alpha\) over the KE region from CESM-HR is a factor of 1.22 smaller than that from observations in winter, while it is about 2 times smaller than the observed for the annual average (Table 1). However, the value of \(\alpha\) over the KE region is still only half of that observed during summer, while it accounts for observation by 71.43\(\%\) over the ARC region. Moreover, the value of \(\alpha\) even accounts for by 90\(\%\) of that observed over the ARC region in winter. It is understood that the atmospheric responses to mesoscale SST perturbations are affected by different mechanisms under different background wind conditions ([PERSON] et al., 2019). To find out whether the differences in coupling strength are related to the different response mechanisms, a further probe is taken to examine the atmospheric responses to mesoscale SST perturbations in the planetary boundary layer (PBL) during winter and summer, respectively.
\begin{table}
\begin{tabular}{l c c c c} \hline \hline & Region & CESM-HR & Satellite & Ratio \\ \hline \(\tau\) and SST & KE & 0.0053 & 0.0102 & 51.96\(\%\) \\ & ARC & 0.0112 & 0.0141 & 78.01\(\%\) \\ \(\
abla\)-\(\tau\) and downwind VSST & KE & 0.3933 & 1.1156 & 35.25\(\%\) \\ & ARC & 0.7969 & 1.5226 & 52.34\(\%\) \\ \(\
abla\times\tau\) and crosswind VSST & KE & 0.3128 & 0.9636 & 32.46\(\%\) \\ & ARC & 0.8057 & 1.4024 & 57.45\(\%\) \\ \hline \hline \end{tabular} _Note._ The regions used for the calculation are indicated by black boxes in Figure 3. The last column is for the ratio of coupling coefficients calculated from CESM-HR to those from satellite observations.
\end{table}
Table 1: Coupling Coefficients Between Nonsseasonal, High-Pass Filtered Wind Stress and SST (Top Rows), Divergence of Wind Stress and Downwind SST Gradient (Middle Rows), _Cut of Wind Stress and Crosswind SST Gradient (Bottom Rows)_
Figure 3: (left) The regression coefficients of high-pass filtered wind stress amplitude time series on high-pass filtered sea surface temperature (SST) for (a) AMSR-E and QuikScat satellite observations, (b) CESM-HR. The colored areas indicate where the correlation is significant at the 95\(\%\) significant level. The boxes indicate the areas where the right scatterplots are calculated. (right) Binned scatterplots with the slope of high-pass filtered wind stress against SST perturbations in (c) KE and (d) ARC. The blue lines indicate AMSR-E and QuikScat satellite observations, and the red lines indicate high-resolution CESM. The vertical bars and dot bars indicate the interquartile ranges and medians.
### Atmospheric Responses to Mesoscale SST Perturbations
The mesoscale perturbations of several atmospheric variables of interest are calculated, which represent responses to the mesoscale SST perturbations over the two regions in summer and winter, respectively. The high-pass filtered SST and SLP fields are shown in Figure 6. In the KE, regions with high (low) SLP perturbations are consistent well with those where cold (warm) SST perturbations are present during summer (Figure 6b), presenting a monopole response pattern. However, regions with high (low) SLP exhibit a spatial shift with those with cold (warm) SST perturbations in the KE during winter and in the ARC during both seasons (Figures 6a, 6c, and 6d). So, there exists a dipole pattern on the two sides over the warm (cold) SST perturbations, corresponding to positive and negative SLP perturbations, respectively.
To further analyze the spatial relationships between the corresponding patterns of SST and SLP perturbations, the high-pass filtered SST, SLP, and planetary boundary layer height (PBLH) along 40\({}^{\circ}\)N and 42\({}^{\circ}\)S are drawn in Figure 7. A close correspondence exists between zonal SST perturbations and PBLH, with higher PBLH being over warm SST perturbations. The PBLH is higher in winter than that in summer, especially over the KE region where PBLH can reach 900 m in winter, but only 350 m in summer (Figures 7a and 7b). The large PBLH in winter suggests that the vertical mixing is strong when the background wind is strong. Note that the PBLH in the ARC during summer is larger than that in the KE due to the higher environment wind speed as indicated in Figure 5. The consistent change holds for the relationship between SST and SLP perturbations, but with the SLP pattern being shifted spatially downwind of SST. The spatial lead-lag correlations between grids of SST and SLP perturbations are calculated to show their spatial relationship, in which the lags represent the longitudinal differences in the forcing-response positions between the SST and SLP perturbations (Figure 8). The significant spatial shift over the ARC region is 0.9\({}^{\circ}\) both in winter and summer. Over the KE region, the spatial shift is 0.7\({}^{\circ}\) in winter while it is 0.2\({}^{\circ}\) in summer. The spatial shift, such as the 0.9\({}^{\circ}\) over the ARC in winter, indicates that the SLP perturbations have a 0.9\({}^{\circ}\) zonal difference in their responses relative to the SST perturbations. Overall, there exists a pronounced zonal shift of about 1.0\({}^{\circ}\) in the ARC region for both seasons and in the KE region for winter, whereas there is a slight shift of 0.2\({}^{\circ}\) in the KE during summer. The 0.2\({}^{\circ}\) spatial shift reflects a spatial covarying in-phase relationship between SST and SLP perturbations, with the centers of the latter being nearly above those of the former. The distributions of SLP perturbations indicate a hydrostatic adjustment in the atmosphere to mesoscale SST perturbations due to vertical heat transport. The monopole response pattern
Figure 4: (a) The ratio of regression coefficients between high-pass filtered wind stress amplitude and sea surface temperature calculated from CESM-HR to those from satellite observations. (b) The climatological wind speed from the CESM-HR.
Figure 5: Time series of the area mean wind speed at 10 m (blue; scale on the left) and the coupling coefficients (red; scale on the right) in (a) KE and (b) ARC.
over the KE region during summer suggests that the atmospheric response to mesoscale SST perturbations is mainly controlled by the PA mechanism, whereas the dipole response pattern in other cases is dominantly controlled by the DMT mechanism.
The inference above is further confirmed by the responses of air temperature, vertical velocity, and vertical zonal wind shear in the PBL to mesoscale SST perturbations in the KE region (Figure 9) and the ARC region (Figure 10), respectively. In the KE region, the vertical velocity perturbations reach more than 600 hPa in winter and its speed is much larger than that in summer, indicating that the vertical motion is stronger in winter (Figures 9a and 9b). During winter, ascending motion and descending motion are seen on the two sides of the SST perturbations. During summer, however, the regions with upward (downward) vertical velocity lie directly above the centers of warm (cold) SST perturbations. The previous study has revealed that the vertical velocity corresponds well with the low-level wind convergence ([PERSON] et al., 2019). Therefore, the distribution of vertical wind speed at the bottom layer also reflects that of wind divergence. The dipole response patterns of vertical velocity and wind divergence indicate that the DMT mechanism exerts the dominant effect in winter, while the monopole response patterns indicate that the PA mechanism plays the dominant role in summer.
The perturbations of air temperature are positive over warm SST perturbations and negative over cool regions, which reflect the direct thermal effect of SST (Figures 9c and 9d). These response perturbations extend far above the PBL to 600 hPa in both seasons. Thermal perturbations exhibit a distinct tilt downwind with the height during summer, due to the relatively strong background wind condition and weak vertical mixing. The related horizontal advection of the air temperature can cause a slight shift of 0.2\({}^{\circ}\) for SLP perturbations relative to SST perturbations as shown above. Then, the vertical mixing intensity of momentum is further measured by vertical zonal wind shear which is calculated by the formula \(-\omega\)d/\(\phi\)p (Figures 9e and 9f). The vertical stability of the atmosphere is enhanced over the cold SST perturbation while it is decreased over warm SST. Thus the turbulence increases above the warm SST, with an increased downward momentum transport that reduces the vertical zonal wind shear. Similarly, over the regions with cold SST and weakening turbulence, the vertical wind shear is enhanced. The vertical turbulence is strong and extends up to 800 hPa in winter while it is weak and limited to the height below 980 hPa in summer. With relatively weak vertical mixing of momentum and low background wind magnitude, the atmosphere within the PBL can fully adjust to mesoscale SST perturbations during summer, forming the corresponding SLP pattern which then acts to adjust the surface wind. The fact that the adjustment of SLP is more distinct than that of atmospheric stability renders the PA mechanism to be a dominant factor in the atmospheric responses to mesoscale SST perturbations in summer. Otherwise, the more distinct adjustment of atmospheric stability renders the DMT mechanism to play a dominant role in winter. This confirms the preceding inferences that the dominant mechanisms are seasonally dependent in the KE region.
\begin{table}
\begin{tabular}{l l c c c} \hline \hline & Region & CESM-HR & Satellite & Ratio \\ \hline Winter & KE & 0.0087 & 0.0107 & 81.31\% \\ & ARC & 0.0135 & 0.0150 & 90.00\% \\ Summer & KE & 0.0033 & 0.0068 & 48.53\% \\ & ARC & 0.0095 & 0.0133 & 71.43\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coupling Coefficients Between Seasonal, High-Pass Filtered Wind Stress, and SST in Winter and Summer
Figure 6: High-pass filtered sea surface temperature (color; unit: \({}^{\circ}\)C) and sea level pressure (contours; interval 0.01 hPa and negative values dashed) in winter (left panels) and summer (right panels). Calculations are made using monthly averaged data in winter (November to February) and summer (May to August) over KE (a and b), and in winter (May to August) and summer (May to August) over ARC (c and d).
Figure 8: Spatial lead-lag correlation analyses between high-pass filtered sea surface temperature (SST) and sea level pressure along 40”N (a and b) and 42°S (c and d). The left column is for the winter season mean and the right column is for the summer season mean. Negative zonal grid point lags indicate that the SST perturbations are lagged to the west of sea level pressure perturbations. The black dots indicate the correlation is significant at the 95% significant level. The red dotted line refers to the lags of the most similarity between SST and sea level pressure perturbations.
Figure 7: High-pass filtered planetary boundary layer height (orange line), sea level pressure (black line), and sea surface temperature (blue line) along 40”N (a and b) and 42°S (c and d). The left column is for the winter season mean and the right column is for the summer season mean. Note that the vertical axis for plotting the distribution of sea-level pressure is inverted.
The same analyses are performed in the ARC region (Figure 10). It is evident that there is little difference in the atmospheric adjustment characteristics to mesoscale SST perturbations between winter and summer, which presents a consistent pattern. The vertical velocity response resides on both sides of the centers of mesoscale SST perturbations and reaches 600 hPa in both seasons. The corresponding air temperature perturbations extend to a height of 800 hPa in winter and a slightly lower height in summer, with a uniform magnitude. Thermal perturbations exhibit a slight tilt downward with the height both in summer and winter, which is due to the relatively weak intensity of vertical mixing compared with the strong vertical mixing over the KE during winter. This suggests that when a strong vertical mixing exists with high vertical velocity perturbations, air temperature is less affected by advection and the tilt of the temperature perturbations is not substantial. Besides, vertical wind shear response is strong in both seasons and extends to 850 hPa. In this region, the adjustment of atmospheric stability is more pronounced than that of SLP, indicating the dominant role played by the DMT mechanism.
To provide a much more rigorous examination of atmospheric response to eddy-induced mesoscale SST perturbations, an eddy composite analysis is performed in KE and ARC regions during both summer and winter, respectively. In the KE region, the composited averages of SST perturbations, corresponding vertical velocity (\(w\)) perturbations at 850 hPa, and SLP perturbations are shown in Figures 11 and 12. During winter, the centers of \(w\) and SLP perturbations both reside on one side of warm (cold) AEs (CEs) centers, presenting a dipole-like response pattern. While during summer, the centers \(w\) and SLP perturbations just reside above those of warm (cold) AEs (CEs), presenting a monopole response pattern. The same composite analysis for the ARC region is shown in Figures 13 and 14. A dipole response pattern is seen during both summer and winter. These results are
Figure 9.— Vertical cross-sections along 40\({}^{\circ}\)N for high-pass filtered vertical velocity (a and b; descent positive), high-pass filtered air temperature (c and d), and high-pass filtered zonal wind shear (e and f), and high-pass filtered sea surface temperature zonal profile along 40\({}^{\circ}\)N (g and h). The left column is for the winter season (November to February) mean and the right column is for the summer season (May to August) mean. The contour intervals are 0.001 pa/s in (a and b), 0.01\({}^{\circ}\)C in (c and d), and \(0.5\times 10^{-5}\) m/s/pa in (e and f).
consistent with the time-averaged analyses above. In the ARC region, the dipole patterns of SLP and vertical velocity responses during both seasons, together with the strong vertical mixing, suggest that the DMT mechanism plays a more important role. In the KE region, the same characteristics of atmospheric responses hold during winter, indicating the main contribution of the DMT mechanism to atmospheric adjustment. During summer, however, the monopole patterns of SLP and vertical velocity responses, together with the weak vertical wind shear, indicate that the PA mechanism plays a dominant role in the oceanic effect on the atmosphere. In both the mechanisms, vertical velocity responses exhibit a coherent relationship with SLP perturbations, having an upward motion above low-pressure and a downward motion above high-pressure, respectively. The PA mechanism mainly exerts an influence on the wind through the adjustment of pressure by vertical heat transport, whereas the DMT mechanism plays a dominant role in affecting vertical mixing of momentum.
## 4 Summary and Discussion
In this study, the CESM-HR products are used to investigate the atmospheric responses to mesoscale SST perturbations which are extracted by a high-pass filter. It is seen that the CESM-HR can well depict the positive correlations between mesoscale SST and wind stress, downwind SST gradient and wind stress divergence, and between crosswind SST gradient and wind stress curl, respectively. The coupling coefficients between mesoscale SST and wind stress perturbations are calculated to assess the strength of the atmospheric response to mesoscale SST perturbations. Then the coupling strength of mesoscale air-sea interaction is also calculated from satellite observations in a similar way and compared with that from the CESM-HR. In general, the coupling strength for the CESM-HR is weaker than that observed in most regions. With a focus on the KE and ARC regions, we demonstrate that the CESM-HR can adequately capture the seasonal variations in coupling strength which is
Figure 10: Same as in Figure 9, but at 42°S for the ARC area. In the southern hemisphere, the winter season mean is calculated during May to August and the summer season mean is during November to February.
Figure 11: Eddy composites in the KE region during winter over (a and b) all AEs and (c and d) all CEs. The left column is for the SLP (contour) and SST (color) perturbations, and the right column is for the w at 850 hPa (contour) and SST (color) perturbations. The \(x\) and \(y\) axes of the composite maps are the normalized distance by the eddy radius \(R\).
Figure 12: Same as in Figure 11, but for summer.
Figure 14: Same as in Figure 11, but for the ARC area during summer.
Figure 13: Same as in Figure 11, but for the ARC area during winter.
strong in winter and weak in summer. Further, the coupling strength in these two regions is separately calculated in summer and winter. In the KE region, the coupling strength only accounts for half of that observed in summer, while it accounts for 80% of that observed in winter. In the ARC region, the coupling strength accounts for more than 70% of that observed in both seasons, which is comparable to that observed. The calculations of coupling strength from the CESM-HR and observations are made during different periods, thus detailed comparisons between the two are probably unwarranted. Evidently, the CESM-HR has good capability to reproduce the mesoscale coupling characteristics to a large extent over the ARC and the KE regions, albeit with the simulated relatively weak coupling strength in the KE during summer.
As the coupling strength from CESM-HR is more comparable with that observed in regions with high background wind, we speculate that the atmospheric responses are affected by different mechanisms in different background conditions. Considering the good performance of the CESM-HR in the representation of extratropical atmospheric responses to mesoscale SST perturbations, its simulations are utilized to clarify the response mechanisms over the KE and ARC regions, respectively. In the KE region, the dipole response patterns of SLP and vertical velocity perturbations together with strong vertical mixing in winter, indicate that the DMT mechanism plays an important role, while the monopole response patterns together with weak vertical mixing indicate that the PA mechanism is a more dominant player during summer. In the ARC region, the DMT mechanism plays a dominant role in the SST effect on the atmosphere during both seasons. These results highlight that the mechanisms for atmospheric responses to mesoscale SST perturbations are regionally and seasonally dependent.
When the DMT mechanism exerts the dominant effect, we can also see signatures of the PA mechanism, as represented by the corresponding air temperature perturbations above mesoscale SST perturbations. Also, in the eddy composite analysis, the shift of \(w\) and SLP perturbations centers is not so significant, presenting a less pronounced dipole pattern. These reflect that both mechanisms can play a role in the atmospheric responses to mesoscale SST perturbations, but with different relative dominances. As for the PA mechanism, the pressure adjustment in PBL to mesoscale SST perturbations is realized through adequate vertical heat mixing, which requires sufficient adjustment time. With high background wind, the atmospheric vertical stability adjusts rapidly to mesoscale SST perturbations, and the adjustment of vertical momentum mixing is more obvious than that of SLP, indicating that the MDT mechanism plays a dominant role. The background wind intensity over the two regions is further analyzed in both seasons. In the KE region, the background wind amplitude is 6.8 m/s in summer and 11.4 m/s in winter; in the ARC region, it is 9.5 m/s in summer and 11.5 m/s in winter. In contrast, wind speed amplitude in the KE region during summer is at the weakest, indicating that the dominant role played by the PA mechanism is related to the low background wind condition. This situation is consistent with the previous studies by [PERSON] et al. (2015) and [PERSON] et al. (2019), who suggested that the DMT mechanism plays an important role with high background wind conditions while the PA mechanism is the dominant player with weak wind conditions. Also as shown by [PERSON] et al. (2016), the mesoscale coupling strength in the Kuroshio is stronger in winter than that in summer due to more unstable atmospheric conditions in winter, pointing to the importance of background conditions in the atmospheric responses. It is further believed that the vertical momentum mixing related to atmospheric stability plays an important role in regulating wind speed that responds to the ocean eddies; thus the DMT mechanism is the dominant one in both summer and winter. As demonstrated here using CESE-HR, our analyses point out the different response characteristics and relationships in the KE region, which highlights that the atmospheric responses are affected by different mechanisms between winter and summer.
The preceding discussion has indicated that the coupling strength over the KE region from the CESM-HR is only half of that observed during summer, with the PA mechanism dominating atmospheric response. In contrast, the coupling strength is comparable to that observed in the ARC region during both seasons and in the KE region during winter when the DMT mechanism exerts a dominant influence on the atmospheric responses. According to the previous studies, the weak coupling strength can be caused by the coarse vertical resolution in the atmospheric model and by the atmospheric model subgrid-scale parameterizations ([PERSON] et al., 2010; [PERSON] et al., 2009). The primary factor limiting the coupling strength in the KE region during summer can be largely ascribed to the inappropriate vertical mixing parameterization of heat, given the fact that the main characteristic of the PA mechanism is related to the atmospheric pressure adjustment by vertical heat mixing. This finding has important implications for improving the parameterizations of the CESM-HR for enhancing high resolution and long-time prediction capability. For further investigations to understand the role played by the parameterizationof vertical heat mixing, it would be necessary to carry out numerical experiments by using high-resolution atmospheric models.
## Data Availability Statement
AMSR data are produced by Remote Sensing Systems and were sponsored by the NASA AMSR-E Science Team and the NASA Earth Science MEASURES Program. Data are available at www.remss.com/missions/amsr.QuikScat data are produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team. Data are available at www.remss.com/missions/qscat. The high-resolution Community Earth System Model data are provided by International Laboratory for High-Resolution Earth System Prediction (HiESP) and Qingdao National Laboratory for Marine Science and Technology (QNLM) at [[http://hebsp.qnlm.ac/data/dataset/182v01c99](http://hebsp.qnlm.ac/data/dataset/182v01c99) ff6 acobf1d2 ddbc3d876a066609a]([http://hebsp.qnlm.ac/data/dataset/182v01c99](http://hebsp.qnlm.ac/data/dataset/182v01c99) ff6 acobf1d2 ddbc3d876a066609a).
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wiley/fb76f8fd_5768_44ab_a343_8a15552f8ae7.md | multi-scale response of runoff to climate fluctuation. And because of the temporal scaling change, an important climate factor influencing on runoff on a certain scale is likely to be a rather little effect on the other one. Therefore, experimental research on the temporal scaling behaviors of runoff and climate fluctuation and the former may help to how we strengthen the management and control of water resources in making research on applicable countermeasures of water against climate change.
As for the expiration, it is an important link of the water balance and energy balance, and is an important process for contacting the hydrology dynamic changes with the variations of vegetation ecology. Namely, the expiration process is the most important link in coupling effect of hydrologic cycle of land atmosphere system ([PERSON] and [PERSON], 1992; [PERSON] _et al._, 2015). In addition, it should be pointed out that river runoff has been evolving with the change of the earth and the world. And its changes are a complex process with multiple dynamic coupled factors such as nature events and human activities. Humid or arid weather conditions occurred in some previous period may impact now and future, accordingly neighboring observed values in the time series are correlated to some extent. Some traditional approaches such as power spectrum analysis, correlation analysis and statistical analysis are suitable for determining the correlation characteristics of stationary signals ([PERSON] _et al._, 2016; [PERSON] _et al._, 2016; [PERSON] _et al._, 2016; [PERSON] _et al._, 2016). However, the runoff time series usually is affected by noise or nonstationary signals, the mean, standard deviation, high order values and correlation function change as time goes on. In order to clearly understand the scaling behavior of inherent mechanism of runoff evolution and robustly analyze its long-range correlation, it is necessary to identify potential trend patterns caused by inherent long-range fluctuation in the data. The trend patterns caused by outside factors are usually smooth or oscillate slowly, hence if the potential trend patterns were not filtered before series analysis, the strong trend patterns remaining in the series would interfere with the long-range correlation analysis and as a result it would not be able to reveal the evolution process and laws of the runoff system in hydro-meteorological environments. The scaling index computation method proposed in the mechanism of deoxyribo nucleic acid, in other words, the detrended fluctuation analysis (DFA) method, can effectively solve this type of problem ([PERSON] _et al._, 2008). Furthermore, multi-scale response of the runoff system to multiple climatic factor can be effectively detected through the detrended cross-correlation analysis (DCCA) method, which is an extension of the DFA method, and very suitable for the power-law long-range correlation analysis of two nonstationary time series ([PERSON] and [PERSON], 2007). Moreover, the two methods have been widely applied in climatological-hydrological process. For instance, [PERSON] _et al._ (2007) applied the DFA method on the scaling properties of river runoff records of the Naab (26 years), the Regnitz (30 years) and the Vils (26 years); [PERSON] _et al._ (2006) studied the temporal correlations and multifractal properties of long river discharge records from 41 hydrological stations around the globe using the DFA, multifractal DFA and wavelet analysis methods. Through calculating the DCCA cross-correlation coefficient \(\rho\), [PERSON] _et al._ (2015) found the cross-correlation between diurnal temperature ranges and the the daily air pollution index (API) was persistent at time scales, more specifically, the correlation with the API presented persistent cross-correlation at smaller time scales, and antipersistent cross-correlation at larger time scales.
The Kaidu River, located in the southern slope of the Tianshan Mountains, was honored as the 'Water Tower of Central Asia' and 'Solid Reservoir'. Its runoff supply is mainly from glacial meltwater and precipitation in the Tianshan Mountains, so both temperature and precipitation changes have significant impacts on the runoff from the mountain pass. These changes in runoff from mountain pass not only affect the water supply of downstream industry and agriculture, but also relate to the regional social and economic sustainable development and ecological safety maintenance. In addition, the global warming mitigation in recent years, the complexities and effects of climate change in the Tianshan Mountains have increased the uncertainty of future regional climatological-hydrological process, and the inflow from origin area shows overall increase while the amount of water into the mainstream of the Tarin River decreases, bringing worries for the future security of water resources; therefore, the management and control of water resources shall be strengthened in making research on applicable countermeasures of water against climate change. Thus, a typical catchment of the headwater region of the Kaidu River was selected as the study target region in this article. In this article, the hydrological and meteorological daily data in the region from 1972 to 2011 were selected as the research object. The multi-scale characteristics of runoff and climate factors were quantitatively evaluated by the DFA method. Moreover, the hydrological responses to climate change were analyzed using the DCCA method. These analyses are scientifically significant for improving our understanding of the inherent mechanism of hydrological process of the Kaidu River, its watershed hydrology and practically significant for improving our water resources management.
## 2 Study area, data and methodology
### Study area
The Kaidu River is the largest river which flows into the Yanqi Basin, the river flows through Hejing, Yanqi and Bohu, originate from Eren Habirga covered by snow all the year around in the middle Tianshan Mountains, Xinjiang, North-west China, and is enclosed between latitudes \(42^{\circ}14^{\prime}\)-\(43^{\circ}21^{\prime}\)N and longitudes \(82^{\circ}58^{\prime}\)-\(86^{\circ}55^{\prime}\)E (Figure 1). The terrain of the Kaidu River Basin is higher in the north-west than in the south-east, so the whole basin is divided into three kinds of types. And the upstream segment length of about 200 km through Eren Wulu, Dayultuz Basin and the canyon, the total length of upper course is about 160 km. The gorge of the middle reaches of the Kaidu River, there is a great difference in the height of hypsography, and stream is rapid, and hydropower resource is mainly concentrated in this segment, where is recharge area of the meltwater from snow and ice, and is the main source of Kaidu River flood. It ends in the Bosten Lake which is located in Bohu County with segment length of the about 120 km ([PERSON] _et al._, 2012; [PERSON] _et al._, 2013; [PERSON] _et al._, 2015).
### Data
The Dashankou hydrological station and five meteorological stations located in the study area as shown in Figure 1. The records used in this article were obtained from a high-quality daily runoff and climate sequence (namely, temperature, precipitation, relative humidity and evaporation) data set spanning from 1 January 1972 to 31 December 2011, processed by the Xinjiang Tairn River Basin Management Bureau and National Meteorological Information Center, respectively. In this article, climate sequences are average daily temperature, average daily precipitation, average daily relative humidity and average daily evaporation from only five meteorological stations, respectively. To determine which data have higher quality, the data have been subjected to extremum, time consistency and other tests. In addition, to overcome the natural nonstationarity of the data due to season trends, we remove the annual cycle from the raw data \(e\) by computing the anomaly series \(e^{\prime}\!=\!e\!-\!<\!e\!>_{d}\) for five data series, where \(<>_{d}\) denotes the long-time average value for the given calendar day ([PERSON] _et al._, 2002). In addition, we apply the standard normal homogeneity test, Buishand and Pettit homogeneity test method to check these data ([PERSON], 1979; [PERSON], 1982; [PERSON], 1986). The stepwise multiple linear regression method was employed to revise the inhomogeneity of time series.
### Methodology
The DFA is an advanced method for determining the scaling behavior of data in the presence of possible trends without knowing their origin. For further detail computation, see [PERSON] _et al._ (1994). In the method, the most important parameter is the root mean square fluctuation \(F(n)\), which behaves as a power-law function of \(n\) then the data present scaling: \(F(n)\!\propto\!n^{\alpha}\). The DFA exponent (\(a\)) is defined as the slope of the regression line for all points [\(\log(n)\), \(\log[F(n)]\)]. Specifically, \(\alpha\!=\!0.5\) indicates the series corresponds to a random walk (namely white noise); \(0.5\!\leq\!\alpha\!\leq\!1\), indicates persistent long-range power-law correlations; \(0.5\!\leq\!\alpha\!\leq\!0.5\), power-law anticorrelations are present; when \(\alpha\!>\!1\), correlations exist but cease to be of the power-law form; \(\alpha\!=\!1.5\) indicates brown noise, the integration of white noise.
In analogy to the DFA, which was proposed by [PERSON] and [PERSON] (2007) for a single time series, DCCA was used for analyzing power-law long-range cross-correlations between different nonstationary time series ([PERSON] _et al._, 2016; [PERSON] and [PERSON], 2016). If the detrended fluctuation covariance function \(F(s)\) and scale \(s\) obey power-law cross-correlations in double logarithmic coordinates as shown \(F^{2}(s)\!\sim\!s^{4}\), where \(\lambda\) is the long-range cross-correlation scale index, there is long-range interrelation between two sequences ([PERSON], 2016). In particular, a value of \(\lambda\!>\!0.5\) indicates a positive long-range cross-correlation between two sequences. To be specific, if a sequence presents
Figure 1: Location of the headwater region of the Kaidu River and the distribution of meteorological and hydrological stations.
growth trend, the other sequence will also show growth trend. \(\lambda<0.5\) indicates that there is negative long-range cross-correlation. When \(\lambda=0.5\), there is nonlong-range cross-correlation between two sequences, that is, the change trend of a sequence exerts no effect on the change of another sequence ([PERSON] _et al._, 2016; [PERSON] and [PERSON], 2017).
## 3 Results and discussion
### The multi-scale characteristics of runoff and climate factors
Figure 2(a) shows the DFA analysis for the daily runoff. In this case, the plot exhibits curvature, showing obviously two different period regimes. \(n_{c}\) is the critical time scale where obvious dividing point occurs. And \(n_{c}\) is about 1 year, reflecting an influence of the annual cycle. For shorter time periods (\(n<n_{c}\)), the plot can be fitted to a straight line with a DFA exponent (\(\alpha_{1}\)) of 0.99 which exhibits high persistence. Over longer time periods, \(n>n_{c}\), a line with a decreased slop (\(\alpha_{2}\approx 0.18\)) that the high persistence changes to antipersistence when the temporal scale is larger than 1 year. Those results indicate that high persistence or long-term memory of the runoff comes up to about 1 year. For time spans greater than 1 year, the runoff displays a high antipersistent behavior. This result is not very clear, which perhaps relates to long-term hydrological processes, the length of the data and the internal dynamics of runoff. It needs more researches and longer series to make an interpretation.
Moreover, the DFA method is applied to the climate factor series of average daily temperature, evaporation, precipitation and relative humidity in the headwater region of Kaidu River from five meteorological stations. The results are shown in Figures 2(b)\(-\)(e), respectively. These data fit not one but two visible lines, which are similar to \(\log(F(n))\sim\log n\) in Figure 2(a) and all \(n_{c}\) are about 1 year. As to precipitation and relative humidity, for \(n<n_{c}\), \(\alpha_{1}\) are approximately 0.78 and 0.98, respectively; while for \(n>n_{c}\), \(\alpha_{1}\) are approximately 1.06 and 1.09, respectively. The relation \(\alpha_{2}>\alpha_{1}>0.5\) comes as a surprise. This shows that when the temporal scale is larger than 1 year, the persistence becomes higher. Hence, the trend dependence may persist more than 39 years for the two climate factors. Moreover, as to the temperature and evaporation time series, the result is similar to that of runoff.
### The response of the runoff to climate change
Figure 3 shows the DCCA analysis results of the Lrc-R-T, Lrc-R-P, Lrc-R-H and Lrc-R-E. There obviously are two or even three scaling regions in the double logarithm curve \(\log F^{2}(s)\sim\log s\) for the two types of four long-rang correlation within the same scaling regime. Namely, the Lrc-R-T, Lrc-R-P and Lrc-R-H show two scaling regimes with two different scale indexes (\(\lambda_{1}\) and \(\lambda_{2}\)) and with a critical time scale (\(s_{x}\)) of about 1 year with the same meaning as \(n_{c}\) in Section 3.1, however, the Lrc-R-E presents three scaling regime with three different scale indexes (\(\lambda_{1}\), \(\lambda_{2}\) and \(\lambda_{3}\)) and with two critical time scales (\(s_{c}\) and \(s_{c}\)\({}^{\prime}\)) of about 1 and 10 years. Linear fitting was respectively conducted on the
Figure 2: DFA of the daily runoff (a), average daily temperature (b), evaporation (c), precipitation (d) and relative humidity (e), respectively.
scaling regimes and their scale indexes \(\lambda\) are obtained. By taking \(s_{c}\) as the cut-off point, the time that \(s_{c}\) position also corresponds to is exactly 1 year, reflecting the multi-scale response of the runoff to climate change in temporal scaling.
In the first scaling range, namely, over shorter time periods (\(s\!<\!s_{c}\)), the scale indexes \(\lambda_{1}\) of the Lrc-R-T, Lrc-R-P, Lrc-R-H and Lrc-R-E are respectively 1.71, 1.78, 1.72 and 1.46, which all are \(>\)1, suggesting that there all are positive long-range correlation with nonpower law form. As an example of the Lrc-R-T, the runoff volume increased (decreased) with increasing (decreasing) temperature, both have stronger synchronicity.
In the second scaling range, namely, over longer time periods (\(s\!>\!s_{c}\)), the scale indexes \(\lambda_{2}\) of the Lrc-R-T, Lrc-R-H and Lrc-R-P are 1.34, 1.35 and 0.97, respectively. This indicates that when the temporal scale is larger than 1 year, their positive correlation becomes weaker. Hence, the trend dependence may persist more than 39 years for the three correlations. As to the Lrc-R-T and Lrc-R-H, the analysis results are both similar to their trend in the first scaling range. That is, the two correlations also display positive correlation with nonpaw-law form; while for the Lrc-R-P, \(\lambda_{2}\!=\!0.97\), indicates that the correlation of runoff and relative humidity manifested as 1/\(f\) noise behavior with power law at a large temporal scale. To point out, compared with the first scaling range, these positive correlations become weaker. As to the correlation of the Lrc-R-E is contrary to that of above the three correlations. While for \(s_{c}\!<\!s\!<\!s_{c}\!^{\prime}\), \(\lambda_{2}\!=\!0.21\). Namely, the runoff volume decreased (increased) with increasing (decreasing) evaporation in the corresponding time period scaling exponent is \(<\)0.5, this show that runoff and evaporation is power-law antilong-range correlation within the scaling regime of more than 1 year. The strong positive long-range correlation changes to antilong-range correlation as the time becomes longer. The runoff volume increased (decreased) with increasing (decreasing) temperature.
In the third scaling range, the correlation of runoff and evaporation is different from the former scaling range. The antilong-range correlation changes to strong positive long-range correlation as the time becomes much longer. That is to say, for \(s\!>\!s_{c}\!^{\prime}\), \(\lambda_{3}\!=\!0.91\), over much longer time periods, the result fully restored transcription to shorter time periods (\(s\!<\!s_{c}\)) once more in the corresponding time period. This suggests that runoff and evaporation still show strong positive long-range correlation when the temporal scale is \(>\)10 years.
The multi-scale response of runoff to the four climate factors reflects mutual influence, dependence and change characteristics of runoff and climate change. In the shorter temporal scaling (\(s\!<\!s_{c}\)), the Lrc-R-T, Lrc-R-P, Lrc-R-H and Lrc-R-E respectively all show stronger positive long-range correlation. With the long-range correlation between the Lrc-R-T as an
Figure 3: DCCA of the daily runoff and average daily temperature (a), precipitation (b), relative humidity (c) and evaporation (d), respectively.
example, if runoff volume of the Kaidu River within 1 year increases (decreases), the temperature also will increase (decrease). However, the degree of the four long-range correlations is different. The strongest correlation is the Lrc-R-P, next are the Lrc-R-T and Lrc-R-H, and Lrc-R-E is the last. When it is more than a year (\(s\!>\!s_{c}\)), there are two kinds of correlation. The Lrc-R-T, Lrc-R-P and Lrc-R-H continue to indicate positive long-range correlation. However, the Lrc-R-E turns into negative correlation over time, becomes longer (\(s_{c}\!<\!s\!<\!10\)a). For much longer time, (\(s\!>\!10\)a), the Lrc-R-T, Lrc-R-P and Lrc-R-H still keep stronger positive correlation, while the Lrc-R-E turn into positive correlation from negative correlation in longer time (\(s_{c}\!<\!s\!<\!10\)a).
The above research results show the long-range correlation characteristics and the temporal evolution properties of runoff between and temperature, precipitation, relative humidity and evaporation, respectively. The different response existed runoff to different climate factor in scale-invariant region. For instance, as all of you know, the effect of humidity on runoff mainly generated by precipitation and evaporation changes. The spatial pattern of the relative humidity change should also be a factor influencing the response of total runoff to the change in the mean relative humidity ([PERSON] _et al._, 2013). Therefore, a direct quantification research can make us more intuitively see the multi-scale response of runoff to relative humidity or the close relationship between them.
## 4 Conclusions
The DFA method is a modified root-mean-square analysis of random walk with advantages. It can avoid spurious detection of correlations that are artifacts of nonstationarity, which often affects the time series data. When the DFA is applied to the time series of hydro-climatic factors, which are runoff, temperature, precipitation, relative humidity and evaporation, respectively, the persistence or long-term memory of intrinsic time scales of hydro-climatic change can be extracted, it is helpful to determine their scaling behavior ([PERSON] _et al._, 2014). Moreover, the DCCA method is applied to detect the multi-scale response of runoff to four climate factors are studied, which are long-range correlation of runoff and temperature (Lrc-R-T), runoff and precipitation (Lrc-R-P), runoff and relative humidity (Lrc-R-H) and runoff and evaporation (Lrc-R-E), respectively. In this study, based on the hydrological and meteorological data in the Kaidu River Basin during 1972\(-\)2011, the multi-scale response of runoff to climate fluctuation were analyzed using the DFA and DCCA methods, the main findings are as follows:
1. The runoff variability and four climate factor fluctuation series follow two different power laws in shorter and longer temporal scaling regimes through the DFA method. In annual cycle, the DFA exponent \(\alpha_{1}\), indicating some similar dynamic characteristics of various hydro-climatic change's temporal evolution. Meantime, in longer temporal scaling regimes, \(\alpha_{2}\) may reveal the inherently different dynamic nature of various pollutant series. The persistence duration may persist about 1 year for runoff and temperature series, while over 39 years for precipitation, relative humidity and evaporation series.
2. The temporal scaling behaviors of runoff and four climate factor series all possess different power laws, which is a significant finding in the article. Those results further validated the dynamic characteristics of temporal evolution of runoff and temperature, runoff and precipitation, and runoff and relative humidity are just the same, and further illustrates multi-scale response of runoff to climate change has consistency. This shows the dynamic characteristics of temporal evolution of runoff and evaporation inter-decade difference, but it returns to positive long-range correlation.
Climatological-hydroological system is composed by several subsystems, and by the interaction of multi-spheres, multi-factors and multi-scale. One or more ways can be internal or external interaction among subsystems, which result in interaction structure of more complex form not only in the time, but also in the space. The results form complex-huge system with expression outside and nonlinear dissipative inside, and the whole shows its complexity. There are many influence factors of climatological-hydrological system, for example, human activities, geographical location, complex surface characteristics and so on. But these factors are not independent of each other, but there are nonlinear interactions at various spatial and temporal scales. These reasons result in which the time evolution process of climatological-hydrological process shows inherent nonlinear and external complex characteristics, which can be difficult to investigate scientifically and accurately their correlation and multiple-time-scale characteristics by way of statistics for stationary time series. DFA and DCCA methods are put forward in nonlinear scientific field, and they can more effectively investigate these features including multi-scale and response characteristics. The findings can help to develop effective warning strategies to reduce impacts on climatological-hydrological environment.
This work was supported by the Science and Technology Project of Jiangxi Provincial Department of Education (GJIJ161097), Open Research Fund of Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing (2016 WICSIP012), the 13 th Five-year Plan Project of Social Science of Jiangxi Province(16 BJ36), the Key Project of Jiangxi Provincial Department of Science and Technology (2016 IBBF60061), China Postdoctoral Science Foundation (2016M600515) and the National Key Technology R & D Program (2015 BAH50F00).
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wiley/fbc0acd5_d521_44cd_bceb_f0914da0959b.md | ## 2 Geological and Petrological Background
The Kamiukotan unit is a tectonic melange zone and distributed over 320 km from north to south within the Sorachi-Yezo terrane (Figure 2a; [PERSON] et al., 2018; [PERSON], 2010; [PERSON] et al., 2020). The Kamiukotan unit consists of ultramafic rocks and high-pressure and low-temperature metamorphic rocks. The Sorachi-Yezo terrane, including the Kamiukotan unit, consists of Late Jurassic to Early Cretaceous ophiolite, Horokanai ophiolite, to foreaven basin ([PERSON] et al., 2012; [PERSON] et [PERSON], 2002; [PERSON] & [PERSON], 1994). The Horokanai ophiolite consists of ultramafic rocks (Kamiukotan unit), gabrobs, amphibiboides, basalts (Sorachi Group), and sedimentary rocks (Figure 2b; [PERSON], 1985, 1987). The Sorachi Group overlies the Horokanai ophiolite and represents an early Cretaceous submarine volcanoes Sedimentary sequence ([PERSON] et al., 2002). The Yezo Group overlies the Sorachi Group and comprises terrigenous sediments deposited in a forearc basin at the late Cretaceous ([PERSON] et al., 2004).
Ultramafic rocks are widely exposed throughout the Kamiukotan unit and in the mantle section of the Horokanai ophiolite (Figure 2a). Ultramafic rocks consist of serpentinites, peridotides, and minor amounts of chromitiites and pyroxenites (e.g., [PERSON] et al., 1999; [PERSON] et al., 2002). Periodicites with wide ranges of olivine Fof# (=89-95), and spinel Cr# (=0.18-0.92) have been interpreted to reflect various degrees of melt extraction ([PERSON] et al., 1999; [PERSON] & [PERSON], 1997; [PERSON], 2002; [PERSON] & [PERSON], 2005, 2006; [PERSON] et al., 1999). Ultra-depleted peridotite bodies consisting mostly of harzburgite and dunite occur in the northern section (Shirikomadake, Takadomari, and Horokanai complex). These periodicites are characterized by high Cr# of spinel (0.60-0.91). In the southern section (Iwanaidake and Nukabira complex), depleted to fertile peridotides bodies are exposed: The Iwanaidake complex is dominated by depleted harzburgites with relatively high spinel Cr# (0.43-0.69) and the Nukabira complex is dominated by fertile herzolites with low spinel Cr# (0.13-0.34; [PERSON] et al., 1999). The Nukabira fertile herzolites with low spinel Cr# have LREE-depleted clinopyroxene compositions similar to those of residual abyssal periodtites ([PERSON] & [PERSON], 2006). These fertile herzolites were therefore interpreted as residues after melt extraction under dry conditions. On the other hand, depleted harzburgites were interpreted as residues that experienced hydrous melting based on hydrous mineral inclusions within spinel, spinel/spinel-diopside lamellae in olivine, and/or relict fluid inclusions in olivine ([PERSON], 1978; [PERSON] et al., 2021; [PERSON] & [PERSON], 1985; [PERSON] &[PERSON], 1987). [PERSON] (2002) suggested, based on geochemical modeling, that the depleted dunites in the Iwanaidake complex were formed by localized melting of the host harzburgite caused by an injection of hydrous melt.
## 3 Petrographic Characteristics of the Takadomari and the Horokanai (TH) Ultramafic Rocks
The Takadomari and Horokanai (TH) periodities mostly consist of harzburgite and decimeter-thick dunite layers and veins are observed in the harzburgite (Figure 2c). Orthopyroxene layers are rarely observed in the periodites, however, when present, sometimes show layering structures ([PERSON], 1985). Dunite consists of olivine (\(>\)99 vol.%), minor amounts of spinel (\(<\)1 vol %), and/or orthopyroxene, and is extensively serpentinized (Figure 3a and Figure S1 in Supporting Information S1). Spinel lamellae and relict fluid inclusions in olivine were reported in dunites (e.g., [PERSON] et al., 2021). Harzburgites are less serpentinized compared to dunite and consist of olivine (ave. 84 vol %), orthopyroxene (ave. 15 vol %), spinel (\(<\)1 vol %), and/or amphibole (Figure 3b and Figure S1 in Supporting Information S1). Rare grains of amphibole (edenite) are observed in harzburgites (Figure 3c). Spinel-hosted hydrous mineral inclusions, amphibole (hornblende) and Na-mica (aspidolite), were observed in dunite and harzburgite (Figure 3d).
Some inclusions within spinel are connected to interstitial serpentines by cracks. Those inclusions are mostly serpentine and phlogopite. Amphibole (template) rarely rimmed orthopyroxenes in the harzburgites. We focus on the igneous process of the ultra-depleted periodites in this study. Therefore, these alteration minerals, serpentine, and tremolite around orthopyroxene were excluded from the discussion.
## 4 Analytical Methods
Major element compositions of minerals in 32 peridotite samples were obtained using the JXA-8800 JEOL electron microprobe at Tokyo Institute of Technology and the compositions of mineral inclusions of spinel were obtained at the University of Tokyo. Analytical conditions were set at an accelerating voltage of 15 kV, 12 nA probe current, and a 3 \(\mu\)m beam spot for the analyses. Natural and synthetic mineral standards were used for calibration and JEOL software, using atomic-number-absorption-fluorescence (ZAF) corrections, was used for data reduction. In-house mineral standards, that is, olivine, chromian spinel, diopside from [PERSON] et al. (2021) were measured to monitor data quality.
Figure 1: Distribution of the clinopyroxene-free ultra-depleted peridotite bodies in the circum-Pacific belt ([PERSON] et al., 2022; [PERSON], [PERSON], & [PERSON], 2008; [PERSON], [PERSON], et al., 2016; [PERSON], [PERSON], & [PERSON], et al., 2016; [PERSON] et al., 2004; [PERSON] et al., 2010; [PERSON] & [PERSON], 2017; [PERSON] et al., 2009; [PERSON] et al., 2013; [PERSON] et al., 2020; [PERSON] et al., 1999; [PERSON] et al., 2010; [PERSON] et al., 2021). Compilation of mineral modes, major element and trace element compositions from these ultra-depleted periodites are available at Zenodo (additional Table S1 in Supporting Information S1) ([[https://doi.org/10.5281/zenodo.7263366](https://doi.org/10.5281/zenodo.7263366)]([https://doi.org/10.5281/zenodo.7263366](https://doi.org/10.5281/zenodo.7263366))). The topographic map is from [PERSON] and [PERSON] (2009).
Trace element compositions of olivine (eight samples), orthopyroxene (four samples), and amphibole (two samples) in periodtites were analyzed using a laser-ablation system (NewWave Research UP-213) coupled with an ICP-MS system (Agilent Technologies) at Kanazawa University. Each analysis was performed using a 90-100 um ablation spot size for orthopyroxene and olivine and a 60 um spot size for amphibole at a 6 Hz repetition rate. The analysis for amphibole inclusions in spinel was performed using a 15 um ablation spot at a 5-6 Hz repetition rate. Standard glass NIST 612 ([PERSON] et al., 2011) was used for calibration with \({}^{29}\)Si as an internal standard, based on the Si content obtained by electron probe microanalysis ([PERSON] et al., 1996; [PERSON] et al., 1997). Details of the analytical method and data quality control were reported by [PERSON] et al. (2005a, 2005b). Due to low trace element abundances in minerals, signals were carefully monitored for spikes or an increase in signals using elements such as B, Ba, Sr, Ba, Pb, Al, and Cr that indicate the presences of serpentine and/or spinel. Prabellation was conducted for a second at a 5-6 Hz repetition rate during every analysis to remove possible surface contamination.
Figure 2.— (a) Distribution of ultramafic rocks (black) in the Kamuikotan unit within the Sorachi-Yezo terrane, Hokkaiido in Japan. The red squared area indicates the studied area (the Takadomari and the Horokanai complex). (b) Geological map of the Takadomari and Horokanai complex modified after [PERSON] (1985). (c) A representative field photograph of the harzburgite and dunite layers.
## 5 Results: Mineral Chemistry
Olivine Fo# and Cr# of spinel in the TH periodities are high (92-95 and 0.60-0.91, respectively; Figure 4a). Olivine Fo# (93-95) and spinel Cr# (0.79-0.91) of dunites tend to be higher than those of harzburgites (Fo# = 92-93, Cr# = 0.60-0.88). Spinel TiO\({}_{2}\) contents are low (<0.1 wt %) for all TH periodities. Orthopyroxene from harzburgite is characterized by high Mg# (=Mg/(Mg + Fe) atomic ratio; 0.92-0.94) with low Al\({}_{2}\)O\({}_{3}\), CaO, and Cr\({}_{2}\)O\({}_{3}\) contents (0.7-1.6 wt %, 0.2-1.4 wt %, and 0.1-0.5 wt %, respectively; Figure 4b). Amphibole inclusions inclusions in spinel are mostly hornblende, and amphibie grains in harzburgite were identified as edenite ([PERSON] et al., 1997). Amphibole inclusions in the Takadomari dunite have slightly lower Na\({}_{2}\)O contents (1.1-2.0 wt %) compared to amphibole inclusions/grains (2.0-2.7 wt %) of the Horokanai harzburgite (Figure 4c).
We obtained abundances of six elements (Ca, Ti, Al, Y, Li, B) for olivine, four to five elements (Sr, Zr, Ti, Y, and/or Yb) for orthopyroxene, and seven elements (Ba, Nb, Ce, Sr, Zr, Ti, Y) for amphibole inclusions. Other elements such as rare earth elements (REE) were below the detection limit of analysis. Titanium in olivine (0.06-0.47 \(\mu\)g/g) of the TH periodities show positive correlations with Ca (22-113 \(\mu\)g/g), Y (0.0002-0.0024 \(\mu\)g/g). Li (0.9-1.2 \(\mu\)g/g), and B (0.3-2.6 \(\mu\)g/g). The abundances of these elements in olivine of dunites are slightly higher than those of harzburgites except for Al. Al in dunitic olivine (1.5-4.1 \(\mu\)g/g) tends to be lower than those in harzburgite olivine (2.8-6.2 \(\mu\)g/g; additional Table S2 in Supporting Information S1). The Ti, Y, and Yb abundances in orthopyroxene of the TH harzburgite are very low (0.8-2.4 \(\mu\)g/g, 0.002-0.01 \(\mu\)g/g, and 0.007 \(\mu\)g/, respectively) but Sr abundances in orthopyroxene are variable (0.01-0.2 \(\mu\)g/g; Figure 5a). Amphiboles are also low in REE. In particular, amphibole inclusions have lower abundances (example, Y: 0.2-0.3 \(\mu\)g/g) compared to amphibole grains (Y: 0.5-1.1 \(\mu\)g/g; Figure 5b).
Figure 3: Photomicrograph and back-scattered electron images of the Takadomari and Horokanai peridotites. (a) Takadomari dunite, which is strongly serpentinized. (b) Takadomari harzburgite, which is less serpentinized relative to dunite. Large grains of orthopyroxene (Opx) and olivine (O1) are observed. (c) Horokanai harzburgite, which rarely contains amphibole (Edenite) grains. (d) Spinel grain from the Horokanai harzburgite, which includes amphibole (Hornblende) and Na-mica (Aspidolite).
Primitive mantle-normalized patterns of orthopyroxenes of the TH harzburgites show Sr and Zr enrichments and Ti and Y depletions (Figure 5a) ([PERSON] & [PERSON], 1989). The trace element patterns and abundances are similar to orthopyroxenes from the circum-Pacific ultra-depleted harzburgites except for orthopyroxene from the Coast Range ultra-depleted harzburgites which have higher incompatible element concentrations ([PERSON] et al., 2010). Orthopyroxene trace element abundances from the ultra-depleted periodicites are much lower than those in orthopyroxene from abyssal fertile-depleted periodicites ([PERSON] et al., 2016; [PERSON] et al., 2009).
Figure 4.— Mineral major element chemistry. (a) Relationship between Cr# of spinel and olivine FoI. Olivine-spinel-mantle-array (OSMA: [PERSON], 1994). (b) Al,O\({}_{3}\) wt % versus Mg# of orthopyroxene. The black lines represent the composition of orthopyroxene obtained by the experimental study for the formation of ultra-depleted periodic under hydrous conditions and the numbers denote the temperature and pressure for the experiments ([PERSON] & [PERSON], 2000). The red line was obtained by least squares linear regressions using orthopyroxene from abyssal periodites, forecare periodicites, and ultra-depleted periodicites (regression parameters shown in the upper left-hand corner). Compositional data of olivine, spinel, and orthopyroxene from forecare periodicites and abyssal periodicites are from [PERSON] (1998), and [PERSON] et al. (2022). References of ultra-depleted periodicites are listed in Figure 1. (c) TiO\({}_{3}\) wt % versus Na\({}_{2}\)O wt % of amphibie grains and inclusions in spinel. The compositional data of amphibic inclusions of spinel in the Ira-Bonin-Mariana (IBM) forecast ductile are from [PERSON] et al. (2011).
Amphiboles of the TH peridotite show flat patterns with slightly enriched LREE and have similar characteristics to orthopyroxene which are enriched in Sr and/or Zr compared to Ti and Y abundance (Figure 5b). The TH amphiboles have lower abundances than amphiboles in dunite from Izu-Bonin-Mariana (IBM) forearc ([PERSON] et al., 2011).
Figure 5.— Primitive mantle-normalized trace element patterns of (a) orthopyroxene and (b) amphibole. (a) Gray and black dashed lines are the compositions of orthopyroxenes from abyssal Iberzolites and harzburtige ([PERSON] et al., 2016; [PERSON] et al., 2009). A blue colored field represents the orthopyroxene compositions from the New Caledonia ultra-depleted harzburties. References of the ultra-depleted peridotite are listed in Figure 1. (b) The light blue line is the composition of amphibole inclusion in spinel from IBM forearc dunite ([PERSON] et al., 2011). The primitive mantle value is from [PERSON] and [PERSON] (1989).
## 6 Discussion
### Geochemical Characteristics of the TH Harzburgites: The Most Depleted Peridotites on Earth?
The origin of the TH harzburgites was interpreted as residual peridotites based on olivine Fo# (92-93) and Cr# (0.60-0.88) of spinel ([PERSON] & [PERSON], 1997; [PERSON] et al., 1999), and the stratigraphic sequence of the ophiolite ([PERSON], 1987). Here, we reassess the geochemical characteristics of the TH harzburgites based on the mineral major and trace element compositions combined with fractional melting models ([PERSON], 1979).
Olivine Fo# and Cr# of spinel in the TH periodicites are similar to the circum-Pacific ultra-depleted harzburgites (Fo# = 91-93, Cr# = 0.48-0.95; Figure 4a). They plot within the chemical range expected for residual peridotite after partial melting of primitive mantle as indicated by the olivine-spinel-mantle-array (OSMA; [PERSON], 1994). High olivine Fo# and spinel Cr# contents in the periodicites suggest their origin as residues after high degrees of partial melting. The Mg# (0.92-0.94) of orthopyroxene of the TH harzburgite also display similar values to those from the circum-Pacific ultra-depleted peridotites (0.91-0.94) and tend to be higher than orthopyroxene in abyssal periodtites (0.89-0.93; [PERSON] et al., 2022; [PERSON], 2016) and forearc periodites (0.90-0.93; [PERSON] & [PERSON], 1998). The Al\({}_{2}\)O\({}_{3}\) contents of orthopyroxenes in residual abyssal and forearc periodites and the circum-Pacific ultra-depleted periodites show a negative correlation with Mg# (\(R^{2}\) = 0.63; Figure 4b). Amphibole grains and amphibole inclusions in spinel of the TH harzburgites have low TiO\({}_{2}\) and Na\({}_{2}\)O contents (<0.1 and 1.1-2.7 wt %, respectively) but are high in Cr\({}_{2}\)O\({}_{3}\) (>2.1 wt %) compared to those in depleted dunites from IBM forearc (Figure 4c; [PERSON] et al., 2011).
These depleted signatures and systematics are consistent with the low Ti, Y, and Yb abundances in orthopyroxene and olivine from the TH harzburgites. The abundances are similar to those in olivine and orthopyroxene from the circum-Pacific ultra-depleted periodites except for the Coast Range periodites and lower than fertile-depleted residual periodites (Figure 6; [PERSON] et al., 2016; [PERSON] et al., 2020; [PERSON] et al., 2009). We, therefore, conclude that the TH harzburgites are among the most depleted residual periodites on Earth, which collectively, are found predominantly in SSZ ophiolites from the Western Pacific region (Figure 1).
We conducted a fractional melting model from a depleted-MORB mantle (DMM; Workman & Hart, 2005). Fractional melting is a process in which melt is formed in equilibrium with the residue and is instantaneously removed from the system during partial melting ([PERSON], 1979). We used partition coefficients from [PERSON] et al. (2000), [PERSON] et al. (2002), [PERSON] et al. (2003), and [PERSON] (2001) and melting modes simplified from Kinzler and Grove (1992) and Parman & Grove (2004) (0.05 SpI + 0.45 Opx + 0.75 Cpx \(\rightarrow\) 0.25 OI + 1M elt for climopyroxene-bearing assemblage and 0.20I + 0.003 Spl + 0.797 Opx \(\rightarrow\) 1M elt for climopyroxene-free assemblage). We also tested the effect of fractional melting under pressure-temperature conditions of the garnet peridotite stability field following [PERSON] et al. (2018). We used melting modes simplified from [PERSON] et al. (2002), and the mineral modes of the garnet peridotite were converted to that of spinel peridotite using the following reaction: 3 Opx + 1 Cpx + 1 SpI = 4 Grt + 1 OI ([PERSON] et al., 1996). Details of melting mode, partition coefficients, and modeling results are provided in Table S3 in Supporting Information S1.
The fractional melting model shows that Ti and Y abundances in residual olivine and orthopyroxene decrease below those of DMM with increasing degree of melting (Figure 6). The melting trends are consistent with orthopyroxene compositions in the TH harzburgites and the circum-Pacific ultra-depleted periodites. The fractional melting in the stability field of garnet peridotite (0%-10%) shows a decrease in Ti abundances but a slight increase in Y abundances with increasing degree of melting. Therefore, when periodities undergo melting in the stability field of garnet peridotite prior to melting in the stability field of spinel peridotite, it requires higher melting degrees to deplete the Y in residues compared to the ones that experienced melting directly from DMM in the spinel stability field. Our fractional melting model suggests that the TH harzburgite and the circum-Pacific ultra-depleted periodites are residues that went through at least 25% of melting from DMM in the spinel stability field.
Estimating the degree of partial melting shows how the fractional melting model most efficiently depletes incompatible elements in residues because fractional melting is a process that occurs if the melts had zero viscosity or the mantle had infinite permeability. Melt fractions retained in the source, which result in less fractionation of incompatible elements in the source, should be considered. Therefore, it should be noted that the fractional melting model estimates the minimum degree of partial melting from the depletion of incompatible elements in the residual phases. In addition, estimating the exact degree is not easy because fractional melting models areparticularly sensitive to minor differences in partition coefficients and melting modes for ultra-depleted periodites, as noted by [PERSON] et al. (2016). In any case, we emphasize that high degrees (>25%) of melting are necessary as a minimum requirement for the formation of the ultra-depleted harzburgites.
Melting Processes for the Formation of the TH Harzburgites: Influx Melting Obtained From the Open-System Melting Model
The Ti and Y abundances in these periodicts show ultra-depleted signatures constrained by the fractional melting model (Figure 6). However, the enrichment of Sr and Zr compared to Y and Ti in orthopyroxene of the TH ultra-depleted periodites cannot be reproduced by the fractional melting model, that is, melting and melt extraction solely from the DMM source in both spinel and garnet stability fields (Figure 7a). This decoupling indicates that these periodicts underwent influx melting, in which fluid/melt flux are added into the system during partial melting and melt extraction (e.g., [PERSON] et al., 2014; [PERSON] et al., 2018; [PERSON] et al., 2021).
We have conducted open-system melting model of [PERSON] (2001) and Ozawa and Shimizu (1995) to constrain the melting conditions and account for the enriched Sr and Zr and depleted Ti and Y in orthopyroxene from the ultra-depleted periodicts. This open-system melting model formulated the input and output of elements during melting processes, which include flux (fluids/melts) input to the system as well as partial melting and melt extraction (an Equation 33 for trace elements of Ozawa, 2001). Therefore, this model allows us to test more complex melting processes, such as fluid/melt influx melting and incongruent melting. Using this model, we have modeled influx melting and investigated starting source and flux compositions and other important parameters, which are
Figure 6: Y and Ti abundances in (a) olivine and (b) orthopyroxene. Blue solid lines were obtained by the spinel stability field fractional melting model and the numbers represent melting degrees. Gray points were obtained by the garnet stability field fractional melting model (0%–10%). Light green plots are the compositions of olivine in relatively depleted periodites from Nahlin ophiolite, Canada ([PERSON] et al., 2020). The open square and triangle are the compositions of olivine in abyssal D’Errico and Marshurgite ([PERSON] et al., 2016; [PERSON] et al., 2009). Light red circles are the compositions of olivine in replicative duntes at the crust-mantle transition zone from Lanzo massif, Italy ([PERSON] et al., 2014, 2017). References of the ultra-depleted periodites are listed in Figure 1.
Figure 7:
critical melt fraction and influx rate. Critical melt fraction (\(\alpha\)) is a parameter, at which the system becomes open to melt separation and dimensionless influx rate (\(\beta\)) is a material influx rate relative to melting rate, which is the amount of material that flows into the system normalized by the amount of the source material. We used a melting mode under hydrous conditions (0.025 pl + 0.52 Opx + 0.56 Cpx \(\rightarrow\) 0.1 OI + 1 Melt) for the clinopyroxene-bearing assemblage from [PERSON] et al. (2000) (Figure 7a: open-system melting after 0%-17.3% of fractional melting). Except for the melting mode in the models in Figure 7a, partition coefficients and melting modes used in these models are the same as those for the fractional melting model. The slab-fluid composition (Sr: 150 pg/g, Zr: 16 ug/g, Y and Ti: 0 ug/g) was also taken from [PERSON] et al. (2000) as flux compositions. Details and results of models and parameters are provided in Table S3 in Supporting Information S1.
Our models for influx melting with starting compositions formed after 17.3% (clinopyroxene-out) of fractional melting from DMM reproduced the enrichments of Sr and Zr and the depletions of Ti and Y in orthopyroxene, suggesting that ultra-depleted harzburgites experienced influx melting (Figure 7a). We conducted open-system melting model, that is, influx melting with a low influx rate (\(\beta\) = 0.05) and a low critical melt fraction (\(\alpha\) = 0.01). It is interesting to note that the similar orthopyroxene compositions are also observed in other circum-Pacific ultra-depleted harzburgites. This indicates that influx melting is a common process among the circum-Pacific ultra-depleted peridotites, or at least in the mantle portion of many SSZ ophiolites.
Next, we investigated the influence of different parameters. We vary Zr concentration in flux, which is fluid in our model (Figure 7b), influx rate (Figure 7c), critical melt fraction (Figure 7d), Ti and Y concentrations in fluid (Figure 7e), and melting mode for testing multistages of melting (Figure 7a). Summary of the models are listed in Table 1.
Higher incompatible elements concentrations in fluid, as well as higher influx rate and critical melt fraction result in less fractionation of these elements in residual orthopyroxene. The compositional differences in fluid (Sr: 150-15,000 ug/g and Zr: 0.1-1,000 ug/g) cause the compositional difference in residual orthopyroxene in the logarithmic scale (Figure 7b and Figure S2 in Supporting Information S1). The difference in influx rate (\(\beta\):
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline & \multicolumn{6}{c}{Parameters of open-system melting models} \\ \cline{2-9} & & \multicolumn{3}{c}{Fluid (flux) composition} & \multicolumn{3}{c}{Crtical} \\ & & & & & & & & melt \\ Figure & Starting material & Sr (ug/g) & Zr (ug/g) & Ti (ug/g) & Y (ug/g) & rate & fraction \\ \hline Figure 7a & \(\bullet\)DMM & & & & & & & \\ & \(\bullet\)Residues after 5\%, 10\%, 15\%, 17.3\% of fractional melting from DMM & 150 & 16 & 0 & 0 & 0.05 & 0.01 \\ Figure 7b & \(\bullet\)Residues after 17.3\% of fractional melting from DMM & 150 & 0.1–1,000 & 0 & 0 & 0.05 & 0.01 \\ Figure 7c & \(\bullet\)Residues after 17.3\% of fractional melting from DMM & 150 & 16 & 0 & 0 & 0.01–1 & 0.01 \\ Figure 7d & \(\bullet\)Residues after 17.3\% of fractional melting from DMM & 150 & 16 & 0 & 0 & 0.05 & 0.001–1 & 0.05 \\ Figure 7e & \(\bullet\)Residues after 17.3\% of fractional melting from DMM & 150 & 16 & 0–1,000 & 0–1,000 & 0.05 & 0.01 \\ Figure S2 in Supporting Information S1 & \(\bullet\)Residues after 17.3\% of fractional melting from DMM & 150–15,000 & 0 & 0 & 0 & 0.05 & 0.01 \\ \hline \hline \end{tabular} _Note. Details of melting mode, partition coefficients and modeled olivine and orthopyroxene compositions are provided in Table S3 in Supporting Information S1._
\end{table}
Table 1 Summary of Melting Conditions and Parameters Used for Geochemical Models
Figure 7.— (a–d) Zr and Ti and (e) Y and Ti abundances in orthopyroxene. Orthopyroxene compositions from abyssal perioditites are from [PERSON] et al. (2016). The blue solid line is the compositional trend reproduced by the spinel stability field fraction model. (a) Open-system melting model, that is, influx melting, with starting compositions formed after 5%–17.3% degrees of fractional melting from DMM (Workman & Hart, 2005) and from DMM. Gray points were obtained by the garnet stability field fractional melting model (0%–10%). (b) Varying Zr abundance in fluid (\(\pi\)flux) ranging from 0.1 to 1.000 ug/g, (c) varying influx rates ranging from 0.01 to 1.(d) varying melt fraction ranging from 0.01 to 0.05 and (e) varying Y and Ti abundances in fluid ranging from 0 to 1.000 ug/g, respectively. References of the ultra-depleted peridotites are listed in Figure 1.
0.01-1) also causes compositional changes in orthopyroxene (Figure 7c). The first few degrees of influx melting (total degrees from DMM: 17.3%-30%) show the largest compositional change in Sr and Zr abundances but the abundances converge in high melting degrees when fluid compositions and influx rates are constant. On the other hand, the difference in critical melt fraction (\(\alpha\) = 0.001-0.05) does not affect Zr and Sr abundances in residual orthopyroxene (Figure 7d).
The Ti and Y abundances in residual orthopyroxene are less sensitive to fluid influx compared to Sr and Zr in our model. Compositional changes of Y and Ti abundances in residual orthopyroxene at the 40% degree of partial melting extent from DMM are not well documented when Y and Ti abundances in fluids are less than 10\({}^{-3}\) times primitive mantle with an influx rate \(\beta\) = 0.05 (Y: 0.01 \(\mu\)g/g, Ti: 10 \(\mu\)g/g in fluid; Figure 7e). On the other hand, Ti and Y abundances in residual orthopyroxene are more sensitive to critical melt fraction, which is retained in the system until melt is connected and removed from the source. High critical melt fractions result in less fractionation of Ti and Y depletions in orthopyroxene (Figure 7d).
Our parametric study indicates that fluid compositions and their influx rates exert primary control on Zr and Sr (and LREE) concentrations in residual orthopyroxene. Melting degrees and critical melt fractions exert primary control on Ti and Y concentrations in the residual orthopyroxene. High melting degrees with a low melt fraction are, therefore, key to depleting Ti, Y (and HREE) in the residue. The models show that the orthopyroxene compositions of the ultra-depleted periodities can be reproduced when the fluid contains high Zr and Sr but low Y and Ti abundances with a low influx rate and a low critical melt fraction (10-100 \(\mu\)g/g for Zr and 150-1,500 \(\mu\)g/g for Sr and \(<\)10 \(\mu\)g/g for Y and \(<\)1,000 \(\mu\)g/g for Ti, \(\beta\) = 0.05 and \(\alpha\) = 0.01). The fluid composition in our model shares the characteristics of slab fluids with low Ti, Y, and HREE and high Sr, Zr, and LREE ([PERSON] et al., 2000; [PERSON] et al., 2013). Therefore, we conclude that these ultra-depleted harzburgites were generated by high degrees (\(>\)30%) of slab-fluid influx melting.
Additionally, we tested the contribution of degrees of melt extraction before undergoing influx melting (two-stage melting model: residue after simple partial melting and extraction followed by influx melting expected in the subduction zone; e.g., [PERSON] et al., 2020). We compared influx melting with starting compositions formed after 5%, 10%, 15%, and 17.3% of fractional melting from DMM and influx melting from DMM in the spinel stability field (Figure 7a). The models show that Zr and Sr concentrations in residual orthopyroxene converge at high degrees of melting (\(>\)30%) when fluid compositions and influx rates are constant. All models in Figure 7a can reproduce the orthopyroxene compositions. It is difficult to determine whether the ultra-depleted periodities experienced partial melting prior to influx melting only based on the modeling results. However, the residual orthopyroxene has slightly higher Ti and Y abundances when the starting material is more fertile prior to influx melting (Figure 7a). Higher trace element concentrations in fluids, influx rates and melt fractions also result in less depletion of the HREE in residual orthopyroxene (Figures 7b-7e). Therefore, it is more likely that the relatively depleted composition of source periodities prior to influx melting is a key factor in the formation of ultra-depleted harzburgites.
The TH amphibes have lower TiO\({}_{\gamma}\) Na\({}_{2}\)O, and HREE abundances with higher Cr\({}_{2}\)O\({}_{3}\) contents compared to amphibes of IBM forearc depleted dunite (Figures 4c and 5b; [PERSON] et al., 2011). This is consistent with the ultra-depleted signatures shown in the coexisting mineral compositions. In addition, the TH amphibes share the characteristics of the enriched Sr and Zr and depleted Ti and Y with orthopyroxene. The orthopyroxene compositions were only reproduced by influx melting as discussed above. Therefore, the high degree of influx melting possibly explains the presence of amphibes and their compositions in the TH peridotites.
### Origin of Ultra-Depleted Dunites: Melt-Depleted Peridotite Interaction
The Ti and Ca (and Y) abundances in olivine decrease in abundance from abyssal Iberzolite, moderately depleted periodites, and ultra-depleted harzburgites ([PERSON] et al., 2022; [PERSON] et al., 2020; [PERSON] et al., 2009; [PERSON] et al., 2020). This is consistent with the fractional melting model (Figure 6a). However, these abundances in olivine are slightly higher in the TH dunites than those in the TH harzburgites although TH dunites tend to have higher olivine Fofi and Cr# of spinel. The TH dunites occur as layers or veins in host harzburgites (Figure 2c; [PERSON] et al., 1999). This suggests that the ultra-depleted dunites were produced by a process involving incongruent melting of orthopyroxene in the host harzburgite triggered by the introduction of hydrous melts ([PERSON], 2002).
Dunite layers in the mantle sections containing slightly higher Ti in olivine compared to host harzburgites were also observed in ultra-depleted and depleted periodites bodies and their origins were interpreted as a product of melt-rock interaction ([PERSON] et al., 2022; [PERSON] et al., 2020). Olivines from the dunite layers in the mantle sections have much lower Ti, Ca, and Y abundances than those in olivine from replacive dunites at the crust-mantle transition zone (Figure 6a). These replacive dunites at the crust-mantle transition zone were produced by melt-rock interaction with high melt/rock ratios and melt composition was suggested to be MORB ([PERSON] et al., 1995; [PERSON] et al., 2014, 2017). Although both dunites are products of melt-rock interaction, their compositional differences indicate that olivine trace element compositions in these dunites are controlled by the melt/rock ratio and by the compositions of the host residual periodites and the melts. We, therefore, conclude that the TH ultra-depleted duties are products of melt-rock interaction at low melt/rock ratios, and both rock, that is, host periodites and melts were depleted in incompatible elements.
### Petrogenesis of Ultra-Depleted Peridotite and Their Link to Boninites
Boninites are characterized by enrichments in Sr and Zr and depletions in Ti and Y ([PERSON] et al., 2015, Figure 8a). The instantaneous fractional melts, which are in equilibrium with ultra-depleted residual harzburgites, reproduced by our open-system melting model, that is, influx melting, show similar characteristics to boninite. However, trace elements abundances in the melts are lower than those in boninite (Figure 8a). The models show that these abundances in the instantaneous fractional melts reproduced by influx melting from DMM are higher at low melting degrees; however, these abundances in the instantaneous fractional melts are lower at higher melting degrees compared to those in boninites (Figure 8a). Therefore, when our influx melting model reproduces the ultra-depleted orthopyroxene compositions, the instantaneous fractional melts are more depleted than boninites. In our model, the enriched Sr and Zr in boninites were only reproduced when these abundances in fluids are very high (Sr: \(>\)1,500 \(\mu\)g/g, Zr: \(>\)1,000 \(\mu\)g/g) or high influx rate (\(\beta>0.5\)). These indicate that boninites are rather accumulated melt and/or fractionated melt from the instantaneous fractional melt. Another possible explanation is that the instantaneous fractional melts experienced inputs of slab fluids/melts in a later process before erupting as boninites.
We also calculated melts in equilibrium with amphibies using the partition coefficients from [PERSON] (2001) and [PERSON] et al. (2017). Although the formation of spinel-hosted inclusions is controversial, it allows us to estimate the melt compositions involved in the system (e.g., [PERSON] et al., 2022; [PERSON] et al., 2021; [PERSON] et al., 2014). The calculated melts equilibrated with the TH amphibes are more depleted compared to the melt equilibrated with amphibole from the IBM foreacre dunite ([PERSON] et al., 2011). The calculated melts characterized by low
Figure 8: (a) Primitive mantle-normalized patterns of the instantaneous fractional melts estimated from the open-system melting model, that is, influx melting. The purple plots are the instantaneous fractional melt compositions generated by influx melting from the DMM source which did not experience fractional melting before the influx melting (the purple-colored model in Figure 7a). Blue plots are instantaneous fractional melts compositions generated by 17.3% degree of fractional melting from DMM. Light blue plots are the instantaneous fractional melts generated by influx melting (20%–35%: the total melting degrees from DMM) with starting compositions formed after 17.3% of fractional melting from DMM (the light blue colored model in Figure 7a). (b) the calculated melts in equilibrium with amphibole grains and inclusions using the amphibole-melt partition coefficients from [PERSON] (2001) and [PERSON] et al. (2017). The black dotted and gray solid lines are the representative patterns of low-Si boninite and high-Si boninite, respectively ([PERSON] et al., 2015). The blue line is the pattern of amphibole inclusion in spinel from the IBM foreacre dunite ([PERSON] et al., 2011). The primitive mantle value is from [PERSON] and [PERSON] (1989).
HREE abundance and positive Sr anomalies are similar to those of high-Si boninite which is one of the most high-field strength elements and heavy REE depleted melts (Figure 8b; [PERSON] et al., 2015, 2018). Findings from the mineral chemistry and modeling suggest that the TH and the circum-Pacific clinopyroxene-free ultra-depleted peridotites are residues after extraction of high-Si boninite melts.
Low-pressure and high-temperature conditions were constrained for the formation of high-Si boninite (0.8 GPa, 1,430\({}^{\circ}\)C; [PERSON] et al., 2015). High Mg# and low Al\({}_{\textrm{O}}\)\({}_{\textrm{s}}\) contents in orthopyroxene of the TH harzburgite also suggest high-temperature conditions. Orthopyroxene compositions from the ultra-depleted peridotites are consistent with those from depleted harzburgites at high temperatures (>1,350\({}^{\circ}\)C) and under hydrous conditions constrained by the experimental study (Figure 4b; [PERSON], 2000; [PERSON], 2004). Therefore, high temperature (>1,350\({}^{\circ}\)C) and continuous supply of fluids are key to the formation of ultra-depleted peridotites and boninitic magma.
The TH ultra-depleted peridotite body occurs in the northern part of the Kamuikotan unit. In contrast, the fertile-depleted peridotite bodies characterized by middle to low spinel Cr# occur in the southern part, that is, the Nukabira and Iwanaidake complex (Figure 2a). The Nukabira peridotite body consisting mostly of fertile herzorolite is interpreted as residual peridoite after some extent of melt extraction under dry conditions ([PERSON] & [PERSON], 2006). These distributions and geochemical features of the TH ultra-depleted peridotites and fertile peridotites can be explained as mantle materials during subduction initiation ([PERSON] et al., 2011). Fertile herzolites from the southern part might be residues after extraction of tholeitic melts (forearc basalt: FAB after [PERSON] et al. (2010)) as a result of decompression melting with a low influx in the earliest stage of subduction (Stage 1 in Figure 9a). Although no boninite has been reported from the studied area, we speculate that the TH ultra-depleted harzburgites are residues after extraction of high-Si boninite melts as a result of slab-fluid influx melting (Stage 2 in Figure 9a). Dunite layers are observed within both ultra-depleted harzburgites and fertile herzolites. These dunites are products of melt-rock interactions (Figure 9b). Compositional differences and mineral assemblage
Figure 9.— (a) Schematic illustrations for the evolution of subduction zone modified from [PERSON] et al. (2011). (b) Schematic illustrations for the formation of the ultra-depleted peridotites in the Kamuikotan unit modified from [PERSON] et al. (1999). Fertile herzolites from the Nukabira complex can be regarded as residues of decompression melting in stage 1. This melting is thought to be caused by the extension associated with slab sinking and counterflow of asthenospheric mantle. On the other hand, ultra-depleted peridotites from the Takadomari and Horokanai complex can be regarded as residues of decompression and slab-fluid influx melting which formed boninites. Then, the residual herzolites and harzburgites reacted with melts respectively. Interactions between melts and residues produced dunites and wall peridotites (harzburgites) in the Nukabira complex. The reaction formed ultra-depleted dunites and orthopyroxeneites in the Takadomari and Horokanai complex.
of dunites, and associated lithology reflects the differences in the compositions of melts and host peridotites ([PERSON] et al., 1999).
The ultra-depleted to fertile peridotites bodies are distributed in the Kamuikotan unit more than 100 km scale. Other circum-Pacific ultra-depleted peridotites bodies also occur with depleted fertile peridotites bodies at a similar scale (Figure 1; [PERSON] et al., 2022; [PERSON], [PERSON], & [PERSON], 2008; [PERSON], [PERSON], & [PERSON], 2008; [PERSON] et al., 2020; [PERSON] et al., 2022). This commonality suggests that the distribution of ultra-depleted to fertile peridotite bodies in the mantle was probably >100 km scale.
## 7 Conclusions
Peridotites from the Takadomari and the Horokanai (TH) complex have high olivine Foff (92-95), Crft (0.60-0.91) of spinel, and Mg# (0.92-0.94) of orthopyroxene. On the other hand, these peridotites have low Al\({}_{2}\)O\({}_{3}\) contents (0.7-1.6 wt %) in orthopyroxene and low Ti and Y abundances in olivine and orthopyroxene. These geochemical signatures suggest that the harzburgites are residues after large extents of melt extraction and among the most depleted peridotites on Earth.
The Takadomari and Horokanai periodites include rare amphibole and/or amphibole inclusions in spinel. Orthopyroxene and amphibole in the ultra-depleted harzburgites show enriched Zr and Sr (LREE) and depleted Ti and Y (HREE) abundances. This decoupling in orthopyroxene was reproduced by the open-system melting model, that is, influx melting and it suggests that ultra-depleted peridotites formed after high degrees (>30%) of slab-fluid influx melting with a low influx rate and critical melt fraction.
The Ti abundance in olivine is slightly higher in the dunite layers or veins than those in ultra-depleted harzburgites but much lower than dunites associated with fertile-depleted peridotites. These suggest that the ultra-depleted dunites are a product of depleted melt-depleted peridotite interaction.
The instantaneous fractional melts equilibrated to ultra-depleted residues produced by the open-system melting model, that is, influx melting and melts equilibrated to amphiboles share the characteristic of enriched Zr and Sr and depleted Ti and Y with boninites. But the instantaneous fractional melts have lower abundances compared to boninites. These indicate that ultra-depleted harzburgites are residues after extractions of depleted boninitic melts. Boninites are probably accumulated melt during the melting processes or fractionated melt from the instantaneous fractional melt. The boninitic melt composition and high Mg# and low Al\({}_{2}\)O\({}_{3}\) contents in orthopyroxene of the TH harzburgite indicate the melting under high-temperature conditions (>1,350 degC).
Distributions of the fertile herzolites in the south and the ultra-depleted peridotites in the north can be explained as mantle materials during subduction initiation. We speculate that the fertile herzolites are residues after the extraction of tholeiitic melts and the ultra-depleted harzburgites are residues after the extraction of boninitic melts. A continuous supply of fluids and high temperature are the key to the formation of ultra-depleted peridotites and boninites at subduction initiation.
## Data Availability Statement
Mineral compositions of ultra-depleted peridotites, modeled compositions, and QGIS files of the studied area are available at Zenodo via [[https://doi.org/10.5281/zenodo.7263366](https://doi.org/10.5281/zenodo.7263366)]([https://doi.org/10.5281/zenodo.7263366](https://doi.org/10.5281/zenodo.7263366)) with CC-BY 4.0.
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wiley/fbb3e4f2_6597_4ae5_a7ce_c70141b5b008.md | # Earth and Space Science
Research Article
10.1029/2023 Ea002933
Evolution of the \(b\) Maps on the Faults of the Major (\(M>7\)) South California Earthquakes
[PERSON]
1 Instituto Nazionale di Geofisica e Vulcanologia--Sezione di Napoli Osservatorio Vesuviano, Napoli, Italy, 1 Department of Mathematics and Physics, Universita della Campania--[PERSON], Caserta, Italy1
[PERSON]
1 Instituto Nazionale di Geofisica e Vulcanologia--Sezione di Napoli Osservatorio Vesuviano, Napoli, Italy, 1 Department of Mathematics and Physics, Universita della Campania--[PERSON], Caserta, Italy1
[PERSON]
1 Instituto Nazionale di Geofisica e Vulcanologia--Sezione di Napoli Osservatorio Vesuviano, Napoli, Italy, 1 Department of Mathematics and Physics, Universita della Campania--[PERSON], Caserta, Italy1
Footnote 1: email: [EMAIL_ADDRESS]
Received 13 MAR 2023
###### Abstract
We use the [PERSON] et al. (2022, [[https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) ea002205]([https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) ea002205)) method for evaluating the \(b\) maps of the faults associated with the largest earthquakes \(M\geq 7.0\) that occurred in California. The method allows an independent evaluation of the \(b\) parameter, avoiding the overlap of the cells and the omission of some earthquakes, while keeping all the available information in the catalog. We analyzed four large earthquakes: Landers, Hector Mine, Baja California, and Searles Valley. The maps obtained confirm that the \(b\) value can be considered as a strain meter and allow us to elucidate the presence of barriers, such as obstacles to the propagation of the fracture, on the fault of the analyzed earthquakes. A further estimated parameter is the time window during which aftershocks occur in the cell, \(\Delta t\). This quantity is very useful for a better definition of the aftershock generation mechanism. It reveals where the stress is released in a short time interval and how the complexity of the faulting process controls the occurrence of aftershocks on the fault, and also the duration of the entire sequence.
The use of the [PERSON] et al. (2022, [[https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) ea002205]([https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) ea002205)) method for evaluating the \(b\) maps for the on-fault seismicity during the occurrence of aftershocks allows us to put some constraints on the faulting process during the aftershock sequences.
2022 The Authors. Earth and Space Science published by Wiley Periodicals
1
## 1 Introduction
The evaluation of the \(b\) value of the Gutenberg and Richter (GR) distribution ([PERSON], 1944) represents a crucial point in the estimation of earthquake hazard.
The \(b\) parameter has been extensively studied for earthquake catalogs and laboratory experiments. Its value has been inversely correlated with the stress state ([PERSON], 2003; [PERSON] and [PERSON], 2010; [PERSON], 1968; [PERSON], 1973) and directly correlated with the thermal gradient ([PERSON] and [PERSON], 1970; [PERSON] et al., 1998) as well as the material heterogeneity ([PERSON], 1962).
\(b\) value have been investigated both in time and space.
The time variation of the \(b\) value has been used mainly to characterize aftershock sequences and distinguish between aftershocks and foreshocks. Generally, \(b\) time variations have been investigated to elucidate the differences between foreshocks and background seismic activity ([PERSON] et al., 1996; [PERSON] et al., 2018; [PERSON], 1973, 1975; [PERSON] and [PERSON], 1972). Conversely, [PERSON] et al. (2018), by stacking many earthquake sequences, found that the \(b\) value increases immediately after the occurrence of a mainshock. Whereas [PERSON] and [PERSON] (2019) could discriminate between foreshocks and aftershocks for some sequences characterized by the occurrence of a large foreshock.
Spatial variations of the \(b\) values are generally investigated by mapping their value on a spatial grid. This allows us to determine the local fluctuation of the stress state. Indeed, this approach has also been used to characterize the stress state on earthquake faults (see among the others [PERSON] et al. (2014) and references therein). Some authors weight each earthquake based on the distance from the node. This method, first introduced by [PERSON] et al. (2014), has been modified and applied to several regions of the world by many authors (see among the others [PERSON] and [PERSON] (2015), [PERSON] et al. (2021), [PERSON] et al. (2021), and [PERSON] et al. (2022)). In all these cases, the most widely used approach is to grid the space into equal-sized cells and select the earthquakes according to certain rules (minimum number of events, maximum distance from the center of the cell, etc.). This approach will cause, in some cases, the overlapping of the cells or, in other cases, the omission of someearthquakes in the node ([PERSON] et al., 2022). This may prevent a formally correct statistical comparison between different cells of the grid.
Due to its inverse relationship with the stress state, the investigation of \(b\) for aftershock sequences assumes a critical role in seismic hazard assessment. \(b\) value time variations in aftershock sequences have been accurately investigated by [PERSON] et al. (2018) and [PERSON] (2019). They carefully consider the Short-Term Aftershock Incompleteness (STAI) ([PERSON], 2004). Here we focus on spatial \(b\) value variations not considering the effect of STAI, simply because the longer time scale makes STAI effects negligible (see data and methods and appendix for a more detailed discussion).
More recently [PERSON] et al. (2022) introduced a parameter-free method for the gridding of space and \(b\) evaluation. This method produces a fully independent mapping of the \(b\) value and reduces the number of earthquakes that are omitted. Here, we adopt this method to build \(b\) maps on the faults of the major (\(M>7\)) South California earthquakes. Moreover, we evaluate the time interval \(\Delta t\) during which each cell of the grid remains active. More precisely \(\Delta t\) represents the time elapsed from the occurrence of the mainshock and the last event that occurred in the cell. The two parameters allow us to follow the dynamics of the aftershock sequence on the fault.
## 2 Data and Method
In our study, we use the relocated South California catalog ([PERSON] et al., 2012) which can be downloaded at the website scedc.caltech.edu/research-tools/altcatalogs.html (SCEDC, 2013) focusing our attention on the earthquakes with magnitudes larger than 7, namely Landers 1992, June 28, \(M_{W}\) 7; Hector Mine 1999, October 16, \(M_{W}\) 7.1; Baja California 2010, April 4, \(M_{W}\) 7.2 and Searles Vallet 2019, July 6, \(M_{W}\) 7.1. For each earthquake, we chose a fault model, then selected all the on-fault earthquakes from the catalog, and finally apply the [PERSON] et al. (2022) method for evaluating the \(b\) maps on the fault using 500 events per cell. In the following, we neglect the occurrence of background activity on the faults. However, this does not imply a loss of generality in our results. Indeed [PERSON] et al. (2009) showed that it is negligible during aftershock.
### Selecting On-Fault Sismicity
We selected the fault geometry using the models provided by the Earthquake Source Model Database at the website [[http://equake-rc.infoo/srcmodo/](http://equake-rc.infoo/srcmodo/)]([http://equake-rc.infoo/srcmodo/](http://equake-rc.infoo/srcmodo/)) ([PERSON] & [PERSON], 2014). Specifically, for Landers, we used the fault geometry model proposed by [PERSON] and [PERSON] (1994), for Hectormine, the fault geometry proposed by [PERSON] et al. (2002), for Baja California, the fault geometry proposed by [PERSON] and [PERSON] (2013), and for Searles Valley, the fault geometry proposed by [PERSON] et al. (2019). These models appear to be representative of the selected fault geometries, which are very similar for all models on the website. Conversely, differences characterize the slip maps, but they do not influence the method that has been adopted. Finally, we selected all earthquakes occurring within a distance of 3 km from the fault plane as being on-fault seismicity. This value represents the minimum distance that allows the selection of several events sufficiently large for our analysis. Our tests confirmed that using smaller values reduced the number of events available for the analysis to an unacceptable level. Conversely, larger values appear to include off-fault seismic activity. The faulting geometry of Landers and Hector Mine is very complex, and the existing models propose three different fault segments for each earthquake. To select the on-fault seismicity, we consider each fault segment as an independent fault with its associated aftershocks. We then compile all chosen events into a comprehensive catalog for the entire fault, eliminating potential redundancies resulting from intersections between fault segments. Even for Searless Valley, a complex fault geometry has been suggested ([PERSON] et al., 2019), however the complexity is limited to the shallower part of the fault. As a consequence, we decided to adopt a single fault plane of a geometrically complex fault with multiple segments, as suggested by the authors. Finally, the adopted model for Baja California is a single fault segment. We selected the fault geometry using the models provided by the Earthquake Source Model Database at the web-site [[http://equake-rc.infoo/srcmodo/](http://equake-rc.infoo/srcmodo/)]([http://equake-rc.infoo/srcmodo/](http://equake-rc.infoo/srcmodo/)) ([PERSON], 2014). Specifically, for Landers, we used the fault geometry model proposed by [PERSON] and [PERSON] (1994), for Hectormine, the fault geometry proposed by [PERSON] et al. (2002), for Baja California, the fault geometry proposed by [PERSON] and [PERSON] (2013), and for Searles Valley, the fault geometry proposed by [PERSON] et al. (2019). These models appear to be representative of the selected fault geometries, which are very similar for all models on the website. Conversely, differences characterize the slip maps, but they do not influence the method that has been adopted. Finally, we selected all earthquakes occurring within a distance of 3 km from the fault plane as being on-fault seismicity. Thisvalue represents the minimum distance that allows the selection of several events sufficiently large for our analysis. Our tests confirmed that using smaller values reduced the number of events available for this analysis to an unacceptable level. Conversely, larger values appear to include off-fault seismic activity. The faulting geometry of Landers and Hector Mine is very complex, and the existing models propose three different fault segments for each earthquake. To select the on-fault seismicity, we consider each fault segment as an independent fault and then rejoin the selected aftershocks in a unique fault, avoiding superpositions. Even for Searles Valley, a complex fault geometry has been suggested ([PERSON] et al., 2019), however the complexity is limited to the shallower part of the fault. Consequently, we decided to adopt a single fault plane of a geometrically complex fault with multiple segments, as suggested by the authors. Finally, the adopted model for Baja California is a single fault segment.
### Building Independent Cells on Faults
We divided the on-fault seismicity into independent cells by adopting the method proposed by [PERSON] et al. (2022). The method individuates the largest event in the catalog not yet assigned to a cell and builds a cell around the chosen earthquake containing \(n\pm n_{sol}\) events. The method presents some advantages: (a) no events in the catalog are left unused (b) there are no cells overlapping, (c) the cells are totally independent (allowing statistical comparison of the \(b\) values obtained), (d) the method does not require any tuning of the parameters, being the cell size variable and automatically selected. The last of these advantages makes the method very suitable for surveillance systems. Here \(n=500\) and \(n_{sol}=50\). When \(M_{\max}-M_{\min}<1.5\), the cell was discarded from the analysis. Different values of \(n_{sol}\) were tested in [PERSON] et al. (2022). The two parameters \(n\) and \(M_{\max}-M_{\min}\) depend on each other. Indeed, a very large \(M_{\max}-M_{\min}\) reduces the number of cells too much and does not allow any interpretation of the results whereas a too small value results in a biased estimation of \(b\). At the same time, a smaller value of \(n\) reduces the number of cells respecting the constraint \(M_{\max}-M_{\min}<1.5\), whereas a very large value significantly reduces the number of cells.
As already showed by [PERSON] et al. (2022) the choice of \(n=500\) appears to be optimal; however, we have checked that by choosing \(n=600\), \(700\) and \(800\) we do not observe significant differences in the \(b\) value maps (see Supporting Information S1). The only difference is represented by the number of cells \(N_{f}\) used to evaluate the \(b\) value maps (\(N_{f}\) vs. \(n\) is shown in the Supporting Information S1): for Hector Mine and Searles Valley, the difference is limited to some units; for Baja California \(N_{f}\) assumes the same value for each \(n\); and for Lander \(N_{f}\) differences reach a maximum value \(10\) (see Supporting Information S1).
### Evaluating the Completeness Magnitude and the \(b\) Value
The completeness magnitude \(M_{c}\) was evaluated in each cell using the [PERSON] and [PERSON] (2022) method. This is based on the observation that the average magnitude \(\langle M\rangle\) should increase with a magnitude threshold \(M_{\min}\). Consequently, the quantity \(\langle M\rangle-M_{\min}\) should assume a constant value \(k\) for each \(M_{\min}\). Of course, this is not true if \(M_{\min}<M_{c}\). [PERSON] and [PERSON] (2022) evaluated \(M_{c}\) as the first \(M_{\min}\) for which \(\langle M\rangle-M_{\min}-k\) crosses the zero lines. They estimated the \(k\) value as the average \(\langle M\rangle-M_{\min}\) in the range \(M_{\min}\in[2.5,4]\). In this study, we improved their method by adopting a more accurate estimate of \(k\). Here \(k\) is evaluated by fitting \(\langle M\rangle-M_{\min}(M_{\min})\) with the function \(y=e^{-\max}+k\). An example of such a fit is presented in the Supporting Information S1. For all the earthquakes analyzed, the maps in the SI show a great variability of \(M_{c}\), with the largest range being [1.0,3.6] for Searles Valley, whereas the smallest range [1.4,3.0] is observed in the case of Hector Mine. This reveals that \(M_{c}\) does not depend only on the seismic station distribution. Indeed, \(M_{c}\) values are significantly different even in very close cells. Fluctuations in a number of factors could influence the \(M_{c}\) values: seismic noise, site effects, rock elastic properties and the STAI ([PERSON], 2004). The impact of STAI requires a further short discussion here. The decrease in the \(M_{c}\) value with the time elapsed from the occurrence of the mainshock has been interpreted as an artifact from the seismic catalog ([PERSON], 2004). Indeed, the capability to detect small earthquakes decreases significantly immediately after the occurrence of the mainshock (see [PERSON] (2004) for a detailed discussion) and is restored after a short time interval depending on the mainshock magnitude. Here, we decided to consider STAI following the approach of [PERSON] and [PERSON] (2023). Namely, for each earthquake, we evaluate the incompleteness magnitude
\[M_{c}=M_{\min}-0.8\,\ln(t_{i}-t_{\min})-1 \tag{1}\]
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline Earthquake & \(n_{s}\) & \(n\) & \(N_{s}\) & \(N_{f}\) & \(N_{sl1}\) & \(N_{sl2}\) & \(N_{s}\) & \(N_{s}\) \\ \hline Landers & 57,754 & 4,381 & 97 & 46 & 5 & 46 & 10–84 & 8 \\ Hector Mine & 14,085 & 1,728 & 28 & 14 & 14 & 0 & 10–78 & 19 \\ Baja California & 8,235 & 529 & 11 & 5 & 0 & 6 & 10–25 & 5 \\ Searles Valley & 30,263 & 316 & 42 & 19 & 2 & 21 & 10–15 & 71 \\ \hline \hline \end{tabular} Note. The total number of cells built using the [PERSON] et al. (2022) method \(N_{s}\) the final number of cells used for the evaluation of the \(b\) maps \(N_{s}\) the number of cells discarded because \(M_{\rm max}-M_{\rm min}<1.5\)\(N_{sl2}\) and the number of cells discarded because \(M_{\rm max}-M_{c}<1.5\)\(N_{sl2}\). \(N_{s}\) represents the range of the discarded number of events in cells with \(M_{\rm max}-M_{c}<1.5\) after the evaluation of \(M_{c}\).
\end{table}
Table 1: The Number of Events Selected for Each Earthquake Here Analyzed and the Number of Events Used for the \(b\) Map Estimationfault, as already observed by [PERSON] and [PERSON] (1997). Conversely, there are only eight cells with \(b>1.3\) (\(b_{\rm max}=1.5\)) where the stress is lower.
### Hector Mine
Even if the faulting process for this earthquake appears to be very complex, being composed of three different segments (Figure 2), the distribution of the \(b\) values in the cells is smoother when compared to the Landers earthquake. Indeed, we find \(b\) values in the range [0.8,1.2]. However, the smallest values are at the fault ridges and at the intersection of two fault segments. Consequently, it could be possible to interpret these values as due to the presence of barriers or kinks in the faults. In general, the \(\Delta t\) assumes values smaller than 8 years, and only for two cells do we observe \(\Delta t\approx 20\) years at the northern edge of the fault.
### Baja California
In this case, the faulting process is very simple and occurs on a planar fault (Figure 3). The small number of on-fault aftershocks and, consequently, the small number of statistically significant cells as well as the small values of \(\Delta t\) reveals that the on-fault aftershock activity is largely controlled by the complexity of the faulting process. For
Figure 1: The map of the \(\Delta t\) and \(b\) values on the Landers earthquake fault. The fault plane is shown by dashed gray lines. The green star represents the mainshock, whereas the black stars are the on-fault aftershocks with magnitudes greater than 4.5.
this earthquake, we were not able to associate the presence of barriers with the \(b\) values because of the very small number of cells.
### Searless Valley
The fault process for this earthquake also appears to be very simple, and we obtain a homogeneous distribution of both the \(b\) values, in the range [0.5,1.1], and the \(\Delta t\) whose maximum value is 0.5 years (Figure 4).
In all cases, the absence of a correlation between \(\Delta t\) and \(b\) reveal that the duration of the aftershock activity does not depend on the stress level. The same observation can be made for the occurrence of the largest aftershocks whose location does not correspond to cells with small \(b\) values.
## 4 Comparison With Previous Results
To the best of our knowledge, the on-fault \(b\) values previously evaluated concern Landers and Hector Mine earthquakes. The first one focused the researchers' attention because it changed the seismicity rate in a large part of California ([PERSON] & [PERSON], 2000). The temporal and spatial variations of the \(b\) value on the Landers fault have been estimated using different approaches ([PERSON] et al., 2014; [PERSON], 2002). They found the highest
Figure 2: The map of the \(\Delta t\) and \(b\) values on the Hector Mine earthquake fault. The fault plane is shown by dashed gray lines. The green star represents the mainshock, whereas the black stars are the on-fault aftershocks with magnitudes greater than 4.5.
\(b\) values in the parts of the fault with the highest slip, lower \(b\) values in the nucleation area, and lowest values along the southern extension of the Landers fault. Their results are compatible with ours (Figure 1), with the exception that we did not observe significant aftershocks in the nucleation zone. Such a result can be easily explained by observing that a large part of the stress released during the mainshock occurs in the nucleation zone. Consequently, the probability of observing aftershocks in this zone is negligible.
[PERSON] et al. (2014) observed that the \(b\) value in the area of the Hector Mine earthquake remained almost constant and close to 1, with a tiny decrease in the very shallow values and an increase below, immediately before the event. After the Hector Mine earthquake, the \(b\) value increases on the fault concerned, and an area of small \(b\) value is evident in the shallow eastern sector. These observations are compatible with our results (Figure 2). In particular, the small \(b\) value highlights the presence of barriers to propagation at the edges of the fault.
The differences between the [PERSON] et al. (2014) observations and ours can be attributed to the different methods. Indeed, many methods exist for the estimation of the \(b\) value variations on a fault: the fixed radius method, the N-nearest earthquakes method, and the Distance Exponential Weighted (DEW) method. The first two
Figure 3: The map of the \(\Delta r\) and \(b\) values on the Baja California earthquake fault. The fault plane is shown by dashed gray lines. The green star represents the mainshock, whereas the black stars are the on-fault aftershocks with magnitudes greater than 4.5.
are implemented in Z-map ([PERSON], 2001), the most used and tested program for \(b\) value estimation, and the third is well described in [PERSON] et al. (2014). The third method takes advantage of the independence from the chosen distance from the fault for earthquakes to be included in the \(b\) value estimation, which is instead an input parameter for the other two methods. In addition, with the DEW method, a parameter must be set that is the gradient of the distance weight decay.
Our method sits in the middle between these approaches as it needs the definition of the maximum distance of the earthquakes from the fault, but it has the advantage of giving a statistically independent value of \(b\)([PERSON] et al., 2022) and shows unsmoothed \(b\) value maps.
## 5 Discussion and Conclusions
The duration of the aftershock sequence, the \(b\) distribution, and the number of on-fault aftershocks appear to strongly depend on the geometrical complexity of the fault. We observe that Lander and Hector Mine present a
Figure 4: The map of the \(\Delta t\) and \(b\) values on the Searles Valley earthquake fault. The fault plane is shown by dashed gray lines. The green star represents the mainshock, whereas the black stars are the on-fault aftershocks with magnitudes greater than 4.5.
more complex fault composed of three segments (Figures 1 and 2), and in both cases the \(b\) distribution is more heterogeneous when compared to Baja California and Searles Valley (Figures 3 and 4).
Interestingly, for Landers, Hector Mine, and Searles Valley, we can perform a correlation between the slip on the fault and the cell distribution. Unfortunately, such analysis cannot be performed for Baja California because of the small number of cells selected by the method used here. Landers exhibits an absence of cells in the fault zone of maximum slip ([PERSON] and [PERSON], 1994). Note that the absence of cells can be caused by a true absence of earthquakes or by a small magnitude seismicity due to \(M_{\max}-M_{\min}<1.5\) or to a small magnitude range \(M_{\max}-M_{e}<1.5\). In all cases, the maximum slip zone is characterized by the absence of significant seismicity. This is a strong indication that the stress was almost completely released during the mainshock faulting process. Conversely, for the Hector Mine significant seismicity (characterized by small \(b\) value and high stress but with a small \(\Delta t\)) occurs at the left of the sininist fault whereas no earthquakes occur at the right of the where we observe the maximum slip in both areas during the mainshock faulting ([PERSON] et al., 2002). A possible scenario is that the faulting nucleates at the left of the kink and then proceeds beyond. As a result, all the stress has been released but the Coulomb stress of this area reactivates the part of the fault to the left of the kink for a short time interval. For Searles Valley earthquakes surrounding the zone of maximum slip ([PERSON] et al., 2019) have small \(b\) and \(\Delta t\) values, suggesting that the stress has been released during the faulting process and increased in the part of the fault not slipped during the mainshock faulting.
Our results confirm that the \(b\) parameter is a good stress meter and can be used to characterize the faulting process. As a concluding remark, we would like to observe that the use of the [PERSON] et al. (2022) method allows a better resolution of the \(b\) values on the fault due to their independence and the small number of earthquakes lost in the griding process.
## Appendix A STAI Influence
In the following we assume some values of the Omori Law ([PERSON], 1894) parameters
\[n(t)=\frac{K}{(t+c)^{p}} \tag{1}\]
where \(n\) is the number of events and \(t\) is the time elapsed since the occurrence of the mainshock.
Assuming \(p=1\), the total number of events \(N\) that occurred in a time interval \(T\) is
\[N=K\ln\left(\frac{T+c}{c}\right) \tag{2}\]
If we choose \(T=8\) years (typical duration of our sub-catalogs except Searles Valley), \(c=1\) hr and \(K=5000\) and measuring time in days we get \(N_{T}\simeq 85,286\). When we consider a typical duration of STAI (\(T=2\) days ([PERSON], 2004; [PERSON], [PERSON], et al., 2019; [PERSON], [PERSON], et al., 2019)) we get some events during STAI \(N_{s}\simeq 48,855\). Now, let us assume that \(M_{c}\) is overestimated by one during the entire STAI periods. Therefore, if \(b=1\), the number of missed events is \(N_{m}\simeq 4,885\) implying a percentage of missed events \(\frac{N_{m}}{N_{T}}=0.057\).
If we fix \(T=0.5\) years, as in the case of Searless Valley, this percentage increases to 0.062.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Data have been provided by the Southern California Earthquake Data Center (SCEDC) and are available at the following website scedc.caltech.edu/research-tools/altcatalogs.html. All the custom codes used in this study are available at the web-site ([PERSON] et al., 2023).
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* [1980] [PERSON], & [PERSON] (2000). Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States, and Japan. _Bulletin of the Statistical Society of America_, 90(4), 898-869. [[https://doi.org/10.1785/0119990114](https://doi.org/10.1785/0119990114)]([https://doi.org/10.1785/0119990114](https://doi.org/10.1785/0119990114))
* [1981] [PERSON], & [PERSON] (2002). Mapping spatial variability of the frequency-magnitude distribution of earthquakes. _Advances in Geophysica_, 45, 259-302. [[https://doi.org/10.1111/j.1365-246X.1973.006506.x](https://doi.org/10.1111/j.1365-246X.1973.006506.x)]([https://doi.org/10.1111/j.1365-246X.1973.006506.x](https://doi.org/10.1111/j.1365-246X.1973.006506.x)) | wiley | Evaluation of the <i>b</i> Maps on the Faults of the Major (<i>M</i> > 7) South California Earthquakes | V. Convertito, A. Tramelli, C. Godano | https://doi.org/10.1029/2023ea002933 | 2,024 | CC-BY |
wiley/fb85e807_b595_407f_be45_dee0f1bc0ac1.md | # Thermal Plasma and Neutral Gas
In Saturn's Magnetosphere
[PERSON]
Center for Space Research
Massachusetts Institute of Technology, Cambridge
###### Abstract
Saturn's magnetosphere contains plasma and neutral particles from Saturn's atmosphere, the rings, the inner icy satellites, and Titan. This paper reviews the observations of plasma and neutrals near Saturn. Plasma conditions were observed during the Pioneer 11 and Voyager 1 and 2 flybys of Saturn. Neutral H was observed by the Voyagers; neutral OH has been observed by the Hubble Space Telescope. The attempts which have been made to understand the physical processes behind the data are also discussed. Saturn's magnetosphere is dominated by neutrals, with a neutral to plasma density ratio of about 10. The neutrals are probably produced by bombardment of the moons by micrometeorites and heavy ions, although there is a discrepancy between predicted sputtering rates and the amount of sputtering necessary to produce the observed neutral densities. Transport of plasma out of the magnetosphere must be very fast, of the order of a few days. Models of the processes occurring in Saturn's magnetosphere are used to determine the densities of neutral and plasma species which cannot be directly observed. These results will be tested when Cassini arrives at Saturn in 2004.
Footnote †: 9501 *
## 1 Introduction
Saturn is the second largest planet with a radius of 60,330 km (equal to \(1~{}R_{S}\)), and its magnetosphere is the second largest in the solar system, with a cross-sectional area of 2500 \(R_{S}^{2}\) (about \(10^{9}\) km\({}^{2}\)) and a length of hundreds of Saturn radii. Figure 1 shows an overview of Saturn's magnetosphere, the region where Saturn's magnetic field creates a cavity in the solar wind. The solar wind is a stream of plasma moving outward from the Sun at speeds of 400\(-\)800 km s\({}^{-1}\) (from left to right in Figure 1). The solar wind cannot cross the magnetic field produced by Saturn, so the flow diverts around this magnetospheric obstacle. Since the solar wind is supersonic, a bow shock forms in front of the planet; the region of shocked plasma downstream of the bow shock is called the magnetosheath. The boundary between the solar wind and the planetary magnetic field is called the magnetopause; behind the planet the solar wind stretches the planetary magnetic field far downstream forming the magnetotail.
The region of Saturn's magnetosphere labeled the trapping region in Figure 1 is filled with plasma and neutral gas. Where does it come from? Inside this magnetospheric cavity are Saturn, the rings, the inner icy satellites (Mimas, Enceladus, Tethys, Dione, and Rhea), and, the vast majority of the time, the large moon Titan. These bodies are all direct and/or indirect sources of neutrals and plasma. Saturn and Titan both have ionospheres; ions and electrons which escape from these ionospheres are direct plasma sources. Neutral atoms and molecules also escape from the atmospheres of Saturn and Titan; many of these neutrals are ionized by solar UV radiation or collisions with electrons and ions, adding to the plasma population. The icy satellites and rings are under constant bombardment by sunlight, plasma, and micrometeorites. This bombardment knocks atoms and neutrals off the surface into the magnetosphere, where some are ionized and contribute to the plasma population. In addition, some solar wind ions do enter the magnetosphere through the tail, and interstellar neutrals, the atoms populating the regions between stars, may enter Saturn's magnetosphere and become ionized therein.
What happens to this plasma? The largest portion recombines back into neutral atoms and goes flying out of the magnetosphere. A significant fraction is transported to the boundary of the magnetosphere and escapes down the magnetotail into the solar wind. Of the rest, some smashes into the rings and moons, knocking off neutrals which then form more plasma, and some enters Titan's and Saturn's atmospheres, providing an energy source to drive atmospheric processes and auroral displays.
Most of our knowledge of Saturn's magnetosphere comes from the brief flyby encounters of Pioneer 11 (1979) and Voyager 1 (1980) and 2 (1981). Recent observations using the Hubble space telescope (HST) also give valuable clues as to the neutral density structure. This paper describes the observations from Saturn's magnetosphere, the current understanding of theprocesses producing the observed structure, and questions which remain. The next mission to Saturn will be the Cassini Orbiter/Huygens Probe, which is expected to return years of data from Saturn's magnetosphere and its vicinity beginning in 2004 and which should answer many of our current questions.
## 2 Rules for Neutrals and Plasma in a Magnetosphere
The motions of neutral particles are governed mainly by the gravitational force and thus by [PERSON]'s laws. Neutral atoms and molecules in the magnetosphere orbit Saturn. These orbits can be perturbed by the moons; a neutral remains in orbit until it collides with something which either ionizes it (ions or electrons), absorbs it (ring particles, moons, or Saturn), or gives it enough energy to escape from Saturn.
The motions of plasma are governed by electromagnetic, gravitational, and inertial forces. The most important rule applicable to Saturn's magnetospheric plasma is the \"frozen-in\" condition, which states that low-energy ions and electrons must remain on the same magnetic field line. Since the magnetic field of Saturn rotates with Saturn, the plasma must also move around Saturn once per Saturnian day (10 hours and 39 min). Since the distance around Saturn is 2\(\pi\)p, where \(\rho\) is the distance from Saturn's rotational axis, the velocity of the ions increases as \(\rho\) increases. Since the plasma is organized by the magnetic field, a parameter called the \(L\) shell is used to label field lines; for a dipole field, \(L=r_{0}/R_{S}\), where \(r_{0}\) is the distance to a field lines equatorial point and \(R_{S}\) is Saturn's radius (60,330 km) [_[PERSON]_, 1961]. Thus a field line crossing the equator at 4 \(R_{S}\) is the \(L=4\) field line. The Saturnian field is fairly well represented by a dipole in the inner magnetosphere (\(L<10\)) [_[PERSON] et al._, 1984].
Magnetic flux tubes can move radially by diffusive or convective processes. Since the strength of the magnetic field varies as \(L^{-3}\), flux tubes which move inward are compressed as they enter higher magnetic field regions; this compression causes the plasma to become more dense and to be heated. If adiabatic compression were the only mechanism at work, the density would vary as \(L^{-4}\), and temperature would vary as \(L^{-8/3}\). Plasma is free to move along magnetic field lines, but since the plasma is rotating rapidly, the centrifugal force confines the plasma to near the equator, the place farthest from the spin axis. Thus the plasma tends to form a rapidly rotating disk confined to the vicinity of the equator.
## 3 Observations
This section will describe the observations of plasma and neutrals in Saturn's magnetosphere. The magnetospheric physics implied by these observations will be
Figure 1: An overview of the Saturnian magnetosphere showing the basic geometry of the interaction of the magnetosphere with the solar wind. The solar wind becomes subsonic at the bow shock, and the magnetosheath plasma is then able to flow around the magnetopause. The magnetic field of Saturn is stretched downstream in the solar wind to form the magnetotail. (Image provided courtesy of the Windows to the Universe Project ([[http://windows.engin.umich.edu/saturn/upper_atmosphere.html](http://windows.engin.umich.edu/saturn/upper_atmosphere.html)]([http://windows.engin.umich.edu/saturn/upper_atmosphere.html](http://windows.engin.umich.edu/saturn/upper_atmosphere.html))). Copyright 1998 The Regents of the University of Michigan.)
discussed simultaneously, with a summary given at the end of the section.
Saturn's existence has been known since ancient times. The rings were discovered by [PERSON] in 1610, Titan was discovered by [PERSON] in 1655, Iapetus, Rhea, Tethys, and Dione were discovered by [PERSON] between 1672 and 1684, and Enceladus and Mimas were discovered by [PERSON] in 1789 (for a historical review see _[PERSON]_[1984]). Figure 2 is a road map of the Saturn system. The region near Saturn is filled with rings. The classical bright rings visible from Earth, the A, B, and C rings, lie between 1.23 and 2.27 \(R_{S}\) from Saturn's center. Around these rings are fainter rings; the D, F, and G rings are narrow, diffuse rings and unimportant as potential plasma sources. The E ring is also diffuse but extends from 3-8 \(R_{s}\) and contains a significant amount of mass. The most important inner satellites (radius \(>\) 100 km) are Mimas, Enceladus, Tethys, Dione, and Rhea. All of these rings and satellites have surfaces composed mainly of water (H\({}_{2}\)O) ice. Titan is Saturn's largest moon with a radius of 2575 km and is the only Saturnian moon with a significant atmosphere; this atmosphere is composed primarily of N\({}_{2}\).
No hint of Saturn's magnetosphere was detected until Pioneer 11 arrived at the planet in 1979. Pioneer 11 discovered that Saturn has a magnetic field of sufficient strength to produce a large magnetosphere [_[PERSON] and [PERSON]_,1980; _[PERSON] et al._,1980]. The surface magnetic field at Saturn is 0.21 \(G\), comparable to the 0.3 \(G\) field at Earth but much less than the 4.2 \(G\) surface field at Jupiter. This field produces a magnetosphere which extends to about 25 \(R_{S}\) from the planet at the subsolar point (where the magnetopause is closest to the planet).
A remarkable feature of Saturn's magnetic field is that the magnetic dipole axis is almost perfectly aligned with the spin axis, although the dipole center is shifted about 0.04 \(R_{S}\) northward (see the review by _[PERSON] et al._[1984] and references therein). Thus the magnetic equator and the rotational equator are in the same plane. This unique feature of Saturn's magnetic field greatly simplifies the analysis of plasma observations for two reasons. Low-energy plasma must, to first order, stay on the same magnetic field line. Where it congregates on that field line depends on its energy. High-energy particle distributions (energy \(E>\) 1 keV) are centered about the magnetic equator. Zero energy particles are located at the centrifugal equator, the point on a field line farthest from the spin axis. Intermediate energy particle distributions are centered between these two equators. With a 0\({}^{\circ}\) dipole tilt, however, these two equators are identical, and all energy particle distributions are centered at the same place. The other simplification is in the trajectory; if the dipole were tilted with respect to the spin axis, the magnetic latitude would oscillate as the planet rotated, giving complicated wiggle plot trajectories when plotted in magnetic coordinates. With no tilt the trajectories are very simple and are the same in magnetic and geographic coordinates.
Figure 2: An overview of the Saturnian system showing the locations of the major moons and rings. From Saturn outward the rings shown are the D, C, A, B, F, G, and E (shown by the shading) rings.
### Neutrals
Neutrals are measured by looking at emission lines. Hydrogen atoms (H) emit Lyman alpha radiation (because of resonance scattering of sunlight) which can be detected by ultraviolet spectrometer (UVS) instruments. The Voyager UVS experiments detected H radiation; the original data interpretation was of a torus of H with density of about 20 atoms cm\({}^{-3}\) in the vicinity of Titan's orbit [_[PERSON] et al._, 1981; _[PERSON] et al._, 1982]. Subsequent analysis of additional UVS spectra suggests that the H cloud probably has two components, one associated with Titan which is azimuthally asymmetric and centered on Titan's orbit and one which extends in to Saturn's surface which has an intensity peak on the dusside of Saturn [_[PERSON] and [PERSON]_, 1992] (although there is a discrepancy between preencounter and postencounter data as to whether the observations are brightest on the dusside or dusside). _[PERSON] and [PERSON]_ [1993] and _lp_ [1996] show that solar radiation pressure can modify the orbits of neutral H near Titan and produce the observed asymmetry.
The other neutral which has been observed is OH (which in the rarefied densities near Saturn is a stable neutral molecule). _[PERSON] and [PERSON]_ [1992] predicted large OH densities based on a model of the chemistry and energy balance. They show that without large neutral densities to collisionally cool the thermal electrons, the electron temperature would be higher than observed. On the basis of this prediction, _[PERSON] et al._ [1993] used the Hubble space telescope to search for OH. The OH molecule scatters solar radiation at a wavelength near 3085 A. The observations at 4.5 \(R_{S}\) show a clear OH feature corresponding to an OH density of about 160 cm\({}^{-3}\). Follow up observations at 4.5, 6, and 10 \(R_{S}\) confirmed the large OH densities and showed a rapid density decrease with distance [_[PERSON] and [PERSON]_, 1995]. _[PERSON] et al._ [1996] took advantage of the edge-on configuration of Saturn's rings in August of 1995 to look for OH closer to Saturn. The edge-on configuration, in which the rings and Earth are in the same plane, minimized the light reflected from the rings so that relatively weak OH signatures could be observed. Observations at distances of 1.9, 2.1, and 2.3 \(R_{S}\) found that the brightness of OH emissions increased outward from 79 to 87 to 111 R (1 R, or Rayleigh, equals 10\({}^{6}\) photons cm\({}^{-2}\) s\({}^{-1}\)) at the three distances. _[PERSON] et al._ [1996] also did a latitudinal scan at 1.9 \(R_{S}\) and found that the OH density decreases with a scale height of 0.45 \(R_{S}\). The geometry of these observations is shown in Figure 3, where the lines of sight of the OH observations are shown in a two-dimensional (2-D) representation which gives a good feel for the actual data coverage. To understand the proper geometry of the observations, mentally rotate the contours around the \(z\) axis to form a torus. Then rotate each line of sight 90\({}^{\circ}\), keeping the slant angle the same. By combining all these observations, coverage of the torus is fairly complete. The OH density contours are from the model of _[PERSON] et al._ [1998], who show that the three sets of observations taken together imply peak OH densities of about 700 cm\({}^{-3}\) near 4.5 \(R_{S}\) and 30 cm\({}^{-3}\) near the rings.
Since the inner moons and rings are mainly water ice, we expect that H\({}_{2}\)O and other dissociation products of H\({}_{2}\)O (H\({}_{2}\) O, and O\({}_{2}\)) will also be present. Likewise, since Titan's atmosphere contains large amounts of N, some N may be present as well, but the radiative efficiencies of these species are too low for them to be observed from Earth.
### Plasma
The important plasma parameters are the density and temperature of each ion and electron component of the plasma and the bulk velocity of the plasma as a whole. Since the low-energy plasma is tied to a magnetic field line and the field lines rotate with Saturn, every plasma component must move with the same velocity. The Voyager 1 and 2 plasma science experiments (PLS) have provided most of our current knowledge on the thermal plasma at Saturn [_[PERSON] et al._, 1981, 1982; _[PERSON] and [PERSON]_, 1983; _[PERSON] et al._, 1983; _[PERSON]_, 1986]. This instrument has four Faraday cup detectors which measure currents with energies from 10 to 5950 eV [see
Figure 3: A schematic diagram showing the lines of sight of Hubble space telescope observations of OH brightness superposed on OH density contours from a model result.
_[PERSON] et al._, 1977]. The instrument has no direct capability to determine the composition of the ions, but the fact that all the ions are moving at the same velocity provides a means to estimate the mass. The energy is proportional to the mass, so that ions with different masses produce current peaks at different energies. Figure 4 shows an example of an ion spectrum observed by the Voyager 1 PLS at 15 \(R_{S}\) as it was inbound from Saturn. The measured current is plotted versus energy. The energy of the measured currents (location along the \(x\) axis) depends on the mass of the particle and the velocity normal to the detector look direction. The amount of current (height on the \(y\) axis) depends on the density. The width of the current peak depends on the temperature (larger width equals larger temperature). The plasma velocity, density, and temperature are determined by finding the values which best fit the observed currents. The best fit to the data in Figure 4 is shown by the solid curve. Two distinct current peaks are present; the one at low energies is assumed to be due to protons. The high-energy peak is then at the proper energy for a mass near 16 amu; however, it cannot be determined if this peak consists of O\({}^{+}\), OH\({}^{+}\), or H\({}_{2}\)O\({}^{+}\) or a combination of these ions since the peak is wide enough to cover all these possibilities. Until [PERSON] makes in situ observations, modeling is needed to obtain estimates for the detailed composition of the heavy ions.
Higher-energy particles are measured by the low-energy charged particle (LECP) experiment (energies of 30 keV-150 MeV for ions and 22 keV-20 MeV for electrons) and by the cosmic ray subsystem (CRS) experiment (energies greater than 1 MeV). Between energies of about 6 and 22 keV, particles are not measured by Voyager. The higher-energy particles are much less dense than the thermal plasma, but because of their higher temperatures, they can dominate the pressure. _[PERSON] et al._ [1996] combine electron data from the PLS, LECP, and CRS experiments (interpolating across the energy gap) to form complete energy spectra. Over 90% of the flux and density is in the PLS energy range, but these electrons contribute less than 50% of the pressure. Although no similar study has been done for ions, the results would probably be similar. This review concentrates mainly on the thermal plasma measured by PLS which composes most of the plasma density.
#### 3.2.1 Density
The density which is observed is dependent on several factors. Clearly, the rates of plasma production and of plasma removal are important. Many possible plasma sources were listed in section 1, so we expect some plasma to be present. If the plasma is transported radially, the density will change with \(L\) shell. The plasma must stay on the same magnetic flux tube, and the volume of a dipolar flux tube decreases as \(L^{4}\). Since the plasma density is inversely proportional to the flux tube volume, the density should increase as \(L^{-4}\). Thus a maximum in density near Saturn would not necessarily indicate a source near Saturn but could result from the plasma being compressed as it moves inward.
Another factor determining the observed densities is how the plasma is distributed; the spacecraft latitude and longitude may or may not pass through dense plasma regions. The plasma is probably distributed relatively uniformly in longitude, at least in the inner magnetosphere, as ion source and loss times are longer than the rotation rate of the planet. The latitudinal distribution of plasma results from a balance of forces. The centrifugal force pushes plasma outward along magnetic field lines toward the equator. At Saturn, where the temperature perpendicular to the magnetic field is greater than that parallel to the magnetic field, the magnetic mirror force also accelerates plasma equatorward. Opposing these equatorward forces is the pressure gradient force which is proportional to temperature. Since electrons are less massive than the ions and thus are less affected by the centrifugal force, they have larger scale heights than ions; this charge imbalance leads to the creation of an ambipolar electric field (an electric field created by charge separation) which maintains charge neutrality by holding electrons closer to the equator and pulling ions to higher latitudes. The effects of the ambipolar field are important for ions as well; if more than one ion species is present, the heavier ion will concentrate near the equator and the lighter ion may have its peak density off of the equator. The peak plasma density, however, is always at the equator; the decrease of density with latitude depends on the anisotrop (\(\mathcal{A}=T_{\perp}/T_{\parallel}-1\)) of the plasma and the plasma temperature. The larger the anisotropy is and lower the temperature is, then the stronger the equatorial confinement of the plasma is.
Figure 5 shows the electron densities observed by the Voyager 1 and 2 PLS instruments. The crosses show the inbound data, and the diamonds show the outbound data. The earliest inbound data shown are in the mag
Figure 4: A spectrum obtained by the Voyager 1 detector which looks into the corotating plasma flow from about 15 \(R_{S}\) from Saturn on the inbound passage. The histogram shows the current in each cup, the solid curves show the simulated currents for protons and heavy ions, and the crosses show the total simulated current. The current is in femtomaps (10\({}^{-15}\) amps). The \(x\) axis shows the channel number, which is a proxy for a roughly logarithmic energy scale increasing from 10 eV to 5950 eV across the plot.
netosheath, the region of shocked solar wind plasma between the bow shock and magnetopause. In this region the densities are fairly constant. After the magnetopause crossing at about 23 \(R_{S}\) the densities decrease to between 0.02 and 0.2 cm\({}^{-3}\) from \(L=16\)-23; this region of the outer magnetosphere is called the plasma mantle. The density spike just inside \(L=20\) is due to plasma streaming outward from Titan. At about \(L=16\), Voyager 1 entered the plasmasphere, a region of relatively stable plasma densities which increase toward the planet. The inbound and outbound densities are very different between \(L=5\) and \(L=8\); this is a latitude effect and will be discussed in section 3.2.4).
Figure 5 shows that Voyager 2 electron densities in the magnetosheath are higher than for Voyager 1. The solar wind dynamic pressure was higher at this encoun
Figure 5: Observed electron densities from Voyager 1 and 2 inbound (crosses) and outbound (diamonds). The spacecraft latitudes inbound (solid curve) and outbound (dashed curve) are shown on the same scale.
ter resulting in a higher pressure and thus a magneto-pause which is more compressed, with the magneto-pause crossing just outside \(L=20\). The mantle region extends from \(L=13\)-20 and is marked by factor of 10 changes in the density. The density increases smoothly in the plasmasphere inside \(L=13\) to \(L=6\); inside \(L=6\) the density appears to decrease, but this is an instrumental effect (the electron energy is too low for electrons to be detected by the PLS instrument). The outbound profile matches the inbound data fairly well inside \(L=9\); outside \(L=9\) the outbound densities are consistently smaller than the inbound densities.
Figure 6 shows the density profiles for protons and heavy ions (mass 16-19 amu) for the Voyager 1 and 2 passes through Saturn's magnetosphere. Since the various heavy ion species which may be present are not resolved, the analysis was performed assuming all ions were O\({}^{+}\). Fewer ion data are shown because the ion analysis requires larger densities than the electron analysis. Also, the ions cannot be observed unless the detectors are pointed into the ion flow. The density rises as Voyager 2 approaches the planet, with a peak density of about 120 cm\({}^{-3}\) at the closest approach to the planet, \(L=2.7\). Note that the latitude of the spacecraft greatly effects the observations; the highest densities are observed when the spacecraft cross the equator. The density oscillations in the plasma mantle (which are very noticeable in the electron data) are not apparent since for ions only the high-density regions can be analyzed. The Voyager 1 densities are higher outbound than inbound; this is probably a latitude effect since Voyager 1 is closer to the equator outbound. The effect of the ambipolar electric field on the ions is shown nicely by the Voyager 1 data. From \(L=6\)-8 inbound, when Voyager 1 is away from the equator, the H\({}^{+}\) density is comparable to or less than the O\({}^{+}\) density; whereas outbound nearer the equator, the O\({}^{+}\) density dominates. Voyager 2 crossed the equator near closest approach at \(L=2.7\). Only O\({}^{+}\) is observed since H\({}^{+}\) energies this close to Saturn are below the 10 eV instrument threshold. The O\({}^{+}\) density rises sharply as the spacecraft nears the equator to a peak density of 120 cm\({}^{-3}\), then decreases again as the spacecraft latitude increases. The strong latitudinal density gradient indicates a large anisotropy, \(A\approx 10\)[_[PERSON] et al._, 1994].
#### 3.2.2 Temperatures
The temperature of the plasma depends on the initial temperature acquired when the ions and electrons were formed and mechanisms which heat or cool the plasma. When an ion is formed from a neutral, the ion's initial thermal speed is the difference between the Keplerian velocity the neutral had when orbiting Saturn and the rotational speed at
Figure 6: Observed proton and heavy ion densities in Saturn’s magnetosphere. Note the different densities observed by Voyager 1 inbound and outbound at the same \(L\) shell; this is because the spacecraft is at a lower latitude outbound than inbound.
which plasma moves around Saturn, \(w_{i}=w_{\rm rot}-w_{\rm Kep}\). The initial energy of a particle is then \(0.5 mw_{i}^{2}\). The formation energy, generally referred to as the pickup energy, is plotted in Figure 7 along the Voyager 1 (solid curve) and Voyager 2 (dotted curve) trajectories. Electrons have little mass and thus have little initial energy, H\({}^{+}\) has energies ranging from a few to 200 eV, and O\({}^{+}\) has 16 times the H\({}^{+}\) energy. The plasma particles can gain and lose energy by many processes. If ions are transported radially, the expansion (for outward movement) or compression (for inward movement) of the magnetic flux tubes causes them to cool or heat adiabatically, with the temperature changing as \(L^{-8/3}\). (This is strictly true for an isotropic distribution; the perpendicular temperature varies as \(L^{-3}\), and the parallel temperature varies as \(L^{-2}\), so for an isotropic distribution the energy varies as \((T_{1}^{2}T_{\rm I})^{-1/3}\) or \(L^{-8/3}\).) Thus a magnetosphere where transport dominates would be characterized by the temperature decreasing with radius, whereas if transport is slow compared to other ion losses the temperature will increase with radius. Particles undergo coulomb collisions (their orbits are affected by the electric field of another particle during a close encounter), with hotter particles losing energy to cooler ones. Thus electrons are heated and heavy ions are cooled by this process. Electrons lose energy by colliding with ions and exciting them into higher states; this energy is radiated away when the ions return to the ground state. Ionization of neutrals and ions via electron impact is also an electron energy sink. Ions and electrons can either gain or lose energy via wave-particle interactions.
The electron temperatures are shown in Figure 8. The Voyager 1 temperatures are a few tens of eV in the magnetosheath, then increase to a few hundreds of eV in
Figure 8: Electron temperatures. The top plots show the thermal component; the bottom plots show the suprathermal component. Inbound data are shown by crosses; outbound data are shown by diamonds. The solid curves show the spacecraft distance above the equator in \(R_{S}\) times 100.
Figure 7: The initial energy of ions and electrons formed in Saturn’s magnetosphere along the Voyager 1 (solid curve) and Voyager 2 (dotted curve) trajectories.
the mantle. The decrease just inside \(L=20\) is due to Titan's wake. The temperature varies between 30 and 200 eV from \(L=10\)-15, then begins a decrease from 100 eV at \(L=10\) to 5 eV at \(L=4.2\). Outbound the temperatures are higher from \(L=4.5\)-9 when the spacecraft is at lower latitudes.
The Voyager 2 temperature profile shows similar characteristics, including the decrease in temperature inside \(L=10\). The one additional feature is the series of increases from 100 to about 500 eV in the plasma mantle; these correspond to the decreases in density in Figure 5. All the electron temperatures are much larger than the pickup or initial energies for electrons shown in Figure 7, so electrons must undergo fairly rapid heating. This heating may be due to coulomb collisions or wave-particle interactions; a general problem for all outer planet magnetospheres is the mechanism for heating electrons to the observed energies.
Figure 9 shows the ion temperature profiles for H\({}^{+}\) and O\({}^{+}\). The Voyager 1 profiles have a maximum at about \(L=10\). The outbound temperatures where Voyager 1 is closer to the equator are again greater than the inbound temperatures from \(L=5\)-8. The Voyager 2 temperature peak is slightly farther out, at \(L=13\)-15. The ion values are only available for the high-density regions, so ion temperatures for the hot tenuous regions in the Voyager 2 mantle are only roughly known.
Superposed on the data are lines showing the pickup energy for H\({}^{+}\) and O\({}^{+}\) ions. The pickup energy matches the shape of the data fairly well out to \(L=11\) and \(L=15\) for Voyager 1 and Voyager 2, respectively. In general, the H\({}^{+}\) and heavy ions are not separated by the full factor of 16 the mass difference implies, suggesting that some energy exchange has occurred, with H\({}^{+}\) gaining energy from the O\({}^{+}\) ions.
#### 3.2.3 Velocity
As discussed in section 2, to first order we expect the plasma velocity to be due solely to the motion of the magnetic field around Saturn. This gives an azimuthal velocity, called the corotation velocity, of 9.9 \(p\) km s\({}^{-1}\), where \(\rho\) is the distance from Saturn's spin axis in Saturn radii. Figure 10 shows the azimuthal velocity component (\(V_{\phi}\)) of the plasma as a function of dipole \(L\). A cylindrical coordinate system is used, where the \(\phi\) component is in the azimuthal direction (the direction of Saturn's rotation), the \(\rho\) component is positive outward from Saturn's spin axis, and the \(z\) component completes a right-handed system and indicates north-south flow. The plot shows the observed velocity and the corotation velocity; clearly, the plasma does not corotate as expected. The plasma moves more slowly than corotation outside \(L=5.5\) for Voyager 1 and \(L=8.5\) for Voyager 2. In some regions the flow is less than half of that predicted. In the Voyager 2 mantle region
Figure 9: Ion temperatures for protons and heavy ions. The solid curves show the pickup energy at each \(L\) shell along the Voyager trajectories.
the flow varies from near corotation to much less than corotation.
The observed deviation from corotation indicates that mass is being added to the magnetosphere faster than the planet's rotation can accelerate this mass. The coupling of the plasma via the magnetic field to the planet's rotation is a complicated two-step process [_[PERSON]_, 1979; _[PERSON]_, 1989]. Looking from the outside in, the magnetic field lines in the magnetosphere have their feet in Saturn's ionosphere. The ionosphere is coupled to the upper atmosphere through collisions of the ionospheric plasma and the neutral atmosphere. The upper atmosphere, in turn, is coupled to all the layers of atmosphere below it through eddy diffusion or the rate of vertical mixing. When plasma is added to the magnetosphere, currents flow along the field lines and close in the ionosphere; the \(\mathbf{J}\times\mathbf{B}\) (where \(\mathbf{J}\) is current) force accelerates the plasma. If mass is added too rapidly, not enough current can flow through the ionosphere to fully accelerate the plasma, so the ionosphere and atmosphere rotate differentially and the plasma moves at less than the corotation velocity. If the atmosphere cannot transfer momentum upward fast enough to provide the energy to accelerate the plasma, then the upper layers of
Figure 10: The azimuthal velocity. The dotted curves show the corotation velocity along the Voyager trajectories.
the atmosphere may lag the planet's rotation, leading to subcorotation of the ionosphere and magnetosphere. So the observed subcorotation of the magnetospheric plasma indicates that Saturn is adding plasma to its magnetosphere at a rate too fast to maintain corotation. The decreases in speed near Rhea and Dione mark these moons as plasma sources, whereas the decrease inside \(L=6\) points to the rings and inner moons as plasma sources. Outside Rhea the plasma remains subcorotational despite the lack of plasma sources between Rhea and Titan. This indicates plasma is moving outward; the corotation speed increases linearly with distance, so the plasma must be accelerated (by the same mechanism) as it moves outward. If the mass outflow is too fast, corotation cannot be maintained.
The profile of \(v_{\varrho}\) in Figure 11 shows that beyond 12 \(R_{g}\) outward flow of tens of kilometers per second is common, although shorter periods of inward flow are also observed. The plot of \(v_{\varrho}\) (north-south) in Figure 11 shows that Voyager 1 observed little north-south flow, whereas Voyager 2 saw substantial northward and southward flows in the mantle region outside \(L=13\). The northward flow generally corresponds to regions of outward flow, and the southward flow corresponds to regions of inward flow.
Two mechanisms probably combine to give the observed nonazimuthal flows in the mantle region. One is the \"breathing\" of the magnetosphere in response to changes in the solar wind pressure. The magnetosphere is in a rough equilibrium between the internal pressure of Saturn's magnetic field and the external push from the solar wind. The solar wind pressure can change by an order of magnitude or more, causing the whole magnetosphere to shrink or expand, which gives rise to plasma flow. This causes the magnetopause location to vary; the three spacecraft encounters crossed the magnetopause upstream of the planet at distances varying from 17 to 24 \(R_{S}\)[_[PERSON] et al._, 1984]. This \"breathing\" gives rise to outward and anticapatorward flow during magnetospheric expansion and inward and equatorward flow during contraction. This process is most effective near the magnetopause. The second mechanism produces a persistent outward flow driven by the centrifugal force due to Saturn's rotation. This force results in blobs of plasma breaking off the outer edge of the plasma sheet at about \(L=12\) and moving outward [_[PERSON]_, 1983]. These flux tubes are then replaced by inward moving, relatively empty flux tubes. Thus the superposition of these mechanisms would suggest that the predominate mass flow is outward throughout the outer magnetosphere, with a superposed, externally driven in-and-out flow.
This picture corresponds well with the observations. The largest nonazimuthal flows are in the mantle region where the effect of both centrifugally driven plasma blobs and magnetospheric size changes are greatest.
Figure 11: The \(p\) (away from spin axis) and \(z\) north-south components of the plasma flow.
Voyager \(1\), near the equator, observes little north-south flow. Voyager 2, which is 4-5 \(R_{S}\) north of the equator, observes northward flow when flow is outward and southward flow when flow is inward, consistent with the breathing model. For both spacecraft the average flow is outward, consistent with the underlying centrifugally driven flow being outward.
#### 3.2.4 Overall Picture
From the very limited view provided by these two passes through the Saturnian magnetosphere, we would like to construct a global picture of the magnetospheric plasma. To achieve this goal, some assumptions are made, the number one assumption being that the magnetosphere is stable in time. This assumption is clearly not valid in the outer magnetosphere where the plasma structure observed by Voyager 1 and Voyager 2 looks very different. The structure in the mantle may be controlled by the external influence of the solar wind. In the region inside \(L=10\)-12 the plasma parameters seem to vary relatively smoothly, with differences between the passes through the same \(L\) shell at least qualitatively ascribable to latitudinal differences in the trajectories. The other assumption is that the magnetosphere is azimuthally symmetric, so that there are no longitudinal or local time variations. The timescale for plasma processes is slower than for the rotation rate, which is consistent with this assumption. However, some parameters, such as the ionospheric conductivity, vary in local time (the conductivities are lower on the nightside since sunlight cannot ionize the atmosphere), so this assumption may not always be correct. Given the paucity of data coverage, however, we must make these assumptions.
A schematic overview from _[PERSON] et al._ (1983) is shown in Plate 1. Plate 1 is color coded by plasma temperature as shown by the color bar. The plasma in the inner magnetosphere is characterized by a cold plasma torus confined to near the equator. The torus increases in width outward to its outer boundary at about \(L=15\). The region outside the plasma torus and at high latitudes contains hot, tenuous plasma; some colder, denser regions in the mantle are the plasma blobs which have broken off the plasma sheet or Titan plumes. New results since Plate 1 was made indicate that the H cloud extends inward to Saturn and that a cloud of heavy neutrals is present in the inner magnetosphere.
A quantitative model of plasma densities (_[PERSON]_, 1990; _[PERSON]_, 1995) uses the equation for parallel pressure (_[PERSON]_, 1983) to calculate plasma densities along magnetic field lines,
\[\frac{\partial P_{\parallel}}{\partial s}-(P_{\parallel}-P_{ \perp})\,\frac{1}{B}\frac{\partial B}{\partial s}-n_{\prime}m_{i}\,\frac{ \partial}{\partial s}\left(\frac{1}{2}\,\Omega^{2}p^{2}\right)\] \[+n_{\prime}\,\frac{\partial}{\partial s}\left(\frac{GM_{\prime}m _{i}}{r}\right)+n_{\prime}Z_{\mathcal{G}}\,\frac{\partial\phi}{\partial s}=0. \tag{1}\]
The first term is the pressure gradient force, where \(s\) is distance along a field line. The second term is the force
Figure 1: A schematic diagram of noon and dawn views of Saturn’s magnetosphere adapted from _[PERSON] et al._ (1983) showing various regions of the magnetosphere coded according to the plasma temperature. Cooler plasma is located in the inner magnetosphere near the equatorial plane. The neutral hydrogen cloud which extends throughout the magnetosphere is shown by the dappled region. The cross-hatched area shows the location where significant OH neutral densities are present. The E ring opacity is indicated by a gray scale, where darker regions have higher opacity. The satellites M, E, T, D, and R are Mimas, Enceladus, Tethys, Dione, and Rhea, respectively.
due to the magnetic mirror effect, which is zero unless the plasma is anisotropic. The third term is the centrifugal force, where \(\rho\) is the distance from the spin axis, \(\Omega\) is the rotation rate of the plasma, and \(m_{\ast}\) and \(m_{\ast}\) are the mass and number density of each ion species \(i\), respectively. This force pushes the plasma outward along field lines and thus toward the equator. The next term is the gravitational force, where \(G\) is the gravitational constant and \(M_{S}\) the mass of Saturn. This term is only important close to the planet, as it becomes small compared to the centrifugal term outside synchronous orbit. The last term is the force exerted by the ambipolar electric field set up by the interaction of plasma components of different mass and charge \(Z\). Each ion and electron component requires an equation of this form. The resulting set of equations is closed using the condition of charge neutrality and can be solved using an iterative method [_[PERSON] and Sullivan_, 1981]. Starting with densities and temperatures at one point on a magnetic field line and using (2), the latitudinal density profile is derived.
The other assumption made is that the temperature and temperature anisotropy are constant along a magnetic field line. This is not true; the plasma distribution tends toward isotropy as the latitude increases [_[PERSON] and [PERSON]_, 1992], and the temperatures of both ions and electrons should decrease with latitude, the ions because they lose energy moving against the centrifugal potential and the electrons because they lose energy moving against the potential due to the ambipolar electric field [_[PERSON]_, 1993]. This is readily apparent in the Voyager \(1\) data where the temperatures at the same \(L\) shell inbound and outbound are higher near the equator. A better representation of the plasma distribution along magnetic field lines taking into account the temperature variations is needed. Until that time we use models which average the observed temperatures and let the anisotropy be a free parameter.
The resulting density contour plots are shown in Figure 12. The plots show the H\({}^{+}\), O\({}^{+}\), and electron densities. Remember that the closest observations were at \(L=2.7\), so values inside this are pure extrapolation. The calculation is cut off at 50\({}^{\circ}\) latitude. Inside \(L=10\) the plasma, and particularly the heavy ions, are tightly confined to the equator. The H\({}^{+}\) ions are lighter and thus extend farther from the equatorial plane. Starting at about \(L=10\), the plasma disk increases in width. Outside \(L=12\), time dependent effects are important; the model attempts to show a representative snapshot of this region, but the actual plasma parameters at any point probably change rapidly.
This model fits the plasma density observations from both Voyager \(1\) and Voyager \(2\) very well. As mentioned above, the free parameter in the model was the temperature anisotropy. This quantity is very difficult to derive from the data since the plasma detector was looking primarily in the perpendicular direction, and derivation of the anisotropy requires knowledge of the temperature both parallel and perpendicular to the magnetic field. Figure 13 shows the anisotropies (\(\mathcal{A}=T_{\perp}/T_{\parallel}-1\)) that give the best fit to the data (the solid curve), that is, best reconcile the Voyager \(1\) inbound, Voyager \(1\) outbound, and Voyager \(2\) inbound data. For H the anisotropy is \(2\) in the inner magnetosphere, relaxing to \(0\) (isotropy) in the outer magnetosphere. The heavy ions are more anisotropic, with values of \(5\) in the inner magnetosphere, again relaxing to \(0\) by \(L=12\). The data points (with \(1\)\(\sigma\) errors) are from the relatively few places where the anisotropy can be derived from the data [_[PERSON]_, 1988; _[PERSON] et al._, 1994].
The anisotropy of the plasma indicates that the source of the plasma is centered near the equator. When ions are created via the ionization of neutrals, they gain perpendicular but not parallel energy. Thus they are formed at their mirror point and cannot move to higher latitudes than their creation latitude. A source of ions near the equator would give ions with much larger perpendicular than parallel energy as observed. Collisions will tend to isotropize the plasma, so the persistence of the anisotropy indicates that the plasma lifetime is shorter than the isotropization time.
## 4 Neutral Sources
### Icy Satellites and Rings
We have seen that Saturn's magnetosphere contains protons and heavy ions with densities which decrease outward. The temperature profile suggests that the plasma is created locally inside \(L=12\). This suggests that the neutral cloud from which the plasma is formed extends throughout this region. Neutrals can be generated from the surface of the rings and satellites by sublimation or by sputtering of the surface by UV photons, ions, electrons, and micrometeorites. The icy satellites and rings are composed primarily of water ice. The physics of sputtering of surfaces by particle bombardment in theory and practice as applied to planetary bodies has largely been developed by [PERSON] and coworkers at the University of Virginia [_[PERSON]_, 1990]. For understanding magnetospheric implications the most important number is the yield, the number of molecules knocked off the surface by each incident particle. Sputtering experiments show that yields increase as the energy of the sputtering particles increases, as the mass of the sputtering particle increases, and as the temperature of the sputtered surface increases. For incident ions with energies greater then 50 keV, yields are about 3 H\({}_{2}\)O for each proton and 55 H\({}_{2}\)O for each oxygen colliding with the surface of a Saturnian satellite or ring particle [_[PERSON] et al._, 1995]. The thermal plasma strikes only the satellite hemisphere facing into the direction of the corotating flow; each incident thermal proton sputters roughly 1 H\({}_{2}\)O, H, H\({}_{2}\), and O\({}_{2}\) from the satellite surface, and each incident thermal O\({}^{+}\) ion sputters about 10 H\({}_{2}\)O, H, H\({}_{2}\), and O\({}_{2}\) from the satellite surface [_[PERSON] et al._, 1985].
The largest source of neutrals seems to be sputtering by energetic ions. Recent laboratory studies of sputtering rates [_[PERSON] et al._, 1995] show that sputtering of Enceladus, Tethys, Dione, and Rhea provides a source of 1.6 \(\times\) 10\({}^{26}\) mol s\({}^{-1}\). Sputtering of the E ring provides another 0.5 \(\times\) 10\({}^{26}\) mol s\({}^{-1}\) and is the dominant neutral source near Enceladus. These numbers are lower limits, as _[PERSON] et al._ [1995] used conservative values for the fluxes of sputerers, and the combination of UV photons, ions, and electrons bombarding the surface could produce larger yields than these processes acting separately.
Photosputtering by solar UV photons is not important for the satellites and E ring, where plasma fluxes are high but may be the dominant source of neutrals in the inner rings. The composition of the sputtered particles is mainly H\({}_{2}\)O, with smaller amounts of H, H\({}_{2}\), and O\({}_{2}\).
Direct sublimation becomes important for surface temperatures of over about 120 K; the Saturnian satel
Figure 12: Contours of proton, heavy ion, and electron density in the Saturnian magnetosphere. The heavy ions are confined tightly to the equatorial plane, while the protons have a larger scale height.
lites have temperatures of 100 K or below [_[PERSON] et al._, 1984], so this process is not important for Saturn. The electron mass is too low for these particles to be effective sputteres.
Micrometeoroids are small particles which can collide with satellites and ring particles and knock off large numbers of neutral molecules. The flux of micrometeoroids is not well known. These particles have radii of 1-100 \(\mu\)m, with fluxes decreasing rapidly with size. Impacts of these particles on satellites and rings eject vaporized H\({}_{2}\)O into the magnetosphere. Estimates of the number of molecules sputtered from the rings range from 8 \(\times\) 10\({}^{26}\) to 5 \(\times\) 10\({}^{29}\) mol s\({}^{-1}\)[_[PERSON]_, 1987]. If the largest estimates of micrometeorite fluxes are correct, then micrometeorite sputtering can compete with ion sputtering as the largest neutral source.
Another mechanism suggested as a source of additional neutrals is collisions of E ring particles with satellites embedded in the ring (which extends from 3 to 8 \(R_{S}\)) [_[PERSON] and [PERSON]_, 1994]. If the ring particles' orbits were circular, then the relative velocity between the moons and ring particles would be small, and collisions would be of low energy and ineffective at producing neutrals. The ring particles can become charged [_[PERSON] et al._, 1995], however, and thus subject to Lorentz forces (the same forces causing the plasma to corotate). These small (1 \(\mu\)m radius) particles act partially as neutrals and partially as charged particles, with the results that the orbits can rapidly become eccentric [_[PERSON] et al._, 1992; _[PERSON]_, 1993]. The difference in speed between the particles on eccentric orbits and the moons can exceed 5 km s\({}^{-1}\), so that collisions with the moons could generate enough ejecta to sustain the E ring and create sufficient neutrals to match the OH observations [_[PERSON] and [PERSON]_, 1994]. However, _[PERSON] et al._ [1995] state that impacts of E ring particles will not directly produce significant water vapor, so this mechanism may not be viable.
The distribution of the neutrals depends on the ejection energy from the sputtered surface and the lifetime of the neutrals. Neutral densities are generally found using a Monte Carlo procedure [i.e., _[PERSON] et al._, 1989; _[PERSON] and [PERSON]_, 1991; _[PERSON]_, 1995]. Particles are launched on trajectories with initial energy distribution and followed through the magnetosphere. Those which collide with Saturn or another body are removed from the calculation. Each time step there is a probability the particle will be lost via collision with a ring particle, ionization, or charge exchange. After enough particles are followed through this process to form a valid statistical sample, the number of neutrals in each trajectory element is summed and scaled to the total source rate to get the neutral density distribution. Results of these models show that the neutral cloud is tightly confined to the equator, especially in the ring region, with density enhancements near each of the satellites. _[PERSON] and [PERSON]_ [1991] use the upper limit of the micrometeorite sputtering range, which provides a total ring source of 4.9 \(\times\) 10\({}^{29}\) mol s\({}^{-1}\), and find peak densities are 39,000 cm\({}^{-3}\) at 1.4 \(R_{S}\). Subsequent HST observations show that these values are probably much too large, as we discuss in section 5.
### Hydrogen Source
Titan has a significant atmosphere composed mainly of N\({}_{2}\) and CH\({}_{4}\). Light neutrals, H and H\({}_{2}\), can escape from Titan's atmosphere and form a neutral cloud in the outer magnetosphere. The source of H is roughly 5 \(\times\) 10\({}^{27}\) H s\({}^{-1}\), or 8 kg s\({}^{-1}\), which escapes into the magnetosphere. Predictions for the escape of H\({}_{2}\) range from 5 \(\times\) 10\({}^{27}\) [_[PERSON] and [PERSON]_, 1983] to 1.5 \(\times\) 10\({}^{28}\) [_[PERSON] et al._, 1984]. The interaction between the corotating magnetosphere plasma and the ionosphere result in a flux of 10\({}^{27}\) s\({}^{-1}\) N\({}_{2}\) escaping into the magnetosphere [_[PERSON]_, 1984]. The only one of these species which can be observed directly is H, which emits Lyman alpha radiation which can be detected by UVS instruments. The Voyager UVS experiments detected this radiation; the original data interpretation was of a torus of H with density of about 20 in the vicinity of Titan's orbit [_[PERSON] et al._, 1981; _[PERSON] et al._, 1982]. Subsequent analysis of more UVS spectra suggests that the H cloud probably has two components, one associated with Titan which is azimuthally asymmetric and centered on Titan's orbit and one which extends in to Saturn's surface which has an intensity peak on the duskside of Saturn [_[PERSON] and [PERSON]_, 1992] which may be due to solar radiation pressure [_[PERSON] and [PERSON]_, 1993; _[PERSON]_, 1996]. Dissoica
Figure 13: Observed anisotropies for protons and heavy ions. The solid curve shows the anisotropies used in the model to best fit all the data.
tion of H\({}_{2}\) in the sunlit hemisphere, which is then ejected from the atmosphere on escape and ballistic trajectories, could account for the observations if the ejected flux is 10\({}^{30}\) atoms s\({}^{-1}\)[_[PERSON] and [PERSON]_, 1992]. _[PERSON] et al._ [1981] detected a cloud of H associated with Saturn's rings with densities of about 400 cm\({}^{-3}\), radial extent 2-3 \(R_{S}\), and vertical extent 1 \(R_{S}\). The same processes that produce the heavy ion cloud in the ring region should produce H as well.
The combined H cloud from the Titan and Saturn source has been modeled numerically taking into account gravitational forces, losses, and collisions [_[PERSON] and [PERSON]_, 1988]. The Titan source is found to produce a cloud with a density of about 60 cm\({}^{-3}\) which is sharply peaked at Titan's orbit. The energetic neutral H from Saturn's upper atmosphere produces a cloud with a density of about 300 cm\({}^{-3}\) at the exobase decreasing to 3-4 cm\({}^{-3}\) near Titan. (The exobase is the point where the mean free path of a particle equals the collision frequency; above the exobase, collisional equilibrium is not maintained.) The density profiles derived by _[PERSON] and [PERSON]_ [1988] would produce UV emissions which match observations by the Voyager 1 and 2 UVS experiments fairly well; a Titan source alone cannot match the observations. Since the observations are fairly well matched by the exospheric source, the ring source of H could be relatively unimportant. A cloud of H\({}_{2}\) with similar densities is expected near Titan as well as a N cloud with densities a factor of 5-10 less than those of H and H\({}_{2}\). These other neutrals do not emit radiation as efficiently as H and have not been detected. _[PERSON] and [PERSON]_ [1993] pointed out that radiation pressure was an important effect neglected by these authors which can lead to asymmetries in the neutral cloud. At the present time the calculation of H densities has not been performed including this effect.
The H atmosphere surrounding the rings has also been modeled using a Monte Carlo technique [_[PERSON]_, 1984]. Photosputtering was ruled out as the source of this cloud since the cloud brightness does not vary over the solar cycle (whereas the Sun's UV output does) or with the inclination of the ring to the Sun. Micrometeoroid impact is sufficient to produce the ring cloud if a rate a factor of 10 above the minimum estimate is used, which is well within the uncertainties for this parameter.
### Neutral Losses
Some neutrals collide with satellites and ring particles and stick, but most are removed via interaction with the plasma and UV environment. A neutral can collide with an ion and lose an electron (charge exchange), it can collide with an electron and have an electron knocked off (electron impact ionization), or a UV photon can knock an electron off the neutral (photoionization). In addition, molecular neutrals (such as H\({}_{2}\)O) can be dissociated by photons and electrons (i.e., H\({}_{2}\)O + hv \(\rightarrow\) H + OH). Figure 14 shows a plot of OH and H\({}_{2}\)O lifetimes as a function of distance from Saturn for loss by various processes using the plasma conditions from Figure 13. Inside 4 \(R_{S}\) the electron temperature is low, and charge exchange with heavy ions dominates the loss of H\({}_{2}\)O. Outside \(L=4.5\), photodissociation and electron impact ionization dominate. Lifetimes for H\({}_{2}\)O range from 4.5 \(\times\) 10\({}^{6}\) to 8.3 \(\times\) 10\({}^{6}\) s (50-100 days). The OH lifetime is longer than the H\({}_{2}\)O lifetime, with losses close to Saturn caused mainly by photodissociation and losses far from Saturn caused by electron impact. For O atoms the dominant loss is charge exchange with O\({}^{+}\) ions inside \(L=8\) and electron impact ionization outside \(L=8\), with lifetimes increasing from 10 days in the inner magnetosphere to 200 days at \(L=12\). For H, charge exchange with protons and heavy ions is equally effective in the inner magnetosphere; outside \(L=6\), electron impact ionization of H becomes important. Lifetimes increase from 20 to 200 days from the inner to outer magnetosphere; note that as the H\({}^{+}\) density increases inside \(L=4\), the lifetimes will decrease. The common theme for all these neutrals is that inside \(L=6\) the dominant loss process is charge exchange, which removes neutrals but does not add new ions. Farther out, where the electron temperature is larger, most of the neutrals produce an increase in the plasma population.
## 5 Models
The observations are limited in what they tell us about the plasma and neutral environment near Saturn. The plasma observations cannot distinguish between heavy ions, and only a few neutral species can be observed and only with line-of-sight measurements. These gaps in measurements can be filled in with models of the physics and chemistry occurring in Saturn's magnetosphere. The goal is to develop models that correctly predict the observations that we do have, then use these models to provide information on parameters not yet observed. These model results can then be tested by Cassini which is scheduled to enter into Saturn orbit in 2004.
All of the plasma models contain a transport term, so a brief discussion of plasma transport in magnetospheres is in order. Transport can occur as an organized convective system with inward flow in some regions and with outward flow elsewhere or as a stochastic process, that is, diffusion. At Saturn the latter process is expected to dominate, since the rapid rotation of Saturn creates a large, stable plasmasphere. Diffusion is thought to be driven by changes in neutral winds, which couple to the ionospheric plasma where the magnetic field lines are anchored [_[PERSON]_, 1972; _[PERSON]_, 1974]. The motions of the field lines driven by these winds result in a stochastic motion of the plasma. This atmospherically driven diffusion has a diffusion coefficient (which determines the diffusion rate) which varies as \(L^{3}\). One way of measuring the diffusion rate is to look at how fast depletions in the plasma density caused by the rings and satellites are refilled with plasma. When a moon or ring is present, the plasma which runs into the moon or ring particles is removed, leaving a hole in its wake. The diffusive transport process fills in the plasma depletion. By estimating how many particles are absorbed and knowing how long ago the particles were absorbed, the diffusion rate can be calculated. _[PERSON]_(1983, 1985, 1989) studied these satellite sweeping signatures and determined the diffusion coefficient varied as \(L^{3}\div 1\), consistent with the atmospherically driven diffusion mechanism. _[PERSON] and [PERSON]_(1986) set limits on the diffusion rate with an uncertainty of about 2 orders of magnitude. The lower limit is derived from the time needed to fill in satellite sweeping signatures (this is a lower limit because it assumes that satellite sweeping is the only loss mechanism). Upper limits are set by two methods; both depend on the observation that the energetic particle phase space density decreases inward. Some of this loss is presumed to be due to particles streaming along field lines and colliding with the atmosphere of Saturn. Particles can only be lost as fast as they can be scattered into the loss cone, the region of phase space with trajectories intersecting the atmosphere. Thus inward transport is limited by this maximum loss rate. The particles which enter the atmosphere produce auroral emissions; the second limit is that inward transport not be so fast that the losses would produce observable aurora (which was not detected). The diffusion limits _Paonessa and Cheng_(1986) obtain from this analysis are roughly \(2\times 10^{-9\times 1}\ L^{3}\ R_{s}^{2}\ \rm s^{-1}\). This is roughly equivalent to a residence time of 10-1000 days at Dione at \(L=6\). Although the uncertainties are large, these numbers provide some constraints on magnetospheric models.
The first and least sophisticated models are zero-dimensional (\"0-D\") models, where continuity equations are solved assuming the neutrals and plasma are constant within a box located at some distance from Saturn. Equations of the form \(\partial n_{i}/\partial t=S_{i}\ -\ L_{i}\) are solved iteratively, where \(n_{i}\) is the density of each species included in the model, \(t\) is time, and \(S_{j}\) and \(L_{i}\) are source and losses, respectively, for each species. Sources for neutrals are sputtering of H\({}_{2}\)O, O\({}_{2}\), H\({}_{2}\), and H from the icy surfaces of rings and satellites by energetic particles, corotating plasma, and micrometeorites. The sputtering by plasma is determined self-consistently; the model determines the plasma density which then determines the sputtering source. Sputtering by energetic particles is
Figure 14: Lifetimes of the major neutral species in Saturn’s inner magnetosphere. Lifetimes for each relevant process are shown in addition to the total lifetime.
based on Voyager data, and sputtering by micrometeorites is based on estimates in the literature. The neutrals can be lost via ionization, charge exchange, or dissociation into other neutrals. The ions are lost by charge exchange, recombination, or transport (transport is added in this type of model as a loss term of the form 1/\(\tau\), where \(\tau\) is the transport time and is varied to give good fits to the data). This type of model gave reasonable agreement with the plasma data (_[PERSON] et al._, 1986) using published sputtering rates if transport rates were negligible inside Rhea's orbit. The observation of large amounts of H in the inner magnetosphere (_[PERSON] and [PERSON]_, 1992) could not be reproduced, however, with the accepted sputtering rates (_[PERSON] and [PERSON]_, 1987). A similar model was used by _[PERSON] and [PERSON]_ (1992); they used energy balance considerations and the observed limits on the O\({}^{+}\)/O\({}^{++}\) ratio to constrain the transport and source rates. Their results showed that large neutral densities are necessary to account for the low electron temperature and that large source rates are needed, 2.8 \(\times\) 10\({}^{27}\) O s\({}^{-1}\) and 3.5 \(\times\) 10\({}^{26}\) H\({}_{2}\)O s\({}^{-1}\). They also found it necessary to use a diffusion time proportional to mass/charge in order to remove protons more rapidly; this is not supported by the generally accepted diffusion theory.
The 0-D model has several obvious problems. A major fault is that is does not account for particles which move in from outside the box. Another is that it treats the system as if it were homogeneous, whereas both neutrals and plasma density and plasma temperature decrease rapidly with latitude. The next step up in modeling is a 1-D model, with the dimension being radial distance. This type of model includes radial diffusion of plasma as well the atomic reactions. The diffusion equation is of the form (_[PERSON]_, 1968; _[PERSON]_, 1978)
\[\frac{\partial N\mathcal{L}^{2}}{\partial t}=L^{2}\frac{\partial}{\partial L} \left(\frac{D_{LL}}{L^{2}}\frac{\partial N\mathcal{L}^{2}}{\partial L}\right)+ S_{s}-R_{s}, \tag{2}\]
where \(N\) is the number of ions in a magnetic flux shell per unit \(L\), \(D_{LL}\) is the diffusion rate, and \(S\) and \(R\) are source and loss terms, respectively. The diffusion rate is usually expressed in the form \(D_{LL}=KL^{m}\), where \(K\) and \(m\) are constants. Inner and outer boundary conditions are necessary; these are usually that the plasma density go to zero at the planet (\(L=1\)) and the magnetopause (\(L=20\)). _[PERSON]_ (1990) used such a model and, assuming all the heavy ions were O\({}^{+}\), found that diffusion was the most important plasma loss process with residence times of 25 days near Dione. He adopted the _[PERSON] et al._ (1989) neutral source rate of 10\({}^{20}\) s\({}^{-1}\) and also found that the model tolerated only small amounts of H.
The next advance was development of a 2-D plasma model which calculated plasma densities as a function of latitude and radial distance (_[PERSON]_, 1992). Including latitude variation allows more accurate modeling of the chemistry since both ion and neutral densities decrease with latitude. This is accomplished by adding the parallel pressure equation (equation (1)).
The results of this model were that heavy ions have a residence time of at least 50 days at Dione and that H densities must be low. The sputtering calculations of _[PERSON] et al._ (1989) and _[PERSON] and [PERSON]_ (1991) showing a source of a few times 10\({}^{27}\) distributed over the entire magnetosphere were used as input in this model.
Models of the neutral cloud have also progressed. _[PERSON]_ (1984) used a Monte Carlo scheme to find the geometry of the H ring cloud for different escape velocities. _[PERSON] et al._ (1989) calculated the extent of neutral clouds produced by sputtering of the inner moons using initial particle velocities based on sputtering experiments and loss rates based on the plasma observations. They found the neutral clouds were tightly bound to the equator with peak densities near the satellites and that the plasma source from this cloud was widely distributed in \(L\) shell. _[PERSON] and [PERSON]_ (1991) added the ring source of H\({}_{2}\)O to this calculation and derived large neutral densities (up to 39,000 cm\({}^{-3}\)) in the ring plane near the planet and showed that the rings are an important plasma source. _[PERSON] et al._ (1995) present improved laboratory results and include the E ring in their calculation of source rates and find a total source of H\({}_{2}\)O in the satellite region of 1.7 \(\times\) 10\({}^{26}\) s\({}^{-1}\).
By 1993 the modeling had reached an impasse, with high neutral density, high source rate, high transport models on one side and low neutral density, low source rate (as determined by sputtering calculations), slow transport models on the other side. This impasse was broken by the observation of _[PERSON] et al._ (1993) of a large OH density, 160 cm\({}^{-3}\), at 4.5 \(R_{S}\). This was larger than even the _[PERSON] and [PERSON]_, (1992) model result and implied a much larger neutral source than previous sputtering work had suggested. Follow-up observations at 4.5, 6, and 10 \(R_{S}\) confirmed the large OH densities and showed a rapid density decrease with distance (_[PERSON] and [PERSON]_, 1995). The _[PERSON] et al._ (1996) observations showed that the neutral OH extended into the ring region. It was quickly recognized that these observations imply a larger source of neutrals than previous calculations had predicted. The University of Virginia group reconsidered the sputtering mechanisms but, even using the most optimistic yields, were short of the required source rate by a factor of at least 4 (_[PERSON] et al._, 1993; _[PERSON] et al._, 1995).
In light of these OH observations the models require revision. A model has been developed which is a composite of the 0-D and 2-D models described earlier (_[PERSON] et al._, 1998). The magnetosphere is divided into a grid with grid size 0.5 \(L\) by 1\({}^{\circ}\) latitude. The neutral source is simulated by adding neutrals to each grid point each time step. The neutral density and scale height of 0.5 \(R_{S}\) is consistent with observations and model results. The radial distribution and scale height of the source above the equator are free parameters adjusted to give good fits to the data. The atomic and molecular reactions are calculated each time step at each grid point, and the densities of each ion and neutral species change as a result of these reactions. The total amount of each ion is then summed along each \(L\) shell, and the plasma is allowed to diffuse according to (1). The diffusion coefficient is the other model parameter which is varied. The plasma density at each latitude is then found using (2), and the process is repeated until steady state is reached. The improvement in this model is that both the plasma and neutral densities are calculated and that plasma transport is included. The weakness is that neutrals are not allowed to move.
Results from this model are shown in Figure 15. The top plot shows a comparison of equatorial proton and heavy ion densities inferred from observations with the calculations. Although the model is run out to 20 \(R_{S}\), the results are not applicable outside 12 \(R_{S}\) where rapid, centrifugally driven transport begins. The best fits are found with the neutral source shown in Figure 16 and a diffusion coefficient of \(1\times 10^{-8}\)\(L^{3}\)\(R_{S}^{2}\) s\({}^{-1}\). The heavy ion profile matches the data fairly well out to \(L=12\). The proton profile does not fit the data as well. The discrepancy inside \(L=4\) is an instrumental affect, since corotating protons begin to fall below the 10 eV threshold of the PLS instrument. However, the calculated
Figure 15: Model results showing the ion and neutral equatorial density profiles predicted by the model. Also shown are the ion observations.
profile is larger than the observed densities throughout the inner magnetosphere. This has been a continuing problem in efforts to understand the inner magnetosphere; large neutral densities lead to larger proton densities than observed.
The model also gives information on the relative importance of each ion species. Figure 17 shows the fraction of the total charge density for each ion and the fraction of the neutral density for each neutral species. Near Saturn, O\({}^{+}\) is the dominant ion, and it remains the primary heavy ion throughout the magnetosphere. Protons make up the largest fraction of the charge density outside 10 \(R_{S}\). Both OH\({}^{+}\) and H\({}_{2}\)O\({}^{+}\) compose 10-20% of the total density outside \(L=4\). Note that since the neutral densities decrease and transport rates increase with distance, the charge fractions approach constants. Near Saturn, OH is the dominant neutral; at about 6 \(R_{S}\), O and H take over as the dominant neutral species.
The neutral densities predicted by the model are shown in Figure 17. The major neutral species are H, O, OH, and H\({}_{2}\)O. The neutral densities all peak at about 4.5 \(R_{S}\) where the source is largest. The OH density is over 700 cm\({}^{-3}\) at 4.5 \(R_{S}\) and 25 cm\({}^{-3}\) at 2 \(R_{S}\). The H density is near 100 cm\({}^{-3}\) from 4.5 to 6.5 \(R_{S}\) and decreases to 3 cm\({}^{-3}\) near the planet. The model predicts O densities of over 100 cm\({}^{-3}\) from \(L=4.5\) to \(L=6.5\) and H\({}_{2}\)O densities which are comparable to the OH densities inside 3 \(R_{S}\) but are a factor of 4 less than the OH densities outside this distance. The total neutral density is 3-10 times the plasma density throughout the inner magnetosphere.
Figure 16 shows the source profile of neutrals which gives the results shown in Figures 15 and 17. The plot shows the number of neutrals in a flux shell of unit width in \(L\). The H\({}_{2}\)O source has a distinct peak at \(L=4.5\), near Enceladus. The H profile we used was constant with \(L\) and much smaller than the H\({}_{2}\)O source in the inner magnetosphere. The scale height of the source which gave reasonable fits to the OH observations is \(H=0.35\)\(R_{S}\). Larger scale heights would produce too much emission at higher latitudes to be consistent with the _[PERSON] et al._ [1996] results. The best fit from the latitude scans at 2.3 \(R_{S}\) gives a scale height of 0.45 \(R_{S}\), but 0.35 \(R_{S}\) is well within the error bars. The total source of H\({}_{2}\)O is 1.4 \(\times\) 10\({}^{27}\) s\({}^{-1}\), and the total source of H is 2.3 \(\times\) 10\({}^{26}\) s\({}^{-1}\). As shown by _[PERSON] et al._ [1998], the OH brightnesses predicted by this model fit the observations fairly well.
One function of such a model is to point out where our understanding of the system is lacking. The neutral densities found here are much less than those given by _[PERSON] and [PERSON]_ [1991] in the ring region. They find peak densities of over 3000 cm\({}^{-3}\) inside 3 \(R_{S}\), a factor of 100 larger than these results. These large densities are directly inconsistent with the HST OH observations and indirectly inconsistent with the Voyager plasma observations, as increasing the neutral density in the ring regions would result in too large an ion density. Since _[PERSON] and [PERSON]_ [1991] use the upper end of the micrometeoroid flux estimates in their model, this discrepancy may suggest that these estimates are too high.
Another problem is that the source in the satellite region is larger than predicted by sputtering. To match the observation of 160 cm\({}^{-3}\) OH at 4.5 \(R_{S}\), the model predicts a total heavy neutral density (including O, OH,
Figure 16: The neutral source profile which shows reasonable agreement with the data.
Figure 17: Fractions of the density composed of each ion and neutral species.
and H\({}_{2}\)O) of about 250 cm\({}^{-3}\). This is more than a factor of 10 larger than the values predicted by _[PERSON] and [PERSON]_ (1991) based on sputtering of the main rings and satellites. If sputtering of the E ring is considered, the source near Enceladus is increased by a factor of 4, but the densities derived from the model, 40\(-\)80 cm\({}^{-3}\), are still a factor of 2-4 below those observed (_[PERSON] et al._, 1995). This problem was first recognized by _[PERSON] et al._ (1993), who suggested micrometeoroid fluxes could be higher than previously thought (but which seems inconsistent with the observations near the rings). _[PERSON]_ (1996) modeled the neutral clouds from different sources and also finds the OH densities are too small by a factor of 2 unless an additional source is added. We discussed in section 4 the possibility that collisions of E ring particles with satellites embedded in the ring are a significant neutral source which could resolve this problem (_[PERSON] and [PERSON]_, 1994). Given that the peak source needs to be near 4.5 \(R_{S}\), Enceladus (3.9 \(R_{S}\)) and Tethys (5.1 \(R_{S}\)) are the most likely candidates. Since peak neutral densities typically occur outside the source, of these two choices Enceladus is probably the most likely.
The important result is that a model of plasma transport and atomic physics can do a reasonable job of simulating observations. Much improvement to the models is left to be done. Ideally, one would like to combine a 2-D model of the neutral cloud of the _[PERSON] et al._ (1989) type with a 2-D plasma transport model. We hope progress will be made in that direction. The current models ignore variations in the azimuthal direction. This neglect can be partially justified since the neutral and plasma lifetimes are longer than either the corotation or orbital periods. However, we know that Jupiter's magnetosphere exhibits azimuthal variation with longitude and local time and by analogy so might Saturn. Future observations may show that 2-D models must be expanded to three dimensions to fully understand Saturn's magnetosphere.
## 6 Timescales
The models combine all the various processes to calculate the steady state plasma densities. A more intuitive feel for what processes are important can be gained by looking at plots of the timescales. These plots are shown in Figures 14 and 18; plasma parameters used in these calculations are those of _[PERSON]_ (1990), except that the fraction of each heavy ion comes from the model result. The transport rate shown is approximated as 1/D\({}_{LL}\), where \(D_{LL}=2.5\times 10^{8}\,L^{3}\,R_{2}^{2}\) s\({}^{-1}\), consistent with the model result. The neutral densities used are from the model. The times are calculated for equatorial densities; for processes depending on density, the characteristic timescales will be greater at higher latitude. Figure 18 shows a plot of neutral lifetimes as a function of distance for loss by various processes. For H\({}_{2}\)O, dissociation into H, H\({}_{2}\), and OH are by far the fastest processes. Only about 10% of the H\({}_{2}\)O becomes ionized. For OH, ionization and dissociation are comparable processes, so we expect more OH\({}^{+}\) than H\({}_{2}\)O\({}^{+}\) to be present. Lifetimes for OH are long compared to those of H\({}_{2}\)O (100-200 days), which is why the model results show much more OH than H\({}_{2}\)O. Most of the O which is formed is ionized via charge exchange with either H\({}^{+}\) or O\({}^{+}\). Lifetimes are about 10 days, but since more O is produced per second than OH (since the
Figure 18: Lifetimes of the major ions species. Lifetimes for each process plus the total lifetime are shown.
H\({}_{2}\)O density is less than the OH density), the total O density is comparable to the OH density. Most of the H is lost via charge exchange inside \(L=7\); outside \(L=7\), about 50% or H is ionized by electron impact, and 50% is ionized by charge exchange.
Figure 18 shows the timescales for the ions. For H\({}^{+}\), charge exchange is the dominant loss inside \(L=7\), and transport is the dominant removal process outside \(L=7\). The situation is similar for O\({}^{+}\), charge exchange removing ions inside \(L=7\) and transport removing ions outside \(L=7\). For H\({}_{2}\)O, recombination removes ions fastest inside \(L=5\), with transport being fastest outside \(L=5\). The plot for OH is similar to that for H\({}_{2}\)O\({}^{+}\). These plots show clearly that a break point occurs at about 6 \(R_{\rm S}\), inside of which transport is relatively unimportant and outside or which transport is the dominant ion removal mechanism.
A serious weakness of the modeling done to date is that energy is not included; the ion and electron temperatures are usually assumed equal to their measured values. We can compare relevant timescales to see if they are consistent with our assumptions. Figure 19 shows the timescales for temperature equilibration, isotropization, radiation, and ion removal for O\({}^{+}\), H\({}^{+}\), and electrons. The O\({}^{+}\) and H\({}^{+}\) are removed from Saturn faster than the timescales on which these other processes become effective; thus we expect the plasma to be anisotropic and for little energy transfer between species to occur. Electrons isotropize very quickly, so the electron population should be isotropic. Radiation is not fast enough to significantly cool the inner magnetosphere.
## 7 Summary and Outstanding Questions
Saturn's magnetosphere continues to surprise us. After the Voyager encounters the picture that first emerged was of a magnetosphere in many ways that of a scaled-down Jupiter. Neutrals were sputtered off the moons, ionized, then removed via atomic processes and transport. Plasma densities were smaller than at Jupiter, but neutrals were unimportant. This preliminary picture began to shift when the reanalysis of the UVS data suggested H densities of 100 cm\({}^{-3}\) in the inner magnetosphere. The detection of large OH densities verified that Saturn's magnetosphere was dominated by neutrals. Saturn's magnetosphere takes an intermediate place between Jupiter and the outer gas giants, Uranus and Neptune, with neutrals dominating the mass and density as at Uranus and Neptune but with plasma playing an important role in the magnetospheric dynamics as at Jupiter.
A consequence of the large neutral density is that the neutral source must be larger than previously assumed. Early sputtering calculations gave total source rates from the satellites of about 1 \(\times\) 10\({}^{26}\) s\({}^{-1}\); using this source gave neutrals densities of less than 10 cm\({}^{-3}\). The larger observed neutral densities require a source of at least 1 \(\times\) 10\({}^{27}\) s\({}^{-1}\), which is within a factor of 2 of recently revised sputtering predictions. Since these predictions are conservative, sputtering seems to be an adequate source.
Another controversial issue has been the importance of transport. The increase of temperature with distance out to at least \(L=12\) seems to be a strong indicator that transport times are longer than the ion lifetimes. This
Figure 19: Timescales for energy processes in the magnetosphere. The isotropization (\(\tau_{\rm iso}\)) and energy transfer times to different plasma components are shown, as well as the ion loss times and radiation loss time for electrons (\(\tau_{\rm rad}\)).
contradicts the calculations shown in Figure 18, however, which show that outside \(L=6.5\) transport is the primary ion loss mechanism. Thus another mechanism must heat the plasma or the neutral density must be larger (and electron density a bit lower) so that charge exchange losses are more important.
[PERSON] is scheduled to spend much time in Saturn's magnetosphere and provide a much better picture of the ion and neutral composition and distribution. The plasma instrument should distinguish between the ion species and give 3-D distribution functions for each mass thus giving a complete view of the ions. The energetic neutral detector will give a global picture of the energetic ion and neutral population by looking at energetic particles which charge exchange with neutrals. As with [PERSON] at Jupiter, we expect many new surprises and many new mysteries to explain.
This work was supported by NASA planetary atmospheres grant NAG 5-6129 and by contract 959203 from JPL to MIT.
[PERSON] was the editor responsible for this paper. He would like to thank [PERSON], [PERSON], and [PERSON] for their reviews.
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wiley/fbb0b00d_d787_4f9e_9c65_b2135d756623.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Releating Megathrust Seismogenic Behavior and Subduction Parameters via Machine Learning at Global Scale [PERSON]
1 Departamento de Geofisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepcion, Concepcion, Chile, 2 Departamento de Ciencias de La Tierra, Facultad de Ciencias Quimicas, Universidad de Concepcion, Concepcion, Chile
[PERSON]
2 Departamento de Ciencias de La Tierra, Facultad de Ciencias Quimicas, Universidad de Concepcion, Concepcion, Chile
###### Abstract
We investigate the relationship between the seismogenic behavior of global megathrusts and various subduction parameters. We performed a parametric approach by implementing three decision tree-based Machine Learning (ML) algorithms to predict the b-value of the frequency-magnitude relationship of seismicity as a non-linear combination of subduction variables (subducting plate age and roughness, slab dip, convergence speed and azimuth, distance to closest ridge and plate boundary). Using the Shapley Additive exPlanations (SHAP) to interpret the ML results, we observe that plate age and subduction dip are the most influential variables. The results suggest that older, shallow-dipping plates contribute to low b-values, indicating higher megathrust stress. This pattern is attributed to the higher rigidity of older plates, increasing flexural strength, and generating a shallow penetration angle, increasing the frictional interplate area and intensifying the megathrust stress. These findings offer new insights into the non-linear complexity of seismic behavior at global scale.
Keytents:
[PERSON] and [PERSON],
arxiv:10.1029/2024 GL110984
## 1 Introduction
The largest earthquakes on Earth occur at convergent plate boundaries along the seismogenic zone of subduction megathrusts. The physical properties of subduction zones vary according to the region and affect the stress state that, in turn, influences their seismogenic behavior ([PERSON] & [PERSON], 2014). To characterize the stress state, different proxies have been used in the literature, such as the maximum recorded magnitude, the seismicity rate or the slope of the log-normal frequency-magnitude distribution of seismicity, known as the b-value of the Gutenberg-Richter law ([PERSON], 1944). Regarding this latter, laboratory experiments and natural examples suggest that the stress state and the b-value have a negative correlation, with larger stresses associated with lower b-values because of a dominance of large earthquakes over small events ([PERSON] & [PERSON], 2014; [PERSON] et al., 2019; [PERSON], 1968, 2015; [PERSON] et al., 2005; [PERSON] et al., 2013; [PERSON] & [PERSON], 1997).
A correlation between type of faulting, dominant focal mechanism and the b-value in California, Japan and elsewhere, allows [PERSON] et al. (2005) to propose that this parameter can be used as a \"stress-meter\" that depends inversely on differential stress, a conclusion supported by [PERSON] (2015) who provided an empirical linear expression for this inverse correlation using data for a wide range of tectonic settings around the globe. Several authors have reported global variations in this parameter at subduction zones, reflecting changes in the stress state along the megathrust (e.g., [PERSON] & [PERSON], 1981; [PERSON] & [PERSON], 2013; [PERSON] et al., 2012; [PERSON] & [PERSON], 2014). On the other hand, a number of studies have attempted to clarify the factors that influence the stress state and thus the seismogenic behavior and seismic potential of the megathrust (e.g., [PERSON] et al., 2018; [PERSON] et al., 2011; [PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] &[PERSON], 2013). Pioneering studies ([PERSON], 1983; [PERSON] & [PERSON], 1980) have suggested that the largest earthquakes seem to occur at subduction zones where the subducting plate is young and the rate of subduction is high. However, this assumption would be inconsistent with the seismicity documented during the 21 st century (i.e., [PERSON] & [PERSON], 2007). On the other hand, [PERSON] and [PERSON] (2014) and [PERSON] (2015) have found remarkable correlations between stress levels measured by the b-value and both plate age and slab pull force. These results allow them to suggest that a younger subducting plate would be associated with a higher buoyancy, which generates a higher normal stress on the upper plate and therefore a lower b-value.
Previous works have been mainly based on the recognition and quantification of possible correlations via linear regression between different parameters characterizing the kinematics and dynamics of subduction zones by one hand and their seismogenic behavior by the other (e.g., [PERSON] et al., 2011; [PERSON] & [PERSON], 2014; [PERSON] & [PERSON], 1980; [PERSON] & [PERSON], 2013). However, the actual relationship between these parameters is likely non-linear which justifies the implementation of Machine Learning (ML) methods that are recommended to understand the nonlinear interdependence between factors influencing processes like seismic behavior in various areas (e.g., [PERSON] et al., 2020; [PERSON] et al., 2021). Among these methods, the work of [PERSON] and [PERSON] (2019) stands out, where an attempt is made to cluster zones of maximum magnitude based on input of subduction parameters and similarity between areas according to different properties.
In this study, measurements of subduction parameters and b-values were conducted across 157 transects (Figure 0(a)), covering most of subduction zones worldwide. The aim was to assess how these variables collectively affect megathrust stress, represented by the b-value. For this, three supervised regression ML algorithms were employed to analyze relationships among input variables and predict the b-value. Subsequently, an interpretation of the generated ML models was carried out using the Shapley Additive exPlanations (SHAP) values ([PERSON] & [PERSON], 2017), which allowed us to understand the contribution of each feature in the prediction of the b-value, enhancing our understanding of processes that regulate the stress state in the megathrust.
## 2 Data and Methods
We created an ensemble of 157 trench-perpendicular transects (Figure 0(a)), covering most of the subduction zones for which a 3D model of slab geometry is available in the Slab2.0 model ([PERSON] et al., 2018). We selected one transect every \(\sim\)2\({}^{\circ}\) along the trench axis of these subduction zones segments. For each, we quantified a number of subduction parameters and computed one b-value as described below grouped in Dataset S1 in Supporting Information S1.
### Quantification of Geometric and Kinematic Parameters of Subduction Zones
For each studied transect we computed values of all the parameters listed in Table S1 in Supporting Information S1, as explained in the caption of Figure S1 in Supporting Information S1. Convergence velocity (vc_10 in Table S1 in Supporting Information S1), azimuth angle (ang_conv in Table S1 in Supporting Information S1) and oceanic plate age at the trench (age in Table S1 in Supporting Information S1) were derived from the plate kinematics model of [PERSON] et al. (2016), interpolating their grids at the intersection of each transect with the trench. Seafloor roughness was derived from the General Bathymetric Chart of the Oceans (GEBCO) bathymetry. To quantify the roughness, the standard deviation of the bathymetry with respect to a polynomial fit along a transect perpendicular to the trench was calculated oceanward (roughness in Table S1 in Supporting Information S1, based in [PERSON] et al., 2018). To measure the distance along the trench between each transect and both the oceanic plate edge and the nearest ridge (Dse and Dcr in Table S1 in Supporting Information S1), ArcGIS Pro software was implemented directly with its basemap as a reference. Finally, the subduction angle between 0 and 60 km depth (ang_60 in Table S1 in Supporting Information S1) was obtained from the Slab2.0 model of [PERSON] et al. (2018). The distribution of all the subduction parameters is shown in Figures S2-S8 in Supporting Information S1.
### Estimation of \(B\)-Value
We use the seismicity catalogue provided by the International Seismological Center (ISC) between years 1900 and 2022. To estimate the b-value for each studied transect, we consider earthquakes with epicenters within an area extending 200 km laterally on both sides of the transect (Figure 0(b)). We consider a 25% overlap between each transect to capture the spatial variability of seismic activity (Figure 0(b)). Four sub-catalogues were then created for each transect considering either all the recorded events or earthquakes located around the slab upper surface at depths between \(\pm\)5, \(\pm\)10 and \(\pm\) 15 km of the Slab2.0 model ([PERSON] et al., 2018, see Figure 1c). From these sub-catalog, magnitude differences between correlative events were calculated and the b-value was estimated using the b-positive method proposed by [PERSON] (2021). This method, which follows the same form as the maximum likelihood estimator ([PERSON], 1965), only considers positive magnitude differences to avoid incompleteness problems and the contamination of long-term b-value computations due to transient fluctuations associated to aftershock sequences. After exploring the sensitivity of resulting b-values to the selected distance
Figure 1: Distribution of transects perpendicular to the trench for the quantification of subduction parameters and b-value. In Figure 1a, the overall distribution of transects in major subduction zones is depicted (dark lines), showing the depth to the subducting plate as reported by the Slab2.0 model ([PERSON] et al., 2018), in addition with seafloor age contours provided by the grid of [PERSON] et al. (2016). Figure 1b provides a close-up view of the areas from each transect along central Chile, emphasizing the 25% overlap with neighboring segments. The estimation of the b-value for each transect considers seismicity located 200 km at both sides of the transect. Figure 1c illustrates an exemplary depth profile of seismicity for one of the transects. Different filters at distances of \(\pm\)5, \(\pm\)10, and \(\pm\)15 km relative to the slab upper surface are applied to evaluate the sensitivity of the b-value estimation to this choice. Figure 1a tectonic plates abbreviations: EUR = Eurasian, ARA = Arabian, IND = Indian, NAM = Northamerican, CAR = Caribbean, JFC = Juan de Fuca, PAC = Pacific, PHI = Philippine, SOM = Somalian, AUS = Australian, NAZ = Nazca, SAM = Southamerican, COC = Cocos plate, SCO = Scotia, ANT = Antarctic, AFR = African.
threshold to the slab upper surface, we decided to show results considering events within \(\pm\)10 km of the slab (see, Figures S9-S19 in Supporting Information S1, for tests with other filters).
### Machine Learning
Figure S20 represents the methodological flow carried out throughout this study. We applied three ML algorithms based on decision trees: CatBoost, GradientBoosting and XGBoost (details in Text S1 in Supporting Information S1), selected for their ability to handle complex data and provide robust performance with small datasets ([PERSON], 2001, p. 2018; [PERSON] et al., 2022). Focused on regression problems, these algorithms aim to predict a target variable (b-value in our case) from a set of input features (subduction parameters). The use of three different supervised ML algorithms is driven by our quest for convergence in conclusions, ensuring consistency in results and strengthening the reliability of interpretations.
For the model's construction, the data were randomly split into training (90%) and test (10%) sets. Subsequently, a cross-validation was performed on the training set to build and validate models using subsets of the data (more details in Text S1 in Supporting Information S1). Here an optimal set of hyperparameters is determined for each algorithm defining the models. Once optimized the hyperparameters for each algorithm and built a model with optimal performance, we evaluated its performance on unseen test data, using metrics such as the Coefficient of Determination (R\({}^{2}\)), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) (see details in Text S1 in Supporting Information S1).
To interpret the inner functioning of the model, SHAP value method ([PERSON], 2017) is implemented. This approach examines the effect of each feature on the predicted outcomes by controlling for the presence of features, which allows us to better understand the decision-making process of the model (Text S2 in Supporting Information S1). In other words, the SHAP value allows us to quantify the influence of each feature (subduction parameter) on the predicted outcome (b-value).
Finally, to analyze the stability of the feature importance in the interpretation of the models, additional tests were performed with different data partitions (80/20 and 70/30) (Figures S21 and S22 in Supporting Information S1). This approach, applied to a small dataset of 157 observations, allows to evaluate the robustness of the constructed models and their sensitivity to specific data partitions. Specific details on metrics and performance of each algorithm are in Supporting Information S1 (Table S2 in Supporting Information S1 and Figures S23-S28 in Supporting Information S1).
## 3 Results
The map in Figure 2 shows the global distribution of the estimated b-values only using earthquakes for \(\pm\)10 km around the slab upper surface. We computed similar maps considering earthquakes \(\pm\)5 and \(\pm\)15 km around the
Figure 2: Computed b-values for each transect considering seismicity recorded within \(\pm\)10 km of the slab upper surface.
slab surface and all available earthquakes (Figure S10-12 in Supporting Information S1). As can be concluded by comparing Figure 2 with Figures S10-S12 in Supporting Information S1, the obtained b-values are not very sensitive to this choice, something that is also apparent in Figures S16-S19 in Supporting Information S1 where we show for each transect the mean b-value averaging the different slab filters with standard deviation commonly lower than 0.15 (i.e., a 20%-25% of the observed range of variations of computed b-values in Figure 2).
A significant variation in the b-values is observed in different regions of the world. For the South American zone, a high variability is observed, with values close to 0.8 dominating and areas of increased b-value coinciding with the subduction of the Juan Fernandez and Carnegie ridges. Likewise, in Cascadia, Sumatra and Aleutians, low b-values (!0.75) predominate, indicating high stress of the megathrust. b-values close to one representing moderate stress are found in the Marianas, Philippines and Tonga-Kermadec. For the Sandwich, Caribbean, Philippines and Central America zones, trends toward b-values higher than one are observed. The highest b-value (near 1.4), indicating lowest stress, is observed particularly for the Central American zone.
The performance of the three ML algorithms is analyzed below based on the metrics provided by R\({}^{2}\) as a measure of the percentage of variability explained by the independent variables in the target variable (other metrics are presented in Table S2 of Supporting Information S1). We focus on results obtained with a 90/10 ratio between training and test data (results with lower ratios are also shown in the Supporting Information S1, Figures S23-S28 in Supporting Information S1).
Overall, at a ratio of 90/10, all three algorithms were found to have considerable predictive ability, with R\({}^{2}\) values of 0.82, 0.88 and 0.83 for CatBoost, GradientBoosting and XGBoost, respectively (Figure S23 in Supporting Information S1) and predicted residual errors lower than 0.15-0.2 (Figure S24 in Supporting Information S1). When interpreting the ML models using SHAP values, regardless of the algorithm and the proportion of training and test data used, a consistency in the data patterns can be seen, despite an expected degradation in the performance quality (lower R\({}^{2}\) and larger residuals) for lower training/test ratios (compare Figures S21 and S22 in Supporting Information S1 with Figure 3, and Figures S25-S28 with S23-S24 in Supporting Information S1). In Figure 3, we present the detailed interpretation of the models with SHAP values for a 90/10 partition of the data, revealing how the input variables contribute to the prediction of the output variable. Similar SHAP values for 80/ 20 and 70/30 partitions can be found in Figures S21 and S22 in Supporting Information S1, and tests for b-values computed considering seismicity within \(\pm\)5 and \(\pm\)15 km from the slab upper surface along with their statistical indicators are shown in Figures S29 to S34 in Supporting Information S1.
From the bar plots in Figures 2(a)-2(c) and 2(e), we observe that the subduction variables having the largest impact in predicting the b-value for the three ML algorithms are consistently the plate age, the subduction angle (ang_60), and the distance to the closest slab edge (Dse). In both GradientBoosting and XGBoost (Figures 2(c) and 2(e)), the plate age and subduction angle are ranked in first and second place, respectively, while in CatBoost (Figure 2(a)), this order is inverted. Notably, when examining the summary plot for the three models (Figures 2(b)-2(d) and 2(f)), we can discern a clear trend in the impact of plate age and subduction angle. For instance, we can see that older subducting plates (red dots) are associated with negative SHAP values that predict low b-values, and vice versa. Conversely, the impact of the subduction angle is observed in the opposite way, where smaller dip angles (blue dots) have negative contributions in the SHAP values and therefore in low b-values, and vice versa. The trend for the impact of the distance to the closest slab edge (Dse) is less clear than the other two variables, showing some variability and outliers in its impact on predictions (no clear trend from red to blue or viceversa along the \(x\)-axis).
The remaining variables (ang_conv, vc_10, Dcr, and roughness) reveal distinct patterns and less relevant contributions to the predictive models. Convergence azimuth angle (ang_conv), while displaying a generally low impact, exhibits a noteworthy trend where smaller to medium angles (i.e., orthogonal to semi-oblique convergence) consistently contribute to low b-values. In the case of convergence velocity (vc_10), all three algorithms present an unclear trend. High values contribute both positively and negatively, rendering its impact ambiguous.
For Dcr, a consistent observation emerges, particularly pronounced in CatBoost and Gradient Boosting: predominantly low Dcr (i.e., when the transect is closer to a subducting ridge) contribute positively to predictions and therefore are associated with high b-values, while large Dcr have a negative impact predicting low b-values. Finally, the subducting plate roughness is consistently indicated as the variable with the least impact across all three algorithms. In addition, its relationship with b-value via SHAP value remains unclear, adding an element of complexity to its role in shaping the predictive accuracy of the models.
The differences observed between the models can be attributed to various technical factors inherent in each algorithm. Although both GradientBoosting and XGBoost use boosting methods to build sequential decision trees, they show differences in their inner workings, with GradientBoosting ([PERSON] et al., 2021). Despite this, both show consistent results in this study, with GradientBoosting showing even better metrics in some cases. However, both algorithms are effective in regression problems, working with continuous variables and allowing effective
Figure 3.— Comparison of feature importance in predicting the b-value for three different models, each trained with a 90/10 train-test partition and using each of the three ML algorithms. Figures 3a–3c, and show the mean absolute SHAP values for each variable for each model, indicating the impact of variables ordered by highest to lowest relevance. Figures 3b–3d, and f show the relative contribution of each feature to the predictions of the ML model. The points on the horizontal axis represent the magnitude of the impact of each feature, where positive SHAP values contribute to higher predictions and negative SHAP values contribute to a lower prediction in the model. The color of each point indicates the value of the feature for that sample, with blue for low values and red for high values. The vertical line in the center reflects the mean value of the model’s predictions, ang_60 = subduction angle between 0 – 60 km depth; ang_conv = convergence azimuth; vc_10 = convergence velocity: Dse = distance between each transect and the closest slab edge along the trench; Dcr = distance between each transect and the closest subducting ridge along the trench, roughness = seafloor roughness 250 km seaward from the trench.
modeling of non-linear relationships. On the other hand, CatBoost is optimized to handle categorical variables ([PERSON] et al., 2018), which could affect the way continuous variables are handled and prioritized. This could consequently affect the interpretation of the results and the consistency in the importance of the variables between the different algorithms, as observed in the prediction of the estimated b-value with seismicity at 5 and 15 km around the slab (Figures S29-S34 in Supporting Information S1).
## 4 Discussions and Conclusions
Variations in performance and differences in feature importance between models reflect the inherent technical differences of each algorithm. Despite these differences, the SHAP values consistently interpret the importance and impact of the subduction variables. Significant variations in predictive ability are observed depending on dataset partitioning, with smaller partitions (80/20 and 70/30) showing lower R\({}^{2}\) values compared to larger partitions (Table S2 in Supporting Information S1 and Figures S25 and S27 in Supporting Information S1). Training the model with smaller datasets (e.g., 80% or 70% of the data) can limit its ability to generalize and capture complex patterns, as reduced data availability decreases the model's information and may increase result variability ([PERSON], 2006; [PERSON] et al., 2013). However, despite a decrease in predictive performance, the SHAP values indicate that the models still capture significant relationships. This reduction in R\({}^{2}\) reflects the impact of dataset size and partitioning on predictive accuracy but does not compromise the model's ability to identify key patterns ([PERSON], 2020). Thus, the robustness in feature interpretation suggests that the conclusions about variable importance and their effects on predictions are based on genuine underlying relationships rather than artifacts of the training dataset.
In this context, results obtained in this study reveal that oceanic plate age at the trench is the subduction parameter with a greater influence on the b-value and therefore on the stress state of the megathrust. In a first glance, this conclusion seems to agree with [PERSON] and [PERSON] (2014, herein [PERSON]&I14), who found that plate age has the highest correlation coefficient (0.60) in a linear regression against \(b\)-value, with convergence velocity and upper plate velocity away from the trench having a rather weak or null correlation. However, the positive correlation between slab age and b-value observed by [PERSON]&[PERSON], which for them implies a dominance of the age-dependent slab buoyancy on megathrust stress state, is at odds with our results since younger subducting plates (blue dots in Figures 3b-3d and 3f) are associated to positive SHAP values translating into greater b-values, and vice versa.
Although we believe that using a linear univariate correlation approach to analyse the likely complex non-linear interaction of different variables is less efficient than using ML, we still computed a linear correlation between our estimates of b-value (as seen in Figure 2) and subducting plate age at the trench, just to repeat the analysis of N&I14 and to have a better base for comparison (see Figure S35b in Supporting Information S1). We found a very weak and negative correlation, with a coefficient of \(-0.12\). We tested this correlation using b-values computed with all the seismicity around each transect (Figure S35d in Supporting Information S1) and only events inside \(\pm 5\) and \(\pm 15\) km from the slab upper surface (Figures S35a and S35c in Supporting Information S1), reinforcing this very weak and negative correlation. We made the same analysis using only events between 1978 and 2009, as done by N&I14 (Figure S36 in Supporting Information S1), finding a somehow stronger negative correlation (coefficients between \(-0.18\) and \(-0.23\)).
This notable disagreement, which challenges the main conclusions of N&I14, can be due to several factors. First, our linear correlation (Figure S35 in Supporting Information S1) was computed considering almost two times more data points than N&I14 (157 vs. 75), covering subduction areas that were excluded from their analyses (Alaska-Aleutians, Cascadia, Southern Chile, Lesser Antilles, Sandwich). We also note that for some regions included in both analyses (e.g., Sumatra, Central America) we obtain very different estimates of b-value compared with N&I14. These differences likely own to differences in: the seismicity catalogue used by both studies (ANSS by N&I14 v/s ISC by us), the time interval considered (1978-2009 by N&I14 v/s 1900-2022 by us), the hypocentral depths of considered events (all events by N&I14 v/s only those around the slab upper surface by us), and the method to compute the b-value (maximum likelihood of Aki (1965) without declustering of aftershock sequences by N&I14 v/s b-positive by us). Particularly this latter point can be significant, since considering only the positive magnitude differences between consecutive events to perform the b-positive method means that the computation of the b-value is not contaminated by the commonly observed transient increase after a mainshock ([PERSON] et al., 2018; [PERSON] and [PERSON], 2019) that is likely due to changes in the catalogue completeness during the early postseismic period ([PERSON], 2021). This can be very relevant in areas that experienced great earthquakes during the considered time interval (like in Sumatra-Java between 2004 and 2007, South-Central Chile between 2010 and 2015, or Alaska 2020-2021).
Accepting that our b-value estimates are well-computed, and they can be considered a good representation of the stress state at subduction megathrusts, then we must discuss an alternative conceptual model to the one proposed by [PERSON] and [PERSON] (2014). For this we also consider the large impact that our ML models unravel for the subduction angle as a predictor of the b-value (high average SHAP values in Figures 3a-3c and 3e). Moreover, our results indicate a positive correlation between both parameters, with shallower/smaller subduction angles (blue dots in Figures 3b-3d and 3f) associated with negative SHAP values meaning lower b-values and higher stress states, thus increasing the likelihood of large earthquakes. This is consistent with [PERSON] and [PERSON] (2019), who also identified shallow subduction angles, along with longer subduction interfaces, as key factors linked to larger earthquake magnitudes. The combined trend of b-value being negatively correlated to plate age and positively correlated with the subduction angle indirectly implies a reverse correlation between these two subduction parameters, something that is partially supported by recent linear regression analysis at global scale (i.e., [PERSON] & [PERSON], 2020), although a role of plate motion in controlling slab dip seems to be dominant ([PERSON] et al., 2005; [PERSON] et al., 2005). Into this framework, we propose a novel conceptual model (Figure 4) where the oceanic plate age exerts its dominance via a control on flexural rigidity of the slab, more specifically on the elastic thickness of the plate. In our model, the elastic core of older and colder plates is thicker than for younger and hot plates, and therefore they tend to subduct with larger radius of curvature generating shallow subduction angles ([PERSON] et al., 2016; [PERSON] & [PERSON], 2012; [PERSON] et al., 2008). This setting further implies a larger contact area between both converging plates across the megathrust and a wider seismogenic zone because of colder conditions, augmenting thus the potential for larger earthquakes to occur. Therefore, zones with older subducting plates will tend to have a greater proportion of large earthquakes, impacting in a smaller b-value.
Our results also suggest that other parameters might play a secondary role modulating the stress state of the megathrust. The distance to the lateral boundaries of subducting plates (Dse in Figure 3) seems to be only marginally less significant than the subduction angle, with transects faraway from boundaries having the lowest b-values and therefore highest stresses. This is in agreement with previous researchers (i.e., [PERSON] & [PERSON], 2013) that found a relative large linear univariate correlation of Dse with the maximum magnitude of megathrust earthquakes. Plate convergence appears to have a secondary impact compared to previously discussed parameters, somewhat in line with global linear regressions ([PERSON] & [PERSON], 2020; [PERSON] & [PERSON], 2014). However, it stands in Figures 3b-3d and \(f\) that most rapid and orthogonal convergence favours low b-values and large megathrust stresses, as can intuitively be supposed. This is in agreement with the findings of [PERSON] et al. (2011), who found that fast subduction zones with cold plates are associated with large plate interfaces, resulting in higher seismic rates (i.e., number of earthquakes that occur in a specific area over a defined period of time). Although the calculated b-values seems to be much less sensitive to the proximity to a subducting aseismic ridge and the roughness of the oceanic crust, our results suggest that megathrust strength tend to be lower (i.e., higher b-values) in subduction areas dominated by ridge subduction. This can be also appreciated in Figure 2 for South America for example, where subduction of the Carnegie Ridge near 5\({}^{\circ}\)S and Juan Fernandez Ridge at 33\({}^{\circ}\)S are clearly related to locally augmented b-values compared to adjacent regions. This has been observed by previous studies in the region ([PERSON] et al., 2012) and supports the notion that subducting rough bathymetry associated to seamount chains decrease the strength of the megathrust and favour convergence absorption via creep and aseismic slip (i.e., [PERSON], 2014; [PERSON] & [PERSON], 2015), contributing to low seismic coupling ([PERSON] et al., 2018; [PERSON] et al., 2018, 2019) and reducing the probability of a large magnitude earthquake.
Figure 4.— Conceptual model comparing subduction zones characterized by old (a) and young (b) oceanic plates. An older, thicker (T), and more rigid plate subducts at a shallower angle (\(\omega\)), which increases the contact surface (red line) and the overall stress on the megathrust. A younger, thinner (t), more flexible plate subducts at a steeper angle (\(\beta\)), which reduces the interplate contact surface (red) and the stress on the megathrust.
Our study did not consider several potentially important parameters affecting the seismogenic behaviour, such as the sediment thickness at the trench (e.g., [PERSON] et al., 2018), gravity anomalies (e.g., [PERSON], 2015; [PERSON] et al., 2021) or temperature (e.g., [PERSON], 2023), also indicated to play a role in the seismogenic behaviour. For instance, the sediment thickness, as shown in [PERSON] et al. (2018) may promote a great lateral rupture propagation, characteristic of almost all giant earthquakes. Gravity anomalies reveal variations in crustal and upper-lithosphere density, which provide insights into the forearc structure. These density variations are suggested to influence the accumulation and release of stresses, thereby affecting seismic activity ([PERSON] & [PERSON], 2015). Finally, the temperature may influence the megathrust frictional properties, impacting the seismogenic behaviour at subduction zones (England, 2018; [PERSON], 2023). Although including additional parameters could provide a more comprehensive understanding of how subduction factors influence seismogenic behaviour, in our study increasing the dimensionality of the dataset poses challenges as a higher number of parameters requires a correspondingly larger dataset to ensure effective generalisation. This is particularly problematic for a dataset like ours based on 157 trench-perpendicular profiles, as the limited amount of data points could lead to issues related to data sparsity, overfitting and complicating the identification of relevant patterns ([PERSON] et al., 2024; [PERSON], 1965).
The complexity of the likely non-linear interactions between subduction variables in terms of their integrated effect over the megathrust stress state means that using ML approaches, as done here, to analyse the possible influence of each variable in the context of all other existing variables is superior compared to previous uni- or multi-variate linear regressions. This underscores the need for a more holistic approach when interpreting seismic phenomena, highlighting the importance of the interrelation of multiple factors in predicting the seismic behaviour of the megathrust. Future works in this line should include other parameters that have been also indicated as significantly affecting the seismogenic behavior emphasising the need to explore more factors to improve our understanding of the complex, non-linear interactions between subduction variables and megathrust stress.
## Data Availability Statement
For obtaining earthquakes events for each subduction zone, we used the ISC bulletin catalog ([[http://www.isc.ac.uk/iscbulletin/search/catalogue/](http://www.isc.ac.uk/iscbulletin/search/catalogue/)]([http://www.isc.ac.uk/iscbulletin/search/catalogue/](http://www.isc.ac.uk/iscbulletin/search/catalogue/))). Convergence velocity and convergence angle were obtained from [PERSON] et al. (2016) cinematic model implemented in GPlates ([PERSON] et al., 2018) software. Plate age was also obtained from [PERSON] et al. (2016) but implemented in ArcGISPro. The global bathymetric grid to calculate seafloor roughness and to measure the distance to the closest ridge was downloaded from GEBCO Gridded Bathymetry Data ([[https://www.geboc.net/data_and_products/gridded_bathymetry_data/#global](https://www.geboc.net/data_and_products/gridded_bathymetry_data/#global)]([https://www.geboc.net/data_and_products/gridded_bathymetry_data/#global](https://www.geboc.net/data_and_products/gridded_bathymetry_data/#global))). The subduction angle was calculated from Slab2.0 model ([PERSON] et al., 2018) implemented in ArcGISPro software (Esri, 2020) version 2.6. From the same model and software, we measured the distance to the closest subducting slab edge. Maps were created both with python libraries matplotlib ([PERSON] et al., 2021), geopandas ([PERSON] et al., 2019) and ArcGISPro (Esri, 2020) version 2.6.
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wiley/fb856891_598b_4b51_9072_a340eb9638e6.md | # IGR Solid Earth
A Comprehensive Stress Drop Map From Trench to Depth in the Northern Chilean Subduction Zone
[PERSON]
Department of Geophysics, Freie Universitat Berlin, Berlin, Germany, \({}^{\mbox{\tiny 2}}\)Lawrence Livermore National Laboratory,
Livermore, CA, USA
[PERSON]
Department of Geophysics, Freie Universitat Berlin, Berlin, Germany, \({}^{\mbox{\tiny 2}}\)Lawrence Livermore National Laboratory,
Livermore, CA, USA
[PERSON]
Department of Geophysics, Freie Universitat Berlin, Berlin, Germany, \({}^{\mbox{\tiny 2}}\)Lawrence Livermore National Laboratory,
Livermore, CA, USA
[PERSON]
Department of Geophysics, Freie Universitat Berlin, Berlin, Germany, \({}^{\mbox{\tiny 2}}\)Lawrence Livermore National Laboratory,
Livermore, CA, USA
###### Abstract
We compute stress drops for earthquakes in Northern Chile recorded between 2007 and 2021. By applying two analysis techniques, (a) the spectral ratio (SR) method and (b) the spectral decomposition (SDC) method, a stress drop map for the subduction zone consisting of 51,510 stress drop values is produced. We build an extended set of empirical Green's functions (EGF) for the SR method by systematic template matching. Outputs are used to compare with results from the SDC approach, where we apply cell-wise obtained global EGFs to compensate for the structural heterogeneity of the subduction zone. We find a good consistency of results of the two methods. The increased spatial coverage and quantity of stress drop estimates from the SDC method facilitate a consistent stress drop mapping of the different seismotectonic domains. Albeit only small differences of median stress drop, strike-perpendicular depth sections clearly reveal systematic variations, with earthquakes at different seismotectonic locations exhibiting distinct values. In particular, interface seismicity is characterized by the lowest observed median value, whereas upper plate earthquakes show noticeably higher stress drop values. Intermediate depth earthquakes show comparatively high average stress drop and a rather strong depth-dependent increase of median stress drop. Additionally, we observe spatio-temporal variability of stress drops related to the occurrence of the two megadrust earthquakes in the study region. The presented study is the first coherent large scale 3D stress drop mapping of the Northern Chilean subduction zone. It provides an important component for further detailed analysis of the physics of earthquake ruptures.
Key. 10.1029/2023 JB027549 10.1029/2023 JB027549 10.
* [11][PERSON] and [PERSON] (2014); [PERSON] and [PERSON] (2017) or [PERSON] et al. (2020), who observe a dependence of stress drop on seismic moment. It has also been pointed out that estimates of the stress drop value strongly depend on the analysis method ([PERSON] et al., 2020; [PERSON] et al., 2019), the model assumptions and the parameter choices ([PERSON] et al., 2022; [PERSON] & [PERSON], 2014, 2015), thus complicating a comparison of results from different studies.
Stress drop values of large to megathrust earthquakes have been analyzed in several global studies (e.g., [PERSON] & [PERSON], 2009; [PERSON] et al., 2016), and crustal earthquakes, both of tectonic and induced origin, have been studied intensively in the last years to infer dependencies on depth, mechanism, magnitude and more (e.g., [PERSON], 1995; [PERSON], 2014; [PERSON] et al., 2020; [PERSON] & [PERSON], 2020; [PERSON] et al., 2011; [PERSON] & [PERSON], 2009; [PERSON] et al., 2006; [PERSON] & [PERSON], 2017). Most studies, however, are limited to a highly focused target zone or a relatively small amount of earthquakes usually not exceeding a few tens or hundreds of events, and systematic stress drop studies in particular of entire subduction zones or at least major parts of them are very rare ([PERSON] & [PERSON], 2009; [PERSON] et al., 2022; [PERSON] et al., 2014). And yet, knowledge of the variability of stress drop across an entire subduction system, which includes conditions for earthquake generation that can vary widely both spatially and temporally within an earthquake cycle, is particularly valuable.
As mentioned above, an important precondition for this type of study is the consistent and careful processing of a large number of events (i.e., many thousands of events), and the Northern Chilean subduction zone with its high seismic activity and dense seismic monitoring provides an ideal setting.
In an earlier study, [PERSON] et al. (2021) implemented and verified a spectral ratio approach (SR) for stress drop estimation for the rupture and aftershock area of the 2014 Mw8.1 Iquique earthquake. Analyzing \(\sim\)600 events, they identified an increase of stress drop with distance from the plate interface, no clear depth dependence and an increase of stress drop with seismic moment. Additionally, they described the spatio-temporal variation of stress drop in association with the Iquique event.
In this work, we expand the analysis to the greater subduction zone in Northern Chile, a region that has been continuously monitored since 2006 by the IPOC network (IPOC, 2006) accompanied by the permanent networks of the CSN (C,C1) and multiple temporary deployments. Based on these data the distributions of several geophysical parameters in this region such as focal mechanisms, stress orientation, fore-, and aftershock distributions, or inter-plate-locking have been studied intensively by various authors (e.g., [PERSON] et al., 2016; [PERSON] et al., 2013; [PERSON] et al., 2018; [PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2012; [PERSON] et al., 2014). An earthquake catalog covering the time period from 2007 to 2014 by [PERSON] et al. (2018) has recently been updated and extended until 2021 ([PERSON] et al., 2023). The new version contains over 180,000 events for the time period from 2007 to 2021. Its uniform processing along with the long time period make it a great basis for a comprehensive stress drop mapping of an entire subduction zone. Additionally, it allows for the detailed study of possible regional variations of stress drop as well as time-dependent variations in connection with the occurrence of two megathrust earthquakes, the 2007 \(M_{\text{w}}\)7.7 Teocpilla earthquake and the 2014 \(M_{\text{w}}\)8.1 Iquique earthquake.
We apply two different methods for calculating the stress drop: (a) the spectral ratio method (SR) and (b) the spectral decomposition method (SDC). Spectral ratio approaches employ empirical Green's functions (EGFs) to eliminate path and site terms in the observed seismogram spectrum and to isolate the event source term (e.g., [PERSON], 2012). While this makes them more robust against systematic errors introduced by over- or under-correcting for attenuation structures and radiation pattern, they require the existence of a suitable nearby EGF event which, in practice, is a rather strong limitation. To overcome this problem, we additionally use a second approach which has proven to be better suited for large data sets and which increases significantly the quantity and spatial coverage of stress drop values. The spectral decomposition method (e.g., [PERSON], 2020; [PERSON] et al., 2021; [PERSON] et al., 2004; [PERSON] et al., 2006) implicates to first unangle path, site, and event terms of multiple earthquakes simultaneously and then produce an EGF-like correction term which can be applied to an event cell rather than just to single events. In this way, the number of stress drop estimates can be multiplied at the cost of a more general correction of the source medium response.
In this study, we use the two methods jointly, which allows exploiting the benefits of both of them, to mutually control results and to produce a database of tens of thousands of stress drop values. The resulting distribution covers all the different seismically active segments of the subduction zone, from shallow depths close to trench down to depths of about 180 km.
## 2 Catalog and Data
We extract the event origin times, P- and S- arrival time picks, event hypocenters and magnitudes from the catalog by [PERSON] et al. (2023), which is an updated version of [PERSON] et al. (2018). In the following, we will refer to the new catalog as the IPOC catalog. It comprises 182,847 double-difference relocated events which occurred in the time period from 2007 to 2021. For our stress drop study, we use waveforms of in total 23 seismic broadband stations of the Integrated Plate Boundary Observatory Chile (IPOC, 2006). The network extends in N-S direction from 17.6\({}^{\circ}\)S to 24.6\({}^{\circ}\)S, a trench-parallel length of about 700 km. The corresponding continuous three-component waveform data, sampled at 100 Hz, were downloaded from the EIDA web service of GFZ Potsdam ([PERSON] et al., 2015). Based on event location, the authors assign a class to each event of the IPOC catalog, picking from the following options:
**UP** Upper plate seismicity, predominantly crustal events within the South American plate, but also some earthquakes in the uppermost mantle.
**P1** Seismicity at or very close to the plate interface.
**P2** A plate interface-parallel band of seismicity in the oceanic Nazca Plate.
**P3** A second, deeper interface-parallel band of seismicity below P2.
**ID** Intermediate depth seismicity (sometimes called IDE). This class comprises by far the largest amount of events (\(\sim\)116,000), and it extends from about 60 km down to 180 km depth.
**MI** Mining events from open pit mines at the surface.
**NN** Not classified events which are located at the less well constrained edges of the catalog region outside the network. The two biggest subgroups are offshore events and deep event in the east, respectively.
Figure 1 displays the seismicity distribution from the IPOC catalog in Northern Chile, color-coded by depth. It includes a West-East depth view of a catalog slice with coloring according to the event class (dashed box). For a more detailed description of the event classification, the reader is referred to [PERSON] et al. (2018).
Stable magnitude estimation is an important prerequisite for consistent stress drop estimates, as the moment is an integral parameter in the estimate. Event magnitudes in the IPOC catalog were computed using a technique by [PERSON] et al. (2020), which applies location-dependent station corrections in order to stabilize the computation against possible reduced or variable station availability. When plotted against relative moments, derived from the low frequency displacement plateau, we find a 1:1 relation (Figure S1 in Supporting Information S1). Thus, we use them to compute seismic moments.
The spectral ratio technique strongly depends on the availability of suitable event pairs which are used as a target and empirical Green's function couple. In order to exploit the existing data set at its best, we first perform an exhaustive event search by template matching, which complements the IPOC catalog by finding additional, small magnitude EGF candidate events. Template matching uses the cross correlation function to detect waveforms in a continuous data set that resemble the predefined patterns (i.e., the template waveforms). It is commonly used in seismology to increase the number of mostly weak events missed in the original earthquake catalog. Event seismograms from the catalog serve as templates, and the resulting detections can be assumed to be closely located and to have similar mechanisms as the template events, if cross correlation values are sufficiently high. This method becomes computationally challenging with an increasing volume of continuous waveform data and a high number of template events in the initial catalog. To make the method feasible for our extensive data set, we applied our own GPU-based template matching code. For each event in the IPOC catalog, template waveforms were extracted for the three closest available stations using the vertical channel only. The minimum length of the template waveform is 15 s and increases with hypocentral distance to include both the P and S phases. Additionally, the data was downsampled to 25 Hz. We define potential pairs of target event and empirical Green's function (EGF) event, if the normalized cross correlation coefficient is at least 0.70 at minimum two stations, with template waveforms derived from the same master event. In this way, the originally \(\sim\)180,000 templates produce 1,836,195 matches, providing a substantial extension of the number of EGF candidates compared to the initial catalog.
## 3 Methods
### Source Model and Stress Drop
We compute the stress drop \(\Delta\sigma\) assuming the widely used circular source model by [PERSON] (1957):
\[\Delta\sigma=\frac{7\pi\mu\overline{D}}{16r}=\frac{7M_{0}}{16r^{3}}. \tag{1}\]Figure 1.— Seismicity from the IPOC catalog by [PERSON] et al. (2023). Color indicates event depth. Red stars are hypocenters of the \(M_{\rm u}\)8.1 2014 lique event (IQ), its largest \(M_{\rm u}\)7.6 aftershock (IQA), and the 2007 \(M_{\rm u}\)7.7 Tocopilla event (TO). Their slip contours are taken from [PERSON] et al. (2012, 2014). Orange triangles show the location of the IPOC seismic stations. The bottom panel shows a depth view of selected events from the dashed box, color-coded by the associated event class, as explained in the text. The slab interface is taken from the model of [PERSON] et al. (2018).
where r is the approximate fault radius, \(\overline{D}\) is the average slip on the fault, \(\mu\) is the shear modulus, and \(M_{0}\) is the seismic moment. In general, slip and fault dimensions are not known, and the stress drop cannot be computed directly ([PERSON] and [PERSON], 1975). We therefore adopt the approach of [PERSON] (1970), who proposed the following relation between source radius and spherically averaged corner frequency (see also [PERSON] and [PERSON], 2014, 2015; [PERSON], 1976):
\[f_{c}=k\frac{\beta}{r}, \tag{2}\]
with the shear wave velocity at the source, \(\beta\), and a constant \(k\) that relates to the spherical average of the corner frequency for a specific theoretical source model. Combination of Equations 1 and 2 leads to the Brune type stress drop ([PERSON], 1970):
\[\Delta\sigma=\frac{7}{16}\left(\frac{f_{c}}{k\beta}\right)^{3}M_{0}. \tag{3}\]
The seismic moment \(M_{0}\) is computed from the refined magnitudes of the IPOC catalog. We use the regional velocity model by [PERSON] et al. (2014) to compute event location-specific shear wave velocities. We use a k-value of \(k_{p}=0.32\) for P-wave spectra, a standard value from [PERSON] (1976), and we obtain \(k_{s}=0.265\) by a least square fit of corner frequencies from both P and S phases for identical events, similar to [PERSON] et al. (2021). In practice, \(k_{s}\) is chosen such that P and S phase-based corner frequencies produce similar stress drop values. According to [PERSON] and [PERSON] (2014) the here obtained k-values correspond to their model of a symmetrical circular rupture with a rupture velocity of \(\mathrm{v}_{r}=0.7\beta\).
The corner frequency \(f_{c}\) is obtained by fitting a spectral model to the earthquake source spectrum. This is not recorded directly, and we only have the observed displacement spectrum \(d(f)\), for which we can write
\[d(f)=e(f)\cdot p(f)\cdot s(f), \tag{4}\]
with the earthquake source spectrum, \(e(f)\), the path response, \(p(f)\) and the site response, \(s(f)\). The source spectrum can be expressed as
\[e(f)=\Omega_{0}\frac{1}{\left(1+(f/f_{c})^{m}\right)^{1/\gamma}}, \tag{5}\]
where \(\Omega_{0}\) is proportional to the seismic moment, \(n\) is the high frequency falloff and \(\gamma\) is a constant which is commonly set to \(\gamma=1\) for the [PERSON] (1970) or \(\gamma=2\) for the [PERSON] (1980) spectral model, respectively.
Separating the terms in Equation 4 in order to apply the spectral model requires careful processing and may be achieved by using one of the following two methods.
### Spectral Ratio Approach
For the spectral ratio approach, we use the processing scheme described in detail in [PERSON] et al. (2021), where a limited region around the 2014 Mw8.1 lquique earthquake was already investigated.
The general idea of the spectral ratio method (SR) is to use for each target earthquake a smaller event with similar location and focal mechanism as an empirical Green's function (EGF) ([PERSON], 2012). By spectral division between target and EGF seismograms the path and site terms which are assumed to be identical are removed (cf. Equation 4), leaving essentially the source term of the target event for frequencies below the corner frequency of the smaller event. The quotient now reads:
\[\frac{d_{i}(f)}{d_{2}(f)}\approx\frac{e_{1}(f)}{e_{2}(f)}=\frac{\Omega_{0i}}{ \Omega_{0i}}\cdot\left[\frac{1+(f/f_{c})^{m}}{1+(f/f_{c})^{m}}\right]^{1/\gamma}. \tag{6}\]
In practice, the similarity of the event locations is ensured by a required minimum cross correlation value between the waveforms of the two events at usually multiple stations. From our template matching results, described in Section 2, we select all templates with a catalog magnitude M \(\geq\) 2 which produced matches having a cross correlation value of \(\mathrm{cc}\geq\) 0.70 at minimum 2 stations (n = 1,836,195). If at least four picks are available, the three-component waveform data are band-pass filtered (0.8-40 Hz) and sliced to maximum 6 and 10 s phase windows for P and S waves, respectively. A shorter S-P arrival time difference leads to shorter windows, accordingly. We require a SNR \(\geq\)3 in the frequency bands 1.5-5, 5-10, 10-15, 15-20, 20-25 Hz, for both template and EGF. Then, the spectral ratio is computed station-wise, and the quotient of the two Boatwright spectral models is fitted to the data. We require the median of the low frequency plateau to be higher than 5 to ensure sufficient difference of seismic moment between target and EGF, a necessity for resolving the corner frequency ([PERSON], 2015). Next, the spectral ratios of all stations are stacked for robustness and resampled to achieve similar weights of low and high frequency content. The fit of the stack to the above Boatwright model quotient yields the corner frequency estimate of the target event. We show a data example of the procedure in Figure 2.
If the value of the corner frequency is within the interval 1-30 Hz, the stress drop is computed for this event. We obtain 25,994 P phase estimates and 36,121 S phase estimates which include multiple results for identical target events, originating from different EGF events. This enables us to estimate the statistical error of the corner frequency. Figure 2(a) illustrates the normalized differences to the median corner frequency for each event, where each data point is computed as \(\Delta f_{sig}=\frac{(\overline{f_{ei}}-f_{ei})}{\overline{f_{ei}}}\), for event i, \(f_{c}\) estimate j, and event wise median corner frequency \(\overline{f_{ei}}\). We obtain a standard deviation of 0.17, meaning that 50% of the estimates have a \(f_{c}\)-difference \(\leq\)17% to their family median.
Further details on the SR procedure, its limitations and error estimates are explained and discussed in [PERSON] et al. (2021).
### Spectral Decomposition Approach
For the spectral decomposition approach (SDC), we use the decomposition procedure by [PERSON] and [PERSON] (2020) as implemented in [PERSON] et al. (2021) and called SNSS (Stacking No assumption of Self-Similarity). The approach exploits the redundancy of existing event-station pairs to separate the displacement spectrum into event term, path term and site response (cf. Equation 4). A robust iterative stacking procedure as described in [PERSON] et al. (2006) is used to solve this over-determined problem, which should account for distance-dependent attenuation and site responses. The specific near-source attenuation, however, is assumed to be common for all event source paths, and therefore it needs to be estimated. For this, a so-called global empirical Green's function (gEGF), which is valid for the specific region, is computed. The gEGF can be used later in a similar way to the spectral ratio approach to compute the event-specific source time function properties such as the corner frequency. The construction of the gEGF is done as described in [PERSON] (2020) and [PERSON] et al. (2021). It consists of (a) a stacking step, where the phase spectra of all available events from the target region are stacked in 0.2 magnitude units, (b) a misfit computation between the lowest stack of those magnitude bins and different test values of corner frequency put into a spectral Brune model, (c) using the misfit as first gEGF and correction of the stacked spectra of all other magnitude bins, allowing for variable stress drop for each bin, (d) a fit of the now corrected spectra to obtain the overall misfit, (e) defining the final the correction function which produces the lowest misfit with each bin as the gEGF. This global empirical Green's function can then be used to correct all target events in the associated region, after which the individual corner frequency can be computed. A data example for a single event is shown in Figure 4.
The spectral decomposition method works best for a sufficiently high number of stacked spectra, that is, many events recorded on many stations in a confined region. The IPOC network consists of 23 stations, but due to the large spatial extent of the network, the weaker events are usually only recorded on a smaller subset of stations. Therefore, a relatively large amount of events is needed for the decomposition and computation of an appropriate gEGF. At the same time, strong variations of ray paths and attenuation are to be expected in a subduction zone. Hence, it makes sense to subdivide the volume into cells with a common gEGF, where the attenuation structure is assumed constant. We define a regular grid over our study region and divide it into cells of 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\)\(\times\) 20 km. For each cell to be processed, a minimum number of 100 catalog events of \(M\geq\) 1.8 is required. The waveforms are band-pass filtered (0.8-40 Hz) and sliced into maximum 6 and 10 s phase windows for P and S waves, respectively, starting 0.1 s before the phase arrival and having shorter windows in case of shorter S-P arrival time differences. We only keep waveforms with an SNR \(\geq\)3 in the frequency bands 1-5, 5-20, and 20-40 Hz. Then, spectra are stacked in bins of 0.2 magnitude units. The bin that is used to compute the initial gEGF (1.8 \(\leq\)\(M\)\(<\) 2.0) must contain at least 30 stacked spectra. After the spectral stacking, the result is checked for convergence by examining the misfit grid search results of the different test stress drop values. If a minimum is found within the grid search interval boundaries, the gEGF is used for this region. For all events with \(M\geq\) 2 and a minimum of four valid spectra, the individual corner frequencies are computed by correcting the individual event term from the earlier decomposition with the gEGF.
The resulting corner frequencies are required to lie between 1 and 30 Hz. To apply this procedure to the entire region of cataloged seismicity, the cells are shifted stepwise by 0.25\({}^{\circ}\) in horizontal and by 10 km in vertical direction. The step size is set to 50% of the cell width to ensure full overlap between cells.
We test the robustness of the multi-cell application of the spectral decomposition method by analyzing the variation of the gEGF with depth for a selected region and comparing it with a decomposition of the events from the same region treated as a single cell. We choose the location 20.5\({}^{\circ}\)-21.0\({}^{\circ}\)\(\times\) 68.5\({}^{\circ}\)-69.0\({}^{\circ}\) and process six cells with
Figure 2.— Spectral decomposition data example (event _20090419060601_). Displacement waveforms for the mother event and the daughter event (EGF) are shown. The utilized phase window is highlighted in gray. The amplitude spectra of the mother event and its associated noise spectrum are shown in black, the spectra for daughter event and its noise in gray. The single station spectral ratios are fitted with a Bautwright model and std is the standard deviation for the fc. The bottom panel shows the stack of all single station spectral ratios. A Bouratwright spectral ratio model is fitted to the data with an optimal corner frequency estimate of 4.28 Hz. Note, that for a better view only z-components are plotted, while more were stacked. All components as well as more examples are shown in the supplement Figures S2–S9.
varying top depths from 80 to 130 km. Figure 5a shows the corresponding gEGF of each cell, together with the single cell gEGF as a dashed line.
A higher value of a gEGF indicates a stronger attenuation correction for this frequency point in the source region. The correction decreases with depth (Figure 5a). Note that the gEGF only represents the spectral correction, which is not already captured in the path term (\(p\) in Equation 4). The single cell gEGF lies in the center of the ensemble of correction functions, representing some sort of average attenuation structure of the region. The corresponding median stress drop curve (Figure 5b) behaves accordingly: compared to the stress drop variation derived from the multi-cell gEGFs (black line), the resulting stress drop variations for the single cell (dashed line) appear under-corrected for deeper events and over-corrected for shallower events, while the variability of single cell stress drop appears smoother in general. We perform a similar test for a north-south multi-cell, crossing the entire catalog in Supporting Information S1 (Figure S10).
The tests demonstrate that the overall variation of stress drop remains similar, but the smaller scale attenuation heterogeneity is lost by using the single cell version. It also shows that the most populated cells dominate the gEGF. For our target area the great majority of cells include 100-1,000 events, while several cells have more than
Figure 4: Spectral decomposition data example for event (_20090419060601_ same as in Figure 2). [PERSON]’s spectral model is fitted to the stack of all available gEGF corrected spectra for the event. The optimal corner frequency estimate (4.1 Hz) is obtained using the variance reduction method ([PERSON] et al., 2010). It is indicated by the star. The dashed line represents the 5% variance limit. More examples for SR and SDC single event results are shown in the supplement (Figure S8 and S9 in Supporting Information S1).
Figure 3: Normalized corner frequency variability from redundant measurements. For each mother event the corner frequency is computed as the median of all estimates from all measurements. (a) The SR technique produces redundant measurements based on multiple EGFs for the same mother event. (b) In the SDC method multiple stress drop estimates occur due to the cell wise computation of the gEGF. The normalized difference (see text) to the event wise median for both groups is fitted with an exponential decay distribution yielding standard distributions of 0.17 and 0.11 for SR and SDC corner frequencies, respectively.
5,000 (cf. Figure 11). These exclusively deep cells would dominate the gEGF of possible larger cells, and the characteristics of the shallower events would be lost.
To further test stability, we additionally computed results for a coarser grid with \(0.7^{\circ}\times 0.7^{\circ}\) cell size and a minimum event number of 400 in each cell. The stress drop distribution is slightly smoother compared to that obtained by using the smaller cells, but very similar in general. To illustrate the similarity we plot the spatial distribution, histogram and depth variability similar to Figures S6 and S7 in Supporting Information S1 (Figure S12).
Because of the utilized overlap between grid cells, many events have up to 16 independent stress drop estimates (8 for P, 8 for S wave) that are expected to vary slightly due to different gEGFs calculated for each cell. From the total number of estimates (695,568) and the total number of events (51,510) we obtain an average of about 14 stress drop estimates per event. The final stress drop value for each single event is computed from the median of all these estimates. Figure 3b shows that the average relative difference between the single corner frequency estimates to their respective family median is small (std = 11%). Hence, the consistency of corner frequency estimates between cells is high. This also confirms that the cell-wise gEGFs involve smooth and mostly subtle rather than abrupt changes of corner frequency. Hence, we do not expect that cell bounds strongly influence the obtained stress drop distribution.
From the performed tests, we conclude that the cell-wise application of the decomposition technique works reasonably well in the given setup. In addition, the following section will show the principal similarity between results from our implementations of the SDC approach and the SR method.
## 4 Results
### Comparison of SR and SDC Results
The spectral decomposition method produces stress drop estimates for 51,510 events which are an almost complete superset of the 4,223 stress drop solutions from the spectral ratio method, meaning that any event that has an SR based stress drop estimate also has an SDC based stress drop estimate. Figure 6 displays map views of stress drop values and their corresponding histograms separately for both methods. Figure 7 displays the overall median stress drop variation against depth for both methods. The evident consistency demonstrates that, qualitatively, the results from both methods are very similar.
In Figure 7c the similarity is quantified as a cross plot of corner frequencies obtained for common events which have stress drop estimates from both methods. We find that SR corner frequencies are systematically higher than SDC corner frequencies, consistent with the study by [PERSON] et al. (2019). We obtain a proportionality factor
Figure 5: (a) Variation of gEGFs for six grid cells with changing depth. The black dashed line is the gEGF where all events from these cells are decomposed simultaneously in the processing. (b) The corresponding variation of median stress drop with depth for the multi-cell test and the single cell test. Albeit the similar curve shape, note the deviation at shallow depth, where the multi-cell gEGF have higher correction values (blue line in A) and the inverse behavior at greater depths.
of 0.75 between the two corner frequency families (fc\({}_{\text{3 DC}}\) = 0.75 x fc\({}_{\text{3D}}\)). With this, stress drops translate as \(\Delta\sigma_{\text{3 DC}}\) = 0.42 x \(\Delta\sigma_{\text{3D}}\). [PERSON] et al. (2019) carefully compared the two approaches and found systematic differences of the calculated stress drops. In order to reconcile the absolute values of both methods, they proposed to fix the corner frequency of the EGF event (fc2 in Equation 6) in the SR method to an optimized value which is then used for all ratios in the data set. We do not focus on the issue of adjusting the methods as we have demonstrated the principal similarity and especially since almost all SR results have an equivalent stress drop estimate from the SDC method.
Summarizing this paragraph, we have shown the high level of similarity of results obtained by both methods. They are qualitatively similar, but the number of SDC estimates is significantly higher. Also they include stress drop estimates for basically all events with SR solutions. The validation of similarity was necessary, as we can
Figure 6.— Stress drop distributions in the target region computed by the spectral decomposition approach (SDC) and by the spectral ratio approach (SR). Each 0.1” x 0.1” grid cell represents the median value of all calculated stress drop estimates within the cell. No smoothing is applied. The colors correspond to the histograms on the bottom, which show log-normal distributions in both cases. Stress drop estimates for 51,510 events are obtained with a median of 2.12 MPa for the SDC approach and 4,223 resulting stress drops with a median of 4.45 MPa for the SR method. The standard deviations are indicated above the distributions. Note the good consistency between results of both methods.
now focus only on the SDC results in greater detail, in the following. For the interested reader, we include SR result based figures for each of the following SDC results based figures in the supplement.
### Stress Drop Estimation Results
The spectral decomposition method yields stress drop values for 51,510 events. For each event, the value is calculated as the median of all available stress drop estimates originating from multiple cells (i.e., different gEGFs) and from both P and S phases. The resulting stress drop distribution is shown in Figure 6, where the event-wise stress drops are averaged on a regular grid using \(0.1^{\circ}\times 0.1^{\circ}\) cells and color-coded according to the color scheme provided in the corresponding histogram. The stress drop histogram shows a well-defined log-normal distribution with a median value of 2.12 MPa. There is an apparent systematic difference between the stress drops in the western and the eastern part of the study region.
An exemplary west-east side view of the entire depth range from trench to about 180 km depth (Figure 8) better resolves the seismically active domains responsible for the stress drop variation which is evident in the map view. It clearly demonstrates the distinct and systematic differences of stress drop associated with specific regions. The seismicity along the plate interface clearly sticks out with low stress drop values whereas the upper plate crustal events have on average relatively high stress drops. The two interface-parallel bands of seismicity show a mixture of low to medium values, and the intermediate depth seismicity band exhibits a depth-dependent increase of stress drop. Hence, the apparent segmentation of the subduction zone based on deviations in stress drop value corresponds well to the event classification from [PERSON] et al. (2023). Consequently, we analyze the stress drop variability based on the predefined event classes in the following.
Figure 9 illustrates the class-wise histograms for stress drops, magnitudes, corner frequencies and S- wave velocities. All classes except the mining events (MI) show log-normal distributions of stress drop. 97.5% of the estimates lie between 0.1 and 100 MPa. Their median values are 1.4 MPa for class P1 events, 1.7 MPa for P2, 2.1 MPa for P3, 3.3 MPa for UP and 2.3 MPa for class ID events. For each class, the spatial distribution of stress drop in map view is plotted separately in Figure 10.
The spatial availability of stress drop estimates generally follows the variation of seismic activity. In consequence, the results for each event class are limited to cells of sufficient earthquake occurrences. Numbers of upper plate
Figure 7: Median stress drop variation with depth for the SDC (a) and SR (b) results, smoothed over three bins (9 km), color coded after event classification. SR results scatter significantly more due to the limited event count and sparser coverage. Note the principally good consistency of the curve shapes between results of both methods, for both the overall depth variation and the class wise variations. (c) Density plot of corner frequency estimates for 1,700 events (M \(\geq\) 2.6), for which stress drops values were found by both methods, the spectral ratio and the spectral decomposition approach. Color indicates event count per cell. The gray lines mark the corner frequency resolution limits. Density is high in the center of the cloud, especially along the regression line, expressing a general agreement between both methods. The obtained relation between results is \(\mathrm{fc}_{\mathrm{20C}}=0.75\times\mathrm{fc}_{\mathrm{20H}}\) which translates into \(\Delta\varepsilon_{\mathrm{20C}}=0.42\times\Delta\varepsilon_{\mathrm{3H}}\).
events, for example, are higher in the latitude range of the Iquique event (approx. 20\"S), which had a shallow rupture origin and activated a shallower part of the megathrust and many crustal events. In contrast, the smaller Tocopilla event in the south, which had a comparatively deep origin and rupture surface did not have large impact on crustal seismicity. Consequently, fewer UP event stress drops could be computed in the southern region, leading to non-uniform sampled average values of the stress drop distributions. Such sparsity is most apparent in the UP and P3 classes. The interface, in contrast, was activated by both megathrust events (cf. Figure 10), leading to large amounts of seismicity in the corresponding areas and their surroundings, which enables a good coverage with stress drop estimates in the P1 class. This heterogeneity of existing data points has to be considered when interpreting the overall results.
Next to the SDC results Figure 6 includes the results from the spectral ratio approach. Limited by the number and availability of suitable EGFs, 62,115 stress drop estimates are found for 4,223 events. Again, each final estimate is the median of the stress drop estimates for each target event, which originate from different possible EGFs as well as the use of both P and S phases. The overall spatial distribution of results is similar to the distribution from the spectral decomposition method, and also the stress drop variation appears to be similar, except that a smaller area is covered (fewer estimates) and that the overall median is higher (4.45 MPa). Despite this discrepancy, the median values between estimates of different event classes keep about the same relative differences with P1, P2, P3, UP, and ID having average stress drop values of 2.0, 1.9, 1.9, 4.0, and 5.2 MPa, respectively. Note that especially P2 and P3 include results for only few events. An equivalent to Figures 9 and 10 for spectral ratio results can be found in Supporting Information S1 (Figures S12 and S13).
Different profiles (west-east, north-south, depth, distance to interface) for the entire stress drop ensemble along with the median short range stress drop variation are shown in the supplement Figure S13 in Supporting Information S1 as well as for each class separately in Figures S14-S20 in Supporting Information S1, for results of both methods.
### Detailed Observations
In this section we describe the main stress drop pattern separately for each event class. The observations mostly relate to the depth-dependent variability (Figure 7), the histograms (Figure 9) or the class-wise maps (Figure 10). More details, such as the variation of the short range median stress drop (for easting, north-ing, depth, and distance to interface) for each separate class is displayed in Figures S14-S20 in Supporting Information S1.
Figure 8: West-east stress drop slice at 21.0”S to 21.5”S. Color indicates single event SDC stress drop value. The inset shows the same section with coloring corresponding to event class, similar to Figure 1. Note the clear visual separation of UP and P1 class events. The low stress drop values along the interface are traceable even into the deeper ID cloud. Also, an increasing stress drop with depth in the ID cloud is clearly visible. The slab interface estimate displayed stems from [PERSON] et al. (2018).
Figure 9.— Distributions of SDC stress drop, magnitude, corner frequency and S velocity at the source for UP, P1, P2, P3, ID, MI, and NN classes, from top to bottom. Stress drops were calculated based on the displayed corner frequencies, seismic moments (from the displayed magnitude distribution) and the S wave velocities at the source (Equation 3). Median stress drops are displayed in the stress drops column legends and total event number in the magnitude column legends. Note the difference in median stress drop between classes, for example, the plate interface (P1) showing the lowest median value and intermediate depth events (ID) or upper plate events (UP) significantly higher median values.
#### 4.3.1 Spatial Variation
**UP** Upper plate seismicity shows a comparatively high median stress drop of 3.32 MPa. We observe an increase of stress drop with depth from 2 MPa to about 4.5 MPa in the uppermost 20 km, below which the median stress drop decreases slowly with depth back to about 2 MPa (cf. Figure 7). Most upper plate stress drop estimates are from the lquique mainshock area between 19.2-20.6\(\lx@math@degree\)S, and from the seismically highly active region just south of it (cf. Figure 10). The highest median values are found from 20.0 to 20.2\(\lx@math@degree\)S (3 MPa) and 21.0 to 21.6\(\lx@math@degree\)S (4 MPa). The upper plate events show a steady increase of stress drop with distance to the interface for the first 30 km upward (Figure S14 in Supporting Information S1). There are two major continuous patches of increased upper plate stress drops observed (Figure 10). One is located above the main rupture patch of the Iquique event, a region that was struck by the crustal Mw6.7 Iquique foreshock and its aftershocks ([PERSON] et al., 2014, 2020). The other one is located at 21.0\(\lx@math@degree\)S-21.7\(\lx@math@degree\)S, starting from the coast and extending about 70 km toward east (green dashed box). Seismicity rates in this area are reportedly elevated, and [PERSON] et al. (2018) proposed a correlation to the decreased locking observed by geodetic studies.
**P1** Interface seismicity, labeled as P1, poses the second-largest class of events (n = 3,724). It includes events from near the trench to about 69.6\(\lx@math@degree\)W inland and almost completely covers the area between 19\(\lx@math@degree\)S and 23.5\(\lx@math@degree\)S. It shows the lowest median stress drop of all classes (1.4 MPa) of natural seismicity. The values found closest to the plate interface are even slightly lower, and increase with distance (cf. Figure S15 in Supporting Information S1) both in down and upward direction. The short range median remains stable at 2 MPa down to 15 km depth, and then decreases down to 1 MPa at 40 km. Below at 50 km, a local maximum of 1.8 MPa occurs, followed by values below 1 MPa at around 65 km depth (cf. Figure 7 and Figure S15 in Supporting Information S1). The stress drop distribution on the plate interface is dominated by fore- and aftershock sequences of the Iquique earthquake and the Tocopilla earthquake. The stress drop distribution in the Iquique region shows low to average values close to the hypocenter locations of both main shock and aftershock (Figure 10). At the western and northern rim of the main shock, high stress drop values are observed. Just between the main and aftershock slip surfaces, a band of low stress drop values is located, similar in values to those located at the southern end of the aftershock slip area.
Figure 10: Stress drop distributions in the target region computed from spectral decomposition approach separated into the classes MI, UP, P1, P2, P3, and ID from left to right, respectively. The color scheme is the same as in Figure 6. Histograms and median values for each class of events are displayed in Figure 9. A detailed description on the spatio-temporal variability of stress drop are found in the text. Two regions of special interest are highlighted by green dashed boxes in the UP and P1 maps, showing particularly high and relatively low stress drops, respectively. The map for the NN class is shown in Figure S14 in Supporting Information S1.
The high slip regions of the Tocopilla event are characterized by low to average median stress drop values, while the down dip edge is dominated by high values and the up dip edge is surrounded by low values. The region north of the Tocopilla event rupture area shows a large patch of low stress drop values (green dashed box), covering parts of the gap northwards to the lquique event aftershock area. Note that this low stress drop patch directly borders the large high stress drop region to its east observed in the upper plate, as described above. Also note that, although the P1 class is only defined down to a depth of about 65 km, low stress drop values along the interface are observed down to a depth of at least 125 km (see Figure 8).
**P2** The first seismically active band below the interface has a slightly higher median stress drop (1.7 MPa, \(n=1,\)816) than the interface seismicity. Similar to P1 it covers a large region almost completely. Maybe due to its lower event count the map shows more fluctuations and less well defined low/high valued patches. Still, the stress drops close to the hypocenters of the lquique event and its main aftershock are recognizable higher than in P1. The low stress drop band between the two major events is also indicated, similar to the low stress drops in the seismic gap between the lquique aftershock and the Tocopilla earthquake, which here extends slightly more to the east. In the central-eastern and southeastern part, some patches of elevated stress drops are observed. The median stress drop depth variation is similar to the P1 curve, having a peak of 2 MPa at about 50 km depth, followed by a decrease. From 65 km on, an increase to about 3 MPa occurs (Figure 7).
**P3** The same variation with depth is seen for the P3 class events, which are part of the second interface parallel band. The limited amount of events (\(n=587\)) is spatially separated into several areas, like the northern part of the Tocopilla earthquake slip surface, associated with low stress drop values and some deeper and more eastern cells,
Figure 11.— (a) Stress drop distribution versus time for events limited to longitudes west of 70”W for the entire observation period. The median is computed over 100 events per bin. Error bars represent the 25% and 75% percentiles. No smoothing is applied. Gray vertical lines denote the Tocopilla and the lquique event. (b) Five weeks of stress drops from the \(M_{\rm w}\)7.7 Tocopilla aftershock area (lat \(\leq-70\), \(-21.5^{\circ}>\) lon \(>-23.25^{\circ}\)). The vertical line is the Tocopilla origin time. (c) Stress drops from the lquique aftershock area (lat \(\leq-70\), \(-19^{\circ}>\) lon \(>-20.25^{\circ}\)) 3 weeks before to 5 weeks after the lquique event. Ray vertical lines denote the Mw.6 7 foreshock, the Mw.8 1 lquique event, and the Mw.7 6 aftershock, respectively. (d) Stress drops from the \(M_{\rm w}\)7.6 lquique aftershock area (lat \(\leq-70\), \(-20.25^{\circ}>\) lon \(>-20.75^{\circ}\)). The second vertical line is its origin time. The gray horizontal line is the long term stress drop median for the corresponding region. For all large events, the stress drop values are elevated close to the origin times of the main shock, followed by a rapid but not instant decline to values below the median, followed by a return to average values within a few days to weeks.
where median values reach up to 6 MPa. Interestingly, this is a higher value than for the neighboring cells, located in the intermediate depth class (ID). Especially the latter group of comparatively deep events is responsible for the relatively high median value (2.13 MPa) found for this class.
**ID** The ID class (or else called IDEs) is the largest group (\(n=41\),462) and shows a higher median of 2.26 MPa compared to the Px group. It is the only class where the stress drop map is locally fully continuous and many cells exceed 1,000 event members. While the ID event stress drop map is dominated by medium to high values (Figure 10) there exist two patches of lower than average stress drop at about 19.5\({}^{\circ}\)S and at 20.75\({}^{\circ}\)S. Especially the latter region is seismically the most active region in the entire data set ([PERSON] et al., 2018) and thus, it contributes many low stress drop values to this event class which otherwise would have an even higher median value. In its shallowest part the depth variation is similar to that of the Px group, with a minimum (1.5 MPa) at about 75 km depth, followed by an increase to 2.2 MPa at about 90 km depth and, after some short decrease, a more rapid rise to about 8.5 MPa at a depth of 140 km. Further down the increase of stress drop appears to cease at 175 km below which stress drops increase again up to values exceeding 10 MPa. Note that this class of events shows the highest range of median stress drop variation with depth. Several possible reasons for the increase will be discussed later.
**MI** We obtain stress drop estimates for 1,004 events from the mining class with a very low median stress drop of 0.08 MPa. 876 of them were labeled MI in the IPOC catalog and 128, which initially were classified as UP events, were reassigned to the MI class because of their particularly low stress drops and their clustered and shallow locations. It is interesting to note that only a small fraction of the events exceed stress drops of 1 MPa while many estimates significantly undercut 0.1 MPa. The statistical distribution of the mining-related events stands out against the other classes of tectonic events and deviates strongly from a log-normal shape as seen in Figure 9.
**NN** The locally less well constrained events from the NN class are basically split into two major groups. The first group are those events which lie far offshore and have poorly constrained depths. The second group are events located far east of the network mostly at great depth (>150 km). Here, the location accuracy is also decreased. Hence, the stress drop values suffer from possibly wrongly assigned S wave velocities. For example, for the shallow group, almost exclusively lower plate mantle velocities are used. Should any of them lie at or closely below the interface, their stress drops would be much higher when using lower plate crustal velocity. The stress drop distribution from Figure 9 reflects the separation of stress drops into two groups by a comparatively large standard deviation and a bimodal shape of the corner frequency distribution. Including this class here has two main reasons. One is the additional depth extent (160-180 km) covered almost exclusively by this event group, and the second is the consistency of the processing with the complete IPOC catalog.
Similarly, as the MI events, we do not further discuss their properties or interpret their stress drops. The corresponding stress drop map for this class is shown in the supplement Figure S14 in Supporting Information S1.
#### 4.3.2 Temporal Variation
Stress drops do not only vary in space, but also in time (e.g., [PERSON] and [PERSON], 2007). We observe such variation for shallow, predominantly interface and upper plate seismicity in Figure 11. Strikingly, the one hundred event median shows maxima at the occurrence times of the large interface events. We therefore show narrower time frames for spatially limited areas around four major earthquakes: the \(M_{u}\)8.1 plutique event, its \(M_{u}\)6.7 foreshock, its \(M_{u}\)7.6 aftershock and the \(M_{u}\)7.7 Tocopilla event. All stress drop curves have similar shapes. Initially, at occurrence time, the median stress drop is high, up to multiple times the long term median of the specific region. In the following days, a decline of stress drop values down to values slightly below average is observed, followed by a recovery back to average values. The decay time is longest for the largest of the four and shortest for the smallest main shock.
This behavior has already been described in [PERSON] et al. (2021) for the lquique event. There, the variability was attributed to the increased moment rates during the immediate post-seismic interval. We observe the same effect here for three additional large magnitude events. To illustrate the influence of the temporal moment rate variability, we plot the time-dependent stress drop variation scaled by event moment rate in the supplement (Figure S25 in Supporting Information S1). Please note, that one potential key aspect in this observation is the apparent moment dependent scaling in our results, discussed later in the text. Also, in the high event rate aftershock period, event detection might be incomplete in the IPOC catalog, favoring large magnitude events which would additionally bias the above observation.
The stress drop scatter in each time bin is significant, as indicated by the 25% and 75% percentiles. The percentiles log-distance is stable between time steps and corresponds well to the overall stress drop standard deviation (Figure 7). This can be understood as a consequence of the natural log-normal distribution of the stress drop. The median stress drop variation between steps is significantly less than the average percentile distance. As percentile markers in Figure 11 always follow the median stress drop variation from step to step, we stick to the description of variability via the median stress drop.
## 5 Discussion
In this section, we first discuss the results of this study in the context of other stress drop studies. Next, we consider implications of the used methods, limitations and possible biases. We then highlight the most interesting aspects of our stress drop distribution and show possible correlations with other research in the northern Chilean subduction zone. In doing so, we exhibit the potential of a comprehensive stress drop map to contribute to interpretations of the tectonic state of, for example, the megathrust, or to questions of source physics and stress distribution in a subduction environment.
### Overall Results
The principal range of obtained stress drops in this work is between 0.1 and 100 MPa (for 97.5% of estimates), a well accepted corridor for natural seismicity found in multiple studies for many events and a broad magnitude range (e.g., [PERSON] and [PERSON], 2007, 2009; [PERSON] et al., 2022; [PERSON] et al., 2014). Median values vary significantly less, ranging from 1 MPa for shallow events to 15 MPa for the deepest in this data set, as well as from 1.4 to 3.1 MPa between different event classes. Median values for spectral ratios are on average about twice as high. This shows that although median stress drop is found to differ between different regions, depths, and classes with good consistency between methods, a single event cannot unambiguously be assigned to a class based solely on its stress drop value. This is also a consequence of the natural log-normal distribution of the stress drop (Figure 9).
Especially absolute values have to be handled with care. Not only the parameters in the chosen source model, but also the methods for determining the corner frequency may introduce additional differences. It is clear that different source model choices, that is, k-values, also produce large deviations in absolute stress drop (e.g., [PERSON] et al., 2022; [PERSON] and [PERSON], 2015). Hence, it is beneficial to process many events similarly and interpret results based on relative differences, if possible confirmed by multiple methods (e.g., [PERSON] et al., 2021).
For northern Chile, only limited stress drop data has been reported, so far. For example, [PERSON] et al. (2021) compute stress drops for six large magnitude events located at shallow intermediate depths in northern Chile. They use kinematic source inversion and find absolute stress drops of 7-30 MPa. These values seem relatively low compared to our results of large magnitude intermediate depth seismicity.
[PERSON] and [PERSON] (2019) estimated corner frequencies from attenuation-corrected spectra for 96 events in northern Chile. They do not provide values for the stress drop, but note that the corner frequencies of intermediate depth earthquakes are significantly elevated compared to shallow depth earthquakes, which would lead to elevated values for the stress drop, consistent with our results. They emphasize that the stress drop depends strongly on the unknown rupture velocity, which can vary from event to event, which is also true for our study. [PERSON] et al. (2018) calculated rupture velocities for small to moderate earthquakes in the Iquique region. The resulting average velocity fits well with the assumed value of 0.7\(\beta\) from this study, but the reported scatter of velocity values is quite large, although the study was limited to shallow seismicity. Therefore, we note that variable rupture velocities are an important source of perturbation to consider. For example, the increase in observed stress drop could be explained simply by a change in the assumed average \(v/v_{s}\) with depth. We did not observe a change in the _f,p,f,s_ ratios with depth, which would have been a clear indication of a change in rupture velocity ([PERSON] and [PERSON], 2014, 2015).
### Method and Limitations
In this study, similar to [PERSON] et al. (2021), we observe a clear dependence of stress drop on moment (Figure 12a), which contradicts the invariance hypothesis of stress drop scaling for our data set in northern Chile. We fit a linear relation (\(\log_{10}(\Delta\sigma)=\epsilon_{0}+\epsilon_{1}log_{10}(M_{0})\)) to stress drop estimates over separate magnitude bins (e.g., [PERSON] and [PERSON], 2017) and we obtain \(0.4<\epsilon_{1}<1.09\). This indicates a moderate to strong dependence of stress drop on moment. Note, that the elevated \(\epsilon_{1}\) values for the M2-2.5 and \(>\)M4.5 bins are an indication for a possible bandwidth limitation/event selection bias ([PERSON] & [PERSON], 2001) at the magnitude interval limits. As a consequence of the high frequency spectral limit (30 Hz), small magnitude stress drop estimates might have too small \(f_{e}\) estimates or get deselected, entirely. This could skew the distribution in that bin. The top bins could be affected in the same way. The inner bins, however, also show a clear moment dependence, which cannot be explained similarly. As reported in [PERSON] et al. (2021) more restrictive quality criteria for spectra included in the analysis may moderately decrease the \(\varepsilon_{1}\) parameter, but the clear positive dependence remains.
Figure 12.— (a) SDC stress drop (no MI events) against moment. The black line is the bin wise linear fit of the SDC data, (b) shows corner frequency versus moment. Gray lines indicate the frequency limits. Panels (c) and (d) are similar to (a) and (b) but for SR results. (e) Depth against normalized stress drop, normalized corner frequency, normalized magnitude, and normalized S wave velocity, demonstrating that the main driver of increased stress drop with depth (\(>\)80 km) is the increase of corner frequency. Solid lines are SDC medians, dashed lines are SR medians. Gray error bars show SDC stress drop percentiles. On the right the event count per bin is shown capped at 1000 (SDC) and 100 (SR) events per bin.
[PERSON] and [PERSON] (2017), have explicitly shown, that there is a fundamental trade-off between n and \(\varepsilon_{1}\) (the scaling factor) when using the spectral decomposition algorithm (SDC). According to them, to obtain scale invariance, the spectral falloff, most commonly set to \(n=2\), must be allowed to vary to lower values. They explain this by an apparently higher spectral content at high frequencies in larger events than predicted by a standard Brune type spectral model. For example, [PERSON] and [PERSON] (2009), have used \(n=1.6\) for analyzing events with magnitude larger M5.5 to obtain scale invariance.
Alternatively, one can drop the scale invariance hypothesis and allow for variable stress drop in the spectral stacking procedure, that is, a more data driven ansatz while keeping n fixed to 2. According to [PERSON] and [PERSON] (2017), both variants are indistinguishable in terms of rms-misfit. In our work, the second approach was taken, by applying the SDC technique called SNSS, initially described in [PERSON] and [PERSON] (2020). As a consequence, stress drop scales with moment as described above. Using similar assumptions, for example, [PERSON] et al. (2013), [PERSON] and [PERSON] (2017), or [PERSON] et al. (2021), report scale dependency comparable to our results \(\left(\Delta\sigma\sim M_{0}^{0.2-0.8}\right)\), as opposed to other studies which report a general scale invariance of stress drop (e.g., [PERSON] (1995), or [PERSON] et al. (2006)). Please note that moment dependent stress drop is also observed in the SR results of our study, where we find \(\Delta\sigma\sim M_{0}^{0.3-0.7}\) (Figure 12c). Moment dependent stress drop was reported in other SR studies as well, for example, [PERSON] et al. (2013). On the downside of allowing the data driven concept, the strong scaling leads to unreasonable high stress drops for large magnitude events in our data (Figure 12a).
Other sources of bias are potential event selection and bandwidth limitations. To systematically check whether the initial quality criteria (e.g., SNR) introduce a significant event selection bias ([PERSON] and [PERSON], 2001) and how the bandwidth limitation can affect the results, we compared the IPOC catalog magnitude frequency distribution with that of the stress drop result catalog. We find that only a small and stable fraction of events in each magnitude bin did not allow computing stress drops (\(<\)10%, Figure S27 in Supporting Information S1) indicating no severe apparent selection bias. The effect of bandwidth limitation is much harder to assess. The overall distribution of computed corner frequencies (Figure S28 in Supporting Information S1) shows the limited amount of events (\(n=163\)) which got discarded due to too high fc. They practically have no impact on the overall statistic. A check on the 5% variance bounds for the estimated corner frequencies ([PERSON] et al., 2010) does not reveal systematic frequency underestimation at the high limits (Figure S29 in Supporting Information S1).
From other studies, however, one might expect more high corner frequency events where \(f_{c}>30\) Hz (even if they are later discarded during processing). The apparent lack of such events in our data could be an effect of the relatively sparse station coverage in northern Chile. Average event station distances, especially for the ID events, which pose the great majority of datapoints, are easily in the 100 km range. If attenuation removed the high frequency content, we would not be able to recontract it, even with highly suitable Green's functions. This might also effect several events below \(f_{c}=30\) Hz.
In sum, we have applied a well accepted processing technique to estimate earthquake stress drop which is data driven, and we assumed the spectral falloff rate of \(n=2\), most commonly used in spectral studies. In doing so, we obtain a dependence of stress drop on seismic moment which is persistent at all magnitude bins and which is observed in our SR results, too. For large magnitudes this leads to unphysically large stress drop estimates and hence can be considered inappropriate. For small magnitude events, band limitations might lead to missing high stress drop events, increasing the apparent moment dependency. Nevertheless, we prefer the data driven approach over the forced scale invariance choice.
To underline the robustness of both the overall results as well as the localized observed variability of our results, we add a stress drop map similar to Figure 6 to the supplement (Figure S26 in Supporting Information S1) where we have limited results to events of magnitudes between M2.8-M4.5. It features are very similar distribution of stress drop through the subduction zone.
### Depth Dependence and Local Variability
A depth dependence of stress drop was reported in many studies (e.g., [PERSON] et al., 2017; [PERSON], 2020; [PERSON] et al., 2014), while others find no such evidence (e.g., [PERSON] et al., 2006). A conclusive explanation of depth dependent stress drop or a convincing correlation to other parameters is still missing. Whether stress drop increases in the crust was recently discussed in detail by [PERSON] et al. (2021), who find that most studies probably overestimate the depth dependency by different ways of under-correcting the depth dependent attenuation. They state that using a spectral ratio approach with good EGFs should principally be unaffected by such problems. We do not find significant qualitative differences of results of our two approaches concerning this question. And we observe both, a stress drop increase in the crust for \(z\leq 20\) km from 2 to 4 MPa and below, a median stress drop that decreases slowly back to about 2 MPa over a range of 40 km (Figure 7 and Figure S15 in Supporting Information S1) with minor fluctuation. In northern Chile, continental crustal thickness ranges up to 60 km ([PERSON] et al., 1999) which is also represented in the utilized velocity model (Figure S30 in Supporting Information S1). Note that the UP class also contains seismicity from the subduction wedge and that the Moho deepens from west to east with the plate interface deepening. Additionally, stress drop sampling in the upper crust is not uniform but concentrated to several regions. The behavior of the average stress drop median with depth might therefore not be unbiased by the subduction geometry and most likely it is not indicative for intra-plate stress drop variability.
The median value of stress drop combined for all classes shows three relative maxima at 20 km, 55 and 85 km depth (Figures 7 and 12e). At these depths median stress drop varies only between 1.25 and 2.5 MPa. Note, that sampling (number of stress drop estimates per depth bin) is not uniform (Figure 12e). At greater depths, (\(>\)100 km) a consistent increase to values up to 8.5 MPa is observed, followed by a plateau and another subsequent increase to values above 10 MPa. To investigate the driving parameter for the increase, we plot corner frequency, magnitude and S wave velocity against depth (Figure 12e). The top 60 km show a complicated behavior of the three curves, but it appears that medium magnitude values remain stable below 40 km and mean velocity is basically constant below 60 km depth. Solely the median corner frequency estimate increases almost steadily with depth, causing the rise in stress drop. Therefore, we conclude that the increase of stress drop with depth is mostly driven by an increase of corner frequency. This holds for both the spectral decomposition and the spectral ratio method (with significantly stronger fluctuation), and we consider this result robust. Note, that different depth might be sampled very differently, as shown in Figure 12e.
Interestingly, and different from this observation, the variability of stress drop with time found for the major earthquakes in the catalog region (Figure 11) appears to be primarily driven by increased moment release rate, rather than temporally elevated average corner frequency (cf. Figure S25 in Supporting Information S1). Indeed, during that period, average corner frequencies appear reduced, which is expected if predominately larger events occur. This reduction, however, does not suffice to compensate the increased moment which results in increased stress drop. Once this effect decays, the overall median stress drop returns to its initial value. Also, on a longer timescale, its alteration is not permanent. For example, the difference of median stress drop for events that occurred earlier than 4 weeks before the Iquique event and events that occurred later than 4 weeks after the Iquique event is about 0.03 MPa. For the Tocopilla event, this difference is 0.09 MPa. A similar observation was made in California, where the 2004 M6 Parkfield earthquake reportedly did not permanently change the stress drop pattern ([PERSON] & [PERSON], 2007).
To our knowledge, a consistent, continuous and comprehensive analysis of the stress drop pattern over the broad depth range of 0-180 km as performed in the present study has not yet been reported elsewhere. We can therefore only compare with studies that cover subdomains of this range. [PERSON] and [PERSON] (2009) studied the distribution of stress drop for global seismicity and found evidence of a downward increase in stress drop from a depth of 30 km. [PERSON] et al. (2015) analyzed the rupture duration of aftershocks from the 2010 Mw8.8 Maule earthquake, Chile, at 35\({}^{\circ}\)S and noticed variability in normalized rupture duration with a minimum at 40 km depth. Since the source duration is inverse to the corner frequency, a reduction corresponds to an increase of stress drop. However, in both studies, no results are calculated below 60 km depth. In Japan, [PERSON] et al. (2014) studied the variation of stress drop in the broader region of the 2011 Tohoku earthquake. Their analysis includes events to a maximum depth of 80 km. They find a sharp increase in stress drop between 30 and 60 km accompanied by plateaus with constant median stress drop below and above. They have no conclusive interpretation for the increase or the plateaus they observed.
Other studies focus on deeper events, such as [PERSON] and [PERSON] (2016), who estimate the stress drop for global ID events and deep events based on estimates of the duration of the source time function. They find mean stress drop values of about 10-20 MPa for their shallowest events at about 150 km depth, with no subsequent increase. Given the general variability in stress drop estimates among authors and methods, these absolute values fit well with the estimates that we obtained for the deepest events in Northern Chile, which also indicate a cessation of stress drop increase near the depth limits of our study. [PERSON] et al. (2022) analyze stress drops from intermediate depth to deep events in the Tonga region and find average values around 5.6 MPa at 90 km depth, followed by decreasing median values to a minimum of 3 MPa at 170-250 km and then by an increase back to 6 MPa at greater depth. They report that they can best associate zones of high stress drop with areas of high plate deformation. In northern Chile, the plate undergoes strong geometric changes as it bends at shallow depths (<60 km), stops bending below (60-100 km), followed by bending that ends with a strong downward kink ([PERSON] et al., 2019, 2023). The strongest geometric deformation is observed between 100 and 140 km depth ([PERSON] et al., 2022), where the plate is bent to a significantly steeper subduction angle. As the depth of this bending process varies laterally, an increasing number of high stress drop events is gathered to calculate their median, which could be the cause of the continuous increase in the median stress drop that would otherwise be more abrupt. At about 21\({}^{\circ}\)-21.5\({}^{\circ}\)S the ID seismicity band is partitioned into a northern and a southern part. At this latitude range the subduction geometry appears significantly perturbed ([PERSON] et al., 2018) possibly inducing additional zones of increased stress. Interestingly, we observe laterally increased median stress drop in this area (between 21\({}^{\circ}\) and 22\({}^{\circ}\)S, cf. Figure 10). If higher plate deformation is indeed a significant driver behind the stress drop increase, one could also suspect that it is responsible for the relative maxima of the median stress drop depth variability at shallower depths.
The depth region of 100-140 km also includes by far the greatest amount of earthquakes in the IPOC catalog, especially between 20\({}^{\circ}\)S and 22\({}^{\circ}\)S. The initially at shallower depths observed parallel bands of seismicity dissolve at 80-100 km depth into a 25-30 km single band of very high activity reaching further down. In addition to the above-mentioned bending, [PERSON] et al. (2019) discuss the spatial coincidence of the vanishing velocity contrast between oceanic crust and underlying mantle in receiver function studies and the transition of the cold nose to the hot part of the mantle wedge indicated by seismic attenuation images. To explain the strongly increased earthquake productivity, they propose the sudden activation of a kinetically delayed metamorphic reaction with negative volumetric component, which further strengthens the local stress level already in place due to the strong slap pull. The increased observed median stress drops in this area might be an expression of the same process which is responsible for the strong increase in seismic activity in this region.
Seismic coupling can be directly compared to the obtained stress drop distribution along the interface. For example, a very low stress drop region is observed between the rupture patches of the Iquique event and the Tocopilla event (cf. Figure 10) called the _Loa_ section of the northern Chilean Margin. One might expect a correlation with low coupling in the same region, but in contrast, several GPS studies find a high coupling (e.g., [PERSON] et al., 2018; [PERSON] et al., 2015; [PERSON] et al., 2014). It is a debated question why neither the Tocopilla earthquake nor the Iquique earthquake have activated this section of the megathrust. One possible explanation might be a creeping behavior, mitigating the potential for large rupture. In California [PERSON] and [PERSON] (2007) have reported low stress drop values in the creeping section of the San Andreas fault to the north of the Parkfield event. Their creeping section, however, is separated by a relatively high stress drop barrier from the locked region. Our stress drop map fits into this picture if we consider the few high stress drop values just south of the Iquique large aftershock slip area as indicative for some kind of such barrier. This is supported by observations of repeating earthquakes at that point ([PERSON] et al., 2022; [PERSON] et al., 2019) which are generally interpreted as indicative for surrounding or adjacent fault creep. Hence, south of the barrier the interface would be considered creeping, also indicated by the relative seismic quiescence, there ([PERSON] et al., 2023). Further south we observe very low stress drop events which increase in average values until they reach the Tocopilla slip area. From gravity data, a locked asperity hosting potential for a large event generally is correlated with decreased values in the residual gravity field ([PERSON] et al., 2003). In contrast to the prior mentioned locking studies, [PERSON] and [PERSON] (2015) report a gravity high for this region, which would rather support the interpretation as a creeping segment.
## 6 Conclusions
In this study, we have computed a comprehensive, consistently processed stress drop catalog for Northern Chile. The database for this work is the IPOC catalog, with over 182,000 events in the time period from 2007 to 2021. We additionally perform template matching using the entire waveform archive to obtain an enlarged set of empirical Green's functions. Stress drops are computed by two different methods. First, a spectral ratio approach (SR), which was recently tested in the Iquique earthquake region, is now applied to the entire northern Chile seismic data providing 4,223 stress drops estimates. While these results show already distinct stress drop patterns for some regions, they are limited by the irregular availability of EGFs. To overcome this restriction and to complement the SR results, we second use a modified spectral decomposition approach (SDC). We carefully test and then apply a modification of the standard SDC technique by using multiple well-defined cells to account for the variability of seismic attenuation in the subduction zone. The SDC approach yields 51,510 stress drop estimates, improving significantly the continuity and coverage of the stress drop catalog. We find a linear relation of the estimated corner frequencies between both approaches, \(\text{fc}_{\text{SDC}}=0.75\times\text{fc}_{\text{SR}}\), translating into \(\Delta\sigma_{\text{SDC}}=0.42\times\Delta\sigma_{\text{SR}}\) for stress drops. Besides the systematic differences in absolute stress drop values, which has also been reported previously in other studies, the two methods produce very similar features.
The SDC- based stress drop distribution represents the first coherent and large-scale stress drop mapping of a subduction zone, including several tens of thousands events. We observe small, but systematic differences of median stress drop values between the seismotectonic domains. Interface seismicity is characterized by the lowest median stress drop of 1.4 MPa. Also, the two slab-parallel seismicity bands within the subduction Nazzaza plate exhibit rather low median stress drop values of 1.7 and 2.1 MPa, respectively. Upper plate events, which occur almost exclusively in the continental crust, show higher stress drops with a median of 3.3 MPa for the SDC method and 4.0 MPa when using the SR method. Intermediate depth seismicity is monitored down to a depth of about 180 km. It shows a median stress drop of 2.3 MPa. Two additional classes are treated separately in the analysis. For mining induced events, we find particularly small stress drops of about 0.3 MPa. The events from the NN class are poorly constrained; they have the largest location uncertainties and they show heterogeneous stress drops.
Both interface seismicity and the two seismicity bands in the down going slab show only small variations of less than 1 MPa with depth in the interval at 0-80 km depth, that is, the variability of the median stress drop along the subduction is low. Starting at 80 km depth, and especially also for the intermediate depth earthquakes, we observe a consistent increase of the stress drop from about 2 to 15 MPa.
The driving parameter for this increase is the rise of corner frequency with depth, consistently observed from SDC and SR processing. As an explanation for the temporally elevated median stress drop that we observe in proximity of the large megathrust events in the region, we have identified the increased seismic moment release during the fore- and aftershock series.
## Data Availability Statement
Waveform data used in this study were recorded by the seismological CX-net of the Integrated Plate boundary Observatory Chile (IPOC, 2006) using STS-2 broadband seismometers. It was obtained from the EIDA/GEOPHONE web page (eida.g.ffz-potsdam.de/webda3/ or geofon.gfz-potsdam.de/waveform/). Picks, magnitudes and event hypocenter were taken from [PERSON] et al. (2023). Data processing and figure production were mainly performed using Python3.5.1 (python.org) and packages IPython4.2.0 ([PERSON] & Granger, 2007), NumPy ([PERSON] et al., 2011), Matplotlib ([PERSON], 2007), ObsPy ([PERSON] et al., 2010) and SciPy ([PERSON] et al., 2020). Some figures were refined using Inkscape (inkscape.org). Results from this study are summarized in a table described and made available in the electronic supplement. They will be permanently stored and openly accessible at [[https://zenodo.org/records/10400960](https://zenodo.org/records/10400960)]([https://zenodo.org/records/10400960](https://zenodo.org/records/10400960)).
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wiley/fb826641_0659_4508_b87f_517b82032eb6.md | # Production Flux of Sea Spray Aerosol
[PERSON]
1 Cimate Change Unit, Finnish Meteorological Institute, Helsinki, Finland.
2 Department of Physics, University of Helsinki, Helsinki, Finland.
2 Department of Air Quality and Climate, TNO Built Environment and Geosciences, Utrecht, Netherlands.
1 Seattle Division, NorthWest Research Associates, Inc., Lebanon, New Hampshire, USA.
3 Naval Research Laboratory, Washington, D. C., USA.
1
[PERSON]
1 Seattle Division, NorthWest Research Associates, Inc., Lebanon, New Hampshire, USA.
4
[PERSON]
5 Naoral Research Laboratory, Washington, D. C., USA.
5 Naoral Research Laboratory, Boulder, Colorado, USA.
6
Footnote 1: footnotemark:
Received 3 August 2010; revised 9 December 2010; accepted 5 January 2011; published 7 May 2011.
2
Footnote 17: footnot
hereinafter LS04, p. 183]. Quantifying light scattering by SSA is thus important for understanding the perturbation by anthropogenic aerosols to Earth's shortwave radiation budget during the industrial period (so-called aerosol direct forcing) [_[PERSON] et al._, 1992; _Intergovernmental Panel on Climate Change_, 2007]. This cooling influence is partly offset by absorption of longwave (thermal infrared) radiation [_[PERSON] et al._, 2005a; _[PERSON]_, 2005]. Production and properties of SSA as CCN are of interest also in proposals to modify climate to offset global warming (\"geopeningering\") by alteration of the properties of marine clouds [e.g., _[PERSON]_, 1990; _[PERSON] et al._, 2006].
[SS] SSA often dominates the mass concentration of marine aerosol, especially at locations remote from anthropogenic or other continental sources, and SSA is one of the dominant aerosols globally (along with mineral dust) in terms of mass emitted into the atmosphere. Estimates of global annual mass emission of sea salt (calculated as the integral over the size-distributed number production flux times the volume per particle times the mass of sea salt per unit volume of seawater) with current chemical transport models (CTMs) and global climate models (GCMs), using various parameterizations of the sea spray source function (SSSF), range over nearly 2 orders of magnitude, from 0.02 to \(1\times 10^{14}\,\mathrm{kg\,yr^{-1}}\) (Figure 1 and Table 1) [_[PERSON] et al._, 2006]. Much of this variation is due to the different dependences on wind speed and to the upper size limit of the particles included. This wide range emphasizes the necessity of specifying the particle size range and the height or residence time in reporting sea spray emission fluxes. Critical analysis of SSA production leads to the conclusions that there are large uncertainties in SSA fluxes and that SSSF parameterizations must be viewed as little more than order-of-magnitude estimates [_[PERSON] et al._, 2002; LS04, section 5.11].
[6] In the past several years, the contribution of organic species to SSA has been quantitatively examined in laboratory studies and field measurements, and measurements of SSA concentrations and production have been extended to sizes smaller than were previously thought to be important. In this paper we provide an overview of recent measurements and experimental investigations pertinent to SSA and its production, with the purpose of examining this work and placing it in the context of previous understanding. The starting point is the review of SSA production by LS04. Since that time, marine aerosol production has been reviewed by _[PERSON]_ [2007] and by _[PERSON]_ [2007]. _[PERSON]_ [2007] focused mainly on wave breaking and provided an overview of sea spray aerosol production based primarily on work prior to 2000, complemented with more recent studies by Polish investigators. _[PERSON] and [PERSON]_ [2007] reviewed both primary and secondary particle formation in the marine atmosphere. With regard to primary SSA production, these investigators reviewed SSSF formulations presented in the period 2000-2006, results from laboratory studies concerning the sizes of the sea spray drops produced, and the first findings by _[PERSON] et al._ [2004] and _[PERSON] et al._ [2004] regarding organic matter in sea spray aerosol. The current review differs from those in that work published since LS04, including laboratory and field experimental results on sea spray production, on the enrichment in organic matter, and on the measurement and parameterization of whitecap coverage, is critically examined and compared with results summarized by LS04 to identify progress.
[7] Throughout this paper, we follow the common convention of specifying the size of an SSA particle by its equilibrium radius at a relative humidity (RH) of 80%, \(r_{80}\). For sea salt particles originating from seawater with typical salinity (34-36), \(r_{80}\) is about one-half the radius at formation. For such particles, to good accuracy \(r_{80}=2r_{\mathrm{dry}}\), where \(r_{\mathrm{dry}}\) is the volume-equivalent dry radius. A simple approximation for the RH dependence of the equilibrium radius ratio of an SSA particle in the liquid phase \(r/r_{80}\) is
\[\frac{r}{r_{80}}=0.54\bigg{(}1.0+\frac{1}{1-h}\bigg{)}^{1/3}, \tag{1}\]
where \(h\) is the fractional relative humidity (\(h=RH/100\)) [LS04, p. 54]. This equation applies in situations for which the effect of surface tension can be neglected (i.e., particles sufficiently large and RH sufficiently low); for other situations a more detailed treatment is required [_[PERSON]_, 2008].
[8] SSA particles are considered in three distinct size ranges based on their behavior in the atmosphere and considerations of the processes that affect this behavior [e.g., LS04, p. 11]: \(r_{80}\leq 1\) \(\mathrm{\SIUnitSymbolMicro m}\) for small SSA particles, \(1\mathrm{\SIUnitSymbolMicro m}\leq r_{80}\leq 25\mathrm{\SIUnitSymbolMicro m}\) for medium SSA particles, and \(25\mathrm{\SIUnitSymbolMicro m}\leq r_{80}\) for large SSA particles. This review is restricted to particles with \(r_{80}\leq 25\mathrm{\SIUnitSymbolMicro m}\). Special attention is paid to new information on composition, concentration, and production of SSA particles with \(r_{80}<0.1\mathrm{\SIUnitSymbolMicro m}\).
[9] Many measurements indicate that the relative concentrations of the major solutes in sea spray particles are similar to their relative concentrations in bulk seawater, although this may not be the situation for some substances as a consequence of the formation process or of exchange with the atmosphere subsequent to formation. SSA particles are said to be enriched in such substances, and the enrichment factor, defined as the ratio of the concentration of a substance to the concentration of one of the major constituents of bulk seawater (typically sodium) in the particle to the same ratio for bulk seawater, may be less than or greater than unity.
[10] In biologically productive seawater, accumulation of organic substances at the sea surface can result in formation of sea spray particles that are considerably enriched in these substances, especially for particles with \(r_{80}<1\mathrm{\SIUnitSymbolMicro m}\)[_[PERSON]_, 1964; _[PERSON] et al._, 1998; _[PERSON] et al._, 2004]. As far back as 1948, _[PERSON]_ [1948] showed that drops produced by bubbles bursting in areas with high concentrations of plankton (dimoflagellates) in red tide could carry irritants across the air-sea interface into the atmosphere. _[PERSON]_ [1963] documented enrichment of organic matter in sea spray and discussed the sea-to-air transport of surface-active material [_[PERSON]_, 1964]. _[PERSON] and [PERSON]_ [1970] further confirmed that bacteria are concentrated at the sea surface, leading to enrichment of bacteria in SSA particles. Later, factors influencing the organic content of marine aerosols were investigated in laboratory studies by _[PERSON] and [PERSON]_[1976]. More recently, the use of instruments such as aerosol mass spectrometers has demonstrated and quantified the presence of organic species in individual particles. For instance, _[PERSON] et al._[1998] reported that more than half of all marine particles with dry diameters greater than 0.16 um at Cape Grim, Tasmania, contained organics during clean marine conditions and that the organics were nearly always found internally mixed with sea salt. _[PERSON] et al._[1997], based on measurements in a region minimally affected by continental emissions, reported that the contribution of organic substances to the aerosol mass from particles with dry aerodynamic diameter less than 0.6 um was greater than that of sulfate, nitrate, or chloride (which would be indicative of sea salt) and suggested a marine source for these particles. _[PERSON] et al._[2000]
Figure 1: Annual average dry SSA mass production flux as computed by several chemical transport and general circulation models participating in the AeroCom aerosol model intercomparison [_[PERSON] et al._, 2006]. A global mean production flux of 10 g m\({}^{-2}\) yr\({}^{-1}\) over the world ocean corresponds to a total global production rate of approximately \(3.5\times 10^{12}\) kg yr\({}^{-1}\). For identification of the models, production methods employed, and references see Table 1. Number given in top right denotes global annual SSA production in \(10^{12}\) kg yr\({}^{-1}\).
reported that organics contributed roughly 20% to the mass of aerosol particles with \(r_{80}\) less than \(\sim\)1.3 um in the marine boundary layer, less than non-sea salt sulfate but about the same as sea salt.
[i] The aerosol consisting of sea spray particles in the atmosphere has traditionally been termed \"sea salt aerosol,\" but in this review it is denoted \"sea spray aerosol\" in recognition of the fact that the composition of the particles may differ from that of bulk seawater. One consequence of this difference is that the hygroscopic and cloud droplet activation properties of sea spray particles may differ from those calculated under the assumption that the particles are composed only of sea salt.
## 2 Production of Sea spray Aerosol and Flux Formulation
[2] SSA particles are formed at the sea surface mainly by breaking waves via bubble bursting and by tearing of wave crests. When a wave breaks, air is entrained into the water and dispersed into a cloud of bubbles [_[PERSON]_, 1992], which rise to the surface and burst. The resulting white area of the sea surface is often denoted a \"whitecap\" on account of enhanced, wavelength-independent scattering of visible radiation by the interfaces between water and bubbles, and the fraction of the sea surface covered by white area is defined as the whitecap fraction, \(W\). When an individual bubble bursts, the bubble cap (or film) may disintegrate into so-called film drops, which are ejected at a wide distribution of angles relative to the vertical. Up to a thousand such film drops may be produced per bubble, with the number and size distribution (and whether or not film drops are produced) depending largely on bubble size [LS04]. These film drops have radii at formation ranging from smaller than 10 nm to several hundreds of micrometers, but most are less than 1 um [e.g., _[PERSON]_, 1963, 1983; _[PERSON]_, 1964]. Individual bubbles with radius less than \(\sim\)1 mm typically do not form film drops [LS04, p. 208]. The majority of SSA particles in the atmosphere with \(r_{80}<1\) um are probably film drops.
[13] After the bubble cap has burst, a vertical cylindrical jet forms in the middle of the cavity left by the bubble. This jet may break up into as many as 10 jet drops, with the number depending largely on bubble size, that are ejected vertically to heights of up to \(\sim\)20 cm above the surface [e.g., _[PERSON]_, 1963, 1983; _[PERSON]_, 1995]. The initial radii of these drops are roughly 10% of the radius of the parent bubble and thus range from slightly less than 1 um to more than 100 um. Individual bubbles of radius greater than 2 mm typically do not form jet drops [LS04]. The majority of SSA particles in the atmosphere with \(r_{80}\) between 1 and 25 um are probably jet drops.
[14] SSA particles of the sizes considered in this review are formed mainly from bursting bubbles. Another production mechanism is the formation of spume drops by tearing of wave crests by the wind when the wind speed near the sea surface exceeds about 10 m s\({}^{-1}\)[_[PERSON] et al._, 1983]. These drops, which are transported nearly horizontally by the wind, are typically quite large, with radii from several tens of micrometers to several millimeters, and consequently fall back to the sea surface within seconds to minutes [_[PERSON]_, 1992]. Spume drops are not considered further here.
\begin{table}
\begin{tabular}{l l l l l l l} \hline & & & & & Global Dry & \\ & & & SSA Production & Reference for SSA & \multicolumn{2}{c}{SSA Mass} & \multicolumn{2}{c}{Maximum \(r_{80}\)} \\ & & & & Method & Production Method & (10\({}^{12}\) kg yr\({}^{-1}\)) & \multicolumn{2}{c}{Particles (μm)} \\ \hline ARQM & _[PERSON] et al._ [2003] & model derived & interactive & _[PERSON] et al._ [2003] & 118 & 41 \\ GISS & _[PERSON] et al._ [2006] & model derived & interactive & _[PERSON] et al._ [1986] & 2.2 & 8.6 \\ GOCART & _[PERSON] et al._ [2002] & GEOS DAS & interactive & _[PERSON] et al._ [1986] & 9.9 & 10 \\ KYU (Spiritars) & _[PERSON] et al._ [2002] & model derived & interactive & _[PERSON] et al._ [1986]; & 3.9 & 10 \\ LOA & _[PERSON] and [PERSON]_ [2004]; & model derived & interactive & _[PERSON] et al._ [1986] & 3.5 & 20 \\ & _[PERSON] et al._ [2005a, 2005b] & & & & _[PERSON] et al._ [2004] fit to & 21.9 & 15b \\ LSCE & _[PERSON] et al._ [2004] & ECMWF & interactive & _[PERSON] et al._ [1986]: & & \\ MPI\_HAM & _[PERSON] et al._ [2005] & model derived & interactive & _[PERSON] and [PERSON]_ [1998] & & \\ & & & _[PERSON] et al._ [2004] fit to & 5.1 & 8b \\ & & & & _[PERSON] et al._ [1986]: & & \\ PNNL & _[PERSON] et al._ [2004] & model derived & interactive & _[PERSON] et al._ [2002] & 7.4 & 15b \\ UIO-CTM & _[PERSON] et al._ [2003] & ECMWF & interactive & _[PERSON] et al._ [2002] & 9.5 & 50 \\ ULAQ & _[PERSON] et al._ [2002] & ECMWF & precalculated monthly & _[PERSON] et al._ [1997] & 3.5 & 20.5 \\ UMI & _Liu and Penner_ [2002] & ECMWF & precalculated monthly & _[PERSON] et al._ [1997] & 3.8 & 10 \\ & _[PERSON] et al._ [2006] & ECMWF & precalculated daily & _[PERSON] et al._ [2003] & 7.9 & 10 \\ \hline \end{tabular} 1
\end{table}
Table 1: Sea Salt Production Methods for Model Calculations in Figure 111[15] The SSSF is a numerical representation of the size-dependent production flux of SSA particles. The following form of this function is employed in this review:
\[f(r_{80})\equiv\frac{dF(r_{80})}{d\log_{10}r_{80}},\]
where the quantity \(f(r_{80})\) denotes the number of particles in a given infinitesimal range of the common logarithm of \(r_{80}\), \(d\log_{10}r_{80}\), introduced into the atmosphere per unit area per unit time and \(F(r_{80})\) is the total number flux of particles of size less than \(r_{80}\). (The subscript 10 denoting the base of the logarithm is suppressed in the remainder of this paper.) Implicit in this definition is that this quantity is averaged over areas and times sufficiently large that rapid fluctuations caused by individual breaking waves are smoothed out.
[16] Because SSA particles may be emitted with an initial upward velocity, because the sea surface is vertically disturbed by waves, and because SSA production is enhanced near wave crests, the nature of the air-sea interface and of interfacial production is difficult to characterize. Additionally, some SSA particles fall back to the sea surface before spending any appreciable time in the atmosphere, the fraction of such particles increasing with increasing \(r_{80}\). For all these reasons, the concept of a source of SSA particles that may be said to be introduced into the marine atmosphere must also, implicitly or explicitly, take into account an effective source height, which may be the mean interfacial height or some specified height above it [LS04]. Recognition of the need to specify an effective source height leads to a useful distinction between the interfacial flux (for which the height is zero) and the effective flux at that height. The interfacial flux is defined as the flux of those particles leaving the sea surface, whereas the effective flux is defined as the flux of those particles produced at the sea surface that attain a given height, typically taken as 10 m above mean sea level (the value used throughout this review), and thus remain in the atmosphere sufficiently long to participate in processes such as cloud formation and atmospheric chemistry.
[17] For many applications such as large-scale models that describe the atmosphere in terms of multiple vertical layers and consider introduction of particles only into the lowest level, it is only this effective flux that is important. For small SSA particles (i.e., those with \(r_{80}\lesssim 1\) um), the effective flux can, for all practical purposes, be considered to be the same as the interfacial flux. For medium SSA particles (those with \(1\,\mathrm{\SIUnitSymbolMicro m}\lesssim r_{80}\lesssim 25\,\mathrm{\SIUnitSymbolMicro m}\)), the effective flux becomes increasingly less than the interfacial flux with increasing \(r_{80}\). For large SSA particles, which have short atmospheric residence times and typically do not attain heights more than a few meters above the sea surface, the effective flux is essentially zero.
[18] An expression for the SSSF required as input to models would represent the size-dependent production flux expressed by equation (2) as a function of the controlling ambient variables \(a\), \(b\), ; i.e., \(f(r_{80}\); \(a\), \(b\), ). Identifying these variables and developing specific parameterizations for equation (2) rest on recognizing and understanding the controlling processes. Wind speed plays a dual role in influencing the effective production flux of SSA: first, by being the dominant factor controlling wave generation (and subsequent breaking) and second, through upward turbulent transport of newly formed particles. The near-surface wind speed, commonly measured and expressed at a reference height of 10 m, \(U_{10}\), is thought to be the dominant factor affecting sea spray production. However, different formulations of the size-dependent SSSF in terms of only \(U_{10}\) vary widely for the same \(U_{10}\). Considerable effort has been devoted to linking SSA production to more fundamentally relevant physical parameters such as wind stress on the surface, \(\tau\) (or the friction velocity, \(u_{*}\), defined by \(u_{*}=(\tau/\rho_{\mathrm{air}})^{1/2}\), where \(\rho_{\mathrm{air}}\) is the density of air), or whitecap fraction, \(W\), with the expectation that such approaches might lead to a tighter relation between production flux and one of these other variables than is currently the situation with wind speed. For example, at a given \(U_{10}\), \(\tau\) can vary by a factor of 2 [_[PERSON] et al._, 2005] and \(W\) by a factor of 10 or more [LS04; _[PERSON] and [PERSON]_, 2006]; this variation is likely due to variability in the wavefield, surface properties, and the like. However, such efforts have not resulted in substantial narrowing of the spread in the SSSF as a function of controlling variables. Other factors that are expected to affect the SSA production flux are those affecting sea state such as fetch (the upwind distance over the water of nearly constant wind velocity) and atmospheric stability (often parameterized by the air-sea temperature difference), which also affects vertical transport; seawater temperature and salinity; and the presence, amount, and nature of surface-active substances.
[19] A simplifying assumption that is sometimes made in parameterizing the SSSF is that the dependences on drop size and controlling variables can be separated into a dimensionless function \(\varphi(a\), \(b\), ) that contains all of the dependences of the SSA production flux on environmental forcing parameters \(a\), \(b\), , including wind speed, and a universal shape function \(g(r_{80})\)
\[\frac{dF(r_{80},\ a,\ b,\dots)}{d\log r_{80}}=\varphi(a,\ b,\dots)_{\mathrm{g }}(r_{80}).\]
However, this assumption has relatively little observational support, and there are several reasons why it would not be expected to hold; for instance, under higher winds more larger particles could be transported upward and thus contribute to, and change the size distribution of, the effective production flux.
## 3 Methods of determining SSA Production Fluxes
[20] Methods that can be used to infer the size-dependent production flux of SSA particles (Table 2) were discussed in detail by LS04. Methods relevant to this review are the steady state dry deposition method, the statistical wet deposition method, micrometeorological methods, and the whitecap method. These methods are briefly reviewed, and for each the following topics are discussed: the basic assumptions inherent in its application, the quantities required and how they are determined, the size range to which the method can be applied and what precludes its application to other sizes, and concerns with its use. Some of the commonly used production flux formulations are also discussed here and presented in Appendix A. New formulations are discussed in section 5.
### General Considerations
[_2_]_ The steady state dry deposition method, the statistical wet deposition method, and micrometeorological methods use field measurements of concentrations and/or fluxes, as do some applications of the whitecap method; thus, these methods infer the effective production flux. Most applications of the whitecap method use SSA size distribution measurements from laboratory-generated whitecaps, which allow inference of the interfacial production flux.
[_2_]_ Methods that rely on field measurements of SSA concentrations involve counting and sizing SSA particles in the atmosphere. However, even such measurements, although seemingly straightforward, encounter practical difficulties as a consequence of the low number concentrations of SSA particles, with values for SSA particles with \(r_{80}>1\) um typically reported as less than several per cubic centimeter and for all SSA particles typically reported as at most a few tens per cubic centimeter [LS04, section 4]. Such low concentrations, the consequences of which become even more pronounced when size-segregated measurements are made, can result in poor counting statistics and require long sampling times to achieve adequate signal-to-noise ratios.
[_2_]_ Another difficulty arises from the presence in the marine atmosphere of particles other than SSA particles, because in some size ranges and locations SSA particles are not the most numerous. Typical concentrations of all aerosol particles in clean marine conditions are several hundred per cubic centimeter. Thus, techniques are required to distinguish SSA particles from particles composed of other substances. This concern becomes increasingly important with decreasing particle size, as SSA particles with radii less than several tenths of a micrometer may constitute only a small fraction of all aerosol particles in this size range [e.g., LS04, Figure 16]. This concern pertains especially to coastal regions or other areas where continental aerosols may be present in high abundances. Additionally, enrichment of SSA particles either during formation at the sea surface or to atmospheric uptake and exchange may make it difficult to determine whether or not an aerosol particle is an SSA particle based on composition or on other properties such as hygroscopicity or thermal volatility.
[_2_]_ Field measurements of SSA particle concentrations or fluxes are often made at coastal regions because of cost, accessibility, ability to install permanent equipment, and other factors. Such measurements offer the possibility of long-term data sets that encompass a wider variety of conditions than may be feasible from an individual cruise. However, concerns with measurements from these locations are coastal influences such as surf-produced SSA and differences in flow properties and upward transport, in addition to the greater possibility of influences of continental aerosol. Typically data are screened so that they are used only when airflow is from ocean to land.
[_2_]_ Each of the methods that use field measurements requires certain conditions for its successful application. One such condition is often referred to as \"steady state,\" but this phrase has been used to mean different things in different applications, and this ambiguity can and has led to confusion. In some instances this phrase refers to conditions in which there is no mean vertical flux of SSA particles, whereas in other instances it refers to conditions in which mean quantities affecting the SSA flux such as wind speed are unchanged over times of interest (e.g., the sampling time required to obtain a statistically representative sample) although there may still be a net upward flux of SSA particles. Whether the required conditions are satisfied is rarely discussed in presentations of SSA flux determinations, but spurious results can occur through failure to take into account other factors that affect measurements. Key among these are time-dependent meteorological conditions, which confound flux measurements, and entrainment of free tropospheric air into the marine boundary layer, which causes a growth in height of this layer and a decrease in particle number concentration through dilution.
### Steady State Dry Deposition Method
[_2_]_ The steady state dry deposition method infers the size-dependent effective production flux of SSA particles by assuming that production of SSA particles with \(r_{80}\) in the
\begin{table}
\begin{tabular}{l c c l} \hline Method & Fluxa & \(r_{80}\) Rangeb (um) & Comments \\ \hline Steady state dry deposition & Eff & 3–25 & Easy to apply \\ Concentration buildup & Eff & \(\lesssim\)10 & Has been applied only once; holds promise \\ Statistical wet deposition & Eff & \(\lesssim\)1 & Simple, provides constraint on production flux \\ Micrometeorological & Eff & \(\lesssim\)10 & Several such methods \\ Whitecap & Int & \(\lesssim\)10 & Several approaches; typically measures production flux from laboratory- \\ & & & generated whitecaps \\ Bubble & Int & \(\lesssim\)100 & Requires knowledge of several quantities \\ Along-wind flux & Int & \(\gtrsim\)50 & Laboratory measurements; often incorrectly applied \\ Direct observation & Int & \(\gtrsim\)500 & Has been applied only in laboratory \\ Vertical impaction & Int & \(\gtrsim\)250 & Has been applied once in oceanic conditions \\ \hline \end{tabular}
\end{table}
Table 2: **Methods Used to Determine SSA Production Flux**size range of interest at a given time and location is balanced by removal at the same time and location through dry deposition, such that the net upward flux of particles of any given \(r_{80}\) in that size range is zero. The effective production flux is thus equal to the dry deposition flux, which in turn is equal to the product of the size-dependent number concentration, \(dN/d\mathrm{log}r_{80}\), and the dry deposition velocity, \(v_{\mathrm{dd}}\), also a function of \(r_{80}\)
\[\frac{dF_{\mathrm{eff}}}{d\log r_{80}}=\frac{dN}{d\log r_{80}}\times v_{\mathrm{ ad}}(r_{80}). \tag{4}\]
The size-dependent SSA number concentration, which is determined by measurements at a given reference height, typically near 10 m, is often parameterized only in terms of wind speed at 10 m, \(U_{10}\). The size-dependent dry deposition velocity is modeled, also usually as a function only of \(U_{10}\). Nearly all such parameterizations are based ultimately on _Slimn and Slinn_[1980], whose treatment accounts for gravitational sedimentation, turbulent transport, impaction to the sea surface, Brownian diffusion, and growth of particles near the sea surface due to the higher RH there, although for a given size range only some of these processes are important.
[27] The assumption of local balance requires steady state conditions with respect to dry deposition during the lifetimes of SSA particles in the atmosphere and thus that the meteorological conditions (i.e., wind speed and other pertinent parameters) under which the particles were produced are the same as those under which they are measured. It further requires that dry deposition be the dominant removal mechanism of SSA particles (i.e., that little or no rainfall has occurred during the lifetimes of these particles in the atmosphere), that there has been negligible decrease in concentration by entrainment and mixing of free tropospheric air, and that the mean size-dependent SSA concentration is independent of time. These assumptions restrict the mean atmospheric residence times of SSA particles for which this method can be accurately applied to a few days at most, corresponding to an approximate size range of 3 um \(<r_{80}<\) 25 um.
[28] There are several concerns with this method in addition to those listed in section 3.1. The large range of values of SSA concentrations reported for nominally the same wind speed, an order of magnitude or more [LS04], results in a correspondingly large range of values for the inferred production flux. Uncertainties in modeled dry deposition velocities can likewise lead to uncertainties in the inferred production flux, and systematic errors can occur if the required conditions for successful application of this method are not satisfied.
[29] This approach, which is appealing because it is seemingly easy to apply, has been used by several investigators (10 formulations based on this method are compared by LS04). One widely used formulation (Appendix A) is that of _[PERSON] et al._[1993], who measured size-dependent aerosol concentrations with optical particle counters (OPCs) for more than 700 h from a 10 m tower on an island off the west coast of Scotland. They used measurements only from maritime air masses and assumed that the majority of particles measured were SSA particles. Their formulation consists of two lognormal size distributions with coefficients that exhibit different dependences on \(U_{10}\); such a formulation is, of course, inconsistent with the separability assumption (equation (3)).
[30] The steady state dry deposition method together with numerous measurements of sea salt aerosol concentration taken from the literature was used by LS04 to determine a formulation (Appendix A) for the effective production flux over the \(r_{80}\) range 3-25 um as a power law in \(r_{80}\) with exponent \(-\)2.5, with the amplitude varying directly as \(U_{10}\) to the 2.5 power. This formulation is characterized by an associated uncertainty of a multiplicative factor of 4 above and below the central value resulting from the variability in size-dependent number concentrations in a given range of wind speeds and from estimated uncertainties in the modeled dry deposition velocity.
### Statistical Wet Deposition Method
[31] The statistical wet deposition method infers the effective SSA production flux necessary to account for measured number concentrations under the assumptions that SSA particles in the size range of interest are removed from the atmosphere only by wet deposition (coagulation being negligible for SSA particles primarily because of their low concentrations) and that precipitation, when it occurs, removes nearly all SSA particles in this size range. These assumptions restrict application of this method to SSA particles with \(r_{80}\lesssim 1\) um and imply that for this size range the size dependence of the number concentration of SSA particles is the same as that of their production.
[32] This method is essentially a budget argument that provides a consistency check, ensuring that unrealistically high production fluxes are not calculated. On average, the total number of SSA particles in a given size range produced since the last precipitation event, per unit area of sea surface, is equal to the column burden (i.e., integral over height) of the concentration of such particles. Because SSA particles in this size range are expected to be nearly uniformly mixed over the height of the marine boundary layer \(H_{\mathrm{mbl}}\) and because concentrations of SSA particles are quite low above the marine boundary layer relative to concentrations within this layer, this column burden can be approximated by the product of the number concentration at an arbitrary measurement height (typically near 10 m) and \(H_{\mathrm{mbl}}\). Consequently, the production flux required to produce the measured concentration is equal to that column burden divided by the time between rainfall events, \(\tau_{\mathrm{wet}}\)
\[\frac{dF_{\mathrm{eff}}}{d\log r_{80}}=\frac{dN}{d\log r_{80}}\times\frac{H_{ \mathrm{mbl}}}{\tau_{\mathrm{wet}}}. \tag{5}\]
This method was applied by LS04 (Appendix A) with the parameters \(\tau_{\mathrm{wet}}=3\) days, \(H_{\mathrm{mbl}}=0.5\) km, and the value \(dN/d\mathrm{log}r_{80}=5\) cm\({}^{-3}\) (based on numerous measurements reported in the literature at typical wind speeds) to yield an estimate of \(dF/d\mathrm{log}r_{80}\approx 10^{4}\) m\({}^{-2}\) s\({}^{-1}\), nearly independent of \(r_{80}\), over the range 0.1 um \(\leq r_{80}\lesssim\) 1 um, with an associated uncertainty of a factor of 5 above and below the central value based on uncertainties in the above quantities.
### Micrometeorological Methods
[33] Micrometeorological methods infer the effective SSA production flux from measurements of fluctuations or gradients of concentration in the lowest portion of the marine boundary layer (typically within several tens of meters from the sea surface). Techniques such as eddy correlation, eddy accumulation, relaxed eddy accumulation, and gradient methods are commonly used to determine net vertical turbulent fluxes of other quantities such as heat, momentum, or gases. Both eddy correlation and gradient methods have been used to determine fluxes of SSA particles. These methods assume that the production of SSA particles is not in steady state with respect to removal of these particles through dry deposition, although steady state conditions in the sense of time invariance of mean quantities over the duration of the measurement are assumed.
#### 3.4.1 Eddy Correlation Method
[34] Eddy correlation [e.g., _[PERSON]_, 1986; _[PERSON] and [PERSON]_, 1994] determines the net vertical flux, \(F_{\chi}\), of a quantity, \(\chi\), such as the number concentration of SSA particles in a given size range by decomposing the vertical wind speed, \(w\), into a mean component, \(\overline{w}\), and a fluctuating component, \(w^{\prime}\), as \(w=\overline{w}+w^{\prime}\), and similarly for \(\chi\), where the overbar denotes an average over a time sufficiently long that meaningful statistics are obtained but sufficiently short that environmental conditions do not appreciably change. Because \(\overline{w}\) is zero, the net vertical flux is \(F_{\chi}=\overline{w^{\prime}\chi}\).
[35] In contrast to the situation for heat, momentum, and gases for which the measured fluxes are due to turbulent transport alone, for SSA particles, dry deposition and gravitational settling, which act as downward fluxes, must be taken into account in determining production fluxes [LS04, p. 81]
\[\frac{dF_{\mathrm{eff}}}{d\log r_{80}}\!=\!\overline{w^{\prime}\left(\frac{ dN}{d\log r_{80}}\right)^{\prime}}\!+\!\overline{\left(\frac{dN}{d\log r_{80}} \right)}\!\times\!\left[v_{\mathrm{dd}}(r_{80})-v_{\mathrm{gav}}(r_{80})\right]\!. \tag{6}\]
Hence the effective production flux of SSA particles exceeds the net flux measured by eddy correlation (the first term on the right-hand side of equation (6)) by the difference between the dry deposition flux, which is calculated from the mean SSA particle number concentration and the dry deposition velocity, and the gravitational flux. As gravitational settling does not contribute to the measured eddy correlation flux, the dry deposition velocity, which includes gravitational settling, must itself be diminished by the gravitational settling velocity. Either of the terms on the right-hand side of equation (6) can be confounded by the presence of other types of aerosol particles.
#### 3.4.2 Gradient Method
[36] Another micrometeorological method is the gradient method, by which the effective production flux of particles sufficiently small that the effect of gravity is negligible compared to upward turbulent diffusion (i.e., \(r_{80}\) smaller than a few micrometers) can be determined from measurements of the dependence of the concentration on height. This approach was proposed by _[PERSON]_ [2003] as an extension of Monin-Obukhov similarity theory, which is commonly used to relate fluxes of quantities such as momentum and heat to the vertical gradients of wind speed and temperature, respectively. _[PERSON] and [PERSON]_ [2006, 2007] and _[PERSON]_ [2007] have argued that in steady state conditions (which in this sense refers to mean quantities being independent of time) and neutral atmospheric stability the height dependence of the number concentration can be written as
\[\frac{dN}{d\log r_{80}}(z)=\left(\frac{-1}{\kappa u_{\bullet}}\right)\! \left(\!\frac{dF}{d\log r_{80}}\right)\ln\!\left(\!\frac{z}{z_{\mathrm{ref}}} \right)+\frac{dN}{d\log r_{80}}(z_{\mathrm{ref}}), \tag{7}\]
where \(u_{\bullet}\) is the friction velocity, \(\kappa\) is the von Karman constant (approximately 0.40), and \(z_{\mathrm{ref}}\) is an arbitrary reference height. Thus, the production flux of SSA particles of a given size could, in principle, be determined from the difference in number concentrations at two heights or from the slope of the number concentration plotted against the logarithm of the height. Because of the small change in the number concentration over heights at which measurements are typically made, accurate determination of this difference, or slope, imposes high-accuracy and -precision requirements on the concentration measurements. For particles with \(r_{80}<\) 1 um, concentration differences are extremely difficult to measure; for larger particles, the concentrations are so small that accurate measurements require very long sampling times. Determination of SSA production fluxes by this approach is discussed in section 4.2.2.
#### 3.4.3 Discussion of Micrometeorological Methods
[37] Successful application of micrometeorological methods requires that the downward flux of SSA particles due to dry deposition, if not negligible, be taken into account. However, because there is typically no discrimination with regard to particle composition, dry deposition of other aerosol particles can lead to spurious results if not accurately taken into account. This effect also reduces the signal-to-noise ratio because uncertainties of modeled dry deposition fluxes of small particles may be greater than the measured upward fluxes themselves. Use of micrometeorological methods implicitly assumes that the ocean surface is a uniform source of particles, but fluctuations caused by the discrete nature of breaking waves would interfere with measurements or at least require long times for averaging. Implementation of these methods also involves several practical difficulties. Gradients and fluctuations in RH must be accurately taken into account, and measurements from a ship at sea, for example, must take into account perturbation of the turbulent characteristics of the flow by the ship or sampling devices and the motion of the ship.
[ss] There are several concerns with micrometeorological methods. Because of the relatively low concentrations of SSA particles in the atmosphere, accurate results require long sampling times, which may be beyond practical limits or extend through meteorological conditions that are changing. The consequences of these low concentrations are more pronounced for micrometeorological methods than for other methods because micrometeorological methods determine the SSA production flux from small differences of much larger quantities; uncertainties can thus result in much greater fractional uncertainty for the estimated flux.
[9] The SSA production flux determined by eddy correlation measurements is based on turbulent deviations of the concentrations from the mean values for a sampling rate on the order of a few tenths of a second. These concentration fluctuations inherently have large uncertainties which are enhanced when concentrations are small. In effect, this approach also determines the production flux as a difference of two much larger values, as the dominant contribution to this flux is provided by the sum of the positive values of \(w\)(\(dN\)/\(d\)log\(r_{80}\))\({}^{\prime}\) minus the sum of the negative values of this quantity. The concern of long sampling times required for accurate results is sometimes addressed by determining total number fluxes at the cost of size resolution. These long sampling times, which become more pronounced with increasing particle size due to the associated decreasing concentrations, provide a practical limit on the size to which these methods can be applied to values of \(r_{80}\) less than several micrometers.
[40] Eddy correlation has been used to infer SSA fluxes in only a few studies. _[PERSON]_ (2001) and _[PERSON] et al._ (2001) made 175 h of measurements of all particles with dry mobility diameter (roughly equal to \(r_{80}\)) greater than 0.01 \(\mu\)m from a ship in the Arctic at wind speeds (at 35 m above sea level) from 4 to 13 m s\({}^{-1}\). Measured number concentrations of particles of these sizes were reported as 100-200 cm\({}^{-3}\). Using modeled dry deposition fluxes, the investigators converted the measured net total (as opposed to size-dependent) flux to a total effective production flux, which they fitted to an exponential dependence on wind speed (Appendix A). There are concerns as to the confidence that can be placed in their formulation because of the large magnitude of the modeled dry deposition flux (which sometimes exceeded the net upward flux), the lack of any significant correlation between wind speed and sea salt mass for dry mobility particle diameter \(d_{\rm p}<0.16\)\(\mu\)m, discrepancies in the relations between wind speed and concentrations of total aerosol number and those of sea salt mass for larger and for smaller particles, and ambiguity about what types of particles contributed to the upward fluxes. Recognizing these concerns, _[PERSON] et al._ (2001) stated that \"a more careful examination of all data is needed before we can make any conclusion about the source and characteristics of the upward aerosol number flux.\" An additional concern with the expression presented by _[PERSON] et al._ (2001) is that it yields an unrealistically high production flux; for \(U_{10}=10\) m s\({}^{-1}\), this expression would result in a rate of increase in the number concentration of aerosol particles (assumed to be uniformly distributed over a marine boundary layer height of 0.5 km) of approximately 320 cm\({}^{-3}\) d\({}^{-1}\). Such a rate would be inconsistent with measured concentrations and a typical residence time against precipitation of \(\sim\)3 days (LS04, p. 72).
### Whitecap Method
[41] The whitecap method infers the SSA production flux from measurements of size-dependent SSA production from laboratory simulations or from the surf zone, as a proxy for oceanic whitecaps, by scaling the production flux per white area, \(dF_{\rm ww}\)/\(d\)log\(r_{80}\), to the ocean using the oceanic whitecap fraction, \(W\). The oceanic production flux is thus given by
\[\frac{dF}{d\log r_{80}}=W\times\frac{dF_{\rm wc}}{d\log r_{80}}.\]
The fundamental assumption of this method is that the number of SSA particles of any given size produced per unit time and area is the same for any white area, either in the laboratory, the surf zone, or over the ocean, independent of the means by which this white area was produced, provided the whiteness exceeds some threshold.
#### 3.5.1 Determination of the Oceanic Whitecap Fraction
[42] The oceanic whitecap fraction has been determined from photographs or video recordings of the sea surface from ships, towers, or aircraft, with aircraft measurements typically yielding values of \(W\) that are up to an order of magnitude greater than those from shipboard photographs (LS04). In the past, video determinations of \(W\) have typically resulted in values roughly an order of magnitude less than those determined by photographs, although technological improvements in video and use of digital video may have changed this situation (an intercomparison of whitecap determination from film, video, and digital images would provide much needed information on this subject). However, for both photos and videos, regardless of the medium (i.e., film, analog magnetic tape, or digital), the decision on what is \"white\" must be made arbitrarily, introducing unavoidable subjectivity in determining \(W\) and thus in the production flux. Moreover, nothing in the choice of this threshold ensures that the resulting values of \(W\) are the pertinent ones for determining SSA production and, in fact, what is \"suitable\" cannot be determined from image analysis.
[43] Observations from space-based sensors offer the prospect of routinely determining \(W\) on regional and global scales and of determining parameterizations by use of local (in situ) or remote-sensing measurements of controlling variables such as wind speed and air and sea temperatures. Such observations would permit characterizing the whitecap fraction, its temporal and spatial variability, and its dependence on controlling variables, with the expectation of leading eventually to improved models of \(W\) and with this of SSSF via equation (8).
[44] The whitecap fraction can be detected with satellite-based instruments because of the distinct remote-sensing signature of whitecaps in several regions of the electromagnetic spectrum (_[PERSON]_, 1986). In the visible region, the whitecap fraction can be quantified photographically on the basis of enhanced reflectivity of solar radiation by whitecaps[_[PERSON] et al._, 1982; _[PERSON] et al._, 1996; _[PERSON]_, 2004]. In the infrared (IR), both reflectivity and emissivity contribute to the signal from the whitecaps [_[PERSON] et al._, 1997; _[PERSON] and [PERSON]_, 2005]. In the microwave region, for which measurements yield the surface brightness temperature \(T_{\rm ps}\), whitecaps are highly emissive compared to adjacent nonwhite areas [_[PERSON] et al._, 1971; _[PERSON] et al._, 2002; _[PERSON] et al._, 2005; _[PERSON] et al._, 2006].
[_4_s_] Different regions of the electromagnetic spectrum exhibit different advantages and challenges for remote sensing of the whitecap fraction. Measurements in the visible region have the advantage of the direct relation of the signal to the white area commonly characterized in laboratory experiments, but correction for extinction and for scattering of light out of and into the optical path through the atmosphere (atmospheric correction) is especially demanding in the visible and IR regions. The advantages of using microwave frequencies, specifically the ability to determine whitecap fraction at night, penetration of microwave radiation through clouds, and minimal difficulty in atmospheric correction, make this approach very attractive. However, difficulties arise in modeling the sea surface emissivity, especially in distinguishing signals emanating from foamy regions (i.e., whitecaps) from those emanating from areas where the sea surface has been roughened by the wind. As noted above, there is no demonstration that the whitecap fraction determined by remote sensing in any region of the electromagnetic spectrum is the most pertinent to SSA production.
[_46_] The oceanic whitecap fraction, \(W\), has typically been parameterized as a function of only \(U_{10}\). Numerous expressions for \(W(U_{10})\) have been proposed, many of which are power laws with an exponent near 3. The expression of _[PERSON]_ [1980, hereinafter MO'M80]
\[W(U_{10})=3.84\times 10^{-6}U_{10}^{3.41}, \tag{9}\]
where \(U_{10}\) is in m s\({}^{-1}\), is frequently used, despite nearly 30 years of subsequent measurements. These later measurements have demonstrated many uncertainties regarding the dependence of \(W\) on \(U_{10}\); as noted in section 2, \(W\) can vary by over an order of magnitude for the same \(U_{10}\) [LS04; _[PERSON]_, 2006]. \(W\) must thus depend also on other atmospheric and/or oceanic properties in addition to \(U_{10}\); attempts to include additional variables in the parameterization of \(W\) are examined in section 4.1.1.
#### 3.5.2 Determination of the SSA Particle Flux per White Area
[_4_] Determinations of the SSA production flux per white area have employed several types of laboratory \"whitecaps,\" both continuous (such as those formed by a falling stream of water or by forcing air through a fit below the water surface) and discrete (such as those formed by simulating a wave-breaking event by colliding two parcels of water). For experiments using the former approach, bubbles and resulting SSA are generated by one of two basic mechanisms: the first being air forced through diffusers, sintered glass filters, or other porous material and the second being plunging water jets or weirs. Each mechanism produces a continuous whitecap from which the resultant SSA is entrained into an air stream in which the number concentration is measured. Measurements of size-dependent number concentrations, \(dN\)/\(d\)log\(r_{80}\), can be used to determine the size-dependent SSA production flux per white area, \(dF_{\rm ww}\)/\(d\)log\(r_{80}\), using the flow rate, \(Q\), of air entraining the resultant SSA and the area of the surface covered by bubbles, \(A\), according to
\[\frac{dF_{\rm ww}}{d\log r_{80}}=\frac{Q}{A}\frac{dN}{d\log r_{80}}. \tag{10}\]
Such an approach requires determination of the \"white\" area, the criterion for which, as in field measurements, is necessarily somewhat arbitrary.
[_4_s_] Estimation of the SSA production flux from measurements involving discrete whitecaps additionally requires knowledge of lifetimes of oceanic whitecaps; these have been determined from photographs or videos of laboratory whitecaps. The SSA production flux per white area has also been estimated from measurements in the surf zone. Specifically, the integral over height of the number concentration of the aerosol resulting from the surf zone is used together with the wind speed and the fraction of the white area in the surf zone to estimate the production flux per white area. For both the surf zone and laboratory approaches, the contribution from background aerosols must be subtracted out, although in many situations this is negligible compared to the much larger signal resulting from active production by the surrogate whitecap.
[_4_s_] Interpretation of the type of flux determined by the whitecap method requires some care. The production flux per white area determined from laboratory whitecaps is an interfacial flux, whereas that determined from measurements of aerosol production in the surf zone more closely approximates an effective flux. Additionally, because laboratory experiments are currently incapable of simulating upward entrainment of SSA particles, they are restricted to determining the interfacial production flux. However, such laboratory experiments determine the flux of only bubble-produced drops and not spume drops and thus yield only a fraction of the interfacial production flux. Because nearly all applications of the whitecap method have been restricted to particles with \(r_{80}\leq 10\) um, over which range the interfacial and effective production fluxes are nearly the same, no further distinction is made regarding the type of flux determined by investigations involving the whitecap method, and it is assumed that such fluxes can be compared with those inferred by other methods discussed here.
[_5_o_] Laboratory investigations allow for controlled experiments on the effects of parameters such as salinity, water temperature, and surface-active substances on the magnitude and size distribution of the production flux. However, interpretation of laboratory experiments requires assumptions regarding the applicability of laboratory conditions to conditions representative of breaking waves in the open ocean. Laboratory breaking waves and whitecaps have different characteristics from those over the ocean and vastly different sizes. Few laboratory experiments have employed more than a single method for producing whitecaps or determined whether scaling holds over a range of sizes of these whitecaps; such work might enhance confidence in extrapolating results from laboratory whitecaps to SSA production by oceanic whitecaps.
[5] A concern with investigations involving bubbles produced by frits is the accuracy with which the size-dependent SSA production flux (including its salinity and temperature dependences) characteristic of breaking waves in the open ocean is modeled by the laboratory study because the bubble formation process at the frit is an entirely different physical process than that by which bubbles are produced in the ocean. Additionally, because bubbles produced by frits are typically smaller than those thought capable of producing film drops and the particles produced are smaller than those reported for jet drops, the question arises as to the extent to which production fluxes determined from these measurements might be artifacts of the experimental approach.
[5] Similarly, a concern with the surf zone approach is the representativeness of surf zone white area as a model for breaking waves and SSA production in the open ocean. In contrast to the open ocean, wave breaking in the surf zone is strongly influenced by drag against the shallow seafloor, whose depth is comparable to that to which air bubbles are entrained by breaking waves. Interaction with the seafloor almost certainly modifies the wave-breaking process and bubble production. The width of the surf zone, the turbulent dispersion velocity, and the height of the plume of the aerosol produced by the surf zone are influenced by wind speed, and these quantities are also affected by local conditions and topography. These influences further call into question the assumption of constant flux per white area needed to extrapolate results from the surf zone to SSA production in the open ocean.
#### 3.5.3 SSA Production Flux Formulations
[5] The whitecap method of estimating the SSA production flux has seen and continues to see widespread use; 10 formulations based on this method are compared by LS04. One widely used formulation (Appendix A) is that of _[PERSON] et al._ [1986], who combined results from measurements of SSA production from a discrete laboratory whitecap of initial area 0.35 m\({}^{2}\), the lifetime of other laboratory whitecaps calculated assuming exponential decay, and equation (9) for \(W\); the stated range of validity was \(r_{80}=\) 0.8-8 \(\mu\)m. Other formulations from the same group differed from this one by as much as an order of magnitude over this size range. A modification of this formulation (Appendix A), which extended the \(r_{80}\) range of applicability to 0.07-20 \(\mu\)m, was proposed by _[PERSON]_ [2003], who tuned the formulation so that size-dependent SSA number concentrations calculated with a 1-D column model matched those reported by _[PERSON] et al._ [1997] from measurements on a single cruise in the North Atlantic. The limits attributed to this formulation might also be questioned; [PERSON] stated (incorrectly) that the _[PERSON] et al._ [1986] formulation applied for \(r_{80}\) up to 20 \(\mu\)m (instead of 8 \(\mu\)m) and that their new formulation yields \"reasonable\" size distributions for \(r_{80}\) as low as 0.07 \(\mu\)m, despite the fact that the measurements of _[PERSON] et al._ [1997] were limited to \(r_{80}>\) 0.1 \(\mu\)m.
[5] Another formulation of the SSA production flux based on the whitecap method was presented by _[PERSON] et al._ [2003], who measured the flux of particles produced from a white area of 3 \(\times\) 10\({}^{-4}\) m\({}^{2}\) formed by forcing air through a frit with pore size (presumably diameter) 20-40 \(\mu\)m that was located 4 cm below the water surface. Based on such measurements at four different temperatures and three different salinities (but only a single fit size and flow rate), [PERSON] et al. presented a formulation for the size- and temperature-dependent production flux per white area at salinity 33 (near that of seawater) for dry mobility particle diameter \(d_{\rm p}\) (approximately equal to \(r_{80}\)) between 0.02 and 2.8 \(\mu\)m. They combined this result with the MO'M80 formula given above for \(W\) (equation (9)) to arrive at a formulation for the oceanic SSA production flux (Appendix A). The temperature dependence of this formulation accounts only for the temperature dependence of SSA production per white area determined in the laboratory and does not account for any possible temperature dependence of the whitecap fraction, although there are indications that such a dependence exists [LS04]. For \(U_{10}=\) 10 m s\({}^{-1}\), this formulation yields a rate of increase in the SSA number concentration (assumed to be uniformly distributed over a marine boundary layer height of 0.5 km) of near 170 cm\({}^{-3}\) d\({}^{-1}\) at 25\({}^{\circ}\)C and near 270 cm\({}^{-3}\) d\({}^{-1}\) at 5\({}^{\circ}\)C, resulting in atmospheric number concentrations much greater than those typically measured.
[55] The surf zone approach was used by _[PERSON] et al._ [2000], who reported concentration measurements at piers at two locations on the coast of California and presented a formulation for the SSA production flux per white area (Appendix A) over the \(r_{80}\) range \(\sim\)0.4-\(\sim\)5 \(\mu\)m on the assumption that the entire surf zone acted like a whitecap (i.e., the whitecap fraction in the surf zone was unity); note that as originally presented, this formulation was missing a factor of 10\({}^{6}\) [LS04, p. 222]. The integral of the number concentration over the height of the plume was based on concentration measurements at two heights (7 and 15 m in La Jolla and 5 and 12 m in Moss Landing) under the assumption of an exponential decrease with height. According to this formulation, the production flux per white area depends exponentially on wind speed, with nearly an order of magnitude difference between the flux at the lowest wind speeds (\(U_{10}=\) 0-2 m s\({}^{-1}\)) and the highest (9 m s\({}^{-1}\)). This dependence likely reflects transport phenomena and possibly higher swell, resulting in more vigorous wave breaking with increasing wind speed, but such a dependence calls into question the extent to which this approach simulates production in the open ocean and additionally violates the assumption of constant production flux per white area.
### Summary
[56] Intrinsic to any formulation for the SSA production flux, either effective or interfacial, is an associated uncertainty. In view of the large spread of determinations of production flux for a given set of environmental conditions, LS04 characterized this uncertainty as a multiplicative quantity, denoted by \(\dot{\div}\), equivalent to an additive uncertainty of \(\pm\) associated with the logarithm of the production flux, and thus in a plot of the logarithm of the production flux versus \(r_{80}\) such a measure of uncertainty corresponds to equal distances above and below the best estimate production flux. They intended this quantity to provide an estimate of the range about the central value within which the actual production flux might be expected to lie such that it would be difficult to restrict the range to much less than this factor. Presenting the uncertainty associated with a given formulation provides a criterion for whether or not two different formulations can be said to \"agree\" and allows a means for determining the precision to which a formulation should be presented. Additionally, such an uncertainty provides context for deciding whether features in the size distribution might be considered to be characteristic of actual production fluxes rather than statistical fluctuations. This uncertainty is essential also as input to subsequent use of a formulation, for example, in assessing the relative enhancement of CCN number concentration pertinent to the enhancement of cloud albedo by anthropogenic aerosols.
[\(\lx@sectionsign\)7] Some 40 SSA production flux formulations were presented and compared by LS04. Based on their analysis of these formulations and numerous other data sets, LS04 proposed a formulation (Appendix A) for the effective SSA production flux for particles with 0.1 \(\upmu\)m \(<r_{80}<\) 25 \(\upmu\)m as a lognormal size distribution of the form \(dF/d\)log\({}_{80}\) with a single mode and a 2.5 power wind speed dependence for 5 m s\({}^{-1}<U_{10}<\) 20 m s\({}^{-1}\). Associated with this formulation is a multiplicative uncertainty of a factor of 5 about the central value. Because of the large number of data sets upon which this formulation was based, LS04 expressed the view that a substantial reduction of this uncertainty would require more than close agreement of a few new formulations.
[\(\lx@sectionsign\)8] Although it had been conclusively demonstrated that sea spray particles with \(r_{80}<\) 0.1 \(\upmu\)m are formed by the bursting of individual bubbles [e.g., _[PERSON]_, 1963; _[PERSON]_, 1964; _[PERSON] and [PERSON]_, 1992] and from bubble bursting associated with swarms of bubbles [_[PERSON] and [PERSON]_, 1981; _[PERSON] et al._, 1983, 1987; _[PERSON] et al._, 2003], extensive measurements from a large number of investigators led LS04 to conclude that sea salt particles with \(r_{80}<\) 0.1 \(\upmu\)m constitute only a small fraction of the number of aerosol particles present in that size range in the marine atmosphere and only a small fraction of the number of sea spray particles produced. However, recent observations (section 4) suggest that SSA particles with \(r_{80}<\) 0.1 \(\upmu\)m may occur in appreciable concentrations in the marine atmosphere. If these observations are correct, then one possibility is that the particles detected are _sea spray_ particles, that is, particles formed at the sea surface by bursting bubbles consisting mostly of organics or other substances but containing little _sea salt_. A possible explanation for the previous results is that differences in composition would result in differences in hygroscopic and other properties, causing the particles not to have been recognized as SSA particles. This issue remains qualitatively and quantitatively unresolved, and the production and fate of SSA particles in this size range are currently major topics in this field.
## 4 Recent experimental and observational findings
[\(\lx@sectionsign\)9] Experimental and data processing techniques have been further developed in the last several years, and results from laboratory and field experiments have provided new insights pertinent to the SSA production flux. These results relate, in particular, to the whitecap method, micrometeorological methods, and the chemical composition of SSA. Sections 4.1-4.3 discuss each of these aspects.
### Whitecap Method
#### 4.1.1 Photographic Measurements of Whitecap
**Fraction**
[\(\lx@sectionsign\)6] Five new data sets of whitecap fraction have been reported, four in coastal regions under fetch-limited conditions [_[PERSON] et al._, 2004, 2007; _[PERSON] et al._, 2007; _[PERSON] et al._, 2008a] and one in open ocean (unlimited fetch) conditions [_[PERSON] et al._, 2008b]. Details of these data sets (Table 3) show the ranges of various meteorological and oceanographic variables (in addition to wind speed) that were recorded to investigate possible dependencies on these other quantities and the means by which the images were collected and processed.
[\(\lx@sectionsign\)6] Recent developments in image processing of sea state photographs have aimed at decreasing the uncertainty in measured whitecap fraction in two ways, both of which have been facilitated by developments in digital technology. One is removing the subjectivity in determining the intensity threshold that distinguishes whitecaps from the surrounding water. The other is averaging a large number of \"instantaneous\" \(W\) values measured during an observation period to obtain a single \(W\) data point.
[\(\lx@sectionsign\)2] To determine more objectively the intensity thresholds separating whitecaps from the surrounding water, the change in instantaneous \(W\) values when the threshold was varied was examined by _[PERSON] et al._ [2007, Figure 5]. An optimum threshold was identified for which a change in threshold of \(\pm\)6% resulted in a relative change in \(W\) of 10-20%; this same threshold was selected and applied to all processed images. An automated whitecap extraction technique was devised by _[PERSON] and [PERSON]_ [2009] that involved two major elements: an \"image structure,\" defined as the fraction of pixels with intensities greater than a given threshold, which decreased as the threshold was increased from a predetermined minimum intensity to the maximum intensity of the image, and analysis of the first, second, and third derivatives of this image structure with respect to the threshold intensity. The image structure was used to identify whether an image contains a whitecap, and the derivative analysis was used to determine the intensity threshold for an image containing a whitecap. This procedure yielded a unique threshold applicable to an individual image [_[PERSON] et al._, 2008a].
[6s] The changes in the value of \(W\) that resulted from increasing the number of individual determinations of \(W\) obtained in series of measurements during 30 min periods to yield an average was also investigated by _[PERSON] and [PERSON]_[2009]. The relative difference of each such value of \(W\) from the data set mean was as great as \(\pm\)25% when 10-30 values were averaged, gradually decreasing to about \(\pm\)10% when 100 values were averaged and to less than \(\pm\)3% when about 500 values were averaged. Such decrease in the relative difference would be consistent with expectation for averages of independent measurements. Although use of a greater number of images reduced the difference from the mean calculated from 700 images, there did not appear to be any bias associated with using fewer images (as would also be consistent with expectation for averages of independent measurements). Similar findings were reported by _[PERSON] et al._[2008a]. Additionally, it was found that the value of \(W\) for many of the images would not be substantially different if sampled only 1 or 2 s apart. _[PERSON] et al._[2008a] noted that the optimal sampling frequency (beyond which little improvement is seen) was once every 3-4 s, approximately the lifetime of an individual whitecap. Several of these data sets would appear to contain valuable information concerning statistics on the lifetimes and sizes of individual whitecaps and on the temporal autocorrelation of \(W\) which have not yet been fully exploited.
[6s] The new whitecap fraction data are plotted in Figure 2 as a function of wind speed, \(U_{10}\), together with previous measurements that are summarized in Table 2 of LS04 and in Table 2 of _[PERSON]_[2006]. The \(W\)(\(U_{10}\)) relationship from MO'M80 (equation (9)) is also shown. As determinations of \(W\) by analog video are thought to not be as accurate as those by film photography [LS04], the \"previous\" measurements in Figure 2 include only photographic determinations of \(W\)[LS04, Table 20]. Three of these new data sets were obtained using digital photography or digital video (Table 3); digital video has better resolution and lower noise than analog video, although it is not yet as good as film photography in spatial resolution and dynamic range [_[PERSON]_, 2009; _[PERSON]_, 2009].
[6s] The newly measured values of \(W\) appear to exhibit less scatter than, but are consistently less than, the bulk of those of the previous data sets. Geometric means of the ratios of the new values of \(W\) to those calculated according to the MO'M80 relationship ranged from 0.24 to 0.64 for the new data sets (Table 3). Furthermore, the wind speed dependence of \(W\) for these new data sets seems to differ from that of the older data sets: At low wind speeds (\(U_{10}<7\) m s\({}^{-1}\)), the new measurements indicate that \(W\)(\(U_{10}\)) increases faster than MO'M80, resulting in a strong increase of \(W\) (from \(\sim\)10\({}^{-5}\) to \(\sim\) 5 \(\times\) 10\({}^{-4}\)) over a narrow range of wind speeds (5-7 m s\({}^{-1}\)). In contrast, and in agreement with the previous results, \(W\)(\(U_{10}\)) increases slowly for \(U_{10}>\) 16 m s\({}^{-1}\), and the few data for \(U_{10}>\) 20 m s\({}^{-1}\) seem to plateau at a constant value; albeit the new data are consistently lower than the MO'M80 curve throughout the entire range of wind speeds. As the new data sets were based on both film photography (two sets) and digital imagery (three sets) and were characterized by both limited fetch (four sets) and open ocean (one set), there seems to be no obvious reason for the consistently lower values.
[66] Most of the new whitecap data [_[PERSON] et al._, 2004, 2007; _[PERSON] et al._, 2007; _[PERSON] et al._, 2008a] have also been examined for their dependence on friction velocity \(u_{*}\), but there seems to be little or no decrease of the scatter in plots of \(W\) versus \(u_{*}\) compared to that in plots of \(W\) versus \(U_{10}\), a similar conclusion to that reached from the analysis of previous data by LS04. It has been suggested that \(u_{*}\) could be more accurately determined if the expression of roughness length explicitly included wavefield characteristics (or combinations of them) such as wave age (a measure of and proxy variable for fetch), significant wave height, wave steepness, or energy dissipation in the breaking waves [e.g., _[PERSON] et al._, 2005]. By the same token, models of \(W\) that directly involve wavefield characteristics might better account for variability in whitecap fraction [cf. _[PERSON]_, 2007, chapter 7]. For example, using the so-called breaking wave parameter or windsea Reynolds number, \(R_{\rm b}=u_{*}^{2}/(\
u_{*}f_{\rm p})\)[_[PERSON] and [PERSON]_, 2001], where \(\
u_{*}\) is the kinematic viscosity of air and \(f_{\rm p}\) the frequency peak of the wave spectrum, to represent the sea state-dependent whitecap fraction has yielded improved prediction of the transfer velocity of CO\({}_{2}\)[_[PERSON]_, 2005; _[PERSON] et al._, 2007]. Consequently, it has been suggested that parameterizations of \(W\) in terms of wave age [_[PERSON] et al._, 2004, 2007; _[PERSON] et al._, 2007; _[PERSON] et al._, 2007; _[PERSON] et al._, 2008a] might lead to similar improvement in predicting the SSA particle flux in equation (8) through improved estimates of \(W\).
[5] The analysis of whitecap observations by _[PERSON] et al._ [2008b] supports this premise. [PERSON] et al. sorted data into periods with decreasing and increasing wind as surrogates for developed (old) seas (defined as a sea state produced by winds blowing steadily for fetch of hundreds of kilometers and duration of several days) and undeveloped (young) seas, respectively, and reported that for \(U_{10}\) below 9 m s\({}^{-1}\), there seemed to be no difference in the relation between \(W\) and \(U_{10}\) between the two data sets, whereas for \(U_{10}\) greater than 9 m s\({}^{-1}\), \(W\) values from periods of decreasing wind were 30-70% higher than those from periods of increasing wind. Although such measurements demonstrate the contribution of sea state to the variability of \(W\) at a given \(U_{10}\), the reported dependence accounts for only a small fraction of this order-of-magnitude variability.
#### 4.1.2 Satellite-Based Measurements of Whitecap Fraction
[ss] Measurements made with satellite-borne microwave sensors infer \(W\) from surface brightness temperature, \(T_{\rm B}\), determined from the emitted radiance, which increases with increasing whitecap fraction, as opposed to detecting individual whitecaps. Although the dependence of \(W\) on \(T_{\rm B}\) might be calculated from a simple empirical relationship [_[PERSON] et al._, 1995], a physically sound approach for obtaining \(W\) requires an algorithm containing multiple steps. The feasibility of acquiring whitecap fraction globally from space using \(T_{\rm B}\) and variables necessary for the atmospheric correction (columnar water vapor and cloud liquid water path) from the Special Sensor Microwave/Imager (SSM/I) was demonstrated by _[PERSON] and [PERSON]_ [2006].
Figure 2: Whitecap fraction \(W\) as a function of wind speed at 10 m above the sea surface \(U_{10}\) from five new data sets (colors) and from previous studies that used film photography (gray) as summarized in Table 20 of _[PERSON]_ [2004] and in Table 2 (data sets 1–5, 7–17, 21, 26) of _[PERSON] and [PERSON]_ [2006]. Points on abscissa denote values less than or equal to 1 \(\times\) 10\({}^{-6}\). The formulation of _[PERSON]_ [1980], equation (9), is also shown.
Because the algorithm uses satellite observations with a wide cross-track swath, \(W\) is determined twice a day (once in the daytime and once at night) at almost every oceanic location on Earth. Each satellite-based determination of \(W\) is a value spatially averaged over the sensor footprint (approximately 50 km \(\times\) 50 km) at a specific local time for a given location.
[69] There are two main contributions to the uncertainty of satellite-based estimates of \(W\). One is the error associated with the accuracy of models used in the algorithm that represent the various relationships needed for determining \(W\), e.g., the emissivities of the rough sea surface and of whitecaps at microwave frequencies. This error might be characterized by comparing satellite- and surface- or aircraft-based observations collocated in time and space. The second source of uncertainty is the measurement error, which results from random and systematic errors in the data used in the determination of \(W\). Random error is quantified as the variance, \(\sigma_{\rm W}^{2}\), of the calculated \(W\). This method does not identify or quantify systematic errors. In their feasibility study, _[PERSON] and [PERSON]_ (2006, section 3.4) evaluated the measurement error and assigned a standard deviation \(\sigma_{\rm W}\) to each \(W\) estimate; lack of concurrent in situ measurements prevented evaluation of the modeling error. Analysis of whitecap fraction determined by the satellite-based method for all days in 1998 showed that the relative standard deviation, \(\sigma_{\rm W}/W\), was less than 30% for about half of the determinations, whereas less than one-third of the individual photographic measurements available at the time had this accuracy [_[PERSON] and [PERSON]_, 2006].
[70] The satellite-based results for \(W\) from the algorithm of _[PERSON] and [PERSON]_ (2006), binned (as arithmetic means) by wind speed in intervals of 1 m s\({}^{-1}\), are compared in Figure 3 to bin (arithmetic) averages of \(W\) determined from photographic measurements and to the \(W(U_{10})\) parameterization of MO'M80. These determinations of \(W\) yield a nearly constant value of approximately 0.03, independent of wind speed over the range 8 m s\({}^{-1}\)\(<\)\(U_{10}\)\(<\) 17 m s\({}^{-1}\), with somewhat lower \(W\) as wind speed decreases for \(U_{10}\)\(<\) 8 m s\({}^{-1}\), in contrast to the much stronger wind speed dependence exhibited by the photographic data and MO'M80 parameterization.
[71] The differences between the satellite results and in situ photographic measurements are likely due to three factors. First, the signal from a whitecap may be different in different regions of the spectrum because of difference in the observed physical process, e.g., skin depth of the foam in the microwave region versus penetration depth of scattered visible radiation. Second, the satellite retrieval algorithm may be incomplete; for instance, simplified emissivity models were employed for foamy and rough surfaces by _[PERSON]_ (2006, section 5). Finally, the influence of various geophysical factors captured by the satellite estimates of \(W\), which are not currently extracted nor reliably
Figure 3: Whitecap fraction \(W\) as a function of wind speed at 10 m above the sea surface \(U_{10}\), arithmetically averaged in intervals of 1 m s\({}^{-1}\), obtained with the algorithm of _[PERSON]_ (2006) (blue) using annually averaged (1998) observations of brightness temperature \(T_{\rm B}\) from SSM/1 in clear sky (no clouds) locations all over the globe. The corresponding \(U_{10}\) values are also from SSM/1. Error bars on \(W\) values represent 1 standard deviation of the data points falling in each \(U_{10}\) bin; the apparent asymmetry of the error bars is a consequence of plotting on the logarithmic ordinate scale. Also shown (gray) are bin-average values of \(W\) from previous photographic determinations shown in Figure 2 and the formulation of _[PERSON]_ (1980), equation (9).
quantified, may be important. Improvement of the satellite-based estimates of \(W\) requires understanding and characterizing all these factors.
[72] In view of concerns over the accuracy of the space-based microwave determination of \(W\), _[PERSON] and [PERSON]_ (2006) suggested several possible modifications of their initial algorithm, including different models for foamy and rough surfaces and independent data sets for atmospheric correction. Microwave observations from the new satellite radiometric sensor WindSat (_[PERSON] et al._, 2004; _[PERSON] et al._, 2006; _[PERSON]_, 2006) in addition to those of SSM/1 provide a possibility to use independent data sets. To better represent the emissivity of whitecaps in different lifetime stages, [PERSON] and [PERSON] suggested using a depth profile of the void fraction within the thickness of the whitecaps instead of a constant value and assuming a distribution of whitecap thicknesses over the ocean. Details of these suggestions are given by _[PERSON]_ (2008) and _[PERSON]_ (2003), respectively.
#### 4.1.3 Laboratory Experiments on SSA Production
[73] Recent experimental studies of SSA production from laboratory-generated bubble plumes by _[PERSON] et al._ (2006), _[PERSON] et al._ (2007), _[PERSON] et al._ (2007), _[PERSON] et al._ (2008), and _[PERSON] et al._ (2010) have provided new data on the effects of salinity, water temperature, means of bubble production, and surfactants on resulting SSA particle size distributions and the resultant size-dependent organic enrichment and hygroscopic properties of these particles. Key features of these experiments, and of prior similar experiments by _[PERSON] et al._ (2003), are summarized in Table 4.
[74] The range of conditions in these experiments could, in principle, provide a test of the key premise of the whitecap method (section 3.5), specifically the assumption that the size-dependent production flux per white area is independent of the means by which that white area is formed. However, several of the investigations reported only normalized concentrations and/or did not report the white area characterizing their experiment. Nonetheless, under the assumption of negligible particle loss such normalized concentrations would exhibit the same size dependence as production fluxes, permitting comparison of the results of the several studies. Those experiments which provided sufficient data to allow determination of both a magnitude and size distribution of a production flux are discussed further in section 5.1.
[75] There are several concerns with laboratory experiments simulating SSA production. One is the extent to which laboratory whitecaps can accurately simulate breaking waves over the ocean as discussed in section 3.5. All of the laboratory whitecaps discussed in this section, whether formed by diffusers or water jets, were continuous, as opposed to open ocean whitecaps, which are discrete. Large bubbles (those thought to be responsible for the production of most of the small drops, i.e., those with \(r_{80}\) less than several tenths of a micrometer, which are thought to be film drops) rise quickly to the surface, and after several seconds the only bubbles that remain in the ocean are smaller ones, which are thought to be too small to produce film drops. Thus the vast majority of the film drops would be produced during only a small fraction of the lifetime of a whitecap in the ocean, in contrast to the laboratory whitecaps. Another concern with laboratory experiments is the possible influences of the sides of the container on the resultant whitecap. In some experiments (e.g., _[PERSON] et al._, 2007; _[PERSON] et al._, 2007) the white area was constrained by the size of the tank such that the white area was nearly the same for a range of bubble volume fluxes (i.e., the rate of air volume in bubbles reaching the surface divided by the white area, which [PERSON] et al. called the superficial bubbling velocity). Other experiments used only one bubble volume flux or varied this quantity only slightly. However, whether the values chosen are in the range of those
\begin{table}
\begin{tabular}{c c c c c c c c} \hline & & & \
\begin{tabular}{c} Bubble \\ Production \\ Method(s) \\ \end{tabular} &
\begin{tabular}{c} White \\ Area \\ (cm\({}^{3}\)) \\ \end{tabular} & Temperature & & \\ \hline _[PERSON] et al._ (2003) & artificial & none & diffuser\({}^{\text{a}}\) & 4 & 3 & -2, 5, 15, 25 & 0, 9.2, 33 \\ _[PERSON] et al._ (2006) & artificial & sodium dodecyl & weir, diffusers\({}^{\text{b}}\) & 2 & not stated & 4, 23 & not stated, presumably \\ _[PERSON] et al._ (2007) & seawater & sulfate & & & & near 35 \\ _[PERSON] et al._ (2007) & artificial & & & & & \\ & seawater, & & & & & 1, 10, 20, 33, 70 \\ _[PERSON] et al._ (2007) & seawater & none & diffuser\({}^{\text{b}}\) & \(\sim\)115 & \(\sim\)150–300 & \(\sim\)27 & not stated, presumably \\ _[PERSON] et al._ (2008) & seawater & none & water jet & not stated & 400 & not stated, presumably \\ _[PERSON] et al._ (2010) & artificial & _Thalassia_ & water jets, & 4–10 & 200 & 18–20 & 35 \\ _[PERSON] et al._ (2010) & seawater, & _rotula_ & diffusers\({}^{\text{a}}\) & & & & \\ & seawater & exudate & & & & & \\ \hline \multicolumn{8}{l}{\({}^{\text{a}}\)Pore size (presumably diameter) is 20–40 \(\mu\)m.} \\ \multicolumn{8}{l}{\({}^{\text{b}}\)Pore size(s) not specified.} \\ \multicolumn{8}{l}{\({}^{\text{c}}\)Pore sizes (presumably diameters) of 80 and 140 \(\mu\)m.} \\ \multicolumn{8}{l}{\({}^{\text{d}}\)Pore sizes (presumably diameter) of 30 \(\mu\)m; the other, an aquarium diffuser with unspecified pore size.} \\ \end{tabular}
\end{table}
Table 4: **Experimental Investigations of Sea Spray Production by Laboratory Bubble Plumes**in oceanic whitecaps, and the possible consequences of those values not being in the oceanic range, are not known.
[76] Another concern with laboratory experiments as models for oceanic behavior of bubbles is the short bubble rise times and distances compared to those for bubbles produced by breaking ocean waves, which reach depths of up to several meters, depending on wave height, as shown by acoustic observations of bubble plumes near the ocean surface (e.g., _[PERSON]_, 1992). Rise distances in laboratory studies are often much shorter. For example, _[PERSON] et al._ (2006) and _[PERSON] et al._ (2010) used bubble rise distances of only a few centimeters. _[PERSON] et al._ (2007) used rise distances of \(\sim\)0.35 m, which they claimed approximated the circulation depth of oceanic bubbles. _[PERSON] et al._ (2007) used bubble rise distances greater than 1 m, over which distance they assumed that the equilibrium size distribution would be attained before bubbles reached the surface and burst.
[77] A possible basis for a dependence of drop production on bubble rise times or distance is the time required for organic substances to equilibrate on the air-water interface of the bubbles. This equilibration time was examined by _[PERSON] et al._ (2010), who provided a theoretical analysis demonstrating that equilibrium with respect to adsorption of organics would be reached within 0.05 ms, much shorter than rise times of bubbles even for the short distances of some of the laboratory studies. On the basis of this analysis, [PERSON] et al. concluded that the depth of bubble generation would play little role in the effect of organics on production and properties of SSA. However, this result would seem to be in contradiction with findings reported in a series of laboratory studies by [PERSON] and colleagues, which indicated that the equilibrium attachment of organics to the air-water interface of bubbles is attained much more slowly. _[PERSON] and [PERSON]_ (1972, 1975) reported that ejection heights of jet drops exhibited a dependence on bubble rise distance over the range 6-23 cm and on bubble age for up to 10-20 s. _[PERSON] and [PERSON]_ (1978) reported that both bubble rise speeds and top jet drop ejection heights decreased with increasing bubble age (time spent in the water), with rise speeds decreasing by nearly a factor of 2 over the first 10 s or so, effects that they attributed to attachment of organic material to the bubble interface. In several studies, [PERSON] and colleagues examined the dependence of enrichment of bacterial concentration in drops relative to the bulk concentration on bubble age or rise distance. _[PERSON] and [PERSON]_ (1970) reported that bacterial enrichment in the top jet drop increased by approximately a factor of 5 when the bubble rise distance increased from 1 to 30 cm. _[PERSON] and [PERSON]_ (1972) and _[PERSON] et al._ (1981) reported that bacterial enrichment in jet drops increased with increasing bubble age for ages of 20 s or more. All of these results, which were attributed to organic attachment to the bubbles, would appear to indicate that this process does not rapidly attain equilibrium.
[78] Several of the size-dependent production flux measurements obtained in the newly reported studies, normalized to the maximum values in the representation \(dF\)/\(d\)log\(r_{80}\), are shown in Figure 4. A common feature is a rather broad maximum of the production flux in this representation at \(r_{80}\) near 0.05-0.1 um, which is rather independent of the means of production and of the bubble size distribution, although the spectral shapes differ markedly among the different examples. The large differences in the size distributions of the normalized concentration (and thus of the production flux), which may be as great as 2 orders of magnitude at \(r_{80}\) = 0.01 um, rather strongly refute the assumption that the production flux per white area is independent of the means by which the white area is produced. The results presented in Figure 4 were obtained for different conditions such as artificial versus natural seawater, water temperature, salinity, effects of surfactants, and bubble generation method, the effects of which were assessed in different studies. The results of these studies are presented here and possible causes for differences are examined.
[79] The effect of salinity on the production flux size distribution was examined by _[PERSON] et al._ (2003) (sali-0, 9.2, and 33) and by _[PERSON] et al._ (2007) (salinities 1, 10, 20, 33, and 70). Both studies reported an increase in particle number production with increasing salinity. [PERSON] et al. (their Figure 5) reported that size distributions for \(r_{80}\) between \(\sim\)0.05 and 0.1 um were nearly the same for salinities 9.2 and 33 and that for larger SSA particles the number fluxes for salinity 33 were increasingly greater than for salinity 9.2 as \(r_{80}\) increased, up to nearly an order of magnitude for \(r_{80}\) larger than approximately 1 um. [PERSON] et al. argued that the size distributions near \(r_{80}\) = 0.05 um shifted to slightly lower sizes at lower salinity, consistent with the hypothesis that formation radii were independent of salinity, although this shift did not occur for larger particles. In contrast to these results, [PERSON] et al. observed little change in the shape of their size distributions, with only a small increase (\(\sim\)15%) in the value of \(r_{80}\) of particles with increasing salinity from 10 to 70 (their Figure 4). [PERSON] et al. did, however, report an increase in total particle number production by a factor of 2.5 with salinity increasing from 10 to 70. As discussed by LS04, there is a transition in the coalescence behavior of bubbles that occurs near salinity 10, which results in very different bubble size distributions and thus perhaps SSA particle size distributions between lower and higher salinities to which it may be possible to attribute some of these results.
[80] The effect of water temperature on the resultant size distribution was investigated by _[PERSON] et al._ (2003) (\(-\)2, 5, 15, and 25\({}^{\circ}\)C) and by _[PERSON] et al._ (2006) (4 and 23\({}^{\circ}\)C). [PERSON] et al. found nearly identical size distributions for \(-\)2 and 5\({}^{\circ}\)C and little change between these and the size distribution at 15\({}^{\circ}\)C, although at both 15 and 25\({}^{\circ}\)C there was a decrease in the magnitude of the production flux by a factor of 2-3 for \(r_{80}\) < 0.1 um and an increase by a factor of 5-10 for \(r_{80}\) > 1 um. [PERSON] et al. reported an increase in the production flux of particles with \(r_{80}\) < 0.7 um at 4\({}^{\circ}\)C relative to that at 23\({}^{\circ}\)C and a decrease at greater \(r_{80}\), although much of this difference could alternatively be attributed to a decrease in the values of \(r_{80}\) by \(\sim\)30% at the lower temperature.
* The effects of different bubble generation methods on the resultant aerosol size distribution and properties were examined by _[PERSON] et al._ (2006), _[PERSON] et al._ (2007), and _[PERSON] et al._ (2010). [PERSON] et al. noted different size distributions (their Figure 2) for different methods, a pair and diffusers with three pore sizes, with d\(N\)/d\(\log\)r\({}_{80}\) exhibiting a maximum near \(r_{80}\) = 0.1 \(\upmu\)m for each method but with the size distribution produced by the weir having a narrower distribution near this maximum and an additional contribution from particles with \(r_{80}\) near 0.35 \(\upmu\)m. [PERSON] et al. reported that the production flux per white area obtained using a diffuser with a pore size (presumably diameter) 140 \(\upmu\)m was up to a factor of 4 greater than when using one with pore size 80 \(\upmu\)m at the same bubbling rate. [PERSON] et al. reported large differences in the magnitude and shape of the number size distribution (their Figure 6) and hence of inferred SSA production flux, produced by plunging water jets and by diffusers with different pore sizes, with the size distribution (in the form \(dN\)/d\(\log\)r\({}_{80}\)) produced by the water jets being bimodal with maxima at \(r_{80}\) near 0.05 and 0.15 \(\upmu\)m, with that from an aquarium diffuser having a single broad maximum near \(r_{80}\) = 0.06 \(\upmu\)m, and with that from a sintered glass filter (pore size, presumably diameter, 30 \(\upmu\)m) having a narrow maximum near \(r_{80}\) = 0.06 \(\upmu\)m with a much smaller secondary maximum near \(r_{80}\) = 0.25 \(\upmu\)m. These size distributions are also shown in Figure 4.
* The dependence of production flux on bubble volume flux was investigated by _[PERSON] et al._ (2007) and _[PERSON] et al._ (2007). [PERSON] et al. reported that a higher bubble volume flux could yield more than an order of magnitude increase in the total number production flux per white area. [PERSON] et al. also reported an increase in the magnitude of this quantity with increased bubble volume flux, although shapes of size distributions were similar. These dependences together with results of _[PERSON] et al._ (2003) are shown in Figure 5. In
Figure 4: Size distributions of SSA production flux normalized to maximum value in representation \(dF\)/d\(\log\)r\({}_{80}\) as a function of \(r_{80}\) from laboratory experiments (_[PERSON] et al._’s (2003) Figure 4c; _[PERSON] et al.’s_ (2006) Figures 2 and 4; _[PERSON] et al._’s (2007) Figure 3 for 5 L min\({}^{-1}\); _[PERSON] et al.’s (2007) Table 1, artificial seawater, and salinity 33; and _[PERSON] et al.’_s (2010) Figure 6) and field measurements (the _[PERSON] et al._ (2006) formulation which is presented in text _[PERSON] et al.’s (2008) Figure 6 at \(U_{10}\) 5, 10, and 12 m s\({}^{-1}\)). Uncertainties in the original data are not shown.
Figure 5: Dependence of total SSA number production flux per white area in laboratory experiments of _[PERSON] et al._ (2003) using artificial seawater (salinity 33) at two different temperatures, _[PERSON] et al._ (2007) using natural (low productivity) seawater, and _[PERSON] et al._ (2007) using artificial seawater (salinity 33) on bubble volume flux (volume of air in bubbles rising to the water surface per unit area and time).
view of the strong dependences shown in Figure 5, bubble volume flux would seem to be an important property of whitecaps influencing the SSA production flux per white area. Certainly it would seem that a whitecap property such as this would be much more useful than an arbitrary threshold of \"white\" in relating SSA production flux to white area and ultimately in developing more accurate parameterizations for SSA production flux.
[s] The effects of surfactants on SSA production were investigated by _[PERSON] et al._ [2006], who added sodium dodecyl sulfate (SDS) to artificial seawater, _[PERSON] et al._ [2007], who investigated natural seawater containing different organic compositions and artificial seawater to which 0.1 and 10 mg L\({}^{-1}\) oleic acid was added; and _[PERSON] et al._ [2010], who added exudate of the diatom _Thalassioira rotula_ to natural filtered seawater at a concentration 512 \(\mu\)M (representative of dissolved organic carbon (DOC) concentration in seawater in areas of high biological activity).
[s4] Particle size distributions produced using artificial seawater were reported by _[PERSON] et al._ [2006] as being similar to those using natural seawater, although they were shifted toward smaller values of \(r_{80}\) for SDS concentrations greater than 3 mg L\({}^{-1}\). The investigators stated that these results should be considered exploratory because their comparison to long-term, seasonally varying data of particle size distributions obtained at the Mace Head atmospheric research station (located on the west coast of Ireland) showed that SDS does not accurately simulate the effects of the surfactants present in the natural environment.
[ss] The natural seawater samples of _[PERSON] et al._ [2007] exhibited differing organic composition because they had been collected in winter (DOC concentration = 2.3 mg C L\({}^{-1}\), chlorophyll concentration = 0.1 mg m\({}^{-3}\)) and summer (DOC concentration = 3.1 mg C L\({}^{-1}\), chlorophyll concentration = 1.8 mg m\({}^{-3}\)). The size distributions of the SSA particles produced in their experiments were nearly the same, regardless of the type of water (artificial, filtered, or unfiltered seawater), with little dependence on the amount of surfactant added. The winter samples of natural seawater produced 20-40% more SSA particles than the summer samples. Comparison of the size distributions of the SSA particles produced with the summer and winter samples showed that the natural organic matter exerted little effect on the numbers or radii of the produced SSA particles. Bubbling artificial seawater artificially enriched with oleic acid produced approximately twice as many drops as natural seawater. The investigators concluded that the nature of organic matter affects foam droplet production and that oleic acid is a poor surrogate for natural organic matter for studies of foam production. These findings, as well as those of _[PERSON] et al._ [2006], would seem to raise questions over the accuracy of laboratory experiments as models for oceanic SSA production.
[ss] Hygroscopic growth and CCN activity for artificial seawater were examined by _[PERSON] et al._ [2010], who reported that these properties were not affected by the bubble generation technique; however, for the organically enriched natural seawater, hygroscopic growth was suppressed, with the degree of suppression depending on the aerosol generation technique. The main differences in hygroscopic growth resulting from different generation techniques were observed for RH \(>\) 75%, with the plunging water jet presenting the greatest suppression of growth. The influence of organics on the CCN activity exhibited little size dependence, with only a slight increase in the critical supersaturation compared to seawater samples to which no organics were added.
[sr] Chamber studies aimed at determining the size-dependent mass fraction of organic material in SSA particles produced from natural seawater were conducted by _[PERSON] et al._ [2007] and _[PERSON] et al._ [2008]. [PERSON] et al. used highly oligotrophic seawater (concentrations of organic substances such as formate, acetate, oxalate, and methylsulfonate were below detection limits) pumped from the ocean into a laboratory near the coast of Bermuda and produced SSA by bubbling the water through diffusers. [PERSON] et al. used highly productive seawater (average chlorophyll-a concentration of 1.4 mg m\({}^{-3}\)) pumped into a sealed tank on a ship in the North Atlantic west of Ireland during an algae bloom and produced SSA using a water jet.
[ss] Enrichment of calcium with respect to surface water concentrations (median enrichment factor of 1.2), which may have been caused by fragments of biogenic CaCO\({}_{3}\) or from complexes with organic matter, was reported by _[PERSON] et al._ [2007]. These investigators also reported that all size-resolved and bulk aerosol samples were highly enriched in organics, with the enrichment decreasing from greater than 10\({}^{5}\) for \(r_{80}\) near 0.06 \(\mu\)m (the lowest size range) to slightly greater than 10\({}^{2}\) for \(r_{80}\) near 4 \(\mu\)m and again increasing slightly to near 10\({}^{3}\) for \(r_{80}\) near 14 \(\mu\)m; the median enrichment factor for all samples was near 400. The organic mass fraction exhibited similar behavior, decreasing from near 80% for \(r_{80}\) near 0.06 \(\mu\)m to 40-50% for \(r_{80}\) between 0.06 and 0.6 \(\mu\)m and to less than a few percent for \(r_{80}\) between 0.6 and 4 \(\mu\)m then increasing again to near 40% for \(r_{80}\) near 14 \(\mu\)m. In all size ranges except the smallest, the dominant contribution to aerosol mass was provided by sea salt.
[ss] A strong dependence of the organic (water-soluble and water-insoluble organic matter) mass fraction on particle size (Figure 6), with the enrichment factor (relative to the bulk seawater) increasing with decreasing particle size, was also reported by _[PERSON] et al._ [2008]. SSA particles with ambient radii greater than 0.5 \(\mu\)m contained more than 90% of the inorganic sea salt mass; particles with ambient radii less than 0.25 \(\mu\)m consisted mainly of organic matter, most of which was water insoluble. This water-insoluble organic matter (WIOM) exhibited substantial enrichment (relative to the bulk solution) with mass fraction increasing from 3 to 77% as radius (at 50-70% RH) decreased from 4 to 0.06 \(\mu\)m, with only a very minor fraction (\(\sim\)3%) of water-soluble organic matter (WSOM); the remaining mass was sea salt. The WIOM was attributed to colloids and aggregates exuded by phytoplankton on the basis of functional nuclear magnetic resonance spectroscopy. Such an increasing fraction of organic matter with decreasing drop radius is consistent with the volume fraction of adsorbed surfactant organic matter as a function of SSA particle size as evaluated with a thermodynamic model [_[PERSON] et al._, 1999]. Despite the small mass fraction of organic matter in larger particles (radius of 2-4 um at 50-70% RH), the total mass of organic matter in these particles was approximately half the total organic mass in aerosol particles with radius (at these RH values) less than 4 um. [PERSON] et al. also reported that the mass ratio of WIOM to sea salt was similar to that observed in aerosol samples at Mace Head.
#### 4.1.4 **Surf Zone Measurements**
[o] The production of SSA in a surf zone was determined by _[PERSON] et al._ [2006] from measurements on a 20 m tower, 20-30 m from the water's edge on a beach in Hawaii, during onshore winds (typical wind speed of 7 m s\({}^{-1}\)). Aerosol properties were characterized using a differential mobility analyzer (DMA), an OPC, and an aerodynamic particle size (APS), which together covered the size range 0.01 um\(<\) s\({}_{\rm 80}\) um. The DMA and OPC included options for sampling aerosol at ambient temperature or at 300-360\({}^{\circ}\)C to permit determination of size distributions of volatile and residual refractory aerosol (the latter being typically sea salt, nonvolatile organics, dust, or soot). These instruments were complemented with two condensation particle counters (CPCs), one operated at ambient temperature and the other at 360\({}^{\circ}\)C; a tandem DMA (TDMA) and a humidified TDMA (HTDMA) to examine the thermal and humidification response of selected sizes; and a three-wavelength nephelometer to determine particle light scattering. Inlets for all these instruments were placed at heights of 5, 10, and 20 m and sampling was cycled at regular intervals.
[o] Comparison of measurements at these three heights showed that the highest level was not influenced by surf production and could thus be used for determining the upwind background concentration. SSA production in the surf zone was evaluated from the SSA concentrations measured at 5 m after correction for background concentrations using the 20 m data. The production flux per white area was determined as described in section 3.5 using a mean whitecap fraction in the surf zone of 40%, based on visual examinations of images. Substantial production of particles with dry radius less than 0.05 um was found.
[o] Heated and ambient sample volumes were used by _[PERSON] et al._ [2006] to discriminate between refractory aerosol particles, assumed to be mainly sea salt, and other components. To further ascertain whether the detected particles were sea salt, the investigators made several tests. First, they noted the strong correlation between the concentrations of the refractory particles, most of which had dry radii less than 0.05 um, and light scattering, which would be dominated by particles with dry radius greater than 0.25 um. Chemical analysis using a flame photometric aerosol sodium detector confirmed that particles with \(r_{\rm 80}>0.09\) um were composed mainly of sea salt. SSA particles with \(r_{\rm 80}\) of 0.05 um (previously heated to 300\({}^{\circ}\)C) exhibited a humidity growth factor near 1.8 from low RH to RH of 76%, as expected for sea salt particles, from which [PERSON] et al. concluded that these particles were composed mainly or entirely (80% up to possibly 100%) of sea salt. They further concluded that most of the particles with \(r_{\rm 80}\gtrsim 0.03\) um produced from breaking waves were primarily sea salt. Based on their measurements, [PERSON] et al. presented an SSSF that extended to \(r_{\rm 80}\) as small as 0.01 um. This formulation, presented in Appendix A and discussed in section 5.1, is shown in Figure 4 as a normalized size distribution.
#### 4.1.5 Summary
[o] The whitecap method requires the ability to measure or model the whitecap fraction, \(W\), under a given set of conditions to known accuracy and demonstration that the whitecap fraction so determined yields, within a given uncertainty, the same size-distributed flux per white area as obtained in laboratory experiments or field studies. So far, these goals have not been achieved. Demonstrating that field measurements of \(W\) are reproducible and transferable would seem, at minimum, to require simultaneous measurements by multiple groups using different platforms (e.g., shipborne, aircraft, satellite, and fixed offshore platforms) and techniques at a variety of locations differing in controlling properties such as fetch and surfactant content. Simultaneous field measurements of production flux per white area would then allow comparison with flux per white area determined in laboratory experiments. Finally, algorithms for calculating \(W\) would have to be compared to measurements under a wide
Figure 6: Mass fraction of sea salt, WSOM, and WIOM as a function of particle radius sampled at approximately 70% RH (a) for seawater bubble-bursting chamber experiments with fresh seawater, conducted in a shipboard laboratory in a plankton bloom over the northeast Atlantic (May-June 2006); (b) for clean marine air at Mace Head, Ireland, May-June 2006; and (c) for clean marine air 200–300 km offshore west-northwest of Mace Head in a plankton bloom coincident in time with aforementioned samples. Adapted from _[PERSON] et al._ [2008].
variety of conditions and locations by different investigators using different techniques. Only when all these requirements are fulfilled would it seem that the SSSF and the associated uncertainty can be considered accurately parameterized and confidently represented in models. However, the laboratory experiments have demonstrated that the size-dependent flux per white area depends on the means by which the white area was created, raising intrinsic questions concerning the applicability and accuracy of the whitecap method, especially with regard to the assumption of a universal production flux per white area.
### Micrometeorological Methods
#### Eddy Correlation Measurements
[94] Eddy correlation measurements were made by _[PERSON] et al._ [2005] at a 22 m tower at Mace Head, Ireland, over a 4 week period in June and July 1992 during which \(U_{22}\) was between 7 and 18 m s\({}^{-1}\). Data were restricted to periods when the winds were from the ocean to the land and during high tide, when the distance from the base of the tower to the water was approximately 80 m. Total concentrations of particles with ambient radii from 0.005 to 0.5 \(\upmu\)m (RH not reported) were measured by a CPC, and total concentrations of particles with dry radii from 0.05 to 0.5 \(\upmu\)m were measured by an OPC; these measurements together with 3-D wind speed measurements were used to determine particle fluxes (Appendix A). The wind speed dependences of the fluxes in the two size ranges were essentially the same. A potential concern with these measurements is coastal influence and effects of surf-produced aerosol on particle fluxes. Footprint analysis by [PERSON], [PERSON], and colleagues [_[PERSON] et al._, 2005] showed that the region contributing to the measured fluxes was almost entirely over water both at high and low tide, at which the distance from the base of the tower to the water was 180 m. However, at low tide at wind speeds less than 10 m s\({}^{-1}\) measured fluxes showed little correlation with wind speed and were greater than at high tide, indicating influence of the exposed intertidal zone and thereby raising concern over the applicability of such measurements even at high tide to determining SSA production fluxes representative of the open ocean. Drag coefficients measured during high tide conditions yielded a slightly stronger dependence on wind speed than mid North Atlantic values but were comparable to values from the North Sea when water depth was greater than 30 m, from which [PERSON] et al. concluded that fluxes measured during high tide conditions were characteristic of open ocean values.
[95] Fast sizing and counting of aerosol particles, required for the application of the eddy correlation technique to determine the size-dependent production flux, has become feasible with the development of the Compact Light Aerosol Spectrometer Probe (CLASP) [_[PERSON] et al._, 2008], which measures the size distribution of particles with radii of 0.1-7 \(\upmu\)m at a frequency of 10 Hz. CLASP is a compact and lightweight OPC which can be mounted close to the wind sensor with minimal flow distortion and a short inlet tube. The combination of high sample rate, high flow rate (50 cm\({}^{3}\) s\({}^{-1}\)), and compact design makes CLASP highly suitable for determining aerosol production flux. The accuracy of the size determination, which is by means of light scattering, depends on particle shape and index of refraction.
[96] Eddy correlation measurements using a CLASP and a traditional OPC (Passive Cavity Aerosol Spectrometer Probe (PCASP)) to determine SSA fluxes were conducted at the 560 m pier at the Field Research Facility (FRF) in Duck (North Carolina, USA) in autumn 2004 and 2005 [_[PERSON] et al._, 2007; _[PERSON] et al._, 2008]. The sonic anemometer and the aerosol infets were mounted at the seaward end of the pier at a height of 16 m above mean sea level. _[PERSON] et al._ [2007] reported measurements of fluxes in three partly overlapping ranges of \(r_{80}\) as inferred from the reported dry radii measured with the PCASP equipped with an inlet heated at 300\({}^{\circ}\)C: 0.11-0.15, 0.15-0.19, and 0.11-0.375 \(\upmu\)m and as an integrated flux over the \(r_{80}\) range from 0.11-9.0 \(\upmu\)m, when the wind was from the ocean at \(U_{10}\) between 3 and 16 m s\({}^{-1}\); flux results for wind speeds lower than 7 m s\({}^{-1}\) were considered unreliable. Based on the analysis of a small subset of the data, the gross particle number fluxes increased with increasing wind speed. These fluxes were fitted to a power law \(U^{b}\), with values of \(b\) between 2.9 and 3.4, although the integrated flux could be better fitted (in terms of minimizing the variance) by a linear function of \(U_{10}\) than by a cubic one. _[PERSON] et al._ [2008] measured SSA particle fluxes in six size ranges of ambient radius from 0.145 to 1.6 \(\upmu\)m during twenty 20 min periods in October 2005, during which the wind was from the ocean with \(U_{10}\) from 4 to 12 m s\({}^{-1}\). Fluxes were converted to \(r_{80}\) values for \(U_{10}\) of 5, 10, and 12 m s\({}^{-1}\) and were fitted as linear functions of wind speed for each of the six size ranges; these fluxes are discussed in section 5 and, normalized to the maximum value at each wind speed, presented in Figure 4, from which they can be seen to exhibit different size dependences from the majority of the production fluxes from the laboratory experiments. Reported fluxes were not corrected for dry deposition (cf. equation (6)); this correction was estimated as 2-30%, depending on the dry deposition formulation employed, well less than the estimated overall uncertainty, suggesting that these measurements may yield an accurate determination of the production flux. Although whitecap fraction was not reported in this study, simultaneous measurement of this quantity in conjunction with such eddy correlation measurements would permit another means of determining the flux per white area, an essential element of the whitecap method. CLASP has also been used to determine SSA production flux on a cruise in the North Atlantic in the spring of 2007 [_[PERSON] et al._, 2009].
#### Gradient Method
[97] The gradient method (section 3.4.2) was applied by _[PERSON] and [PERSON]_ [2006] to determine the SSA production flux from 61 measurements of vertical profiles of the aerosol concentration obtained during four cruises in Arctic seas (Norwegian Sea, Greenland Sea, and Barents Sea) in 2000-2003 [_[PERSON]_, 2003; _[PERSON] and [PERSON]_, 2006]. The wind speed range was 5 m s\({}^{-1}<U_{10}<\) 12 m s\({}^{-1}\) and stability conditions were close to neutral. Concentrations of particles with ambient radii from 0.25 to 15 \(\upmu\)m, at RH varying between 65 and 95%, were measured with an OPC [_[PERSON]_, 2005]; a single instrument was used for consecutive measurements at five levels between 5 and 20 m above sea level, with at least four 2 min measurements at each level.
[98] There are several concerns with this work. For many of the size ranges, the concentrations showed no obvious decrease with height [_[PERSON] and [PERSON]_, 2006, Figures 3 and 4], with scatter around the logarithmic profile fit much larger than the stated relative uncertainties in the concentrations of 1% for particles with radius 1 \(\upmu\)m to 20% for radius 10 \(\upmu\)m. _[PERSON] and [PERSON]_ [2006] considered only those size bins for which the concentrations could be fitted to logarithmic profiles in height with a given accuracy, although only 60% of all measured profiles matched this criterion; such a procedure might be expected to bias the results. A wind speed dependence of \(U_{10}^{\rm{2}}\) was drawn on a graph of the calculated flux of surface area, although this dependence does not seem to be supported by statistical analysis (a linear least squares fit of the logarithm of the flux versus the logarithm of the wind speed results in an exponent of \(1.75\pm 0.45\) if all the data are included or \(1.07\pm 0.71\) if two data for \(U_{10}<3\) m s\({}^{\rm{-1}}\) are excluded).
### Chemical Composition of Sea Spray Aerosol
[99] The size-dependent chemical composition of SSA, especially the distribution of organic material, is important in determining the RH-dependent growth of SSA particles and their ability to serve as CCN. Although prior work going back to the 1940s has shown the presence of organic material in SSA particles (section 1), only recently have studies attempted to quantify the organic mass fraction as a function of particle size and elucidate the production mechanisms. Here recent field measurements that complement studies that have shown substantial organic fraction of laboratory-generated SSA are examined.
[100] In a series of field measurements at Mace Head, Ireland, conducted in clean marine air with minimal anthropogenic or terrestrial influences (wind from ocean to land; number concentration of particles with radii at 40-70% RH greater than 0.007 \(\upmu\)m less than 700 cm\({}^{\rm{-3}}\) and black carbon mass concentration less than 50 ng m\({}^{\rm{-3}}\)), [PERSON] and colleagues [_[PERSON] et al._, 2004; _[PERSON] et al._, 2004; _[PERSON] et al._, 2007] found substantially greater concentrations of organic matter in SSA during periods of high biological activity than during periods of low biological activity, which occurred during winter and during which the composition was predominantly sea salt. The enrichment of organic matter was much greater for SSA particles with ambient radius (at approximately 70% RH) in the range 0.03-0.5 \(\upmu\)m than in the range 1-4 \(\upmu\)m (Figure 7). During periods of low biological activity, particles with ambient radii greater than 0.25 \(\upmu\)m were composed almost entirely of sea salt, with only 2-3% of the mass consisting of organic material and a substantial fraction of that was WSOM. For smaller particles (ambient radius 0.06-0.25 \(\upmu\)m), sea salt accounted for about 70% of the mass, with the principal remaining components being nss sulfate and organic carbon, each contributing about 15%. Of the organic aerosol mass, roughly 60% was WIOM. Also during high biological activity periods, larger particles (ambient radius 0.5-4 \(\upmu\)m) were composed almost entirely of sea salt, although the organic mass fraction increased marginally to about 5%. However, in contrast to the low biological activity periods, organic material contributed 60% to the mass of particles with ambient radius in the range 0.125-0.25 \(\upmu\)m, with the organic fraction increasing to 85% for particles with ambient radius 0.03-0.06 \(\upmu\)m. Also striking was that the WIOM constituted approximately two-thirds of the total organic aerosol mass. Approximately half of the total WIOM mass resided in particles with ambient radius less than 0.5 \(\upmu\)m.
[101] The hypothesis that WIOM was primary in origin was examined by [PERSON] and colleagues [_[PERSON] et al._, 2008] by means of the vertical gradients of concentrations of aerosol constituents. Measurements were made of chemically speculated mass concentration for particles with ambient radii less than 0.5 \(\upmu\)m at heights of 3, 10, and 30 m above the shore at Mace Head. Footprint analysis determined that the peak contribution to the flux was approximately 1.5-3 km offshore and that the vast majority of the contribution was from less than 10 km. These measurements showed that concentrations of sea salt and WIOM decreased with increasing height between 3 and 10 m (Figure 8), indicative of a surface source, whereas concentrations of WSOM and nss sulfate increased with increasing height over the same range, indicative of an atmospheric source. A concern with this study is that at times the measurements at the lower two heights were influenced by surface properties differently from the measurements at the highest level as discussed in section 4.2.1; it is thus likely that in such situations the flow at these heights was perturbed by the land and hence that observed gradients were not representative of mixing processes in the unperturbed atmosphere and cannot be used to derive quantitative flux information on transport and removal processes. Nevertheless, the gradients suggest important qualitative information on production processes, namely a surface, or primary, source for WIOM but a surface sink for WSOM, pointing to secondary aerosol formation processes. A further caveat to quantitative interpretation is that an undetermined fraction of WSOM may have originally been produced as primary WIOM and through chemical aging may have become more oxidized and hence water soluble. The similarity of mass ratio of WIOM to sea salt in ambient aerosols measured simultaneously over productive waters in the northeast Atlantic and at Mace Head by _[PERSON] et al._ [2008], noted above, provides additional evidence for a primary source of the WIOM in marine aerosol.
[102] A series of field studies by [PERSON], [PERSON], and colleagues suggests that aerosol particles with dry radius smaller than 0.1 \(\upmu\)m produced by bubble bursting over the ocean consist almost entirely of organic matter [_[PERSON] and [PERSON]_, 2008]. In these studies, the particles were sampled by an impactor operating at vacuum, and their chemical properties were examined with transmission electron microscopy [_[PERSON]_and [PERSON]_, 2001). Initially, _[PERSON] and [PERSON]_ (1999) and _[PERSON] and [PERSON]_ (2001) reported occurrences of a relatively large concentration (up to 300 cm\({}^{-3}\)) of solid, water-insoluble aerosol particles with dry radii less than about 0.025 \(\upmu\)m in the Arctic marine boundary layer. These particles were accompanied by larger particles (\(r_{\rm dry}>0.05\)\(\upmu\)m), obviously of marine origin such as bacteria and fragments of diatoms that showed very similar characteristics to colloidal particles present in bulk seawater.
[103] Strong temperature inversions during the measurements of _[PERSON] and [PERSON]_ (1999) excluded the possibility of a tropospheric source, and the presence of these particles in stable air masses over the ice that had not been in contact with open water for at least 4 days suggested a surface source for the observed particles. To identify such a source, _[PERSON] et al._ (2004) sampled the microlayer of open water between ice floes in the Arctic and reported the presence of suspended particulate organic matter with dry radii of 0.005-0.025 \(\upmu\)m. Comparing the properties of the particles from the [PERSON] et al. microlayer samples to those of aerosol particles previously observed in the overlaying atmosphere in the Arctic Ocean, _[PERSON]_ (2005a, 2005b) concluded that the particles originated from the ocean surface microlayer and were ejected into the atmosphere via bubble bursting.
[104] Subsequent studies in tropical regions have shown the presence of particles with \(r_{80}\) of a few hundredths of micrometers having chemical composition similar to that observed in particles in the Arctic, including scopolymer gels, marine microorganisms, fragments of marine biota, and bacteria; sea salt was markedly absent from such particles (_[PERSON] and [PERSON]_, 2005b, 2008). This, according to these investigators, suggests a common pattern over the ocean. The implications of these findings and the discrepancy
Figure 7: Average mass concentration of total particulate matter (black line, right axis) and mass fraction (colors, left axis) of sea salt, NH\({}_{4}\), nss SO\({}_{4}\), NO\({}_{3}\), WSOM, WIOM, and black carbon (BC) in several size ranges for North Atlantic marine aerosol sampled at Mace Head, Ireland, in clean marine air during periods of (a) low biological activity, November (2002), January (2003), and February (2003) and (b) high biological activity, March-October (2002). Radius corresponds to relative humidity approximately 70%. For low biological activity mass concentrations of aerosol constituents other than sea salt were below detection limits for the size range 0.03–0.06 \(\upmu\)m. Oceanic chlorophyll-a concentrations over the North Atlantic for periods of (c) low and (d) high biological activity are 5 year averages (1998–2002) over the same months as for the composition measurements, based on satellite measurements of ocean color (courtesy of Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project, NASA Goddard Space Flight Center, and Orbital Imaging Corporation (ORBIMAGE)). Adapted from _[PERSON] et al._ (2004).
[_[PERSON] and [PERSON]_, 2008] between these results and those of others are discussed in section 6.2.
## 5 Parameterizations of the SSA spray production flux
[105] In view of the importance of the SSA as background, nonanthropogenic, aerosol over much of the planet, much effort has been directed to representing this aerosol in chemical transport models and climate models to examine its effects and those of anthropogenic aerosols on clouds, atmospheric radiation, atmospheric chemistry, and air quality. Such models generally simulate the life cycle of aerosols and therefore represent emissions, new particle formation, chemical and physical transformations, interactions with clouds, and removal by wet and dry deposition. An essential component of such life cycle models is representation of the size- and composition-dependent emission of aerosol particles as a function of time and location, specifically including primary production of SSA particles as a function of meteorological and other controlling variables. Since the publication of LS04, several new estimates of such fluxes have been presented or may be calculated from reported laboratory studies discussed in section 4.1.3. These newer formulations are discussed below and presented in Figure 9 for \(r_{80}\) (or \(r_{\rm amb}\) or \(d_{\rm p}\)) between 0.005 and 25 \(\mu\)m. To provide context, several previous flux estimates are also included in Figure 9. Both the recent and older formulations discussed in this section are listed in Appendix A together with the applicable size and wind speed ranges.
[106] Nearly all formulations of the SSA production flux presented before 2004 were discussed, evaluated, and compared by LS04. Based on their analysis of these formulations and numerous other data sets these investigators presented the parameterization for the production flux of sea salt aerosol particles for 0.1 \(\mu\)m \(<\)\(r_{80}\)\(<\) 25 \(\mu\)m, which is presented in Figure 9 for \(U_{10}\) = 8 m s\({}^{-1}\) together with its associated uncertainty to allow comparison of formulations based on newly available measurements. Several other parameterizations of the SSA production flux discussed in section 3.1 are also presented in Figure 9 at \(U_{10}\) = 8 m s\({}^{-1}\); those of _[PERSON] et al._ [1993] and LS04 (together with associated uncertainty) based on the steady state dry deposition method; that of LS04 (together with associated uncertainty) based on the statistical wet deposition method; that of _[PERSON] et al._ [2001] based on eddy correlation; and that of _[PERSON] et al._ [1986], extrapolation of this formulation by _[PERSON]_ [2003], and formulations of _[PERSON] et al._ [2003] and _[PERSON] et al._ [2000], all based on the whitecap method. The parameterizations of [PERSON] et al. and of [PERSON] et al. used the MO'M80 formulation for \(W\) as a function of \(U_{10}\) (equation (9)). The flux reported by _[PERSON] et al._ [2001], a particle number production flux without size resolution, is plotted as if the flux is independent of \(d_{\rm p}\) (approximately equal to \(r_{80}\)) over the indicated size range, such that the measured number flux is obtained as an integral over this range.
### Whitecap Method
[107] Laboratory experiments and field measurements that have been or might be used to infer the SSA production flux per white area and its dependence on water temperature, salinity, and surfactant concentration were described in section 4.1.3. The investigations by _[PERSON] et al._ [2007] and _[PERSON] et al._ [2007] provided sufficient information to permit determination of the production flux per white area. As noted in section 4.1.3, the magnitudes of these production fluxes also differed greatly depending on experimental conditions such as the bubble volume flux, resulting in large differences even among SSA production flux estimates from a given study. These estimates, used together with the dependence of \(W\) on wind speed according to MO'M80, yield size-dependent SSA production fluxes.
[108] The size dependence of the production flux per white area in the representation \(dF_{\rm ww}/d\)log\(r_{80}\) was approximated by _[PERSON] et al._ [2007] as a single lognormal, with the geometric mean \(r_{80}\) between approximately 0.085 and 0.115 \(\mu\)m and the geometric standard deviation between approximately 1.6 and 1.8 depending on conditions, specifically bubble volume flux and pore size of the diffuser used to produce the bubbles (their Table 1). The magnitude of the concentration of the particles thus produced increased linearly with bubble volume flux (their Figure 5), implying that the production flux per white area (taken as the surface area of water in the apparatus) increased nearly quadratically with bubble volume flux according to equation (10) (Figure 5),
Figure 8: Vertical profiles of mass concentration of sea salt, WIOM, non-sea salt sulfate, and WSOM at Mace Head, Ireland, normalized to the sum of the concentrations of the species at the three heights, for particle radius (at ambient relative humidity) less than 0.5 \(\mu\)m sampled in clean marine air. All values are averages of nine individual 7 day samples analyzed from April-October 2005 except WIOM, which is shown for an average of three samples where a positive WIOM flux was observed and which represented periods when the organic-enriched waters were within the flux footprint as discussed in the text. Uncertainty bars represent the standard deviation from the normalized concentration average. Adapted from _[PERSON] et al._ [2008].
varying by nearly a factor of 60 for the different bubble volume fluxes for salinity 33. Examples of size-dependent production fluxes for artificial seawater of salinity 33 at two different bubble volume fluxes are shown in Figure 9 for \(U_{10}\) = 8 m s\({}^{-1}\), based on the MO'M80 parameterization for \(W\).
[109] The SSA production flux per white area determined from the laboratory studies of _[PERSON] et al._ [2007] exhibits a nearly linear dependence on bubble volume flux (their Figures 3 and 4), in contrast to the quadratic dependence found by _[PERSON] et al._ [2007] (Figure 5). An estimate of the SSA production flux at \(U_{10}\) = 8 m s\({}^{-1}\) based on the production flux per white area for a single bubble volume flux from [PERSON] et al. together with the MO'M80 formulation for \(W\) is shown in Figure 9.
[110] Measurements of SSA production resulting from a surf zone were used by _[PERSON] et al._ [2006] (section 4.1.4) to derive a new formulation for the size-dependent SSA production flux per white area for dry particle diameter (approximately equal to \(r_{\rm{80}}\)) range 0.01-8 um. This formulation together with the MO'M80 formulation for \(W\) provides a formulation for the SSA production flux; this is shown in Figure 9 for \(U_{10}\) = 8 m s\({}^{-1}\). According to this formulation, the daily rate of increase of the number concentration of aerosol particles (assumed to be uniformly distributed over a marine boundary layer height of 0.5 km) for \(U_{10}\) = 10 m s\({}^{-1}\) would be nearly 150 cm\({}^{-3}\). As discussed in section 4, [PERSON] et al. concluded that the majority of particles were sea salt particles.
[111] With respect to application of the whitecap method, in addition to uncertainty arising from the SSA production flux per white area, any uncertainty in whitecap fraction \(W\) also transfers directly to production flux. From examination of Figure 2, this uncertainty at \(U_{10}\) = 8 m s\({}^{-1}\) appears to be roughly a factor of \(\div\)5. Also if the lower values of \(W\) shown in Figure 2 relative to previous measurements are sustained by further observations, a high bias in \(W\) from values calculated by the MO'M80 parameterization by roughly a factor of 3 at this wind speed, previous estimates of production fluxes using that expression for \(W\) would appear to likewise be biased high by such a factor.
### Eddy Correlation
[112] Eddy correlation measurements by _[PERSON] et al._ [2005] at Mace Head (section 4.2.1) in each of two size ranges, \(r_{\rm{amb}}\) = 0.005-0.5 um and \(d_{\rm{p}}\) = 0.1-1 um, corrected for dry deposition to yield production fluxes, were expressed
Figure 9: Parameterizations of size-dependent SSA production flux discussed in text and presented in the Appendix A, evaluated for wind speed \(U_{10}\) = 8 m s\({}^{-1}\) (or \(U_{22}\) = 8 m s\({}^{-1}\) for _[PERSON] et al._ [2005]). Also shown are central values (curves) and associated uncertainty ranges (bands) from review of _[PERSON]_ [2004], which denote subjective estimates by those investigators based on the statistical wet deposition method (green), the steady state deposition method (blue), and taking into account all available methods (gray); no estimate was provided for \(r_{\rm{80}}\) \(<\) 0.1 μm. Lower axis denotes radius at 80% relative humidity, \(r_{\rm{80}}\), except for formulations of _[PERSON] et al._ [2001], _[PERSON] et al._ [2003], and _[PERSON] et al._ [2006] which are in terms of dry particle diameter, \(d_{\rm{p}}\), approximately equal to \(r_{\rm{80}}\) and those of _[PERSON] et al._ [2005], _[PERSON]_ [2006] (dry deposition method), and _[PERSON] et al._ [2008] which are in terms of ambient radius, \(r_{\rm{amb}}\). Formulation of _[PERSON]_ [2006] by the dry deposition method is based on expression in Appendix A. Formulations of _[PERSON] et al._ [2007] are for artificial seawater of salinity 33 at the two specified bubble volume fluxes. Formulations of _[PERSON] et al._ [2001] and _[PERSON] et al._ [2005] of particle number production flux without size resolution are plotted arbitrarily as if the flux is independent of \(r_{\rm{amb}}\) over the size ranges indicated to yield the measured number flux as an integral over that range.
as exponential functions of wind speed at 22 m above the sea surface, \(U_{22}\). The resulting fluxes are plotted in Figure 9 for \(U_{22}=8\) m s\({}^{-1}\), as if the fluxes in the representation \(dF/d\)02\(g_{\rm amb}\) (or \(dF/d\)02\(g_{\rm p}\)) are independent of \(r_{\rm amb}\) (or \(d_{\rm p}\)) over the respective size ranges, such that the measured number fluxes are equal to the integrals over these size ranges. According to these expressions, the daily increases in the number concentration of aerosol particles (assumed uniformly distributed over a marine boundary layer height of 0.5 km) for \(U_{10}=10\) m s\({}^{-1}\) would be 320 and 135 cm\({}^{-3}\) for the two size ranges.
[113] Noting that an exponential wind speed dependence can introduce an artificial bias in sea spray production at low wind speeds, _[PERSON] et al._ [2008] refitted the data in the larger size range as a power law for their regional climate model (section 5.6). This fit agreed with that presented by _[PERSON] et al._ [2005] to within \(\sim\)20% for \(U_{22}\) greater than 6 m s\({}^{-1}\), below which there were only two measurements; in view of the limited range of the measurements, it would seem that either functional form (or perhaps others) would yield equally good fits to the observations and thus it is not possible to identify a preferred wind speed dependence.
[114] Eddy correlation measurements of \([PERSON]\)_et al._ [2008] at Duck, North Carolina, were parameterized in terms of an exponential dependence on either \(U_{10}\) or \(u_{*}\) in six ranges of ambient radius. There was no clear reduction in the scatter of the flux estimates based on \(u_{*}\) compared to that based on \(U_{10}\). As these measurements were not corrected for dry deposition, they net fluxes rather than production fluxes, although as noted in section 4.2.1, the corrections are likely small. The fluxes according to this formulation are shown in Figure 9 for \(U_{10}=8\) m s\({}^{-1}\). According to this formulation, the daily rate of increase of the number concentration of aerosol particles (assumed to be uniformly distributed over a marine boundary layer height of 0.5 km) for \(U_{10}=10\) m s\({}^{-1}\) would be near 50 cm\({}^{-3}\).
### Gradient Method
[115] The size-dependent production flux formulation presented by _[PERSON] and [PERSON]_ [2006], based on the gradient method using measurements of the vertical distribution of aerosol concentration, was modified by _[PERSON]_ [2007; see also _[PERSON]_, 2007] to include a factor of \(\kappa\), the von Kamman constant. According to this formulation, the size dependence of the production flux depends on wind speed. This production flux, including the factor of \(\kappa\), is presented in Figure 9 for \(U_{10}=8\) m s\({}^{-1}\). As noted in section 4.2.2, there are serious concerns with these measurements that limit the confidence that can be placed in this parameterization.
### Steady State Dry Deposition Method
[116] The steady state dry deposition method was applied by _[PERSON] and [PERSON]_ [2006] to determine SSA production fluxes for ambient radii 0.25-7.5 \(\upmu\)m based on concentrations of aerosol particles measured during cruises to the Arctic _[PERSON]_, 2005]. The dry deposition velocity required to obtain the production flux from measured concentrations was parameterized using a formulation of _[PERSON]_ [1986], which includes only gravitational settling and turbulent diffusion (and not impaction, molecular diffusion, or growth of particles due to increased RH near the sea surface); this formulation yields dry deposition velocities that are considerably greater than those from most other formulations for \(r_{80}\) less than several micrometers. Measured concentrations were converted by _[PERSON]_ [2005] to \(r_{80}\) values and fitted to the product of an exponential function of wind speed (despite a poor correlation) and a factor that gives the dependence on \(r_{80}\), with a multiplicative uncertainty given as a factor of 7. Concentrations were plotted by _[PERSON]_ [2005] for radii up to 7.5 \(\upmu\)m, although the resulting production fluxes were plotted for radii up to only 5 \(\upmu\)m by _[PERSON] and [PERSON]_ [2006]; as noted in section 3.2, the dry deposition method can be accurately applied only for \(r_{80}\) greater than approximately 3 \(\upmu\)m. Additionally, as the concentrations measured by _[PERSON]_ [2005] were not specific as to composition and included all marine aerosol particles, it was implicitly assumed that all particles counted were sea salt particles, with resultant overestimation of the production flux by the proportion of particles that were not SSA particles. The SSA production flux according to the formulation of _[PERSON] and [PERSON]_ [2006] is presented in Figure 9 (without the multiplicative uncertainty) for \(U_{10}=8\) m s\({}^{-1}\), evaluated according to the expression in Appendix A, which employs values of the drag coefficient and gravitational settling velocity not specified by these investigators.
### Other Formulations
[117] Several investigators have used combinations of different SSSF formulations in models. This is evident in the models listed in Table 1. One such recent approach is that of _[PERSON] et al._ [2006], which was based on the _[PERSON] et al._ [1986] formulation for \(r_{80}\) from 0.3 to 5 \(\upmu\)m (although the [PERSON] et al. expression had been given by the original investigators for \(r_{80}=0.8\)-8 \(\upmu\)m) together with that of _[PERSON] et al._ [1993] for \(r_{80}\) from 5 to 30 \(\upmu\)m, as corrected by _[PERSON] et al._ [2002], to account for what those investigators had considered spume drops (although it has not been established that those particles in this range were spume drops). [PERSON] et al. accounted for the findings of _[PERSON] et al._ [2003] and _[PERSON] et al._ [2006] of a large production flux of particles with 0.02 \(\upmu<r_{80}<0.2\)\(\upmu\)m by multiplying the _[PERSON] et al._ [1986] production flux (extended to \(r_{80}=0.02\)\(\upmu\)m) by a factor (their equation (2))
\[C(r_{80})=0.794\binom{(r_{80}^{\rm stars})}{\infty}\left(1+\frac{0.4}{r_{80}}\right), \tag{11}\]
where \(r_{80}\) is in \(\upmu\)m (here the expression is given in terms of \(r_{80}\) rather than \(r_{\rm dry}\) as given by [PERSON] et al., with \(r_{80}\) taken as \(2r_{\rm dry}\)). Production, transport, wet and dry deposition, and clear-air and in-cloud reactions of sea salt aerosol were represented in a 33 bin (0.02 \(\upmu\)m\(<r_{80}<50\)\(\upmu\)m) sectional model. For the conditions examined, SSA contributed 20-30% of the CCN concentration for the activation threshold taken as \(r_{80}=0.066\)\(\upmu\)m.
[118] Yet another production flux formulation based on that of _[PERSON] et al._ [1986] was presented by _[PERSON] et al._ [2008], who extended the [PERSON] et al. production flux (which had been given only for \(r_{80}\geq 0.8\)\(\mu\)m) to \(r_{80}=0.015\)\(\mu\)m, multiplied by a factor to better reproduce high concentrations of SSA particles reported by _[PERSON] et al._ [1997]. Specifically, for \(0.015\)\(\mu\)m \(<r_{80}<0.2\)\(\mu\)m this factor is given by
\[C(r_{80})=\exp\biggl{\{}-6.43\biggl{[}\log\biggl{(}\frac{r_{80}}{0.2\ \mu{\rm m}} \biggr{)}\biggr{]}^{2}\biggr{\}} \tag{12}\]
(as above, this expression is presented here in terms of \(r_{80}\) rather than \(r_{\rm dry}\), with \(r_{80}\) taken as \(2r_{\rm dry}\)). This production flux formulation was employed in a regional climate model to determine the climate influences of sea salt aerosol. As the model represented SSA by only two size bins and as the \(r_{80}\) range of the lower size bin was 0.1-2 \(\mu\)m, it would seem that the consequences of the modification to the production flux would be minimal, especially so as the reported emissions and concentrations were presented on a mass basis.
[119] Although formulations such as those of _[PERSON] et al._ [2006] and _[PERSON] et al._ [2008] permit calculation of SSA production fluxes to \(r_{80}\) as low as 0.02 \(\mu\)m or below in large-scale models, it would seem that little confidence can be placed in such formulations or in the resultant calculations, especially in the extended size ranges owing to the large extrapolations and the paucity of data upon which they were based. As seen in Figure 9 there remains substantial uncertainty in SSA production flux estimates in this size range.
### Organic Production Formulation
[120] A key finding of recent work is the identification of a large contribution of biogenic WIOM to SSA (section 4.3). [PERSON] and colleagues have presented several formulations of the production flux of this substance and its representation in global models [_[PERSON] et al._, 2008; _[PERSON] et al._, 2008a, 2008b; _[PERSON] et al._, 2010] based on the concentration of chlorophyll-a in the ocean surface layer as determined by satellite observations as a proxy for the mass fraction of WIOM in sea spray, \(\Phi_{\rm om}\). These observations together with seasonal variation of \(\Phi_{\rm om}\) determined from measurements of aerosol chemical composition have been combined with an SSA production flux formulation to yield the oceanic production flux of WIOM associated with sea spray production and to examine WIOM emissions in several model studies.
[121] The relation between \(\Phi_{\rm om}\) and chlorophyll-a concentrations was investigated by _[PERSON] et al._ [2008] using aerosol composition measurements from the 3 year data set of _[PERSON] et al._ [2007] from Mace Head, Ireland, in which only clean marine air masses were sampled. It was assumed, based on experimental work discussed in section 4.3, that the aerosol mass for \(r_{80}\) less than approximately 1 \(\mu\)m was composed mainly of sea salt and WIOM, with a minor contribution from WSOM, arbitrarily taken as 5% of the WIOM mass concentration. Chlorophyll-a concentration, _Chl_, was taken as the spatial average over a grid of 1000 km \(\times\) 1000 km upwind of Mace Head. A linear fit of \(\Phi_{\rm om}\) to _Chl_ for 37 data points was presented by _[PERSON] et al._ [2008] and a revised fit, taking into account small corrections to the chemical analysis, was presented by _[PERSON] et al._ [2008b] (as corrected by _[PERSON] et al._ [2010]). More recently a fit to a subset (24) of these data was presented by _[PERSON] et al._ [2010] as
\[\Phi_{\rm om}=0.435\biggl{(}\frac{Chl}{\rm mg\ m^{-3}}\biggr{)}+0.14,\ Chl<1.43\ {\rm mg\ m^{-3}} \tag{13}\]
(the range of validity was incorrectly stated as \(Chl<1.43\ {\rm mg\ m^{-3}}\) in their equation (3)). The different fits are shown in Figure 10. Only about 30% of the variance of \(\Phi_{\rm om}\) is accounted for by any of the fits.
[122] To obtain a formulation for the size-dependent production flux of WIOM in SSA, _[PERSON] et al._ [2008] assumed that the size dependence of the SSA production flux was given by a lognormal distribution with the geometric mean value of \(r_{80}\) given as a function of time of year, so as to capture changes in \(\Phi_{\rm om}\) (although a more physically based quantity such as water temperature or chlorophyll-a concentration would be more appropriate). The magnitude of the SSA production flux was given by the formulation of _[PERSON] et al._ [2005] for particles with dry diameter \(d_{\rm pr}=0.1\)-1 \(\mu\)m, which was refitted to a power law as \(F\) (m\({}^{-2}\) s\({}^{-1}\)) = \(1.854\times 10^{3}\)\(U_{22}^{2.706}\). The WIOM mass fraction \(\Phi_{\rm om}\) was constrained to a maximum value of 0.9.
Figure 10: Mass fraction of water-insoluble organic matter in sea spray aerosol with \(0.1\ \mu\)m \(\leq\)\(r_{\rm amb}\) \(\leq 0.5\)\(\mu\)m measured at Mace Head, Ireland, under clean marine conditions as a function of spatial average oceanic surface water chlorophyll-a concentration over an upwind grid of 1000 km \(\times\) 1000 km as determined from MODIS satellite measurements of ocean color, revised from _[PERSON] et al._ [2008] and provided by [PERSON] (2010). Original fit presented by _[PERSON] et al._ [2008] and fits to revised data presented by _[PERSON] et al._ [2008b] (corrected by _[PERSON] et al._ [2010]) and _[PERSON] et al._ [2010] are also shown.
This procedure yielded a parameterization of the production flux of SSA number and chemical composition for particles with an approximate \(r_{80}\) range 0.1-1 \(\upmu\)m and was combined with monthly average wind speed fields (from SeaWinds on the QuickScat satellite) and chlorophyll-a concentrations (from Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua and Terra satellites) to produce estimates of the global annual production of WIOM as 2.3 Tg C yr\({}^{-1}\) for 2003 and 2.8 Tg C yr\({}^{-1}\) for 2006 (_[PERSON] et al._, 2008b).
[123] A similar approach was used by _[PERSON] et al._ [2010] to determine the production flux of WIOM associated with sea spray in the accumulation mode (approximate \(r_{80}\) range 0.1-1 \(\upmu\)m), for which the size dependence of the production flux was assumed to be a lognormal with geometric mean radius at 80% RH equal to 0.09 \(\upmu\)m and the magnitude of the production flux was that of _[PERSON] et al._ [2003]. The maximum value of \(\Phi_{\rm em}\) was constrained to 0.76. This formulation was used in a global chemical transport model to determine the production of WIOM and sea salt in this mode for a 1 year period in 2002-2003 (Figure 11). Global annual emissions of WIOM and sea salt in this mode were 8.2 and 24 Tg, respectively. It should be noted that there is likely a significant but to date unquantified flux of WIOM in particles with \(r_{80}>1\)\(\upmu\)m [_[PERSON] et al._, 2008]. The production rate for WIOM estimated by _[PERSON] et al._ [2010] was nearly 3 times that reported by _[PERSON] et al._ [2008b]; no reasons for the difference were presented. A possible explanation is that the model of [PERSON] et al., in contrast to that of [PERSON] et al., used a single fixed particle size (\(r_{80}\) = 0.09 \(\upmu\)m) and did not account for possible variation of particle size with _Chl_.
[124] Although a calculation such as this can hardly be taken as a definitive estimate in view of the uncertainties associated with the production flux formulation, the estimate of the organic fraction of the primary SSA emission flux, and the poor correlation between satellite determinations of chlorophyll-a concentrations and organic mass fraction, this methodology suggests an approach for modeling these emissions on a global scale as input to chemical transport models and climate models.
## 6 Discussion
[125] As discussed in section 1, there is continuing and indeed heightened interest in characterization of the number concentration, composition, and other properties of SSA and in the processes that govern its production. Unfortunately, the present state of understanding of production, concentrations, and removal rates of SSA particles is so low that it is not possible to constrain the mass emission flux even to an order of magnitude, as reflected in the differing emission rates shown in Figure 1, and the situation for particle number production is even more uncertain.
[126] This review has examined recent findings regarding the size-dependent production of SSA and parameterizations of this production flux since the critical review of _[PERSON] and [PERSON]_ [2004]. New work has added a substantial body of findings to those which were presented in that review. An important new finding is the recognition that sea spray contains other substances in addition to sea salt and that the major and in some instances dominant contribution to SSA in some size ranges is from organics, especially at smaller sizes. Along with this finding comes the recognition that SSA production extends to much lower sizes than were previously recognized, with both laboratory experiments and field measurements showing substantial production of SSA at values of \(r_{80}\) below 0.1 \(\upmu\)m and down to as low as 0.01 \(\upmu\)m, as many of these smaller particles are composed primarily of organic substances. However, despite the new work, there seems to be little convergence on understanding important elements of the SSA production process, as characterized by quantities needed to determine SSA production fluxes such as the flux per white area and the whitecap fraction. This discussion examines the several approaches taken in recent
Figure 11: Global distribution of mass flux of (top) sea salt and (bottom) water–insoluble organic matter in sea spray with 0.1 \(\upmu\)m \(<r_{80}<1\)\(\upmu\)m averaged over a 1 year period in 2002–2003 using the TM5 chemical transport model [_[PERSON] et al._, 2010]; [PERSON], private communication, 2010].
work to measure the quantities pertinent to the determination of SSA production flux, its dependence on controlling variables, and the numerical representation of this production flux.
### Laboratory Investigations of SSA Production
[127] Key among the findings of recent work is the demonstration in laboratory experiments that the SSA production flux per white area can depend strongly, by up to 2 orders of magnitude, on the volume flux of air in bubbles passing through the white area (Figure 5). However, experiments to date have explored only a very limited subset of the physical and chemical variables controlling SSA production flux per white area. With respect to physical conditions, the studies of _[PERSON] et al._ [2007] and _[PERSON] et al._ [2007] relied on artificial constraints on the size of the bubble swarm reaching the surface, specifically confinement of the resulting white area by the walls of the vessel in which these bubbles were produced. Whether such a constraint is a good mimic of the barrier to lateral diffusion of bubbles in an unconfined situation such as the open ocean following entrainment of air during wave breaking is not known. One fruitful line of future investigation would be systematic examination of the SSA production flux as the flow rate of air is varied through an array of multiple diffusers (frits) in a vessel sufficiently large that the spread of the bubble swarm would not be limited by the vessel walls. Likewise it would seem essential to examine other possible reasons for differences between the production flux per white area in the studies of _[PERSON] et al._ [2003], _[PERSON] et al._ [2007], _[PERSON] et al._ [2007], and _[PERSON] et al._ [2010] such as dependence of production flux per white area on the depth of the diffuser producing the bubbles, which differed in these experiments by more than an order of magnitude, from a few centimeters to more than a meter. Another fruitful line of investigation might be the systematic examination of the effects of temperature on bubble formation, bubble dynamics, and bubble bursting as components of the SSA production process. Experiments such as these would permit measurement of the bubble spectrum and volume flux that might be compared to such fluxes following wave breaking in the open ocean.
[128] Oceanic bubble spectra obtained to date are averages over long periods and thus include breaking waves and background spectra which do not contain the large bubbles generated just after wave breaking, which are responsible for the generation of film drops. These very large bubbles are probably not generated in any of the laboratory experiments discussed above. Considerations such as these also invite determination of the bubble spectrum and volume flux resulting from wave breaking as a function of location and time relative to wave breaking in laboratory studies and in the open ocean and relating bubble volume flux and SSA production in such studies to \"whiteness\" determined by optical measurements. Also, a systematic examination of the dependence of SSA production flux on bubble volume flux (and perhaps other variables) beyond the measurements reported to date would be useful, especially given the substantial differences reported by different investigations shown in Figure 5. Such studies would be valuably informed by laboratory investigations examining the dependence of SSA production on means of bubble production such as that of _[PERSON] et al._ [2010]. It might be noted that for none of these methods is it established that the bubble spectrum and resultant SSA production are representative of open ocean conditions. In this regard the conclusion reached by some of the investigators that a weir is more appropriate than bubbles produced by diffusers for generating SSA has little justification.
[129] A further open question amenable to laboratory investigation is the mechanism responsible for the temperature dependence of SSA production that has been observed in laboratory experiments [_[PERSON] et al._, 2003; _[PERSON] et al._, 2006], as temperature might affect bubble generation at the fit employed to generate the bubbles and the dynamics of bubble rise in addition to the production of particles associated with bubble bursting through the temperature dependence of viscosity, surface tension, or other controlling properties. Systematic examination of these dependences might lead to improved understanding and parameterization of the overall dependence of SSA production on temperature.
### Composition of SSA
[130] A very important line of investigation in recent studies has been the dependence of SSA composition as a function of particle size in laboratory experiments and field measurements and the role of seawater composition on particle composition. These studies have shown, especially for particles with \(r_{80}<0.25\)\(\mu\)m, that organic material can comprise a substantial fraction of SSA particles that approaches unity, especially under conditions of high biological activity [_[PERSON] et al._, 2004; _[PERSON] et al._, 2008]. It seems increasingly likely that production of particles highly enriched in organic material derives from fragmentation of the film cap from which much of the seawater has drained prior to bursting, leaving behind a film that is highly enriched in surfactant material. Laboratory studies with flowing seawater (on ships or at coastal laboratories) would be well suited to systematic examination of such influences, especially as studies with organic compounds introduced into laboratory-prepared artificial seawater as proxies for actual oceanic organic material have not proved very successful in reproducing the effects observed in actual seawater. These studies also raise questions regarding the attribution of high-production fluxes of SSA particles to inorganic sea salt in instances where the composition has not been determined by chemically specific methods. It appears [e.g., _[PERSON]_, 2008] that the water-insoluble organic matter associated with very small particles may be persistent at temperatures as high as 300\({}^{o}\)C, which have been used in many studies to distinguish what has been taken as refractory material such as inorganic sea salt from substances such as sulfates and secondary organic matter which are volatilized at such temperatures. Thus, the use of volatility alone is not sufficient to determine the composition of particles that originate from the ocean surface and suggest the need for specific chemical determination in future such studies.
[131] A major development in the past several years has been sustained measurements of the size-distributed composition of marine aerosol at a coastal site downwind of open ocean. By restricting the measurements to the oceanic sector it has been possible to obtain a much larger data set than would be available from cruises of limited duration. Although there is much precedent for such measurements at island and coastal sites [_[PERSON]_, 2002] that has established the role of long-range transport of mineral dust and continental anthropogenic aerosols to the marine environment, the new measurements show the value of much better size resolution in the range \(r_{80}<1\) um together with determination of the size-dependent organic component of the aerosol. Importantly, these measurements have shown that the organic material is present predominantly in particles of \(r_{80}\lesssim 0.5\) um. Examination of vertical profiles of composition (Figure 8) provides convincing evidence that the organic material, specifically WIOM, has an origin at the sea surface, i.e., is a component of SSA.
[132] Extended measurements of size-distributed composition of marine aerosols over several years [_[PERSON] et al._, 2004; _[PERSON] et al._, 2008] have permitted examination of the hypothesis that WIOM is of biological origin, specifically from surfactant materials in the surface layer that arise from biological activity, perhaps exudates or chemical decomposition products of organisms. The data from these measurements have been employed in a first systematic attempt to relate organic material in marine aerosol to biological activity in seawater by examination of correlation with _Chl_ obtained from satellite measurements of ocean color [_[PERSON] et al._, 1998]. Although aerosol organic fraction exhibited some correlation with _Chl_ (\(r^{2}=0.3\)), there is much variation in this fraction that is not accounted for in the oceanic chlorophyll data product (Figure 10). As this variation is much greater than the scatter between in situ measurements of _Chl_ and the satellite data product [_[PERSON] et al._, 1998], it would seem that _Chl_ is not wholly adequate as a proxy for the biological activity responsible for the organic material comprising the aerosol. Nonetheless, the relationship between aerosol organic matter and satellite-determined oceanic chlorophyll concentration provides convincing evidence of the role of biological activity in producing this organic matter.
[133] The correlation of organic matter in SSA with satellite-derived _Chl_ found by [PERSON] and colleagues [_[PERSON] et al._, 2010] has been incorporated into a parameterization of the organic component of a SSA production flux to calculate the global distribution of WIOM production. However, this correlation is based only on measurements at a single nonrepresentative site being a region of high biological productivity; this situation suggests the need for additional similar studies at other locations. For these reasons, at the present stage of understanding calculations such as those of [PERSON] et al. should perhaps be viewed more as proof of concept than as definitive estimates of the globally distributed production of primary marine organic aerosol. Certainly, the insights gained thus far by the extended measurement campaigns by [PERSON] and colleagues at the Mace Head, Ireland, site suggest the utility of conducting such measurements at other sites characterized by different temperature, different biological productivity, and the like to build a more comprehensive global picture of the composition of marine aerosols generally and of the concentration and properties of sea spray aerosol.
[134] Although the identification and quantification of organic material in very small SSA particles represents a substantial advance, an important piece of the picture that is still missing is the mixing state (internal versus external) of sea salt and organic matter in particles in the \(r_{80}\) range from approximately 0.05 to 0.2 um. This mixing state would be expected to influence the ability of these particles to serve as CCN and consequently their turnover times against removal through wet deposition. The suggestion of recent research that many, perhaps most, of the SSA particles with \(r_{80}\lesssim 0.1\) um consist of WIOM thus has important implications for the budget of these primary aerosol particles. The need for information on particle mixing state suggests the utility of alternative means of characterizing the composition and properties of SSA particles. Aerosol mass spectrometry and single-particle aerosol mass spectrometry provide real-time information on aerosol composition that has greatly informed understanding of aerosol properties and processes in terrestrial environments but that has thus far seen limited application in the marine environment and specifically for characterization of SSA particles. It seems likely as well that much important information on the properties of SSA particles would be gained from developing and applying techniques that can determine the composition of particles with \(r_{80}<0.1\) um, which are difficult to study by mass spectrometry such as transmission electron microscopy, which can examine the composition and structure of individual particles, or more exotic techniques such as X-ray absorption fine structure, which can determine composition and oxidation state of material present in ensembles of particles.
[135] The variability in the amount and nature of organic material and the resulting surfactants in seawater would appear to be major sources of variability in the SSA production flux. Based on a combination of laboratory experiments with observations on the open ocean and at the coastal site at Mace Head, _[PERSON] et al._ [2008] showed that the composition of particles generated in laboratory experiments with bursting bubbles was similar to that observed in aerosols in the open ocean. Furthermore, the seasonality of sea spray emissions and chemical composition follows the chlorophyll cycle obtained using satellite measurements [_[PERSON] et al._, 2006]. When biological activity is low in the ocean with resultant low concentrations of organic matter in the ocean surface layer, sea spray is comprised predominantly of inorganic sea salt. In contrast, when biological activity is high and organic matter is present at the ocean surface, this organic matter is enriched in sea spray particles with \(r_{80}<0.25\) um. These considerations suggest that improving knowledge in this area will require combinationsof laboratory and field experiments and that this effort will require multidisciplinary cooperation among oceanographers, marine biologists, meteorologists, physicists, and chemists to understand the effects of biological species such as phytoplankton and algae on the formation, physical properties, and composition of SSA.
[136] Although [PERSON] and colleagues [_[PERSON] et al._, 2004; _[PERSON] et al._, 2004; _[PERSON] et al._, 2007; _[PERSON] et al._, 2008] report the fraction of the mass of SSA particles that is composed of organics varying, depending on the season and the size of the particles, from 2-3% to 60-80% (section 4.3), _[PERSON] and [PERSON]_ [2008] argue that bubble-mediated particles with \(r_{80}<0.1\) um are purely organic (section 4.3). In contrast, the experiments by _[PERSON] et al._ [2006] argued that particles with \(r_{80}>0.03\) um produced from breaking waves in the surf zone were composed almost entirely of sea salt. The contrasting findings raise the question of whether _[PERSON] et al._ [2004] and _[PERSON] and [PERSON]_ [2008] observed the same type of particles. For example, the size distributions of concentration reported by _[PERSON] et al._ [2004] appeared as two separate modes, whereas _[PERSON] et al._ [2004] observed a continuous size distribution of organic aerosols.
### Whitecap Fraction
[137] A further important line of recent investigation is the examination of the dependence of the whitecap fraction on controlling factors. Recent studies using digital photographic techniques have indicated systematically lower whitecap fraction at a given wind speed (by as much as a factor of 4 or so) than has characterized the bulk of previous determinations of this quantity as summarized by LS04. The reasons for this difference are not known, although one possibility is differences in technique, for example, differences in the dynamic range of digital photography versus that of film; a similar situation resulted in the whitecap fraction as determined by analog video being an order of magnitude lower than that determined by film photography. It is clear that the reasons for these differences need to be better understood than they are at present.
[138] Studies examined in section 4.1.1 reported advances in image processing, specifically in defining thresholds that distinguish white area from nonwhite area. However, although such approaches to defining thresholds remove the subjectivity from determining white area in individual images, this subjectivity is transferred to the choice of the threshold for the batch processing. More intrinsically, it is not established which if any threshold yields a white area that corresponds to that for which the flux per white area has been determined in laboratory studies. It seems likely that there may be variation in the \"whiteness\" that characterizes the bubble swarm that follows a breaking wave as the bubble volume flux diminishes with time following a wave breaking event; a whitecap property such as this would be much more useful than an arbitrary threshold of \"white\" in relating SSA production flux to white area and ultimately in developing more accurate parameterizations for SSA production flux.
[139] A major strength of the digital photography technique is the ability to quantitatively examine the temporal variation of white area both by following the course of white area and whiteness subsequent to the breaking of individual waves and by statistical techniques such as examination of the temporal autocorrelation of whiteness, which may yield information on the statistical independence of successive photographs and on the duration of white area following wave breaking as a function of wind speed thus leading to improved estimates of whitecap behavior and of SSA production flux.
[140] Another recent advance is the availability of satellite determination of whitecap fraction through microwave radiometry. Initial developments show that this approach offers the potential for further understanding and parameterizing this quantity and for determining \(W\) globally on spatial scales of 50 km with daily or better temporal resolution, which could in turn diminish the uncertainty of SSA production as obtained with the whitecap method. However, at present there are discrepancies of an order of magnitude or more between whitecap fraction determined by satellite-borne microwave radiometers and those determined by photographic measurements at visible wavelengths, especially the high values of \(W\) found at low wind speed by the microwave measurements (Figure 3); possible reasons for these discrepancies are examined in section 4.1.2. Based on these comparisons satellite measurements are not sufficiently accurate at present to provide reliable estimates of whitecap fraction. It would seem essential to use airborne radiometers in conjunction with simultaneous airborne photographic measurements to facilitate further developments of this approach.
### SSA Production Flux Parameterization
[141] Many parameterizations of the SSA source function continue to be based on the whitecap method, according to which the SSA production flux is evaluated as the product of the production flux per white area, assumed to be a constant in both the magnitude of the flux and the size dependence, independent of the nature or properties of the white area, and the whitecap fraction, a function of meteorological and ocean conditions but in practice parameterized mainly in terms of wind speed (equation (9)). It should be stressed that the separability of the production flux into the product of two such independent quantities remains an unproved assumption. Indeed this separability is subject to increasing question, especially on the basis of recent laboratory studies and field measurements summarized in Figure 4, which show strong differences in the size dependence of the SSA production flux under different conditions. These differences, if not measurement artifacts, are orders of magnitude in some size ranges. Likewise the measurements of the production flux per white area of _[PERSON] et al._ [2007] and _[PERSON] et al._ [2010] indicate that the magnitude of this quantity can depend strongly on the nature of the white area. Finally, the composition, especially of particles with \(r_{80}<0.25\) um, depends strongly on the organic composition of the seawater as determined by in situ measurement or as inferred from proxy measurements. In sum, these measurements raise important questions over the accuracy of the whitecap method in its current formulation (equations (3), (8), and (9)), especially as this method has provided parameterizations for the SSA production flux which are widely used by the aerosol modeling community. It would thus seem essential to reexamine the premises of the whitecap method in laboratory experiments and field measurements to determine how this method can be reformulated.
[142] Alternatively, the SSA production flux determined by field measurements for particular meteorological conditions and ocean state can be compared to that evaluated by the whitecap method for the wind speed of the measurement and/or to that evaluated for whitecap fraction. In this respect, the measurements of _[PERSON] et al._ [2006] of SSA production in the surf zone and of _[PERSON] et al._ [2007] and _[PERSON] et al._ [2008] of SSA production at a coastal site during onshore winds provide determinations of SSA production under specific meteorological and oceanic conditions. Such measurements, in principle, could be extended to a variety of conditions. It would also be important to increase the size resolution of such measurements in view of the large variation in particle properties such as CCN activity within the range of size bins of existing instrumentation. The surf zone method would seem limited in its application to rather specific situations and might suffer from site-specific conditions that make the results not representative of the open ocean (e.g., the influence of bottom drag on the wave breaking process). Eddy correlation with fast, size-resolved measurements of the net particle flux, which may be employed on long piers, offshore platforms, or ships in the deep ocean, might provide a repertoire of measurements that would permit evaluation of the whitecap method and/or become the basis for a more differentiated picture of the SSA production flux and its dependence on controlling variables.
[143] Recent estimates of the SSA production flux (Figure 9) appear to be greater than previous estimates, especially toward smaller particle sizes. Although these new estimates coincide with that of LS04 for the largest particles (\(r_{80}\gtrsim 3\) um), toward smaller sizes they are increasingly higher, by up to 1-2 orders of magnitude at \(r_{80}=0.1\) um, near which size these fluxes, in the representation \(dF/\)dlog\(r_{80}\), exhibit their maximum values. Possible reasons for and consequences of this behavior are discussed in section 6.5.
### Consistency Between SSA Production and Observed Particle Concentrations
[144] As the number concentration of aerosol particles in clean marine air, often as low as 200 cm\({}^{-3}\) (section 3), is controlled by transport, production, and removal, consideration of rates of removal processes together with reported number concentrations leads to a check on the consistency of estimates of SSA production flux by various formulations.
[145] Removal processes are wet deposition, dry deposition, and coagulation onto larger particles and cloud drops, of which wet deposition is dominant in most circumstances. Coagulation in the marine atmosphere is almost certainly not important for two reasons: first, the low concentration of aerosol particles that could scavenge such smaller particles and second, the low diffusion coefficients of these small particles, with that for particles with \(r_{80}>0.01\) um being too low for this to be an important process. Coagulation on cloud drops is slow for similar reasons and is diminished further by the time that particles spend in clouds at the top of the marine boundary layer. For particles of the sizes under consideration, dry deposition, through gravitational sedimentation, impaction on and diffusion to the sea surface, although highly uncertain, is expected to be so slow that characteristic removal times would be at least several days to a week. Removal through activation during nonrepetiplating periods might still occur, but cloud drop concentrations are too low for this to be a major removal mechanism, and additionally, a large fraction of the marine aerosol particles of the size range under consideration are too small to activate in the low-updraft conditions of the marine environment. The major removal mechanism is thus almost certainly wet deposition, through both activation to form cloud drops that precipitate and scavenging by falling hydrometores, which typically occurs on a time scale of several days. Thus, unless other currently unknown or unappreciated loss processes are found, it must be concluded that characteristic turnover times of SSA particles with \(r_{80}<0.1\) um are several days.
[146] A turnover time of 3 days [LS04, p. 72], together with the assumption of a typical marine boundary layer height of 0.5 km and the observation that the marine boundary layer is largely decoupled from the free troposphere (implying little transport out of the marine boundary layer), allows estimation of the number concentration of SSA particles that would be expected to be present in the marine boundary layer for a given SSA production flux. For this flux taken as \(1\times 10^{6}\) m\({}^{-2}\) s\({}^{-1}\) as is indicated by several of the production flux formulations shown in Figure 9, the rate of increase in concentration would be nearly 200 cm\({}^{-3}\) d\({}^{-1}\), resulting in a steady state number concentration of sea spray particles alone of about 500 cm\({}^{-3}\). Such a concentration would be comparable to or exceed typical measured number concentrations of all marine aerosol particles in clean conditions, several hundred per cubic centimeter (section 3.1), raising concerns over formulations yielding such large production fluxes. This concern is heightened by the fact that aerosol particles in the clean marine boundary layer may derive from sources other than production at the sea surface and the resultant possibility that SSA particles often constitute only a fraction, perhaps only a small fraction, of measured total particle number concentrations. Apportionment of the particles that derive from primary production at the sea surface is difficult and this difficulty hinders extension of the statistical wet deposition method beyond sea salt aerosol (as by LS04) to sea spray aerosol.
## 7 Conclusions
[147] A major finding of recent work is the recognition of the large contribution of organic substances to SSA particles, especially in locations of high biological activity,which becomes increasingly important with decreasing particle size and may be dominant for \(r_{80}<0.25\)\(\mu\)m, leading to the distinction noted in section 1 between _sea salt_ particles (the focus of the review by LS04) and _sea spray_ particles. Possible consequences of this difference in composition are differences in properties such as cloud-drop activation and resultant error in models that do not account for these differences.
[148] Determinations of the SSA production flux have been made at sizes smaller than those previously examined, with some formulations extending to particle size as low as \(r_{80}=0.01\)\(\mu\)m; no estimate for the production flux of sea salt aerosol particles with \(r_{80}<0.1\)\(\mu\)m was presented by LS04. However, as noted above, uncertainties remain in the composition of such particles and in what is responsible for the variable amount of organic material in these particles. Additionally, the magnitude and the size distribution of the production flux of particles with \(r_{80}<0.3\)\(\mu\)m are both highly variable (Figures 4 and 9), and laboratory experiments have demonstrated that the means by which the white area is produced results in large differences in both of these quantities that cannot be accounted for by factors such as temperature. Consequently, it must be concluded that the assumption, central to applications of the whitecap method, that the SSA production flux per white area is independent of the means by which that white area is produced is not valid, and thus determinations of the SSA production flux based on the whitecap method are potentially subject to large error. A possible fruitful direction for research would be to investigate the dependence of the SSA production flux on the means of production of white area, as discussed in section 6.1.
[149] The best estimate for the production flux of SSA particles with \(r_{80}>1\)\(\mu\)m remains that given by LS04 based on multiple methods, with uncertainty a multiplicative factor of \(\frac{\times}{4}\)-5 (Figure 9; dashed black line and gray shaded region). For decreasing \(r_{80}\) from 1 to \(\sim\)0.3\(\mu\)m, recent flux determinations are increasingly greater than the best estimate of LS04, and for smaller sizes, they are greater still. However, a concern with such large SSA production flux formulations is that they imply number concentrations for SSA particles in the marine boundary layer that are unrealistically high as discussed in section 6.5. The realization that some or much of the aerosol may consist of organic matter rather than sea salt may resolve some of but by no means all this discrepancy.
[150] Recent advances in determination of the whitecap fraction \(W\), also central to evaluation of the SSA production flux by the whitecap method, by both photographic methods and satellite retrievals may eliminate some of the subjectivity in measurement of this quantity, but direct relation to SSA production is lacking. Recent determinations of \(W\) by digital photographic measurements are systematically lower, by up to a factor of 4, than those previously determined by film photography for reasons that are not yet understood. Satellite retrieval of \(W\) by brightness temperature at microwave frequencies is a promising possibility, but this approach is currently unable to capture the dependence of this quantity on wind speed that is exhibited in photographic measurements at visible wavelengths.
[151] Based on long-term measurement of aerosol chemical composition and its relation to biological activity at a coastal site (Mace Head, Ireland), it is clear that similar data sets from other sites could permit assessment of the generality of conclusions drawn from those measurements and more broadly on the factors that control the properties of marine aerosols. Additionally, measurements of composition and structure of individual marine aerosol particles with \(r_{80}<0.1\)\(\mu\)m at multiple sites and over multiple seasons would provide a wealth of data that could help elucidate sources and production mechanisms. Laboratory experiments of SSA production under varying conditions and determination of the composition of these laboratory-generated particles may provide some insight into controlling mechanisms, but it would seem that direct measurement of SSA fluxes, e.g., by eddy correlation measurements, would yield a quicker route to determination of the SSA production flux and in any event would be essential to evaluate models of the production flux.
[152] Despite the many gains in understanding in recent years, the uncertainty in the SSA production flux remains sufficiently great that present knowledge of this quantity cannot strongly constrain the representation of emissions of SSA in chemical transport models or climate models that include aerosols. As a consequence, it is not yet possible to improve the modeling of these emissions much beyond the state of affairs represented in Figure 1, which shows a nearly 2 orders of magnitude spread in current estimates of global annual SSA emissions. It is also clear that this situation cannot be resolved by demonstration of the ability to generate reasonable concentration fields with one or another source function, given the demonstrated ability of such greatly varying emissions to yield concentration fields that compare reasonably with observations [_[PERSON] et al._, 2006]. Rather it would seem essential that the SSA production flux be constrained directly by field observations or preferably be overconstrained by consistency of determinations by multiple approaches.
[153] In addition to representing mass concentrations of SSA in chemical transport models and climate models, it is essential that such models also include some representation of SSA number concentration, both magnitude and size distribution, given the importance of these aerosol properties: magnitude affects cloud properties and both magnitude and size distribution affect the optical depth (commonly used as a measure of skill of such models) and atmospheric radiation transfer. Finally, as it is becoming clear that the organic fraction of SSA depends on particle size and likely on the composition of seawater as influenced by biological activity, it would seem important that this component of SSA be represented in models, especially as composition may exert a strong influence on the cloud nucleating properties of these aerosols, affecting the microphysical properties of marine clouds and the sensitivity of cloud properties to perturbation by anthropogenic aerosols.
## Appendix A SSA Production Flux for Formulations
[154] This appendix presents expressions for the SSA production flux based on previously published formulations. The units of total and size-dependent fluxes (\(F_{\rm eff}\)\(dF_{\rm eff}\)/\(\rm dlogr_{80}\), \(dF_{\rm int}\)/\(\rm dlogr_{80}\), \(dF_{\rm int}\)/\(\rm dlogr_{\rm\mu}\), \(dF_{\rm eff}\)/\(\rm dlogr_{\rm amb}\) and \(dF_{\rm net}\)/\(\rm dlogr_{\rm amb}\)) are m\({}^{-2}\) s\({}^{-1}\); \(U_{10}\) and \(U_{22}\) are m s\({}^{-1}\); and \(d_{\rm p}\) (dry mobility diameter; \(d_{\rm p}\)\(\approx r_{80}\) for most sizes), \(r_{\rm amb}\) (ambient radius), and \(r_{80}\) are \(\rm\mu m\).
### Steady State Dry Deposition Method
[155] Expressions based on prior formulations are as follows:
[156] 1. From _[PERSON] et al._ [1993],
\[\frac{dF_{\rm eff}}{d\log r_{80}}=1400\times\exp(0.16~{}U_{10})\exp\Biggl{\{} -3.1\left[\ln\biggl{(}\frac{r_{80}}{r_{1}}\biggr{)}\right]^{2}\Biggr{\}}\]
where \(r_{1}=2.5~{}\rm\mu m\) and \(r_{2}=11~{}\rm\mu m\), for \(r_{80}=1\)-25 \(\rm\mu m\) (as noted above, this formulation cannot be accurately applied to particles with \(r_{80}\la 3~{}\rm\mu m\)) and for \(U_{10}<34~{}\rm m~{}s^{-1}\).
[157] 2. Following _[PERSON] and [PERSON]_ [2004],
\[\frac{dF_{\rm eff}}{d\log r_{80}}=\left(800~{}\frac{U_{10}^{2.5}}{r_{80}^{2.5 }}\right)\stackrel{{>}}{{\la}}4,\]
for \(r_{80}=0.25\)-7.5 \(\rm\mu m\) (as noted above, this formulation cannot be accurately applied to particles with \(r_{80}\la 3~{}\rm\mu m\)) and for \(U_{10}<17~{}\rm m~{}s^{-1}\); this expression was obtained from that presented by the original investigators with drag coefficient taken as 0.0013 and gravitational terminal velocity (Stokes' law) as given by equation (2.6-8) of LS04.
### Statistical Wet Deposition Method
[159] _[PERSON] and [PERSON]_ [2004], presented the formulation
\[\frac{dF_{\rm eff}}{d\log r_{80}}=10^{4}\stackrel{{>}}{{\la}}5,\]
for \(r_{80}=0.1\)-1 \(\rm\mu m\) and \(U_{10}=5\)-20 m s\({}^{-1}\).
### Whitecap Method
[160] Previously published formulations for \(dF_{\rm wc}\)/\(\rm dlogr_{80}\) have been converted to \(dF_{\rm int}\)/\(\rm dlogr_{80}\) using \(W(U_{10})\) from _[PERSON] and [PERSON]_ [1980], as follows:
[161] 1. From _[PERSON] et al._ [1986], based on laboratory experiments
\[\frac{dF_{\rm int}}{d\log r_{80}}=3.2~{}U_{10}^{3.41}r_{80}\times \left(1+0.057~{}r_{80}^{3.45}\right)\]
for \(r_{80}=0.8\)-8 \(\rm\mu m\).
[162] 2. From _[PERSON]_ [2003], modified from _[PERSON] et al._ [1986]
\[\frac{dF_{\rm int}}{d\log r_{80}}=3.2U_{10}^{3.41}r_{80}\times \left(1+0.057~{}r_{80}^{3.45}\right)\]
with \(\Theta=30\), for \(r_{80}=0.07\)-20 \(\rm\mu m\).
[163] 3. Following _[PERSON] et al._ [2003], based on laboratory experiments
\[\frac{dF_{\rm int}}{d\log d_{p}}=U_{10}^{3.41}\left(a_{4}d_{p}^{4}+a_{3}d_{p}^ {3}+a_{2}d_{p}^{2}+a_{1}d_{p}+a_{0}\right),\]
for \(d_{\rm p}=0.02\)-2.8 \(\rm\mu m\); the coefficients for salinity 33, which are linear functions of temperature and take different values in each of three size ranges, are presented in Table 1.
[TABLE:A2. Coefficients for the Expression for the SSA Production Flux of _[PERSON] et al._ [2006] in Each of Three Size Rangesa
\begin{table}
\begin{tabular}{l c c c} \hline & \(d_{\rm p}\) Range (\(\rm\mu m\)) & \\ \hline
0.01–0.132 & 0.132–1.2 & 1.2–8 \\ \hline \(a_{0}\) & \(-1.920\times 10^{2}\) & 1.480 \(\times\) 10\({}^{2}\) & 1.727 \(\times\) 10\({}^{1}\) \\ \(a_{1}\) & \(3.103\times 10^{4}\) & 4.485 \(\times\) 10\({}^{2}\) & 3.222 \(\times\) 10\({}^{1}\) \\ \(a_{2}\) & \(-7.603\times 10^{5}\) & \(-2.524\times 10^{2}\) & \(-2.071\times 10^{1}\) \\ \(a_{3}\) & \(8.402\times 10^{6}\) & 3.852 \(\times\) 10\({}^{3}\) & 4.677 \\ \(a_{4}\) & \(-4.393\times 10^{7}\) & \(-2.4603\times 10^{3}\) & \(-4.658\times 10^{-1}\) \\ \(a_{5}\) & \(8.794\times 10^{7}\) & 5.733 \(\times\) 10\({}^{2}\) & 1.733 \(\times\) 10\({}^{2}\) \\ \hline \end{tabular}
\end{table}
Table 2: Coefficients for the Expression for the SSA Production Flux of _[PERSON] et al._ [2003] in Each of Three Size Rangesa
\begin{table}
\begin{tabular}{l c c} \hline & \(d_{\rm p}\) Range (\(\rm\mu m\)) & \\ \hline
0.02–0.145 & 0.145–0.419 & 0.419–2.8 \\ \hline \(a_{0}\) & \(-(1.00013+0.110637)\times 10^{2}\) & \((1.6786-0.025897)\times 10^{3}\) & \((6.0442+0.83757)\times 10^{1}\) \\ \(a_{1}\) & \((3.8735-0.0115327)\times 10^{4}\) & \(-(2.1336-0.045437)\times 10^{4}\) & \(-(1.2545+0.159947)\times 10^{2}\) \\ \(a_{2}\) & \(-(3.9944+0.10097)\times 10^{5}\) & \((1.1611-0.031297)\times 10^{5}\) & \((9.0994+1.20277)\times 10^{1}\) \\ \(a_{3}\) & \((1.6611+2.27797)\times 10^{5}\) & \(-(2.8549-0.0923147)\times 10^{5}\) & \(-(3.3435+0.377897)\times 10^{1}\) \\ \(a_{4}\) & \((5.8236-0.998187)\times 10^{6}\) & \((2.5742-0.094167)\times 10^{5}\) & \((4.0196+0.416647)\) \\ \hline \end{tabular}
\end{table}
Table 1: Coefficients for the Expression for the SSA Production Flux of _[PERSON] et al._ [2003] for Salinity 33 in Each of Three Size Rangesa[164] 4. From _[PERSON] et al._ [2000], based on surf zone measurements
\[\frac{dF_{\rm int}}{d\log r_{80}}=4.0\times\exp(0.23~{}U_{10})\times U_{10}^{;41 }\times r_{80}^{-0.65},\]
for \(r_{80}\) = 0.4-5 \(\mu\)m and \(U_{10}\) = 0-9 m s\({}^{-1}\).
[165] 5. Following _[PERSON] et al._ [2006], based on surf zone measurements
\[\frac{dF_{\rm int}}{d\log d_{p}}=U_{10}^{;41}\Big{(}a_{\rm r}d_{p}^{\rm s}+a_{ \rm r}d_{p}^{\rm d}+a_{\rm r}d_{p}^{\rm s}+a_{\rm r}d_{p}^{\rm e}+a_{\rm r}d_{p }+a_{\rm r}\Big{)},\]
for \(d_{\rm p}\) = 0.01-8 \(\mu\)m; the coefficients, which take on different values in each of three different size ranges, are presented in Table 2.
### Micrometeorological Methods
[166] Expressions based on prior formulations are as follows:
[167] 1. From _[PERSON]_ [2001] and _[PERSON] et al._ [2001], based on eddy correlation
\[F_{\rm eff}=1.9\times 10^{4}\exp(0.46~{}U_{10}),\]
for \(d_{\rm p}\) > 0.01 \(\mu\)m and \(U_{10}\) = 4-13 m s\({}^{-1}\).
[168] 2. From _[PERSON] et al._ [2005], based on eddy correlation measurements
\[F_{\rm eff}=1.9\times 10^{5}\exp(0.23~{}U_{22}),\]
for \(r_{\rm amb}\) = 0.005-0.5 \(\mu\)m and \(U_{22}\) = 7-18 m s\({}^{-1}\), and
\[F_{\rm eff}=6.5\times 10^{4}\exp(0.25~{}U_{22}),\]
for \(d_{\rm p}\) = 0.1-1 \(\mu\)m and \(U_{12}\) = 4-17 m s\({}^{-1}\).
[169] 3. Following _[PERSON] and [PERSON]_ [2006], modified by _[PERSON]_ [2007], based on the gradient method
\[\frac{dF_{\rm eff}}{d\log r_{\rm amb}} = 1.2\times 10^{3}\exp(0.52~{}U_{10}-(0.05~{}U_{10}+0.64)r_{\rm amb})\] \[\times r_{\rm amb},\]
for \(r_{\rm amb}\) = 0.25-7 \(\mu\)m and \(U_{10}\) = 5-12 m s\({}^{-1}\).
[170] 4. From _[PERSON] et al._ [2008] for the net flux (i.e., not corrected for dry deposition), based on eddy correlation
\[\frac{dF_{\rm net}}{d\log r_{\rm amb}}=a_{0}\exp(a_{1}~{}U_{10}),\]
for \(U_{10}\) = 4-12 m s\({}^{-1}\), where the coefficients \(a_{i}\), which take on different values in each of six size ranges, are presented in Table 3.
### Multiple Methods
[171] _[PERSON] and [PERSON]_ [2004] presented the formulation
\[\frac{dF_{\rm eff}}{d\log r_{80}}=50~{}U_{10}^{;2.5}\exp\left\{-\left(\frac{1 }{2}\right)\left[\frac{\ln\left(\frac{\mu\alpha}{n}\right)}{\ln(4)}\right]^{2} \right\}\stackrel{{\chi}}{{\div}}5,\]
for \(r_{80}\) = 0.1-25 \(\mu\)m and \(U_{10}\) = 5-20 m s\({}^{-1}\), where \(r_{1}\) = 0.3 \(\mu\)m.
[172] **ACKNOWLEDGMENTS.** The work of [PERSON] and [PERSON] was supported by the EU (European Union) FP6 projects MAP (Marine Aerosol Production, project GOCE-018332), EUCAARI (European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions) project 036833-2, and MACC (Monitoring Atmospheric Composition and Climate: FP7 Collaborative Project). Work by [PERSON] was further supported by the Irish EPA and HEA PRTL14 program and the EU FP6 project GEMS (Global and Regional Earth-System (Atmosphere) Monitoring Using Satellite and In Situ Data, contract S1P4-CT-2004-516099). The U.S. Office of Naval Research supported [PERSON]'s work on this project with award N000140810411. Work by [PERSON] and [PERSON] was supported by the U.S. Department of Energy's Atmospheric System Research Program (Office of Science, OBER, contract DE-AC02-95 CH10886). Work by [PERSON] was supported by the U.S. Office of Naval Research, NRL program element 61153N. Work by [PERSON] was supported by NOAA's (National Oceanic and Atmospheric Administration) Office of Climate Observations and NOAA's Health of the Atmosphere Program. We thank three anonymous reviewers for helpful comments and suggestions.
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## References
* (1)
* [PERSON] (2010) --. _J. Geophys. Res._, _112_, 100-121, doi:10.1016/j.j.1002.002/ | wiley | Parameterizations for sea spray aerosol production flux | Aijing Song, Jianlong Li, Narcisse T. Tsona, Lin Du | https://doi.org/10.1016/j.apgeochem.2023.105776 | 2,023 | CC-BY |
wiley/fb6c7c10_3530_4720_83d1_ab7a10287788.md | to characterize the internal structure of rocks including their pore fabric, and provides the basis for digital rock physics (DRP) models that predict physical properties of rocks, especially acoustic and flow properties ([PERSON] et al., 2013; [PERSON] et al., 2011; [PERSON] & [PERSON], 2009; [PERSON] et al., 2012; [PERSON], 2016). [PERSON] et al. (2009) and [PERSON] (2012) reported a good fit between numerical calculation and direct porosity and permeability measurements using Berea sandstone and carbonate rocks. A crucial prerequisite for meaningful comparisons between model and measurement is that both are conducted on representative sample volumes. Sample sizes ranging from sub-micrometers to a few centimeters are commonly used for XRCT ([PERSON] & [PERSON], 2013; [PERSON], 2018; [PERSON] et al., 2009; [PERSON] & [PERSON], 2010; [PERSON], 2012). Larger samples may be more representative of the investigated rock, but suffer from lower spatial resolution (Figure 1). Unresolved pores can result in up to 32% difference between modeled and measured data ([PERSON] et al., 2009).
Indirect methods characterize pore fabrics by measuring the anisotropy of specific physical properties influenced by pore fabrics, for example, permeability and seismic anisotropy and magnetic anisotropy of samples impregnated by ferrofluid. They provide average information on pore space properties, which is sufficient for many applications (e.g., [PERSON] et al., 2011). Note that although permeability anisotropy is considered an indirect measurement of pore fabric, it is the most direct assessment of a rocks' fluid transport properties. Permeability anisotropy is a symmetric second-order tensor, requiring at least six independent directional measurements for full description ([PERSON] & [PERSON], 1958). Otherwise, a priori information on the fabric orientation is needed, for example, lineation and foliation directions, in case that measured directions disagree with the principal permeability directions, thus underestimating permeability anisotropy. Another indirect description for pore fabric is elastic anisotropy. However, elasticity is a fourth-order tensor, thus requiring a large number of directional measurements or symmetry assumptions. Analogously to permeability anisotropy, each directional velocity is generally measured along a separate oriented core. Moreover, seismic velocities are affected by microcracks, grain boundaries and intrinsic elastic anisotropy of each grain in addition to pore fabrics, so seismic-based pore space characterization is challenging ([PERSON] et al., 2003; [PERSON] et al., 2017; [PERSON] et al., 2004; [PERSON] et al., 2014).
Magnetic pore fabrics (MPFs) provide a fast and efficient tool for pore fabric characterization. The samples' pore space is impregnated with ferrofluid, followed by measuring the anisotropy of magnetic susceptibility (AMS) ([PERSON], 1990), and thus only connected pores, which contribute to flow, are targeted by MPFs. MPFs can be applied on a single sample, without any priori information on the fabric, thus avoiding underestimating anisotropy by heterogeneity. Additionally, the method has been ascribed the ability to capture pores and pore
Figure 1: Sample size (diameter of the cylindrical core) versus resolution for X-ray computed micro-tomography (XRCT) and magnetic pore fabric (MPF) methods (XRCT modified from Crudde & Boone, 2013; [PERSON] et al., 2011; [PERSON] et al., 2009; [PERSON], 2012). The MPF resolution is 10–20 nm for sample sizes ranging from 6 to 25.4 nm diameter ([PERSON] et al., 2011; [PERSON] et al., 2006; [PERSON] et al., 2012; [PERSON] et al., 2016; [PERSON] et al., 2014).
tronats down to 10-20 nm (Figure 1) ([PERSON] et al., 2011; [PERSON] et al., 2006; [PERSON] et al., 2012; [PERSON] et al., 2016; [PERSON] et al., 2014). Pores and throats smaller than magnetic nanoparticles (10-20 nm diameter) are not captured by MPF. In practice, the threshold of pores that are impregnated depends on pore throat geometry and wettability ([PERSON] et al., 2014), and 100 nm has been put forward as a more realistic threshold ([PERSON] et al., 2022). Empirical relationships have been established between MPFs and pore fabrics: (a) the maximum and minimum principal susceptibility axes are sub-parallel to the average generations of major and minor pore axes ([PERSON] et al., 2000; [PERSON], 2007; [PERSON] et al., 2006; Pfleiderer & Halls, 1990, 1994), (b) the degree of magnetic anisotropy increases when pore shapes become more anisotropic ([PERSON] et al., 2006; Pfleiderer & Halls, 1990, 1993; [PERSON] et al., 2014), and (c) oblate or prolate MPFs are related to flattened or elongated pore shapes ([PERSON] et al., 2006; Pfleiderer & Halls, 1990). MPFs have been compared to permeability anisotropy ([PERSON] et al., 2003; [PERSON] et al., 1999; [PERSON] et al., 2005; [PERSON] et al., 2009; Pfleiderer & Halls, 1994), and used to predict anisotropy of elastic properties ([PERSON] et al., 2011). Unfortunately, empirical relationships vary largely between different studies, making the results hard to interpret ([PERSON] et al., 2011; [PERSON] et al., 2003; [PERSON] et al., 2006; [PERSON] et al., 2005; [PERSON] et al., 2009; Pfleiderer & Halls, 1990, 1993, 1994; [PERSON] et al., 2014). The variability may be explained partly by that large pores contain large volumes of ferrofluid, whereas the preferred orientation of pore connections is more relevant for permeability anisotropy (Pfleiderer & Halls, 1994). Pore shape, orientation and arrangement control MPFs, and ferrofluid susceptibility and measurement conditions largely influence MPF--pore fabric relationships ([PERSON], 2019; [PERSON] et al., 2021). Many MPF studies focused on simplified samples ([PERSON], 2019; [PERSON] et al., 2006; Pfleiderer & Halls, 1990), and factors affecting the relationships between MPFs and pore space in natural samples are not yet fully understood.
Two complementary pore fabric characterization methods are investigated and correlated quantitatively in terms of the portion of pore space they characterize, and obtained fabric orientation, degree and shape: XRCT as a standard method, and MPF which has great potential but is rarely used. Two sedimentary rocks, calcarenite and molasse, were included with variability in porosity and pore complexity. A new second-order tensor quantity, the total shape ellipsoid, is derived from XRCT data, for direct comparison with MPF in terms of fabric orientation, anisotropy degree and shape.
## 2 Materials and Methods
### Sample Description
Samples with porosity of 10%-55% were chosen, molasse and calcarenite, applying for typical porosity of reservoir rocks varying between 5% and 40% ([PERSON], 2019; [PERSON], 1980). Ideally, a single rock type would have been used for all porosities to minimize the number of variables. Because the collected molasse samples have 10%-30% porosity with micropores, calcarenite with large pores was included, extending the porosity range to \(\sim\)50%.
The studied calcarenites are Plio-Pleistocene in age and recovered from the Gravina Formation in Apulia, Italy (Figure 2a) ([PERSON] et al., 2015). They possess high porosity (16%-60%) and a large proportion of interconnected pores (>99.5% of pore space on average) ([PERSON] et al., 2015). Different pore types are identified in BSE images, such as inter- and intragranular porosity, microporosity, and moldic porosity (Figure 2b). Calcarenite cores MI-1-Z3, MI-2-Y3, MI-2-Y8, MI-2-Y10, MI-3-X15, MI-3-X11 were drilled from the same block along three perpendicular directions, indicated by X, Y and Z in the sample names. Samples MI-5-Z21 and MI-5-X22 were drilled from another block. Molasse sandstone was collected in four areas from the Upper Marine Molasse (OMM) in the Swiss molasse basin (SMB): (a) Rueggisberg, BE, samples D1121Z, D1112Y, D1263Y2, D1234X, D1221X, D1261X, (b) Entebuch, LU, samples C43Y, C334Y, BE42 AY, (c) Dultingen, FR, Switzerland, sample 5256X, and (d) Tafers, FR, Switzerland, sample F31Z1 (Figure 2c). The molasse samples are characterized by cross and parallel bedding (Figure 2d). OMM consists mainly of shallow marine and tidal-influenced sandstones and mudstones, deposited in a shallow seaway from 20 to 17 Ma ([PERSON] et al., 2010; [PERSON] & [PERSON], 2019). The OMM sandstone displays porosities from 5% to 20% ([PERSON] et al., 2010; [PERSON] et al., 1997), mainly including intergranular porosity and microporosity (Figure 2d). Being an important aquifer in the SMB, OMM may provide pore space to store and transfer CO\({}_{2}\) and geothermal fluids ([PERSON] et al., 2017; [PERSON] et al., 2010; [PERSON] et al., 2010; [PERSON], 2019). All rocks were drilled and cut to obtain standard-sized cores of 25.4 mm diameter and 22 mm length. Initial sample characterization involved porosity measurements by comparing grain volume (obtained from a Micromeritics AccuPyc 1340 Automatic Gas (He) Pycnometer system in the Petrophysics Laboratory at the University of Bern) with bulk volume (calculated by core diameter and length).
### XRCT Data Acquisition and Processing
The Bruker SkyScan 2211 3D X-ray micro-tomography scanner perform initial scans at the University of Fribourg (15 \(\upmu\)m pixel size), and a Bruker SkyScan 1273 obtain later measurements at the University of Bern (9 \(\upmu\)m or 5.5 \(\upmu\)m pixel size). Samples D1112Y and C334Y were measured on both systems for different resolution (Table S1 in Supporting Information 5). However, the direct comparison between both systems was not performed for all samples, as part of them (M1-1.23, MI-2-Y3, MI-2-Y10, MI-3-X15, MI-3-X11, D1212, D1234X, D1221X, D1261X, C43Y, and BE42 AY) were impregnated or destructively analyzed after initial scanning with the Bruker Skyscan 2211, while others (MI-2-Y8, MI-5-Z21, MI-5-X22, D1263Y2, and 5256X, F31Z1) were measured only on the SkyScan 1273 for later analysis. XRCT data of impregnated samples were not further analyzed due to impregnation rendering the segmentation between ferrofluid/resin and solid fraction difficult. Rather, additional cores, so-called sister samples, were drilled from the original block in close proximity, assuming that both cores represent the same pore fabric. Pairs of sister samples are given as Core1/Core2, where XRCT data were obtained on the first core, and MPF on the second, for example, MI-3-X15/MI-3-X11. Where possible, XRCT data were obtained on Core1, and MPF data were obtained on both sister samples, allowing to test between-sample heterogeneity, for example, MI-2-Y8/MI-2-Y10 and D1234X/D1221X. Sample MI-2-Y3 was
Figure 2: (a) Location of calcarenite samples, (b) Backscattered electron image of calcarenite sample and photograph of calcarenite sample and core, (c) location of molase samples, (d) thin section image and photograph of molase sandstone with sketch on internal structure and drilling directions. Note the cross-stratification in the molase sandstone. The core axis was generally oriented parallel or perpendicular to lineation, provided that lineation could be clearly identified. Coordinates of MI are 40\({}^{\circ}\)49741.5”N, 16\({}^{\circ}\)2525.0”E; for D 46\({}^{\circ}\)4945.6”N, 7\({}^{\circ}\)2404.4”E; for C 46\({}^{\circ}\)5852.4”N, 8\({}^{\circ}\)0348.3”E; for BE 46\({}^{\circ}\)854.3”N 8\({}^{\circ}\)0347.7”E; for 5256 46”4811.2”N, 7\({}^{\circ}\)1051.2”E, and for F 46\({}^{\circ}\)4809.8”N, 7\({}^{\circ}\)1100.9”E. All molase samples are OMM, even though mainly USM is present in the area where samples C and BE were obtained. Geological maps are modified after [PERSON] et al. (2019) (a), [PERSON] et al. (2012) and [PERSON] et al. (2020) (c).
drilled along the same direction as MI-2-Y8/MI-2-Y10 but further away, and similar situation for D1261X with D1234X/D1221X. The D12 block has a visible macroscopic fabric, parallel bedding, and thus similar pore fabrics are expected for samples along the same orientation.
Initially, different filters, voltage, current, and exposure time were used on each sample, in accordance with minor changes in their physical properties. Conditions for the X-ray source on the Bruker Skyscan 2211 were 80 kV/230 \(\mu\)A for the calcarenites, and 100-156 kV/200-445 \(\mu\)A for the molase sandstones. Filters of 0.5 mm Al, 0.5 mm Ti, 0.5 mm Mo and 0.5 mm Cu were chosen for different samples. Images were acquired at 220 ms exposure time for calcarenite, and 100-300 ms for the molase sandstone (Table S1 in Supporting Information S1). Different settings resulted in different contrast and artifacts, which could be corrected and removed during the reconstruction. Then it became evident that one consistent set of settings was sufficient for all samples to obtain images with good contrast and reduced artifacts. Only resolution was decisive in defining image quality. Settings on the Bruker Skyscan 1273 were the same for all samples with 100 kV/80 \(\mu\)A, 1 mm Al + 0.038 mm Cu filter, and 275 ms exposure time (Table S1 in Supporting Information S1). Reconstructions were performed using NRecon, and images were compensated for misalignment, corrected for ring artifacts and beam hardening artifacts ([PERSON], 2011).
After reconstruction, the unsharp masking filter ([PERSON] et al., 2000; [PERSON], 1996) was applied to noisy images, to sharpen and enhance image details in Avizo versions 2019.4 and 2020.1. Single thresholding segmentation was applied to differentiate pores from the solid fraction based on the attenuation coefficients, expressed as grayscale values (Figure 3). Because the determination of a threshold value is user-dependent and affects the segmentation of pixels with intermediate values ([PERSON] et al., 2013; [PERSON] and [PERSON], 2019; [PERSON] et al., 2017; [PERSON] et al., 2018), a watershed segmentation was applied to assign intermediate greyscale values ([PERSON] and [PERSON], 2000). The uncertainties in calculated porosity were estimated by testing different thresholds (Figure S1 in Supporting Information S1).
To ensure the representativeness of the volume for XRCT-derived calculations while minimizing computational cost, the representative elementary volume (REV) was determined, by calculating porosity (defined as relative abundance of pixels with greyscale values identified as pores) or pore size distributions as a function of included volume. Porosity and pore size distribution were calculated for cubes of increasing size, from \(100\times 100\times 100\) voxels (\(0.9\times 0.9\times 0.9\) mm\({}^{3}\)) to \(500\times 500\times 500\) voxels. For small volumes, XRCT-derived parameters vary largely with increasing volume, reaching a plateau as cube size increases above a critical threshold. This threshold volume is the REV, that is, the smallest volume representing the entire sample. Note that the REV can vary depending on the property of interest. Here, the REV for determining porosity is \(100\times 100\times 100\) voxels (cf. Figure 3), while for pore size distributions, the REV is \(300\times 300\times 300\) voxels (Figures 4a and 4b). To further estimate the uncertainty associated with sample heterogeneity, calculated porosities from five \(5\times 5\times 5\) mm\({}^{3}\) cubes located at different positions within the sample were compared to calculate a mean porosity with deviation (Table 1). Then, one cube was chosen arbitrarily for pore shape analysis (Figure 3).
The segmented pore space was separated into individual pores to characterize pore shape and size distribution ([PERSON], 2017; [PERSON], 2000). Pore size is given as equivalent diameter of a sphere with the same volume. Individual pores are approximated with best-fit ellipsoids, represented mathematically by symmetric second-order tensors whose eigenvalues \(a\geq b\geq c\) correspond to the lengths of the major, intermediate and minor ellipsoid axes, and the eigenvectors \(V1\), \(V2\), and \(V3\) describe their orientations (Figure 3 and Text S1 in Supporting Information S1) ([PERSON], 2020). Pore fabrics are traditionally characterized by orientation density functions (ODFs) of the major and minor pore axes ([PERSON], 1979). In the present study, ODFs are however strongly affected by artifacts arising from small pores whose geometry remained unresolved. A series of filters was applied to remove pores smaller than \(4\times 4\times 4\) voxels up to \(16\times 16\times 16\) voxels, to investigate related changes in the ODFs. Additional difficulties inherent to the characterization of major and minor axes by ODFs are that all pores contribute equally, independent of size, and the lack of information on pore shape. For example, in a strongly elongated pore, the minor and intermediate axes may be similar, so that the orientation of the minor axis is poorly defined.
An alternative approach to analyze the average pore fabric is introduced here to reduce these difficulties: the total shape ellipsoid, which is calculated by adding the unnormalized second-order tensors reflecting individual pores. Advantages of the total shape ellipsoid include: (a) The calculation was adapted from averaging normalized second-order tensors to compute a mean anisotropy of a group of samples ([PERSON] and [PERSON], 1978).
Figure 3.— Workflow for X-ray computed micro-tomography image processing and magnetic pore fabric (MPF). The samples are scanned in field of view to obtain 28–29 mm width of images. Increasing voxel sizes are related to increasing fields of view. For 5.5 μm voxel size, results of two scans are stitched together after scanning in two horizontal positions. Absorption images are converted to cross-section images of greyscale CT intensity values during reconstruction. Hierarchical watershed segmentation divides the reconstructed volume into pores (blue) and solid fraction (red). Once the pore network is extracted from the segmented image, the bulk pore space is separated using the Skeleton-Aggressive algorithm which creates a connectivity network between the individual pores based on nodes and throats. The representative elementary volume is selected based the relationship between calculated porosity and sample size. The individual pore size is given as the equivalent diameter (EqDiameter) of a sphere that has the same volume as the pore, and the shape and orientation are defined by eigenvectors and eigenvalues of the covariance matrix \(M\) (a second-order tensor) (Text S1 in Supporting Information S1) ([PERSON], 2020). The orientation density functions and total shape ellipsoids are derived from the matrices of single pores. The cores are impregnated by ferrofluid before measuring MPF.
Normalized tensors ensure that each contribution has the same weight, so that the average is controlled by the most anisotropic item. Unnormalized tensors allow to give more weight to larger and better defined pores, and minimize resolution-related artifacts compared to ODFs; (b) the orientation distribution, pore shape distribution, and distribution of aspect ratios are integrated in one single measure; and (c) the total shape ellipsoid can be directly compared to other second-order tensor properties, including permeability and MPF. Finally, because the total shape ellipsoid is calculated from a large number of individual pores, its statistical robustness can be assessed by bootstrapping ([PERSON] and [PERSON], 1990; [PERSON] et al., 1998). Here, 500 total shape ellipsoids were calculated from randomly and repetitively choosing subsets including 579-14,913 pores for different samples and resolutions ([PERSON], 1963; [PERSON] and [PERSON], 1978; [PERSON], 2000). Finally, confidence ellipses were calculated based on those bootstrapped total shape ellipsoids and plotted by TomoFab ([PERSON] et al., 2020).
The anisotropy of the individual pores as well as that of the total shape ellipsoid are described by the anisotropy degree \(P_{\mathrm{s}}=a/c\), and their shape by \(U_{\mathrm{s}}=(2^{\ast}b-a-c)/(a-c)\). The definitions are analogous to standard parameters used for the characterization of magnetic anisotropy, \(P_{\mathrm{m}}=k1/k3\) and \(U_{\mathrm{m}}=(2^{\ast}k2-k1-k3)/(k1-k3)\), where \(k1\geq k2\geq k3\) are the principal susceptibilities ([PERSON], 1981). \(P_{\mathrm{m}}\) and \(P_{\mathrm{s}}\) range in the interval (1, \(\infty\)),
Figure 4: Results of pore size distribution for all X-ray computed micro-tomography scans. (a) and (b) present changes in pore size distribution associated with changing the included volume for calcarenite M1-5-Z21 and molasse D1112Y. The representative elementary volume for pore size distribution is \(300^{\circ}\) voxels for both because the \(300^{\circ}\) voxels are the minimum volume to present similar pore size distribution. If the volume is smaller than \(300^{\circ}\) voxels, there are not enough pores to present the full range of distribution, and hence maxima and minima vary. (c) and (d) are pore size distributions for different calcarenites and molasse sandstones. The pore size is given as the equivalent diameter (EqDiameter) of a sphere that has the same volume as the pore. Only data obtained prior to impregnation are shown. The red vertical lines represent the threshold of \(4\times 4\times 4\) voxels (EqDiameter = 27 μm for voxel size of 5.5\({}^{\circ}\) μm\({}^{\circ}\), or 45 μm for voxel size of 9\({}^{\circ}\) μm\({}^{\circ}\), or 74 μm for 15\({}^{\circ}\) μm\({}^{\circ}\) voxel size).
where 1 means isotropy and increasing values relate to increasing degrees of anisotropy. The values of \(U_{\rm m}\) and \(U_{\rm s}\) vary in the range (\(-\)1, 1), where \(-\)1 describes rotationally prolate ellipsoids and +1 indicates rotationally oblate ellipsoids.
To investigate how different pore size windows affect pore fabrics, the fabrics of pores with EqDiameter \(\geq\)100 and \(\leq\)100 \(\mu\)m in sample MI-3-X15 were compared.
### Magnetic Pore Fabric Measurements
The AMS of the dry samples was measured using a 15 directions measurement scheme to determine the anisotropy of the rock itself ([PERSON], 1977). Two instruments were used, the magnetic susceptibility bridge SM150 from ZH instruments (Czech Republic) for initial measurements, followed by the MFK1-FA susceptibility bridge from AGICO (Czech Republic). The measurement frequencies were set to \(\sim\)4, \(\sim\)16, and \(\sim\)512 kHz for the SM150, using a field of 80 A/m, the maximum available at all frequencies. On the MFK1-FA, frequencies of \(\sim\)1, \(\sim\)4, \(\sim\)16 kHz were used with the standard field of 200 A/m. Five repeated measurements were obtained for every direction at each frequency, to increase data quality and assess the significance of anisotropy against the instrumental noise level ([PERSON] et al., 2013). The noise level of the MFK1-FA is orders of magnitude lower than that of the SM150, so that the former is able to detect anisotropy where the latter cannot. Therefore, samples were
\begin{table}
\begin{tabular}{|l c c c c|} \hline & Porosity (resolution: & Porosity (resolution: & & \\ & 15 \(\mu\)m/Skyscan 2211) & 9 \(\mu\)m/Skyscan 1273) & & Porosity (HP) \\ & (\%) (threshold for pores, & (\%) (threshold for pores, & AccuPyc 1340) (\%) & (\%) \\ Sample & 0–255) & 0–255) & & Provsity (He pycommetry, & (MPF) \\ \hline Calacenite & & & & \\ MI-1-Z3 & \(43\pm 4\) (70) & \(\blacktriangle\) & \(52\pm 1\) & 29.4 \\ MI-2-Y3 & \(36\pm 4\) (73) & \(\blacktriangle\) & \(51.6\pm 0.3\) & 46.0 \\ MI-2-Y8/MI-2-Y10 & \(\blacktriangle\)\(\blacktriangle\) & \(33\pm 3\) (74)\(\blacksquare\) & \(53.1\pm 0.4/55.2\pm 0.5\) & 15.5/28.7 \\ MI-3-X15/MI-3-X11 & \(31\pm 5\) (65)\(\blacktriangle\) & \(\blacktriangle\)\(\blacksquare\) & \(51.2\pm 0.4/54.7\pm 0.3\) & \(\blacktriangle\)28.9 \\ MI-5-Z21 & \(\blacktriangle\) & \(35\pm 3\) (71) & \(55.2\pm 0.2\) & 17.5 \\ MI-5-X22 & \(\blacktriangle\) & \(34\pm 5\) (68) & \(53.8\pm 0.2\) & 12.7 \\ Molasse (Rüegsighberg) & & & & \\ D1121Z & \(5\pm 2\) (45) & \(\blacksquare\) & \(19.04\pm 0.02\) & 25.6 \\ D1112Y & \(6\pm 3\) (45) & \(6\pm 1\) (45) & \(20.78\pm 0.03\) & 11.8 \\ D1263Y2 & \(\blacktriangle\) & \(9\pm 2\) (55) & \(21.78\pm 0.01\) & 3.84 \\ D1234X/D1221X & \(9\pm 3\) (55)\(\blacktriangle\) & \(\blacksquare\)\(\blacksquare\) & \(19.01\pm 0.01/20.29\pm 0.01\) & 10.7/9.26 \\ D1261X & \(\blacktriangle\) & \(\blacktriangle\) & \(20.26\pm 0.02\) & 5.55 \\ Molasse (Entlebuch) & & & & \\ C43Y & \(4\pm 4\) (60) & \(\blacksquare\) & \(16.0\pm 0.2\) & 7.63 \\ C334Y & \(0.6\pm 0.1\) (55) & \(1.9\pm 0.8\) (60) & \(13.5\pm 0.7\) & 5.60 \\ BE42 AY & \(6.4\pm 0.5\) (65) & \(\blacktriangle\) & \(12.05\pm 0.01\) & 6.69 \\ Molasse (Dudingen) & & & & \\
5256X & \(\blacktriangle\) & \(4\pm 1\) (60) & \(11.13\pm 0.01\) & \(\blacktriangle\) \\ Molasse (Tafers) & & & & \\ F31Z1 & \(16.4\pm 1\) (5.5 \(\mu\)m) (68) & \(30.78\pm 0.07\) & 9.22 \\ \hline \end{tabular} Note. Uncertainty was estimated by calculating the standard deviation of five cube volumes (\(5\times 5\times 5\) mm) in five positions (XRT–X-my computed micro-tomography) or the standard deviation of five measurements (He pycommetry). Triangle indicates data not measured and square indicates data not shown because they were measured after impregnation.
\end{table}
Table 1: Porosity Comparison of Numerical Calculations Based on XRCT Data, Laboratory Measurements by He Pycommetry and Estimation From MPFremeasured on the MFK1-FA, except MI-1-Z3 and MI-2-Y3, which had been cut after impregnation to check the spatial variability of impregnation efficiency.
After characterizing their initial anisotropy, samples MI-1-Z3, MI-2-Y3 and MI-3-X15 were impregnated with oil-based ferrofluid (EMG 909 with an intrinsic susceptibility of 1.38 SI) diluted at 1:25 volume ratio of ferrofluid to light hydrocarbon carrier oil offered by Ferrotec. These samples were impregnated under vacuum for 24 hr at 100 kPa, following the technique outlined in [PERSON] et al. (2016). After initial experiments had shown difficulties with impregnation efficiency, the remaining samples were impregnated with oil-based ferrofluid diluted by resin and hardener (hardener:resin = 1:4) under vacuum for 1 hr at 100 kPa. As the resin solidifies, it is thought to keep the magnetic nanoparticles immobile within the pores ([PERSON] et al., 2016). Ferrofluid was diluted at volume ratio of 1:50 for molase MI-2-Y10, MI-3-X11, D1121Z, D1112Y, D1234X, D1221X, C43Y, BE42 AY, F31Z1 and 1:30 for the remaining molase, and all calcarine samples (Table S2 in Supporting Information S1). Any resin-ferrofluid mixture on the surface of the sample was cleaned before solidification to avoid artifacts. Unfortunately, the elimination was not thorough for samples MI-2-Y8, MI-5-X22, MI-5-Z21, D1263Y2, D1261X and C334Y, resulting in artifacts during MPF measurements. These samples were polished to remove leftover resin from the surface. Samples MI-3-X15 and 5256X broke during the impregnation experiment. New experiments will be performed once more sophisticated impregnation methods are available ([PERSON] et al., 2021).
To test which proportion of the pore space was impregnated, the susceptibility of impregnated samples was compared to the independently measured susceptibility of diluted ferrofluid and ferrofluid-resin mixtures. From this, the ferrofluid porosity, and susceptibility-based impregnation efficiencies were calculated ([PERSON] et al., 2016). The susceptibility was divided by a coefficient 1-1.3 for 512-1 kHz to correct frequency dependence ([PERSON] et al., 2021). The MPFs were measured as magnetic anisotropy after impregnation, following the same protocol as for AMS described above. Samples MI-1-Z3 and MI-2-Y3 were measured at 4, 16 and 512 kHz on the SM150. Samples MI-3-X11, D1121Z, D1234X and C43Y were measured at 1 kHz, 4 and 16 kHz on the MFK1-FA, and all remaining samples were measured at 1 kHz on the MFK1-FA, once it became clear that anisotropy is higher and better defined at lower frequency ([PERSON] et al., 2021).
The data quality and statistical significance of the anisotropy compared to instrument noise for AMS and MPF are described by \(R1\)([PERSON] et al., 2013) as well as confidence angles \(E13\) (=\(E31\)), \(E12\) (=\(E21\)) and \(E23\) (=\(E32\)) based on the 15 mean directional susceptibilities ([PERSON], 1963; [PERSON], 1977, 1981). Large \(R1\) values and small confidence angles indicate significant anisotropy and well-defined directions. Note that magnetic anisotropy measurements on dry samples are called AMS in this study, whereas the term MPF is used to indicate results on the impregnated samples. The susceptibility of the dry calcarine samples is \(\sim\)3 orders of magnitude lower than that of the impregnated samples, and a factor of 4-10 lower for dry compared to impregnated molasse samples. Additionally, the AMS is not significant in many of the investigated rocks. Therefore, the AMS can be neglected, and only the MPF results will be discussed further.
### Correlation of XRCT and MPF Data
The size range of pores captured by XRCT or MPFs is different, and they yield different types of data: XRCT provides a grid of voxels identified as pores, whereas the MPF is an average representation of the overall pore fabric. Nevertheless, they can be compared when calculating a total shape ellipsoid, which represents the pore fabric of all pores larger than \(4\times 4\times 4\) voxels. Both total shape ellipsoids and MPFs are second-order tensors and represent the entire sample volume, which allows a direct comparison of fabric orientation, as well as the anisotropy degree and shape parameters. Abbreviations used as subscript are explained in Table S3 in Supporting Information S1. Note that the MPF \(P\)-value depends on the intrinsic susceptibility of the fluid used for impregnation in addition to the average pore shape ([PERSON], 2019; [PERSON] et al., 2006). Therefore, \(P_{m}\) will always be lower than \(P_{v}\) and it is also expected to be lower when the ferrofluid was more diluted. Nevertheless, an increase in \(P_{m}\) with increasing \(P_{s}\) is expected as long as the susceptibility of the fluid is constant.
## 3 Results
### XRT Results
#### 3.1.1 3D Reconstructions and Porosity
The calcarenites present 31%-43% XRT-derived porosities and 51.2%-55.2% He porosities, and molasse sandstones have 0.6%-16.4% XRT-derived porosities and 11.13%-30.78% He porosities (Table 1). There is no clear and uniquely defined limit in gray-scale values that distinguishes pores and solid fraction, due to averaging of the attenuation coefficients of pore and matrix in voxels containing a mix of both. Adjustment of the threshold value from 73 to 85 causes a change in calculated porosity for the calcarenite MI-2-Y3 of \(\sim\)10% (Figure S1 in Supporting Information S1). Additionally, pore throats are narrower than pores and thus harder to resolve by XRT, leading to overestimating the isolated porosity and underestimating the connected porosity. The discrepancy between XRT and He porosities is larger for molasse samples than calcarenites, due to the smaller pore size of molasse, resulting in a larger fraction of pores being below the spatial resolution of XRT. These small pores are included in the He porosity, indicating that 46%-95% of the pore space in molasse sandstones and 17%-43% for calcarenites are not resolved by the XRT data.
#### 3.1.2 Pore Size Distributions
The REV of pore size distribution was presented above (Figures 4a and 4b). Note that additional pores smaller than the voxel resolution (5.5\({}^{\circ}\)um\({}^{\circ}\), 9\({}^{\circ}\)um\({}^{\circ}\) or 15\({}^{\circ}\)um\({}^{\circ}\)) may be presented. The different resolutions cause different datasets. Between 1% and 22% of the identified pores occupy a small number of voxels, generating unresolved shape and orientation. A lower threshold of 4 \(\times\) 4 \(\times\) 4 voxels was chosen for orientation and shape analyses, including 78%-99% of the XRT-derived pore space and \(<\)83% of the pore space defined by He pycnometry. Calcarenites display bimodal pore size distributions, with two maxima at \(\sim\)20 and \(\sim\)300 um equivalent pore diameter for samples measured with 15-um pixel size or at \(\sim\)12 and \(\sim\)150 um for samples with 9-um pixel size, as the range of pore sizes detected depends on the resolution. Molasse sandstones have a unimodal pore size distribution, where 95%-99% of micropores (1%-22% of the pore volume) have sizes below the threshold for shape/ orientation resolution. For samples D1112Y and C334Y measured at both resolutions, additional micropores are identified at higher resolution, and C334Y also displays additional large pores at higher resolution (Figure 4).
#### 3.1.3 Pore Orientation
As the orientation of pores below a certain size limit cannot be resolved, causing extreme maxima parallel to the sample \(x\), \(y\) and \(z\)-axes when including all identified pores for analysis. These artifacts are reduced when increasing the lower threshold of analyzed pore sizes from 4 \(\times\) 4 \(\times\) 4 voxels to 16 \(\times\) 16 \(\times\) 16 voxels at the expense of diminishing the number of included pores. The total shape ellipsoids appear unaffected by these artifacts, and display similar orientations and anisotropy degrees, even when including the large number of small pores (66%-84% of the number of XRT-derived pores but 1%-5% of XRT-derived pore volume) (Figure 5a).
#### 3.1.3.1 Calcarenite
All samples whose names start with MI-1, MI-2 and MI-3 were drilled from the same block, in perpendicular directions. For MI-1-Z3, \(V1_{\text{s-individual}}\) group sub-parallel to the sample \(x\)-axis. The minor axes \(V3_{\text{s-individual}}\) form a girdle distribution in the \(yz\)-plane, with a sub-maximum parallel to \(z\). The bootstrapped total shape ellipsoid displays a similar \(V1_{\text{s-total}}\) direction (at 36\({}^{\circ}\) from the sample \(x\)-axis), and the mean \(V3_{\text{s-total}}\) direction is at 26\({}^{\circ}\) to the sample \(y\)-axis (Figure 5a). A comparison of the total shape ellipsoid with individual pore orientations shows that \(V3_{\text{s-total}}\) is defined by the absence of \(V1_{\text{s-individual}}\) axes rather than a grouping of \(V3_{\text{s-individual}}\). Sister samples MI-2-Y8/MI-2-Y10, and MI-2-Y3 were drilled in the same orientation, but display different fabric orientations. In MI-2-Y3, \(V1_{\text{s-individual}}\) show a girdle distribution in the \(yz\)-plane than with three sub-maxim, and \(V3_{\text{s-individual}}\) group closely around \(z\). The orientation of total shape ellipsoid, with \(V3_{\text{s-total}}\) at 33\({}^{\circ}\) to the \(x\)-axis and broad distributions of \(V1_{\text{s-total}}\) and \(V2_{\text{s-total}}\) is dominantly controlled by the \(V1_{\text{s-individual}}\) distribution (Figure 5b). Conversely, the \(V1_{\text{s-individual}}\) axes of sample MI-2-Y8 show a girdle distribution within a plane rotated \(\sim\)30\({}^{\circ}\) from the \(xz\)-plane around the \(z\)-axis, and \(V3_{\text{s-individual}}\) axes are grouped at \(\sim\)30\({}^{\circ}\) to the \(y\)-axis in the \(xy\)-plane. The \(V1_{\text{s-total}}\) and \(V2_{\text{s-total}}\) axes show a broad distribution in the plane defined by the \(V1_{\text{s-individual}}\) girdle (Figure 5c). For MI-3-X15, both \(V1_{\text{s-individual}}\) and \(V1_{\text{s-total}}\) are sub-parallel to the \(z\)-axis. The \(V3_{\text{s-individual}}\) and \(V3_{\text{s-total}}\) directions group close to the \(y\)-axis. For EqDiameter \(\leq\)100 and \(\geq\)100 um of pores, \(V3_{\text{s-total}}\) axes of both size windows are close to the \(y\)-axis and \(V1_{\text{s-total}}\) and \(V2_{\text{s-total}}\) are in the \(xz\)-plane (Figure 5d).
Figure 5:
Samples MI-5-Z21 and MI-5-X22 were drilled from a second block, and their orientations are mutually perpendicular, but unrelated to previous calcarenite samples. Nevertheless, they show similar pore fabrics: \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_individual}}\) group sub-parallel to \(y\), and \(V_{\rm 1_{\_individual}}\) groups sub-parallel to \(z\), defining \(V_{\rm 1_{\_total}}\) (Figures 5e and 5f).
The calcarenites MI-1-Z3, MI-2-Y3, MI-2-Y8 and MI-3-X15 are mutually perpendicular, and can be used to assess how representative fabrics on cores are for the entire block. If the block is perfectly homogeneous, the total shape ellipsoids should coincide once all datasets in a common coordinate system. After rotating all datasets to the sample coordinates of MI-1-Z3, the \(V_{\rm 1_{\_total}}\) axes of MI-1-Z3, MI-2-Y3, MI-2-Y8, and MI-3-X15 are at 9\({}^{\circ}\)-36\({}^{\circ}\) to the \(x\)-axis, but are statistically distinct at 95% confidence. The orientations of \(V_{\rm 2_{\_total}}\) and \(V_{\rm 3_{\_total}}\) axes are largely variable (Figure S2 in Supporting Information S1). Additionally, the type of grouping is different for each sample: in MI-1-Z3, the \(V_{\rm 1_{\_total}}\) form a point distribution, whereas the \(V_{\rm 3_{\_total}}\) form a point distribution in MI-3-X15. This indicates between-sample heterogeneity, and implies that a large number of standard-sized samples would need to be measured and averaged to obtain a pore fabric representative of this rock.
#### 3.1.3.2 Molasse
Samples D11 and D12 were drilled from two different blocks collected at the same site. Samples C43Y and C334Y were also drilled from blocks from the same location, but with different orientations. Sample 5256X was from another block. For molasse D1121Z, the \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_total}}\) group around the \(z\) direction, and the \(V_{\rm 1_{\_individual}}\) present a gridle distribution in the \(x\) plane, which is also reflected by the total shape ellipsoid (Figure 5g). Sample D1112Y was measured at both resolutions, 15- and 9-\(\mu\)m, and both datasets show girdle distributions of \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 1_{\_total}}\) axes rotated \(\sim\)30\({}^{\circ}\) around the \(z\)-axis from the \(x\)-plane. The directions for \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_total}}\) group at \(\sim\)30\({}^{\circ}\) from \(y\) in the \(xy\)-plane. Despite these similarities, the ODFs change significantly with resolution. For example, the grouping of \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 3_{\_individual}}\) is more pronounced in the higher-resolution data. These differences are reflected by the total shape ellipsoids (Figure 5h), and may be a result of resolution artifacts, or indicate size-dependent pore orientation. For D1263Y2, the orientation of the total shape ellipsoid is controlled by the main groupings of \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 3_{\_individual}}\) (Figure 5i). Conversely, for D1234X, \(V_{\rm 2_{\_total}}\) is sub-parallel to the maximum grouping of \(V_{\rm 3_{\_individual}}\), while \(V_{\rm 1_{\_total}}\) aligns with the maximum of a broad distribution of \(V_{\rm 1_{\_individual}}\). Thus, it is the absence of \(V_{\rm 1_{\_individual}}\) rather than the presence of \(V_{\rm 3_{\_individual}}\) that define the orientation of \(V_{\rm 3_{\_total}}\) (Figure 5j).
For molasse sample C43Y, the \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 1_{\_total}}\) axes are sub-parallel to \(x\). The \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_total}}\) show a pronounced maximum along \(z\) (Figure 5k). Sample C334Y displays largely different ODFs for data obtained with 15 and 9 \(\mu\)m resolution. The 15 \(\mu\)m data show the \(V_{\rm 1_{\_individual}}\) sub-parallel to \(x\) and \(V_{\rm 3_{\_individual}}\) along \(z\). Conversely, the higher-resolution data shows a concentration of \(V_{\rm 1_{\_individual}}\) parallel to \(z\), that is, along the preferred directions of \(V_{\rm 3_{\_individual}}\) as identified by 15 \(\mu\)m data. Also the orientation of the total shape ellipsoid is resolution-dependent, although the discrepancy is less than observed in the ODFs (Figure 5l). This observation highlights the importance of adequate resolution in XRCT studies. For sample BE42 AY, the \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 1_{\_total}}\) axes are along \(z\). The \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_total}}\) are at \(\sim\)30\({}^{\circ}\) from \(x\) in the \(xy\)-plane (Figure 5m).
A relatively small number of pores was identified above the size threshold suitable for fabric analysis in 5256X, resulting in ODFs with many sub-maxima. As a consequence, the total shape ellipsoid is poorly defined, especially in the V2-V3 plane (Figure 5n). The confidence angles of the total shape ellipsoid may thus indicate the quality of the underlying XRCT data. Sample F31Z1 shows the \(V_{\rm 1_{\_individual}}\) and \(V_{\rm 1_{\_total}}\) axes along \(x\). The directions for \(V_{\rm 3_{\_individual}}\) and \(V_{\rm 3_{\_total}}\) group at \(\sim\)20\({}^{\circ}\) from \(z\) in the \(yz\)-plane (Figure 5o).
Figure 5: Comparison of point distribution and orientation density functions (ODFs) of pore axes, bootstrapped total shape ellipsoids, and magnetic pore fabrics (MPFs) for calcarenites and molasses. ODFs include pores larger than 4 x 4 x 4 voxels to reduce resolution artifacts. Pore orientation and MPF results are shown on upper hemisphere equal area stereonets. V1, V2, and V3 indicate the maximum, intermediate and minimum axes of the total shape ellipsoid. The ellipses show the 95% confidence based on bootstrapping ([PERSON], 1990; [PERSON], 1963; [PERSON], 1978; [PERSON], 2000; [PERSON] et al., 1998). The total shape ellipsoid with confidence ellipses is drawn using the TomoFab MATLAB code, and the red dashed line highlights the \(V1\)–\(V2\) plane, that is, the foliation defined by the SPO; the lineation corresponds to the direction of V1 ([PERSON] et al., 2020). Principal susceptibility directions are shown for averaged (solid symbols), and individual datasets (open symbols). (a) Presents the comparison of point distributions and orientation density functions of pore axes and total shape ellipsoids as a function of pore size threshold for MI-1-Z3. \(P_{\_}{\rm r}\) is the anisotropy degree of total shape ellipsoid. (d) Presents the comparison of point distributions and orientation density functions of pore axes and total shape ellipsoids with different pore size windows (EqDiameter \(\leq\) 100 \(\mu\)m and \(\geq\)100 \(\mu\)m) for MI-3-X15.
#### 3.1.4 Pore Shape and Anisotropy Degree
For all samples, the individual pores present a large range of pore shapes (\(U_{\text{\tiny{individual}}}\) varies from \(-0.99\) to \(+0.99\)) and anisotropy degrees (\(P_{\text{\tiny{individual}}}\) varies from 1.14 to 2,826). The total shape ellipsoid shows a lower anisotropy degree than the individual pores (\(P_{\text{\tiny{total}}}\) of 1.07-2.41), and a slightly smaller range of \(U_{\text{\tiny{s-total}}}\) values from \(-0.99\) to 0.98, which reflects the large variability in pore orientations (Figure 6).
### MPF Results
After impregnation, the volume-normalized mean susceptibility is 1.47-20.60 \(\times\) 10\({}^{-3}\) SI for calcarenites and 4.44-19.03 \(\times\) 10\({}^{-4}\) SI for molasse sandstones (Table S4 in Supporting Information S1). The susceptibility of diluted ferrofluid is 4.36-4.39 \(\times\) 10\({}^{-2}\) SI (1:25 oil), 1.16 \(\times\) 10\({}^{-2}\) SI (1:30 resin) and 7.11-7.39 \(\times\) 10\({}^{-3}\) SI (1:50 resin). The MPF-derived porosity is 12.7%-47.1% for calcarenites and 3.84%-26.2% for molasse sandstones
Figure 6: Anisotropy degree \(P_{\text{\tiny{s-individual}}}\)\(P_{\text{\tiny{s-total}}}\) and shape \(U_{\text{\tiny{s}}}\)\((U_{\text{\tiny{s-total}}}\)\(U_{\text{\tiny{s-total}}})\) of individual pore best-fit ellipsoids, total shape ellipsoid and bootstrapped total shape ellipsoid for all samples.
(Table 1), reflecting \(I.E._{\rm{max}}\) of 23.7%-91.3% and 17.6%-138%, respectively. \(I.E._{\rm{max}}\) with diluted oil (52%-91.5%) is higher than one with resin mixture (23.7%-53.0%) for calcarenites (Table S4 in Supporting Information S1).
#### 3.2.1 Magnetic Fabric Orientation
Not all calcarenites display well-defined MPFs; MI-1-Z3 shows no significant anisotropy (Figure 5a). Samples MI-2-Y3 (measured at 512 kHz) and MI-2-Y10 (1 kHz) display significant anisotropy, but their principal directions are poorly defined (Figures 5b and 5c). Samples MI-2-Y8, MI-3-X11, MI-5-Z21 and MI-5-X22 show significant anisotropy, and well-defined directions (Figures 5c-5f, and Table S4 in Supporting Information S1). The \(V_{\rm{2 nMPF}}\) of sample MI-2-Y8 is sub-parallel to the \(z\)-axis. The \(V_{\rm{1 nMPF}}\) is at 31\({}^{\circ}\) to \(x\)-axis in the \(xy\)-plane (Figure 5c). For sample MI-3-X11, the MPFs measured at different frequencies are co-axial, with largest confidence angles at 16 kHz, and \(V_{\rm{1 nMPF}}\) at 36\({}^{\circ}\) to the \(y\)-axis in the \(xy\)-plane, \(V_{\rm{3 nMPF}}\) sub-parallel to the \(z\)-axis (Figure 5d). For sample MI-5-Z21, the \(V_{\rm{1 nMPF}}\) deviates 24\({}^{\circ}\) from the \(x\)-axis, and \(V_{\rm{3 nMPF}}\) is oriented along \(z\)-axis (Figure 5e). The \(V_{\rm{1 nMPF}}\) of sample MI-5-X22 is parallel to the \(x\)-axis, and \(V_{\rm{2 nMPF}}\) and \(V_{\rm{3 nMPF}}\) lie within the \(yz\)-plane (Figure 5f).
Most molase samples show significant anisotropy and well-defined directions. Sample D1221X possesses significant anisotropy but poorly defined directions, and samples D1234X and D1261X have a well-defined \(V_{\rm{1 nMPF}}\), but large confidence angles in the \(V_{\rm{2 nMPF}}\)--\(V_{\rm{3 nMPF}}\) plane (Figure 5). For sample D1121Z, the MPFs show similar orientation independent of frequency and the \(V_{\rm{1 nMPF}}\), \(V_{\rm{2 nMPF}}\) and \(V_{\rm{3 nMPF}}\) are along to the \(y\)-, \(x\)- and \(z\)-axes, respectively. Largest confidence angles are observed at 16 kHz (Figure 5g). The \(V_{\rm{1 nMPF}}\) of sample D1112Y is \(\sim\)10\({}^{\circ}\) from the \(x\)-axis, and \(V_{\rm{2 nMPF}}\) and \(V_{\rm{3 nMPF}}\) are in a plane that is rotated ca 10\({}^{\circ}\) around \(z\) from the \(yz\)-plane (Figure 5h). Both samples D1263Y2 and D1234X show well-defined \(V_{\rm{1 nMPF}}\) sub-parallel to the \(y\)-axis, and \(V_{\rm{2 nMPF}}\) and \(V_{\rm{3 nMPF}}\) in the \(xz\)-plane (Figures 5i and 5j). Sample D1221X and BE42 AY have significant anisotropy of MPFs but poorly defined directions. Sample D1261X shows well-defined \(V_{\rm{2 nMPF}}\) along \(z\)-axis, and \(V_{\rm{1 nMPF}}\) and \(V_{\rm{3 nMPF}}\) rotated \(\sim\)30\({}^{\circ}\) around the \(z\)-axis in the \(y\)-plane (Figures 5j and 5m). The MPFs of sample C43Y in different frequencies possess the same well-defined \(V_{\rm{1 nMPF}}\), \(V_{\rm{2 nMPF}}\) and \(V_{\rm{3 nMPF}}\) at \(\sim\)10\({}^{\circ}\) to the \(x\), \(y\), and \(z\) directions, respectively (Figure 5k). Sample C334Y has well defined \(V_{\rm{1 nMPF}}\) and \(V_{\rm{2 nMPF}}\) in a plane rotated ca 45\({}^{\circ}\) around \(z\) from the \(xz\)-plane and \(V_{\rm{3 nMPF}}\) at \(\sim\)45\({}^{\circ}\) to \(x\)-axis (Figure 5l). For sample F31Z1, MPF axes are well defined. The \(V_{\rm{1 nMPF}}\) is at \(\sim\)20\({}^{\circ}\) from the \(xy\)-plane, and \(V_{\rm{3 nMPF}}\) is at \(\sim\)30\({}^{\circ}\) to the \(z\)-axis (Figure 5o).
#### 3.2.2 Anisotropy Degree and Shape of the Magnetic Fabric
The MPF anisotropy degrees of calcarenites are 1.01-1.05, and the shape values \(U_{\rm{mMPF}}\) vary between \(-\)0.79 and 0.52 for samples with significant anisotropy. Note that the anisotropy shape is poorly defined for samples with low anisotropy and noisy data ([PERSON] et al., 2013), which explains the large variability in these datasets. The molase sandstones show higher anisotropy degrees, with \(P_{\rm{mMPF}}\) between 1.01 and 1.20, and the shape values \(U_{\rm{mMPF}}\) range from \(-\)0.86 to 0.37. The samples that were measured at several frequencies mostly show different \(U_{\rm{mMPF}}\) values and similar \(P_{\rm{nMPF}}\). Conversely, sample D1121Z shows similar \(U_{\rm{mMPF}}\) values at all frequencies, but \(P_{\rm{mMPF}}\) appears to vary with measurement frequency, and is higher than for other molase samples from the same block (Figure 7).
### Comparison of XRCT and MPF Data
#### 3.3.1 Porosities
For calcarenite, XRCT-derived porosities are 13.6%-21.3% higher than MPF-derived ones except MI-2-Y3 (10% lower), and molase presents opposite results (0.3%-20.0% lower) except D1263Y2 and F31Z1 (5.2%-7.2% higher). MPF-derived porosities with diluted oil (29.4%-46.0%) are higher than ones with resin mixture (12.7%-28.9%) for calcarenites. For calcarenites, the XRCT-derived porosities (31%-43%) have lower variability than MPF data (12.7%-46.0%). For molases, both methods have large variability (0.6%-16.4% for XRCT and 3.8%-25.6% for MPF) (Table 1).
#### 3.3.2 Directional Comparison
For MI-2-Y3, \(V1\) and \(V3\) directions of total shape ellipsoids and MPF at 512 kHz agree with each other at 95% confidence level. Similarly, total shape ellipsoids and MPFs are generally coaxial in samples D1121Z, D1112Y, D1234X, D1261X, and D1221X. The principal directions of the total shape ellipsoid and MPF are sub-parallel in C43Y, C334Y, and BE42 AY but distinct at 95% confidence. For MI-5-X22, D1263Y2, and F31Z1, V3 directionsFigure 7: (a) and (b) Anisotropy degree and shape of the magnetic fabric. Sample MI-2-Y3 was measured at 4, 16, and 512 kHz on the SM150. MI-3-X1, D1121Z, D1234X, C43Y, and BE42 AY were measured at 1 kHz, 4 and 16 kHz on the MFX1-FA. Remaining samples were measured at 1 kHz on the MFX1-FA. (c) Degree of magnetic anisotropy (\(P_{m-MP}\)) against anisotropy degree of total shape ellipsoid (\(P_{m-MP}\)). All samples were measured in 15 μm, 9 μm or 5.5 μm. X-ray computed micro-tomography and impregnated by oil-based ferrofluid (EMG 909), using different concentrations.
of total shape ellipsoid and MPF are similar but their \(V1\) and \(V2\) axes are distinct. Conversely, directions are statistically distinct at 95% confidence in samples MI-2-Y8 and MI-5-Z21 (Figure 5).
#### 3.3.3 Comparison of Anisotropy Degree and Shape
The MPF anisotropy degree is lower than that of the total shape ellipsoid in all samples. It is expected that \(P_{\text{m-MPF}}\) increases with \(P_{\text{s-expr}}\) and a higher-susceptibility ferrofluid causes stronger increase. Inconsistent correlations are presented in our data, partly due to measurement uncertainty, and only few datasets existing with the same ferrofluid susceptibility and measurement frequency, hindering statistical analysis. For similar reasons, it is impossible to evaluate whether \(P_{\text{m-MPF}}\) displays a consistent frequency dependence (Figure 7). Anisotropy shapes agree within uncertainty for total shape ellipsoid and MPF in samples MI-2-Y3, MI-2-Y8, MI-5-Z21, D1234X, D1261X, D1221X, BE42 AY, and F31Z1, but are different for both fabric measurements in the remaining samples (Figure 8). Comparing higher and lower resolution XRCT data suggests that both D1112Y and C334Y show similar anisotropy degree and shape at both resolutions (Figures 8g and 8k).
Figure 8: Comparison of anisotropy degree and shape derived from X-ray computed micro-tomography (total shape ellipsoid) and magnetic pore fabric datasets. Samples MI-1-2, MI-2Y3 and MI-3-X15 were measured at 4 kHz, 16 and 512 kHz on the SM150. MI-3-X11, D1121Z, D1234X, C43Y, and BE42 AY were measured at 1 kHz, 4 and 16 kHz on the MFK1-FA. Remaining samples were measured at 1 kHz on the MFK1-FA.
## 4 Discussion
3D pore fabrics of calcarenite and molasse sandstone were investigated directly by XRCT, and indirectly by MPF. The XRCT technique is commonly used to characterize the internal structure of reservoir rocks because of non-destructiveness and 3D descriptions on pore fabrics ([PERSON] and [PERSON], 2013; [PERSON], 2018; [PERSON] and [PERSON], 2010; [PERSON] et al., 2017). However, due to limited resolution and related artifacts, the smallest pores are unresolved by XRCT, and distinguishing isolated and connected pores is challenging because of narrow pore throats ([PERSON] et al., 2008; [PERSON] et al., 2009; [PERSON] et al., 2009; [PERSON], 2012). The voxel size is 5.5, 9 or 15 \(\upmu\)m, corresponding to a spatial resolution of 10\({}^{\prime}\)648, 46\({}^{\prime}\)656 or 216\({}^{\prime}\)000 \(\upmu\)m\({}^{3}\) (4 x 4 x 4 voxels) for characterizing pore fabrics. Selecting 4 x 4 x 4 voxels as filter was a compromise between keeping as many pores as possible and reducing resolution-related artifacts that affect the ODFs of the major and minor pore axes at the expense of losing 1%-22% of XRCT-derived pores (Table 1), decreasing the representativeness. Fabric orientations in different pore size windows show sub-parallel axes and different confidence angles, because window of smaller pores includes more unresolved micropores (Figure 5d). The comparisons of different resolutions (9 and 15 \(\upmu\)m) indicate higher resolution detects more micropores, and also more small grains decreasing pore volume. One sample presents additional pores in all sizes with higher resolutions, probably because changing XRCT threshold to segment pores caused more pores resolved in all sizes. For these, different fabric orientations are observed between two datasets (Figures 5h and 5l), indicating that different pore sizes display different pore fabrics. Conversely, anisotropy degrees and shapes appear independent of resolution (Figures 6h, 6l, and 8g, 8k). This suggests that the pore shapes and aspect ratios are similar across all pore sizes, while their orientations vary.
A total shape ellipsoid is introduced to minimize the effect of resolution-related artifacts without excluding small pores, providing a more stable measurement of pore fabric. In addition to reducing artifacts, the total shape ellipsoid can also derive an average pore fabric from a poorly defined and noisy ODF, and it allows a direct comparison of pore fabrics with second-order tensor properties, such as magnetic susceptibility, permeability or thermal diffusivity. We recommend this strategy for future analyses of pore or grain shape distributions in studies about average fabric determination, or when modeling physical properties for reservoir evaluation and characterization. We expect that analyses based on total shape ellipsoids are particularly applicable to rocks with simple ellipsoidal pores. An alternative approach in need of further tests, is to use the best-fit ellipsoids of pores as input for a numerical model calculating MPFs for given pore assemblies and ferrofluid susceptibility ([PERSON], 2020). Complex pore shapes may need more sophisticated descriptions from further investigations.
The MPF method has been proposed as an efficient pore fabric characterization technique to capture pores down to 10 nm ([PERSON], 1993; [PERSON] et al., 2014). If reaching this limit, it would provide insight into the fabric of small pores unresolved by XRCT. There is no linear trend between the concentration and fluid susceptibility because susceptibility is lower when using resin rather than oil for dilution ([PERSON] et al., 2021). Fluid susceptibility still varies (<4%) after correcting frequency dependence, possibly because of the discrepancy between this study and [PERSON] et al. (2021), for example, time dependence. If changing corrected coefficient, all derived quantities, for example, impregnation efficiency will change. The impregnation efficiency varies largely for different samples when using the standard vacuum impregnation method commonly applied in MPF studies ([PERSON] et al., 2016; [PERSON] et al., 2021) (Table S4 in Supporting Information S1). \(I.E._{\text{sec}}\) and MPF-derived porosities with diluted oil are higher than with resin mixture, due to higher viscosity of resin causing harder impregnation. He-pycommeter porosity is higher than MPF and XRCT-derived porosities. MPF presents higher porosity than XRCT for most molasses but opposite for most calcarenites, possibly because in the large pores, ferrofluid particles may aggregate and sediment (Figures 2b and 2d). XRCT-derived porosities for calcarenites present lower variability than ones for molasses, may due to large pores easily resolved by XRCT. Ferrofluid on the sample surface was not entirely eliminated, may causing \(I.E._{\text{sec}}>100\%\) and MPF-derived porosity > He-pycommeter porosity in the corresponding samples and MPF-derived porosities varying for different samples and diluents. The anomalies may also result from inhomogeneous fluid, and the uncertainty in the determination of fluid susceptibility/frequency dependence, because of the time-dependent nature of fluid properties. Nevertheless, results presented here show a quantitative relationship between MPF and XRCT-derived pore fabric. Six out of 12 samples exhibit the same fabric orientation for XRCT and MPF data at 95% confidence, including only one calcarenite, probably because very weak anisotropy of calcarenite makes it impossible to interpret orientation. With very large pores, ferrofluid sedimenting to the bottom of pore may cause changes to MPF, especially for an almost isotropic sample, for example, calcarenite. The additional three samples showsub-parallel fabric orientations, though they are distinct at 95% confidence. Three samples possess fabrics with minimum axes that are co-axial between XRCT and MPF data but one of them shows deviations in the other two axes. In the other, the orientations of \(V1\) and \(V2\) axes cannot be compared, as \(V1_{\text{+total}}\) and \(V2_{\text{+total}}\) directions are not statistically significant. Observed discrepancies in the XRCT and MPF fabric measures may be related to artifacts with either method, for example, incomplete or inhomogeneous impregnation may affect MPF data, and resolution artifacts affect XRCT, as evidenced by differences in the fabric obtained on the same sample when measured at different resolutions and when considering different pore size windows in the same sample. Where XRCT data at 9 and 15 \(\upmu\)m resolution did not agree, the higher-resolution XRCT data was compared with the MPFs, as this captures more pores, and better reflects the pores targeted by MPFs. Related to the observation that XRCT scans at different resolutions produce different pore fabric orientations, MPFs may show different fabrics as they capture smaller pores than XRCT. In this case, the investigated methods target different parts of the pore space, and thus provide complementary information when used together. Thus, discrepancies between MPF and XRCT fabric orientations in some samples indicate a variation of pore fabric with pore size, provided that other sources such as measurement uncertainty and impregnation artifacts can be excluded. To investigate this further, a complete set of XRCT data measured at different resolutions would be necessary, which may become possible after technological advancements. Until then, the agreement of XRCT and MPF fabric orientations in two thirds of the samples investigated here highlight the potential of the MPF method, and suggest that it could be useful to characterize the fabric of pores with sizes below the XRCT-resolution on standard-sized cores. Previously published empirical relationships between average pore shape and MPF, or the average pore elongation direction and the maximum principal susceptibility of the MPF ([PERSON] et al., 2000; [PERSON] et al., 2006; [PERSON], 1993) are partly confirmed, and the concept of the total shape ellipsoid further expands these relationships, as it allows quantitative comparison.
The magnetic anisotropy degree is lower than the anisotropy degree of the total shape ellipsoid. This is expected, given the physics of self-demagnetization and shape anisotropy, and the low susceptibility of the ferrofluid and high measurement frequency ([PERSON], 2019; [PERSON] et al., 2021; [PERSON] et al., 2006). The relationship between pore axial ratio and MPF has been described by the equivalent pore concept ([PERSON] et al., 2000), and corrections thereof ([PERSON] et al., 2006). However, because not only the geometry of individual pores, but also their orientation and spatial arrangement influence the MPF, there is no unique and straightforward relationship and predicting MPFs for a given pore space needs numerical modeling ([PERSON], 2020). Here, no clear correlation was observed, partly because measured susceptibility decreases with increasing frequency ([PERSON] et al., 2021). Therefore, higher fluid susceptibilities and measurement frequency of 1 kHz are recommended for MPF studies ([PERSON] et al., 2021). Half of the samples display similar anisotropy shapes for both fabric measures within measurement uncertainty, while the others displayed discrepancies in anisotropy shape. This may be related to the different parts of the pore space captured, or an inherent difference between methods, and needs to be investigated further.
It remains to be established whether or not the MPF and total shape ellipsoid do relate to permeability. There are empirical correlations of MPF, pore fabrics and permeability anisotropy ([PERSON] et al., 2011; [PERSON] et al., 2003; [PERSON] et al., 1999; [PERSON] et al., 2009; [PERSON] and [PERSON], 1994). Permeability anisotropy is also a second order tensor property, and essential for reservoir characterization, but the measurement method should be improved to obtain a full tensor with estimating uncertainty and heterogeneity. Future work will need to investigate whether the total shape ellipsoids and MPFs defined here correlate clearly with laboratory-measured permeability anisotropy. This study lays the foundation for the quantitative comparison between a variety of fabric measures and second-order properties. More types of reservoir rocks and fabrics need to be analyzed for a detailed and thorough understanding of MPFs and their ability to predict pore fabrics and permeability anisotropy in the future, following the procedure outlined here.
## 5 Conclusions
The main goals of the study were (a) to establish quantitative relationships between XRCT-derived pore fabric data and MPFs, and (b) to investigate how the methods can complement each other in order to improve 3D pore space description for reservoir characterization. The comparison of pore fabrics calculated from XRCT and MPF data was accomplished by defining the total shape ellipsoid, an average measure of the pore fabric, integrating information on the pore shapes and orientation density derived from the XRCT data. The total shape ellipsoid is mathematically represented by a second order symmetric tensor, and can thus be directly compared to second order tensor properties such as susceptibility or permeability. It is therefore useful not only in MPF studies, but also a wide range of fluid flow applications, or when predicting other physical rock properties relevant for reservoir evaluation and hydrocarbon exploitation.
Generally, a good agreement was observed between the total shape ellipsoid and MPFs in terms of fabric orientation, and partly in terms of anisotropy shape. This confirms and expands previous empirical relationships between average pore shape or preferred pore orientation with MPFs. Anisotropy degrees cannot be compared directly, because the susceptibility of the ferrofluid plays an important role in controlling the MPF anisotropy degree. Some open questions remain, including whether MPFs really are able to capture micropores (>10 nm of magnetic nanoparticle) as suggested in previous studies, and how the total shape ellipsoid is affected by resolution-artifacts and segmentation uncertainties. Nevertheless, the ability to quantitatively correlate MPF and total shape ellipsoid data will make the MPF method more useful in future applications.
## Data Availability Statement
XRCT particle analyses and MPF data obtained in this study can be obtained from [[https://doi.org/10.5281/zenodo.6782552](https://doi.org/10.5281/zenodo.6782552)]([https://doi.org/10.5281/zenodo.6782552](https://doi.org/10.5281/zenodo.6782552)).
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wiley/fb58dc3e_8803_4920_a367_d23182a2d9c3.md | # Frames
###### Abstract
The Laurentian Great Lakes are the world's largest freshwater system and regulate the climate of the Great Lakes region, which has been increasingly experiencing climatic, hydrological, and ecological changes. An accurate mechanistic representation of the Great Lakes thermal structure in Regional Climate Models (RCMs) is paramount to studying the climate of this region. Currently, RCMs have primarily represented the Great Lakes through coupled one-dimensional (1D) column lake models; this approach works well for small inland lakes but is unable to resolve the realistic hydrodynamics of the Great Lakes and leads to inaccurate representations of lake surface temperature (LST) that influence regional climate and weather patterns. This work overcomes this limitation by developing a fully two-way coupled modeling system using the Weather Research and Forecasting model and a three-dimensional (3D) hydrodynamic model. The coupled model system resolves the interactive physical processes between the atmosphere, lake, and surrounding watersheds; and validated against a range of observational data. The model is then used to investigate the potential impacts of lake-atmosphere coupling on the simulated summer LST of Lake Superior. By evaluating the difference between our two-way coupled modeling system and our observation-driven modeling system, we find that coupled-like atmosphere dynamics can lead to a higher LST during June-September through higher net surface heat flux entering the lake in June and July and a lower net surface heat flux entering the lake in August and September. The unstratified water in June distributes the entering surface heat flux throughout the water column leading to a minor LST increase, while the stratified waters of July create a conducive thermal structure for the water surface to warm rapidly under the higher incoming surface heat flux. This research provides insight into the coupled modeling system behavior, which is critical for enhancing our predictive understanding of the Great Lakes climate system.
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size of the Great Lakes and also hints at their important role in the environmental and socio-economic condition of the coastal regions. The Great Lakes provide over 151 million liters (151,000 m\({}^{3}\)) of water every day to the US alone for drinking water, power generation, industrial uses and agriculture ([PERSON] et al., 2019). With at least 153 species of fishes in the lakes ([PERSON], 1998) and over 34 million people living within the Great Lakes basin (approximately 8% and 32% of US and Canada's population respectively), the Great Lakes also supports one of the largest regional economies in the world, which includes a 57 billion a year fishing and 516 billion a year tourism industry ([PERSON] et al., 2019).
In the past few decades, climate change has warmed the Great Lakes basin to the extent where air temperature and lake surface temperature (LST) have undergone disproportionate changes. For example, over the Great Lakes basin, the average near-surface air temperature for the 1986-2016 period is higher than that for the 1901-1960 period by 0.9\({}^{\circ}\)C ([PERSON] et al., 2019). This increase is larger than the contiguous US average of 0.7\({}^{\circ}\)C (USGCRP, 2018). Likewise, LST has undergone an accelerated warming, particularly in Lake Superior - the largest among the Great Lakes. Lake Superior has warmed dramatically after 1997-1998, with the mean summer LST for 1998-2012 being 2.5\({}^{\circ}\)C higher than the mean summer LST for 1982-1997 ([PERSON] et al., 2016). An astounding 71% reduction in ice cover over the Great Lakes during 1973-2010 ([PERSON] et al., 2012) further highlights the potential for an unusually warmer Great Lakes basin under future climate change. Such persistent warming negatively impacts the lake's ecology through increased lake heatwave severity ([PERSON] et al., 2021), fish redistribution ([PERSON] et al., 2019), mass die-offs ([PERSON] et al., 2019) and cyanobacterial blooms ([PERSON] et al., 2008). Therefore, to better understand how the Great Lakes will respond to climate change, improved modeling of the regional climate has been stressed by the Great Lakes scientific community in recent years ([PERSON] et al., 2018).
Dynamically downscaling low-resolution General Circulation Models (GCMs) using high-resolution Regional Climate Models (RCMs) has been the most widely used climate modeling technique to assess climate change impacts in the Great Lakes region in recent years ([PERSON] and [PERSON], 2019). RCMs, by focusing on a regional geographical area and by considering the local topographical features on a higher spatial resolution, dynamically extrapolates the large-scale forcings from GCMs using an explicit representation of physics to produce a more regionally accurate climate simulation. As such, RCMs capture small-scale climate dynamics better than GCMs, which is crucial for regional climate studies. More importantly, RCMs are able to better simulate the Great Lakes and their impact on the regional climate through dedicated coupled lake models ([PERSON] et al., 2017, 2022). The Great Lakes act as a constant moisture source to the atmosphere, and combined with their large thermal inertia, low surface roughness and large variation of surface albedo depending on ice cover, they have a profound effect on the regional climate through lake-land-atmosphere interactions ([PERSON] and [PERSON], 1972; [PERSON] et al., 2013; [PERSON] and [PERSON], 1996). Unlike RCMs that can be coupled to dedicated lake models, most GCMs have, if any, a very crude representation of the Great Lakes (such as lakes being treated as oceans or static water surfaces) and therefore, are unable to accurately simulate the lake dynamics, ice formation, and lake-land-atmosphere interactions ([PERSON] et al., 2021).
An accurate mechanistic representation of the lakes is paramount to realistically capturing lake-land-atmosphere interactions and producing credible climate simulations of the Great Lakes region. Yet, till now, the most common way of representing the Great Lakes has been through one-dimensional (1D) lake column models. Although better than GCMs' crude representations of the Great Lakes, 1D lake models still struggle to accurately simulate the lake's three-dimensional (3D) circulation and the associated turbulent mixing, which inevitably lead to biases in the simulated lake thermal structure and lake-atmosphere fluxes ([PERSON] et al., 2014; [PERSON] et al., 2017). Studies like [PERSON] et al. (2014) and [PERSON] et al. (2016) have made efforts to improve the 1D lake models by modifying and tuning the model parameters like diffusivity and albedo. Such efforts improved the model performance in simulating shallow regions of the Great Lakes, but the models still underperformed in the deeper regions, particularly for simulating LST. The 1D lake models struggle to simulate the thermal structure of the Great Lakes primarily due to their inability to properly resolve horizontal and vertical mixing and ice movement in the lakes ([PERSON] et al., 2014; [PERSON] et al., 2016). Thus, even though such 1D models have been two-way coupled to RCMs, their model performance and future projections are still not robust enough to realistically demonstrate the impacts of climate change on the lakes and the lake-land-atmosphere interactions. A fully 3D two-way coupled modeling system with an RCM and a 3D lake model is, therefore, highly desired by the regional climate modeling community ([PERSON] and [PERSON], 2019; [PERSON] et al., 2018).
Studies using two-way coupled 3D lake models are slowly emerging with [PERSON] et al. (2017) being the first study to do so by two-way coupling the fourth version of the International Center for Theoretical Physics (ICTP) Regional Climate Model (RegCM4) ([PERSON] et al., 2012) with a 3D hydrodynamic lake and ice model based on the Finite Volume Community Ocean Model (FVCOM) ([PERSON] et al., 2006, 2013). [PERSON] et al. (2020) followed up by two-way coupling the Climate-Weather Research and Forecasting to an FVCOM-based 3D lake and ice model. [PERSON] et al. (2022) and [PERSON] et al. (2022) later built upon the framework from [PERSON] et al. (2017) and derived projections for the Great Lakes under climate change. However, as far as we know, [PERSON] et al. (2017) and [PERSON] et al. (2020) are still the only two studies dedicated to documenting the two-way coupling of an RCM to a 3D lake model for the Great Lakes.
Furthermore, due to the rarity of two-way coupled RCMs with 3D lake models for the Great Lakes, a complete mechanistic understanding of the impact of lake-atmosphere coupling on the simulation of Great Lakes LST is lacking. Unlike in historical simulations where available observational data can be used to supplement models or even circumvent model limitations, future projections for the Great Lakes LST rely completely on the results from RCM and lake model including the lake-atmosphere coupling between them. The role of such an interactive process between the atmosphere and lake model on the simulated LST has not been adequately resolved and studied in previous studies as they used rudimentary lake models like a lumped ([PERSON] et al., 2015) or a 1D lake model ([PERSON] et al., 2016). So, it is imperative to understand the influence of lake-atmosphere coupling on Great Lakes LST simulation and the mechanism behind it.
The two main objectives of this paper are to: (a) present a fully 3D two-way coupled lake-land-atmosphere modeling system for the Great Lakes using an RCM and a 3D lake model, and (b) assess the role of lake-atmosphere coupling on simulated summer LST. In this study, the Weather Research and Forecasting (WRF) model and an FVCOM-based 3D hydrodynamic lake and ice model are two-way coupled to each other. This fully 3D two-way coupled regional modeling system supplements the scarce modeling literature of RCMs with two-way coupled 3D lake models in the Great Lakes. Additionally, by performing a set of twin experiments where each experiment has a different coupling framework between WRF and FVCOM, this study aims to resolve and assess the impact of lake-atmosphere coupling on Lake Superior's summer LST in the two-way coupled model system. Lake Superior was chosen for this analysis because it has experienced an accelerated summer warning in recent decades ([PERSON], 2007; [PERSON] et al., 2016) and because Lake Superior, by virtue of being the deepest and largest among the Great Lakes, requires a comprehensive 3D lake model to accurately capture its hydrodynamics.
The remaining parts of this paper are organized as follows. In Sections 2 and 3, we describe the models and the model validation data used in this study along with the design of the numerical simulations. In Section 4, we validate the modeling results by comparing them to in-situ and satellite-based observation datasets. In Section 5, the role of lake-atmosphere coupling on Lake Superior's summer LST in the two-way coupled model system is presented, followed by discussion in Section 6 and conclusion and summary in Section 7.
## 2 Models and Data
### Regional Climate Model
The RCM used in this study is the WRF model version 4.2.2 with the Advanced Research WRF (ARW) dynamic core ([PERSON] & [PERSON], 2008). The WRF physics opted for this study includes the Thompson microphysics scheme ([PERSON] et al., 2004, 2008), the Rapid Radiative Transfer Model for GCMs longwave and shortwave schemes ([PERSON] et al., 2008), the Yonsei University planetary boundary layer scheme ([PERSON] & [PERSON], 2006; [PERSON] et al., 2003) and the revised scheme of the surface layer formulation based on the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) parameterization ([PERSON] et al., 2012). Additionally, the land surface processes which include soil-vegetation physics are modeled by the Unified Noah land surface model within WRF ([PERSON] & [PERSON], 2001).
The WRF domain for this study (Figure 1), centered at 85.0\({}^{\circ}\)W, 45.5\({}^{\circ}\)N, covers the entire Great Lakes region with 544 \(\times\) 485 horizontal grid points at 4 km grid spacing. Vertically, the atmosphere is modeled with 50 stretched vertical levels topped at 50 hPa. The initial and boundary conditions for WRF to dynamically downscale are from the 3-hourly 0.25\({}^{\circ}\) fifth generation atmospheric reanalysis data (ERA5) ([PERSON] et al., 2020) of the European Centre for Medium-Range Weather Forecasts (ECMWF). Here, no boundary nudging is applied so WRF is allowed to develop its own variability (e.g., spatial and internal variability) across the domain.
For the standalone WRF simulation used in this study (more details in Section 3), we used the satellite-derived LST and ice cover from the National Oceanic and Atmospheric Administration (NOAA) Great Lakes EnvironmentalResearch Laboratory (GLERL) Great Lakes Surface Environmental Analysis (GLSEA) as the overlake surface boundary condition. GLSEA LST was found to be able to capture the very fine spatial features (1.3 km) of LST better than ERAS's SST data, leading to a better model performance in air temperature, and evaporation. See [PERSON] et al. (2022) for more details about the standalone WRF model setup and difference in model performance when using different LST datasets as overlake surface boundary conditions.
### Hydrodynamic Lake and Ice Model
In our two-way coupled modeling system, WRF v4.2.2 is interactively linked to an FVCOM-based 3D lake model to simulate the hydrodynamics, thermal dynamics, and ice dynamics of the Great Lakes. FVCOM is a prognostic, free-surface, 3D primitive equation coastal ocean circulation model that is numerically solved over an unstructured triangular grid using the finite-volume method ([PERSON] et al., 2006, 2013). As mentioned in Section 1, the Great Lakes have been successfully represented in 3D within regional climate modeling systems using FVCOM (e.g., [PERSON] et al., 2020; [PERSON] et al., 2017, 2022). Similar to [PERSON] et al. (2022), the FVCOM variant used in this study is based on FVCOM version 4.1 without any nudging or other similar non-physical constraints so the lake hydrodynamic conditions freely interact with atmospheric conditions over the simulation period. WRF and FVCOM are run simultaneously with a two-way information exchange between them at 1-hr intervals using the OASIS3-MCT coupler ([PERSON] et al., 2017). Here, the LST and ice cover are dynamically calculated by FVCOM and are provided to WRF as overlake surface boundary conditions. In turn, the atmospheric forcings required by FVCOM are dynamically calculated and provided by WRF.
The horizontal resolution of the FVCOM unstructured triangular grid (Figure 2) ranges from \(\sim\)1 to 2 km near the coast to \(\sim\)2-4 km in the lake's offshore region. Vertically, the lakes are represented by 40 sigma layers to provide a vertical resolution ranging from \(<\)1 m in nearshore waters to \(\sim\)2-5 m in the lake's offshore regions. The Mellor
Figure 1: WRF’s spatial domain (green) along with the outline for the Great Lakes Basin (magenta), the Great Lakes (cyan) and the locations for National Data Buoy Center (NDBC) buoys.
Yamada level-2.5 (MY25) turbulence closure model ([PERSON], 1982) is used for simulating vertical mixing processes, including eddy viscosity and vertical diffusivities. The horizontal diffusivity, on the other hand, is calculated using the Smagorinsky numerical formulation ([PERSON], 1963). Finally, ice dynamics, ice thermal dynamics, and ice-water interaction processes are simulated by an unstructured-grid version of the Los Alamos Community Ice Code (CICE) embedded within the FVCOM framework (see [PERSON] et al. (2018) for more details).
### Observation Data for Model Validation
The spatial pattern of seasonal air temperature and precipitation over the Great Lakes region from the standalone WRF and the WRF two-way coupled with FVCOM are evaluated against the Precipitation-Elevation Regressions on Independent Slopes Model (PRISM) data set developed by [PERSON] et al. (1994, 1997, 2008). PRISM provides gridded temperature and precipitation data over the contiguous US at a spatial resolution of 1/8\({}^{\circ}\) latitude \(\times\) 1/8\({}^{\circ}\) longitude. PRISM values are corrected for systematic elevation effects by using climate-elevation regression of weighted station data, with weights being assigned based on the station's physiology. Such correction is critical as elevation plays a major role in temperature and precipitation. Additionally, observation stations over high elevated regions (e.g., Appalachian, partially covered by our study domain) are preferentially located at lower elevations which leads to an underestimation of the true reading of precipitation, and overestimation of temperature, making corrections of elevation effects crucial. While PRISM has much higher spatial resolution in comparison to other widely used datasets such as the Global Air Temperature and Precipitation compiled by the University of Delaware ([PERSON] et al., 1998) and the Climatic Research Unit data (CRU) ([PERSON] et al., 2020), it only covers the contiguous US. We, therefore, also use CRU at a grid spacing of 50 km (which covers the land of the entire globe) as the second source to evaluate the model performance of our standalone WRF and WRF two-way coupled with FVCOM. None of these observation datasets, however, have data over the Great Lakes. Thus, for air temperature, we also use the data from nine NOAA National Data Buoy Center (NDBC) scattered across the Great Lakes as shown in Figure 1.
The simulated latent and sensible heat fluxes over the lakes, which play a significant role in determining the LST of the lakes, are validated against the flux estimates derived from the NDBC buoy data. The fluxes were
Figure 2: Unstructured triangular grids (red lines) used to represent the Great Lakes in Finite Volume Community Ocean Model.
calculated using the Monin-Obukhov theory as described in [PERSON] (2002) with slight modification to the Charnock coefficient to align it with the value used in WRF (see [PERSON] et al. (2022) for more details).
Simulated LST are compared against GLSEA LST. Using satellite-derived imageries from the NOAA Advanced Very High Resolution Radar (AVHRR) and the Visible Infrared Imaging Radiometer Suite onboard the Suomi National Polar-Orbiting Partnership spacecraft (VIIRS S-NPP) and the NOAA-20 spacecraft, GLSEA produces one of the best available datasets to evaluate the spatial and temporal variability of the Great Lakes LST.
## 3 Design of Numerical Simulations
To achieve this study's objectives, two distinct model configurations (Figure 3) are used to couple WRF and FVCOM. In the first configuration, WRF is run as a standalone model with the overlake surface boundary conditions (i.e., the LST and ice cover) prescribed from the daily gridded GLSEA data, as in [PERSON] et al. (2022). GLSEA data is considered to be one of the best available representation of overfake surface boundary conditions for WRF to achieve an ideal WRF simulation; yet it is only available for historical simulations. FVCOM is then driven by the atmospheric outputs from the standalone WRF described above. This configuration is hereafter referred to as Observation-driven WRF-FVCOM (one-way) Coupling or OWFC in short. In the second configuration, WRF and the FVCOM model are run simultaneously with a two-way information exchange between them at 1-hr intervals using the OASIS3-MCT coupler. The LST and ice cover are dynamically calculated by FVCOM and are provided to WRF as overlake surface boundary conditions. Meanwhile, the atmospheric forcings required by FVCOM are dynamically calculated and provided by WRF. This configuration is hereafter referred to as WRF-FVCOM Two-way Coupling or WF2C in short. WF2C is designed to allow for as many variables as needed to be exchanged between WRF and FVCOM. A list of commonly used variables in different coupling scenarios in WF2C includes surface air temperature, surface air pressure, relative and specific humidities, total cloud cover, surface winds, downward shortwave radiation, downward longwave radiation, precipitation, evaporation, sensible and latent heat fluxes, LST, ice cover, and lake surface currents. The variables exchanged in this study under both OWFC and WF2C are illustrated in Figure 3. The difference between WF2C and OWFC is that the transfer of data between WRF and FVCOM is unidirectional in OWFC that is, FVCOM receives atmospheric forcing produced from standalone WRF simulations, and the overlake surface boundary conditions for WRF are prescribed using GLSEA data, rather than being dynamically calculated by FVCOM. On the contrary, WF2C eliminates the requirement of the observation data for the overlake boundary conditions in WRF. The LST and ice cover calculated by FVCOM, and the atmospheric variables calculated by WRF are allowed to freely interact with each other and evolve over time within WF2C. This advantage is pivotal as it sets the foundation for WF2C to be further developed to provide reliable future climate projections.
Since OWFC uses GLSEA data, which is one of the most accurate representations of LST and ice cover, to specify WRF boundary conditions while WF2C eliminates the requirement of the GLSEA data, validating WF2C's performance to be as comparable to that of OWFC would thereby attest to WF2C's ability to capture the regional climate and the lake-atmosphere dynamics of the Great Lakes. More importantly, the role of lake-atmosphere coupling on LST can be isolated and inferred from the discrepancy between the FVCOM simulated LSTs from WF2C and OWFC. Both WF2C and OWFC are initialized with the same initial condition for a continuous simulation period of May 2018 to December 2019, with May 2018 as the spinup period. Aimed for understanding the
Figure 3: Schematic view of the configurations of (a) OWFC and (b) WF2C.
impact of lake-atmosphere coupling on summer LST, when the lake thermal structure is complex with stratification, the validation and analysis for this study are focused on the summer (June, July, August (JJA)) and fall (September, October, November (SON)) seasons of 2018 and 2019.
## 4 Model Evaluations
### Air Temperature and Precipitation
As mentioned in Section 3, as OWFC relies on GLSEA data for an accurate representation of LST and ice cover to drive WRF, whereas WF2C does not, we expect that if the two-way coupling between WRF and FVCOM performs well, then OWFC and WF2C will have similar performance in reproducing the air temperature and precipitation over the Great Lakes region when compared to CRU, PRISM and NDBC buoys (Figures 4, 6, and 7). The comparison of spatial distribution of seasonal air temperature from PRISM, CRU, OWFC, and WF2C are shown in Figure 4. CRU, which has a coarser spatial resolution than PRISM, produces a similar spatial distribution of air temperature to PRISM for the US Great Lakes region. As shown in Figure 4, overdland, the spatial correlations of WF2C with CRU and PRISM, which are 0.943 and 0.951 for JJA, respectively, and 0.975 and 0.980 for SON, respectively, are similar or slightly higher than the correlation between OWFC and the observation datasets. WF2C captures the meridional gradient in air temperature well with higher air temperature simulated for lower latitudes. Higher air temperature observed in the southwestern portion during JJA is also replicated by WF2C. The root mean square difference (RMSD) of WF2C with CRU and PRISM are relatively small with 1.565\({}^{\circ}\)C and 0.832\({}^{\circ}\)C for JJA respectively and 1.527\({}^{\circ}\)C and 0.929\({}^{\circ}\)C for SON respectively. These RMSDs of WF2C are similar or slightly smaller than the RMSDs of OWFC. Also, in general, the correlations are higher and RMSDs are smaller when comparing the models with PRISM than with CRU, indicating the importance of high spatial resolution observation datasets when evaluating high resolution models.
Over the lakes, both WF2C and OWFC have very high spatial correlation to each other but WF2C simulates noticeably warmer air than OWFC during JJA, especially over Lake Superior (Figure 5). The air over the central basin of Lake Superior is warmer by up to 3\({}^{\circ}\)C in WF2C relative to OWFC. The warmer overlake air also affects Lake Superior's summer LST which is discussed in Section 4.3 and Section 5. In comparison to the overlake
Figure 4: Spatial distribution of near surface air temperature (T2) from CRU (a, e), PRISM (b, f), OWFC (c, g) and WF2C (d, h) in JJA and SON averaged over 2018 and 2019. Figure panels c, d, g and h have the spatial correlation (COR) and the root mean square difference of the models with CRU and PRISM (in that order).
air temperature from the buoys across the Great Lakes, WF2C and OWFC both reproduce the air temperature remarkably well (Figure 6). They perform similarly to each other with both WF2C and OWFC having a correlation >0.945 and an RMSD <1.5\({}^{\circ}\)C with buoy observations, except for the month of July in Lake Superior (Figures 6a, 6d, and 6f), where WF2C overestimates the air temperature.
Although the primary focus of this study is on summertime, and both WF2C and OWFC have been successfully calibrated and validated for summer and fall, it's worth noting that the current WRF configuration exhibits a relatively larger cold bias for near-surface air temperature during winter and spring, reaching up to 5\({}^{\circ}\)C over some locations. Employing the Noah-MP land surface model ([PERSON] et al., 2011) can partially mitigate this cold bias in air temperature during these seasons, but it tends to produce a larger warm bias in other seasons. As such, future investigations will be necessary to address the limitations of the WRF model when simulating colder seasons.
Figure 7 compares the summer and fall precipitation patterns over the Great Lakes region between the observation datasets and the models. Unlike in air temperature, PRISM and CRU differ noticeably with PRISM unsprisingly having finer spatial variations due to its higher spatial resolution. Both OWFC and WF2C successfully reproduce PRISMs finer spatial variations in precipitation that are absent in CRU such as the higher precipitation upwind of the Great Lakes (e.g., in Wisconsin) likely caused by mesoscale convective systems and downwind of Great Lakes (e.g., southeast of Lake Erie) likely caused by isolated deep convections ([PERSON] et al., 2022). As such, this serves as an excellent illustration of why it is preferable to use high-resolution observation datasets like PRISM for validating the models. Upon closer examination, we see the WF2C performs slightly better than OWFC when validating against PRISM. Compared to OWFC, WF2C exhibits a marginally smaller RMSD when compared with CRU and PRISM with 1.077 mm/day and 1.324 mm/day for JJA respectively and 1.024 mm/day
Figure 5.— Spatial distribution of near surface air temperature (T2) from WF2C (a, d), OWFC (b, e) and their difference (c, f) in JJA and SON averaged over 2018 and 2019. Figure panels c and f have the spatial correlation (COR) and the root mean square difference between WF2C and OWFC for JJA and SON respectively. Figure panels a, b, d, and e are the same as Figures 4d, 4c, 4h, and 4g respectively but with the near surface air temperature over the lakes included.
and 1.217 mm/day for SON respectively. The spatial correlations of WF2C with CRU and PRISM are 0.461 and 0.362 for JIA respectively and 0.523 and 0.568 for SON respectively, which are generally slightly higher than the correlation of OWFC with CRU and PRISM (Figure 7).
Figure 6.— Observed air temperature from nine NDBC buoys (blue) and the simulated air temperature from WF2C (orange) and OWFC (yellow) at the nine buoy locations (Figure 1) averaged over 2018 and 2019. Each figure panel provides the spatial correlation (COR) and the root mean square difference of WF2C and OWFC with the buoy data.
### Latent and Sensible Heat Fluxes
Figure 8 presents a temporal and statistical comparison of latent and sensible heat fluxes between the buoys, WF2C, and OWFC. Both WF2C and OWFC effectively reproduce the seasonality of the fluxes. They capture not only the overall magnitude of the fluctuations, but also the rapid changes in sensible heat on daily to weekly scales in the fall (Figure 8a-8j). Compared to OWFC, statistically, WF2C has a noticeably higher correlation with observations as well as lower RMSD (Figures 8k and 8l). In particular, for Buoy 45001 in Lake Superior, during July, OWFC overestimates a large outgoing latent and sensible heat fluxes while the buoy data suggests that the fluxes are incoming fluxes of relatively smaller magnitudes. WF2C, in contrast, aligns more closely with the buoy data. For latent heat flux, the average correlation between observation and WF2C is higher than between observation and OWFC by 0.05 while the average RMSD of WF2C is smaller than that of OWFC by 2.85 W/m\({}^{2}\). For sensible heat flux, the average correlation between observation and WF2C is higher than that between observation and OWFC by 0.06 while the average RMSD of WF2C is smaller than the average RMSD of OWFC by 2.06 W/m\({}^{2}\).
### Lake Surface Temperature
The spatiotemporal comparison of LST between GLSEA, OWFC, and WF2C is shown in Figure 9. During June to November, the Great Lakes undergo an increase and a subsequent decrease in LST with distinct spatial differences in the meridional direction. As the northernmost and the deepest lake, Lake Superior is always the coolest lake while Lake Erie, being the southernmost and shallowest lake, is the warmest lake. This warming gradient is particularly noticeable in July as Superior maintains a lakewide average LST of \(\sim\)13\({}^{\circ}\)C while Lake Erie uniformly warms to a lakewide average of \(\sim\)24\({}^{\circ}\)C. Both WF2C and OWFC capture this inter-lake variation very well, although both produce a noticeable warm bias for Lake Superior in July. The models are also able to capture the spatial heterogeneity within each lake such as the distinct north-south gradient in Lakes Michigan during July-August (Figures 9e-9k) and the distinct east-west gradient in Lake Erie during September (Figures 9m-9o).
In addition to resolving the spatial variability of monthly LST, WF2C and OWFC also track the magnitude and the temporal evolution of the lakewide average LST well (Figure 10). Both WF2C and OWFC have good
Figure 7: Spatial distribution of precipitation from CRU (a, b), PRISM (c, d), OWFC (e, f) and WF2C (g, h) in JJA and SON averaged over 2018 and 2019. Figure panels c–h have the spatial correlation (COR) and the root mean square difference of the models with CRU and PRISM (in that order).
Figure 8.— Latent (a, c, e, g, i) and sensible (b, d, f, h, j) heat fluxes from NDBC buoys (blue), WF2C (orange) and OWFC (yellow) averaged over 2018 and 2019. Only one buoy from each lake is considered in this figure as the other buoys show similar results. Additionally, Buoy 45003 in Lake Huron and Buoy 45006 in Lake Superior are not included in this figure as they do not have latent heat flux estimates due to missing observation of dew point temperature. Negative (positive) radiation values represent outgoing (incoming) fluxes. Figure panels k and l plots the spatial correlation (COR) and the root mean square difference of WF2C and OWFC with the buoy data. WF2C are represented in blue symbols and OWFC are represented in red symbols. Buoys 45001, 45002, 45005, 45008, and 45012 are represented by cross, circle, diamond, plus and square symbols respectively.
correlation (\(>\)0.960) and RMSD (\(<\)2\({}^{\circ}\)C) when compared with GLSEA. Looking at the previous studies that used 1D ([PERSON] et al., 2014; [PERSON] et al., 2015) and 3D lake models ([PERSON] et al., 2013; [PERSON] et al., 2017, 2022), it is clear that such a close tracking of LST, particularly the spring-early summer warming and the summer peaks, is only achievable through the use of 3D lake models. The models, however, do have some biases including a warm and cold bias during July-September of Lake Superior (\(\sim\)2\({}^{\circ}\)C) and a persistent cold bias in Lake Ontario (\(\sim\)2-3\({}^{\circ}\)C). Such LST biases can be expected as modeling the physical processes of deep lakes is challenging ([PERSON] et al., 2013; [PERSON] et al., 2014; [PERSON] et al., 2016; [PERSON] et al., 2017) and Lake Superior and Lake Ontario are the deepest and second deepest lakes among the Great Lakes in terms of average depth, respectively. Nevertheless, when compared to a more constrained, atmospheric data-driven driven FVCOM simulation such as the standalone FVCOM driven by reanalysis data in [PERSON] et al. (2013), both WF2C and OWFC perform admirably. For example, in Lake Superior and Erie, both WF2C and OWFC produce a lower lakewide average LST RMSD than [PERSON] et al. (2013) by \(\sim\)0.15\({}^{\circ}\)C and \(\sim\)1.3\({}^{\circ}\)C respectively. For Lake Ontario, [PERSON] et al. (2013) has a lakewide
Figure 9: Spatial distribution of lake surface temperature from Great Lakes Surface Environmental Analysis, OWFC, WF2C and WF2C minus OWFC during each month from June to November averaged over 2018 and 2019.
average LST RMSD of 1.14\({}^{\circ}\)C while both WFC and OWFC have just slightly higher RMSDs of 1.80\({}^{\circ}\)C and 1.91\({}^{\circ}\)C respectively.
The performance of WF2C and OWFC in reproducing LST is quite similar, with WF2C generally achieving a similar, if not slightly lower, RMSD than OWFC for the lakewide average LST (by up to 0.117\({}^{\circ}\)C) for all lakes, with the exception of Lake Superior. The apparent discrepancies in Lake Superior between WF2C and OWFC during July and August is noteworthy (Figures 9, 9, and 10a). For July, while both OWFC and WF2C produce a warm bias for the lakewide average LST, WF2C has a higher bias of \(\sim\)2\({}^{\circ}\)C and OWFC has a lower bias of \(\sim\)1\({}^{\circ}\)C. It is interesting to note that even though OWFC overestimates a large outgoing latent and sensible flux (Figures 8a and 8b)--which would favor a cooling of LST--it still produces a warm LST bias in July. This suggests that changes in other variables within OWFC, such as radiation fluxes and lake mixing, are compensating for the
Figure 10. Daily lake surface temperature from June to November from Great Lakes Surface Environmental Analysis (GLSEA), WF2C and OWFC for Lake Superior (a), Michigan (b), Huron (c), Erie (d) and Ontario (e) averaged over 2018 and 2019. Each figure panel provides the spatial correlation (COR) and the root mean square difference of WF2C and OWFC with GLSEA.
outgoing latent and sensible fluxes, preventing the LST from dipping below the observed value. Similarly, even though WF2C's latent and sensible heat fluxes closely track the observation, it still has a \(\sim\)2\({}^{\circ}\)C bias, implying that other variables must be playing a role in warming the simulated LST. For August, WF2C accurately captures the peak LST magnitude while OWFC underestimates the peak by \(\sim\)2\({}^{\circ}\)C. This discrepancy is likely due to their respective simulated antecedent (July) LST, as well as the synchronic surface heat fluxes and lake hydrodynamic conditions in August. The difference between WF2C and OWFC fundamentally stems from the presence and absence of information exchange between FVCOM and WRF that is, lake-atmosphere coupling. It is therefore possible to infer and examine the impact that lake-atmosphere coupling has on Lake Superior's summer LST through our twin experiment of WF2C and OWFC (discussed in Section 5).
## 5 Impact of Coupled Lake-Atmosphere Dynamics in Summer LST Simulation
Understanding the impact of coupled lake-atmosphere dynamics on the simulation of the Great Lakes LST is critical not only for explaining observed historical warming but also for ensuring the accuracy of future LST projections, which inevitably rely on a coupled lake-atmosphere system. Current understanding is hampered by the prevalent use of 1D lake models in regional climate modeling, which results in an insufficient representation of coupled lake-atmosphere dynamics and leads to a drift in simulated LST from its true state. The two-way coupled WRF-FVCOM system offers us the opportunity to examine how lake-atmosphere coupling could impact the Great Lakes LST by deriving insights from the discrepancies between WF2C and OWFC simulations. In this section, we focus on the role of lake-atmosphere coupling in influencing the summer LST simulation of Lake Superior, the largest and deepest one among the five lakes, which contains more than 50% of total water mass of the Great Lakes. Lake Superior's hydrodynamic summer is typically considered to be from July-September, a period during which the lake exhibits the warmest surface temperature. Hence, our analysis in this section focuses on the period from late spring to the end of the hydrodynamic summer, that is, from June to September.
Our experiment shows that coupled lake-atmosphere dynamics increases the simulated summer LST (i.e., the differences between WF2C and OWFC) as shown in Figure 11. LST from WF2C is consistently higher than LST from OWFC during June-September. The trend and magnitude of the LST difference between WF2C and OWFC are very similar in both years, suggesting it is a consistent pattern due to lake-atmosphere coupling rather than being an isolated episodic event. The increase in LST commences from mid-June, reaching a peak in late July or
Figure 11: Daily Lake Superior lake surface temperature from WF2C and OWFC during June to September in 2018 (a) and 2019 (c). The differences between WF2C and OWFC are shown in figure panels (b) and (d) for 2018 and 2019 respectively.
early August with a magnitude of approximately +1.3\({}^{\circ}\)C. The increase in LST is then more or less sustained until mid-August after which it suddenly drops and gradually levels out at around +0.3\({}^{\circ}\)C.
The lake-atmosphere coupling elevates the summer LST by modifying the surface heat fluxes going into or out of the lake. The surface heat fluxes responsible for LST changes are upward longwave radiation (ULW), downward longwave radiation (DLW), sensible heat flux (SH), latent heat flux (LH) and net shortwave radiation (NSW). The Net Heat (aggregate of ULW, DLW, SH, LH and NSW) that the lake receives is the primary driving factor for lake warming. The magnitude of the surface heat fluxes in both WF2C and OWFC for June 2018 are compared in Figure 12. By examining the differences between WF2C and OWFC for June 2018, we see that the lake-atmosphere coupling results in a higher Net Heat into the lake (by 11.02 W/m\({}^{2}\)). This increase in Net Heat is primarily due to the increase in the SH entering the lake (by 5.01 W/m\({}^{2}\)) and decreases in the LH exiting the lake (by 6.41 W/m\({}^{2}\)). Figure 13a summarizes these differences in surface heat fluxes between WF2C and OWFC for June 2018. Figures 13b-13h similarly encapsulate the differences for other months.
Figure 13 shows that, due to the lake-atmosphere coupling, the lake gains more energy (positive Net Heat change) in June and July and gains less energy (negative Net Heat change) in August and September. The most significant heat gain occurs in July, with 22.07 W/m\({}^{2}\) in 2018 and 23.33 W/m\({}^{2}\) in 2019. The largest loss is in September, with 16.26 W/m\({}^{2}\) in 2018 and 29.21 W/m\({}^{2}\) in 2019. The energy gain (loss) is primarily due to the decrease (increase) of outgoing latent heat and increase (decrease) in the incoming sensible heat. Importantly, note that the changes in Net Heat between WF2C and OWFC and the changes in LST between WF2C and OWFC are not synchronous due to the lake seasonal mixing, as depicted in Figure 14.
In the unstratified waters of June, even though more heat (positive Net Heat change) is directed into the lake in WF2C, the surplus heat disperses throughout the water column, leading to a very minor increase in LST when compared to OWFC. Then in July, as shown in Figure 11, the LST in WF2C undergoes a rapid increase relative to OWFC. This rapid warming is due to two reasons. First, the surplus heat is the largest in July and second, the water is stratified in July, which creates an ideal condition for the warming to be restricted just to the surface layer of the water. Later in August, less heat (negative Net Heat change) enters the lake in WF2C compared to OWFC, which curtails the rapid LST increase seen in July. However, the reduced heat input in WF2C, combined with the fully stratified water, is sufficient to sustain (but not further increase) the LST difference between WF2C and OWFC established in July. Finally, in September, the combination of weakening stratification and further reduction of the incoming heat in WF2C relative to OWFC leads to a diminishing LST difference between the two simulations, culminating in a convergence of the LSTs from the two simulations (Figure 11). It is intriguing to observe the slightly warmer deeper waters of OWFC during August and September shown in Figure 14. This occurs, in part because, in the WF2C model, a higher LST along with stronger stratification slows down the vertical water mixing, thereby keeping the deeper water cooler during the July-August period, while keeping the upper layer warmer. Conversely, in the OWFC model, the relatively weaker stratification facilitates an easier distribution of heat throughout the water column. This results in the deeper waters of OWFC being slightly warmer than those in WF2C, with a correspondingly cooler upper layer.
Figure 12. Magnitude of surface heat fluxes (in W/m\({}^{2}\)) in June 2018 for Lake Superior from WF2C (left) and OWFC (right). The arrows pointing down (yellow) are surface heat fluxes that put heat into the lake. The arrows pointing up (red) are surface heat fluxes that take heat from the lake. The arrows are overlaid on top of a spatial map of the lake’s lake surface temperature for June 2018. See Table S1 in Supporting Information S1 for a tabular format.
Figure 13. Differences between WF2C and OWFC in surface heat fluxes from June–September 2018 (left panels) and June–September 2019 (right panels). The arrows pointing down (yellow) are surface heat fluxes that put heat into the lake. The arrows pointing up (red) are surface heat fluxes that take heat from the lake. Negative values mean the flux has a lower magnitude in WF2C than OWFC. Positive values mean the flux has a higher magnitude in WF2C than OWFC. See Tables S1 and S2 in Supporting Information S1 for a tabular format.
As discussed above, lake-atmosphere coupling affects the modeled LST by modifying surface heat fluxes between WF2C and OWFC. This is realized through lake-atmosphere coupling influencing various meteorological state variables interacting with LST. The impact of lake-atmosphere coupling on surface heat fluxes and the associated meteorological state variables are demonstrated in Figure 15 for 2018 and Figure 16 for 2019. For instance, the changes in SH are mainly due to the changes in the difference between air temperature and LST. In June and July, the air temperature increases more rapidly than the LST. This leads to a larger increase in the difference between air temperature and LST, resulting in an increase in SH in the 2 months when comparing WF2C and OWFC simulations (Figures 15), 15, 16), and 16). Similarly, the changes in LH (Figures 15 and 16) are due to the changes in the difference between saturated and actual specific humidity (Figures 15 and 16). Although wind speed is also one of the factors that affects sensible and latent heat flux, the changes in wind speed averaged over the entire lake are relatively small (Figures 15 and 16).
These causal relationships of sensible and latent heat flux with the meteorological state variables are represented by the bulk transfer equation of heat fluxes ([PERSON], 2001). The ULW and DLW are also largely controlled by the state of LST and air temperature, as expressed by the Stefan-Boltzmann law of radiation (Figures 15, 15, 16, and 16). These interactive processes further impact atmospheric conditions such as cloud formation and NSW. However, it is important to note that more comprehensive analysis is needed to disentangle the detailed processes that led to these changes. This includes examining both large-scale and local forcings, along with the interactions among various atmospheric state variables.
## 6 Discussion
### Sensitivity of Model LST to Varying Coupling Approaches
In the previous section, we showed that the warm bias in Lake Superior in July is larger in WF2C than in OWFC. While there are a number of factors in the model configurations that affects model performance--such as grid resolution, WRF domain and lateral boundary forcing, WRF parameterization schemes (for microphysics, cumulus convection, planetary boundary layer, radiation, and land surface), and FVCOM turbulent schemes--this is not the main focus of this study. This study concentrates on the impact of lake-atmosphere coupling on LST, as reflected in the difference between WF2C and OWFC simulations under identical model configuration except with and without two-way coupling. With that in mind, we wanted to ensure that such a difference was not caused by any potential inconsistencies in the calculation of fluxes in WRF and FVCOM. Specifically, in the state-variable-based coupling described above, WRF and FVCOM directly exchange state variables and calculate fluxes within each model separately; meteorological variables such as wind, air temperature, cloud coverage, and relative humidity are transferred from WRF to FVCOM. This method, widely used in coupled ocean-atmosphere or lake-atmosphere coupling, can provide more accurate results by leveraging the different grid resolutions in atmospheric and hydrodynamic models ([PERSON] et al., 2020; [PERSON] et al., 2010; [PERSON] et al., 2015, 2017), given both models have compatible formulations for computing the fluxes. Within FVCOM, the Coupled Ocean-Atmosphere
Figure 14: The vertical profiles of Lake Superior near the NDBC Buoy 45001 location for June–September 2018.
Figure 15: First column: magnitude of lake surface temperature (LST) (a), near surface air temperature (T2) over the lake (e), near surface air temperature over the lake minus LST (i), saturated specific humidity minus near-surface specific humidity over the lake (m), cloud cover over the lake (q) and wind speed over the lake (u) for 2018. Second column: difference between WF2C and OWFC for the adjacent first column panel’s atmospheric variable. Third column: magnitude of ULW (c), DLW (g), SH (k), LH (o), NSW (s) and Net Heat (w) for 2018. Positive fluxes represent surface heat fluxes that put heat into the lake while negative fluxes represent surface heat fluxes that take heat from the lake. Fourth column: difference between WF2C and OWFC for the adjacent third column panel’s surface heat fluxes. See Table S1 in Supporting Information S1 for exact numbers.
Figure 16: First column: magnitude of lake surface temperature (LST) (a), near surface air temperature (T2) over the lake (e), near surface air temperature over the lake minus LST (i), saturated specific humidity minus near-surface specific humidity over the lake (m), cloud cover over the lake (q) and wind speed over the lake (u) for 2019. Second column: difference between WF2C and OWFC for the adjacent first column panel’s atmospheric variable. Third column: magnitude of ULW (c), DLW (g), SH (k), LH (o), NSW (s) and Net Heat (w) for 2019. Positive fluxes represent surface heat fluxes that put heat into the lake while negative fluxes represent surface heat fluxes that take heat from the lake. Fourth column: difference between WF2C and OWFC for the adjacent third column panel’s surface heat fluxes. See Table S2 in Supporting Information S1 for exact numbers.
Response Experiment (COARE3) ([PERSON] et al., 2018; [PERSON] et al., 2014; [PERSON] et al., 2003) scheme is used to calculate surface fluxes based on these atmospheric variables and the LST. Conversely, lake temperature and ice cover from FVCOM serve as WRF's over-lake boundary conditions, and WRF uses the revised MM5 surface layer scheme to calculate surface fluxes ([PERSON] et al., 2012). While both schemes are based on the Monin-Obukhov similarity theory, and the revised MM5 surface layer scheme indeed adopts the COARE3 similarity function for unstable atmospheric conditions, it is important to ensure that both schemes compute compatible fluxes for consistency. In other words, we need to ensure that the warmer LST in WF2C in Lake Superior in July is not due to the use of different surface flux schemes in FVCOM and WRF.
Therefore, we implemented an alternative flux-based coupling approach for cross-validation ([PERSON] et al., 2014; [PERSON] et al., 2014, 2020). In the flux-based coupling, WRF and FVCOM directly exchange surface fluxes of energy, momentum, and mass across the lake-atmosphere interface. Specifically, FVCOM provides WRF with LST and ice cover as its overlake boundary conditions. Meanwhile, FVCOM directly receives calculated fluxes from WRF as driving forces, instead of calculating surface fluxes within FVCOM. These fluxes include heat/radiation fluxes (sensible, latent, longwave, and shortwave radiation) and momentum flux (wind stress). This flux-based coupling approach ensures strict consistency in the fluxes exchanged between the lake and atmosphere within both the atmospheric model and lakes, as they are all calculated within WRF. However, it does not allow WRF and FVCOM to leverage their varying spatial resolutions to calculate surface fluxes.
In our case, the two coupling approaches--flux-based and state-variable-based--exhibit highly consistent results when the grid resolutions of WRF and FVCOM are similar (WRF: 4 km and FVCOM: 1-4 km). This comparison addressed our concern about any potential inconsistency arising from using the revised MM5 surface layer scheme in WRF and the COARE3 scheme in FVCOM. As shown in Figure 17, there is only a 2% difference (\(\sim\)0.16\({}^{\circ}\)C) in the simulated LSTs between the flux-based coupling and state-variable-based coupling in our case, with the warming patterns being nearly identical. Therefore, the differences in warming between WF2C and OWFC indeed stems from the two-way coupling of WRF and FVCOM and is not related to the different surface flux schemes in FVCOM and WRF.
### Computational Cost
The computational effort differs between running WF2C and OWFC, with WF2C requiring approximately 1.1-1.3 times more computational time than OWFC. This is due to the end-to-end coupling process in WF2C. The increase in computational time stems from two major factors: (a) the extra time required for data exchange at each coupling time step, and (b) the inconsistent computing time required by the two coupled components. That is, the slower model determines the overall performance, as both models must reach the same simulation step before data exchange can occur, causing the faster model to idle while waiting for the slower one. This difference in computation time could be significant, especially for multi-decadal simulations. Given the comparable
Figure 17: Comparison of simulated lake surface temperature using flux-based coupling and state-variable-based coupling for Lake Superior.
performance of WF2C and OWFC, OWFC could still be a viable option when one is only interested in historical simulations. However, OWFC is not suitable for future projections due to its inherent reliance on a robust observational LST data set, which is required by the atmospheric model (WRF) as the lower boundary condition.
### WF2C's Potential for Long-Term Climate Simulation
We acknowledge that more extended simulations are crucial for a comprehensive evaluation of the WF2C's performance in long-term climate simulation. However, it's important to highlight that our 2-year simulation yielded valuable insights, particularly in the context of long-term climate modeling. Our 2-year simulation was designed to investigate whether the observed warming bias in the WF2C would progressively intensify, thereby causing the model to gradually deviate from real-world conditions. If this scenario were to manifest, WF2C would fail to qualify for further application in long-term, climate-scale simulations. In contrast, we observed that the warm bias emerged annually, following a consistent pattern, and crucially, this bias subsided and lessened during the autumn months in the lake-atmosphere coupled simulation. This implies that the warm bias does not perpetually accumulate over years; thereby, providing us with confidence in WF2C's potential for further development for long-term simulations and future projections.
## 7 Conclusion and Summary
In this study, we developed a fully coupled modeling system (WF2C) with WRF and FVCOM to accurately capture the Great Lakes and its two-way interaction with the atmosphere. We also developed an observation-driven WRF-FVCOM (one-way) Coupling (OWFC) in which we first ran a standalone WRF that uses satellite-derived LST and ice cover from GLSEA as overlake surface boundary conditions and then used the standalone WRF output to drive FVCOM to simulate the 3D status of the lakes. The fundamental distinction between WF2C and OWFC simulation lies in the fact that in WF2C, the overlake surface boundary condition for WRF is dynamically calculated by FVCOM, while in OWFC, the overlake surface boundary condition for WRF needs to be prescribed using observational data of LST and ice cover (GLSEA). WF2C and OWFC were validated against in-situ and satellite-based observation datasets, with both showing strong performance in reproducing the historical conditions of the Great Lakes during summer and fall.
OWFC simulations, due to their dependence on satellite-derived LST and ice cover for defining overlake surface boundary conditions, are suited only for historical analysis. On the other hand, W2 FC can potentially be utilized for future climate projections as it allows the lake hydrodynamic conditions and atmospheric conditions to evolve internally, with the atmosphere and lake and freely interacting with each other over the entire course of climate simulation. The fact that WF2C has achieved similar performance to the OWFC while eliminating the requirement of the GLSEA data is exciting because it sets the foundation for future studies to explore WF2C's potential to produce reliable climate projections and accurately simulate the lake-atmosphere dynamics of the Great Lakes under future climate conditions that could differ significantly from climate condition represented in the observational record.
We also used the WF2C and OWFC simulations to analyze the role of lake-atmosphere two-way coupling in affecting the simulated components of the summertime lake-atmosphere surface heat fluxes over Lake Superior. This analysis is vital not only for accurately simulating LST, but also for effectively evaluating, understanding, and documenting the behavior of the newly developed model. Acknowledging both its strengths and limitations is crucial to the model's continual development. Our study highlights that in any coupled-model development, the two-way coupling process inherently permits free interactions between different model components. This allows for unimpeded propagation of dynamic processes and sometimes also leads to amplification of perturbations and errors within the coupled system. The warm biases in this case, are an example of how errors can propagate and amplify, but they could also manifest as cold biases or other formats, depending on model configurations. It is essential that these phenomena are not only accurately documented, but also thoroughly understood by the model development community.
By inferring the impact of coupled lake-atmosphere dynamics from the difference between WF2C and OWFC, our results show that lake-atmosphere coupling in WF2C can lead to higher LST during the summer period through modifying surface heat fluxes and influencing various meteorological state variables interacting with LSTs. Notably, although OWFC seems to have a smaller warm bias in simulating July LST than WF2C does,OWFC actually overestimates the outgoing latent and sensible heat fluxes when compared to observation. Furthermore, WF2C has a larger warm bias of July LST and overlake air temperature than OWFC despite having a better reproduction of latent and sensible heat fluxes than OWFC, as discussed in Section 4. The overestimation of LST can be caused by a combination of various factors including the atmospheric ([PERSON] et al., 2022) and hydrodynamic processes ([PERSON] et al., 2019) simulated in each model as well as the lake-atmosphere coupling.
Comparisons in the simulated surface heat fluxes in WF2C and OWFC clearly reveal new processes are activated in the WF2C simulation, underscoring the importance of coupling for accurate prediction of lake-atmosphere heat exchange. These mechanisms are currently not well understood and warrant more focused investigation in the future Great Lakes studies. These results highlight the complexity of the coupled lake-atmosphere system and sheds light on the importance of process-oriented studies to reveal key processes that influence the model state and allow us to improve regional climate simulations. This study identified lake-atmosphere coupling as a necessary feature of Great Lakes hydrodynamic simulations, as it provides reasonably accurate estimates of summer LST and surface heat fluxes even for simulation unconstrained by observations.
Lastly, while our study focused on summertime lake-atmosphere interaction and their impacts on LST, it is important to note that during the colder months of the year, snow and ice are also a major part of the lake-atmosphere interaction. For example, ice cover over the lakes acts as a physical barrier between the lake and the atmosphere, thus affecting the surface heat fluxes ([PERSON] et al., 2020; [PERSON] et al., 2013). These new variables, which come into play during the colder seasons, add another layer of complexity to the coupled system. This complexity is exemplified by our WRF configuration which produces a relatively larger cold bias during winter and spring while performing remarkably well during summer and fall. So future studies should carefully consider snow and ice cover to provide an annual picture of the importance of lake-atmosphere coupling on the Great Lakes hydrodynamic and regional climate simulations.
## Data Availability Statement
The source codes for the two-way coupled WRF and FVCOM used in this study are available at [[https://doi.org/10.5281/zenodo.7574675](https://doi.org/10.5281/zenodo.7574675)]([https://doi.org/10.5281/zenodo.7574675](https://doi.org/10.5281/zenodo.7574675)) ([PERSON], 2023b) and [[https://doi.org/10.5281/zenodo.7574673](https://doi.org/10.5281/zenodo.7574673)]([https://doi.org/10.5281/zenodo.7574673](https://doi.org/10.5281/zenodo.7574673)) ([PERSON], 2023a) respectively. Observation datasets used in this study may be openly accessed and downloaded at the following webpages: ERA5: [[https://doi.org/10.24381/cds.adbb2d47](https://doi.org/10.24381/cds.adbb2d47)]([https://doi.org/10.24381/cds.adbb2d47](https://doi.org/10.24381/cds.adbb2d47)) ([PERSON] et al., 2023), PRISM: [[https://prism.oregon-state.edu/](https://prism.oregon-state.edu/)]([https://prism.oregon-state.edu/](https://prism.oregon-state.edu/)) (PRISM Climate Group, 2016), CRU: [[https://crudata.uea.ac.uk/cru/data/nrg/](https://crudata.uea.ac.uk/cru/data/nrg/)]([https://crudata.uea.ac.uk/cru/data/nrg/](https://crudata.uea.ac.uk/cru/data/nrg/)) (Climatic Research Unit & NCAS, 2023; [PERSON] et al., 2020), NDBC: [[https://www.ndbc.noaa.gov/](https://www.ndbc.noaa.gov/)]([https://www.ndbc.noaa.gov/](https://www.ndbc.noaa.gov/)) (NDBC, 2023) and GLSEA: [[https://coastwatch.glerl.noaa.gov/glsea/doc](https://coastwatch.glerl.noaa.gov/glsea/doc)]([https://coastwatch.glerl.noaa.gov/glsea/doc](https://coastwatch.glerl.noaa.gov/glsea/doc)) (GLSEA, 2023).
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wiley/fb518f84_e214_4f46_a01f_31de0471749a.md | # Water Resources Research
Early Warning Indicators of Groundwater Drought in Mountainous Regions
[PERSON]\({}^{1}\)
\({}^{1}\)Department of Earth Sciences, Simon Fraser University, Burnaby, BC, Canada, \({}^{2}\)River Forecast Centre, Ministry of Forests, Victoria, BC, Canada
[PERSON]\({}^{1}\)
\({}^{1}\)Department of Earth Sciences, Simon Fraser University, Burnaby, BC, Canada, \({}^{2}\)River Forecast Centre, Ministry of Forests, Victoria, BC, Canada
[PERSON]\({}^{2}\)
\({}^{1}\)Department of Earth Sciences, Simon Fraser University, Burnaby, BC, Canada, \({}^{2}\)River Forecast Centre, Ministry of Forests, Victoria, BC, Canada
###### Abstract
Aquifers in mountainous regions are susceptible to drought. However, the diverse hydroclimatology, the small and responsive aquifers, and the varied nature of interactions between groundwater and surface water lead to complex groundwater level responses that are challenging to interpret for understanding groundwater drought. In this study, generalized additive models (GAMs) are used to explore the sensitivity of summer groundwater levels to various climate and hydrological predictor variables (indicators) in each of a snowmelt- and rainfall-dominated hydroclimatic regime in British Columbia, Canada. A sensitivity analysis explores individual seasonal predictor variables, station versus gridded climate data, teleconnection indices, and time series length. GAMs are then generated for different combinations of predictor variables to identify the best combination for each region. In the snowmelt-dominated regime, maximum spring temperature, maximum snow water equivalent, and the winter Nino 3.4 index is the best combination of variables for predicting summer groundwater levels. In the rainfall-dominated regime, maximum spring temperature, winter precipitation, and spring streamflow is the best combination. The unique combinations of predictor variables for each region can be used as early warning indicators for groundwater drought preparedness by water managers prior to the beginning of the summer. The Standardized Groundwater Level Index (SGI) is also effective at indicating which wells had pronounced responses to periods of drought in each region. However, the SGI differed among aquifers of similar type, suggesting other factors such as aquifer response mechanism and groundwater pumping may have an important influence on the SGI.
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These decreases can occur on different time scales, from months to years to decades due to the lag in response time of aquifers ([PERSON] & [PERSON], 2010; [PERSON] & [PERSON], 2000). If the groundwater levels have decreased below a critical (or threshold) level over a certain time period of time, a groundwater drought is said to have occurred ([PERSON] & [PERSON], 1996; [PERSON] & [PERSON], 1999).
The groundwater response to changing recharge conditions can be highly diverse, both on small and large scales ([PERSON] et al., 2015; [PERSON] & [PERSON], 2017; [PERSON] et al., 2016; [PERSON] et al., 2014). [PERSON] et al. (2016) and [PERSON] et al. (2014) consistently found that typical timescales of drought propagation into groundwater are site-specific. Thus, while the occurrence of groundwater drought is closely linked to meteorological input, it is also influenced by the surface and subsurface properties ([PERSON] et al., 2022; [PERSON] & [PERSON], 2010). The absolute elevation of a catchment, for example, can influence snow storage and the timing of melt ([PERSON] & [PERSON], 2015). The subsurface hydraulic properties (i.e., hydraulic conductivity and specific storage) influence the groundwater level response. Low storage or fast responding aquifers such as karst and fractured bedrock aquifers are sensitive to drought, while high storage or slower responding aquifers of porous media are less sensitive ([PERSON] et al., 2014) and thus can buffer hydroclimatic variations and drought propagation ([PERSON] & [PERSON], 1999; [PERSON] et al., 2021; [PERSON] et al., 2003). A slow response also means that the aquifer has memory ([PERSON] et al., 2022; [PERSON] et al., 2022; [PERSON] et al., 2014); therefore, antecedent recharge conditions are a key factor for groundwater drought severity.
Aquifers in mountainous regions are susceptible to drought (e.g., Europe: [PERSON] et al., 2016; Germany: [PERSON] & Schmalz, 2021; Scotland: [PERSON] et al., 2021; Central-Western Argentina: [PERSON] et al., 2021; Alpine European Region: [PERSON] et al., 2021; China: [PERSON] et al., 2021; Southwestern United States: [PERSON] & [PERSON], 2016). However, the diverse hydroclimatology (snowmelt and/or rainfall dominated); topography (high relief, steep slopes, deeply incised valleys); variable bedrock and alluvium geological conditions ([PERSON] & [PERSON], 2004); nested groundwater flow systems ([PERSON], 1962; [PERSON] et al., 2003); often small and responsive valley bottom aquifers; and varied nature of interactions between groundwater and surface water ([PERSON] et al., 1998), lead to complex groundwater level responses that are challenging to interpret ([PERSON] et al., 2010), particularly for understanding groundwater drought. Drought propagation may also differ as hydrological processes vary from high to low elevations. In the Alpine European Region, [PERSON] et al. (2021) identified that drought impacts occurred mostly in the summer and into the early autumn, and that there were differences in the proportions of drought impacts across identified drought years (1976, 2003, 2015, 2018) and in the different regions (e.g., high altitude, pre-alpine, northern and southern). These findings led the authors to suggest a need for different seasonal indices in an impact-targeted drought monitoring and early warning system across the Alpine region.
Drought monitoring and early warning systems and associated drought response plans are used in many countries to enhance drought preparedness; for example, the European and Global Drought Observatories (European Commission, 2023); the Drought Early Warning System in the United States (National Oceanic and Atmospheric Administration, 2023); the British Columbia (BC) (Canada) Drought and Water Scarcity Response Plan (Goverment of British Columbia, 2023); among many others. These systems are based on different drought indicators or indices, which are variables describing drought conditions derived from predominantly meteorological or hydrological data. Common drought indicators include the Standardized Precipitation Index (SPI) based solely on temperature ([PERSON], 1998; [PERSON] et al., 1993); the Standardized Precipitation Evaporation-Index (SPEI) based on the SPI and temperature ([PERSON] et al., 2010); and the Palmer Drought Severity Index (PDSI) based on temperature, precipitation and the moisture holding capacity of soils ([PERSON], 1965). However, there is no widely accepted indicator of groundwater drought; although a few have been proposed, including the Standardized Water-level Index (SWI; [PERSON], 2004), the Groundwater Resource Index (GRI; [PERSON] et al., 2008), and the Standardized Groundwater Level Index (SGI; [PERSON] & [PERSON], 2013). [PERSON] and [PERSON] (2013) found a site-specific relationship between the SPI and SGI; however, their study was limited to the analysis of local-scale behavior of groundwater droughts at 14 sites across the United Kingdom. [PERSON] et al. (2016) highlighted the shortcomings of using the SPI as a groundwater drought indicator at both local and regional scales, stressing the need for more groundwater observations and accounting for regional hydroecological characteristics in groundwater drought monitoring. Other metrics used to define groundwater droughts include groundwater recharge ([PERSON] et al., 1994) or discharge, for example, as springs ([PERSON] & [PERSON], 2012) or to streams ([PERSON] et al., 2003), but recharge and discharge can be difficult to measure. Timely groundwater drought analysis often is hampered by a lack of real-time data ([PERSON] et al. (2017). Therefore, groundwater drought studies often rely on historical datasets, with approaches for reconstructing groundwater levels ranging from establishing relationships between meteorological and groundwater drought indices (e.g., [PERSON] et al., 2022; [PERSON] et al., 2013; [PERSON] et al., 2017), using streamflow deficits ([PERSON] et al., 2016), using groundwater storage anomalies from Gravity Recovery Climate Experiment (GRACE) data for large regions (e.g., [PERSON] et al., 2014; [PERSON] et al., 2017), and using tree rings (e.g., [PERSON] et al., 2020). Modeling approaches have also been used for drought prediction (e.g., [PERSON] et al., 2020; [PERSON] et al., 2006). Importantly, these approaches generally rely on data measured during or following the drought, although [PERSON] et al. (2017) attempted to use near real time data in their analysis.
For drought preparedness, early warning indicators of groundwater drought are needed--indicators that can be used to anticipate forthcoming drought conditions and allow for adjustments to or curtailment of water use. Identifying early warning indicators of groundwater drought, however, presents numerous challenges, particularly in mountainous regions. The indicators should be applicable to the wide range in climatology and physiology characteristic of mountainous regions, and account for the hydraulic connection between aquifers and streams. Moreover, groundwater level monitoring is sparse in mountainous regions. Therefore, the indicators should not rely heavily on observed groundwater level data. For example, in mountainous BC, Canada, groundwater levels are monitored in only 226 Provincial Observation Wells (as of July 2022), despite over 1,100 aquifers extending over more than 30,000 km\({}^{2}\) having been mapped. This means that only a small fraction of aquifers have regularly monitored groundwater level information.
The purpose of this study was to identify early warning indicators of groundwater drought that can be used for drought preparedness in mountainous regions. A key element of the study was characterizing the sensitivity of summer groundwater levels to seasonal climate and hydrologic variables. We focused on two regions of BC that represent a snowmelt-dominated hydrologic regime (South Central BC) and a rainfall-dominated hydrologic regime (Fraser Valley, BC) (Figure 0(a)). We used generalized additive models (GAMs) ([PERSON] and [PERSON], 1986) in a novel fashion to explore associations of individual and combinations of seasonal predictor variables with summer groundwater levels measured in BC Observation Wells. GAMs are a nonparametric extension of generalized linear models, which are used often when there is no a priori reason for choosing a particular response function (such as linear, quadratic, etc.), allowing the data to \"speak for themselves.\" GAMs allow us to take into account non-linearities that are not possible through linear models or by using simple variable transformations such as log, power, or square root. As such, GAMs offer several advantages such as flexibility in shapes of the relationships as well as the distribution of the output variable. GAM results can be difficult to interpret because no parameter values are returned (although significance tests of each term are; see Section 2.3). Nevertheless, GAMs can be very good for prediction, as well as exploratory analyses about the functional nature of a response. In particular, as a non-linear model, GAMs are suitable for modeling hydrological processes, which are naturally non-linear. GAMs have been used for regional flood frequency analysis ([PERSON] et al., 2014; [PERSON] et al., 2018), predicting vegetation distribution ([PERSON] et al., 2002), evaluating water quality ([PERSON] et al., 2019) and in hydroecological studies ([PERSON] and [PERSON], 2022). [PERSON] et al. (2020) used multivariate GAMs to identify the significant factors affecting the runoff coefficient change (RCchange) from 10 catchment characteristics. Their results indicated that the aridity index and mean elevation are the two most important factors that affect the spatial pattern of RCchange between drought and non-drought years. [PERSON] and [PERSON] (2019) used a GAM to develop a non-stationary SPI (NSPI) that incorporates various climate indices as external covariates to capture the non-stationary and non-linear characteristics of precipitation, and thereby droughs.
In this study, we used summer groundwater level as the response variable in the GAMs because drought conditions are observed during the summer in BC. The analyses were carried out using groundwater level records from different aquifer types and with different response mechanisms, recharge-driven or streamflow-driven, as described in Section 2.2, to capture potential streamflow influences on groundwater levels. First, we conducted a sensitivity analysis using single predictor variable GAMs to identify which seasonal variables had the strongest association with summer groundwater levels. Predictor variables tested included seasonal climate variables such as temperature, precipitation, and snow water equivalent (SWE), as these affect the amount of diffuse recharge into an aquifer. Streamflow, a hydrological variable, was also tested because of the hydraulic connection between aquifers and streams. The sensitivity analysis also explored different options for incorporating the predictor variables into GAMs, specifically using station versus gridded climate data, and short versus long period time series. The associations with the Niho 3.4 index, representing the El Niito Southern Oscillation (ENSO), and the Pacific Decadal Oscillation (PDO) were also explored. Based on the findings of the single predictor variable GAMs, the predictor variables with the strongest associations to summer groundwater levels were used in multiple predictor variable (or multivariate) GAMs to identify the most robust combination of variables for predicting summer groundwater levels. To evaluate the GAM approach, we compared the standardized predictor variables with the number of wells in each region that had average summer groundwater levels lower than the 15 th percentile of the historical record. We also evaluated the Standardized Groundwater Level Index (SGI) as a post summer indicator of groundwater drought.
## 2 Materials and Methods
### Data Sources and Pre-Processing
Groundwater level data from the Provincial (BC) Groundwater Observation Well Network (PGOWN) were used in this analysis (Province of British Columbia, 2023). As of November 2020 (the time of this analysis), the PGOWN included 220 observation wells across the province (Figure 1a). A subset of wells from South Central BC (snowmelt-dominated; Figure 1b and Figure S1 in Supporting Information S1) and the Fraser Valley, BC (rainfall-dominated; Figure 1c and Figure S2 in Supporting Information S1) were analyzed. Examples of
Figure 1: (a) Map of British Columbia (BC) showing the observation wells in the Provincial Groundwater Observation Well Network (PGOWN) in orange. (b) Map for South Central BC showing the locations of analyzed observation wells, Okanagan Center climate station (#1125700), hydrometric stations (08 NN002, 08 MC018, 08 LE108, 08 NN116, 08 LF002, 08L002), and the Mission Creek snow station (#2P05P). (c) Map for the Fraser Valley showing the analyzed observation wells, the Sumas Canal climate station (#1107785), and the Fishtrap Creek at International Boundary hydrometric station (#08 MHI153).
statistical well hydrographs are shown in Figures S3 to S5 in Supporting Information S1. Hourly groundwater level data were downloaded from 1 October 2005 to 30 September 2020. While some of the groundwater level records are longer than 30 years, we used data measured since 2005 when pressure transducer dataloggers were deployed to measure groundwater levels hourly. The data were divided quarterly into seasons using an \(R\) script ([PERSON], 2015): October, November and December, JFM (January, February, and March), AMJ (April, May, and June), and JAS (July, August, and September). The seasons were divided such that they fall within a single water year (WY); a WY extends from October 1 st of the previous calendar year to September 30 th of the following calendar year (e.g., the 2015 WY starts 1 October 2014 and ends 30 September 2015). A seasonal rather than monthly analysis was used to limit the number of models while capturing the seasonal variability.
Well hydrographs with reported trends in groundwater level (Environmental Reporting B.C., 2019) were removed from the analysis, as were some wells that did not have complete records, either because the well became part of the PGOWN at a later start date or due to missing data. Any wells that were missing 23 or more days of data for the summer months (JAS) were excluded from the analysis because the analysis focused on summer groundwater levels. In addition, wells that had missing data from the 2015 drought year were removed because 2015 was a significant drought year across the province. The well hydrographs were next analyzed to determine the response mechanism (recharge-driven or streamflow-driven), as described in Section 2.2. Any wells that could not be classified were removed from this analysis because we specifically wanted to investigate whether the response mechanism of the aquifer (and the aquifer type) were important determinants of groundwater drought. Finally, the groundwater level data were standardized using the 2005 to 2020 data period using the \"scale\" R base function (R Core Team, 2020). The scale function subtracts the mean seasonal value from each yearly seasonal average and divides by the standard deviation for the same period. Standardization was done to enable comparison of groundwater level anomalies among the wells. Table S1 in Supporting Information S1 provides a list of all wells in each region and those used in the analysis.
For South Central BC, climate data were obtained from Environment and Climate Change Canada (ECCC) Okanagan Center (#1125700) climate station (Figure 0(b)). Snow water equivalent data were obtained from the BC Ministry of Environment and Climate Change Strategy (ENV) Mission Creek snow station (#2F05P) (Figure 0(b)). For the Fraser Valley, climate data were obtained from the ECCC Sumas Canal (#1107785) climate station (Figure 0(c)). BC Federal-Provincial Hydrometric Network streamflow data were obtained from ECCC for Fishtrap Creek (#08 MH153) hydrometric station (Figure 0(c)).
The ENSO and PDO have been shown to influence the climate in Western Canada ([PERSON] et al., 2001; [PERSON] and [PERSON], 2010; [PERSON] et al., 1997; [PERSON] and [PERSON], 1996). The duration of cycles of each oscillation differs, with ENSO having a shorter duration than PDO ([PERSON] and [PERSON], 2010). In BC, and elsewhere in the Pacific Northwest, a positive Niho 3.4 index, or El Nino, has been correlated to warmer surface temperatures and dry conditions, while a negative Niho 3.4 index, or La Nina, is correlated to cooler surface temperatures and more precipitation ([PERSON] and [PERSON], 2010). The effect of ENSO in BC is most evident during the winter (JFM) months ([PERSON] and [PERSON], 2010) so we included both the winter and annual Niho 3.4 indices. For this study, the Niho 3.4 index data were obtained from the Global Climate Observing System Working Group on Surface Pressure (GCOS-WGSP, 2021). The PDO index data were obtained from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO, 2021).
### Classification of Observation Well Data
Although the groundwater level records were analyzed individually, wells were grouped according to aquifer type ([PERSON] et al., 2009) and by response mechanism ([PERSON] et al., 2021) to assist in the interpretation of results across the diverse hydrogeology and physiography of the two study regions.
#### 2.2.1 Aquifer Type
Aquifers in BC are divided into six different types (unconfined fluvial or glacifluvial along a river or stream, unconfined deltaic, unconfined alluvial fan or colluvial, glacial or pre-glacial origin, sedimentary rock, and crystalline rock aquifers) with some distinguished by subtype (Table S2 in Supporting Information S1). The hydraulic properties, and thus the amplitude and timing of hydraulic responses, vary between the different aquifer types; therefore, it is important that aquifer type be considered in the analysis. Aquifers along rivers and streams (types 0(a), 0(b), and 0(c)), as well as deltaic aquifers (type 2), commonly have a hydraulic connection to surface water ([PERSON] al., 2009). However, bedrock aquifers, types 5a, 6a, and 6b, may be drained by local creeks ([PERSON] et al., 2010). Confined aquifers (type 4b) likely have limited or no hydraulic connection to surface water unless the confining layer is thin or discontinuous.
#### 2.2.2 Response Mechanism
To characterize the interactions between groundwater and surface water in mountainous regions, [PERSON] et al. (2010) classified aquifer-stream system types using a two end-member system representing the aquifer response mechanism: recharge-driven systems and streamflow-driven systems (Figure 2). In recharge-driven systems, diffuse recharge over an aquifer footprint causes groundwater levels to rise, with a subsequent increase in the contribution of groundwater to the stream. The groundwater level response leads the streamflow response year-round; therefore, a reduction in diffuse recharge associated with drought can reduce streamflow. In streamflow-driven systems, water flows from the stream to the aquifer during peak flow (causing a rise in the groundwater levels), and from the aquifer to the stream when stream stage is reduced (causing a decrease in the groundwater levels).
Figure 2: Schematic diagram showing the two aquifer response mechanism end-members: (a) recharge-driven and (b) streamflow-driven. Below each schematic are example hysteresis and cross correlation plots used to characterize the response mechanism. In recharge-driven systems (a) diffuse recharge to the aquifer discharges to the stream year-round. Thus, changes in streamflow lag changes in groundwater level creating a positive or clockwise hysteresis loop. In streamflow-driven systems (b) the water flows from the stream to the aquifer during peak flow (causing a rise in the groundwater levels), and from the aquifer to the stream post peak flow (causing a decrease in the groundwater levels). Therefore, changes in the groundwater level lag changes in the streamflow, creating a negative or counter-clockwise hysteresis loop (data from Province of British Columbia Observation wells 384 and 217, and Environment and Climate Change Canada hydrometric stations 08 LC002 and 08 NN002).
The streamflow response leads the groundwater level response year-round; therefore, a reduction in streamflow due to drought can lower the groundwater level.
As part of the current study, [PERSON] et al. (2021) classified 164 (of 220) PGOWN wells by response mechanism. These 164 wells had a Water Survey of Canada hydrometric station on a stream that flows over or adjacent to the mapped aquifer - a necessary requirement for the analysis. Wells that did not have a suitable active hydrometric station nearby were not analyzed. Wells with a nearby hydrometric station that did not have sufficient overlap between the periods of record of the hydrometric data and groundwater level data also were not classified.
[PERSON] et al. (2021) used a combination of hysteresis plots and cross-correlation plots as diagnostic tools (two examples are illustrated in Figure 2). A hysteresis plot is simply a scatter plot of the average groundwater level and the corresponding average stream discharge each day. Each month is given a separate symbol, and each year is given a different color. By tracking the symbols, the direction of hysteresis can often be determined. The hysteresis plots were examined for the general direction (clockwise, CW, or counter-clockwise, CCW) indicating whether the groundwater level leads (CW or positive) or stream discharge leads (CCW or negative) the response. Cross-correlation plots between groundwater level and stream discharge were constructed using the ccf function in R. Cross-correlation is a measure of similarity of two signals (waveforms) as a function of a time lag applied to one of them. A high cross-correlation demonstrates a strong correlation between two variables at specific time lags, in this case, between stream discharge and groundwater level. Appendix B of [PERSON] et al. (2021) shows these plots for all provincial observation wells analyzed.
Of the 164 wells analyzed across the province, only 123 were classified as either recharge-driven or streamflow-driven (Appendix A in [PERSON] et al., 2021). The remaining 26 wells were classified as indeterminant because either (or both) the hysteresis plot or the cross-correlation plot yielded indeterminant results. A subset of the 123 classified wells that are located in each of South Central BC and the Fraser Valley were considered for further analysis in this study (Table S1 in Supporting Information S1).
### Generalized Additive Models (GAMs)
GAMs are a class of statistical models that use sums of smoothed functions of covariates or predictor (explanatory) variables to infer associations with a univariate response variable ([PERSON] and [PERSON], 1986). GAMs take each predictor variable in the model and separate it into sections (delimited by \"knots\"), and then fit polynomial functions to each section separately, with the constraint of no kinks at the knots (second derivatives of the separate functions are equal at the knots). These non-linear \"smooth\" functions (i.e., splines) are thus able to model and capture the non-linearities in the data. An example of a smooth function is shown in Figure 2(a). Here, the maximum daily spring (April, May, June; AMJ) temperature is used as the only predictor variable in a GAM with standardized summer (July, August, September, JAS) groundwater level as the response variable (i.e., the effect). The quality of the fitted model can be judged based on (a) the confidence interval (gray shaded area) and the significance (\(p\) values) for each of the smoothed terms for the predictor variable used (\(p\) = 0.002 in Figure 2(a)), (b) the resulting adjusted \(r^{2}\) value of the observed (response) and modeled (fitted) groundwater levels (\(r^{2}\) = 0.83 in Figure 2(b)) and (c) the Akaike Information Criterion (AIC) (AIC = 14.26 in Figure 2(b)). The adjusted \(r^{2}\) value is the amount of explained variance, where both the original variance and residual variance are estimated using unbiased estimators ([PERSON], 2022). The AIC is an estimate of the model's predictive accuracy and considers the sample size as well as the number of model parameters ([PERSON] et al., 2004). The AIC is calculated as:
\[\text{AIC}=2k-2\ln(L) \tag{1}\]
where, \(k\) is the number of independent variables used and \(L\) is the log-likelihood estimate. If a model is more than 2 AIC units lower than another model, then it is considered significantly better than that model. AIC values can be positive or negative. Generally, a low AIC indicates the more accurate model with the fewest parameters.
The \"gam\" function in the \(mgcv\) R Package was used to create the GAMs ([PERSON], 2011, 2017). The \(k\) value, which controls the upper limit on the degrees of freedom for the smooth, was chosen to be 3, so as to not over fit the model and to set the estimated degrees of freedom to a value of 2 (\(k\)-1), and was checked using the \"k.check\" function such that the \(k\)-index is not far below 1. The smoothing parameter estimation method used was the restricted maximum likelihood, as it produces the best results ([PERSON], 2022). The \"summary.gam\" function in the _mgcv_ package was used to obtain the \(p\) values for each predictor variable and the adjusted \(r^{2}\) and AIC values. Additionally, the _gratia_ R Package ([PERSON], 2022) was used to visualize the effect of each smoothed predictor variable on the summer groundwater level, as illustrated in Figure 3a.
As mentioned previously, summer groundwater level was used as the response variable in the GAMs to produce fitted models based on predictor variables. For each season, the individual predictor variables included, the maximum and minimum daily temperatures, total precipitation, maximum SWE, average streamflow, and the Nino 3.4 index. These predictor variables are commonly measured in most regions and so are suitable for use in GAMs.
#### 2.3.1 Sensitivity Analyses
The sensitivity analyses included exploring:
1. _Single Predictor Variables_. GAMs were generated for each well using each individual seasonal predictor variable. The goal was to identify which seasonal variables are most strongly associated with summer groundwater levels. Different variables were used to reflect the different hydroclimatic regimes. For the snowmelt-dominated South Central BC region, maximum SWE was included for both the current year and the previous year, but maximum SWE was not used in the Fraser Valley, which is rainfall-dominated. The individual predictor variables that resulted in the most statistically robust GAMs were used in different combinations in multiple predictor variable GAMs for each study region (Section 2.3.2).
2. _Station versus Gridded Climate Data_. While most provincial groundwater observation wells have a climate station located in close proximity, some do not. In this sensitivity analysis, station data and gridded climate data for the same location as the climate station were used in GAMs in South Central BC. The intent was to explore if gridded data might be used in a GAM if station data are not available. The ECCC Okanagan Center (#1125700; Figure 1b) was used as the station data. Monthly gridded (\(0.5^{\circ}\times 0.5^{\circ}\)) climate data for 2005-2020 were obtained from ClimateBC ([PERSON] et al., 2016) for the latitude and longitude of the climate station. The monthly gridded climate data were standardized by season. Six observation wells in South Central BC were used in these GAMs (217, 364, 381, 262, 344, 384; Figure 1b). The predictor variables included maximum AMI temperature and maximum JAS temperature (station and gridded), along with the maximum SWE, and the Nino 3.4 JFM index.
3. _Teleconnections_. GAMs were created using the yearly average as well as the JFM average of both ENSO and PDO indices. Because the phases of ENSO and PDO have different durations, both short (8 years) and long time periods (12-40 years, depending on well record length) were used for the analysis of both teleconnections. The short duration is intended to capture the effect of the ENSO, while the longer duration is intended to capture the effect of the PDO. The same six wells from South Central BC as were used in the station versus
Figure 3: The results of a generalized additive model using the maximum spring (April, May, June; AMI) temperature as the only predictor for the summer groundwater level response of Provincial Observation Well 364. (a) The smooth function showing the effect of maximum spring temperature on summer groundwater level. The tick marks on the \(x\)-axis are the observed data points. The shaded area indicates the 95% confidence interval. The significance value (\(p\) value) is indicated. (b) The response (observed summer groundwater levels) versus the fitted (modeled) results. The dashed red line shows the regression line with the associated \(r^{2}\) value and the AIC for the model.
gridded climate data sensitivity analysis were used in this analysis. Note that for the long time period analyses, the groundwater level data for two wells pre-date 2005 (1970 for well 217 and 1980 for well 262). Groundwater levels were recorded monthly rather than hourly prior to 2005.
4. _Short versus Long Time Series._ The GAMs for two wells (262 and 344) were re-run using short and long time series to test if the length of the data record affects the model outcome. The GAMs for the short period were run using data from 2008 to 2016 (8 years). For the long period, the entire period of record (1980-2020) was used for well 262, and 2000-2020 for well 344. The predictor variables included the maximum SWE, maximum AMI temperature, maximum IAS temperature, and the Nino 3.4 JFM index. Similar to the teleconnections sensitivity analysis, groundwater levels prior to 2005 were measured monthly.
#### 2.3.2 Multiple Predictor Variable GAMs
Based on the individual seasonal predictor variables that resulted in the most statistically robust GAMs (Section 3.1), the predictor variables were combined to create multiple predictor variable GAMs for each study region (Section 3.2). Because groundwater levels may be influenced by more than a single variable, multiple predictor variable GAMs are best suited for identifying the associations with multiple variables.
### Evaluation of Predictor Variables
To evaluate the GAM approach, which was carried out using a limited number of wells, we compared the predictor variables from the best GAM in each region with the number of wells that had average summer groundwater levels lower than the 15 th percentile of the historical record. For South Central BC, groundwater levels from 31 wells were used, and for the Fraser Valley from 13 wells. Only six wells in South Central BC and only eight wells in the Fraser Valley were used for the GAM analysis; therefore, this evaluation was a form of model validation. The groundwater levels, streamflow and climate variables were standardized in R using the scale function, using data spanning 2005 and 2020. In the Fraser Valley, precipitation data were missing for 2008-2011 from the climate station, and temperature data were missing from 2007 to 2010, so data spanning 2011-2020 were used in the analysis. The 5 th, 10 th, and 15 th percentiles of the average summer groundwater levels for each well were calculated over the same time period.
### Evaluation of the Standardized Groundwater Level Index (SGI)
The Standardized Groundwater Level Index (SGI) ([PERSON] and [PERSON], 2013) was evaluated as a potential post summer indicator of groundwater drought. The SGI is estimated at a monthly timescale because groundwater often exhibits a high persistence (large memory) ([PERSON] et al., 2015; [PERSON] et al., 2016; [PERSON] et al., 2022). The SGI is calculated by applying a normal scores transform (non-parametric normalization of data), whereby a value is assigned to the monthly groundwater level based on its rank for a given month for a particular well hydrograph (i.e. groundwater level record). The normal scores transform then applies the inverse normal cumulative distribution function to \(n\) equally spaced \(p_{i}\) values ranging from 1/(2 \(n\)) to 1\(-\)1/(2 \(n\)). Here, \(n\) is total number of observations and \(p_{i}\) is the probability that a value drawn at random from the fitted distribution is less than or equal to the observed groundwater level for that month. The values that result are the SGI values. They are then re-ordered such that the largest SGI value is assigned to the \(i\) for which \(p_{i}\) is largest, the second largest SGI value is assigned to the \(i\) for which \(p_{i}\) is second largest, and so on. The SGI distribution that results from this transform will always pass the K-S normality test.
## 3 Results
### Sensitivity Analysis
#### 3.1.1 Single Predictor Variable GAMs
Up to 16 different single predictor variable GAMs were created for each groundwater well in each study region (Table 1). The \(p\), \(r^{2}\), and AIC values were examined for each GAM. The AIC values were generally similar among models (mid-20s) and so were not scrutinized. GAMs with both \(p\leq 0.1\) and \(r^{2}\geq 0.5\) for the individual predictor variables (bold values in Tables S3 and S4 in Supporting Information S1) were considered significant for this analysis. Arguably, these statistics are not particularly strong evidence of good models. However, very few GAMs met these criteria, which was expected because it is unlikely that there would be a single predictor of groundwater level. Therefore, these thresholds were chosen to identify those variables that are more strongly associated with summer groundwater levels so that they could be explored in the multiple predictor variable GAMs. Two or more wells needed to meet the threshold for both \(p\) and \(r^{2}\) values to be considered one of the best GAMs. Table 1 identifies the predictor variables in each region (black dots) that resulted in the \"best\" fit GAMs. The number of wells used in the analysis are shown for each region, and the number of wells meeting the statistical thresholds are identified in brackets.
For South Central BC, maximum AMJ temperature, minimum JAS temperature, maximum SWE, AMJ streamflow and JFM Nino 3.4 resulted in the best single predictor variable GAMs based on the statistics (Table 1; Table S3 in Supporting Information S1). In the Fraser Valley, maximum JFM temperature, maximum AMJ temperature, JFM precipitation, JFM Nino 3.4 and AMJ streamflow resulted in the best single predictor GAMs based on the statistics (Table 1; Table S4 in Supporting Information S1).
#### 3.1.2 Station Versus Gridded Data
Four of six GAMs using the Okanagan Center station data for the climate predictor variables (maximum AMJ temperature and maximum JAS temperature) had higher \(r^{2}\) values and lower AIC values compared to the GAMs using gridded data (bold values in Table S5 in Supporting Information S1). GAMs using the station data had \(r^{2}\) values ranging from 0.8 to 1.0 and AIC ranging from \(-\)11.8 to 15.8. GAMs using the gridded data had \(r^{2}\) values ranging from 0.6 to 1.0 and AIC ranging from \(-\)15.6 to 22.1. Two wells, 364 and 262, had better GAMs using the gridded data. Interestingly, well 262 is located closest to the climate station and the grid cell, while well 364 is located the furthest away (Figure 0(b)).
#### 3.1.3 Teleconnections
The GAMs using the Nino 3.4 index as the predictor variable had lower AIC values (range 22.4-30.1) using shorter time periods compared to the longer time periods (range 39.4-116.1) (Table S6 in Supporting Information S1). The \(r^{2}\) values for both time periods were low, with a highest \(r^{2}\) value of 0.6 for well 384 using the shorter time period. With the exception of two wells (364 and 384) with low \(p\) values of 0.04 for the short period, the \(p\) values were elevated for both time period lengths (range 0.14-0.80). These results suggest that the Nino 3.4 index is strongly associated with summer groundwater levels in certain wells and at short time periods of 8 years.
GAMs using the PDO for short time periods had the lower AIC values (range 25.5-29.9) compared to the GAMs using the long periods (32.4-110.1) (Table S7 in Supporting Information S1). None of the \(r^{2}\) values were significant (\(r^{2}\) value were \(>\)0.5) for either time period length. Several wells had \(p\) values \(<\) 0.15 for both the short and long periods; well 364 had the lowest \(p\) value (0.05) for the long period. Because the groundwater records are limited in length (only since 2005 have data been recorded hourly), they are likely not long enough to include an entire PDO cycle. Here, the longest periods of record are for wells 262 and 217 (38 and 39 years, respectively; Table S7 in Supporting Information S1). These two wells had the lowest AIC values for the long time periods, suggesting that the longer the record, the more likely the PDO index is associated with low summer groundwater levels. However, this should be confirmed by examining other wells with long records.
#### 3.1.4 Short Versus Long Time Series
For both wells analyzed, 262 and 344, the GAMs using the short time periods had the lower AIC values (15.8 and \(-\)11.8, respectively) and higher \(r^{2}\) values (0.8 and 1.0, respectively) compared to the GAMs using the longer time periods (AIC values of 77.1 and 64.0, respectively; \(r^{2}\) values of 0.63 and \(-\)0.14, respectively) (Tables S8 and S9 in Supporting Information S1, respectively). Overall, these results suggest that the GAMs are more robust over shorter time periods compared to longer time periods. This finding may relate to the influence of climate
\begin{table}
\begin{tabular}{l c c} \hline Predictor variable & South central BC (6 wells) & Fraser valley (8 wells) \\ \hline Max Temp JFM & (1) & (2) \\ Max Temp AMJ & (3) & (4) \\ Max Temp JAS & (1) & (0) \\ Min Temp JFM & (0) & (0) \\ Min Temp AMJ & (1) & (0) \\ Min Temp JAS & (2) & (0) \\ Precipitation JFM & (0) & (3) \\ Precipitation AMJ & (1) & (0) \\ Precipitation JAS & (1) & (0) \\ Max SWE & (2) & \\ Max SWE Prev Year & (0) & \\ Nino 3.4 Year Ave. & (2) & (2) \\ Nino 3.4 JFM & (2) & (5) \\ Streamflow JFM & (0) & (0) \\ Streamflow AMJ & (2) & (4) \\ Streamflow JAS & (2) & (1) \\ \hline \end{tabular} _Note._ The number of wells analyzed is indicated in the header row. The black dots indicate the predictor climate variables with \(p\leq 0.1\) and \(r^{2}\) values \(\geq\) 0.5, The white dots indicate that the predictor variable did not have at least two wells meeting the significance levels. The number of wells meeting the significance levels are indicated in brackets beside each dot. (JFM = January, February, March; AMJ = April, May, June; JAS = July, August, September; OND = October, November, December). SWE = snow water equivalent.
\end{table}
Table 1: The Predictor Variables Used in Generalized Additive Models for Each Study Region (Dots)cycles, such as ENSO (see Section 3.2.2), where the GAMs using the JFM Ninfo 3.4 index were more robust using short time periods compared to long time periods.
Interestingly, the significance of the smooth functions (\(p\) values) for maximum AMJ and JAS temperatures were considerably \(<\)0.05 for well 262 using the long time period (51 years) compared to the short period (8 years). In contrast, for well 344, the GAM using the short time period (8 years) resulted in a better fitting model compared to the long time period (20 years).
### Multiple Predictor Variable GAMs
The single predictor variables with the strongest association with summer groundwater levels (solid dots in Table 1) were used in different combinations in GAMs (multiple predictor variable GAMs) for each region to identify the combination that is most strongly associated with summer groundwater levels. Different combinations of variables were tested (Table 2). The \(r^{2}\) and AIC values from the fitted versus response of the summer groundwater levels were used to determine the best fitting GAM for each region. Only the \(r^{2}\) values are reported below. AIC values were similar for all models.
#### 3.2.1 South Central BC
Summer groundwater levels from 2008 to 2016 for six wells (217, 364, 381, 262, 344, 384) were used as the response variable for seven different GAMs in South Central BC (Table 2). Both response mechanisms and three different aquifer types are represented in the analysis: 1b (\(n=2\)), 4a (\(n=1\)), and 4b (\(n=3\)).
Generally, GAMs 1 and 2, which included the maximum AMJ and JAS temperatures, had the higher \(r^{2}\) values compared to GAMs 3 and 4, which used the minimum AMJ and JAS temperatures (Table 2). GAM 2 was the only combination of predictor variables that returned high \(r^{2}\) values (all \(\geq\)0.8) of the fitted summer groundwater levels compared to the observed summer groundwater levels. However, GAM 2 included the JAS maximum temperatures, which would make this set of predictor variables not useable to \"predict\" summer groundwater levels, because the JAS temperature data would not be available until the end of September. Therefore, the same combination of predictor variables as GAM 2 was tested with the maximum JAS temperature excluded as GAM 6. The response and fitted summer groundwater level from GAM 6 also resulted in higher \(r^{2}\) values (all but one \(\geq\)0.8), showing that this combination of predictor variables can be used in the absence of the JAS temperatures. Additionally, JFM Ninfo 3.4 index was included in GAMs 2, 4, and 6. Due to the limited number of wells in South Central BC with a nearby hydrometric station, AMJ streamflow was only included for three wells in GAM 7. GAM 7 resulted in the highest \(r^{2}\) values for the two wells classified as streamflow-driven but performed poorly for well classified as recharge-driven. These results suggest that if streamflow data are available, streamflow should be included as a predictor of summer groundwater levels for streamflow-driven wells.
#### 3.2.2 Fraser Valley
Groundwater level data from 2011 to 2019 for eight wells (002, 008, 272, 275, 301, 353, 361, 255) were used as the response variables for four different GAMs in the Fraser Valley (Table 3). Three different aquifer types are represented: 4a (\(n=6\)), 4c (\(n=1\)), and 6b (\(n=1\)) all of which were classified as streamflow-driven.
GAM 3, which included maximum AMJ temperature, JFM precipitation, and AMJ streamflow, was the best fit. GAM 3 had the highest \(r^{2}\) values--six of the eight wells (all type 4a aquifers) had \(r^{2}\) values \(\geq\) 0.9 (Table 3). Well 361 in the 4c aquifer and well 255 in the 6b aquifer had \(r^{2}\) values = 0.8.
\begin{table}
\begin{tabular}{l c c c c c c} \hline AQ type & 1b & 1b & 4a & 4b & 4b & 4b \\ \hline Response mechanism & sf & sf & sf & \(r\) & \(r\) & \(r\) \\ \hline Well \# & 217 & 364 & 381 & 262 & 344 & 384 \\ \hline GAM 1 & 0.8 & 0.8 & 0.7 & **0.8** & **1.0** & 0.2 \\ Max SWE & & & & & & \\ Max Temp AMJ & & & & & & \\ Max Temp JAS & & & & & & \\ GAM 2 & **0.9** & **0.9** & **1.0** & **0.8** & **1.0** & 0.8 \\ Max SWE & & & & & & \\ Max Temp AMJ & & & & & & \\ Max Temp JAS & & & & & & \\ Max Temp JAS & & & & & & \\ Max Temp JAS & & & & & & \\ Max Temp JAS & & & & & & \\ Max Temp JAS & & & & & & \\ Max Temp AMJ & & & & &
### Evaluation of Predictor Variables
Figures 4 and 5 show the standardized climate variables for South Central BC and the Fraser Valley, respectively, plotted with the number of wells that had average summer groundwater levels lower than the 15 th percentile. In South Central BC, the years with a combination of above average maximum AMJ temperature, below average maximum SWE, and a positive JFM Nino 3.4 index corresponded with a greater number of wells with water levels lower than the 15 th percentile (Figure 4). For example, in summer 2015, the maximum AMJ temperature was the highest recorded over the entire 2005-2020 period. Additionally, the maximum SWE was the lowest in 2015. Over half (15 of 29) of the wells with available data had summer groundwater levels lower than the 15 th percentile, and eight wells had levels lower than the 5 th percentile. In 2012, a low maximum AMJ temperature, higher maximum SWE, and a negative Nino 3.4 index corresponded with only two wells (wells 122 & 405) with water levels lower than the 15 th percentiles.
In the Fraser Valley, the years with a combination of above average maximum AMJ temperature, below average JFM precipitation, and below average AMJ streamflow corresponded with a greater number of wells with water levels lower than the 15 th percentile (Figure 5). For example, the maximum AMJ temperature was highest in 2015 and 2018. In 2019, the JFM precipitation was the lowest for the time period examined and nine wells had water levels lower than the 15 th percentiles. AMJ streamflow was the lowest in 2015 and 2016. Over half (7 of 12) of the wells with available data were lower than the 15 th percentile of the summer groundwater levels in 2015, 2016, and 2019.
### Comparison With the Standardized Groundwater Level Index (SGI)
Figure 6 shows a heat map of the SGI values for the aquifer type 1a wells in South Central BC. Type 1a aquifers are predominantly unconfined sand and gravel aquifers of fluvial or glacio-fluvial origin that found along major rivers of higher stream order. The proximity and likely hydraulic connection to a stream suggests the aquifer response mechanism would be classified as streamflow-driven; however, this is not the case. Wells 75 and 203 are in recharge-driven systems, and wells 185 and 407 are in streamflow-driven systems. The well density (number of wells/km\({}^{2}\)) classified by the province as low, medium and high is shown to recognize potential anthropogenic influences on the groundwater levels.
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline AQ type & 4a & 4a & 4a & 4a & 4a & 4a & 4c & 6b \\ \hline Response mechanism & sf & sf & sf & sf & sf & sf & sf & sf \\ \hline Well \# & 002 & 008 & 272 & 275 & 301 & 353 & 361 & 255 \\ \hline GAM 1 & **0.9** & 0.9 & 0.7 & 0.8 & 0.7 & 0.7 & 0.3 & 0.4 \\ Max Temp AMJ & & & & & & & & \\ Precip JFM & & & & & & & & \\ GAM 2 & 0.8 & **1.0** & 0.7 & 0.9 & **1.0** & 0.7 & **1.0** & 0.8 \\ Max Temp AMJ & & & & & & & & \\ Precip AMJ & & & & & & & & \\ Nino 3.4 JFM & & & & & & & & \\ GAM 3 & **0.9** & 0.9 & **1.0** & **1.0** & **1.0** & **1.0** & 0.8 & **0.8** \\ Max Temp AMJ & & & & & & & & \\ Precip JFM & & & & & & & & \\ Streamflow AMJ & & & & & & & & \\ GAM 4 & **0.9** & 0.9 & 0.7 & 0.6 & **1.0** & 0.3 & 0.8 & 0.4 \\ Max Temp AMJ & & & & & & & & \\ Streamflow AMJ & & & & & & & & \\ \hline \hline \end{tabular} Note. Predictor variables used for each GAM are listed. Aquifter types 4a, 4c, and 6c are represented. All wells are classified as streamflow-driven (sf). The highest \(r^{2}\) values for each well are indicated in bold.
\end{table}
Table 3: \(r^{2}\) Values for Generalized Additive Models for Each Well in the Fraser ValleyThe SGI for these four wells fluctuates between periods of drought as defined by [PERSON] and Marchant (2013) as SGI < 0 (in red) and non-drought with SGI > 0 (in blue). Importantly, the SGI values are visibly quite different, even in 2015 which was a drought year across much of BC. The variability in SGI values among these same aquifer types suggests that the response to drought can be different even for aquifers of the same type. Other factors, such as response mechanism or groundwater use may influence the SGI more strongly.
Broadly, however, the SGI may be a useful indicator for mountainous regions. In South Central BC, the SGI was compared between a drought (2015) and non-drought (2020) year. In 2015, 23 of the 31 wells had at least one negative SGI value in the summer months (JAS). During summer 2020, 19 of the wells had positive SGI values for each month, indicating a non-drought year, with only three wells having SGI values less than \(-1\). In the Fraser Valley, the SGI was compared between a drought year (2015) and a non-drought year (2011). In summer 2015, all 12 wells had negative SGI values indicating a drought year. Only well 354 had positive SGI values in the summer of 2015. In summer 2011, only two wells had positive SGI values for all three summer months. The SGI values ranged from \(-0.68\) to \(1.15\). The lowest SGI (\(-1.08\)) was for well 301. All wells, with the exception of wells 375 and 359, are located in aquifers with a high well density, suggesting that anthropogenic factors likely strongly influence the SGI.
## 4 Discussion
### General Findings and Limitations
GAMs proved to be a valuable tool for understanding how both individual and combinations of seasonal climate and hydrological variables influence summer groundwater levels. At the outset of this study, linear relations between different climate and hydrological variables were explored, but this proved challenging because, as illustrated in Figure 3, the groundwater level response to most variables was non-linear. Thus, the main advantage of using GAMs is the ability to model non-linear responses. The single predictor variable GAMs were generally
Figure 4: The three selected standardized climate predictor variables for South Central BC: (a) maximum AMJ temperature, (b) maximum snow water equivalent and (c) JFM Nii0.3.4 index. Red shading reflects above average (in a and d) or below average (in b) standardized values. (d) The percentage of wells with available data within each summer groundwater level percentile category per year. The number of wells with available data for each year is labeled in italics.
quite poor, as expected, because summer groundwater levels are not expected to be strongly associated with any single predictor variable. However, the multiple predictor GAMs using various combinations of predictor variables were statistically robust, achieving \(r^{2}\) values of 0.8-1.0 for some combinations for all the wells tested. This result is promising because aquifer systems in themselves are complex, with different hydraulic properties and different hydraulic connection with streams. Moreover, the GAMs were tested in two hydroclimatic regimes, snowmelt- and rainfall-dominant, and while the set of predictor variables was different for each region, the GAMs performed well.
Within each study region, wells are located in varying geographic locations, some at considerable distance to the climate station used in the analysis (Figure 1). For both study regions, climate data from a single common climate station were used because the selected climate station had the most complete record for the region. It is possible that GAMs using a climate station situated near the well would have even better performance.
The GAMs were generally better if station data rather than gridded data were used. This may be because the wells are located at lower elevations (valley bottoms), similar to the climate station. The gridded data are at 5\({}^{\circ}\)\(\times\) 5\({}^{\circ}\) (\(\sim\)50 km \(\times\) 50 km) resolution; therefore, each grid square represents the surrounding steep topography rather than just the valley bottom. Additional modeling using station and gridded data closer to these well locations may have produced stronger models. Likewise, gridded data may produce better results for wells located at higher elevation.
The Nifo 3.4 index is generally more strongly associated with summer groundwater levels if short time periods are used (\(\sim\)8 years) rather than longer
Figure 5: The three selected standardized climate predictor variables for the Fraser Valley: (a) maximum AMJ temperature, (b) JFM precipitation and (c) AM streamflow. Red shading reflects above average (in a and d) or below average (in b) standardized values. (d) The percentage of wells with available data within each summer groundwater level percentile category per year. The number of wells with available data for each year is labeled in italics.
Figure 6: Heatmap of the Standardized Groundwater Level Index (Standardized Groundwater Index (SGI)) values for aquifer type 1a in South Central British Columbia. Negative SGI values (drought periods) are shown in red, while positive SGI values (non-drought periods) are shown in blue. The response mechanism for each well is labeled in italics (R for recharge-driven and S for streamflow-driven) as well as the reported well density of the aquifer (Low, Moderate, High).
periods (up to 40 years). In contrast, the PDO only had a strong association with summer groundwater levels in the wells with records closer to 40 years. Similarly, the GAMs were stronger when shorter climate time series lengths were used rather than longer ones. These results suggest that climate variables are less well associated with summer groundwater levels over longer time scales; however, more analysis is needed to confirm this. Further analysis also could be conducted on well records using periods less than 8 years.
The number of wells used in the GAM analysis was limited (only six wells were used in South Central BC and only eight in the Fraser Valley) because we wanted to explore whether the recharge mechanism (streamflow-driven vs. recharge-driven) and aquifer type were important determinants of groundwater drought. The response mechanism could be classified only for a handful of wells in each region. Unfortunately, all wells in the Fraser Valley are classified as streamflow-driven, so we could not explore the role of recharge mechanism in that region. However, in the Fraser Valley, the GAMs for wells classified as streamflow-driven were better fit using the AMJ streamflow data compared to the JFM and JAS streamflow data, while the GAMs for the wells classified as recharge-driven were better fit using the JAS streamflow data. In South Central BC, three wells are streamflow-driven and three recharge-driven (Table 2). As a general observation, the GAM results for the recharge-driven wells are poorer; however, all wells classified as recharge-driven are also type 4b aquifers (confined; Table S2 in Supporting Information S1), so the relative importance of recharge mechanism versus aquifer type is indeterminant. In hindsight, we should have carried out the analysis using all wells with suitable records, regardless of whether we were able to classify the response mechanism. All wells have been assigned an aquifer type, so aquifer type could have been explored and the data set expanded. [PERSON] et al. (2022) analyzed memory and response time in different aquifer types and found that wells in confined sand aquifers can have a groundwater drought memory and response time over 4 years, and nearly 2 years in unconfined sand. However, there was variability, which they attributed to factors such as vadose zone thickness and diffusivity. They did not consider response mechanism in that study.
### Region Specific GAMs, the SGI and Potential Uses
GAMs that used summer predictor variables (e.g., JAS maximum daily temperature) or annual conditions (e.g., annual Nino 3.4 index) ultimately were not selected as the best GAMs in each study region because the goal was to identify predictor variables for use prior to the summer season to \"predict\" if groundwater drought might occur. Thus, the observed JFM and AMJ climate variables were chosen climate predictors in each region.
In South Central BC, GAM 6, which included maximum SWE, maximum AMJ temperature, and JFM Nino 3.4, was identified as the best GAM for predictive use (Table 2). GAM 6 is broadly applicable across all the aquifer types represented in the analysis and both response mechanisms. In the Fraser Valley, GAM 3, which included maximum AMJ temperature, JFM precipitation, and AMJ streamflow, was identified as the best GAM (Table 3). This GAM had the highest \(r^{2}\) values--greater than 0.75 for all wells. However, the other GAMs also had high \(r^{2}\) values, suggesting that the other combinations of predictor variables are associated with summer groundwater levels.
The region-specific combinations of predictor variables identified in this study may be used in the spring by the BC Drought Response Team and regional and provincial water managers to anticipate groundwater droughs based on readily available climate and hydrological data prior to the beginning of the drier summer (JAS) months. The larger subset of wells used to evaluate the GAM results (Section 3.3) can be used to track groundwater levels throughout the summer to potentially curtail water use in drought sensitive aquifers. The wells might also be used to analyze post-drought groundwater level data, using, for example, the SGI. Overall, the SGI appears to be a good indicator to retroactively check how the groundwater levels responded in drought and non-drought years. The SGI could be used, for example, to identify historical groundwater drought in different aquifers and to identify wells (aquifers) that have been susceptible to drought. However, the SGI was variable among wells in the same aquifer type possibly due to different aquifer response mechanisms or anthropogenic factors, such as groundwater pumping. Given the potential influence of well density/groundwater use on the SGI, this indicator also could be used to identify trends in the SGI associated with groundwater abstraction, particularly if climate conditions are normal. While the SGI has been used primarily to identify low groundwater levels associated with drought, it could also be used to identify high groundwater levels.
Finally, droughs of the future are likely to be more frequent, severe, and longer lasting than they have been in recent decades (Ault, 2020). Mountain regions can be expected to become more susceptible to snow drought (alack of snow accumulation in winter) ([PERSON] et al., 2019), leading to lower runoff, less groundwater recharge, significantly longer and more severe summer low flows ([PERSON] et al., 2018). In high altitude areas of the Alpine European Region, winter snow accumulation and generally lower air temperatures led to fewer drought impacts due to better water availability in spring and early summer (i.e., during the spring melt period) ([PERSON] et al., 2021). This finding is consistent with our study, which highlighted a strong association between summer groundwater levels and SWE in the snowmelt-dominated region, such that above normal snowpack is associated with above normal summer groundwater levels, and vice versa. The strong association between summer groundwater drought and snowpack suggests that more frequent snow drought years or even the gradual decline in winter snowpack into the future may lead to lower summer groundwater levels and consequent reductions in baseflow, which could have significant impacts to aquatic ecosystems.
Finally, the observed and attributed frequency of compound events, namely co-concurrent heatwaves and droughts, has increased since 1950 and there is high confidence this trend will continue with higher global warming ([PERSON] et al., 2021). As a recent example, the U.S. Drought Monitor reported that the \"heat dome\" that affected the Pacific Northwest (PNW) in late June 2021 was unprecedented in the contemporary data record (National Oceanic and Atmospheric Administration (NOAA), 2021). The most recent drought in BC in the summer of 2022 resulted in 12 different water basins having extremely to exceptionally dry conditions lasting into November (BC Ministry of Forests, 2022). Groundwater levels in many BC aquifers fell significantly below the historical lows. The unexpected long dry summer was largely the cause of the drought. Because some GAMs in this study were strengthened by including the summer season (JAS) predictor variables (see GAM2 in Table 2), these summer variables could be used during the summer to predict late summer to early fall groundwater drought.
## 5 Conclusions
The analysis of summer season (JAS) groundwater levels using GAMs showed that the groundwater levels in different hydroclimatic regimes are influenced uniquely by different combinations of climate and hydrologic variables. In the snowmelt-dominated South Central BC region, maximum AMJ temperature, maximum SWE, and the JFM Nino 3.4 index was the best combination of climate predictor variables. Using a larger data set for verification of the GAM results, years with a combination of above average maximum AMJ temperature, below average maximum SWE, and a positive JFM Nino 3.4 index corresponded with a greater number of wells with water levels lower than the 15 th percentile. In the rainfall-dominated Fraser Valley, the maximum AMJ temperature, JFM precipitation, and AM streamflow was the best combination of climate predictor variables. In this region, the years with a combination of above average maximum AMJ temperature, below average JFM precipitation, and below average AMJ streamflow corresponded with a greater number of wells with water levels lower than the 15 th percentile. These region-specific climate and hydrological variables could be used by water managers as early warning indicators of groundwater drought to aid in drought preparedness. The Standardized Groundwater Level Index (SGI) is generally effective at indicating which wells had pronounced responses to periods of drought in each region. However, SGI values differ among aquifers of the same type in the same region and is likely influenced by other factors such as aquifer response mechanism and groundwater pumping and so should be used with caution.
### Data Availability Statement
All datasets used for this research are publicly available. Datasets include the British Columbia Provincial Groundwater Observation Well Network (PGOWN) (accessible at [[https://governmentofbc.maps.arcgis.com/apps/webappviewer/index.html?id=b53](https://governmentofbc.maps.arcgis.com/apps/webappviewer/index.html?id=b53) cb0 bJ3f6848e79d66 ff0409b74f00d]([https://governmentofbc.maps.arcgis.com/apps/webappviewer/index.html?id=b53](https://governmentofbc.maps.arcgis.com/apps/webappviewer/index.html?id=b53) cb0 bJ3f6848e79d66 ff0409b74f00d) or by searching for Groundwater Level Data Interactive Map--Province of British Columbia; climate station data from Environment and Climate Change Canada (ECCC) ([[https://climate.weather.gc.ca/historical_data/search_historic_data_e.html](https://climate.weather.gc.ca/historical_data/search_historic_data_e.html)]([https://climate.weather.gc.ca/historical_data/search_historic_data_e.html](https://climate.weather.gc.ca/historical_data/search_historic_data_e.html))); hydrometric data from BC Federal-Provincial Hydrometric Network ([[https://wateroffice.ec.gc.ca/search/historical_e.html](https://wateroffice.ec.gc.ca/search/historical_e.html)]([https://wateroffice.ec.gc.ca/search/historical_e.html](https://wateroffice.ec.gc.ca/search/historical_e.html))). The report by [PERSON] et al. (2021) on the classification of Provincial Groundwater Observation Wells in BC includes a digital version of Appendix A ([[https://a100.gov.bc.ca/pub/acat/public/viewReport.do?reportId=59107](https://a100.gov.bc.ca/pub/acat/public/viewReport.do?reportId=59107)]([https://a100.gov.bc.ca/pub/acat/public/viewReport.do?reportId=59107](https://a100.gov.bc.ca/pub/acat/public/viewReport.do?reportId=59107))).
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* [PERSON] et al. (2017) [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2017). The spatiotemporal variations and propagation of droughs in Plateau Mountains of China. _Science of the Total Environment_, _805_, 150257. [[https://doi.org/10.1016/j.scitastro.2021.150257](https://doi.org/10.1016/j.scitastro.2021.150257)]([https://doi.org/10.1016/j.scitastro.2021.150257](https://doi.org/10.1016/j.scitastro.2021.150257)) | wiley | Early Warning Indicators of Groundwater Drought in Mountainous Regions | A. Gullacher, D. M. Allen, J. D. Goetz | https://doi.org/10.1029/2022wr033399 | 2,023 | CC-BY |
wiley/fb4f8029_c3d2_40d7_ba03_6fbddecac71e.md | in the oceanic lithosphere (abyssal peridotites) occurs in the geologic record as the lowermost structural portion of ophiolitic sequences that have been obducted during orogen ([PERSON], 2014; [PERSON], 2003). Ophiolitic ultramafic rocks and their hydrated (serendinites) and carbonated equivalents are observed in all major Phanerozoic orogenic belts ([PERSON], 2014 and references therein) and may host Ni-Fe-Cu-PGE mineralization and, thus, have historically been, and continue to be common targets for resource exploration (e.g., [PERSON], 2017; [PERSON], 1997). Recent work has demonstrated that (serendinized) ultramafic rocks are particularly reactive with carbon dioxide to the extent that they are prime targets for carbon sequestration (e.g., [PERSON], 2009; [PERSON] et al., 2018, 2020; [PERSON] et al., 2018; [PERSON] et al., 2013; [PERSON] et al., 2020). Mineral carbonation may be achieved using either _ex situ_ or _in situ_ techniques; the former involves exposure of fine-grained material, such as mine tailings, to either atmospheric CO2 or from a concentrated source, whereas the latter involves injecting CO2 to a depth of \(>\)2 km. Ex _situ_ techniques take advantage of the increased reactive surface area of tailings and the high reactivity of minerals such as brucite (e.g., [PERSON] et al., 2013, 2018, 2020; [PERSON] et al., 2019), whereas _in situ_ techniques exploit the elevated temperatures and pressures at depth to accelerate reactions and fully carbonate the rock (e.g., Kelemen & Matter, 2009; [PERSON] et al., 2018). As resource extraction invariably requires the consumption of energy and emission of CO2, whether it be for transportation of materials and personnel or for ore processing/extraction, any deposit hosted in ultramafic rocks should explore their potential to sequester CO2 and so offset or prevent emissions and promote an environmentally sustainable mining industry (e.g., [PERSON] et al., 2020; [PERSON] et al., 2013, 2018, 2020; [PERSON] et al., 2014).
Although there are many possible reactions involved in serpentinization (e.g., [PERSON] et al., 1990), they can be simplified:
R1: olivine \(\pm\) orthopyroxene + H2O \(\rightarrow\) serpentine \(\pm\) brucite \(\pm\) magnetite
Clinopyroxene may also be present; however, it is particularly resistant to alteration and will, instead, typically result in the formation of chlorite or tremolite ([PERSON] & [PERSON], 2014). The abundance of minerals occurring in serpentinites, their chemistry, and the extent of serpentinization are subject to significant variability depending on such factors as olivine/pyroxene in the protolith, extent of melt extraction, Mg/ Fe in the primary silicates, and temperature, pH, silica activity, and oxygen fugacity of the system (e.g., [PERSON], 2008; [PERSON] et al., 2009; [PERSON] et al., 2017; [PERSON] et al., 2013, 2014, 2020; [PERSON], [PERSON], [PERSON], et al., 2020; [PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2014; [PERSON] & [PERSON], 1993; [PERSON] et al., 2020). Commonly, serpentinization is considered to be largely isochemical with respect to the major-element cations (Mg, Fe, Ca, Si), involving primarily the addition of water (e.g., [PERSON] et al., 2013; [PERSON] et al., 2020; [PERSON] et al., 2012; [PERSON], 2004; [PERSON] et al., 2020). However, nonisochemical Si-metasomatism and/or Mg-loss/replacement by Ca has been inferred in abyssal periodites at mid-ocean ridges (e.g., [PERSON] et al., 2004; [PERSON] & [PERSON], 2018; [PERSON], 2015; [PERSON] et al., 2006; [PERSON] & [PERSON], 1995).
Highly serpentinized ultramafic rocks are particularly susceptible to carbonation by CO2-bearing fluids and follow three simplified reactions (e.g., [PERSON] et al., 2005):
R2: olivine + brucite + CO2 + H2O \(\rightarrow\) serpentine + magnesite + H2O
R3: serpentine + CO2 \(\rightarrow\) magnesite + talc + H2O
R4:talc + CO2 \(\rightarrow\) magnesite + quartz + H2O
Carbonation is also commonly considered to behave isochemically with respect to the major-element cations ([PERSON] & [PERSON], 2015; [PERSON] et al., 2005; [PERSON] et al., 2018), resulting primarily in the formation of (hydro-)magnesite (e.g., [PERSON] et al., 2005), except for at high degrees of alteration in which some Ca may be added to the system (e.g., [PERSON] et al., 1991; [PERSON] & [PERSON], 2015). These carbonation reactions serve as a proxy for the reactions that are commonly used in experimental carbon sequestration models (e.g., [PERSON] et al., 2020).
Serpentinization and carbonation reactions result in changes in the physical properties of ultramafic rocks, particularly density and magnetic susceptibility (e.g., [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON] et al., 2002; [PERSON] et al., 1990); density is directly related to the volume-integrated density of the rock's mineralogy, whereas magnetic susceptibility is related to the concentration, distribution, and size of ferro-magneticminerals--primarily magnetite ([PERSON] et al., 2020; [PERSON], 2010). Pristine ophiolitic ultramafic rocks should have density and magnetic susceptibility values similar to those of olivine and pyroxene (3.10-3.30 g/cm\({}^{3}\) and \(\sim\)1 \(\times\) 10\({}^{-3}\) SI, respectively). Because serpentinites are dominated by serpentine, brucite (densities of 2.57 and 2.39 g/cm\({}^{3}\), respectively) ([PERSON], 1996), and magnetite, highly serpentinized rocks are typically less dense and show a higher magnetic susceptibility than their unaltered protoliths (e.g., [PERSON] et al., 2016; [PERSON], 1994; [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON], 1997; [PERSON] et al., 1990).
Sperpentization may also result in a volume increase of up to 40%-50% (e.g., [PERSON] et al., 1966; [PERSON], 2020). Although serpentinites do not typically show the particularly high porosity (e.g., [PERSON] et al., 2012) that would be expected considering the significant volume change, the inherent porosity of serpentine and brucite mineral structures may be sufficient to accommodate the fluid flow required for serpentinization to proceed ([PERSON] et al., 2016). Carbonation reactions consume serpentine, brucite, and magnetite to form magnetite with subordinate talc and quartz ([PERSON] et al., 2005; [PERSON], 2009; [PERSON] et al., 2018); magnesite has a density of \(\sim\)3.00 g/cm\({}^{3}\). Thus, fully carbonated ultramafic rocks should be denser and show lower magnetic susceptibilities than serpentinites (e.g., [PERSON] et al., 2005; [PERSON] et al., 2017).
The physical properties associated with the serpentinization and carbonation of ultramafic rocks have been studied for decades in various capacities (e.g., [PERSON] & [PERSON], 1990; [PERSON], 1968; [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON], 1969; [PERSON] et al., 1990; [PERSON], 1975). However, most studies have focused on one or the other process (cf. [PERSON] et al., 2005; [PERSON] et al., 1990) and typically focus on the behavior of the volumetrically dominant harzburgtic rocks (e.g., [PERSON] et al., 2014; [PERSON] et al., 1990). Additionally, most studies focus on either the geochemistry or physical properties of serpentinites. In this contribution, we use \(>\)400 samples of variably serpentinized and carbonated ophiolitic ultramafic rocks collected from the Cache Creek/Atlin terrane in the western Canadian Cordillera (Figure 1) and combine petrographic observations, major-element chemistry, estimates of mineral abundance through quantitative X-ray diffraction (qXRD) and thermogravimetric analysis (TGA), and physical properties (magnetic susceptibility, density, porosity, natural remanent magnetization [NRM]) to constrain the relationships and changes in physical properties that occur during alteration and to determine if and how these may vary as a function of location, protolith, and degree of alteration. Using these results, we present several formulations for determining the %serpentinization of a given sample using chemistry and physical properties and we present a model that uses the physical properties to estimate--at a first order--the mineralogical variability in ophiolitic ultramafic rocks. Due to the carbonation potential of highly serpentinized rocks, we suggest applications of our results to geophysical survey analysis with the goal of remotely identifying the most prospective ultramafic rocks for carbon sequestration.
### Study Sites
The 441 samples in this study were collected from the western Canadian Cordillera by various research groups (e.g., [PERSON] et al., 2004, 2005; [PERSON] et al., 2017, 2018; [PERSON] & [PERSON], 2019; [PERSON] et al., 2018; [PERSON] et al., 2020; [PERSON] et al., 2018 and references therein) from the traditional territories of the Taku River Klingit, Kaska Dena, Tiltan Koneilne, Carcross/Tagish, Tesla Tlinpitt, Tlaztan, Binche Whufen, Yekooche, and Takla First Nations. All localities comprise rocks that are part of the Atlin (equivalent to the undivided Cache Creek in southern B.C.) terrane (Figure 1), which represents Middle Permian to Middle Triassic discontinuous, dismembered ophiolitic mass that may have formed either as ocean core complexes or in supra-subduction zone settings ([PERSON] et al., 2018). The samples were not subjected to greater than greenschist-facies conditions post-emplacement ([PERSON] et al., 2005; [PERSON], 2019; [PERSON] et al., 2020; [PERSON] et al., 2018) and, thus, should preserve their serpentinization- and carbonation-related physical properties ([PERSON] et al., 1988). The northern segment is subdivided into the ophiolitic Atlin terrane and sedimentary overlap assemblages of the Cache Creek complex, whereas the southern segment remains undivided ([PERSON] et al., 2018). The sample set is dominated by rocks from the Decar, Atlin, and Nahlin areas with complementary samples from King Mountain, Hogem, and South Yukon. A summary of the sample suites and data sets used as part of this study are provided in Table S1 and all sample location information and data are given in Table S2.
Figure 1: Lithtectonic map of the Canadian Cordillera (after [PERSON] & [PERSON], 2011) indicating the six main localities used in this study. Note that the extent of the Cache Creek (gray transparent field) and Atlin terranes are clearly demarcated in northern BC/southern Yukon, whereas they are not sub-divided in the south; subdivision after [PERSON] et al. (2018). Town abbreviations: CC, Cache Creek; DI, Dese Lake; FSI, Fort St. James. Province abbreviations: AB, Alberta; BC, British Columbia; MB, Manitoba; NT, Northwest Territories; NU, Nunawut; ON, Ontario; SK, Saskatchewan; YT, Yukon Territory.
## 2 Materials and Methods
We mostly relied on published major-element chemistry data sets ([PERSON], 2005; [PERSON] et al., 2017, 2018; [PERSON], 2019; [PERSON], 2021; [PERSON], 2020). Samples from the Hogem area did not have corresponding published major-element chemistry and these were sent to Geoscience Laboratories for lithogeochemical analysis using the XRF-M01 and IRC-100 packages ([[https://www.mndm.gov.on.ca/sites/default/files/2021_geo_labs_brochure.pdf](https://www.mndm.gov.on.ca/sites/default/files/2021_geo_labs_brochure.pdf)]([https://www.mndm.gov.on.ca/sites/default/files/2021_geo_labs_brochure.pdf](https://www.mndm.gov.on.ca/sites/default/files/2021_geo_labs_brochure.pdf))). Samples that did not have published CO2 estimates were analyzed for their total inorganic carbon at the Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia (EOAS-UBC) using a UIC Inc. CM5130 acidification module and a CM5014 carbon dioxide coulometer.
Quantitative mineralogy for all whole-rock powders was determined by qXRD at the Electron Microbeam and X-ray Diffraction Facility, EOAS-UBC; Atlin samples of [PERSON] (2005) were analyzed in 2004, whereas all other samples were analyzed in 2019-2020; for all instrumentation details and running conditions, see Table S3. Qualitative results for Atlin samples are reported in [PERSON] (2005) and quantitative estimates for the samples were then determined as part of this study. As qXRD estimates for minerals occurring in low abundance (\(\sim\)1%) are relatively uncertain, brucite abundances from Atlin and Dcer samples were further characterized by TGA. The robust correlations between the qXRD and TGA data sets from Atlin and Dcer was used to correct the qXRD results, for which there are a greater abundance of data across the sample set (Figure S1). The correlations between qXRD and TGA data from the two localities differed, which is expected given the different instrumentation and analytical settings; qXRD of Atlin samples were corrected using their respective correction factor, whereas the qXRD of all other samples were corrected according to the Dcer correction factor. All weight% (wt%) qXRD results have been converted to volume% (vol%) abundances using typical densities for each mineral as this more directly relates to the physical properties.
The magnetic susceptibility and density of all samples were first measured at EOAS-UBC. Magnetic susceptibility (\(x\)) was measured using a ZH Instruments SM30 and applying thickness and demagnetization corrections (Table S4 and Figure S2). The reported values reflect the mean of five measurements and the uncertainty reflects the 2 SD. Densities were determined using the masses of samples in air and in water using specific gravity mode of an A&D Company Ltd. EJ-6100 balance. To assess the accuracy of our magnetic susceptibility and density measurements, and to provide additional information on the porosity and NRM, a subset of samples that reflect the full diversity of rock types and degrees of alteration were sent to the Paleomagnetism and Petrophysics Laboratory (PPL) at the Geological Survey of Canada-Pacific (GSC-P) in Sidney, British Columbia; all reported porosity and NRM values reflect analyses done at the PPL. Measurements at PPL were done on a 2.5 cm diameter core of unwenstered material using the methodology and instrumentation as described in [PERSON] et al. (2020). Comparison of physical property results from EOAS-UBC and GSC-P show a near 1:1 linear relationship with an \(R^{2}\) of 0.92 for density (Figure S3a) and a near-linear relationship of log (magnetic susceptibility) with an \(R^{2}\) of 0.97. Both data sets show slight offset to higher values for the GSC data (Figure S3b) and, as such, EOAS-UBC measurements were corrected based on the relationships of the two data sets. The final physical property values that are reported reflect GSC-P physical property measurements when available, otherwise, the corrected EOAS-UBC were used.
## 3 Petrographic Observations, Protoliths, and Volatile Behavior
### Petrographic Observations
Relatively fresh dunitic rocks consist dominantly of 1-6-mm-sized equigranular olivine and primary spinel (Figure 2a). Serpentine in relatively fresh samples is primarily localized along grain boundaries and fine intragrain fractures (Figure 2a). With increasing degrees of serpentinization, olivine grains are cut by serpentine veins of increasing thickness (Figure 2d) until they are fully replaced by mesh texture (Figure 2g); serpentine occurring as massive veins and as mesh texture are likely lizarddite (e.g., [PERSON], 2010; [PERSON] and [PERSON], 1977). Bructice increases in abundance with increasing degrees of serpentinization; in fresher rocks, it occurs in close association with relict olivine grains, whereas in highly serpentinized rocks it occurs as discrete or aggregate grains intergrown with mesh-serpentine or in veins with magnetite. Magnetite is typically absent in the freshest dunitic rocks.
Fresh harzburgtic/lherzolite rocks occur in all study areas and consist of anhedral orthopyroxene (2-6-mm-sized) and clinopyroxene (0.5-3-mm-sized), anhedral to euhedral olivine, and subhedral to euhedral equant Cr-spinel (Figure 2b) ([PERSON] et al., 2018; [PERSON] and [PERSON], 2019). Serpentinization in the relatively fresh samples affects olivine almost exclusively, with orthopyroxene, clinopyroxene, and spinel remaining relatively unchanged with the exception of minor magnetite occurring along grain boundaries (Figures 2b and 2e) and minor orthopyroxene alteration to bastite ([PERSON] et al., 2018). Early serpentinization of olivine in harzburgtic/lherzolite rocks is similar to duitic rocks in that it is primarily restricted to cross-cutting lizardite veins (Figure 2b) that increase in thickness with progressive serpentinization. In the more pervasively serpentinized harzburgtic/lherzolite rocks, olivine and pyroxene are progressively pseudomorphed by lizardite or antigorite, which occurs as blocky to tabular interlocking crystals in the matrix, as anastomosing vein networks, and as bastite (Figure 2h). Although the textures are typical of lizardite and antigorite, the specific serpentine variety was not ascertained. Some pervasively serpentinized samples also exhibit evidence for a third stage of serpentinization involving the formation of chrysotile in veins (e.g., [PERSON], 2021). Brucite in harzburgtic/lherzolite rocks that are >60 %serpentinized occurs in close association with olivine, as grains in the lizardite groundmass, or as aggregates or veins spatially associated with serpentine and/or magnetite (Figure 2h). Rocks in which antigorite dominates rarely contain brucite. Magnetic occurs both as a pseudomorp of primary spinel and as newly formed grains in the serpentine matrix, as veinlets along former grain boundaries, as larger cross-cutting veins and, locally intergrown with awaruite and sulphides ([PERSON], 2017; [PERSON], 2019); magnetite clearly increases in grain size and abundance with greater degree of serpentinization (Figure 2h).
Pyroxene-rich rocks, which include olivine-websterites and wetherites/pyroxenites (<10% olivine) are typically relatively fresh (Figure 2c), with hydration resulting mainly in the replacement of any olivine that
Figure 2. Representative photomicgraphs of the main ultramafic procliths at three increments of their serpentinization process with degree of serpentinization increasing from top to bottom; (dunite: a, d, g; (harzburgtic/lherzolite: b, e, h); (pyroxene-rich samples: c, f, i). The scale bar in each photomicrograph is 1 mm. Also included for each, are the corresponding loss on ignition (LOI) (in wt%), density, and magnetic susceptibility. IL-Atg, interlocking antigorite; V-Lz, vein lizardite.
is present by serpentine (Figures 2f and 2i). As with the other ultramafic protoliths, early serpentinization is localized along olivine intragrain fractures with progressive serpentinization fully replacing the grains. Brucite is typically not observed in pyroxene-rich lithologies and magnetite occurs in relatively low abundances and is restricted to areas in which olivine has been serpentinized. Pyroxene-rich rocks commonly contain talc, chlorite, and/or tremolite.
Early carbonation consists of thin magnesite-calcite veins cross-cutting serpentine veins, as small grains within a matrix of interlocking antigorite, or within basite grains. Such rocks are termed oligosaccharides and are characterized by mineral assemblages dominated by serpentine with minor magnesite and talc (<20 vol% each) (Figure 3a). Progressive carbonation results in the formation of soapstone, which is characterized by a mineralogy dominated by magnesite, with >10 vol% talc, <10 vol% quartz (Figure 3b), and the gradual disappearance of serpentine from the assemblage. The most highly carbonated rocks are termed listwanite (also referred in the literature to as listvenite, listvanite, or listwaenite: e.g., [PERSON] et al., 2018) and these consist primarily of magnesite and >10 vol% quartz with minor talc, and local fuchsite (Cr-mic) (Figure 3c). Brucite in carbonated rocks is restricted to uncarbonated sub-domains in a relatively minor number of opicharbonates. Magnetite is restricted to relief serpentinite sub-domains in opichcarbonate and soapstone.
### Protolith Discrimination and Changes in Volatile Content
The changes in major-element composition during the alteration of ultramafic rocks is generally thought to result from passive dilution by volatiles (e.g., [PERSON] et al., 2013; [PERSON] et al., 2005; [PERSON], 2004). In such a system, the molar ratio [(Mg + Fe\({}^{\mathrm{tot}}\) + Ca)/Si] (herein referred to as the OPE: olivine-pyroxene elemental ratio: [PERSON], 2021) of the samples should provide a reasonable approximation of the olivine/pyroxene in the protolith with OPE >1.93 = opx-poor outline (95-100 wt% olivine), OPE 1.42-1.93 = opx-rich dunite (90-95 wt% olivine) and harbarburite/herzolite/wehrlite (50-90 wt% olivine), OPE 1.15-1.42 = olivine website-terite (10-50 wt% olivine), and OPE <1.15 = websterite/pyroxenite (<10 wt% olivine); opx-rich dunite was combined with harzburgites as there were not many samples in this category. At a given OPE (isolines in Figure 4a), the samples show a systematic increase in loss on ignition (LOI) susceptibility.
Figure 3: Representative photomicrographs of the three main carbonated assemblages with degree of carbonation increasing from top to bottom; (a) ophivalentane; (b) soapstone; (c) listvanite. Scale bar in each photomicrograph is 1 mm. Also included for each, are the corresponding loss on ignition (LOI) and CO\({}_{2}\) (in wt%), density, and magnetic susceptibility.
CO\({}_{2}\) (\(y\)-intercept) and (b) continued increase in CO\({}_{2}\) at 0 wt% H,O. A regression of samples representing R2 to R4 yields a slope of \(-\)2.43 \(\pm\) 0.07 (\(R^{2}\) = 0.92; \(n\) = 121: Figure 4b), which is identical to what would be expected on the basis of changes in the molar mass of a system in which each molecule of H\({}_{2}\)O is being replaced by CO\({}_{2}\) (\(-\)2.44) (Figure 4b). Although some samples show small deviations from the expected volatile regression, significant loss or gain of the principal cation constituents would have resulted in deviations from such a trend and more scatter in the regression. This provides additional evidence that the systems appear to have behaved broadly isochemically with respect to the major elements and involved mainly passive dilution due to the addition of volatiles. The continued gain in CO\({}_{2}\) in H\({}_{2}\)O-free samples likely reflects some nonison-chemical behavior given that many of these samples also plot to the left of the OPE = 2.00 isoline (Figure 2a); this may be in the form of Mg, Ca, or Fe gain or Si loss (e.g., [PERSON] et al., 2004; [PERSON], 2015; [PERSON] et al., 2006; [PERSON] & Dick, 1995).
## 4 Mineralogical and Physical Property Changes During Serpentinization and Carbonation
### Determining %Serpentinization From Major-Element Chemistry
To calibrate LOI as a proxy for degree of serpentinization, the LOI of uncarbonated samples were normalized to their OPE and this was compared to the volt% of nonrelict minerals as determined by qXRD (Figure 5). This normalization accounts for the tendency for olivine-rich samples to yield
Figure 4: Major-element changes with progressive serpentinization and carbonation (a) using [(Mg + Fett + Ca)/Si] to characterize the proportion of olivine (2.00) to pyroxene (1.00) in the ultramafic protolith; solid isochemical lines indicate a peridotritic protolith, while dashed lines indicate an (olivine-)websteritic protolith. (b) Serpentinization and carbonation reactions tracked by H\({}_{2}\)O and CO\({}_{2}\) contents; concentrations of H,O are determined by subtracting CO\({}_{2}\) from loss on ignition (LOI). Red arrows are the trajectories expected based on changes in the molar proportions of H,O and CO\({}_{2}\) whereas the solid black line is a regression of samples with CO\({}_{2}\) > 1 wt% and H,O > 0 wt% and the dashed lines represent the 95% confidence interval.
Figure 5: A calibration for determining %serpentinization using loss on ignition (LOI) and olivine-pyrosene elemental (OPE) ratio. The black solid line represents a regression of the sample set and dashed lines represent the 95% confidence interval. Note the more condensed color scale for LOI compared to Figure 4a.
greater abundances of brucite (e.g., [PERSON] et al., 2020), which would have a higher bulk-rock LOI at a given %s serpentinization due to the greater water content of brucite relative to serpentine (e.g., [PERSON] and [PERSON], 2004). A regression of the data yields a linear relationship (\(R^{2}=0.91\)) for determining %s serpentinization:
\[\%\text{s serpentinization}=13.3\left(\pm 0.4\right)\left(\frac{\text{LOI}}{ \text{OPE}}\right)-1\left(\pm 2\right) \tag{1}\]
where LOI is in wt%, OPE is the olivine-pyroxene elemental ratio, and %s serpentinization refers to 100%--(vol% olivine + pyroxene); uncertainties were determined by quadratic addition of slope and intercept uncertainties. We note that \(\upi\)XRD results have typical relative errors of \(\pm 10\%\)-15% ([PERSON] et al., 2018; [PERSON] et al., 2009) although these effects may be relatively minimal as the data are remarkably consistent despite having been analyzed on two different instruments using different analytical procedures and 15 years apart. Additional uncertainty in this formulation may be introduced due to the potential occurrence of primary spinel, secondary metamorphic olivine, or dehydration due to subsequent metamorphism; however, this too we consider to have minimal effect as primary spinel is typical at abundances of <2 vol% and metamorphic olivine is relatively uncommon in the studied samples. From here on, the %s serpentinization of any uncarbonated samples use the value determined by Equation 1.
### Changes in Mineralogy and Physical Properties During Serpentinization
Weakly serpentinized (<25 %s serpentinized) samples exclusively have OPE <1.42 (Figures 6 and 7) requiring significant pyroxene content; this would dilute the amount of olivine available for serpentinization and is consistent with the higher resistance of pyroxene--particularly clinopyroxene--to hydration relative to olivine. Moderately to pervasively serpentinized (>25 %s serpentinized) samples typically have OPE >1.42 and CaO <1 wt%, indicating that they are dominated by olivine and orthopyroxene. For such rocks, the increasing serpentinization (as indicated by LOI) is also reflected in the quantitative estimates of decreasing relict mineral (olivine + pyroxene) and increasing serpentine abundances (Figure 6a). Brucite and total spinel (i.e., spinel + magnetite) abundances are variable at a given LOI (0-10 vol% and 0-6 vol%, respectively); however, they occur in rocks with as low as 3-4 wt% LOI (30 %s serpentinized) and generally increase in abundance with increasing LOI (Figure 6a-inset). Brucite abundances increase for samples with higher OPE (Figure 7a). Spinel abundances also increase for samples with higher OPE but peak at values of \(\sim\)1.65 after which abundances decrease; above OPE of 1.93 (>95 vol% olivine) spinel abundances sharply decrease (Figure 7b). Rocks with very high brucite contents (>4 vol%) typically have low spinel contents (<2 vol%) (Figure 7).
With increasing serpentinization, the density of the samples decreases consistently from \(\sim\)3.20 g/cm\({}^{3}\) to \(\sim\)2.55\(-\)2.65 g/cm\({}^{3}\) (Figures 6b, 8a, and 9). Within a given interval of low- to moderate-s serpentinization (25%-50% and 50%-75%), density decreases with increasing OPE; however, above 75 %s serpentinization, densities are similar across all samples (Figure 8). The decreasing density with increasing serpentinization defines a linear relationship (\(R^{2}=0.94\); \(n=214\); \(11\) rejected) (Figure 9a):
\[\%\text{s serpentinization}=-169\left(\pm 3\right)\times\left[\text{Density}-3.224 \left(\pm 0.008\right)\right] \tag{2}\]
Figure 6.— (a) Mineralogical and (b–e) physical property variations during serpentinization and carbonation; mineral abundances were determined by quantitative X-ray diffraction (XRD) and alteration is tracked by changes in volatile content (loss on ignition: LOI in wt%); \(K\), magnetic susceptibility; NRM, natural remanent magnetization.
where %serpentinization is defined by Equation 1, and density is in g/cm\({}^{3}\); the 11 samples rejected from the regression have residuals outside 2 SD of the mean.
Samples typically have porosities of \(<\)1% regardless of the degree of serpentinization and OPE, with the exception of samples with an intermediate OPE of 1.42-1.63 (equivalent to 40-60 vol% olivine) and LOI \(>\)10 wt%, which have porosities of up to 3.25% (Figure 6c). Density and brucite contents linearly correlate only for samples with OPE \(>\)1.93 (\(>\)95 vol% olivine) and appears locality specific: samples from Atlin and Nahlin, which occur immediately along strike of each other ([PERSON] et al., 2018) show lower brucite contents for a given density compared to the other localities (Figure 9b).
At a given LOI, magnetic susceptibility varies by over two orders of magnitude. Rocks that are \(<\)25 %serpentinized have magnetic susceptibilities \(<\)3 \(\times\) 10\({}^{-3}\) SI for (Figure 8). From 25 to 75 %serpentinization, the median values and the range in observed values increases across all OPE classes (Figure 8). Above 75 %serpentinization, samples with OPE between 1.42 and 1.93 (40-95 vol% olivine) show relatively consistent and high magnetic susceptibilities values, while samples with OPE \(<\)1.42 and \(>\)1.93 show greater variability and much lower median values (Figure 8).
The general increase in magnetic susceptibility with %serpentinization (Figure 9c) is best defined by an exponential regression (\(R^{2}=0.31\); \(n=203;8\) rejected):
\[\%\text{serpentinization}=\frac{\ln\kappa}{0.037}-2.54 \tag{3}\]
where %serpentinization is defined by Equation 1, and \(\kappa\) is magnetic susceptibility in SI \(\times\) 10\({}^{-3}\). Although this formulation is by no means robust, the data show that magnetic susceptibilities of \(>\)20 SI \(\times\) 10\({}^{-3}\) rarely occur in samples that are \(<\)60 %serpentinized with the exception of those with OPE \(>\)1.93. Magnetic susceptibility correlates strongly with spinel contents for the various OPE intervals (\(R^{2}>0.85\): Figure 9d).
The samples show a wide range of NRM values, spanning \(\sim\)4 orders of magnitude and these broadly increase with increasing serpentinization (Figures 6e and 8c). NRM does not appear to vary systematically as a function of OPE except for samples that are \(>\)75 %serpentinized for which it generally decreases with increasing olivine content. The samples hold relatively high Koenigsberger ratios (\(Q\)-ratio) (Figure 8d) with 48% having values greater than 1. Samples that are \(<\)50 %serpentinized show a wide range in values that do not vary systematically with increases in %serpentinization or OPE (Figure 8). For rocks that are \(>\)50 %serpentinized, there is significant overlap in the \(Q\)-ratios across the various OPE categories; however, in general, for rocks that are 50-75 %serpentinized, the median \(Q\)-ratio values broadly increase with increasing olivine content, whereas for rocks that are \(>\)75 %serpentinized, median values show the reverse relationship (Figure 8d).
### Changes in Mineralogy and Physical Properties During Carbonation
The first phase of carbonation (R2) involves a gradual decrease in serpentine and increase in magnesite abundance, to form ophicarbonate rocks. This is reflected in samples with LOI as low as 8-10 wt% but is most common beginning at \(\sim\)12-13 wt% LOI; ophicarbonate rocks have LOI up to \(\sim\)20 wt% (Figure 6a). The first stage of carbonation is also associated with a disappearance of brucite from the assemblage (Figure 6a-inset). The physical properties of ophicarbonate samples are indistinguishable from those of highly serpentinized samples with OPE 1.42-1.93 (Figure 8).
The second phase of carbonation (R3) is identified by a sharp drop in serpentine abundance concomitant with a more pronounced increase in magnesite and talc abundance to form soapstone (Figure 6a). The median density of soapstone is higher than that of ophicarbonate at \(\sim\)2.86 g/cm\({}^{3}\) (Figures 6b and 8a) and
Figure 7: Olivine-pyroxene elemental (OPE) ratio versus (a) brucite and (b) total spinel abundance as determined by quantitative X-ray diffraction (XRD).
Figure 8:
porosity is relatively low (\(<\)1%: Figure 6c), while median values of magnetic susceptibility, NRM, and \(Q\)-ratio are lower than ophicarbonate samples, although there are variable degrees of overlap (Figures 6d, 6e and 8b-8d).
The final stage of carbonation (R4) involves the final consumption of serpentine-group minerals, a continued increase in magnesite abundance, a decrease in talc content, and an increase in quartz abundance to form listwanite (Figure 6a). Such rocks may also locally contain the Cr-mica, fuchsite. Relative to soapstone, listwanite samples show a further increase in the median density to \(\sim\)2.91 g/cm\({}^{2}\) (Figures 6b and 8a), have variable porosity (up to 2.5%: Figure 6c), and show a continued decrease in median magnetic susceptibility and NRM to \(<\)10 SI \(\times\) 10\({}^{-3}\) (Figures 6d and 8b) and \(<\)1 A/m (Figures 6e and 8c), respectively. The \(Q\)-ratios for listwanite samples are typically \(<\)1, which is similar to that of soapstones (Figure 8d).
Figure 8.— Box-and-whisker plots of (a) density, (b) magnetic susceptibility, (c) natural remanent magnetization (NRM), and (d) Koenigsberger ratio (\(Q\)-ratio) for various degrees of serpentinization and carbonation. The boxes are drawn around the interquartile range (IQR) with the horizontal line representing the median value, which is given to the right of its respective box. Whiskers represent minimum and maximum values with outliers excluded, which were determined using the Tukey test where filled circles are beyond 1.5 x IQR and open circles beyond 3 x IQR. Colors for serpentinites reflect the ophic-pyroene elemental ratio (OPE) scale shown in Figure 6 with the exception of the blue boxes, which represent all samples with OPE \(<\)1.42. Colors for carbonated samples also reflects the symbology shown in Figure 6.
Figure 9.— Changes in (a) density and (c) magnetic susceptibility as a function of %serpentinization showing the most appropriate regression (solid line) and the 9% confidence interval (dashed lines). Variations in (b) brucite and (d) spinel contents with density and magnetic susceptibility, respectively. XRD, X-ray diffraction.
### Co-Variation of Density and Magnetic Susceptibility
On the Henkel plot (density vs. log magnetic susceptibility) the serpentinite samples follow two main trajectories (Figure 10a). The first (T1: Figure 10a) involves a decrease in density and increase in magnetic susceptibility with serpentinization from \(\sim\)3.2 g/cm\({}^{3}\) and 0.3 SI \(\times\) 10\({}^{-3}\) converging to values of 2.6-2.7 g/cm\({}^{3}\) and 100 SI \(\times\) 10\({}^{-3}\); this is followed by most harzburtic samples and a minor proportion of dunitic samples. The second trajectory (T2: Figure 10a) involves decreasing density with only slight increases in magnetic susceptibility from \(\sim\)3.2 g/cm\({}^{3}\) and 0.3 SI \(\times\) 10\({}^{-3}\) converging to values of 2.6-2.7 g/cm\({}^{3}\) and 0.5-20 SI \(\times\) 10\({}^{-3}\);
Figure 10: Forward models of ultramafic rock mineralogy shown on the Henkel plot (density vs. log(magnetic susceptibility) for (a) serpentinites and (b) carbonated ultramafic rocks. Mineral end-members were estimated based on both the theoretical physical properties and the observed physical properties and quantitative X-ray diffraction mineral abundances for the samples. Data from [PERSON] et al. (1990) and references therein and [PERSON] et al. (2014) shown as black data points in part (a). OPE, olivine-pyroxene elemental.
this is commonly observed for dunitic samples and a relatively minor number of harzburgtic samples. The high susceptibility trajectory is widely reported (e.g., [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON] et al., 1990); however, the low susceptibility trajectory, although proposed by [PERSON] et al. (1990) on the basis of typical serpentinization reactions; is rarely observed and documented. [PERSON] et al. (1990) proposed that harzburgtic samples would follow the first trajectory regardless of the volumetric proportions of olivine and orthopyroxene (e.g., Equations 25-32 in Figure 4D of [PERSON] et al., 1990) and this is clearly reflected in our data set that show samples with variable OPE converging to a relatively consistent point. The first trajectory also appears to reflect the majority of samples globally (e.g., [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON] et al., 2002; [PERSON] et al., 1990). The second low susceptibility trajectory, although not commonly observed or documented, has been proposed to occur for both dunitic and harzburgtic rocks in a high fluid/rock environment (e.g., Equations 19-21 in Figure 4C of [PERSON] et al., 1990).
For carbonated rocks (Figure 10b), the physical properties of ophicarbonate rocks are identical to the majority of highly serpentinized samples (high magnetic susceptibility and low density). The most prominent change occurs with subsequent carbonation of ophicarbonate samples and is reflected in increasing density and decreasing magnetic susceptibility observed in soapstone and listwanite samples; the main difference between soapstone and listwanite samples is in a slight increase in density.
## 5 Magnetic Susceptibility Alone Is Not an Accurate Predictor of Extent of Serpentinization
Most prior studies investigating the physical property changes occurring during serpentinization have been focused on rocks with harzburgtic protoliths (e.g., [PERSON] et al., 2014; [PERSON] et al., 1990) as they volumetrically comprise the bulk of ophiolitic complexes ([PERSON] & [PERSON], 2014). Our data on rocks spanning the full range of ultramafic protoliths have added new insight into the behavior of rocks during serpentinization and corroborate the previous works on the stability of magnetite.
Due to the mineralogical simplicity of ultramafic rocks, their chemistry and physical properties vary relatively predictably during serpentinization. We have presented three new formulations (Equations 1-3) for determining the %serpentinization of a given ultramafic rock on the basis of whole-rock major-element chemistry (LOI and OPE), density, or magnetic susceptibility, which were calibrated using quantitative mineralogical estimates (Figure 4), the major-element chemistry- and density-based formulations are far more robust than that based on magnetic susceptibility as has been noted previously (e.g., [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON] et al., 2002). The principal requirement for using these formulations is that it must be ascertained that a given sample is minimally carbonated (<1 wt% CO\({}_{2}\)). In uncarbonated rocks, increased volumes of brucite will tend to result in higher LOI, while in ophicarbonate rocks, carbonation may not always be obvious petrographically as it can be highly domainal and fine-grained, which could also potentially skew LOI to higher levels. These two factors could account for inconsistencies observed in using LOI in previous studies (e.g., [PERSON] et al., 2013). Density-based calibrations have been previously calibrated (e.g., [PERSON], 1997; [PERSON] et al., 2002) and yield similar results to Equation 2; ours differs in that the %serpentinization of the rock has been robustly constrained using quantitative mineralogical determinations and whole-rock chemistry on >200 samples. We have also shown here (Figure 9b) that for dunitic rocks, density should be a relatively accurate predictor of brucite content but that this may be site specific.
Estimating %serpentinization using magnetic susceptibility is far less reliable than density and chemistry as indicated by the regression statistics in Equation 3 and as shown in [PERSON] et al. (2014). This inconsistency may be a product of many factors, including that our samples reflect the full diversity of ultramafic of protoliths and role of mineral chemistry (Mg/Fe in the primary silicates) and the extent and conditions of serpentinization (temperature, pH, \(\alpha\)SiO\({}_{2}\) and oxygen fugacity) in controlling the stability of magnetite and that of the specific serpentine polymorphs and brucite (e.g., [PERSON], 2008; [PERSON] et al., 2009; [PERSON] et al., 2017; [PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON], [PERSON], [PERSON], et al., 2020; [PERSON], [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2014; [PERSON], 1993). A two-stage serpentinization process for ophiolitic harzburgtic is commonly inferred involving: (a) initial replacement of olivine to form Fe-rich lizardite serpentine and brucite at temperatures <200\({}^{\circ}\)C; (b) orthopyroxene breakdown and Si release, which leads to the formation of more magnesium antigorite serpentine and brucite, magnetite, and hydrogen at temperatures of 200-300\({}^{\circ}\)C (e.g., [PERSON] et al., 2006; [PERSON] et al., 2009; [PERSON] et al., 2013; [PERSON] et al., 2014, 2020; [PERSON] et al., 2014). As dumitic rocks lack or contain only minimal orthopyroxene, only the first serpentinization stage would be expected for such lithologies and magnetite production would not be expected. The data set presented herein demonstrates this well in that highly serpentinized dunitic rocks typically contain similar spinel contents to their less-spertinized equivalents (Figure 9) and consequently show relatively low magnetic susceptibilities (\(<\)10 SI \(\times\) 10\({}^{-3}\)) compared to hazburgite-hezlorolite rocks (Figure 7), which show consistently high values (\(>\)50 SI \(\times\) 10\({}^{-3}\). Figure 8). This would indicate that, while magnetic susceptibility may be able to accurately identify highly serpentinized hazburgite rocks, it may not be able to do so for dunitic or pyroxenite-rich lithologies or to distinguish if the rocks are slightly carbonated (ophicarbonates rocks). We do note; however, that the reverse temperature trend has been shown for some abyssal periodites (e.g., [PERSON] et al., 2015); although this seems to be in the minority. Additionally, this two-stage process for the generation of magnetite may only apply to ultramafic rocks originating in the oceanic crust (ophiolitic or abyssal) as highly magnetic dunitic rocks have been observed in komatitis units and mafic-ultramafic intrusions (ter [PERSON] et al., 2019; [PERSON], 2009).
Although hazburgite-hezlorolitic rocks, in general, behave more predictably in terms of their increased magnetite production with serpentinization, there is a subset of samples with OPE between 1.42 and 1.74 that shows high degrees of serpentinization, but very low magnetic susceptibilities (\(<\)10 SI \(\times\) 10\({}^{-3}\)) (Figure 6). These are dominated by samples from the Nahlin locality with a minor number of samples from Decar. The Decar samples exhibiting low magnetic susceptibilities are relatively uncommon and are distinct in that they show evidence for a third stage of serpentinization comprising mainly of chrysofite that overprints the more typical pervasive lizardite and/or antigorite serpentinization (e.g., [PERSON] and [PERSON], 2019; [PERSON], 2021). Since rocks nearby do not show evidence for this third serpentinization phase and do contain abundant magnetite, it is most likely that these samples simply reflect localized regions of transient permeability that destabilized magnetite. Interpretation of the Nahlin samples is more problematic due to a lack of access to the samples or detailed textural documentation of serpentinization. Nevertheless, among the 38 hazburgite-hezlorolitic Nahlin samples, only five of these show magnetic susceptibilities \(>\)10 SI \(\times\) 10\({}^{-3}\) despite being \(>\)50 %serpentinized. There is evidence that the melt-depleted rocks of the Nahlin ophiolite were re-fertilized prior to serpentinization to form intergranular base metal sulphides, clinopyroxene, and Cr-spinel ([PERSON] et al., 2020). Such an event may be the reason that magnetite formation was inhibited. It would, thus, seem that although magnetic susceptibility in general tends to behave predictably for hazburgite rocks, which comprise the bulk of ophiidic ultramafic rocks, there are locality-specific features or events that may inhibit the use of magnetic susceptibility as a proxy for estimating %serpentinization.
## 6 Identifying Ultramafic Carbon Sinks Using Physical Properties
Mineral carbonation of ultramafic rocks can be done through either _in situ_ or _ex situ_ methods; the former involves injection of pressurized CO\({}_{2}\) at depths of \(>\)2 km (e.g., [PERSON] and [PERSON], 2009), whereas the latter would involve introduction of CO\({}_{2}\) into finely crushed material at the surface or passive exposure to the atmosphere (e.g., [PERSON] et al., 2013). For _ex situ_ carbonation, the occurrence of brucite is key due to its high reactivity at surface pressure and temperature conditions, whereas _in situ_ carbonation models invoke the use of olivine as the prime mineral target for carbonation ([PERSON] and [PERSON], 2009). The CO\({}_{2}\) and H\({}_{2}\)O contents of the rocks in this study clearly define two linear arrays (Figure 4b) documenting an initial serpentinization (hydration) event followed by a later carbonation event. No samples have volatile contents that plot between these two arrays suggesting that carbonation only occurred where ultramafic rocks were previously highly serpentinized. We suggest several explanations for this observation:
1. Although serpentinization and carbonation reactions are both thermodynamically favored at low temperatures ([PERSON] et al., 2020), there may be major kinetic barriers to the direct carbonation of olivine and pyroxene (olivine + pyroxene\(\rightarrow\)carbonate + quartz), such that carbonation may only proceed after hydration reactions have created layered silicates (serpentine) and hydroxides (brucite). If serpentinization is a prerequisite for the carbonation of ultramafic rocks, then both _ex situ_ and _in situ_ carbon sequestration plans (e.g., [PERSON] and [PERSON], 2009; [PERSON] et al., 2013) should consider targeting serpentinized rather than fresh mantle rock.
2. The restriction of carbonation to previously serpentinized rock may reflect the evolution of fluid pathways in these initially dry ultramafic rocks whereby initial serpentinization caused by the infiltration of H\({}_{2}\)O-rich fluids along fractures would increase permeability (e.g., [PERSON] & [PERSON], 2012), resulting in preferred pathways for fluid flow which were later used by CO\({}_{2}\)-bearing fluids. In this scenario, the carbonated portions of the ultramafic massits in this study all experienced a similar two-stage fluid infiltration history with early H\({}_{2}\)O-rich fluids followed by later CO\({}_{2}\)-bearing fluids, with the latter only infiltrating fully serpentinized fracture zones.
3. Carbonation is driven by the infiltration of H\({}_{2}\)O-rich, CO\({}_{2}\)-bearing fluids (e.g., [PERSON] et al., 2012) that drives serpentinization fronts ahead of carbonation fronts as a natural consequence of the relative abundances of the two chemical components and the fluid composition being buffered by carbonation reactions. If this reaction pathway is a natural consequence of the infiltration of H\({}_{2}\)O-rich, CO\({}_{2}\)-bearing fluids into peridotite, then _in situ_ direct carbonation of olivine without prior serpentinization (Fo + CO\({}_{2}\)\(\rightarrow\)Mg + Qz) would presumably require the injection of CO\({}_{2}\)-rich solutions; none of the localities in this study provide a geologic record of such a process.
### Modeling Ultramafic Rock Mineralogy
Maximum serpentine and brucite contents occur in samples with 10-14 wt% LOI (>75 %serpentinized) (Figure 6a). In the absence of characterizing the mineral abundance and reactivity of samples in great detail, the physical properties of ultramafic rocks should be effective at predicting--at a first order--mineral content and, thus, a rough estimate of the reactivity of a given volume of rocks. Such an approach has been used to identify the boundaries and extent of carbonation within a serpentinite body (e.g., [PERSON] et al., 2005; [PERSON] et al., 2017) and scanning magnetic microscopy has been used to identify magnetic sources at the micron-scale ([PERSON] et al., 2018); geophysical techniques have yet to be applied for identifying highly serpentinized ultramafic rocks at the outcrop-scale. Two approaches for doing so for serpentinites include: (a) taking physical property measurements of hand-samples or drill-core and/or (b) using physical property models to inform geophysical survey inversions. We follow the methods outlined in [PERSON] et al. (2020), in which the relationship between physical properties and mineral abundances were used as a forward model to calibrate the Henkel plot (Figure 10) and then to inverse model the mineralogy based on physical properties. In this approach, minerals with similar physical properties and that behave in a similar way are grouped together into mineral endmembers and mixing lines with volumetric proportions are calibrated. Three endmembers are used to construct two models: one for (uncarbonated) serpentinites and another for carbonated rocks. In both, end-members and mineral mixing lines are constructed by considering both the theoretical published values for various minerals and the vol% abundance of constituent minerals in the samples as constrained by QXRD.
#### 6.1.1 Forward Modeling
For the serpentinites (Figure 10a), the three mineralogical end-members that we consider are: ultramafic silicates (UM), serpentine and brucite (SB), and magnetite (M). For UM, we use a density of 3.224 g/cm\({}^{3}\) and magnetic susceptibility of 0.3 SI x 10\({}^{-3}\); the former is based on the intercept of Equation 2, while the latter was chosen to encompass all minimally serpentinized samples. For SB, we use a density of 2.558 g/cm\({}^{3}\) and magnetic susceptibility of 0.03 SI x 10\({}^{-3}\); the density was determined from using a 100 %serpentinized value applied to Equation 2 and then assuming 3 vol% magnetite as this would be consistent with the magnetic susceptibility of the samples. The magnetic susceptibility of the SB component was chosen to encapsulate all uncarbonated samples with minimal porosity. A major unknown for ultramafic rocks is the proportion of primary spinel to magnetite; the former is most common in unserpentinized rocks and cannot be distinguished using XRD. Consequently, for the M endmember, we use a density and magnetic susceptibility of 5.20 g/cm\({}^{3}\) and 3000 SI x 10\({}^{-3}\), respectively, which is based on empirical studies that suggest these values to be representative of magnetite regardless of grain size ([PERSON] et al., 1996; [PERSON], 2003). On the Henkel plot for carbonated rocks (Figure 10b), the same SB and M end-members are used for serpentinites but UM is replaced with an endmember reflecting the physical properties of magnesite (MS); although quartz and talc may also be present in carbonated rocks, magnesite is by far the most volumetrically significant. For MS, we use a density of 3.00 g/cm\({}^{3}\) and magnetic susceptibility of 0.3 SI x 10\({}^{-3}\); the former is based on the density of magnesite, while the latter was chosen to fully encapsulate all samples.
#### 6.1.2 Inverse Modeling
For rocks that plot within the curves defined by the forward modeling, we can invert the model to provide estimated volumetric mineral abundances. Following the same framework as in [PERSON] et al. (2020), for the serpentinite model we have three relationships with three unknowns:
\[\begin{split}\text{UM}+\text{SB}+\text{M}=1\\ \left(\text{UM}\text{$\sim$}d_{\text{UM}}\right)+\left(\text{SB} \text{$\sim$}d_{\text{SH}}\right)+\left(M\times d_{\text{M}}\right)=d\\ \left(\text{UM}\text{$\sim$}K_{\text{UM}}\right)+\left(\text{SB} \text{$\sim$}K_{\text{SH}}\right)+\left(M\times K_{\text{M}}\right)=K\end{split}\]
where \(d=\) density \(K=\) magnetic susceptibility, and UM, SB, and M, refer to the volumetric mineral abundances of ultramafic minerals, serpentine + brucite, and magnetite. These are combined as follows:
\[\begin{split}\begin{pmatrix}1&1&1\\ d_{\text{UM}}&d_{\text{SB}}&d_{\text{M}}\\ K_{\text{UM}}&K_{\text{SB}}&K\end{pmatrix}\begin{pmatrix}1\\ \text{SB}\\ \text{M}\end{pmatrix}=\begin{pmatrix}1\\ d\\ K\end{pmatrix}\end{split}\]
Thus,
\[\begin{split}\begin{pmatrix}\text{UM}\\ \text{SB}\\ \text{M}\end{pmatrix}=\begin{pmatrix}1&1&1\\ d_{\text{UM}}&d_{\text{SB}}&d_{\text{M}}\\ K_{\text{UM}}&K_{\text{SB}}&K_{\text{M}}\end{pmatrix}^{\!\
using qXRD. The model magnetite contents are consistently lower than the total spinel as determined by qXRD, which is incapable of separating out the magnetite concentration; this result is to be expected and the model results are considered an accurate estimate of the abundance of magnetite based on there being no (or only negligible quantities) of other highly magnetic minerals present in these rocks (e.g., magnetic sulphides and alloys).
When the inverse model is applied to the carbonated samples, the carbonation minerals (mostly magnetite + talc + quartz) are consistently overestimated for ophicarbonates and underestimated for listwaintes and the opposite is true for hydrous minerals (mostly serpentine). This discrepancy can be explained by the model assumptions that the MS end-member is approximated by the physical properties of magnetite. Overestimation of MS in ophicarbonates could be caused by the presence of relict primary ultramafic minerals, which are still present in such rocks at abundances of up to 15 vol%. Overestimation of MS in listwaintes likely reflects the presence of quartz in the assemblage at abundances of up to 20 vol%. The correlation between calculated and qXRD abundances is shown in Figure 11 and can be used to correct for the systematic bias. In carbonated samples, the calculated magnetite contents of carbonated rocks are highly variable but cluster around the 1:1 line with qXRD spinel abundances. We note that several samples of our samples fall outside the field defined by the mixing lines and would thus yield negative modal abundances according to the inverse model. Samples with densities lower than the SB-M mixing line, likely reflect increased porosity; porosities of 1%-4% are observed in our samples.
### Using Geophysics to Identify and Quantify Ultramafic Carbon Sinks
For a given identified ultramafic body, whose mapped boundaries are relatively well known, the ultimate goal would be to identify and quantify the volumes of serpentinized rocks using remote sensing (i.e., geophysical surveys). The most accurate interpretations of geophysical data sets, such as aeromagnetic or gravity surveys, will involve integration of robust physical property-lithology models. Dunitic protolithus (OPE >1.93) tend to generate the highest brucite content and, thus, will be most reactive, however, harzburgtic rocks (OPE 1.42-1.93) can contain relatively high brucite contents and are volumetrically the most significant in ophiolite massfs and, thus, their physical properties will dominate any geophysical signature.
The systematic drop in density with increased serpentinization across all protolithus indicates that gravity surveys should be the most accurate means for assessing the degree of alteration of a given ultramafic body. If available, and at a sufficiently high resolution, an upper limit of \(\sim\)2.8 g/cm\({}^{3}\) would be effective at identifying most highly serpentinized rocks while excluding fresher and moderately to highly carbonated rocks. However, high-resolution gravity surveys are expensive. Although using magnetic susceptibility to predict the degree of serpentinization is subject to more unpredictable physical property behavior, magnetic surveys are more widespread. In general, highly serpentinized harzburgtic rocks show values of \(>\)20 SI \(\times\) 10\({}^{-3}\) with median values of \(>\)50 SI \(\times\) 10\({}^{-3}\). A lower cut-off of 20 SI \(\times\) 10\({}^{-3}\) should identify all highly serpentinized harzburgtic samples and would exclude many rocks that are \(<\)60 %serpentinized and those that are moderately to highly carbonated (soapstones and listwaintes).
We note that weakly carbonated rocks (ophicarbonates) have identical physical properties to harzburgtic rocks (Figures 7 and 10) and, thus, cannot be discriminated using physical properties and, by extension, geophysical surveys. While the above physical properties limits will result in the identification of false positives--mostly commonly in the form of weakly carbonated rocks--it will rarely result in false negatives. For _ex situ_ carbonation, which relies on highly reactive minerals such as brucite that are no longer stable in the presence of any CO\({}_{\eta}\), the inclusion of ophicarbonates will dilute the overall reactivity of a given volume as ophicarbonate rocks are commonly in close proximity to, or intercalated with, uncarbonated rocks. On the other hand, for _in situ_ carbonation, which could also make use of serpentine minerals, ophicarbonates are still a viable option given the abundance of such minerals in these rocks.
A complication of applying magnetic susceptibility models to magnetic survey data is that the total magnetization of a given anomaly will reflect a combination of its remanent and induced magnetic fields ([PERSON], 2007). Any samples with Koenigsberger ratios (Q-ratio) \(<\)1 will have total magnetization signatures dominated by their induced magnetization (magnetic susceptibility). Samples with Q-ratio >1 will have total magnetization signatures dominated by their NRM and the strength of a given anomaly will depend on its coherence (direction). The high _Q_-ratios recorded in many harzburgitic samples that are <75 %serpentinized (Figure 8d) likely reflects the lack of high volumes of serpentinization-related magnetite and, thus, relatively low observed magnetic susceptibilities (Figures 6d, 8a and 8b). In contrast, the observation of a large range in NRM values (Figures 6e, 8a and 8b) but decreasing median _Q_-ratios (Figure 8d) in more serpentinized samples likely reflects the increased magnetite production during serpentinization. In the absence of information on the direction of the preserved NRM, we refrain from calculating hypothetical total effective susceptibilities; future work will include detailed analysis using oriented samples. Nevertheless, the power of physical property models of ultramafic rocks to inform geophysical inversions with the goal of prospecting for serpentinites was demonstrated by [PERSON] et al. (2020). More detailed analysis of NRM will refine such models for a more accurate assessment of the carbon sequestration capacity of a given volume of ultramafic rock.
### Implications for Imaging Hydration and Carbonation in Subduction Zones
At depths >30-50 km in subduction zones, H2O-CO2 fluids liberated from the downgoing plate infiltrate and react with the overlying forearc mantle wedge, which in turn provides a record of slab-derived fluid infiltration integrated over millions of years (e.g., [PERSON] and [PERSON], 2003). Experiments by [PERSON] et al. (2014) demonstrate that hydration reactions are rapid (months to weeks) confirming the rate of serpentinization is likely controlled by the H2O flux to the reaction front ([PERSON] and [PERSON], 1985). The hydration and carbonation history of ultramafic rocks detailed in this study provides insight into similar reactions expected to occur in the mantle wedge. Rock density systematically decreases with increasing serpentinization, but later carbonation increases rock density (Figure 6b) suggesting that gravity data cannot be simply inverted to determine the degree of mantle-wedge serpentinization. Similarly, strong, deep magnetic anomalies have been cited as evidence of extensive forearc serpentinization in Cascadia ([PERSON] et al., 2005) and other subduction zones. The results presented here suggest serpentinization dramatically increases the magnetic susceptibility of harzburgite, but not dunite. If these results can be extrapolated to the elevated _P_-_T_ conditions of mantle-wedge serpentinization, this implies that the hydrated Cascadia mantle wedge is made up mostly of harzburgite.
This study documents the sequential replacement of serpentinites during CO2 infiltration to form magnesite, talc, and ultimately quartz, which occurred, in part because the ultramafic rocks were interleaved with, and obducted onto, carbonate-bearing sedimentary rocks of the Cache Creek terrane (e.g., [PERSON] et al., 2018). In the case of ultramafic rocks occurring in the mantle wedge in subduction zones worldwide, although the infiltration of CO2-bearing fluids likely occurs as a result of the subduction of carbonate sediments and carbonate-bearing oceanic crust, the reactions and resulting mineral assemblages would be expected to be similar to those observed here and the resulting rheological changes to subduction zone dynamics could be profound. Specifically, deformation experiments ([PERSON] et al., 2008; [PERSON] and [PERSON], 2008) demonstrate that talc is an extremely weak mineral over a wide range of crustal _P_-_T_ conditions, and serpentinite is dramatically weakened by the presence of minor amounts of talc ([PERSON] and [PERSON], 2011). If such minerals were to form along the base of the mantle wedge, this would affect the rheology of the subduction plate interface.
## 7 Conclusions
We present petrological observations, major-element chemistry, quantitative mineralogy, and physical properties from >400 samples of variably serpentinized and carbonated ophiiltic ultramafic rocks collected from the Cache Creek (Atlin) terrane in British Columbia to constrain the physio-chemical changes that occur during the alteration of ultramafic rocks. The samples show a systematic decrease in density during serpentinization that largely reflects a drop in relict ultramafic mineral abundances and an increase in serpentine minerals and an increase in density during carbonation that mostly reflects the formation of magnesite. The samples show two magnetic susceptibility trends during serpentinization: one involves a 100-fold increase in magnetic susceptibility and is followed by most harzburgitic samples, whereas the second involves very little change in magnetic susceptibility and is followed by most dunitic samples and a minor proportion of harzburgitic samples. Using the quantitative mineralogy and physical property relationships, we provide a model that can be used to estimate the mineralogy of variably altered ultramafic rocks (at a first-order). These results can be used as a basis for interpreting gravity or magnetic geophysical surveys in order to prospect for the most prospective ultramafic rocks for carbon sequestration and, potentially, to aid in imaging subduction zone lithological heterogeneity.
## Data Availability Statement
All data forming the basis for this paper are available at [[http://doi.org/10.5281/zenodo.5213140](http://doi.org/10.5281/zenodo.5213140)]([http://doi.org/10.5281/zenodo.5213140](http://doi.org/10.5281/zenodo.5213140)).
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wiley/fb41e296_21ea_4561_aa7e_90b0fcd95440.md | # JGR Atmospheres
Research Article
10.1029/2023 JD039723
Role of Surface Energy Fluxes in Urban Overheating Under Buoyancy-Driven Atmospheric Conditions
[PERSON]
1 Unit of Environmental Engineering, University of Innsbruck, Innsbruck, Austria, 2 Institute of Environmental and Process Engineering (UMTEC), Eastern Switzerland University of Applied Sciences (OST), Rapperswill, Switzerland, 1
[PERSON]
2 Institute of Environmental and Process Engineering (UMTEC), Eastern Switzerland University of Applied Sciences (OST), Rapperswill, Switzerland, 2
[PERSON]
3 Department of Civil Engineering, Monash University, Clayton, VIC, Australia, 4 High Performance Architecture, School of Built Environment, University of New South Wales, Sydney, NSW, Australia3
[PERSON]
1 Unit of Environmental Engineering, University of Innsbruck, Innsbruck, Austria, 2 Institute of Environmental and Process Engineering (UMTEC), Eastern Switzerland University of Applied Sciences (OST), Rapperswill, Switzerland, 1
[PERSON]
1 Unit of Environmental Engineering, University of Innsbruck, Innsbruck, Austria, 2 Institute of Environmental and Process Engineering (UMTEC), Eastern Switzerland University of Applied Sciences (OST), Rapperswill, Switzerland, 1
Footnote 1: email: [EMAIL_ADDRESS]
###### Abstract
Urbanization alters land surface properties in absorbing, reflecting and emitting radiation as well as infiltrating, evaporating and storing water. This consequently modifies surface energy and water fluxes and, thus, urban climates. Weak synoptic flow, clear sky conditions and higher surface temperatures in cities compared to their rural surroundings create a buoyancy-driven atmospheric circulation, in which surface energy fluxes become the main determinants of urban daytime overheating. Here, we demonstrate the role of surface energy fluxes for warming and cooling processes in the urban canopy layer under buoyancy-driven atmospheric conditions. We improve and apply an integrated CFD-GIS modeling approach to provide a detailed analysis of fine-scale land-atmosphere interactions and assess the surfaces' profound implications on energy and water exchange. We show that variations in the ratios of the surface energy fluxes to the net radiation can be separated from meteorological conditions (wind speed, air temperature and incoming solar radiation) and emissivity values, varying explicitly with changes in land surface type and water availability for vegetated areas. Based on the energy flux ratios, we introduce an approach to assess the surface-induced warming and cooling effect and its contribution to urban overheating in the urban canopy layer, under buoyancy-driven atmospheric conditions, directly applicable to strategic urban planning for climate change adaptation. Independent of meteorological conditions, this approach can be used to evaluate different surface materials (both natural and artificial) and climate adaptation measures, such as urban nature-based solutions and blue-green infrastructures, and to monitor changes in the energy and water balance.
2023 JD039723
2023 JD039723
4 AUG 2023
Accepted 18 JUN 2024
**Author Contributions:**
**Conceptualization:** [PERSON]
**Data curation:** [PERSON]
**Formal analysis:** [PERSON]
**Funding acquisition:** [PERSON]
**Investigation:** [PERSON]
**Methodology:** [PERSON], [PERSON]
**Project administration:**
**[PERSON]**
**Resources:** [PERSON],
**[PERSON], [PERSON]
**Software:** [PERSON]
**Supervision:** [PERSON]
**[PERSON], [PERSON]
**Visualization:** [PERSON]
**[PERSON], [PERSON]
**Visualization:** [PERSON]
**Writing - original draft:** [PERSON]
**Role of Surface Energy Fluxes in Urban Overheating Under Buoyancy-Driven Atmospheric Conditions**
**[PERSON]**1 Unit of Environmental Engineering, University of Innsbruck, Innsbruck, Austria, 2 Institute of Environmental and Process Engineering (UMTEC), Eastern Switzerland University of Applied Sciences (OST), Rapperswill, Switzerland, 2
Footnote 1: email: [EMAIL_ADDRESS]
Footnote 1: email: [EMAIL_ADDRESS]
###### Abstract
Urbanization alters land surface properties in absorbing, reflecting and emitting radiation as well as infiltrating, evaporating and storing water. This consequently modifies surface energy and water fluxes and, thus, urban climates. Weak synoptic flow, clear sky conditions and higher surface temperatures in cities compared to their rural surroundings create a buoyancy-driven atmospheric circulation, in which surface energy fluxes become the main determinants of urban daytime overheating. Here, we demonstrate the role of surface energy fluxes for warming and cooling processes in the urban canopy layer under buoyancy-driven atmospheric conditions. We improve and apply an integrated CFD-GIS modeling approach to provide a detailed analysis of fine-scale land-atmosphere interactions and assess the surfaces' profound implications on energy and water exchange. We show that variations in the ratios of the surface energy fluxes to the net radiation can be separated from meteorological conditions (wind speed, air temperature and incoming solar radiation) and emissivity values, varying explicitly with changes in land surface type and water availability for vegetated areas. Based on the energy flux ratios, we introduce an approach to assess the surface-induced warming and cooling effect and its contribution to urban overheating in the urban canopy layer, under buoyancy-driven atmospheric conditions, directly applicable to strategic urban planning for climate change adaptation. Independent of meteorological conditions, this approach can be used to evaluate different surface materials (both natural and artificial) and climate adaptation measures, such as urban nature-based solutions and blue-green infrastructures, and to monitor changes in the energy and water balance.
## Plain Language Summary
The aim of this study is to better understand the impact of different surface characteristics (both natural and artificial) on soil-surface-atmosphere interactions and, consequently, on the urban meteorology. This is important to improve the assessment of climate change impacts and adaptation strategies in cities. We present an approach, directly applicable in strategic urban planning for climate change adaptation, that can describe the surface-induced warming and cooling effect under low wind and clear sky conditions, when surface thermal forcing is the dominant factor in urban overheating. Separable from meteorological conditions (wind speed, air temperature and incoming solar radiation) and emissivity values, our approach can be used to rapidly evaluate changes to the surface characteristics, for example, through the implementation of urban nature-based solutions and blue-green infrastructure in cities. We highlight the importance of water availability in heat mitigation strategies to ensure evaporative cooling from green areas, and the hazardous potential of impermeable artificial surfaces to increase diurnal and nocturnal heat transfer.
## 1 Introduction
Changes in land use and land cover alter the land-atmosphere coupling, leading to changes in water, energy and carbon cycles, affecting atmospheric circulation and resulting in regional changes in climate ([PERSON] & [PERSON], 2016; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2021). A shift from permeable to sealed surfaces alters the partitioning of the surface energy fluxes ([PERSON] et al., 2017), increases runoff while reducing infiltration and evapotranspiration rates ([PERSON] et al., 2017; [PERSON] et al., 2013), thereby modifying the relationship between the surface energy and water balances and directly affecting climatic conditions at multiple scales ([PERSON] et al., 2014; [PERSON] et al., 2006; [PERSON] et al., 2013). Current trends in global urbanization are exacerbating urban overheating ([PERSON] et al., 2022), substantially impacting livability and sustainability in cities as well as human health ([PERSON] et al., 2017). With evapotranspiration representing a primary
## 4 Journal of Geophysical Research: Atmospheres
### Writing - review & editing:
[PERSON], [PERSON]
### Writing - review & editing:
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON]
However, synoptic-scale weather conditions (i.e., large-scale weather patterns extending >1,000 km) and local background climate have been shown to play an important role in the genesis, development and magnitude of urban overheating ([PERSON] et al., 2021; [PERSON] & [PERSON], 2000; [PERSON] et al., 2018). [PERSON] et al. (2014) demonstrated that the geographic variation in urban daytime overheating in different cities in the US can be related to the local background climate, which, depending on the climate regime ([PERSON] et al., 2022), affects the efficiency of cities in heat convection from the surface to the lower atmosphere and exceeds evapotranspiration in controlling urban daytime overheating.
At the urban microscale, horizontal heat and momentum advection manipulate meteorological conditions in both the urban boundary layer (air mass above the rooftops) and the urban canopy layer (air mass between the ground and the rooftops), with critical effects on the near-surface temperature and urban overheating ([PERSON] et al., 2022; [PERSON] & [PERSON], 2022; [PERSON] et al., 2021). Increased surface roughness and thermal properties in cities lead to warmer conditions and reduced wind speed at the near-surface layer ([PERSON] & [PERSON], 1999a). However, the complex interactions between the surface and the boundary layer sometimes lead to opposite effects, such as urban cooling ([PERSON] et al., 2011; [PERSON] et al., 2015) and an acceleration of wind speed ([PERSON] et al., 2018). Using a 2.5D integrated modeling approach based on the coupled capabilities of Computational Fluid Dynamics (CFD) and Geographic Information System (GIS) software, that allows for fine-scale (0.2 m horizontal accuracy) analysis of micro- and bioclimatic conditions in urban areas, [PERSON] et al. (2023) demonstrated the interactions between wind speed and air temperature patterns, land surface temperature and human thermal comfort using the Universal Thermal Climate Index (UTCI) ([PERSON] et al., 2010), and their small-scale horizontal and vertical variations in a specific part of the alpine city of Imsbruck, Austria. Their results highlight the importance of horizontal heat and momentum advection, which if neglected could lead to misinterpretation of hot and cool spots in the city.
In contrast, weak synoptic flow and clear sky conditions support the development of thermal effects in cities ([PERSON] et al., 2017). Weak wind conditions (typically less than 3 m/s) and higher surface temperatures in cities compared to their rural surroundings create a buoyancy-driven atmospheric circulation that carries surface influences upward, causing the urban boundary layer over a city to appear as dome shaped ([PERSON] et al., 2017; [PERSON] & [PERSON], 2002; [PERSON] & [PERSON], 2022). In this case, surface energy fluxes become the main determinants of urban daytime overheating. The surface energy balance is fundamental in the interconnected earth-atmosphere system and is commonly expressed as,
\[\text{Q}=\text{LE}+\text{H}+\text{G}, \tag{1}\]
comprising the net all-wave radiation (Q), latent heat flux (LE), sensible heat flux (H) and substrate heat flux (G) ([PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2016). At the surface, net all-wave radiation is partitioned into the three energy fluxes. Latent heat and the available water absorbing the energy govern evaporation and transpiration processes, transporting water vapor away from the surface by diffusion or advection. Sensible and substrate heat control the heat transfer between the surface, the underlying soil and the overlying atmosphere by conduction and convection. The ratio of sensible heat flux to latent heat flux is termed the Bowen ratio ([PERSON] & [PERSON], 2014). Surfaces exhibiting a Bowen ratio greater than one imply, (a) that a larger proportion of energy is repartitioned as sensible heat ([PERSON] et al., 2017), (b) lower soil moisture availability ([PERSON] et al., 2014), and (c) increased land surface temperature and enhanced heat exchange by convection. This increases near-surface air temperature ([PERSON] et al., 2017). Surfaces with a Bowen ratio below one imply, (a) that a larger proportion of energy is repartitioned into latent heat ([PERSON] et al., 2017), (b) higher soil moisture availability ([PERSON] et al., 2014), and (c) decreased land surface temperature and favor the evapotranspiration-driven cooling effect, thereby decreasing near-surface air temperature ([PERSON] et al., 2014). Soil moisture availability manipulates water fluxes and energy partitioning at the surface and, thus, the processes of plant transpiration and bare soil evaporation ([PERSON] et al., 2017; [PERSON] et al., 2010). As urban areasstrongly influence the urban water cycle, a higher degree of surface sealing causes higher runoff rates, less groundwater recharge and, consequently, lower evapotranspiration ([PERSON] et al., 2017). The surface energy balance and the surface water balance are thus directly related through evapotranspiration and latent heat respectively. The surface water balance is mathematically expressed as:
\[P=E+R+I, \tag{2}\]
which describes the partitioning of precipitation (P) into evapotranspiration (E), runoff (R), and infiltration (I) ([PERSON] et al., 2017; [PERSON] et al., 2010). Changes in land cover and land use modify the partitioning of both surface energy and surface water balances, as schematically illustrated in Figure 1 for four different land cover types, with common Bowen ratios (typical mean values are indicated in bold, expected ranges for the different land cover types in brackets) and annual mean values for individual components of the surface water balance after [PERSON] et al. (2017). Components of the surface energy balance are schematically presented as ratios of the individual surface heat fluxes (LE--latent heat flux, H--sensible heat flux and G--substrate heat flux) to the net radiation (Q).
Given the importance of synoptic weather conditions, local background climate and horizontal heat and momentum advection for the genesis of the urban climate and the development and magnitude of urban overheating, this study focuses on the role of surface energy fluxes for the warming and cooling processes in the urban canopy layer under buoyancy-driven atmospheric conditions.
Assessing changes in the surface characteristics is becoming increasingly important to understand the impacts of climate change and to improve adaptation strategies in cities. Reducing the degree of surface sealing and increasing the amount of vegetation promotes multiple benefits, including the reduction of urban overheating ([PERSON] et al., 2021). Urban nature-based solutions and blue-green infrastructures are therefore often proposed as an adaptation strategy ([PERSON] et al., 2023; [PERSON] et al., 2022). However, to assess climate change impacts and evaluate adaptation strategies, studies rely on air temperature measurements ([PERSON] et al., 2021), modeled human thermal comfort ([PERSON] et al., 2021), or remotely sensed surface temperatures ([PERSON] et al., 2021; [PERSON] et al., 2019), all of which depend on meteorological conditions and, thus, overlook the contribution of changing surface characteristics to urban overheating. As such, there is a need for an approach that can assess the effects of
Figure 1: Partitioning of the surface water balance components (annual mean values based on [PERSON] et al. (2017)) and the surface energy balance components (schematically illustrated)—created using Biorender (2024).
changing surface characteristics on urban overheating independently of meteorological conditions in order to analyze the driving forces of warming and cooling processes in the urban canopy layer under buoyancy-driven atmospheric conditions. This study addresses this need.
We further improved and applied an integrated modeling approach according to [PERSON] et al. (2021, 2023), based on CFD and GIS software capabilities for spatial analysis, and additionally set up an analytical model to provide a detailed analysis of fine-scale land-atmosphere interactions. We describe the role of surface energy fluxes, and their relationship to water availability in the evapotranspiration-driven cooling effect and in the heat transfer between surface and atmosphere. Detailed analysis of conducted simulations in the analytical model show that variations in the ratios of the surface energy fluxes to the net radiation (schematically illustrated in Figure 1) can be separated from meteorological conditions (wind speed, air temperature and incoming solar radiation) and emissivity values, varying explicitly with changing vegetation health (quantifiable by means of the Normalized Difference Vegetation Index--NDVI) and, thus, changes in land surface type and water availability for vegetated areas. With direct application to strategic urban planning for climate change adaptation, we introduce an approach to describe the surface-induced warming and cooling effect based on the ratios of surface energy fluxes to the net radiation. This approach can be used to (a) evaluate different surface materials (both natural and artificial by means of water availability and the thermal admittance), and climate adaptation measures, such as urban nature-based solutions and blue-green infrastructures, (b) monitor changes in the energy and water balance, and (c) assess the surface-induced warming and cooling effect and its contribution to urban overheating. While (a) and (b) can be conducted independently of meteorological conditions, (c) is only applicable under buoyancy-driven atmospheric conditions.
## 2 Methodology
### Study Area
The case study is a specific area of interest in the alpine city of Innsbruck, the capital of Tyrol in western Austria, situated at 47 deg16'N and 11 deg24'E in the Inn Valley at an altitude of approximately 574 m above sea level. Our area of interest is located north-east of the city center (black outline in Figure 2), where we have carried out a detailed analysis of land-atmosphere interactions using an integrated modeling approach. Land cover within the case study, comprising five classes (roads, dry grass, irrigated grass, buildings and trees--shown in Figure 2), was reclassified as per [PERSON] et al. (2021). Located at the intersection of the zonal oriented Inn valley and the meridional oriented Wipp valley, the strongest winds are southerly \"foen\" winds, whereas under weak synoptic forcing and clear sky conditions, thermally driven flows in the Inn valley are favored, with down valley (westerly) winds at night and up valley (easterly) winds during the day ([PERSON] et al., 2020).
Figure 2: The alpine city of Innsbruck, geographic location and land cover classification for the case study area (black outline).
### Data Acquisition and Software Used
We used a digital elevation model (DEM) with an accuracy of 0.5 m, color-infrared (CIR)-image rasters with an accuracy of 0.2 m and a building vector layer. The DEM and CIR airborne remote sensing images were provided by the local government \"Land Tirol.\" The building vector layer of Tyrol (ESRI Shapefile format) is freely accessible (Federal Ministry of Finance, 2024). CIR images are false color photographs that show the reflected electromagnetic waves from an object. On the basis of the CIR images, we derived the NDVI. Information from the CIR image and the NDVI respectively was further used to derive substrate heat flux, Bowen ratio and vegetation water content. NDVI represents a well-established and widely used spectral vegetation index and is typically used to classify vegetation health and density ([PERSON] et al., 2012; [PERSON] et al., 2012) or estimate the phytomas ([PERSON] and [PERSON], 2014). Within urban areas, the NDVI can be used for land cover classification ([PERSON] et al., 2012) or urban tree canopy mapping ([PERSON] et al., 2012). A relationship between the NDVI and land surface temperature associated with urban land use types and patterns has also been observed ([PERSON] et al., 2007). The NDVI is calculated based on the ability of the surface to reflect certain wavelengths within the electromagnetic spectrum. Depending on the condition of the vegetation, Near Infrared (NIR) reflectance is reduced for stressed plants and increased for actively growing vegetation. Therefore, the NDVI can be calculated using Equation 3, which is based on the relationship between the NIR reflectance and the reflectance of the red light (Red) from the visible light spectrum.
\[\text{NDVI}=\frac{(\text{NIR}-\text{Red})}{(\text{NIR}+\text{Red})} \tag{3}\]
The NDVI displays values ranging between \(-1\) and \(1\). Negative values are a good indication for impervious surfaces and water. The higher the value, the healthier and vital the vegetation. Essential meteorological parameters (air temperature, wind speed and direction, relative humidity, cloudiness and vapor pressure) were measured at a meteorological station within the case study area. We utilized the commercial GIS and CFD software packages ESRI ArcMap v10.8.1 (ESRI, 2019) and Ansys(r) Fluent, Release 2020 R1 (Ansys, 2020) to conduct our analyses and evaluate simulation results. Input values for global, direct and diffuse radiation were calculated using the ArcMap _Area Solar Radiation_ tool, including slope and aspect information from the DEM (at an accuracy of 0.5 m) and radiation parameters according to the atmospheric conditions for the selected day and time step (15 th July 2020 at 3 p.m.). The tool is based on the hemispherical viewshed algorithm developed by [PERSON] et al. (1994) and further developed by [PERSON] (2000) and [PERSON] (2002). With the position of the sun and the heights of the buildings and trees included, the algorithm calculates global, direct and diffuse radiation considering the shadowing effect. Using the DEM and the classification mentioned in Section 2.1, building and tree heights were determined.
### Coupled CFD-GIS Modeling Approach
We improved and applied an integrated modeling approach according to [PERSON] et al. (2021, 2023), based on CFD and GIS software capabilities, to provide a detailed analysis of fine-scale land-atmosphere interactions using the data described in Section 2.2. Improvements to the modeling approach were made by including the capabilities to calculate the turbulent heat fluxes, the potential evapotranspiration (measure of the ability of the atmosphere to remove water from the surface through the processes of evaporation and transpiration assuming sufficient water supply) and the vegetation water content. To avoid excessive reference, the following description of the modeling approach can be consulted in detail in [PERSON] et al. (2021, 2023).
In general, we use the GIS software to conduct all necessary calculations on a 2D basis and the CFD software to additionally provide horizontal and vertical variability in air temperature and wind speed on a 3D basis. The basis for all calculations in the GIS software is a raster-based CIR image combined with the information on meteorological conditions, thermal characteristics (i.e., diffuse, direct and incoming solar radiation, as was described in Section 2.2) and surface characteristics (i.e., emissivity, Bowen ratio and sky view factor). Based on this combined data set and well-established physical relations in the model set-up, we use an adapted approach from [PERSON] et al. (2010) and [PERSON] et al. (2010) to first evaluate Land Surface Temperature (LST), followed by the Mean Radiant Temperature (MRT) and, finally, the UTCI. The modeling approach calculates the micro- and bioclimatic conditions based on the information of the combined data sets according to a specific sequence of equations to be solved for each individual grid cell. The resolution of this combined geospatial raster data set isthat of the input CIR image. In this study, we use CIR images with a resolution of 0.2 m. The output of the modeling approach is a fine-scale (0.2 m) raster image that allows access to and display of all variables used in the equations, as well as the LST, MRT, and UTCI of each individual grid cell. So long as relevant input data is available, the modeling approach can be repeated at different times of the day. However, this initial approach is static, as the values for air temperature and wind speed were set to be the same for each individual grid cell. Hence, values for air temperature and wind speed respectively were assumed to be steady throughout the case study area.
To effectively account for the effects of flow dynamics on these variables in an urban environment, we use the capabilities of CFD methods. The CFD solver runs independently of the GIS-based modeling approach, generating detailed data sets of the air temperature and wind speed, which are then transferred to the GIS-based model. For CFD simulations, we prepared a sufficiently detailed 3D representation of the urban infrastructure within our case study area. The 3D model includes accurate dimensions and placement of the majority of the buildings, approximate number and height of trees and the size and extent of open areas. However, rooftops were assumed to be flat and trees were generalized as simple cuboids to reduce model mesh complexity. This 3D model was then used to generate an optimal mesh to be used as the solution domain for the CFD solver. Other details incorporated into the CFD simulation included constant temperature conditions for buildings, horizontal surfaces and the initial air temperature and wind velocities. Further details on the mesh generation and preparation of the CFD simulation can be found in [PERSON] et al. (2023).
The CFD solver simulates the behavior of fluid flow (in this case, air) as it interacts with the urban infrastructure (including the trees), while also accounting for heat transfer between the different media. As the air flows and interacts with different surfaces with different thermal conditions, the air properties also change. The vertical distribution of wind speeds, follow the log wind profile. Again we refer to [PERSON] et al. (2023), where this relationship was demonstrated and the vertical distribution of wind speed, air temperature and the UTCI was analyzed. Information about underground structures and soil properties was not considered in this study.
Furthermore, spatial mean surface temperatures were assigned to the different land types in the 3D building model (i.e., trees, surface, and buildings). Surface temperature was calculated using the initial GIS-based modeling approach according to [PERSON] et al. (2021). As the output raster represents a fine-scale image that would be too precise for the CFD software (accuracy of 0.2 m according to the CIR image used), spatial mean values were generated through raster resampling for the three land types mentioned. Temperature data of building envelopes were approximated by measuring exemplary surface temperatures of building walls from the four cardinal directions using a thermal camera and associated post-processing software (InfraTec GmbH, 2015). The resulting four temperatures were assigned to each building within the case study area. With the initial air temperature and wind speed set, the simulation created a detailed air velocity-temperature contour for the case study.
Finally, spatially distributed air temperature and wind speed data sets from the CFD software were spatialized in the GIS software. Data sets were converted from the CFD software into a text format (\(c\)sx file) with associated x and y coordinates. These data sets were added to the GIS software as point clouds with air temperature and wind speed attached to the x and y coordinates. Points were then interpolated into a spatial raster and georeferenced according to the coordinates of the case study area. As the simulations in the CFD software are run on a 3D basis, generated air temperature and wind speed data sets can be extracted for different heights. Specifically, a height of 1.75 m was used to model bioclimatic conditions (MRT and UTCI), while a height of 0.2 m was used to calculate the LST. Air temperature and wind speed data for the two different heights were combined with the aforementioned CIR image, thermal and surface characteristics. At this stage, each individual grid cell of the combined geospatial raster data set now provides different air temperature and wind speed values according to the flow dynamics in our case study and underlying boundary conditions.
Hereon, the GIS-based modeling approach calculates the micro- and bioclimatic conditions based on the information of the combined data set, including the CFD-generated air temperature and wind speed data, according to the specific sequence of equations to be solved for each individual grid cell. At this point, we refer to the Supporting Information S1, where the equations used are described in detail. We used Equations S1-S10 in Supporting Information S1 based on [PERSON] et al. (2021, 2023) to calculate micro- and bioclimatic conditions and Equations S11-S21 in Supporting Information S1 to calculate the turbulent heat fluxes, the potential evapotranspiration and the vegetation water content. The following Section 2.4 provides further details on the simulations of micro- and bioclimatic conditions in this study.
### Conducted Simulations
For a detailed analysis of land-atmosphere interactions in an urban area, we used CIR images with an accuracy of 0.2 m. This level of accuracy is necessary to account for the heterogeneity of surface characteristics in cities and their influences on water and energy exchange between soil, surface and atmosphere as well as on micro- and bioclimatic conditions on a small scale. However, images of such accuracy at a reasonable spatial extent are limited by their temporal availability. Therefore, we were only able to use one CIR image captured in late August 2016 (shown in Figure 2) for the initial detailed analysis in the integrated modeling approach and two additional images captured in late August 2019 and 2022 for the demonstration of the model's direct applicability to assess surface-induced warming and cooling effect and its contribution to urban overheating.
The three aerial CIR images, provided by the local government \"Land Tirol,\" represent a static point in time and, thus, limit this study in terms of the temporal variability of CIR images and NDVI information on a daily to monthly basis. However, a comparison of all three images shows differences in surface characteristics, as the images are influenced by changes in urban infrastructure and by different precipitation patterns during the preceding summer months (June, July, August), which affected vegetation health and, thus, NIR reflectance. The CIR image captured in late August 2016 represents wet preconditions, with the recorded accumulated daily precipitation for the summer months (490 mm) well above the long-term average of accumulated daily summer precipitation between 1961 and 1990 (358 mm). The CIR image captured in late August 2019 represents dry preconditions, with a recorded accumulated daily precipitation for the summer months of 269 mm. The 2019 image represents the summer drought ([PERSON] et al., 2022) and heatwave ([PERSON] et al., 2020; [PERSON] et al., 2020) that prevailed across the European continent and, therefore, including Innsbruck. The CIR image captured in late August 2022 represents average preconditions, with a recorded accumulated daily precipitation for the summer months of 338 mm. Values of recorded accumulated daily precipitation were obtained from Geosphere Austria (2024).
We can represent spatially distributed conditions for a given point in time and under given meteorological conditions with very high accuracy, provided that CIR images can be provided in rapid succession to capture diurnal variations. We conducted our analysis by setting up the coupled CFD-GIS modeling approach using the 2016 CIR image, including the specific sequence of Equations S1-S21 in Supporting Information S1 solved individually for each grid cell, in our case study area.
In order to set up and run the coupled CFD-GIS modeling approach as described in Section 2.3, further data was required. Measurements using a thermal camera to approximate the temperature data of the building envelope, as well as measurements of different surface types throughout the case study, were conducted on 15 th July 2020 around 3p.m. These data sets have previously been used in [PERSON] et al. (2023) for validation between modeled and measured LST. As we used the same data sets to approximate the temperature data of the building envelope as input values to the CFD software, we also used the same time of year (15 th July 2020 around 3p.m.) to set the meteorological conditions in the models accordingly. To conduct simulations using the coupled CFD-GIS modeling approach, we first calculated air temperature and wind speed patterns in our case study using the CFD software. According to the conditions on 15 th July 2020 at around 3 p.m., we set the input variables for the CFD simulation as follows: The initial air temperature was set to 23.7\({}^{\circ}\)C, the initial wind speed was set to 4 m/s, surface temperature was set to 39.4\({}^{\circ}\)C, building roof temperature was set to 47.1\({}^{\circ}\)C and tree temperature was set to 27\({}^{\circ}\)C. The following temperatures were assigned to the four cardinal directions of the building walls: north (23.0\({}^{\circ}\)C), east (29.0\({}^{\circ}\)C), south (42.0\({}^{\circ}\)C) and west (27.0\({}^{\circ}\)C). The CFD software generates 3D air temperature and wind speed patterns throughout the case study. We extract air temperature and wind speed data for heights of 0.2 and 1.75 m above ground.
After translating the spatially distributed air temperature and wind speed data sets for two different heights, 0.2 and 1.75 m above ground, from the CFD software into the GIS software, we set the atmospheric conditions in the ArcMap _Area Solar Radiation_ tool accordingly and calculated global, direct and diffuse radiation. Likewise, we set the meteorological conditions according to 15 th July 2020 at around 3 p.m. in the coupled GIS modeling approach to calculate all variables using the specific sequence of Equations S1-S21 in Supporting Information S1 solved individually for each grid cell. In addition to the already included CFD-generated air temperature and wind speed data sets, vapor pressure was set to 945.0 hPa, cloudiness was set to 2.0 Okta and relative humidity was set to 42.8%. These data sets are measured data from a meteorological station set up in the case study area, as already mentioned in Section 2.2.
Due to the disadvantage in computational time in CFD modeling and the consequent limitation in the spatial extent of our analysis, we set up an analytical model including the same specific sequence of equations, solved individually for each NDVI value from 1.0 to \(-\)0.5. An NDVI value of \(-\)0.5 is the minimum value observed in the images that still represents a sealed surface and not water. Whilst the coupled CFD-GIS modeling approach allows spatially detailed analysis within the boundaries of our case study, the analytical setup of the modeling approach allows detailed analysis of individual variables and the relationship between these variables, the micro- and bioclimatic conditions and the NDVI. Air temperature, wind speed, incoming solar radiation and emissivity values can be set at will to analyze their influence on all calculated variables.
For calculations in the analytical model, we selected a specific location in the case study area that is representative of an open field and took specific values from the coupled CFD-GIS generated raster data set to be set accordingly in the analytical model. Thus, we set incoming solar radiation to 837 W/m\({}^{2}\) (with diffuse radiation to 93.30 W/m\({}^{2}\) and direct radiation to 743.69 W/m\({}^{2}\)), wind speed to 4 m/s, air temperature to 23.7\({}^{\circ}\)C, surface emissivity to 0.96, sky view factor to 0.68, vapor pressure to 945.0 hPa, cloudiness to 2.0 Okta and relative humidity to 42.8%, and calculated the Bowen ratio, the surface energy fluxes, the ratios of energy fluxes to the net radiation, VWC, PET, LST, and UTCI for the entire NDVI range using the specific sequence of Equations S1-S21 in Supporting Information S1. Air temperature, wind speed, incoming solar radiation and emissivity values were varied to analyze their influence on the energy fluxes, LST and UTCI for different NDVI values and Bowen ratios.
## 3 Results
Based on the spatially distributed patterns of investigated variables (i.e., Bowen ratio, the surface energy fluxes, the ratios of energy fluxes to the net radiation, VWC, PET, LST, and UTCI), we investigate the role of surface energy fluxes, and their relationship to water availability in: (a) the evapotranspiration-driven cooling effect and (b) the heat transfer between the surface and the atmosphere. Further detailed analysis of conducted simulations in the analytical model show that variations in the ratios of surface energy fluxes to the net radiation (LE/Q, H/Q, G/ Q) can be separated from meteorological conditions (wind speed, air temperature, incoming solar radiation) and emissivity values. They vary explicitly with changing NDVI values and, thus, changes in land surface type and water availability for vegetated areas.
### Evaportranspiration-Driven Cooling Effect
The amount of potential evapotranspiration positively correlates with the proportion of latent heat fluxes (Figure 3a), describing the transport process of absorbed energy as water vapor away from the surface. PET and LE are linear in Figure 3 because the latent heat of vaporization (see Equation S20 in Supporting Information S1) only changes between 2.446 and 2.410 with air temperature changing between 23.3 and 38.5\({}^{\circ}\)C in our study. Air temperature is the only variable in the equation. Assuming sufficient water availability, PET varies between 0.0 and 0.91 mm/hr (Figure 3b) strongly relating to the amount of energy available for latent heat (Figure 3c) and, thus, the Bowen ratio (Figure 3d). As the Bowen ratio decreases, PET increases (Figure 3a), favoring the evapotranspiration-driven cooling effect. As PET assumes sufficient water availability ([PERSON] and [PERSON], 2016), information about the vegetation water content (VWC) is essential. It has been shown that diurnal variability of the Bowen ratio is primarily driven by water availability ([PERSON] and [PERSON], 2012). This relationship is clearly visible in Figures 3d and 3e. Results show that VWC varies between 0.0 and 1.9 kg/m\({}^{2}\) for grassland and 7.5 and 8.5 kg/m\({}^{2}\) for trees (mixed forest) in this study (Figure 3c). To enhance the evapotranspiration-driven cooling effect, vegetation health must be maintained or improved by water supply, which in turn is recognizable by higher VWC and lower Bowen ratios. Correspondingly, the available energy is preferably repartitioned into latent heat rather than sensible heat (Figures 3c and 3d). A higher amount of radiation would also result in a greater amount of latent heat, as more available energy is repartitioned into both turbulent heat fluxes, simultaneously increasing PET, but, consequently, exposes vegetation to higher heat stress. This would result in a higher amount of water supply to maintain vegetation health status, leading to a decrease in the VWC, if not sufficiently supplied with water via precipitation or irrigation.
### Heat Transfer Between the Soil, Surface, and Atmosphere
The ratio of substrate heat fluxes to net all-wave radiation (G/Q) indicates the amount of stored energy as a percentage of the net all-wave radiation (Figure 4a), which can vary between 30% and 50% in urban areas([PERSON] & Oke, 1999b; [PERSON], 2003). Due to the high resolution of the data sets used in this study, we can observe this ratio varying between 10% and 50%. Absorbed radiation leads to an increase in substrate heat fluxes (G) (Figure 4b). During the day, substrate heat fluxes transfer heat from the surface into the underlying soil by
Figure 4: Relationship between the ratio G/Q and the Bowen ratio (a). The vertical axis depicts the ratio G/Q, and the horizontal axis depicts the Bowen ratio. Spatial distribution of (b) substrate heat flux (G), (c) Bowen ratio (\(\beta\)), (d) land surface temperature (LST), and (e) the ratio of substrate heat flux to net radiation (G/Q).
Figure 3: Relationship between PET, LE, and Bowen ratio (a). The vertical axis depicts PET, and the horizontal axis depicts LE. Spatial distribution of (b) potential evapotranspiration (PET), (c) latent heat flux (LE), (d) Bowen ratio (\(\beta\)), and (e) vegetation water content (VWC).
conduction, whereas during night-time this relationship is reversed, leading to a heat transfer from the surface to the atmosphere. These effects are amplified with an increase in Bowen ratio (Figure 4c) and are also visible in higher surface temperatures (Figure 4d). Not to be neglected is the fact that over the course of the day, shadows have a large effect on surface energy fluxes by reducing incoming solar radiation and, thus, LST, but increasing, human thermal comfort ([PERSON] and [PERSON], 2011). This can be observed, for example, in the shaded areas close to the building walls (Figure 4d). Our results indicate a relationship between the Bowen ratio and G/Q (Figure 4a), the latter mathematically quantifiable as a logarithmic function of the Bowen ratio (\(R^{2}=1\)). The fact that the coefficient of determination of the logarithmic function fits perfectly directly results from the substitution of the two equations used to calculate the Bowen ratio and the substrate heat flux (see Equations S1 and S2 in Supporting Information S1). Using this relationship, we identify a threshold at G/Q = 0.31, corresponding to a Bowen ratio of 1.0, representing the point at which the proportion of sensible heat fluxes exceeds that of latent heat fluxes. As such, this threshold reveals areas of increased heat transfer from the surface into the underlying soil, which, when reversed at night, contributes to an increase in nocturnal intraurban heat due to heat transfer from the surface to the atmosphere.
### Independence From Meteorological Conditions
We analyzed the effects of varying wind speed (Figure 5a), air temperature (Figure 5b), incoming solar radiation (Figure 6a) and emissivity values (Figure 6b) on surface energy fluxes, LST and UTCI in the analytical model. In addition to LE, H, and G, we considered the effects of combined sensible heat and substrate heat fluxes (H + G) (Figures 5 and 6). Both Figures 5 and 6 show the effects on surface energy fluxes, LST and UTCI for four different variation runs of changing wind speed, air temperature, incoming solar radiation and emissivity values. The initial conditions for all runs were set as described in Section 2.4 with the exception of wind speed which was set to 0 m/ s. By definition, sensible and latent heat fluxes intersect at a Bowen ratio of 1.0. The amount of energy transferred into the underlying soil positively correlates with the Bowen ratio, simultaneously reducing the available energy for the turbulent heat fluxes. By adding substrate heat fluxes to sensible heat fluxes, a second point of intersection becomes visible, where the latent heat flux exceeds this sum and vice versa. This intersection occurs at a Bowen ratio of 0.52, representing a threshold, similar to the turning point already mentioned by [PERSON] et al. (2021) to differentiate between urban vegetation and artificial surfaces and their effects on LST. Figures 5 and 6 show that, with changes in wind speed, air temperature, incoming solar radiation and emissivity values, quantitative values of energy fluxes change. However, both intersection points (indicated using vertical dashed lines in Figures 5 and 6) do not change, remaining at a Bowen ratio of 0.52 and 1.0, respectively. Thus, we observe the relationship between H + G and LE maintaining its validity despite changes to meteorological conditions and emissivity values. This led us conclude that quantitative values of the surface energy fluxes change with variations in these variables. However, their proportions remain unaffected.
Following from this observation, we analyzed the effects of changing meteorological conditions (air temperatures, wind speed) on the ratios of surface energy fluxes to net radiation (LE/Q, H/Q, and G/Q). Figures 7a-7c shows the ratios of energy fluxes to the net radiation (LE/Q, H/Q, G/Q) calculated using the CFD-GIS modeling approach and depicted in the GIS software. Despite substantial variations in both wind speed and air temperature across the study area (Figures 7d and 7e), LE/Q, H/Q, and G/Q appear unaffected by these patterns (Figures 7a-7c). Notably, the only variable influencing their change is the NDVI (Figure 7f). Furthermore, since we calculate the Bowen ratio directly from NDVI data using Equation 5, the aforementioned statement applies equally for the Bowen ratio. With increasing NDVI values, LE/Q also increases, while both H/Q and G/Q decrease and vice versa.
Since we calculated emissivity values based on the NDVI, Figure 7 does not include variations in emissivity values. However, changing emissivity values in the analytical model (with wind speed and air temperature kept unchanged) shows that the proportions of surface energy fluxes LE/Q, H/Q, G/Q remain unchanged, much like the observations in Figures 5 and 6. Likewise, the Bowen ratio does not change with varying meteorological conditions and emissivity values but solely with changes in the NDVI. We emphasize, that, for this purpose, we did not use the initial Bowen ratio calculated based on the NDVI using Equation S2 (see Supporting Information S1) but instead recalculated the Bowen ratio based on results using Equations S11 and S12 (see Supporting Information S1), which include variations in meteorological conditions. Nevertheless, as the Bowen ratio is unaffected by these variables, values based on Equations S11 and S12 (see Supporting Information S1) are very similar to those from the NDVI-based Equation S2 (see Supporting Information S1). This evidence overall, supports the fact that, variations in the ratios of surface energy fluxes to net radiation can be separated from meteorological conditions (air temperature, wind speed and incoming solar radiation) and emissivity values, varying explicitly with changing NDVI values and, thus, changes in land surface type and water availability for vegetated areas.
## 4 Application in Strategic Urban Planning for Climate Change Adaptation
For direct application in strategic urban planning for climate change adaptation, we introduce an approach based on the ratios of surface energy fluxes to the net radiation and the Bowen ratio as the determinant to describe the surface-induced warming and cooling effect in the urban canopy layer under buoyancy-driven atmospheric conditions. We define Bowen ratio-based thresholds that explain the effects of different proportions of LE/Q, H/ Q, G/Q, and H + G/Q on the surface-induced warming and cooling effect, different climate/soil moisture regimes and on the heat transfer between the soil, surface and atmosphere by means of the ratio of the thermal admittance between the soil and the atmosphere. We are able to extend the approach to the entire city and demonstrate its direct and rapid applicability to evaluate different surface materials (both natural and artificial) and to monitor changes in the energy and water balance by comparing data sets from 2016, 2019, and 2022. Using our approach
Figure 5: Effects of variations in wind speed (a) and air temperature (b) on the Universal Thermal Climate Index (UTCI), the land surface temperature (LST) and the surface energy fluxes (LE, H + G, G, and H). The vertical axes denote temperatures (’C’) at the top and energy (W/m’) at the bottom, and the horizontal axis depict the Bowen ratio, which applies to all graphs in (a) and (b).
enables detailed assessment of the surfaces' profound implications on energy and water exchange, urban overheating and the warming and cooling processes in the urban canopy layer, independently of meteorological conditions. The coupled CFD-GIS modeling approach, including the disadvantage in computational time of CFD modeling, is no longer required and detailed and rapid analysis at multiple scales (citywide to microscale) is possible.
### The Surface Induced Warming and Cooling Effect
We use the correlation between the proportion of the surface energy fluxes and the Bowen ratio and their separability from meteorological conditions and emissivity values to introduce a tipping point distinguishing the surface-induced cooling effect (higher proportion of latent heat fluxes increasing evaporative cooling) from the surface-induced warming effect (higher proportion of combined sensible and substrate heat fluxes increasing heat transfer between the soil, surface, and atmosphere). This tipping point is notably detectable at the exact Bowen ratio (0.52) and NDVI band value (0.33). The latter is determined by Equation S2 (see Supporting Information S1), as we calculate the Bowen ratio solely based on the NDVI. From here, we use the Bowen ratio values as
Figure 6: Effects of variations in incoming solar radiation (a) and emissivity values (b) on the Universal Thermal Climate Index (UTCI), the land surface temperature (LST) and the surface energy fluxes (LE, H + G, G, and H). The vertical axes denote temperatures (”C) at the top and energy (W/m\({}^{2}\)) at the bottom, and the horizontal axis depict the Bowen ratio, which applies to all graphs in (a) and (b).
the determinant of surface-induced warming and cooling effect based on the ratios of surface energy fluxes to the net radiation and explain in the following Section 4.2, the implications of surface energy fluxes on the warming and cooling processes in the urban canopy layer, under buoyancy-driven atmospheric conditions.
A value-add of this relationship is the ability to scale calculations up to citywide observations without running further CFD-GIS simulations. We calculated the Bowen ratio from the 2016 NDVI data set across the entire city (Figure 8a) down to an accuracy of 0.2 m (Figure 8b). Once NDVI data sets are available, the Bowen ratio can be rapidly calculated using Equation S2 (see Supporting Information S1). Figure 8 illustrates which areas contribute to a cooling effect and which areas contribute to a warming effect. Forests surrounding the city and patches of green areas within the city clearly contribute to the evapotranspiration-driven cooling effect. With Bowen ratios below 0.52, these areas indicate consistent presence of water, through either precipitation or irrigation, only depending on energy for enhanced evapotranspiration. Within the city, such areas can be considered cool spots. Agricultural land in both west and east corners of the city show a variability in Bowen ratios stretching from wet (well irrigated) to dry (not irrigated fallow fields) regimes. The city center, the airport runway, and further built-up areas (industrial, commercial and residential areas) in the western and eastern districts exhibit Bowen ratios above 2.0. These areas can be considered hot spots, as contribution to a warming effect proceeds during the day and night.
Figure 7.— (a-c) Ratios of surface energy fluxes to net radiation (H/Q, G/Q, and LE/Q). (d) Spatial wind speed distribution at 0.2 m. (e) Spatial air temperature distribution at 0.2 m. (f) The graphs show a certain number (\(n=1,000\), except for NDVI \(=-0.5\); \(n<1,000\)) of raster cells (\(0.2\times 0.2\) m) in the study area representing a specific NDVI (0.5, 0.3, 0.1, \(-0.1\), \(-0.3\), and \(-0.5\)). The vertical axes depicts air temperature on the right hand side and proportion of the ratios of surface energy fluxes on the left hand side, and the horizontal axis depicts wind speed.
### Implications of Surface Energy Fluxes on Warming and Cooling Processes
Under buoyancy-driven atmospheric conditions, we show the effects of varying proportions of LE/Q, H/Q, G/Q, and H + G/Q on the warming and cooling processes in the urban canopy layer, distinguishing between natural and artificial surfaces. Specific Bowen ratio values indicate thresholds that distinguish between the surface warming and cooling effect (Figure 9a), different energy or water limited climate/soil moisture regimes (Figure 9b) and the heat transfer between the soil, surface and atmosphere by means of the ratio of the thermal admittance between the soil and the atmosphere (Figure 9c). The presented values in Figure 9 are born from the conducted simulations in the analytical model (see Section 2.4). The correlations drawn in Sections 4.2.1 and 4.2.2 for natural and artificial surfaces are based on the work of [PERSON] et al. (2010) and specifically found in Chapter 6.3.1 of [PERSON] et al. (2017), respectively. The color schemes representing the Bowen ratio in Figures 8 and 9a are the same. As such, the implications of the different surfaces on the warming and cooling processes in the city, based on varying proportions of LE/Q, H/Q, G/Q, and H + G/Q, indicated by Bowen ratios as the determinants, are visible.
#### 4.2.1 Natural Surfaces
The evaporative fraction defined by the ratio of latent heat fluxes to net radiation (LE/Q) correlates with the VWC and the Bowen ratio (Figure 9). [PERSON] et al. (2010) presented relationships between climate/soil moisture regimes and evapotranspiration regimes and the correlation with LE/Q. Thereby, with an increase in the evaporative fraction, the regime changes from dry and transitional conditions, implying a soil moisture dependency, to a wet condition, implying an energy dependency ([PERSON] et al., 2010). We argue that the transitions from dry to transitional, wet conditions, and, thus, from a soil moisture limited to an energy limited regime, can be identified based on the ratios LE/Q, H/Q, G/Q, and H + G/Q, using the specific Bowen ratio thresholds as determinants (Figures 9b and 9d). Three thresholds arise from this: (a) a Bowen ratio between 0 and 0.52 (LE/Q > H/Q + G/Q) to imply a wet climate/soil moisture regime and an energy limited evapotranspiration-driven cooling effect, (b) a Bowen ratio between 0.52 and 1.0 (LE/Q < H/Q + G/Q but LE/Q > H/Q and LE/Q > G/Q) to imply a transitional climate/soil moisture regime and a soil moisture/water limited evapotranspiration-driven cooling effect and (c) a Bowen ratio above 1.0 (LE/Q < H/Q + G/Q and LE/Q < H/Q and LE/Q < G/Q) to imply a dry
Figure 8: Calculated Bowen ratio from an NDVI data set representing the situation in late August 2016 for the entire city of Innsbruck, Austria (a) and a detailed extent representing the case study area (b). The Bowen ratio is used as the determinant to show the surface induced warming and cooling effect valid under buoyancy-driven atmospheric conditions.
climate/soil moisture regime and a soil moisture/water limited evapotranspiration-driven cooling effect. From Figure 9 it can be seen that only a wet energy limited climate/soil moisture regime contributes to a cooling effect.
#### 4.2.2 Artificial Surfaces
For Bowen ratios above one, we suggest that the main driver of the variability of LE/Q, H/Q, G/Q, and H + G/Q is the thermal admittance (\(\upmu\)) of the material present, thus its capability of transferring heat between the soil, surface and atmosphere. The thermal admittance is linked to the ability to store heat as well as to the diurnal fluctuation of surface temperatures ([PERSON] et al., 2017). The ratio of the thermal admittance of both the substrate (\(\upmu\)) and atmosphere (\(\upmu\)) describes the sensible heat shared between the two media (H/G) ([PERSON] et al., 2017). From this, a threshold appears (Figures 9c and 9d) at a Bowen ratio of 2.0 with: (a) a Bowen ratio between 1.0 and 2.0 implying a higher proportion of sensible heat (H/G \(>\) 1.0) and surfaces that quickly heat up during the day and quickly cool down during the night and (b) a Bowen ratio above 2.0 implying a higher proportion of substrate heat (H/G \(<\) 1.0) and surfaces that slowly heat up during the day but also slowly cool down during the night. The latter contributes to increased nocturnal urban heat as the energy stored during the day is released at night when the turbulent heat fluxes are reversed.
### Citywide Application
The value-add of the established analytical relationship based on the CFD-GIS modeling approach is the ability to rapidly scale-up relationships to the entire city without the need to re-run or adapt the simulation model. To
Figure 9: Implications of different surfaces, indicated by Bowen ratios (\(\upbeta\)) as the determinants, in correlation with the vegetation water content (VWC) for grassland, on the warming and cooling processes, based on varying proportions of the ratios of surface energy fluxes to the net radiation (LE/Q, H/Q, G/Q, and H + G/Q). (a) Surface-induced warming and cooling effect. (b) Wet, transitional and dry climate/soil moisture regime and energy or water limited evapotranspiration-driven cooling effect for natural surfaces. (c) Ratio of the thermal admittance of the substrate (\(\upmu\)) and atmosphere (\(\upmu\)) describing the sensible heat (H) shared between the two media (H/G). (d) Specific \(\upbeta\)-based thresholds at 0.5, 1.0, and 2.0 and associated NDVI band values. The vertical axes depicts VWC on the left hand side and the proportion of the ratios of surface energy fluxes on the right hand side, and the horizontal axis depicts \(\upbeta\). This illustration was created using Biorender (2024).
demonstrate the capabilities of this approach for immediate application in strategic urban planning for climate change adaptation, we calculated the Bowen ratio from NDVI data sets (based on the CIR images of 2016, 2019, and 2022 provided by the local government \"Land Tirol\") across the entire city (Figures 10a-10c) and used the thresholds described in Section 4.2 and shown in Figure 9 to show the surface-induced warming and cooling effects down to an accuracy of 0.2 m (shown in Figure 8), valid under buoyancy-driven atmospheric conditions. We present the results in Figure 10, differentiating between green spaces and sealed surfaces to highlight the effects of different preconditions (wet--average--dry) on the two different surfaces.
Comparing the different years highlights the effects of precipitation and irrigation deficits in 2019. Conveniently, the 2019 data represents the summer drought ([PERSON] et al., 2022) and heatwave ([PERSON] et al., 2020; [PERSON] et al., 2020), which prevailed across large expanses of Europe including Innsbruck (Figure 10b). With water availability and vegetation substantially influencing the energy partitioning, increasing the degree of vegetation in cities effectively increases the cooling effect. However, if not sufficiently supplied with water the evapotranspiration-driven cooling effect diminishes. This is clearly visible across the entire city during the heatwave and dry period in 2019 (Figure 10b). Due to changing surface properties toward drier conditions, less energy is repartitioned into the latent heat flux (LE), which would favor the evaporative cooling effect. In the 2019 image (Figure 10b), the evaporative cooling effect over the city appears predominantly soil moisture/water limited, as most of the urban green spaces have shifted to a transitional soil moisture regime due to the lack of water availability. Simultaneously, more energy is repartitioned into the sensible heat flux (H) and the surface heat flux (G) on green spaces and sealed surfaces, increasing surface-atmosphere heat transfer and deteriorating the human thermal comfort.
Almost all built areas must be considered hot spots, with Bowen ratios high above 2.0. Additionally, dense areas with a low degree of vegetation indicate hazardous locations of extreme heat, posing potential health risks. Under buoyancy-driven atmospheric conditions, increased sensible and substrate heat fluxes, and, thus enhanced heat
Figure 10.— Surface induced warming and cooling effect based on thresholds using the Bowen ratio as the determinant for the entire city of Innsbruck, Austria, for 2016 (a), 2019 (b), and 2022 (c), valid under buoyancy-driven atmospheric conditions. The images represent the effects of different preconditions: wet in 2016, dry in 2019 and average in 2022, differentiating between green spaces and sealed surfaces. All graphs in (a)–(c), indicating accumulated daily summer precipitation, are from Gesophere Austria (2024).
transfer between the soil, surface and atmosphere, are the main contributors to the overheating process. The lack of water from precipitation and irrigation (visible in Figure 10b) exacerbates the heating process, reducing the energy repartitioned into latent heat and diminishing the evapotranspiration-driven cooling effect. This highlights the importance of water availability for the urban vegetation to ensure that the cooling effect exceeds the warming effect. Thereby enhancing evapotranspiration and increasing human thermal comfort by reducing UTCI values.
## 5 Discussions
Advancements in remote sensing over the past decades have improved the quality of urban heat assessments and Urban Heat Island (UHI) studies, with large-scale satellite and airborne-based LST measurements able to overcome the challenges of conducting high-resolution air temperatures at similar scale level ([PERSON] et al., 2019). Emerging from these improvements, an increasing number of assessment and mitigation studies elaborated on the spatio-temporal behavior of UHIs, with enhanced foci on LST-based Surface Urban Heat Island (SUHI) ([PERSON] & [PERSON], 2017; [PERSON] et al., 2018; [PERSON] et al., 2021). The positive correlation between LST and the degree of surface sealing describes the intensity of the SUHI which, identical to the UHI effect, is higher in urban environments compared to rural areas ([PERSON] et al., 2018; [PERSON] et al., 2021). However, limitations in UHI approaches ([PERSON] & [PERSON], 2010) and uncertainties and deviations between modeled and measured LST-based SUHI are still apparent. [PERSON] et al. (2021) found LST-based SUHI to overestimate heat stress and the contribution of urbanization to the local temperature, when compared to crowdsourced air temperatures. [PERSON] et al. (2023) demonstrated that LST correlates with thermal conditions near the ground surface rather than with those at elevated heights (1.75 m), which are, however, more representative of the human thermal comfort. With wind speed generally lower near the ground surface, the strength of the correlation between air temperatures, human thermal comfort and LST decreases with increasing height. Their results support the hypothesis that studies solely based on LST overestimate human thermal discomfort. Other studies emphasized seasonal differences and variations across climate zones ([PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2022) and different diurnal and nocturnal driving mechanisms of the SUHI ([PERSON] et al., 2012).
From the continuously growing scientific literature on UHI intensity and heat mitigation studies, [PERSON] et al. (2020), pointed out the difficulties of using the concept of the UHI effect and its magnitude to study and evaluate urban heat mitigation strategies. This is supported by the fact that the UHI magnitude is a function of different features (e.g., morphology, roughness and surface characteristics) of both urban and rural environments ([PERSON] et al., 2020). To avoid possible misinterpretations, they suggest a shift from temperature difference-based heat assessments between cities and their rural surroundings, to analyzing temperature differences within urban areas such as between different Local Climate Zones (LCZ) as presented in [PERSON] and [PERSON] (2012). Furthermore, using the term \"urban heat mitigation\" to describe strategies aiming at cooling cities seems more accurate than referring to reducing UHI intensities ([PERSON] et al., 2020). Building upon [PERSON] et al. (2020), our work supports their findings and extends these reflections one step further.
We present quantitative evidence arguing for a timely transition from temperature difference-based to surface energy flux-based studies under buoyancy-driven atmospheric conditions. For cities such as Sydney, Australia, where the overheating process is dominated by advective air mass movement, studies must include urban advection and synoptic scale weather conditions for comprehensive urban heat analysis. In particular, this includes all coastal cities and cities near desert landmasses. Under buoyancy-driven atmospheric conditions, our approach can be used to assess the surface-induced warming and cooling effect across an entire city and/or in different parts of the city with different LCZs, as proposed by [PERSON] and [PERSON] (2012). In this way, surfaces that contribute excessively to a potential overheating process can be located and the effectiveness of urban adaptation strategies, such as urban nature-based solutions and blue-green infrastructures, can be analyzed. Furthermore, different LCZs can be assessed and compared based on their annual or periodic (summer months) mean values of the partitioning of the ratios of surface energy fluxes to the net radiation. Moreover, our results indicate that variations in the ratios of the surface energy fluxes to the net radiation can be separated from meteorological conditions, varying explicitly with changes in land surface type and water availability for vegetated areas. Therefore, independent of meteorological conditions, the ratios allow to evaluate and compare different surface materials (both natural and artificial), by means of water availability and the thermal admittance. Finally, improving the energy and water balance of our cities is essential to meet future challenges. The ratios of the surface energy fluxes to the net radiation can describe the energy and water exchange between the soil, surface and atmosphere for a variety of surface characteristics. Hence, these ratios can be applied to monitor changes in the energy and water balance. As such, applying our approach to urban greening can improve irrigation strategies across the city. Depending on the available data sets, the approach is applicable from citywide to urban microscale.
## 6 Limitations
As the underlying data sets represent one particular point in time in late August 2016, 2019, and 2022, diurnal and seasonal variations in the ratios are not depicted in this study. In addition, our study results are born from modeling environmental processes and, thus far, lack specific field measurements validating the outcomes. As such, further in-depth studies are necessary, including both measurement campaigns and modeling of diurnal and nocturnal conditions. Ratios of surface energy fluxes to the net radiation could be derived from measured surface energy fluxes, for example, from reference meteorological stations provided by the FLUXNET network ([PERSON] et al., 2022), and compared with data sets obtained using the approach presented in this study. Thus, our results are derived from theoretical and conceptual analyses, whose plausibility can be assured, but which still need to be validated by comparison with concrete measurements or comparable data sets. The modeling approach and the underlying equations presented in this study include vital environmental factors and well-established physical relations to accurately represent land-atmosphere processes and their effects on urban micro- and bioclimatic conditions. Therefore, we retain a high degree of confidence in the results of this study. It must be reiterated that the results of this study promote the application of the approach under buoyancy-driven atmospheric conditions to assess the surface-induced warming and cooling effect and its contribution to urban overheating. However, evaluation of different surface materials and climate adaptation measures, such as urban nature-based solutions and blue-green infrastructures, and monitoring of changes in the energy and water balance can be carried out independently of meteorological conditions and emissivity values.
## 7 Conclusions
We demonstrated the relationship between the surface energy fluxes, potential evapotranspiration (PET), vegetation water content (VWC), land surface temperature (LST), the human thermal comfort (by means of the UTCI - Universal Thermal Climate Index), the Bowen ratio and the NDVI (Normalized Difference Vegetation Index), in dependency of varying meteorological conditions, using fine-resolution results (0.2 m) from an integrated modeling approach based on the coupled capabilities of Computational Fluid Dynamics (CFD) and Geographic Information System (GIS) software. Additionally, we set up an analytical model using the same specific sequence of equations to provide a detailed analysis of fine-scale land-atmosphere interactions, investigating the effects of changing meteorological conditions (wind speed, air temperature and incoming solar radiation) and emissivity values. Analyzing the effects of changing meteorological conditions and emissivity values on the surface energy fluxes revealed that the ratios of surface energy fluxes to the net radiation (LE/Q, H/Q, G/Q, and H + G/Q), can be separated from meteorological conditions and emissivity values, varying explicitly with changing NDVI values and, thus, changes in land surface type and water availability for vegetated areas.
For direct application in strategic urban planning for climate change adaptation, we introduce an approach based on the ratios of surface energy fluxes to the net radiation and the Bowen ratio as the determinant to describe the surface-induced warming and cooling effect in the urban canopy layer under buoyancy-driven atmospheric conditions, that is, weak wind and clear sky conditions. We introduced a threshold to separate the surface induced cooling effect (higher proportion of latent heat fluxes increasing evaporative cooling) from the warming effect (higher proportion of combined sensible and substrate heat fluxes increasing heat transfer between the surface, soil, and atmosphere). This threshold is indicated by a Bowen ratio of 0.52 matching an NDVI value of 0.33. Using our approach enables detailed assessment of the surfaces' profound implications on energy and water exchange, urban overheating and the warming and cooling processes in the urban canopy layer, independently of meteorological conditions. Furthermore, different surface materials (both natural and artificial, by means of water availability and the thermal admittance), as well as climate adaptation measures, such as urban nature-based solutions and blue-green infrastructures, can be evaluated and changes in the energy and water balance can be monitored.
The results and conclusions drawn from our findings are based on well-established physical relations including vital environmental factors that accurately represent land-atmosphere interactions, using a modeling approach that has so far only been applied to a specific case study area in the alpine city of Innsbruck in Austria. As the modeling approach is based on verified mathematical and physical principles and is able to account for detailed meteorological and biogeophysical processes within the urban canopy layer, we are confident that our statements remain valid in other cities under similar conditions (i.e., buoyancy-driven atmospheric conditions), although we are aware that further research (i.e., comparison with other approaches and measured data) is needed to confirm the results.
Our findings highlight that a lack of water from precipitation and irrigation exacerbates the heating process under buoyancy-driven atmospheric conditions, reducing the energy repartitioned into latent heat and diminishing the evapotranspiration-driven cooling effect. Therefore, we emphasise the importance of water availability in heat mitigation strategies to ensure an evapotranspiration-driven cooling effect on vegetated areas, and highlight the dangerous efficacy of artificial impermeable surfaces in increasing diurnal and nocturnal heat transfer. Enabling detailed and rapid analysis on a citywide scale, our approach can significantly contribute to a better understanding of the role of surface energy fluxes in daytime urban overheating and improve the assessment of the impacts of land cover and land use change on ecological and human systems.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The digital elevation model (DEM), the color-infrared (CIR)-image raster and the building vector layer, used as input data sets in the integrated CFD-GIS modeling approach calculating specific parameters, were provided by the local government \"Land Tirol\" and can be downloaded from the Austrian national open data repository (Federal Ministry of Finance, 2024). We used the commercial software packages ESRI ArcMap v10.8.1 (ESRI, 2019) and Ansys(r) Fluent, Release 2020 R1 (Ansys, 2020) to conduct our analyses and evaluate the simulation results, and used Biorender (2024) to generate Figures 1 and 9. [PERSON] et al. (2023) explain in detail the CFD-GIS modeling approach that we used to calculate specific parameters in this paper. The paper is freely available. Equations S11 and S12 in Supporting Information S1 for the calculation of the turbulent heat fluxes are based on the Bowen ratio approach. They have been taken from [PERSON] et al. (1997), where they are referred to as Equations 5 and 6. The calculations of the potential evapotranspiration (Equations S13-S20 in Supporting Information S1) are based on the simplified Priestley-Taylor equation described in [PERSON] et al. (2013) and [PERSON] et al. (2017). Equation S21 in Supporting Information S1 for the calculation of the vegetation water content was taken from [PERSON] et al. (2013), where it is referred to as Equation 1.
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wiley/fb3071e2_0f10_4303_9baa_f6bf8dac1327.md | # IGR Earth Surface
Research Article
North Pamir--Tian Shan Inferred From Cosmogenic \({}^{10}\)Be and Low-Temperature Thermochronology
[PERSON]
1 Institute of Geosciences, University of Potsdam, Potsdam-Golm, Germany, \({}^{3}\)School of Earth, Atmospheric and Life Sciences, University of Wollongong, Wollongong, NSW, Australia, \({}^{3}\)ARC Centre of Excellence for Australian Biodiversity and Heritage (CABAH), University of Wollongong, Wollongong, NSW, Australia, \({}^{3}\)ARGA, Wettingen, Switzerland, \({}^{4}\)Australian Nuclear Science and Technology Organisation (ANSTO), Lucas Heights, NSW, Australia, Institute of Seismology, National Academy of Science of Kryrygszstan, Bishkice, Kyrygszstan, \({}^{6}\)GZern Research Centre for Geosciences, Postdam, Germany, \({}^{7}\)Centro Nacional de Investigacion sobre la Evoluciona Humana (CENIEF), Burgos, Spain, \({}^{8}\)Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology, Dresden, Germany, \({}^{10}\)Isotope Physics, Faculty of Physics, University of Vienna, Vienna, Austria
###### Abstract
We explore the spatial and temporal variations in denudation rates in the northern Pamir--Tian Shan region using \({}^{10}\)Be-derived denudation rates from modern (\(n=110\)) and buried sediment (2.0-2.7 Ma; \(n=3\)), and long-term exhumation rates from published apatite fission track (AFT; \(n=705\)) and apatite (U-Th-Sm)/He (AHE; \(n=211\)) thermochronology. We found moderate correlations between denudation rates and topographic metrics and weak correlations between denudation rates and annual rainfall, highlighting complex linkages among tectonics, climate, and surface processes that vary locally. The \({}^{10}\)Be data show a spatial trend of decreasing modern denudation rates from west to east, suggesting that deformation and precipitation control denudation in the northern Pamir and western Tian Shan. Farther east, the denudational response of the landscape to Quaternary glaciations is more pronounced and reflected in our data. Modern \({}^{10}\)Be denudation rates are generally higher than the long-term AFT and AHe exhumation rates across the studied area. In the Krygsyz Tian Shan, on average, the highest \({}^{10}\)Be denudation rates are recorded in the Terskey range, south of Lake Issylk-Kul. Here, modern denudation rates are higher than \({}^{10}\)Be-derived paleo-denudation rates, which are comparable in magnitude with the long-term exhumation rates inferred from AFT and AHe. We propose that denudation in the region, particularly in the Terskey range, remained relatively steady during the Neogene and early Pleistocene. Denudation increased due to glacial-interglacial cycles in the Quaternary, but this occurred after the onset and intensification of the Northern Hemisphere glaciations at 2.7 Ma.
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## 1 Introduction
The evolution of orogens depends on the balance between rock uplift and denudation, which reflects complex interactions among tectonics, climate, and surface processes (e.g., [PERSON], 1996; [PERSON] et al., 2003; [PERSON] & [PERSON], 1990; [PERSON] & [PERSON], 2002; [PERSON], 1992; [PERSON], 2009). However, these interactions are often interdependent, and their relative importance for denudation is mainly controlled by regional and local conditions (e.g., [PERSON] et al., 2022; [PERSON] & [PERSON], 2011). Denudation has been argued to either increase with the late Cenozoic onset of the Northern Hemisphere glaciations ([PERSON] et al., 2022; [PERSON] & [PERSON], 2016; [PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON], 2004; [PERSON] & [PERSON], 2017; [PERSON] et al., 2011; [PERSON] et al., 2001), or remain steady ([PERSON] & [PERSON], 2016; [PERSON] & [PERSON], 2010). Alternatively, other studies argue that denudation rates are primarily controlled by enhanced tectonic activity ([PERSON] & [PERSON], 2017; [PERSON] & [PERSON], 2009) or by post-torogenic isostatic rebound of foreland basins ([PERSON] & [PERSON], 2022). However, other studies show that late Cenozoic denudation rates are too poorly resolved to determine any global patterns (e.g., [PERSON] et al., 2018).
During the Cenozoic, Central Asia experienced extensive tectonic deformation associated with the uplift of the Tibetan Plateau, the Pamir mountains, the Tian Shan, and the Altai mountains (e.g., [PERSON], 1975) as well as dramatic changes in climate associated with the onset of Quaternary glacial-interglacial cycles ([PERSON] et al., 2021; [PERSON] et al., 2016). Moreover, the Tian Shan creates an important topographic barrier to moisture-bearing westerly winds, playing a crucial role in the Cenozoic aridification of Central Asia (e.g., [PERSON], 2018).
Studies on the Quaternary denudation in the Pamir ([PERSON] et al., 2015; [PERSON] et al., 2018) and the eastern (Chinese) Tian Shan ([PERSON] et al., 2011, 2017, 2023; [PERSON] et al., 2022; [PERSON] et al., 2016; [PERSON] et al., 2011; [PERSON] et al., 2017) shed light on spatial and temporal variations in denudation throughout northern Central Asia (Figure 1), yet denudation within the Kyrgyz part of the Tian Shan, situated between the Pamir and Chinese Tian Shan, has been poorly studied. Available thermochronology data from the Kyrgyz Tian Shan help to constrain exhumation rates averaging over million-year timescales (e.g., [PERSON], 2016); however, these data are not suitable for evaluating the variability of late-Cenozoic denudation rates following the Plio-Pleistocene onset of Northern Hemisphere glaciations (e.g., [PERSON], 2006).
Here we present previously unpublished \({}^{10}\)Be-derived basin-wide denudation rates from modern river sediment (\(n\) = 54) from across the Kyrgyz Tian Shan and the Kazakh part of the Trans Illi (Zaili) and Kungey ranges (Kyrgyz data set), as well as \({}^{10}\)Be-derived paleo-denudation rates from buried river sediment dated 2.0-2.7 Ma (\(n\) = 3) from the southern side of the Issyk-Kul basin (Figure 1a). We compare these data to published \({}^{10}\)Be-derived basin-wide denudation rates from the western Tian Shan and northern Pamir (Western data set; \(n\) = 20; [PERSON] et al., 2018) and eastern (Chinese) Tian Shan (Eastern data set; \(n\) = 34; [PERSON] et al., 2023), as well as to long-term exhumation rates calculated from published apatite fission track (AFT) (\(n\) = 705) and apatite (U-Th-Sm)/He (AHe, \(n\) = 211) thermochronology data from across much of the Tian Shan. We also explore relationships between denudation rates and geomorphic, tectonic, and climatic parameters to identify potential controls on denudation at the regional and local scales. Taken together, these data provide insights into spatial and temporal variations in denudation in the Tian Shan and allow us to untangle the effects of tectonics and climatic changes on denudation across the orogen.
## 2 Tectonic and Climatic Setting
The Tian Shan is a 2,500-km long intracontinental mountain belt, situated between the Tarim and Tajik basins to the south and the Kazakh platform to the north and extending over the territories of north-western China, Kyrgyzstan, southern Kazakhstan, eastern Uzbekistan, and northern Tajikistan (Figure 1).
The Tian Shan is formed by accretion and collision of oceanic fragments, island arcs, and continental blocks during the Paleozoic, which resulted in the formation of the Northern, Middle, and Southern terranes in the Kyrgyz portion of the Tian Shan (e.g., [PERSON] & [PERSON], 2001; [PERSON] et al., 2003; [PERSON] & [PERSON], 2010; [PERSON] et al., 1990, 2007). The terranes are cross-cut by the dextral strike-slip Talas-Fergana Fault and separated by the sinistral strike-slip Nikolaev Line and the Southern Tian Shan Suture (Figure 1a) ([PERSON] et al., 2017;[PERSON] & [PERSON], 2004; [PERSON] et al., 2011). In the Mesozoic and Cenozoic, the Tian Shan was periodically reactivated in response to distal collisions ([PERSON], 2003; [PERSON] et al., 1992; [PERSON] et al., 2010) with an intervening period of tectonic quiescence ([PERSON] et al., 2001; [PERSON] et al., 2013).
The present topography of the Tian Shan and the Pamir is a result of crustal shortening triggered by deformation due to the India-Asia collision ([PERSON] & [PERSON], 1975). The northward movement of the Pamir and the Tarmi block causes shortening and deformation in the Tian Shan, and the Main Pamir Thrust separates the two orogens (Figure 1). Deformation in the Tian Shan started in the late Oligocene at ca. 25 Ma, as indicated by thermochronology, and remained tectonically confined to the major fault zones ([PERSON], 2016; [PERSON], [PERSON], & [PERSON], 2006). Cenozoic shortening in the Tian Shan decreases from south to north and from west to east, deformation progressed out of sequence; associated surface uplift rates varied along the strike ([PERSON] et al., 1996; [PERSON], [PERSON], [PERSON], & [PERSON], 2017; [PERSON], 2016; [PERSON] et al., 2011; [PERSON] et al., 2014; [PERSON] et al., 2014; [PERSON] et al., 2002; [PERSON] et al., 2010).
Figure 1.— Topographic maps of the Tian Shan based on the 90-m SRTM DEM and distribution of samples. (a) Positions of \({}^{19}\)Be, apatite fission track (AFT), and AHe samples across the Tian Shan, distribution of present-day glaciers, and major tectonic structures. Glacier extent based on the Global Land Ice Measurements from Space (GLIMS) database ([PERSON] et al., 2007) and tectonic structures based on H-D. [PERSON] et al. (2022). (b) Distribution of \({}^{19}\)Be, AFT, and AHe samples by region within the Tian Shan. Regions 1–3: western Tian Shan and northern Pamir. Regions 4–11: Kyrgyz Tian Shan. Regions 12–14: eastern (Chinese) Tian Shan. (c) Position of the Tian Shan in Central Asia.
North-south shortening and deformation in the Tian Shan intensified at ca. 15-5 Ma and caused widespread thrusting at ca. 10 Ma (e.g., [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON], 2017; [PERSON] et al., 2003; [PERSON] et al., 2010; [PERSON] et al., 2022; [PERSON] et al., 2014; [PERSON] et al., 2023; [PERSON] et al., 2010). Deformation in the interior ranges possibly intensified at ca. 3-2 Ma (e.g., [PERSON] et al., 2010, 2011; [PERSON] et al., 2014; [PERSON] et al., 2014) mostly in the western and partly in the central parts of the Tian Shan ([PERSON] et al., 2023). The strike slip displacement of the Talas-Fergana Fault commenced at ca. 25 Ma and was relatively rapid until ca. 13.5 Ma ([PERSON], [PERSON], [PERSON], & [PERSON], 2017). Quaternary shortening is distributed across the entire Tian Shan and rates are inferred to be similar to modern shortening rates. The most rapid Quaternary shortening documented in the Kyrgyz Tian Shan occurred in the Naryn basin ([PERSON] et al., 2002). However, seismicity seems to be concentrated along the northern margin, including a significant series of five large-magnitude earthquakes between 1885 and 1938 (\(M_{\ast}\) 6.9 to \(>\)8) (e.g., [PERSON] et al., 2016). The present-day shortening rate is about 20 mm yr\({}^{-1}\) in the Kyrgyz Tian Shan, which is approximately half of the present-day India-Asia convergence rate ([PERSON] et al., 1996; [PERSON] et al., 2010), and 10-15 mm yr\({}^{-1}\) in the western Tian Shan and in the Pamir ([PERSON] et al., 2013; [PERSON] et al., 2014).
In the Pamir, significant Cenozoic deformation commenced in the Eocene; a second major pulse was recorded in the early Miocene; in the north Pamir, the latter is typically linked to motion along the north-vegent Main Pamir Thrust (Figure 1), which bounds the northern Pamir (e.g., [PERSON], 2010; [PERSON] et al., 2017). Deformation migrated to the bounding basins in the middle-late Miocene (e.g., [PERSON] et al., 2020; [PERSON] et al., 2015). Although there are debates about the magnitude and mechanism of Pamir shortening (e.g., [PERSON], 1993; [PERSON] et al., 2016; [PERSON] et al., 2020), Pamir-Tian Shan convergence is certainly driven by the northward motion of India.
The Cenozoic climate in Central Asia has been arid and mainly influenced by the northern mid-latitude westernlies, which transport moisture eastward across Eurasia (e.g., [PERSON] et al., 2015, 2016). Aridification was likely caused by a decrease in the westerlies' moisture flux, which resulted from Cenozoic global cooling and Parathephys retreat ([PERSON] et al., 2012; [PERSON] et al., 1997), as well as the creation of orographic barriers due to surface uplift of the Tibetan Plateau, the Tian Shan, and the Pamir mountains ([PERSON], 2018; [PERSON] et al., 2009; [PERSON] et al., 2023; [PERSON] et al., 2020). The Tian Shan has interacted with the westerlies since the late Oligocene ([PERSON] et al., 2020). In the mid-Piocene and during Quaternary interglacial periods, northerly migration of the westerlies induced higher precipitation, whereas their southward migration during Quaternary glacial periods led to drier climate conditions ([PERSON] et al., 2022).
Modern precipitation in the Tian Shan and the Pamir is controlled by interactions between the westerlies and the Siberian High ([PERSON] et al., 1997; [PERSON] et al., 2017; [PERSON], 2012). The westerlies bring moisture from the North Atlantic, the Mediterranean, and the Black Sea ([PERSON] et al., 2006; [PERSON] et al., 2014). In winter, the Siberian High reaches the Tian Shan and blocks the midlatitude westerlies, resulting in cold conditions and reduced precipitation ([PERSON] et al., 2001; [PERSON] et al., 2001). The South and East Asian monsoons never consistently reached the Tian Shan and do not influence precipitation and long-term climate within the range ([PERSON] et al., 2015; [PERSON] et al., 2022). Presently, an orographic barrier created by the range is responsible for the seasonality of precipitation, with dominantly winter-spring precipitation on the windward (north-western) side of the Tian Shan and summer precipitation within the range and on its leeward (south-eastern) side ([PERSON] & [PERSON], 2016). This seasonality occurs because during the winter, the prevalent Siberian High and weak westerlies lead to orographic rainout of the westerly moisture on the windward side, while strong cyclonic activity at high elevations in the summer leads to rainfall at high elevations ([PERSON] & [PERSON], 2019).
Summarizing the above, high topography of the Tian Shan developed during the Neogene due to the India-Asia collision, with the most significant intensification at 15-5 Ma. The range prevents the westerly moisture from reaching the Chinese part of Central Asia, playing a part in aridification.
## 3 Materials and Methods
### Cosmogenic \"Be Analysis
Cosmogenic \"Be produced in quartz has proven to be the best suited technique for studying the denudation of Earth's continental topography over millennial timescales ([PERSON] et al., 2022). Indeed, \"Be-based denudation rates have now been determined in more than 4,000 river basins--mostly from mountain landscapes--providingus with a large inventory of denudation rate estimates ([PERSON] et al., 2018, 2022). The concentration of \({}^{10}\)Be nuclides in river sediments is proportional to their exposure age, with the highest \({}^{10}\)Be concentrations reflecting longer exposure time and, consequently, slower denudation ([PERSON], 2014; [PERSON] et al., 2022).
#### 3.1.1 Sampling
We collected 54 modern river sediment samples to calculate \({}^{10}\)Be-derived millennial-scale basin-wide denudation rates (Figure 1a and Figure S1 in Supporting Information S1, Table S1 in Supporting Information S2). Sampling was performed in locations across Kyrgyzstan accessible by road with the purpose of covering the largest possible area of the Kyrgyz Tian Shan and covering several catchments in individual ranges, if possible. River sediment was sieved in the field to isolate the 250-500 um fraction for analysis. At two sampling locations we also collected material in the 8-16 mm (samples KYR16-01B and KYR16-02B) and 16-32 mm (sample KYR16-01C) grain size ranges. Sampling of buried sediments for calculation of \({}^{10}\)Be-derived paleo-denudation rates and calculation of ages using isochron burial data (Figure 1a, Table S2 in Supporting Information S2) are described in [PERSON] et al. (2023). Our sample inventory includes one modern river sediment sample (KYR-DRMS1) previously reported by [PERSON] et al. (2016).
#### 3.1.2 Sample Preparation
Quartz was purified following the procedures described in [PERSON] (1992) using froth flotation to separate feldspars from quartz. For all samples except those labeled \"DRMS\" in Table S1 in Supporting Information S2, beryllium was separated at the University of Wollongong (UOW) following procedures described in [PERSON] et al. (2023). Samples were spiked with \(\approx\)300 pg of \({}^{9}\)Be from a low-level beryllium carrier solution added prior to complete HF dissolution. \({}^{10}\)Be/\({}^{9}\)Be ratios were measured using the 10 MV ANTARES accelerator (samples with cathode ID's in Table S1 starting with \"B\" in Supporting Information S2) and using the 6 MV SIRUUS accelerator (samples with cathode ID's in Table S1 starting with \"Be\" and \"XBE\" in Supporting Information S2) at the Australian Nuclear Science and Technology Organisation (ANSTO) ([PERSON] and [PERSON], 2007; [PERSON] et al., 2017, 2019, 2022), and were normalized to the KN-5-2 and KN-5-3 ([PERSON] et al., 2007) standards. Analytical uncertainties for the final \({}^{10}\)Be concentrations (atoms g\({}^{-1}\)) include AMS measurement uncertainties (the larger of counting statistics or standard deviation of repeats and blank corrections) in quadrature with \(1\%\)-\(2\%\) for \({}^{10}\)Be standard reproducibility (depending on the individual AMS measurement conditions) and \(1\%\) uncertainty in the \({}^{9}\)Be carrier concentration. Samples labeled \"DRMS\" were prepared and analyzed at the DREAMS facility at Helmholtz-Zentrum Dresden Rossendorf ([PERSON] et al., 2016).
#### 3.1.3 Denudation Rates From Modern Samples
We used the open-source program CAIRN v.1 ([PERSON] et al., 2016) to calculate denudation rates from our Kyrgyz samples, and to recalculate published denudation rates from [PERSON] et al. (2018) and [PERSON] et al. (2023). Basin-averaged nuclide production from neutrons and muons was calculated with the approximation of [PERSON] et al. (2011) and using a sea-level and high-latitude total production rate of 4.3 atoms g\({}^{-1}\) yr\({}^{-1}\) for \({}^{10}\)Be ([PERSON] et al., 2016). Production rates for catchment-wide denudation rates were calculated at every grid cell of a hydrologically enforced 90-m SRTM DEM ([PERSON] et al., 2007) using the time-independent Lal/Stone scaling scheme ([PERSON], 2000). Atmospheric pressure was calculated via interpolation from the NCEP2 reanalysis data ([PERSON] et al., 2011). For consistency with the denudation rates compiled in the OCTOPUS database ([PERSON] et al., 2018, 2022), we applied topographic shielding corrections to our data. The latter was calculated from the same DEM using the method of [PERSON] (2006) with \(\Delta\theta=8^{\circ}\) and \(\Delta\phi=5^{\circ}\). For completeness and in line with [PERSON] (2018), we also calculate denudation rates without correcting for topographic shielding. The uncorrected denudation rates are provided in Tables S1 in Supporting Information S2 and overlap with those corrected for topographic shielding at 1\(\sigma\) uncertainty.
In mountain regions, not accounting for snow or glacier ice shielding will result in an overestimation of \({}^{10}\)Be-derived denudation rates ([PERSON] and [PERSON], 2014; [PERSON] et al., 2022). The lack of detailed meteorological data on snow thickness from the study area prevents us from rigorously correcting our denudation rates for snow shielding. To determine whether not accounting for snow shielding could bias our denudation rates, we calculate snow shielding-corrected denudation rates assuming an average annual snow depth of 5 cm (equivalent to 20 cm over the winter months) uniformly covering the surface of each sampled basin. This snow depth value is equivalent to the maximum mean snow depths recorded in the Tian Shan over the last century ([PERSON] et al., 2019) and thus represents an upper limit. End-member snow-depth corrected denudation rates are about \(8\%\) lower than the uncorrected ones and the two overlap at 1\(\sigma\) uncertainty. Actual snow shielding values are lower than our assumed end-member case, and thus, not accounting for snow shielding has minimal impact on the reported denudation rates (Table S1 in Supporting Information S2). Given the lack of meteorological data required for rigorous snow shielding corrections, and given that both topographic shielding and snow shielding corrections have minimal impact on the obtained denudation rates, and for consistency with denudation rates compiled in the OCTOPUS database ([PERSON] et al., 2018, 2022), in subsequent analyses we use denudation rates that were corrected for topographic shielding but not corrected for snow shielding.
Due to the presence of glaciers in the study area we also explore the potential impact of present and past glaciations on the inferred \({}^{10}\)Be denudation rates. To this end, we calculate end-member \({}^{10}\)Be denudation rates for the entire \({}^{10}\)Be data set using present-day glacier extents mapped in the Global Land Ice Measurements from Space (GLINS) database ([PERSON] et al., 2007; [PERSON] et al., 2013) by assuming that glaciated areas contribute with sediment in proportion to their surface areas and that this sediment has a \({}^{10}\)Be concentration of zero. [PERSON] et al. (2013) have mapped the extent of glaciated valleys throughout the Kyrgyz section of the Tian Shan, and we use these data to calculate end-member \({}^{10}\)Be denudation rates for our Kyrgyz data accounting for the maximum extent of Quaternary glaciations. Similar to our present-day glacier calculations, we assume that the sediment sourced from glaciated valleys have \({}^{10}\)Be concentrations equal to zero. Results are summarized in Table S1 in Supporting Information S2 and discussed below.
#### 3.1.4 Paleo-Denudation Rates From Buried Samples
Paleo-denudation rates were calculated using three buried amalgamated sand samples (250-500 \(\upmu\)m grain size) from south of lake Issyk-Kul (Figure 1a), taken from the same stratigraphic layers as the individual clasts collected for isochron burial dating by [PERSON] et al. (2023). The \({}^{28}\)Al and \({}^{10}\)Be concentrations measured in the sand samples plot near (sample AKT) or intersect (samples PET-QTS) the lines defined by the isochron clast samples (Figure S2 in Supporting Information S1), indicating that the sands and clasts have experienced similar exposure and burial histories. We calculate paleo-denudation rates by first correcting the \({}^{10}\)Be concentrations measured in the sand samples for radioactive decay using the isochron burial ages calculated for each location (see Table S2 in Supporting Information S2 and [PERSON] et al., 2023). To account for uncertainties related to the average elevation of the sediment's source areas and to the possibility of incomplete burial or lengthy exposure to cosmic radiation prior to sampling, we express paleo-denudation rates for each of the three localities as a range of values in addition to a central value obtained by assuming complete and continuous burial (Table S2 in Supporting Information S2).
### AFT and AHe Thermochronology
Thermochronology is used to reconstruct the time at which rocks cooled through a temperature window, which allows the estimation of the timing and rate of exhumation for rocks that are currently at the surface (e.g., [PERSON] and [PERSON], 2006). Different thermochronological systems have different closure temperatures (dependent on mineral used or decay scheme targeted), and different closure temperatures result in different averaging timescales of exhumation. The temperature windows for the AFT and AHe systems are 60-120 and 40-85\({}^{\circ}\)C, respectively, and the typical closure temperatures are 110 and 70\({}^{\circ}\)C, respectively (e.g., [PERSON] and [PERSON], 2006).
To estimate long-term exhumation rates across the Tian Shan, we compile AFT (\(n=705\), Table S3 in Supporting Information S2) and apatite (U-Th-Sm)/He (AHe, \(n=211\), Table S4 in Supporting Information S2) ages available in the published literature (see Tables S3 and S4 in Supporting Information S2 for list of publications). We calculate one-dimensional, steady-state exhumation rates from the published AFT and AHe cooling ages using the _age2 echnume_ MATLAB code ([PERSON] and [PERSON], 2023).
The _age2 exhume_ code incorporates surface temperature based on a defined mean annual temperature at sea level (\(T_{0}\)) and a temperature lapse rate. Using mean annual temperature values for the Tian Shan from the WorldClim Global Climate database ([PERSON], 2017), we estimate a value for \(T_{0}\) of 19\({}^{\circ}\)C. Based on values estimated for the Chinese Tian Shan ([PERSON] et al., 2016), we assume a temperature lapse rate of 5\({}^{\circ}\)C km\({}^{-1}\). To explore the sensitivity of the calculated exhumation rates to our choices of \(T_{0}\) and lapse rate, we also calculated exhumation rates using \(T_{0}=15^{\circ}\)C and 25\({}^{\circ}\)C, and lapse rates of 4 and 4.5\({}^{\circ}\)C km\({}^{-1}\) (Tables S3 and S4 in Supporting Information S2). The average difference in obtained exhumation rates for a change in \(T_{0}\) from 15 to 25\({}^{\circ}\)C is 11% for AFT and 21% for AHe (Figure 2), and for a change in the lapse rate from 4 to 5\({}^{\circ}\)C km\({}^{-1}\) the differences are 2.6%and 5.7% for AFT and AHe, respectively (Figure 2). Given the orders-of-magnitude range in exhunation rates (and denuduation rates) explored here, the above differences are not significant. We set the initial geotherm to 25\({}^{\circ}\)C km\({}^{-1}\); as required to initiate the model, but a steady-state geotherm is calculated for each sample as the model runs (see [PERSON], 2023). We assume a (default) thermal diffusivity of 30 km\({}^{2}\) Myr\({}^{-1}\), and a model thickness of 30 km. Model results are not sensitive to the assumed model thickness (see sensitivity tests in [PERSON] der Beek & Schildgen, 2023); this value was chosen as a rough estimate of the starting thermal field for the model, which encompasses typical depths from which rocks were tectonically exhuned in the Tian Shan.
Figure 2: Summary of \({}^{10}\)Be, apatite fission track (AFT), and AHe results. (a)-(c) Spatial distribution of modern \({}^{10}\)Be-derived denuduation rates (a), and AHe (b) and AFT (c) exhunation rates. Black dashed lines show the location of major tectonic features (see Figure 1 for more details). (d) Interquartile-range (IQR) box and whisker plots showing AFT and AHe exhunation rates, and modern \({}^{10}\)Be-derived denuduation rates from across the Tian Shan. (e) Averaging timescales for the AFT, AHe and \({}^{10}\)Be denuduation/exhunation rates shown in (d). (f) Percent differences between AFT and AHe exhunation rates modeled using different values for \(T_{0}\) and temperature lapse-rate, respectively.
Kinetic parameters for the AHe system are derived from [PERSON] (2000) and for the AFT system from [PERSON] and [PERSON] (2006). A local relief correction, \(\Delta h\), for each sample is calculated based on the difference between the sample elevation and a smoothed version of the modern topography that approximates the relief on the closure-temperature isotherm (for details, see [PERSON] & Schildgen, 2023). To calculate a smoothed version of the DEM from which \(\Delta h\) values are derived, the 90-m resolution SRTM DEM was smoothed over a circular radius equal to 70 pixels (6,300 m) for the Aft system, and 105 pixels (9,450 m) for the AFT system. These distances are equivalent to assuming a closure depth (\(z_{\circ}\)) of ca. 2 km for the AHe system, and ca. 3 km for the AFT system, with a smoothing radius equal to \(\pi\) * \(z_{\circ}\) ([PERSON] & [PERSON], 2013). The \(\Delta h\) values for each sample (modern elevation minus smoothed DEM) are included in Tables S3 and S4 in Supporting Information S2. Our approach assumes exhundamental steady state and neglects track length data, which is not available for many AFT samples. For AFT samples with pre-Cenozoic ages, our simplifying assumptions likely overestimate the exhunation rates; however, the rates calculated from these samples are already quite low.
We acknowledge that for sites with both AFT and AHe data, it would be possible to model the data together to obtain more accurate exhunation histories, but for the purposes of this study, in which we simply aim to explore how exhunation rates change over time, we opted for an approach that could be rapidly and consistently applied to all samples.
### Geomorphic, Climatic, and Tectonic Parameters
To explore potential environmental controls on \({}^{10}\)Be-derived denuduation rates, we calculate the average of various geomorphic, tectonic, and climatic metrics for each drainage basin (Figure 3). For geomorphic metrics, we use a hydrologically enforced 90-m SRTM DEM ([PERSON] et al., 2007). We calculate the topographic gradient using the algorithm proposed by [PERSON] (1981), and we calculate local relief as the elevation range within a moving circular window with a radius of 2 km. We calculated the normalized channel steepness index (\(k_{\text{\tiny m}}\)) with the Topographic Analysis Kit for the TopoToolbox MATLAB package (Forte & Whipple, 2019; Schwanghart & Kuhn, 2010; [PERSON] & Scherler, 2014) using the _KsnChiBatch_ tool with the reference concavity set to 0.5 and with the _output_ parameter set to \"_ksn_\" and a stream network basin area threshold of 1 km\({}^{2}\). The latter produces a stream network with \(k_{\text{\tiny m}}\) values for each stream segment, as opposed to a continuous raster with interpolated \(k_{\text{\tiny m}}\) values. We use these raw stream network \(k_{\text{\tiny m}}\) values as opposed to an interpolated \(k_{\text{\tiny m}}\) raster to calculate our summary statistics for each basin. As metrics for climate, we use the bioclimatic variables available as part of the World-Clim Global Climate database ([PERSON], 2017), namely BIO12 (mean annual rainfall) and BIO13 (rainfall of the wettest month), and the global aritoly index (AI) map ([PERSON] et al., 2022). As a metric for tectonic deformation, we use data from the Global Strain Rate Model ([PERSON] et al., 2014). The extracted metrics are summarized in Tables S5A and S5B in Supporting Information S2. Lastly, we extract the dominant lithological units for each basin using the Global Lithological Map (GLiM) database ([PERSON], 2012) and present the results in Figure S3 in Supporting Information S1.
### Data Grouping
To facilitate a meaningful comparison between the \({}^{10}\)Be-derived denuduation rates and the long-term exhunation rates inferred from the published AFT and AHe data, we divide our Kyrgyz \({}^{10}\)Be data set into eight regions (Figures 0(b) and 2, Figure S1 in Supporting Information S1, Table S5 in Supporting Information S2): Issyk-Kul North (\(n=14\)), Issyk-Kul South (\(n=8\)), Song Kul (\(n=13\)), Naryn (\(n=5\)), Kyrgyz range (\(n=4\)), Toktogul (\(n=3\)), Jalal Abad (\(n=4\)), and Osh (\(n=3\)). The grouping strategy is focused on the regional distribution of our modern sediment \({}^{10}\)Be data. The published denuduation rates from [PERSON] et al. (2018) and [PERSON] et al. (2023) are divided into regions proposed by the corresponding authors. In each region we include AFT and AHe datapoints that are located within, or in the proximity, of the drainage basins with \({}^{10}\)Be data and belong to the same tectonic position (e.g., footwall/hanging wall). In total data are grouped into 14 regions, shown in Figure 0(b).
## 4 Results
The \({}^{10}\)Be concentrations of modern river sands in the Kyrgyz Tian Shan range between 7.92 \(\pm\) 0.83 \(\times\) 10\({}^{3}\) and 1,460.12 \(\pm\) 29.24 \(\times\) 10\({}^{3}\) atoms g\({}^{-1}\) (Table S1 in Supporting Information S2 and Figure 2). Basin-wide denudation rates calculated from these concentrations ranged between 17.3 and 2,780.4 mm kyr\({}^{-1}\) (uncorrected for modern glacial cover), with a mean value of 393.8 mm kyr\({}^{-1}\) and a median value of 179.6 mm kyr\({}^{-1}\) (Tables S1 and S6 in Supporting Information S2). Averaging time range between 15.3 and 0.2 kyr, with one outlier value of 34.8 kyr (sample KYR16-39) in the Song Kul region (Figures 2a and 2e; Tables S1 and S5A in Supporting Information S2). Recalculated \({}^{10}\)Be-derived denotation rates from the western Tian Shan and northern Pamir ranged between 142.3 and 1,861.8 mm kyr\({}^{-1}\), with a mean value of 1,234.8 mm kyr\({}^{-1}\) and a median value of 1,391.8 mm kyr\({}^{-1}\), and averaging times between 0.3 and 4.2 kyr (Figures 2a and 2e; Table S5B in Supporting Information S2). Recalculated \({}^{10}\)Be-derived denotation rates from the eastern (Chinese) Tian Shan range between 43.8 and 743.2 mm kyr\({}^{-1}\), with the mean value of 274.2 mm kyr\({}^{-1}\) and median value of 243.6 mm kyr\({}^{-1}\), and averaging times between 0.8 and 13.7 kyr (Figures 2a and 2e; Table S5B in Supporting Information S2). Correcting for the maximum impact of present-day glaciers yields end-member basin-wide denotation rates that are on average 21% lower than the uncorrected values (Tables S1, S5A, and S5B in Supporting Information S2), however this difference has negligible impact on the overall distribution of denotation rates and on their comparison to the AFT- and AHe-derived exhunation rates (Figures 4 and 5).
Figure 3.— Maps showing the spatial distribution of topographic, tectonic, and climatic metrics across the Tian Shan. Topographic gradient (a), local relief (b), and normalized channel steepness—ksn (c) were calculated using the 90-m SRTM DEM ([PERSON] et al., 2007). For clarity of the maps, the topographic gradient and normalized knn are shown as average values within a 5 km radius moving window. The second invariant of the model strain rate field (d) was obtained from the Global Strain Rate Model ([PERSON] et al., 2014), annual rainfall (e) was obtained from the WorldClim Global Climate database ([PERSON], 2017), and the aridity index (f) was obtained from [PERSON] et al. (2022).
The cosmogenic nuclide concentrations, ages, and paleo-denotation rates of buried samples from the southern part of the Issylk-Kul basin are shown in Figure 4 and Table S2 in Supporting Information S2. The \({}^{10}\)Be and \({}^{25}\)Al concentrations (\(\times 10^{3}\) atoms g\({}^{-1}\)) of the buried samples are as follows: \(30.80\pm 1.01\) and \(57.34\pm 6.56\) (\({}^{10}\)Be and \({}^{25}\)Al respectively, AKT-U); \(92.04\pm 2.53\) and \(272.15\pm 16.11\) (PET-QTS-L); and \(114.78\pm 3.16\) and \(227.15\pm 17.31\) (PET-QTS-PIT). Paleo-denotation rates (mm kyr\({}^{-1}\)) obtained by assuming complete and continuous burial are \(72.2\pm 11.7\) (AKT-U; burial age \(2.71\pm 0.37\)), \(33.0\pm 3.5\) (PET-QTS-L; burial age \(=2.08\pm 0.14\)), and \(18.7\pm 1.8\) (PET-QTS-PIT; burial age \(=2.75\pm 0.15\)). Allowing for uncertainties related to the average elevation of the sediment's source areas and to the possibility of incomplete burial or lengthy exposure to cosmic radiation prior to sampling, we obtain the following paleo-denotation rate ranges for the three sites: \(50.6\pm 8.2\)-\(204.0\pm 32.8\) for AKT-U; \(22.9\pm 2.5\)-\(94.1\pm 10.0\) for QTS-L; and \(12.9\pm 1.2\)-\(53.8\pm 5.1\) for QTS-PIT.
The calculated long-term AFT and AHe exhunation rates from the entire Tian Shan are summarized in Figures 2 and 4 and in Tables S3 and S4 in Supporting Information S2. Inferred AFT exhunation rates (\(T_{0}\) = 19\({}^{\circ}\)C, lapse rate = 5\({}^{\circ}\)C km\({}^{-1}\)) range between 11.1 and 831.4 mm kyr\({}^{-1}\), and inferred AHe exhunation rates (\(T_{0}\) = 19\({}^{\circ}\)C,
Figure 4.— Interquartile-range (IQR) box and whisker plots showing apatite fission track and AHe exhunation rates, and \({}^{10}\)Be-derived modern and paleo-denation rates for (a) the Kyrgyz Tian Shan, (b) northern Pamir and western Tian Shan, and (c) eastern (Chinese) Tian Shan. Blue box plots with no fill show end-member \({}^{10}\)Be-derived modern denotation rates corrected for the maximum effect of present-day glacier cover on diluting the \({}^{10}\)Be-signal exported by rivers from each sampled drainage basin (see text for details).
lapse rate = 5\({}^{\circ}\)C km\({}^{-1}\)) range between 3.9 and 1,044.2 mm kyr\({}^{-1}\). The compiled AFT and AHe data that are not included in the 14 regions (see Section 3.4 above) are still used for the calculation of the mean and median values for the Kyrgyz, Western, and Eastern data sets (see Figure 2d). Mean and median AFT/AHe exhumation rates in the Kyrgyz data set are 212.0 and 96.0 mm kyr\({}^{-1}\)/94.1 and 39.4 mm kyr\({}^{-1}\), respectively. Mean and median AFT/AHe exhumation rates in the Western data set are 268.3 and 291.9 mm kyr\({}^{-1}\)/300.4 and 227.0 mm kyr\({}^{-1}\), respectively. Mean and median AFT/AHe exhumation rates in the Eastern data set are 69.4 and 41.7 mm kyr\({}^{-1}\)/110.7 and 41.9 mm kyr\({}^{-1}\), respectively. The mean and median values for the \({}^{10}\)Be-derived millennial-scale denotation rates, AFT-, and AHe-derived long-term exhumation rates for each of the regions are summarized in Table S6 in Supporting Information S2.
When considering the entire \({}^{10}\)Be data set, we found moderate but statistically significant (at \(p<0.001\)) correlations between the log-transformed \({}^{10}\)Be-derived modern denotation rates and topographic metrics (elevation, topographic gradient, and local relief) and strain rate (\(R\approx 0.5\); Figure 6). Weak, but still statistically significant correlations are obtained between the log-transformed \({}^{10}\)Be-derived modern denotation rates and normalized channel steepness (\(R\approx 0.3\); \(p<0.001\)), and between the log-transformed rates and rainfall (annual and wettest month) (\(R\approx 0.2\); \(p<0.05\)) and the AI (\(R\approx 0.3\); \(p<0.01\)) (Figure 6). At the intermediate scale, the North Pamir and western Tian Shan data sets show a strong correlation between the log-transformed \({}^{10}\)Be-derived denotation rates and elevation (\(R\approx 0.8\); \(p<0.001\)), and a moderate correlation between log-transformed rates and the rainfall of the wettest month and the AI (\(R\approx 0.6\); \(p<0.01\)) (Figure 6). The Kyrgyz data set shows statistically weak but significant correlations between the log-transformed \({}^{10}\)Be-derived denotation rates and topographic metrics (topographic gradient and local relief) (\(R\approx 0.4\); \(p<0.001\)) and a weak correlation between log-transformed rates and mean annual rainfall (\(R\approx 0.3\); \(p<0.05\)) (Figure 6). In the eastern (Chinese) Tian Shan, correlations are moderate between the log-transformed \({}^{10}\)Be-derived denotation rates and topographic metrics (\(R\approx 0.5\); \(p<0.001\)), and weak but still statistically significant between log-transformed rates and climatic metrics (\(R\approx 0.4\); \(p<0.05\)) (Figure 6). At the regional scale, the picture becomes more complicated with correlations between denotation rate and predictors likely reflecting local conditions (Table S7 in Supporting Information S2), and a strong influence of the reduced sample counts. Only seven of the 14 regions have sufficient sample numbers to justify a correlation analysis, and even here the low sample counts likely bias the results.
Figure 5.— Dgelication ages in the Tian Shan and links between \({}^{10}\)Be-derived modern denotation rates and modern and past glaciers. (a) Map summarizing \({}^{10}\)Be-derived deglaciation ages across the Tian Shan obtained from the ExpAge database ([[https://expage.github.io](https://expage.github.io)]([https://expage.github.io](https://expage.github.io))). Ages are grouped in clusters based on their geographic locations (blue circles) and for each cluster the map lists the median age (MED; green box) and the interquartile-range (Q1 and Q2 respectively). The size of circles is proportional to the number of ages within each cluster. (b) and (c) Log-transformed \({}^{10}\)Be denotation rate versus percentage of basin area covered by present-day glaciers (b) and glacial valleys (c). Box plots summarize log-transformed denotation rates for basins with no glacial impact (red circles) and basins with glacier impact (blue circles).
The absence of detailed geology maps for the entire study area prevents us from completing a detailed assessment of potential lithological controls on \({}^{10}\)Be-derived denudation rates. However, using the GLiM database ([PERSON], 2012), we found no correlation between denudation rates and the dominant major lithological units of the sediments' source areas (Figure S3 in Supporting Information S1).
## 5 Discussion
### The Impact of Present-Day Glaciers on Denudation Rates in the Tian Shan
Alpine glacial cover may impact cosmogenic \({}^{10}\)Be abundances via two mechanisms: (a) excavation of material from depth, and (b) shielding of bedrock from cosmic radiation. Both mechanisms lead to a decrease in \({}^{10}\)Be concentration in the sediment mix exiting a glaciated drainage basin, and consequently, can result in an overestimation of \({}^{10}\)Be-derived denudation rates ([PERSON], 2014; [PERSON] et al., 2022). Based on the GLMS database ([PERSON] et al., 2007), present-day glaciers occupy about 3% of the land surface area of the Tian Shan and 79 of the 110 drainage basins included in this study (72%) are glaciated.
Concerning the timing and extent of past glaciations, a re-evaluation of existing cosmogenic nuclide exposure ages from the Tian Shan (Figure 5a) by [PERSON] et al. (2016) suggests that the only well-constrained regional glacial expansion occurred during Marine Isotope Stage (MIS) 2 (29-14 ka; [PERSON] & [PERSON], 2005), with glacier extent restricted to valley glaciation due to arridity ([PERSON] et al., 2016 and references therein). The largest glacial cover during this time developed in the eastern part of the Kyrgyz Tian Shan ([PERSON] et al., 2016). Glacial deposits from the central Kyrgyz and eastern Chinese Tian Shan have apparent minimum ages overlapping with MIS 3 and MIS 5 (29-57 and 71-130 ka, respectively; [PERSON] & [PERSON], 2005) (Figure 5), however, given the paucity of the data and/or the poor resolution of the dating, any attempts at correlating regional scale glacial chronologies beyond MIS 2 are speculative ([PERSON] et al., 2016).
In the Kyrgyz Tian Shan, drainage basins with present-day glaciers, and those that are currently ice-free but were glaciated in the past (i.e., basins hosting glacial valleys) record on average higher \({}^{10}\)Be-derived modern denudation rates than those basins that were never glaciated (Figures 5b and 5c). Given the relatively short averaging timescales characterizing our \({}^{10}\)Be denudation rates (average = 3.5 kyr and median = 2.1 kyr) as compared to the \"ages\" of the glacial valleys (at least MIS 2; Figure 5a), it is unlikely that elevated denudation rates are the result of glacial valleys contributing sediment depleted in \({}^{10}\)Be and therefore diluting the \({}^{10}\)Be signal exported by rivers. Rather, a more likely cause of the apparent elevated \({}^{10}\)Be-derived denudation rates in these basins is the coincidence of glacial valleys with higher elevations, steeper topographic gradients, and higher local reliefs (Figure S4 in Supporting Information S1).
Unlike glacial valleys, there is evidence to suggest that the presence of modern glaciers in a basin does influence the \({}^{10}\)Be-derived denudation rate inferred for that basin. For example, in the Kyrgyz Tian Shan, there seems to
Figure 6: Correlation matrix displaying Pearson’s correlation coefficients for \({}^{10}\)Be-derived denudation rates and different topographic, tectonic, and climatic metrics calculated for data from northern Pamir and western Tian Shan ([PERSON] et al., 2018), the Kyrgyz Tian Shan (this study), and the eastern (Chinese) Tian Shan ([PERSON] et al., 2023).
be a correlation between the log-transformed \({}^{10}\)Be denudation rate and the percentage of basin area occupied by modern glaciers (Figure 5b). Furthermore, relatively high \({}^{10}\)Be-derived denudation rates in the Issyk-Kul South region (Figure 4) compared to other sampled regions in the Kyrgyz Tian Shan suggest increased denudation of the northern flank of the Terskey range. The reason for these elevated rates, however, is unclear. This region receives a low amount of precipitation (Figure 3e, Table S5A in Supporting Information S2), it is not dissimilar to other regions in terms of topography, and exhunation rates in the Terskey range did not increase after 5 Ma ([PERSON] et al., 2014). Presently, the northern peripheral ranges of the Tian Shan, including the Terskey range, are experiencing severe glacier shrinkage ([PERSON] & [PERSON], 2009; [PERSON] et al., 2012). The Terskey range receives most of precipitation in summer, when rainout occurs at high elevations ([PERSON] & [PERSON], 2019), during which time streams probably transport sediments from previously glaciated areas of the drainage basins. Also, the Tian Shan drainage basins with a higher portion of glaciated area, especially the northern slope of the Terskey range, show a substantial increase in runoff due to glacier reduction ([PERSON] et al., 2013 and references therein). Additionally, the strong positive correlation between \({}^{10}\)Be-derived denudation rates and precipitation of the wettest month (Table S7 in Supporting Information S2) indicates that river runoff might be amplified by summer rainout despite the generally low precipitation. Therefore, relatively high \({}^{10}\)Be-derived denudation rates in the Issyk-Kul South region may reflect an increase in denudation due to higher summer runoff, possibly combined with admixing of previously shielded sediments with lower \({}^{10}\)Be concentration.
It is not possible to accurately correct every single \({}^{10}\)Be-derived denudation rate for the likely dilution effect of modern glaciers on the \({}^{10}\)Be concentrations exported from basins, but it is possible to estimate the maximum effect by calculating end-member \({}^{10}\)Be denudation rates by assuming that: (a) each glaciated portion of a basin contributes with sediment to the total mix exported in proportion to its surface area, and (b) that this sediment is completely depleted in \({}^{10}\)Be. Modern-glacier corrected end-member \({}^{10}\)Be denudation rates are on average 21% lower than the uncorrected values (interquartile range between 7% and 31%). However, when denudation rates are amalgamated in the various regions for comparison with the AFT and AHe exhunation rates (Figure 4), differences are insignificant for all but two regions, namely the North Pamir and Vakhsh-Alai, where the corrected and uncorrected data sets have non-overlapping interquartile ranges (Figure 4b). Notwithstanding these differences, end-member \({}^{10}\)Be-derived denudation rates are still significantly higher than their respective AFT and AHe exhunation rates. In light of the above, we suggest that our uncorrected \({}^{10}\)Be denudation rates are generally not significantly overestimated, especially in the Kyrgyz and eastern (Chinese) Tian Shan.
### Temporal Changes in Denudation Rates in the Kyrgyz Tian Shan
2.1 Increase of the Denudation Rates in the Terskey Range (Kyrgyz Tian Shan) After the Onset of Quaternary Glaciations
Denudation/exhunation rates derived from AFT, AHe, and \({}^{10}\)Be have very different averaging timescales. More recent rapid exhunation results in younger AFT and AHe cooling ages and faster exhunation rates, while old ages show that the majority of exhunation occurred long ago and that recent exhunation was minor or slow. Ultimately, averaging timescales for AFT and AHe are equal to the measured cooling age, and the resulting exhunation rates represent an average for the entire period of exhunation (Figure 2e). \({}^{10}\)Be-derived denudation rates are averaged over the period necessary to erode about 60 cm of surface rock (or 100 cm of sediment), which in tectonically active landscapes are usually on the order of several thousand years. Therefore, our comparison of AFT, AHe, and \({}^{10}\)Be data relies on the fact that different thermochronology-derived exhunation rates and \({}^{10}\)Be-derived denudation rates reflect a recent change in denudation rates in comparison to a long-term general denudational trend.
[PERSON] et al. (2016) suggested that in glaciated areas--such as our study area--there is a time-dependent bias of higher denudation rates toward the present with shorter averaging time scales caused by the discrete nature of erosional processes. Their model shows that when using a power law distribution, erosional hiatuses result in a systematic increase in denudation rates toward the present and this mechanism might be invoked to explain the observed increase in \({}^{10}\)Be-derived modern denudation rates as compared to the long-term AFT- and AHe-derived exhunation rates. However, the difference between our modern denudation rates and the \({}^{10}\)Be-derived paleo-denudation rates--that are also similar in magnitude to the AFT- and AHe-derived rates--suggests that the observed temporal increase in denudation rates in the Kyrgyz Tian Shan is real rather than an artifact of differing averaging timescales.
Sample AKT-U, in the south-western part of the Issyk-Kul basin, dated to 2.71 \(\pm\) 0.37 Ma ([PERSON] et al., 2023), yields a paleo-denudation rate between 50.6 \(\pm\) 8.2-204.0 \(\pm\) 32.8 mm kyr\({}^{-1}\), whereas the nearest modern river sediment sample (KYR16-05) yields a rate of 612.1 \(\pm\) 112.8 mm kyr\({}^{-1}\). Farther east, samples PET-QTS-L (2.08 \(\pm\) 0.14 Ma) and PET-QTS-PIT (2.75 \(\pm\) 0.15 Ma) ([PERSON] et al., 2023) yield paleo-denudation rates between 22.9 \(\pm\) 2.5-94.1 \(\pm\) 10.0 and 12.9 \(\pm\) 1.2-53.8 \(\pm\) 5.1 mm kyr\({}^{-1}\), respectively, which are lower than those obtained from the nearest modern river sediment samples: 154.7 \(\pm\) 28.6 mm kyr\({}^{-1}\) (KYR16-03), 871.9 \(\pm\) 158.8 mm kyr\({}^{-1}\) (KYR16-55), 727.0 \(\pm\) 131.3 mm kyr\({}^{-1}\) (KYR16-01B), and 798.17 \(\pm\) 144.31 mm kyr\({}^{-1}\) (KYR16-01C) (Tables S1 and S2 in Information S2 in Information S2). The elevated \({}^{10}\)Be-derived modern denudation rates compared to both the 2.0-2.7 Ma \({}^{10}\)Be-derived paleo-denudation rates and the long-term AFT and AHe exhunation rates indicate that in the Terskey range of the Kyrgyz Tian Shan, denudation remained relatively steady until an increase in the Quaternary, after ca. 2 Ma.
The Northern Hemisphere placations initiated in the Pliocene ([PERSON] et al., 2020) and intensified after 2.7 Ma ([PERSON] et al., 2020; [PERSON] et al., 2009), but our 2.0-2.7 Ma \({}^{10}\)Be-derived paleo-denudation rates from the southern side of the Issyk-Kul basin do not seem to reflect these global climatic changes. Furthermore, thermochronological data suggest that the Terskey range (situated on the southern side of the Issyk-Kul basin; Figure 1a) formed in the Miocene and did not experience strong deformation and exhunation afterward ([PERSON] et al., 2014). The strongest glacial erosional response to Quaternary glaciations is predicted by numerical modeling to occur in regions with extensive glaciations, moderate rock uplift rates (i.e., 0.3-1 mm per year), and a wet climate, whereas in arid regions, the response time of glacial erosion is predicted to be long and of small magnitude ([PERSON] et al., 2018). Given the above, we propose that the aridity of the Tian Shan has dampened and delayed the denudational response to climatic forcing and that the Quaternary glacial-interglacial cycles played a primary role in increasing millennial-scale denudation rates in the Kyrgyz Tian Shan and particularly in the Terskey range.
#### 5.2.2 Implications of the Onset of Plo-Pleistocene Glaciations in the Kyrgyz Tian Shan
The similarity in magnitudes between the 2.08 Ma and 2.7 Ma \({}^{10}\)Be-derived paleo-denudation rates and the long-term AFT and AHe exhunation rates implies a relatively steady denudation throughout the Miocene, Pliocene, and early Pleistocene. The three samples used to determine our \({}^{10}\)Be-derived paleo-denudation rates were collected from rare and thin fine-grained lenses in conglomerates from the Sharpyl Dak sedimentary group, which was deposited above finer-grained sediments and is analogous to the Xiyu formation conglomerates in the Chinese Tian Shan ([PERSON] et al., 2001; [PERSON] et al., 2002; [PERSON] et al., 2007). The deposition of the SharpyD Dak and Xiyu conglomerates is dachronous across the Tian Shan, varying from mid-Moicene to Pleistocene ([PERSON] et al., 2009; [PERSON] et al., 2002; [PERSON] et al., 2007; [PERSON] et al., 2023), and is considered to mark either the intensification of tectonic activity or the onset of Plo-Pleistocene glaciation in the region ([PERSON] et al., 2021). Samples AKT-U (2.71 \(\pm\) 0.37 Ma) and PET-QTS-PIT (2.75 \(\pm\) 0.15 Ma) were taken from the basal parts of the conglomerates, whereas sample PET-QTS-L (2.08 \(\pm\) 0.14 Ma) was collected from the youngest outcropping Sharpyl Dak conglomerates ([PERSON] et al., 2023). Therefore, the commencement of the deposition of the SharpyI Dak conglomerates was synchronous with the global intensification of Northern Hemisphere glaciation at 2.7 Ma ([PERSON] et al., 2020; [PERSON] et al., 2009). Nevertheless, despite the transition from fine-grained to conglomerate deposition, our data do not indicate an acceleration of denudation at 2.7 Ma.
In the Tian Shan, denudation is generally slow due to arid conditions, despite tectonic activity, high relief, and glaciations ([PERSON] et al., 2016; [PERSON] et al., 2021). The absence of a denudational response to the Plo-Pleistocene onset of glaciations inferred from our data may indicate that significant glaciation in the Terskey range of the Kyrgyz Tian Shan only initiated after 2 Ma, or that the onset of Plo-Pleistocene glaciations did not cause a detectable increase in denudation rates. Determining which of the two explanations is more likely is complicated by poor constraints on the onset of glaciations in the Tian Shan (see [PERSON] et al., 2016 and discussion above), although there is evidence suggesting that glaciations there occurred asynchronously with those in Europe and North America ([PERSON] et al., 2008; [PERSON] et al., 2011). It is important to note that the \({}^{10}\)Be-derived paleo-denudation rates reported here are likely not representative of the entire Kyrgyz Tian Shan, but rather reflect local conditions of the Terskey range (Figure 1a). For example, [PERSON] et al. (2011) reported a \({}^{10}\)Be-derived erosional pulse from 3.0 to 1.7 Ma in the eastern (Chinese) Tian Shan, suggesting a transient increase in denudation in response to the onset of Quaternary glaciations. However, this conclusion is based only on data from a single drainage basin. Conversely, [PERSON] et al. (2017) reported \({}^{10}\)Be-derived paleo-denudationrates from four localities in the eastern (Chinese) Tian Shan, indicating that denudation continuously increased in 9 Ma and remained relatively steady since 4 Ma (i.e., since before the onset of glaciations). Additionally, [PERSON] et al. (2017) found an increase in the spatial and short-term (<1 Myr) temporal variability of denudation rates between 3 and 1 Ma, suggesting a transient response of the landscape to glacial-interglacial cycles.
Taken together, the above evidence suggests that the erosional response and adjustment of the landscape to the onset of Plio-Pleistocene glaciation may vary spatially and temporally across the Tian Shan. Furthermore, each studied drainage basin may be affected by local tectonic processes. However, it is intriguing that the recent sequence of large magnitude earthquakes in the Kyrygz, Kungey, and Trans IIi ranges ([PERSON] et al., 2016) does not seem to be specifically reflected within the modern \({}^{10}\)Be-derived denudation rates.
### Spatial Differences in Denudation/Exhumination Rates in the Tian Shan
#### 5.3.1 West to East Decrease in Denudation/Exhumination Rates Across the Tian Shan
Comparison of our Kyrygz \({}^{10}\)Be data with the Western ([PERSON] et al., 2018) and the Eastern ([PERSON] et al., 2023) data sets illustrates a west to east trend of decreasing average \({}^{10}\)Be-derived modern denudation rates (Figures 2 and 7). A similar decreasing west to east trend is also observed in the AFT and AHe data, yet the \({}^{10}\)Be-derived denudation rates remain higher than AFT and AHe across the Tian Shan (Figure 2). Elevated exhunation and denudation rates and notably higher strain rates in the western Tian Shan and northern Pamir most likely reflect strong deformation caused by the northward motion of the Pamir (Figure 7c; [PERSON] et al., 2023). High denudation rates might also be sustained by higher precipitation because the Pamir acts as a topographic barrier to the westerlies (Figure 3e; [PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON] et al., 2022). Conversely, in the eastern (Chinese) Tian Shan, exhunation and denudation rates are relatively low (Figure 7) and denudation rates stayed relatively steady since at least the Pleistocene ([PERSON] et al., 2011, 2017, 2023). Geodetically determined north-south shortening rates decrease eastward within the Tian Shan ([PERSON] et al., 2010). Taken together, the available data suggest that strong tectonic activity and higher precipitation rates exert a pronounced control on denudation in the northern Pamir and western Tian Shan, whereas further east, precipitation and tectonically driven denudation decrease and the denudational response of the landscape to Quaternary glaciations becomes detectable.
Figure 7: Interquartile-range (IQR) box and whisker plots showing modern \({}^{10}\)Be-derived denudation rates, topographic gradient, and strain rate from northern Pamir and western Tian Shan ([PERSON] et al., 2018), the Kyrygz Tian Shan (this study), and the eastern (Chinese) Tian Shan ([PERSON] et al., 2023). The horizontal gray bands highlight the IQRs for the Kyrygz data.
#### 5.3.2 Kyrgyz Range--Outlier Region in the Kyrgyz Tian Shan
The exhumation of the Kyrgyz range, the only area in the Tian Shan showing modern \({}^{10}\)Be-derived denudation rates that are lower than exhumation rates derived from thermochronology, commenced at 11-7 Ma and propagated eastward ([PERSON] et al., 2001, 2003; [PERSON], [PERSON], et al., 2006). Before that time, this area was a basin filled with ca. 2 km of young, relatively poorly consolidated sediments. For this reason, elevated AFT exhumation rates recorded for the Kyrgyz range likely represent rapid exhumation of these poorly consolidated sediments at the beginning of the range growth ([PERSON] et al., 2003; [PERSON], [PERSON], et al., 2006). \({}^{10}\)Be-derived modern denudation rates in the Kyrgyz range are similar to those recorded in other Kyrgyz regions (Figure 4a), suggesting a deceleration of denudation after removal of the poorly consolidated sediments and a subsequent adjustment of denudation rates to the glacial conditions across the Kyrgyz Tian Shan.
Influence of Topographic, Tectonic, and Climatic Factors on \({}^{10}\)Be-Derived Denudation Rates
When considering the entire \({}^{10}\)Be data set, our analyses reveal weak but statistically significant correlations between log-transformed \({}^{10}\)Be-derived modern denudation rates and climatic metrics (precipitation and AI), and moderate correlations with strain rate (expressed as the second invariant of the model strain rate field; [PERSON] et al., 2014) and topographic metrics (Figure 6). However, the pattern changes when considering the three data sets (namely (a) norther Pamir and western Tian Shan, (b) Kyrgyz Tian Shan, and (c) eastern (Chinese) Tian Shan) separately (Figure 6) and the regions within them (Table S7 in Supporting Information S2). The three data sets exhibit stronger correlations with topographic metrics and weaker correlations with climatic metrics. Both the Kyrgyz and the eastern (Chinese) Tian Shan data sets show moderate correlations with slope and relief and weak correlations with annual rainfall. Western and eastern Tian Shan data sets show moderate (western) and weak (eastern) correlations with precipitation of the wettest month and AI. Elevation is a strong predictor in the western Tian Shan data set and only moderate in the eastern one. The normalized channel steepness (\(k_{u}\)) is a moderate predictor only in the eastern Tian Shan data set. Among separate regions, a strong correlation is observed only between denudation rates in the western Tian Shan and topographic gradient. The majority of other regions show moderate and weak correlations with topographic metrics, and several regions have weak correlations with climatic metrics (Table S7 in Supporting Information S2).
The above likely reflects moderate but primary tectonic and topographic control on denudation rates in general across the Tian Shan and both strong deformation and high precipitation rates in the Pamir. Interestingly, in the Issyk-Kul South region (Terskey range of the Kyrgyz Tian Shan), denudation rates only show a statistically significant correlation with the precipitation of the wettest month and AI, implying that denudation in the Terskey range is primarily controlled by summer rainfall despite the generally low amount of precipitation. This pattern is notably different from other regions of the Tian Shan, where topographic metrics are more significant predictors than climatic ones. The lack of a strong correlation between denudation rates in separate regions and topographic metrics is not unusual, considering the complex interplay among surface processes, tectonics, and climate ([PERSON] et al., 2022; [PERSON], 2016; [PERSON], 2011). This result is consistent with findings by [PERSON] et al. (2018) in the western Tian Shan and northern Pamir and [PERSON] et al. (2023) in the eastern (Chinese) Tian Shan--both studies reported weak correlations between \({}^{10}\)Be denudation rate and topographic metrics. Furthermore, our analysis found no statistically significant correlation between denudation rates in the three data sets and separate regions and strain rate (expressed as the second invariant of the model strain rate field; [PERSON] et al., 2014).
The lack of strong correlation and the variability in dominant predictors between regions is not surprising and is likely explained by the large spatial spread of our \({}^{10}\)Be data set--especially in the Kyrgyz Tian Shan--and the influence of local factors. Despite a relatively large \({}^{10}\)Be sample count (\(n=110\)), due to the large spatial spread of the data set, the individual groups (Figure 1b) have relatively few \({}^{10}\)Be data points, some too few to even warrant correlation analyses. It is likely that even in the relatively larger groups for which we did undertake correlation analyses (i.e., those included in Table S7 in Supporting Information S2), outliers may have too much influence on the obtained correlation coefficients. For this reason, correlation analyses are included here for their heuristic value and need to be interpreted with caution.
## 6 Conclusions
We report \({}^{10}\)Be-derived basin-wide denudation rates from modern river sediment from across the Kyrgyz Tian Shan and the Kazakh part of the Trans Ili and Kungey ranges, as well as \({}^{10}\)Be-derived paleo-denudation ratesfrom buried river sediment dated to 2.0-2.7 Ma from the southern side of the Issyk-Kul basin. We compare these data to published \({}^{10}\)Be-derived basin-wide denudation rates from the western Tian Shan and northern Pamir and eastern (Chinese) Tian Shan, as well as long-term exhumation rates, calculated from published AFT and apatite (U-Th-Sm)/He (AHe) thermochronology data from this entire region, and explore the spatial and temporal variations in denudation rates in the Tian Shan and northern Pamir as well as relationships between denudation rates and geomorphic, tectonic, and climatic metrics to identify potential controls on denudation at the local scale.
Our results show that the \({}^{10}\)Be-derived denudation rates obtained from modern river sediment are generally higher than long-term AFT and AHe exhumation rates across the entire study area, except for the Kyrgyz range (Figures 2 and 4). There, \({}^{10}\)Be-derived modern denudation rates are lower than long-term exhumation rates, likely because of rapid exhumation and removal of poorly consolidated sediments at the beginning of the range growth. On average, within the Kyrgyz data set, the highest \({}^{10}\)Be-derived denudation rates are recorded in the Terskey range, south of lake Issyk-Kul. Here, \({}^{10}\)Be-derived modern denudation rates are higher than \({}^{10}\)Be-derived paleo-denudation rates obtained from material dated to 2.0-2.7 Ma, which are comparable in magnitude to long-term exhumation rates inferred from AFT and AHe. The high \({}^{10}\)Be-derived denudation rates on the southern side of the Issyk-Kul basin compared to other sampled regions in the Kyrgyz Tian Shan suggest a recent increase in denudation rates on the northern slope of the Terskey range due to high glacial meltwater runoff, and/or admixing of previously shielded sediments with low \({}^{10}\)Be concentration.
We find that denudation in the Kyrgyz Tian Shan, particularly in the Terskey range, remained relatively steady during the Neogene and early Pleistocene despite the late Pliocene facies change from fine-grained sediment to conglomerates. Denudation in the Terskey range increased in the Quaternary, but this occurred after the onset and intensification of the Northern Hemisphere glaciations at 2.7 Ma. This delay in the denudational response of the landscape could indicate that glacial erosion in arid regions is detectable using cosmogenic radionuclides only after substantial cooling and extensive growth of glaciers. We acknowledge, however, that our \({}^{10}\)Be-derived paleo-denudation rate data are limited in size and areal extent and so might not be representative of the entire Kyrgyz Tian Shan and that other parts of the orogen might exhibit different temporal patterns of denudational response to Quaternary climate changes.
Comparison of our \({}^{10}\)Be-derived modern denudation rates with published data from the western Tian Shan, Northern Pamir and eastern (Chinese) Tian Shan show a spatial trend of decreasing denudation rates from west to east (Figure 2). This suggests that denudation in the Pamir and western Tian Shan is controlled by deformation caused by the northward motion of the Pamir, as well as high precipitation rates due to an orographic barrier to the westerlies created by the Pamir and Tian Shan. Further east, precipitation and tectonically driven denudation decrease and the denudational response of the landscape to Quaternary glaciations becomes detectable (Figure 7).
When considering the entire \({}^{10}\)Be data set, our analyses reveal weak but statistically significant correlations between log-transformed \({}^{10}\)Be-derived modern denudation rates and climatic metrics (precipitation and AI), and moderate correlations with strain rate and topographic metrics (Figure 6). When analyzed separately, the three data sets (namely, northern Pamir and western Tian Shan, Kyrgyz Tian Shan, and eastern Tians Shan) exhibit stronger correlations with topographic metrics and weaker correlations with climatic metrics. At the local scale, the picture is more complicated: albeit a moderate correlation is observed between denudation rate and topographic metrics in most of the regions with enough data points to warrant an analysis, climatic metrics such as annual rainfall, the rainfall of the wettest month, and the AI are stronger predictors of \({}^{10}\)Be denudation rate in some regions including the Terskey range, south of lake Issyk-Kul. The above highlights the complex linkages among tectonics, climate, and surface processes that may lead to local variations in the dominant controls on denudation.
## Appendix A Joint of Geophysical Research: Earth Surface
### Acknowledgments
Funding was provided by the Deutsche Forschungsgemeinschaft e. V. (DFG) Grant S. 34G9-1 to [PERSON], as well as by the German Federal Ministry of Education and Research (project TFIPTM) support code (0308069) and Volkswagen Foundation (Grant ZA. 75 86860) to [PERSON] and [PERSON], [PERSON] was also funded by the University of Wollimago (UOW) Faculty of Science, Medicine and Health and the UOW University Physgraduate Award fund. We are grateful to [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] for their help with sampling and logistics during field work in Kyrgyzin. We thank [PERSON] for sample preparation work and [PERSON] for assistance with R. We acknowledge support from the Center for Accelerator Science at the Australian Nuclear Science and Technology Organisation (ANSTO) through the National Collaborative Research Infrastructure Strategy (NCHS). Parts of this research were carried out at the Reen Science and Technology Center (IBC) at the Helmholtz-Zentrum Deskron-Rossendorf & V., a member of the Helmholtz Association, We thank the DREAMS team, especially [PERSON], for assistance with AMS-measurements. Open Access funding enabled and organized by Projekt DEAL.
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wiley/fb2b7424_2283_4717_9558_d99140452764.md | # Camera trapping with photos and videos: implications for ecology and citizen science
[PERSON]
1 Department of Anthropology, Durham University, Durham DH1 3 LE, UK
[PERSON]
2 Conservation Ecology Group, Department of Bioscience, Durham University, Durham DH1 3 LE, UK
[PERSON]
3 School of Natural and Environmental Sciences, Newcastle University, Newcastle NE 17 RU, UK
[PERSON]
1 Department of Anthropology, Durham University, Durham DH1 3 LE, UK
###### Abstract
Camera traps are increasingly used in wildlife monitoring and citizen science to address an array of ecological questions on a wide variety of species. However, despite the ability of modern camera traps to capture high-quality video, the majority of studies collect still images, in part because of concerns with video performance. We conducted a camera trap survey of a forested landscape in the UK, using a grid of paired camera traps, to quantify the impact of using video compared to photos on the outcomes of ecological research and for participation and engagement of citizen scientists. Ecological outputs showed no difference between photo and video datasets, but comparison between expert and citizen science classifications showed citizen scientists were able to classify videos more accurately (average accuracy of 95% for video, 86% for photo). Furthermore, citizen scientists were more likely to volunteer additional information on age (provided for 61% videos and 30% photos) and sex (provided for 63% videos and 45% photos) of animals in video footage. Concerns over slow trigger speeds for videos did not appear to affect our datasets or the inferences gained. When combined with citizen science, video datasets are likely to be of higher quality due to increased classification accuracy. Consequently, we encourage researchers to consider the use of video for future camera-trapping projects.
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## 1 Introduction
The use of camera traps for research has seen exponential growth over the last two decades ([PERSON] et al., 2021). While this growth may slow, development of technology, analytical methods and coordinated data sharing platforms will allow for continued diversification of the topics and questions that can be addressed using camera trap data ([PERSON] et al., 2021). Furthermore, the practical advantages of camera traps during times of uncertainty and restricted travel have recently become more evident ([PERSON] et al., 2021). In light of this, there is a pressing need to consider how to optimize camera trap set-ups for specific purposes.
While the majority of camera trap research uses photographs, video footage may be more suitable for applications such as behavioural studies ([PERSON] et al., 2017; [PERSON] et al., 2021; [PERSON] et al., 2018), monitoring group size ([PERSON] et al., 2016; [PERSON] and [PERSON], 2018; [PERSON] et al., 2019) or density estimation of unmarked species ([PERSON] et al., 2020; [PERSON] et al., 2017; [PERSON] et al., 2018). Video footage may also increase public engagement and facilitate easier identification of species and individuals for citizen scientists ([PERSON] et al., 2017; [PERSON] et al., 2014). Despite these advantages, a number of issues may deter researchers from using video. First, camera traps can have slower trigger speeds and longer recovery times when set to video and therefore risk missing some events ([PERSON] and [PERSON], 2018; [PERSON] et al., 2020). Second, videos have larger file sizes, leading to faster filling of memory cards, and increased power consumption when recording, leading to shorter battery life ([PERSON] et al., 2021; [PERSON] et al., 2021). A final concern is the longer processing time needed to view videos, which may be exacerbated by a lack of support for video management in softwaredesigned to streamline camera data management. Processing times are already an issue for many projects collecting photo data ([PERSON] et al., 2019; [PERSON] & [PERSON], 2016; [PERSON] et al., 2018) and can slow research and lead to potentially valuable data on non-target species being left unanalysed ([PERSON] et al., 2017).
Despite these concerns, little work has quantified the impacts of using video on the outcomes of ecological research. While some research has explored the impact of different camera trap settings, this has focused on controlled scenarios, such as using domestic animals to trigger cameras ([PERSON] & [PERSON], 2018; [PERSON] & [PERSON], 2021) and typically uses relatively small numbers of camera traps and sites. Fewer studies have compared photo and video settings; those that have were focused on a small number of species ([PERSON] et al., 2020; [PERSON] et al., 2013; [PERSON] et al., 2019), or on the identification of individuals of a species ([PERSON] et al., 2017). Instead, studies have focused on the influence of camera model ([PERSON] et al., 2017; [PERSON] & [PERSON], 2021), camera position ([PERSON] & [PERSON], 2018; [PERSON] & [PERSON], 2018; [PERSON] et al., 2016; [PERSON] et al., 2021), flash type ([PERSON] et al., 2021) or sensitivity settings ([PERSON] et al., 2021).
To support the time-consuming matter of data processing, camera trap researchers may turn to citizen science ([PERSON] & [PERSON], 2016). Camera-trapping citizen science projects have burgeoned recently and been shown to provide ecologically meaningful data ([PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON] et al., 2016; [PERSON] et al., 2016). Factors such as camera settings and location can impact classification accuracy; specifically, sequences with multiple photos have been found to have higher classification accuracy than those with single photos ([PERSON] et al., 2020). Camera trap videos could allow for easier species identification because movement can make animals easier to locate within the footage, and because more information is available to an observer, such as different views of an animal, their gait or movement profile, and sound. However, probably owing to the concerns outlined above, most camera trap citizen science projects use photographs and there has been little assessment of citizen science classification accuracy of videos (but see [PERSON] et al., 2021). Gaining adequate numbers of classifications is important for timely processing and for combining multiple classifications to achieve higher confidence in classification accuracy ([PERSON] et al., 2018; [PERSON] et al., 2020; [PERSON] et al., 2018; [PERSON] et al., 2016). Attracting participants and maintaining engagement are, therefore, important considerations for citizen science projects ([PERSON] & [PERSON], 2016). Including blank photos in a dataset can increase engagement, leading to longer classification sessions ([PERSON] et al., 2015). This is thought to be due to the increased feeling of reward when an image containing an animal is seen ([PERSON] et al., 2015). Other than this, little work has addressed how citizen scientists engage with different types of camera trap content. The sound and movement provided by videos could create a more immersive and engaging experience, but we are not aware of studies comparing how citizen scientists engage with photo _versus_ video content.
Here, we present data collected from a camera trap survey in the Forest of Dean, UK. Paired cameras were placed across the site with one set to take photos and the other set to take video. We ran common camera trap analyses, including species richness, occupancy, activity level and detection rate, to determine whether there were any ecologically meaningful differences between the photo and video datasets. Data were uploaded to the citizen science platform, MammalWeb (www.mammalweb.org) ([PERSON] et al., in press), into parallel photo and video projects for classification. We compared classification accuracy between different lengths of photo sequence and video footage as well as looking at participation and engagement with both types of media. Our aim was to inform the choice of photos _versus_ videos in camera settings in future ecological surveys, particularly those looking to engage citizen scientists in the classification process.
## Materials and Methods
### Study site - Forest of dean
The Forest of Dean (\(51^{\circ}46^{\prime}59.99^{\prime\prime}\)N, \(-2^{\circ}32^{\prime}59.99^{\prime\prime}\)W), extends across Gloucestershire, Herefordshire and Monmouthshire, UK, and consists of a mixture of broadleaf and conifer woodland, with patches of young trees. Our survey covered two forest areas, the larger covered approximately 65 km\({}^{2}\) with a smaller patch of approximately 20 km\({}^{2}\). Land is managed by Forestry England and fieldwork was undertaken in partnership with the Gloucestershire Wildlife Trust. The site is ecologically interesting to citizen scientists, as it is home to a variety of UK mammal species, including reintroduced populations of wild boar (_Sus scrofa_) ([PERSON] et al., 2015) and pine marten (_Martes martes_) ([PERSON] & [PERSON], 2021). The mammal assemblage (Table S1) enabled ecologically meaningful comparisons between photo and video footage for species ranging in abundance, body size and activity level.
### Fieldwork
A grid of points spaced 1 km apart was overlayed on a map of the Forest of Dean using QGIS (QGISDevelopment Team, 2018). The grid covered the main forest area, plus the additional patch around Symonds Yat approximately 2.5 km west of the main block (Fig. 1). The main forest area was divided into four sections, each containing 15 points; the forest at Symonds Yat constituted a fifth area. Fifteen pairs of camera traps were deployed between the 19 November 2019 and 24 March 2020, with the survey conducted during this period to avoid dispersal and breeding/birthing seasons. This period is characterized by reduced vegetation cover, increasing the field of view available to camera traps, and reducing the risk of false triggers. Camera traps were placed as close as possible to the specified grid points, while ensuring sites were accessible for servicing, avoided the river, and, to reduce risk of damage or theft, were out of sight of public footpaths. Mean displacement of camera stations from planned locations was 94 m. Cameras were deployed at sites in the main forest for between 25 and 30 nights before being rotated to new sites. Camera traps in the fifth and final location were in place for either 14 or 15 nights, as surveying was curtailed by the Covid-19 pandemic and uncertainty over site accessibility.
At each camera station, a pair of Browning Recon Force Extreme (2017 model) camera traps was mounted side-by-side on a metal bracket. Cameras were placed at a mean height of 51 cm from the ground and secured to a suitable tree with a camera strap and a python lock. Signs were attached to each camera station, informing people of the purpose of the study, requesting that the cameras not be disturbed, and providing contact information. One camera trap from each pair was set to record bursts of eight photos, and the other to record 20-s videos. Half-way through deployment at each site, cameras were serviced, with the batteries checked and memory cards changed. Batteries used were either Varta alkaline or Ene-loop rechargeable, with the same type of battery used in both cameras in each pair. In order to account for any slight differences in camera position, the camera settings were switched half-way through deployment so that the camera taking photos would take videos, and _vice versa_. Cameras use an infrared flash and manufacturer specifications suggest a trigger speed of 0.4 s and 0.8 s recovery time for photos. Trigger interval was set to 5 s.
## Data processing
To explore the impacts of video length and number of photos in a sequence, we created three versions of each camera trap sequence. Each video was clipped to create two additional versions, the first containing only the first 10 s and the second only the first 5 s of the clip. Images were first allocated into sequences with a greater than 10-s interval between images used to define a new sequence. Images were then labelled according to sequence and image number within sequence for each camera deployment. This followed the standard image processing method for footage added to MammalWeb ([PERSON] et al., 2018) and allowed manipulation of the number of images from each sequence. Three versions of the photo sequence dataset were created: one containing the first eight images in each sequence, one containing the first three images in each sequence, and one containing only the first photo from each sequence. There were, thus, six versions of the dataset: short (5 s), medium (10 s) and long (20 s) videos and short (one photo), medium (three photos) and long (eight photos) photo sequences.
All videos and photo sequences were tagged in the open-source photo management tool 'digiKam' ([[https://www.digikam.org](https://www.digikam.org)]([https://www.digikam.org](https://www.digikam.org))) to create expert classified datasets. Metadata and tags were extracted from photos and videos using the R package 'camtrapR' ([PERSON] et al., 2016).
## MammalianWeb
Separate Forest of Dean photo and video projects were established on MammalWeb, with matching descriptions and display images, so that the projects differed only in containing either photos or videos for classification. To prevent potential bias from a user repeatedly classifying the same piece of footage, only one version (short, medium or long) of each video or photo sequence was uploaded to MammalWeb. Footage was uploaded to MammalWeb between the 20 February and 3 June 2020 and the two projects first became available for public classification on 9 March 2020. MammalWeb contributors can choose to participate in a specific project or select the 'classify all' button, which will then serve the user a selection of footage from all active projects on the site. Users were able to participate in the Forest of Dean projects as 'Sportters', which involves viewing the footage and adding tags to identify the species present. Participants classifying an animal in a photo sequence or video could supply additional information about the animal, including sex (male or female) and age (adult or juvenile). A default option of 'Unknown' was set for both age and sex. Spotters could also 'like' the sequence or video that they were viewing. Time, date and anonymous user ID number were recorded by the website for each classification submitted.
Classification data were downloaded on 11 June 2021, after all footage had been available for classification for at least 1 year and all footage had received at least one classification. Classifications submitted by citizen scientists via the MammalWeb platform were compared to expert classifications to determine whether each classification was correct. All classifications submitted were used in accuracy analysis, but data were split into discrete classification sessions to compare participation rates between the photo and video projects. The minimum requirement for a session was three or more consecutive classifications of footage within either the photo project only or video project only by one user within a 30-min period. This was designed to exclude classifications by participants who had selected 'classify all' and had randomly been served footage from the Forest of Dean projects. This ensured that sessions were analysed only where a user had specifically chosen to classify from that particular project. A session ended if there was a greater than 30-min interval between classifications submitted.
## Data analysis
### Ecological outputs
Analyses were conducted using R 3.6.2 (R Core Team, 2019). Diversity and richness estimates were generated for all six datasets using 'iNEXT' ([PERSON] et al., 2020). More detailed ecological analysis focused on a subset of species. Selection criteria were mammals with a body size greater than 250 g (a small rodent), which might reasonably be expected to be detected by our camera trap set up, and that yielded sufficient detections (\(n=40\) detections at a 30-min independence level). The species comprised Eurasian badger (_Meles males_), red fox (_Vulpes vulpes_), fallow deer (_Dama dama_), Reeves muntjae (_Muntiacus reveisi_), roe deer (_Carpelous caproclus_), wild boar (_Sus scrofa_), European rabbit (_Oryctolagus cuniculus_) and grey squirter (_Sciurus cardiensis_).
Detections were compared between the datasets by generating presence-absence data at each camera station for each of the focal species detected at that site, for every half-hour during the active period of each camera station. A half-hour period was chosen as this is a common interval for discrning independent detections ([PERSON] et al., 2015; [PERSON] & [PERSON], 2016; [PERSON], 2018). To assess differences in species detections between different media types and lengths, we used general linear mixed models (GLMMs) with a binomial distribution in 'lme4' ([PERSON] et al., 2015). We defined separate models to check for the effect of length within each media type and then to check for differences between photo and video datasets. Analyses were
Figure 1. Forest area included in the study with locations of camera tap stations. Inset shows map of the UK with the location of the study site. Different deployments indicate the different time periods during which each area of the forest was surveyed. The time periods for each deployment are as follows: Deployment 1 = 19/11/2019-17/12/2019; Deployment 2 = 18/12/2019-13/01/2020; Deployment 3 = 13/01/2020-11/02/2020; Deployment 4 = 11/02/2020-09/03/2020; Deployment 5 = 09/03/2020-24/03/2020.
separated to avoid replication of the same datasets (across length variants) when comparing photos and videos. Species and camera station were specified as random factors. Half-hour time slot or'survey period' was included as an additional random factor in the photo/video comparison model. Model comparison tables were generated using the MuMIn package to assess whether including media type or length-improved model performance ([PERSON], 2020).
For each focal species, activity levels (the proportion of time species spent active per day; see [PERSON] et al., 2014) from each length of video or photo sequence were compared using the R-package 'activity' ([PERSON], 2021). Data were species detections with 5-min intervals between events. Even though some events may not be independent, this time period was chosen to trade-off the risk of non-independence with the aim of resolving activity to a reasonably fine scale. A Wald test was used to assess differences in activity level between the datasets produced by the different media and media lengths for each individual species and the combined dataset.
Detection histories were generated for each of the focal species from each length of video and photo sequence dataset. Detection histories were based on 24 h survey periods and were generated using 'camtrapR' ([PERSON] et al., 2016) and then used to fit occupancy models using the package 'unmarked' ([PERSON] and [PERSON], 2011). Outputs were back-transformed to give occupancy probability and the probability of detection. No covariates were included because our aim was the comparison between inferences from different media (and the paired design of the data collection ensured covariate differences did not introduce bias in these parameters), rather than to identify the factors driving occupancy of each species.
### Citizen science classifications
Citizen science classifications were analysed using GLMMs to assess species classification accuracy, likelihood of submitting age and sex classification data, likelihood of footage receiving a 'like', and length of classification session.
Classification accuracy models were initially split into photo and video datasets, using sequence or video length as a fixed factor. Length did not have a detectable influence on classification accuracy for either photo or video, so it was excluded from models using the combined photo and video datasets. Classification accuracy models were then fitted to the full data set and to each focal species' data. The response variable for classification accuracy was a binary indicator of whether or not a citizen science classification matched the expert classification for that footage (1 if classifications matched, 0 if they did not). Age classification likelihood models were fitted to footage containing any of the eight focal species as these are common mammals for which participants might reasonably be expected to identify adult or juvenile forms. Sex classification likelihood models were fitted only to footage containing one of the three deer species present at the study site, because only these species show clear sexual dimorphism. The response variables for age and sex classification models were also binary indicators of whether or not an age or sex classification had been provided alongside a species classification (1 if an age or sex classification was given, 0 if the corresponding classification was not given). Models determining the probability of liking footage used the full dataset. Again, the response variable was a binary indicator (1 if the footage was liked, 0 if it was not). Fixed factors in all classification models were media type (photo or video) and whether or not the flash was activated (i.e. whether footage was full colour or black and white/grey scale). Length of video or photo sequence was included as a fixed factor in age, sex and like classification models. Random factors were camera site ID and anonymous user ID, which were used in all classification models other than for accuracy of rabbit classifications where only anonymous user ID was used, due to the small number of different sites at which rabbits were detected. For each model, we first fitted the full model and then used the dredge function of the MuMIn package (Barton, 2020) to fit all possible additive variable permutations for the fixed factors described above. For the classification accuracy model a single interaction between media type and activation of flash was also included. Models were ranked according to AIC (Tables S5-S8). We then used effect size and p value of factors in the top model (using model averaging where there was more than one model within six AIC of the top) to assess strength and classical statistical significance of the effect of these predictors.
Length of session was measured in two ways: time difference between first and last classifications submitted in a session, and number of classifications submitted in a session. For both models, media type was used as fixed factor and anonymous user ID as a random factor.
## Results
Camera traps taking photos were active and functional for a total of 1734 trap nights across 73 camera stations, while cameras taking videos were active for 1730 nights across 73 stations. The slight differences were due to camera malfunction. Of the original 75 planned sites, one was excluded due to bracken causing high levels of false triggers and filling memory cards, with no meaningful data collected from that site. A second site was excluded due to the theft of the cameras during the fourth rotation.
This meant only 14 sites were available for the fifth rotation; since this was the smaller forest patch, coverage was not greatly affected. Other than the one theft, cameras were left undamaged and were not tampered with at any other site, despite evidence they were detected by people on multiple occasions.
The displays showed photo cameras used, on average, 0.8% of battery per week with video cameras using 3.8%. Photo cameras recorded a mean of 415 individual photos per week and video cameras a mean of 29 videos. Each 20-s video had a file size of approximately 31 MB and each photo had a file size of approximately 0.8 MB. Based on the above rates of capture, an average of 332 MB and 899 MB of memory storage were needed per week for photos and videos, respectively.
### Ecological outputs
Only data from 70 sites where video and photo cameras were active at the same time were used in analysis of ecological outputs. Diversity and species richness and species accumulation rates were similar for all datasets (Table 1; Fig. 51). The same 13 mammal species were detected in all lengths of photo sequence and video, and 18 and 15 bird species were detected in video and photo footage, respectively (Table S1).
### Species detection
Trapping rates for all of the eight focal species were very similar across all lengths of photo sequence and video (Fig. 2). Neither length of video or photo sequence, nor choice of video _versus_ photo influenced the probability of detecting a species event; model selection showed no improvement in model performance when media type or length were included compared to null models (AALCs of null models = 0, AALCs of models including fixed effects <6; Table S2).
### Activity
There was no difference between the activity levels derived from the different lengths of photo sequence and video for any of the focal species (_P_-values between 0.4 and 1; Fig. 3; Table S3).
### Occupancy
Due to lack of difference in species detections between the different lengths of video and photo sequence, occupancy analyses used only the 20-s video and eight-photo sequence datasets to compare the two media. Occupancy and detection probability estimates were the same or very similar for photo and video. Where slight differences occurred, standard errors overlapped, indicating no meaningful difference in outputs (Table S4).
### Citizen science classifications
5,326 photo sequences and 5,610 videos were uploaded to MammalWeb for classification. All photo sequences and videos received at least one classification and, overall, 17,474 photo and 12,429 video classifications were submitted.
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline & Five-second & Ten-second & Twenty-second & One-photo & Three-photo & Eight-photo \\ & videos & videos & videos & sequences & sequences & sequences \\ \hline Species richness observed & 30 & 31 & 31 & 28 & 28 & 28 \\ Species richness estimator & 36.25 (7.55) & 37.25 (7.55) & 33.67 (3.48) & 28.25 (0.73) & 28.25 (0.73) & 28.5 (1.32) \\ (SE) & & & & & & \\ Shannon diversity & 10.2 & 10.54 & 10.78 & 10.43 & 10.42 & 10.45 \\ observed & & & & & & \\ Shannon diversity & 10.3 (0.23) & 10.64 (0.26) & 10.87 (0.27) & 10.51 (0.25) & 10.49 (0.27) & 10.52 (0.22) \\ estimator (SE) & & & & & & \\ Simpson diversity & 7.46 & 7.6 & 7.74 & 7.57 & 7.55 & 7.56 \\ observed & & & & & & \\ Simpson diversity & 7.48 (0.18) & 7.63 (0.18) & 7.76 (0.18) & 7.6 (0.18) & 7.56 (0.18) & 7.59 (0.16) \\ estimator (SE) & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Species diversity estimates from a camera trap survey of the Forest of Dean, UK, where photo bursts and video data were collected simultaneously using a paired camera setup. Diversity estimates are given based on the first photo, first three photos and first eight photos in each burst, and for the first 5 s, first 10 s and full 20 s of each video clip. Observed differences were due to three species of bird detected in video footage but not in photos. These species were blue tilt, marsh it and tree creep, all of which are small birds for which we would not consider our camera trap setup a suitable method for surveying.
### Species classification accuracy
Media type and flash activation both affected the probability of a citizen science classification being correct (Table 2). Use of video had a positive effect with a higher probability of correct classifications than for photo sequences (Fig. 4; Table 2). Activation of flash had a negative effect on classification accuracy of both video and
Figure 3: Activity distribution over a 24 hr. period with 95% confidence limits for each of eight focal species recorded during a camera trap survey of the Forest of Dean, UK, based on 8-photo and 20-s video datasets collected by paired cameras. Data were species detections with, at a minimum, 5-min intervals between events.
Figure 2: Boxplots of trapping rates for each of eight focal species detected during a camera trap survey of the Forest of Dean, UK, using 73 camera stations with paired cameras recording videos and photo bursts. Trapping rates were acquired for each camera trap station at which the species was detected, calculated as number of half-hour periods in which a species was detected, divided by number of operational camera days. Trapping rates were calculated using detections in datasets comprising: the first photo in every photo sequence; the first three photos in a sequence, the first eight photos in a sequence, the first 5 s of each video clip; the first 10 s, and 20-s video clips (the full length of each video). Bars and boxes indicate median and interquartile range (IQR), whiskers show the largest and smallest values within 1.5*IQR, with individual outliers plotted as solid fill circles.
photo footage, with participants more likely to submit a correct classification when shown full colour than footage taken using infrared flash.
When analysed individually, all focal species were classified more accurately in video footage; this effect was statistically significant (p \(<\) 0.05) in models for all species apart from fox and roe deer (Table 2). Activation of flash was the only significant effect in the analysis of roe deer classification and had a negative influence on classification accuracy. For grey squirrel classifications, there was a significant interaction between media type and flash activation (Table 2) with the negative effect of flash activation being greater for photo footage than for video. Activation of flash was included in top models for fallow
(Table 2; Fig. 5). Use of video had a positive effect on likelihood of an age or sex classification being submitted, as did the use of longer videos or photo sequences. Activation of flash was included in the top age classification model and had a slight positive effect on likelihood of an age classification being provided (Table 2; Fig. 5).
### Citizen science engagement
A total of 183 contributors participated in at least one of the Forest of Dean projects; 126 users classified at least one sequence from the photo project, 117 users classified at least one video from the video project; 60 users participated in both projects. Eighty-six users took part in a combined total of 411 classification sessions for the photo project and 59 users took part in 365 sessions for the video project. Video classification sessions had a mean duration of 27 min 5 s (range: 46 s-173 mins 51 s) with a mean of 33 (range: 3-281) videos classified in a session. Photo classification sessions had a mean length of time of 26 min 34 s (range: 23 s-184 min 49 s) with 42 (range: 3-305) photo sequences classified per session. Mean time taken to classify was 42 s (range: 7.7 s - 259 s) for a photo sequence and 60 s (range: 15.3 s - 450 s) to classify a video.
Figure 4: Proportion of citizen science classifications that matched expert classifications for each of eight focal species and for the full data set of classifications of footage collected in a camera trap survey of the Forest of Dean, UK. Proportions are given separately for photo and video footage, both with and without the flash activated. Error bars show 95% confidence intervals.
Figure 5: A) Proportion of camera trap footage for each of eight focal species for which an age category (adult or juvenile) was supplied by citizen scientists alongside a species classification and B) proportion of camera trap footage for three deer species for which a sex category (male or female) was supplied by citizen scientists alongside a species classification for different lengths of photo sequence and video. Error bars show 95% confidence intervals.
### Classification session length
More classifications were submitted per session for the photo project than for the video project. Model fit was improved by including media type as a predictor (Table 58) and the effect of media type was statistically significant (p \(<\) 0.001) in this model. However, there was still large variation and considerable overlap between the two projects (Fig. 6). For session duration, there was no difference in model performance when media type was included and model-averaged results show no significant difference (p = 0.41) between photo and video projects (Table 58; Fig. 6).
### 'Liked' footage
Media type and length of photo sequence or video had an effect on probability of footage being 'liked' by a citizen scientist (Table 2). The probability that a video was liked was 14 times greater than for photo sequences, with longer videos being most popular (Fig. 7). Single photos were more likely to be liked than both 3-photo and 8-photo sequences. Footage was more likely to be liked if the flash had been activated (Table 2).
## Discussion
We tested whether camera traps set to video could collect ecological data of the same quality as that obtained by cameras set to record photos. Moreover, we tested for differences in citizen science classification accuracy and engagement between photo and video datasets. We found that photo and video settings did not affect the ecological inferences, but that citizen scientists were more accurate and provided more detail when classifying video footage. Overall, there was a 9% difference in footage classification accuracy between photo (average accuracy 85%) and video (average accuracy 94%) footage when the flash was activated and a 7% difference when flash was not activated (average photo accuracy was 89%, video was 96%). The percentage of video footage containing one of the focal species that was given an age classification was twice that of age classifications given to photo footage (age classification provision for video was 61% and 30% for photo). The percentage of footage containing deer that was given a sex classification was also higher for video, with an 18% difference (sex classification provision for video was 63% and 45% for photo).
### Ecological analyses
Based on datasets from expert classification, we found no differences in species diversity, occupancy, activity or detection rates between the photo and video datasets. This is in contrast to concerns that slow trigger and recovery speeds limit the value of video datasets, and is reassuring for those researchers wishing to use video based on its advantages in behavioural research
Figure 6: Boxplots of the length of time citizen scientists spent classifying camera trap footage from parallel photo and video projects in a continuous classification session, and the number of classifications that were submitted per classification session by MammalWeb participants. Bars and boxes indicate median and interquartile range 0 QR), whiskers show the largest and smallest values within 1.5“IQR, with individual outliers plotted as solid fill circles.
([PERSON] et al., 2017), individual ID ([PERSON] et al., 2017) and density estimation of unmarked individuals ([PERSON] et al., 2020; [PERSON] et al., 2017). While videos did take up more battery and memory, we found this had no real impact on our study, so need not be a deterrent to using video. Of course, in areas of higher animal activity, or where site access is necessarily infrequent, these factors may still need careful consideration. In such conditions, shorter videos could provide a good compromise, as we found that 5-s videos recorded species as reliably as 20-s videos.
We tested only one model of camera trap in one ecological system and other studies have found differences in performance between photo and video settings ([PERSON] et al., 2020; [PERSON] et al., 2019). As different camera traps perform differently ([PERSON] and [PERSON], 2018; [PERSON] et al., 2017; [PERSON] et al., 2021; [PERSON] and [PERSON], 2018; [PERSON] et al., 2013; [PERSON] and [PERSON], 2021), more research is needed to determine whether our findings will generalize across cameras and study species. Nevertheless, as camera traps continue to be upgraded, we would expect video performance to improve further over time.
### Citizen science classifications
Overall, video footage was classified more accurately than photo sequences (Fig. 4). There was no difference in classification accuracy between videos of 5-s or 20-s length, highlighting that projects could benefit from improved accuracy even when short video clips are used. Citizen scientists were not only more accurate when classifying species in video, but they were also more likely to add age and sex category classifications, suggesting this was easier to identify in videos than photos. Alternatively, the increase in age and sex classifications may reflect a deeper level of engagement with video footage. Preliminary examination of the data suggests that age and sex classifications, when provided, were accurate for both videos and photo sequences (approximately 95% correct) indicating that video footage could provide valuable additional demographic data. However, since the study was conducted when few juvenile animals were present and most male deer still had their antlers making them easier to recognize, further analyses across seasons are needed to determine more precisely the ability of citizen scientist to identify age and sex of animals accurately from photo and video footage. It is likely that more citizen science projects will start requiring human observers to move beyond species classifications; provision of additional detail is already evident in projects asking participants to identify age and sex ([PERSON] et al., 2021) and individual ID ([PERSON] et al., 2021; [PERSON] et al., 2018). Further research is needed to establish optimum camera settings for accurate identification of these traits, although video appears to offer clear benefits over traditional photos.
Confidence in accuracy and verification of citizen science ecological data is important for trust and acceptance of the value of the data ([PERSON] et al., 2021; [PERSON] et al., 2016). The higher classification accuracy of video footage could, thus, increase the value of video datasets. Organizations harnessing citizen science invest considerable effort in data verification, with common methods including expert verification and community consensus; however, expert verification can be time consuming,
Figure 7: Proportion of camera trap footage of each species which was “fixed” by a citizen scientist while they were classifying species in that footage. Proportions are given for different lengths of photo sequence and video for footage containing one of eight focal species, and for all footage combined from a survey of the Forest of Dean, UK. Error bars show 95% confidence intervals.
particularly for large camera trap datasets [PERSON] et al. (2021). Community consensus can be used to increase final classification accuracy but requires a large number of participants to gain enough classifications [PERSON] et al. (2018); [PERSON] et al. (2016). Video footage could be advantageous, therefore, particularly for smaller projects, since community consensus could be achieved more easily.
Similar numbers of participants engaged with the MammalWeb photo and video projects although many spotters only participated in one project, suggesting they have different preferences for classifying photo or video footage. Participants spent similar amounts of time classifying per session in the photo and video projects but more photo sequences were classified per session than videos because people spent longer classifying each video. Participants spent around a minute, on average, classifying each video, which implies the video clip was watched multiple times. This could either be due to a determination to identify the video correctly or simply enjoyment of the clip. MammalWeb participants 'liked' more video footage than photos, suggesting that videos were more engaging and enjoyable to watch. Engaging enough participants is a challenge faced by many citizen science projects, particularly in light of the growing number of projects available to choose from [PERSON] (2015); [PERSON] (2016); [PERSON] et al. (2021); [PERSON] et al. (2019). Using video could help with engagement while also gathering more accurate and detailed species classifications, thus generating higher quality datasets with fewer classifications needed per video. This would be advantageous to small projects as a high confidence in classification accuracy could be obtained with only a small number of participants viewing each video.
### Video for camera trapping and citizen science
Detection probability in camera trap studies consists of several components, including the probability that an animal is identifiable in a photo or video [PERSON] et al. (2020); [PERSON] et al. (2019). We found that citizen scientists classified videos more accurately, and it is likely that expert accuracy would also be improved through the use of video. Concerns over slow trigger speed reducing detection probability in videos were shown to be unfounded in this study. Therefore, due to increased animal identification accuracy, the use of video could increase detection probability, particularly for citizen science classified datasets. Consequently, we advocate for increased use of video in camera trap studies based on improved detection probability and citizen science engagement benefits.
More coordinated monitoring efforts are needed to identify global trends in biodiversity [PERSON] et al. (2017); [PERSON] et al. (2017) and there are now several initiatives combining camera trap footage from a range of participants in order to monitor wildlife across a wide area, such as MammalWeb [PERSON] et al. (in press), the Tropical Ecology Assessment and Monitoring (TEAM) Network Rovero & Ahumada (2017), and both Snapshot USA Cove et al. (2021) and Snapshot Europe ([[https://www.ab.mpg.de/358074/snapshot-europe](https://www.ab.mpg.de/358074/snapshot-europe)]([https://www.ab.mpg.de/358074/snapshot-europe](https://www.ab.mpg.de/358074/snapshot-europe))). These projects rely on large numbers of participants to collect enough data for meaningful ecological analysis. Our results show that it would be possible to combine datasets containing photo and video footage without risking loss of data quality. To support this, more camera trap data management software needs to be able to handle video footage. Artificial Intelligence (AI) is increasingly used to classify camera trap images and can be combined with citizen science for efficient data processing [PERSON] et al. (2020). It is encouraging that AI for video classification is fundamentally no different to that for photo classification in that each video frame can be treated like a single photo (e.g. [PERSON] et al., 2019), and that AI video analysis offers other potential advantages over photo classification (e.g.Johanns et al., 2022).
Integrating video could encourage a greater number of participants in collaborative projects, both from citizen science volunteers who prefer to use video and from researchers or practitioners undertaking surveys that fit other project criteria, but are currently unable to submit video footage. Allowing the use of video in such projects is of great importance for making efficient use of all camera trap data being collected, especially in the field of conservation, where resources are limited and data on even common species are still lacking [PERSON] et al. (2017).
## Acknowledgements
We thank Forestry England for permission to deploy camera traps across the Forest of Dean. We also thank the Gloucestershire Wildlife Trust, in particular [PERSON] and [PERSON] for their assistance with fieldwork. This work is supported by a NERC IAPETUS DTP PhD scholarship for [PERSON]; grant number NE/L002590/1. We are grateful to the Associate Editor and two anonymous reviewers for comments that helped improve the final version of the manuscript.
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## Supporting Information
Additional supporting information may be found online in the Supporting Information section at the end of the article.
**Table S1**. Full list of species detected. ***Species only detected in video footage. All other species detected in both photo and video
**Table S2**. Model comparison of GLMMS used to test for influence of video length, photo sequence length or media type on detections of the eight focal species. Comparison is given between null models and those including either media type or length as a fixed factor with the coefficient estimate, standard error and p value outputs for fixed factors from each full model (described in bold).
**Table S3**. Results of a Wald test comparing activity level derived from the short (5 s) and long (20 s) video data sets and short (one photo) and long (eight photo photo sequence data sets for eight focal species. Long (20s videos and 8-photo sequence) data sets were used in video _vs_. photo comparisons. Difference = differences between activity level estimates produced by the difference data sets, \(\mathrm{SE=Standard}\) error of the differences, \(\mathrm{W=Wald}\) statistics, \(\mathrm{P=p}\) values
**Table S4**. Occupancy and detection probabilities with standard errors (SE) for focal species for each media type and length data set based on expert classifications. ***SE** not available for these estimates due to lack or variability in presence across sites, that is this species was detected at all or almost all study sites.
**Table S5**. Species classification accuracy model comparisons showing all models within six AIC units of the top model for the global species set and individual focal species. Full model is given in bold with results of model selection below.
**Table S6**. Age classification model comparison showing all models within six AIC units of the top model. Full model is given in bold with results of model selection below.
**Table S7**. Sex classification model comparison showing all models within six AIC units of the top model. Full model is given in bold with results of model selection below.
**Table S8**. Results of GLMM model comparison for classification sessions measured in number of classifications and in length of time spent submitting classifications. Full model is given in bold with results of model selection below.
**Table S9**. 'Liked' footage model comparison showing all models within six AIC units of the top model. Full model is given in bold with results of model selection below.
**Table S10**. Breakdown of the number of photo sequences/videos in species categories for the different data sets.
**Table S11**. Number of detections of focal species used in activity analysis. | wiley | Camera trapping with photos and videos: implications for ecology and citizen science | Sian E. Green, Philip A. Stephens, Mark J. Whittingham, Russell A. Hill | https://doi.org/10.1002/rse2.309 | 2,022 | CC-BY |
wiley/fb2eb1f4_da3b_4a7f_aadd_4ec17873337d.md | # Geochemistry, Geophysics, Geosystems
10.1029/2022 GC010537
###### Abstract
Slow slip events in the northern Hikurangi margin of Aotearoa New Zealand occur every 18-24 months and last for several weeks before returning to average convergence rates of around 38 mm/yr. Along this plate boundary, the Hikurangi plateau subducts beneath the overlying Australian plate and slow slip events occur along their plate interface at depths between 2 and 15 km. To explore whether there is a temporal relationship between slow slip events and earthquake occurrence, the Regressive ESTimator automated phase arrival detection and onset estimation algorithm was applied to a data set of continuous waveform data collected by both land and ocean bottom seismometers. This detector uses an autoregressive algorithm with iterative refinement to first detect seismic events and then create a catalog of hypocenters and P and S wave arrival times. Results are compared with an available catalog of manually detected seismic events. The auto-detector was able to find more than three times the number of events detected by analysts. With our newly assembled data set of automatically detected earthquakes, we were able to determine that there was an increase in the rate of earthquake occurrence during the 2014 slow slip event.
1 Cooperative Institute for Research in Environmental Sciences and Department of Geological Sciences, University of Colorado Boulder, Boulder, CO, USA, 2 Now at Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI, USA, 3 Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA 3
2010
1 Cooperative Institute for Research in Environmental Sciences and Department of Geological Sciences, University of Colorado Boulder, Boulder, CO, USA, 2 Now at Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI, USA, 3 Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute, Troy, NY, USA 3
2022 GC010537
24 FA82022
2022 GC010537
24 FA82022
Tohoku-Oki earthquake. Although these laboratory and field-based results are suggestive, the potential connection between SSEs and seismicity requires additional investigation.
An ideal target to investigate SSE-seisincity linkages is a recurring and shallow SSE along the North Island of New Zealand. At the northern Hikurangi subduction margin, the westward Pacific plate converges with the North Island section of the Australian plate at an average rate of 4.5 cm/yr (Figure 1). This margin has frequent SSEs that take place every 18-24 months and last for a few weeks ([PERSON], 2020; [PERSON] et al., 2016). One of these regular SSEs was targeted by a year-long temporary network of ocean floor pressure and seismic instruments deployed between June 2014 and May 2015 as part of the Hikurangi Ocean Bottom Investigation in Tremor and Slow Slip, or HOBITSS experiment (described in more detail in [PERSON] et al. (2019)). An approximately two-week SSE was successfully recorded geodetically from late September to early October 2014 (approximately 23 September-9 October 2014). This offshore SSE had a maximum slip of 250 mm and occurred along the upper 15 km of the plate interface ([PERSON] et al., 2016; Figure 1). Overlying the displaced SSE area, the HOBITSS ocean bottom seismometers registered ground motions (including tremors and microearthquake seismicity) throughout the entire duration of the SSE. In conjunction with the permanent land seismic network operated by GeoNet, the HOBITSS record allows us to investigate the evolution of seismicity before, during, and after the 2014 SSE.
The temporal association of seismicity with the 2014 SSE was explored previously in land and ocean bottom seismic records using fully or partially hand-picked detection methods to identify seismic events. These studies
Figure 1.— Location of study area in the North Island of New Zealand. Green rectangle outlines the limits of the 3D velocity model of [PERSON] et al. (2021) down to 94 km depth. Gray shaded patch with contours marks the region that was displaced during the September–October 2014 SSE. Contour interval is 50 mm as annotated ([PERSON] et al., 2016). Blue dashed line outlines the 2014–2015 microseismicity gap according to the manually built earthquake catalog in [PERSON] et al. (2019). Red and black triangles mark the location of GeoNet and HOBITSS seismometers, respectively. Inset map in the top left shows the tectonic setting of the study area.
provided valuable insights into the understanding of the seismological characteristics of the northern Hikurangi margin throughout this 2014 SSE event. For example, [PERSON] et al. (2018) discovered two tremor episodes that correlate spatially with both shallow subducted seamounts and the 2014 SSE areal displacement. These tremor episodes also temporally overlapped the SSE event and persisted for a couple of weeks after the SSE tapered off ([PERSON] et al., 2018). Using HOBITSS and GeoNet data, we manually built a catalog of microearthquake seismicity and found that the seismicity rates increased at the start of the SSE and sustained elevated seismicity for 2 months after the end of the SSE. ([PERSON] et al., 2019). [PERSON] and [PERSON] (2019) applied an automated template-matching earthquake detection technique on the hand-picked microearthquake catalogs of [PERSON] et al. (2018) and [PERSON] et al. (2019). Their results revealed repeating earthquakes located at the downdip edge of the subducted seamount toward the end of the 2014 SSE ([PERSON] and [PERSON], 2019). These three studies demonstrated that temporal correlations exist between the 2014 SSE and the timing of Hikurangi margin seismicity. However, these investigations all use or have some connection to hand-picked seismicity records that are subject to interannuallyst and intrananalyst biases and inconsistencies ([PERSON] et al., 2018).
A more complete, uniform, and comprehensive catalog of earthquakes is needed to accurately compare the seismicity record with the 2014 SSE timing. An automated catalog would provide consistency and repeatability and avoid analyst biases. Uniform and reliable wave phase arrivals in seismograms are crucial for hypocenter calculation and travel time inversions ([PERSON] and [PERSON], 2012; [PERSON] et al., 2009; [PERSON] et al., 2006). Furthermore, temporal analyses of seismic features that may evolve with time could be affected by inherent errors in the manual process.
To detect earthquakes over a wide range of magnitudes, improve the manual earthquake catalog, and mitigate systematic bias by human analysts, we built a new automated catalog of earthquakes for the joint data set of the ocean bottom and land seismometers during a time period spanning the 2014 SSE using the Regressive ESTimator (REST) algorithm for automated event detections, phase onset estimation, and hypocenter location ([PERSON] et al., 2019; [PERSON] et al., 2022; [PERSON] et al., 2017). We created this catalog to (a) evaluate whether the use of an automatic catalog substantially expands the amount and quality of arrivals and event detections, and (b) further query the timing of seismicity before, during, and after the 2014 SSE.
## 2 Data and Methods
The HOBITSS experiment included an array of 15 ocean bottom seismometers deployed over the ocean floor from the abyssal plain near the subduction trench to the thick sedimentary wedge, ranging from around 3,500 meters below sea level (mbsl) to as shallow as 650 mbsl (Figure 1). The land data are derived from 24 broad band and short period permanent seismometers located on the North Island and operated by GeoNet (www.geonet.org.nz). For this study, we selected 60 days of waveform data from the ocean bottom HOBITSS array together with terrestrial data from GeoNet. Specifically, we chose data from 1 September to 31 October 2014 to include the two-week-long 2014 SSE. This subset of data was chosen to evaluate the seismicity in the days before, during, and after the 2014 SSE.
Identification of P- and S-wave arrivals in seismograms is fundamental to creating a comprehensive catalog of earthquake hypocenters. An automated version of this process is carried out by the REST algorithm ([PERSON] et al., 2019), which integrates autoregressive estimation of seismic noise for signal detection and onset estimations ([PERSON] et al., 1990; [PERSON] et al., 1987) with windowing and refinement schemes similar to those of [PERSON] and [PERSON] (2015).
The REST software produces an automatically detected catalog of P and S arrivals through iterative refinement of the onset estimations. Details of the algorithm are described elsewhere (e.g., [PERSON] et al., 2019; [PERSON] et al., 2019). To summarize, the autoregression technique described in [PERSON] et al. (1990) is used to detect potential phase arrivals as any change (statistically defined) in a time series relative to background noise above a user-specified threshold. These detections are sorted chronologically and, if a sufficient number (in this case four) occurs within a designated time window (e.g., one that would extend from the first P to the last S arrival for any event in the region of interest), a \"potential event\" is declared. The onset estimation procedure described in [PERSON] et al. (1987) is then used on the vertical components of windows of data from these potential events to identify potential P arrivals. If a viable hypocenter can be determined using some combination of available onsets by grid search (using procedures from [PERSON] et al., 2006) in an appropriate wavespeed model, an additional search is performed using windows based on arrival times predicted by that hypocenter. If that search is successful, the procedure is repeated two additional times with both horizontal components included to estimate onsets for S arrivals. If, at the end of these four iterations, a viable hypocenter is determined, the result is added to the catalog.
We employed REST to identify seismic events in an area covering the easternmost part of the North Island and the seafloor off the coast of Gisborne to the subduction trench (green rectangle in Figure 1), using the Hikurangi margin 3D velocity model of [PERSON] et al. (2021). The initial search for detection examined seismograms using a single pass Bessel filter with a high-pass corner of 1 Hz and low pass corner equivalent to half the Nyquist frequency of the analyzed seismogram (Nyquist frequencies for instruments are 50 Hz for broadband seismometers and 100 Hz for the short period instruments). Following [PERSON] et al. (2019), successful identification of an earthquake was defined by the following criteria: (a) a minimum of 4 associated arrivals, (b) a travel time residual for each arrival of either less than 1.2 s or no larger than 4% of the total travel time, and (c) a standard deviation of travel time residuals less than 1 s.
When a sufficient number of reasonable quality waveforms are available, the REST algorithm can estimate Richter-type magnitudes by finding the maximum amplitude of the P coda (\(A\)) and the difference in arrival times of the P and S waves (\(dt\)). Often referred to as the local magnitude (\(M_{L}\)), the relation used is based on one defined for earthquakes in southern California:
\[M_{L}=a*log~{}A+b*log~{}dt-c, \tag{1}\]
where \(a\), \(b\) and \(c\) are regionally dependent constants that account for geometrical spreading, attenuation, and calibration of the local magnitude to the original Richter magnitude scale ([PERSON] and [PERSON], 2010). The usual equivalent relation for New Zealand's local earthquake magnitude scale is stated by [PERSON] et al. (2016) as:
\[M_{L}=log~{}A(R)+1.49*log~{}R+\left(1.27\times 10^{-3}\right)*R-0.29, \tag{2}\]
whereas \(R\) is hypocentral distance in kilometers. Effectively, the \(M_{L}\) definition for New Zealand is defined in terms of hypocentral distance, while the one used in REST is a function of difference in time between P and S (which serves as a proxy for distance). To translate REST-generated magnitude values into locally representative \(M_{L}\), we performed a linear regression of the magnitudes computed by REST with the magnitudes of the same earthquakes computed in the manual catalog ([PERSON] et al., 2019), which used the New Zealand local magnitude computation (Figure 9). An additional correction was applied to account for differences in how instrument responses were applied, specifically the REST magnitude (\(M_{L}\)old) was found to relate to the locally representative magnitude (\(M_{L}\)new) by:
\[M_{L}\mathrm{new}=(M_{L}\mathrm{old}*0.83)-0.14\]
Using this regression to produce a conversion factor, we were then able to compute corrected magnitude for 421 of the earthquakes located using REST with values ranging between \(-0.4\) and \(3.2\). With these magnitudes, we evaluated the statistical characteristics of the microearthquake activity in the region using the frequency-magnitude distribution (or Gutenberg-Richter law). We used the goodness-of-fit method of [PERSON] (2000) to establish the \(b\)-value and magnitude of the completeness when the fitness of the distribution is at its maximum.
## 3 Results
The initial catalog created by applying REST to the 2 months of continuous waveforms discussed here resulted in 1,739 seismic events corresponding to 20,368 P and 16,891 S arrivals for a total of 37,259 arrivals. On average, the seismic events registered 16 arrivals between the P and S phases. For each station used in this study, the program identified a minimum of 571 and a maximum of 1,500 P and S arrivals. By comparison, the manual catalog for the same time period consisted of 265 events with a total of 2,560 P and S wave arrival times ([PERSON] et al., 2019). An example of an earthquake detected using REST that did not appear in the original catalog is shown in Figure 2.
We also found that of the 1,739 autopicked microearthquakes, 222 were also in our manually picked catalog. The reasons for the nondetection of the 43 missed events are variable, but mostly result from the metrics used by REST to assess onset estimation quality (based mostly on the shape of the estimation function), which prevented a sufficient number of reasonable quality arrivals to be identified to allow the determination of a hypocenter. Indeed, visual inspection of these events revealed that several of the manually detected P and S arrivals were not clear and in hindsight should not have been picked, and only 6 events out of those missing 43 events have greater than or equal to 10 arrivals.
As the initial catalog is likely to include poorly constrained locations, we applied additional criteria similar to those used in [PERSON] et al. (2019) to develop a more robust and reliable catalog of hypocenters. Specifically, seismic events were culled from the initial set by requiring a minimum of 10 arrival times, with at least two S arrivals, and a location more than 3 km from the boundaries of the velocity model. This selection resulted in 853 earthquakes in the area bounded by the 3D velocity model of [PERSON] et al. (2021).
We also evaluated the P and S wave arrival times from a set of 222 events identified in both manual and automated data sets. Results of this comparison showed that the difference between auto-picked and manually picked P phases is no more than a few hundredths of a second (Figure 3), the automated picks are on average 0.062 s later. This DC offset is most likely a result of differences in phase delay due to the digital filters employed (both used bandpass filters between 3 and 8 Hz, but the manual picking used a two-pass IIR filter while REST uses a one-pass Bessel filter). We note that if the DC offset is removed from the P residuals, then 77% of the onset
Figure 3.— Time differences between common picks in manual versus automated catalogs for events common to both. The average of the residuals is shown with a solid gray vertical line.
Figure 2.— Example of an \(M_{1}\) 1.51 earthquake detected using REST and not detected previously using hand-picking of arrivals. P and S arrivals mark the auto-pick using REST (event id: 200007 in the catalog). Traces are bandpass filtered between 3 and 8 Hz.
differences are less than 0.1 s and 91% are less than 0.2 By comparison, the differences between manual and automated S arrivals skew negative (i.e., automated picks are more often later) with an asymmetric distribution that has a longer negative tail (Figure 3). When the average difference is 0.25 s, most automated arrivals are about 0.15 s later, with about 67% of these arrivals being within 0.2 s of each other. S picks in general are less precise, but the reason for the negative skew is likely a consequence of how the picks are made. While the manual picks are generally made on the more energetic horizontal component, REST considers both components simultaneously, and hence is less likely to pick S-P phase conversions that arrive prior to the main S phase.
With the use of a 3D velocity model ([PERSON] et al., 2021) in the automated catalog generation instead of the 1D velocity model of [PERSON] et al. (2019), changes were expected in the hypocenter locations of the 222 corresponding events. An analysis of the horizontal and vertical changes in hypocenter location shows that most of the hypocenters shift primarily to the west in the automated catalog, varying horizontally from 0 to 20 km (Figure 4a). The focal depth of these hypocenters changes by an average of 2.2 km toward shallower depths in the automated catalog (Figure 4b).
A map view of this final catalog of the selected 853 earthquakes (Figure 5) shows their geographic relation to the microseismicity gap and 2014 SSE. A histogram of earthquake depths shows that hypocenter locations are predominantly shallow, with depths peaking between 20 and 25 km and at least 75% of the events occurring
Figure 4: (a) Polar plot of azimuthal and horizontal distance change from manual (center of polar plot) to automated catalog. Radial axis serves as both distance change (in km) and for number of earthquakes in azimuthal histograms in bins of \(10^{\prime}\). (b) Vertical changes between the manual and automated catalogs (for reference, a positive vertical change represents that the automated earthquake detection and location resulted in a shallower depth than the one calculated in the manual catalog of [PERSON] et al. (2019)).
shallower than 35 km (Figure 6). Viewed in cross-section (Figure 7), these hypocenters appear unusually scattered. To test if this scatter is real, we applied strict selection criteria, namely that the 2-sigma uncertainties derived from the marginal probability distribution function for depth be less than 10 km, and compared those locations with the larger data set. As the plot using this more restrictive subset (dark green circles in Figure 7) shows essentially the same amount of scatter, we conclude that it is most likely real. We note that offshore, the hypocenters are close to the plate interface, but also with depths as deep as 40 km. Onshore, the hypocenters are also located in the overlying continental plate with some clusters close to the plate interface. To demonstrate that the patterns in seismicity shown in Figure 7 are not an artifact of absolute location methodology, we selected a subset of 249 of the better constrained locations, removed suspected outliers (based on absolute travel time residuals), and relocated them using the double-differencing and demeaning approaches described in [PERSON] et al. (2021). For these well-recorded events, the double-differenced locations did not change significantly from the absolute locations (in most cases by less than one km). We find the same patterns, and in particular the apparent scatter in hypocenters, with the double-difference analysis as in the original locations shown in Figure 7.
To determine how these microearthquake hypocenters may spatially and temporally relate to the region that slipped during the 2014 SSE, we weighted hypocenter locations by their distance to the maximum slip (250 mm)
Figure 5: Map of earthquakes from 1 September to 31 October 2014 detected and located using REST. Earthquakes are color coded by onset time and sized according to local magnitude. Earthquakes without an estimated magnitude are plotted as a six-point star. Shaded gray is the area of the 2014 slow slip event that registered displacements of at least 50 mm ([PERSON] et al., 2016). Dotted black line outlines the microscinecingly gap detected with the manual catalog ([PERSON] et al., 2019). Thick black line outlines a subducted seamout ([PERSON] et al., 2018). Dark blue line (X-X) denotes the cross section in Figure 7. Blue lines denote active faults in the region ([PERSON] et al., 2016): AF: Anrakhi Fault, OTF: Otoko-Totangi Fault, RF: Repongare Fault, PF: Pangopango Fault, FF: Fernside Fault, xF: unnamed fault.
of the SSE (see contours in Figure 1 and weight in Table 1). The results of this distance weighting scheme were then temporally averaged with a moving window of 4 days. The temporal distribution of the number of earthquakes per day is compared to the approximate start and end of the 2014 SSE as defined by GPS results (Figure 2 in [PERSON] et al. (2016)) (Figure 8a) and contrasted with a distance to slow slip area weighted count of the number of earthquakes per day (Figure 8b).
## 4 Discussion
The relationship between seismicity and the occurrence of SSEs around the world is not well understood. In the northern Hikurangi margin over the year 2014, one of these SSEs was recorded while a temporary network of ocean bottom seismometers was deployed. This offshore array of seismometers in conjunction with the permanent seismic network of New Zealand enabled us to study the behavior of seismicity throughout the duration
Figure 6: Histogram of earthquake depths for selected events. Dashed line marks the point where at least 75% of events are shallower than 35 km.
Figure 7: Cross-sectional view of earthquake hypocenters (circles) within 30 km of line X-X’ in Figure 5. Dark green circles represent those earthquakes with 2-sigma depth uncertainties less than 10 km. Black dashed line is the projection of the plate interface from [PERSON] et al. (2013).
of the 2014 SSE. A detailed catalog of earthquakes is essential to study such relationships and to assist other seismological studies (such as seismic tomography, anisotropy, attenuation, among others) that depend on the earthquake detections and their seismic wave phase arrivals.
One of the potential advantages of using an automated method to pick arrivals and detect events is that the biases associated with an analyst (or multiple analysts) can be avoided ([PERSON] & [PERSON], 2012; [PERSON] et al., 2009; [PERSON] et al., 2006). Consequently, temporal analyses of earthquake occurrence tend to be more reliable in automated earthquake catalogs than when performed on a manually built catalog. Our automated catalog throughout the 2014 SSE reveals further insights into the temporal and spatial distribution of seismic events during a regional slow slip event.
The detector and onset estimator program REST was used in this study to automatically generate an earthquake catalog. This method detected a total of 1,739 hypocenters in the period between 1 September and 31 October 2014, 853 of which were considered well constrained. Over the same period, a manually built catalog detected a total of 265 events ([PERSON] et al., 2019), indicating that this automatic method can potentially detect at least 3 times more events than a manually built catalog. For events found by both manual and automatic picking, we found that the number of picks identified per event was also larger for the automatic method, with an average of 20 or more P and S arrivals per event compared to the number of phases picked manually. It is also worth noting that during the comparison of these autopicked events with our previous manually picked catalog, we discovered that at least five of the previously reported earthquakes were in error. These \"false positive\" events provide additional arguments for why an autopicking program may be preferable as the manual databases are prone to human error.
Hypocenter locations for the high-quality 853 events registered using automated detection show similar patterns of previously reported (e.g., [PERSON] et al., 2019) seismicity and may be correlated with North Island fault traces. We note that our new catalog shows these patterns with analysis of just 2 months of data, whereas the original study needed a full year of data. Our new autopicked catalog retains the microseismicity gap and is generally consistent with the spatial distribution of seismicity that was previously shown in manually built catalogs (Figure
\begin{table}
\begin{tabular}{l c c} Region of earthquakes & Weight & Number of earthquakes in region \\ \hline Outside 50 mm contour & 1 & 753 \\ Within 50 and 100 mm & 2 & 44 \\ Within 100 and 150 mm & 4 & 30 \\ Within 150 and 200 mm & 8 & 10 \\ Within 200 and 250 mm & 16 & 15 \\ Within 250 mm & 32 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: Weighting Factors by the Location of Earthquakes Relative to the Contours of Slip (in mm) of the 2014 SSE Contours
Figure 8: (a) Moving sum of the number of earthquakes per day for the 2 months studied (b) Moving sum of weighted count of earthquakes relative to slow slip event (SSE) contours as a function of time (see Table 1). The moving sum is for 4 days. The shaded gray patch marks the duration of the 2014 SSE, with the start and end times determined in [PERSON] et al. (2016).
7 in [PERSON] et al., 2019) or catalogs that use template-matching or repeating earthquake techniques (e.g., the large number of earthquakes adjacent and downdip from seamounts in Figure 2 in [PERSON] and [PERSON], 2019). Offshore seismicity in the automatic catalog also correlates with a cluster of earthquakes toward the down dip edge of a subducted seamount identified using magnetotellurics ([PERSON] et al., 2018). The northeast-southwest linear trend of earthquakes toward the west of our study region may be associated with the Arakishi fault in the southern portion ([PERSON] et al., 2009) or with the Fernside fault in the northern portion of the lineation ([PERSON], 1984) (see lines labeled AF and FF in Figure 5). The Arakishi fault lies supradallel to the Repongare fault, a 4.5 km long active fault that may be connected with the Arakishi fault, with the most recent event recorded at c. 3,400 years BP ([PERSON] et al., 2009). The Fernside fault is an east-dipping active fault with a 1 km long scarp over the southern portion of the fault ([PERSON], 1984). In summary, the use of an automatic method, as opposed to the manual picking method employed in previous studies, yielded results that are consistent with the previously published catalogs (e.g., [PERSON] and [PERSON], 2019; [PERSON] et al., 2018; [PERSON] et al., 2019) but also expanded the detection so that the seismicity record potentially reveals active faults that have not been reported from prior seismic studies (Figure 5).
The automatic earthquake detection and location algorithm used in this study implemented the 3D velocity model of [PERSON] et al. (2021) as opposed to the two 1D velocity models used in a previous study ([PERSON] et al., 2019). Systematic shifts in earthquake locations of hypocenters calculated using 1D versus 3D velocity models have been identified previously in other studies that targeted highly lateral heterogenous media such as other subduction zones or the San Andreas fault ([PERSON] and [PERSON], 1993; [PERSON] and [PERSON], 2002; [PERSON] et al., 2013). This study also found systematic shifts of earthquake locations relative to the manual catalog with 1D velocity models, with most of the earthquakes shifting toward the west (or landwards) and toward shallower depths. Most likely these shifts are a result of mantle velocities (\(\sim\)8.2 km/s) determined at shallower depths ([PERSON] et al., 2021) in the onshore portion of our study area than those used in the 1D velocity model applied by [PERSON] et al. (2019). For example, the onshore 1D velocity model was set to have mantle velocities at depths \(>\)38 km, but seismic tomography imaging revealed that near the shore, mantle velocities can occur at depths as shallow as \(\sim\)25 km ([PERSON] et al., 2021).
Taking advantage of the uniformity and consistency in automatic earthquake detection and localization, we analyzed the temporal and spatial record of earthquake occurrences relative to the 2014 SSE event. The results suggest that, during the SSE, there was an increase in the number of earthquakes weighted by their location relative to the SSE patch, growing in weighted occurrence over the course of, and mostly during roughly the second
Figure 9: Distribution of magnitudes for earthquakes that are common to the automated (vertical axis) and manual (horizontal axis) catalogs. Dashed line shows the linear regression and the dotted line marks the bounds of 95% confidence interval bounds.
half of, the SSE (Figure 8). This increase in the rate of seismicity started a few days after the onset of the 2014 SSE (approximately on October 1 st) and continued to increase until the end of the SSE (around 10 October). For several days after the termination of the SSE, the seismicity near the SSE decreases to background rates with small oscillations. Although the microearthquake seismicity per day decreases, the number of earthquakes in the end of the SSE remains high until mid-October 2014. During the 2 weeks following the end of the SSE, the area under the curve in Figure 8b is around 1.8 times larger than the area under the curve between the start and end of the SSE. We also observe that the seismicity during the week after the SSE (9 October-16, 2014) is almost as much as the cumulative weighted seismicity during the SSE (23 September-9 Oct. 2014). Increases in the rate of seismicity or tremor activity associated with the 2014 SSE, with largest increases toward immediately or after the end of the slip event, have been previously reported for this area ([PERSON] et al., 2022; [PERSON] and [PERSON], 2019; [PERSON] et al., 2018; [PERSON] et al., 2019). Studies of other regions where shallow SSEs have been documented, such as the Nazca subduction zone in Ecuador, the Cocos subduction zone in Costa Rica, and the Nankai subduction zone in Japan, have shown that increases in the rate of seismicity often occur during SSE sequences and the associated earthquakes may use the same source faults ([PERSON] et al., 2017; [PERSON] et al., 2018; [PERSON] et al., 2013).
Finally, the Gutenberg-Richter frequency-magnitude relation based on the 451 events for which REST-based estimates of magnitude were available shows a \(b\)-value of 1.3 corresponding to the linear portion of the slope, and a magnitude of completeness (\(M_{c}\)) of 1.7 (Figure 10). The application of quality control criteria on magnitude estimations resulted in our data set of calculated magnitudes being only a subset of the total catalog; thus, our auto-detector results are not directly comparable with the magnitude detection threshold of [PERSON] et al. (2019).
## 5 Conclusions
We tested an automatic seismic event detector as a tool to increase microearthquake detections and perform temporal analyses of earthquake occurrence. With the automated detection software, we found three times as
Figure 10: Frequency-magnitude relation for corrected magnitudes in automated earthquakes. Solid red squares mark the cumulative Gutenberg-Richter curve for the number of earthquakes with greater magnitude \(M_{c}\). Open black triangles mark the curve for incremental values in \(0.1\) Log(\(M_{c}\)) magnitude unit bins. Black solid line shows the resulting \(b\)-value of 1.3.
many events as were found in the same time period using manual methods. In addition to increasing the catalog of events by threefold, the automated method is uniformly applied and avoids possible analyst biases and inconsistencies. The auto-detected record of earthquakes revealed a possible temporal relationship between micro-seismicity and the cessation of the 2014 SSE, with an increase in weighted and raw occurrence of earthquakes throughout the duration of the SSE, remained high for 2 weeks after the SSE, then decayed to background levels of seismicity. The expanded detection also reveals seismicity along active faults that have not been reported in other studies covering this time period. We recommend the future use of automated seismic event detection software to enhance catalog completeness, reduce analyst biases, and reveal underlying trends in microearthquake spatial and temporal patterns.
## Data Availability Statement
The raw seismic data from the HOBITSS experiment are archived at the Incorporate Research Institutions for Seismology Data Management Center (IRIS-DMC) with DOI: [[https://doi.org/10.7914/SN/YH_2014](https://doi.org/10.7914/SN/YH_2014)]([https://doi.org/10.7914/SN/YH_2014](https://doi.org/10.7914/SN/YH_2014)). The land seismic data are openly available through GeobNet (www.geonet.org.nz). The catalog of automated earthquake hypocenters and the list of P- and S-wave arrivals for the two months around the 2014 slow slip event are openly available in Zenodo at [[https://doi.org/10.5281/zenodo.7274399](https://doi.org/10.5281/zenodo.7274399)]([https://doi.org/10.5281/zenodo.7274399](https://doi.org/10.5281/zenodo.7274399)). Some figures were plotted with Generic Mapping Tools (GMT) ([PERSON] et al., 2019; [PERSON], 1995). The software used to calculate the magnitude of completeness and b-value is from EQcorrscan ([PERSON] et al., 2017).
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* [PERSON] and [PERSON] | wiley | Temporal Relationship of Slow Slip Events and Microearthquake Seismicity: Insights From Earthquake Automatic Detections in the Northern Hikurangi Margin, Aotearoa New Zealand | Jefferson Yarce, Anne F. Sheehan, Steven Roecker | https://doi.org/10.1029/2022gc010537 | 2,023 | CC-BY |
wiley/fb254d4a_d483_4524_9390_98b8f9a15783.md | clouds and precipitation over a city ([PERSON] and [PERSON], 2004; [PERSON], 2005; [PERSON] and [PERSON], 2008).
The atmospheric flow around us comprises horizontal and vertical convection. Since thermals are convective structures of the maximum spatial scale in the convective boundary layer (CBL), generally in several hundred meters to one kilometer, they significantly impact pollutant and heat diffusion in the boundary layer ([PERSON] and [PERSON], 1994; [PERSON] et al., 2004). For example, [PERSON] (1989) simulated pollutant diffusion in a CBL developed on a flat plane. [PERSON] et al. (2019) used a large-eddy simulation (LES) model to simulate pollutant dispersion on a flat plane and in idealized cities. Daytime atmospheric flow comprises vertical and horizontal convection. Recently, UHIC simulations have been performed using an LES model with a spatial resolution (model grid size) sufficient to resolve turbulence, including thermals ([PERSON] and [PERSON], 2008; [PERSON] et al., 2020). When simulating UHIC and turbulence, it is crucial to reproduce UHIC with a spatial scale similar to that of a city and resolve thermals with a spatial scale of one to two orders of magnitude smaller than that of the city. Few studies have been conducted on the coexistence of UHIC and thermals. We elucidate how UHIC and thermals coexist based on the separation of UHIC and thermals from various perspectives.
The spatial and temporal scales of UHIC and thermals differ significantly. UHIC is a phenomenon where the spatial patterns do not vary much as compared to the thermals, which have a lifetime of approximately 10 min ([PERSON], 1988). Previous studies have focused on differences in spatial scales and have not paid sufficient attention to such differences in temporal scales. Separating UHIC and thermals by focusing on the temporal variation in spatial patterns might provide findings that differ from those of existing studies.
The flow around us is a combination of characteristic components (modes) on various spatiotemporal scales. Separating and interpreting these modes should benefit, for example, predicting the flow field at a low computational cost using a reduced-order model ([PERSON] and [PERSON], 2022). One of the most common dimensionality-reduction methods is proper orthogonal decomposition (POD), known as empirical orthogonal functions (EOF) in the meteorological field. This method extracts dominant spatial patterns of flows based on spatiotemporal correlations. Several examples of the modal decomposition of flow fields using POD exist (e.g., [PERSON] et al., 1993). Recently, methods resembling POD, such as spectral POD ([PERSON] et al., 2018) and dynamic mode decomposition (DMD; [PERSON], 2010), have been proposed. Both methods focus on temporal variations, which are challenging to analyze using conventional POD.
DMD is a modal decomposition method focusing on temporal changes in flow fields. Its unique aspect is that temporal changes are assumed to be a linear system and decomposed. Therefore, the characteristics of temporal changes can be analyzed in more detail than in conventional POD. DMD has recently been applied in various fields, such as motion detection ([PERSON] and [PERSON], 2016) and neural reactions ([PERSON] et al., 2016). Moreover, DMD has been applied in meteorology to model large-scale flows ([PERSON], 2022) and pattern extraction ([PERSON] and [PERSON], 2021).
Using the DMD method mentioned above, this study challenges separating UHIC and thermals based on the temporal changes of flow fields. This study applied DMD to a flow field, as in [PERSON] and [PERSON] (2021); however, the spatial scale of the phenomenon was disparate. In particular, we attempt to distinguish the phenomena with different spatial scales, mesoscale circulation (UHIC), and turbulence. This study aims to deepen our understanding of how UHIC and thermals coexist and influence each other using DMD, a modal decomposition method of flow fields focusing on time variation.
## 2 Methods
### Numerical simulation
We conducted a numerical simulation of idealized urban and suburban settings where UHIC and thermals coexist. The simulation details are described below.
We use City-LES ([PERSON] et al., 2015) developed at the Center for Computational Sciences, University of Tsukuba. The LES model considers the effects of atmospheric stratification; therefore, it was considered suitable for this study. The detailed information of City-LES is described in [PERSON] et al. (2015). The validation experiments of various aspects were conducted in previous studies (e.g., [PERSON] et al., 2024; [PERSON] and [PERSON], 2023). In these validation experiments, this model shows good agreement with the result of wind tunnel experiment and previous simulation results.
The basic equation is nonhydrostatic Boussinesq approximation equations. The model predicts the three-dimensional wind speed, pressure perturbation, potential temperature, and mixing ratio of water vapor, cloud, and rainwater. This study predicts only wind speed, pressure perturbation, and potential temperature. A standard Smagorinsky model was used as the subgrid-scale model (\(\text{Cs}=0.18\)). The three-stage Runge-Kutta scheme ([PERSON] and [PERSON], 2002) was used for time integration. A fifth-order upwind scheme ([PERSON] et al., 2008) was used for spatial differentiation of the advection scheme. The simplified marker and cell method ([PERSON] and [PERSON], 1970) was used to predict pressure perturbation.
Figure 1 shows the simulation domain configuration. As shown in Figure 1, a city on a band stretching from north to south was set in the center of the domain. The city's width was set at 8 km, and the spatial resolution at 25 m. The number of grids in the simulation domain was east-west, north-south, and vertical = 1024, 800, and 254, respectively. A grassland was placed next to the city. The urban and grassland areas were characterized by sensible heat flux \(H\) and roughness parameter \(z_{0}\). In particular, we set \(H=150\) W\(\cdot\)m\({}^{-2}\), \(z_{0}=0.5\) m in the urban area, and \(H=30\) W\(\cdot\)m\({}^{-2}\), \(z_{0}=0.12\) m in the grassland area. The lateral boundary conditions were periodic for the east-west and north-south directions. The momentum fluxes at the surface were calculated using the bulk method. The bulk transfer coefficient was calculated using [PERSON]'s (1995) method. A numerical simulation was performed for 3 h, and the last 81 min were used for analysis. UHIC expands throughout the simulation because we set a constant sensible heat flux at the surface.
The initial conditions were as follows: No wind was introduced, and a stable atmosphere with a potential temperature lapse rate of 0.004 K\(\cdot\)m\({}^{-1}\) was used as the initial potential temperature profile.
### DMD
DMD is similar to EOF, except it focuses on the temporal variation in spatial patterns. In DMD, the temporal variation is assumed to be a linear system. The characteristic feature of DMD is that the temporal variation in the spatial patterns can be decomposed and analyzed by performing an eigenvalue decomposition of the linear system. Originating from fluid analysis ([PERSON], 2010), DMD has been applied to climate data analysis ([PERSON], 2021; [PERSON], 2022). The DMD algorithm (based on [PERSON], 2010) is as follows:
Prepare a matrix \(\mathbf{X}\) comprising \(n\) snapshots in a time window \(1\leq t\leq n\) and a matrix \(\mathbf{Y}\) shifted in time by \(\Delta t\) for all snapshots from \(\mathbf{X}\). In DMD, a linear system is assumed between \(\mathbf{X}\) and \(\mathbf{Y}\), indicating that
\[\mathbf{Y}=\mathbf{A}\mathbf{X}. \tag{1}\]
The decomposed mode (called dynamic mode) is defined as the eigenvector of linear system \(\mathbf{A}\). The simplest method of obtaining \(\mathbf{A}\) is to find the Moore-Penrose inverse of matrix \(\mathbf{X}\):
\[\mathbf{A}=\mathbf{Y}\mathbf{X}^{\dagger}. \tag{2}\]
However, since matrix \(\mathbf{X}\) is large and comprises multiple (output) vectors with the dimension of the number of grid points (\(m\) grid points, for example, \(\mathbf{X}\in R^{m\times n}\)), obtaining the Moore-Penrose inverse matrix is challenging. [PERSON] (2010) proposed a computationally inexpensive and simple method using singular value decomposition.
First, the singular value decomposition of \(\mathbf{X}\) (\(\mathbf{X}=\mathbf{U}\mathbf{\Sigma}\mathbf{W}^{H}\)) is performed. By substituting this into Equation (1) and rearranging it, we can define \(\mathbf{\tilde{S}}\):
\[\mathbf{U}\mathbf{A}\mathbf{U}^{H}=\mathbf{U}^{H}\mathbf{Y}\mathbf{W}\mathbf{\Sigma}^{-1}\equiv\mathbf{ \tilde{S}} \tag{3}\]
Using the eigenvector \(\mathbf{y}_{i}\) of \(\mathbf{\tilde{S}}\) (\(\mathbf{\tilde{S}}\mathbf{y}_{i}=\lambda\mathbf{y}_{i}\)) and the left singular vector of \(\mathbf{X}\), the dynamic mode \(\phi_{i}\) can be obtained using Equation (4):
\[\phi_{i}=\mathbf{U}\mathbf{y}_{i} \tag{4}\]
The dynamic mode obtained using Equation (4) is called the projected DMD mode ([PERSON] et al., 2014). Using \(\phi_{i}\) and the corresponding eigenvalue \(\lambda_{i}\), the temporal evolution of the flow can be analyzed by separating multiple spatial patterns.
Next, we describe reconstructing the actual flow field using the decomposed dynamic mode. Since the dynamic mode is obtained through the eigenvalue decomposition of a linear system \(\mathbf{A}\) between two snapshots with a time difference of \(\Delta t\), the field at time \(t\) after the initial value \(x_{1}\) can be reconstructed using \(p\) modes as follows:
\[x_{i}=\mathbf{A}x_{i-1}=\sum_{k=1}^{p}\lambda^{\hat{k}}x_{1}\phi_{k}, \tag{5}\]where \(\operatorname{diag}(\Lambda)=\lambda_{k}\). From Equation (5), we can distinguish the flow characteristics using the eigenvalue \(\lambda_{l}(\in C)\). The corresponding mode is a temporally amplifying mode if \(|\lambda_{l}|>1\), it is a decaying mode with time if \(|\lambda_{l}|<1\), and experiences neither amplification nor decay if \(|\lambda_{l}|\sim 1\).
This study used the last \(81\,\min\) of the 3-h numerical simulation, from \(100\) to \(180\,\min\) results. Matrixes \(\boldsymbol{X}\) and \(\boldsymbol{Y}\) were constructed by combining \(80\,\min\) of three-dimensional output data sampled every minute, and the interval between them was \(1\,\min\) (Figure 2).
## 3 Results and discussion
### Overview of the flow field
This section describes the flow field reproduced using the LES model. Figure 3 shows the horizontal cross-sections of the horizontal and vertical winds in the lower layer (\(z=125\,\min\)). The convergence toward the urban area is observed in the horizontal wind snapshot, a typical characteristic of UHIC. The time-averaged flow field shows similar characteristics. However, in Figure 2(a),c, the flow
Figure 3: The cross-sections of flow fields at \(z=125\,\min\): (a) the horizontal cross-section of instantaneous horizontal wind at \(180\,\min\), (b) the horizontal cross-section of instantaneous vertical wind at \(180\,\min\), (c) the horizontal cross-section of time-averaged horizontal wind in the last \(10\,\min\), (d) the horizontal cross-section of time-averaged vertical wind in the last \(10\,\min\), (e) the vertical cross-section of time-averaged horizontal wind in the last \(10\,\min\), and (f) the vertical cross-section of time-averaged vertical wind in the last \(10\,\min\). \(x,y\), and \(z\) axes indicate east–west, north–south, and vertical axes, respectively.
is not homogeneous in the north-south direction, but there are smaller-scale turbulences (thermals) throughout the region. A striated structure in the east-west direction can be observed in the time-averaged cross-section. We can observe the organized mesh pattern due to thermals near the domain's east and west edges in the vertical wind snapshot (Figure 2(b),d). A striated structure can be seen in the domain's inner region, similar to that of the time-averaged horizontal wind component. Above the urban area is a strong line-shaped upwelling, a well-known feature of UHIC. The multiple snapshots (figure omitted) show that the thermals are advected due to UHIC convergence. This phenomenon is consistent with the point claimed by previous studies, such as [PERSON] et al. (2013).
### Separation using DMD
Figure 4 shows the scores obtained using DMD for the horizontal wind snapshots. The scores plotted in Figure 4 provide information about the temporal change of corresponding spatial patterns. Here, the scores \(\mu_{i}\) are mapped using the following relationship (according to [PERSON], 2010), \(\mu_{i}\!=\!\frac{\log[\mu_{i}]}{\Delta t}\). Additionally, the frequency \(f_{i}\) was obtained using \(f_{i}\!=\!\frac{\operatorname{Im}[\log[\mu_{i}]]}{\Delta t}\). We used \(\Delta t\!=\!1\) min, as mentioned in Section 2. From Figure 4, all modes except mode 1 have \(\operatorname{Re}[\mu_{i}]\!<\!0\), indicating decaying modes. Here, \(\operatorname{Re}[a]\) and \(\operatorname{Im}[a]\) indicate the real part and imaginary part of complex \(a\), respectively. Mode 1 shows \(f_{1}\!=\!0\) and \(\operatorname{Re}[\mu_{1}]\!\sim\!0\). Therefore, mode 1 does not amplify, decay, or oscillate (i.e., its temporal change is small). Considering the flow field characteristics, it is likely that a pattern with a small temporal variation corresponds to UHIC, and the other decaying modes correspond to turbulent modes, such as thermals. In this study, the term decaying indicates that the spatial pattern changes into a different one (disappearing). This study focuses on four modes (modes 1, 4, 6, 16) to discuss the behavior of UHIC and thermals (red plots in Figure 4). The reasons why we chose these four modes are as follows: mode 1 is the only one mode which shows no decay and oscillation. Mode 4 has low frequency and clear decaying compared to the neighboring modes. Mode 6 has low frequency similar to mode 4, but it is not significantly decaying. Mode 16 shows the frequency which is similar to that of the
lifetime of thermals (\(\sim\)10 min), and not significantly decaying compared to the other modes that have similar frequencies.
Figure 5 shows the horizontal cross-sections of the dynamic modes to discuss the features of each. This study only shows the real part of the dynamic modes. Mode 1, which had a small temporal variation, showed convergent flow toward the center of the urban area. These characteristics are similar to those of UHIC. Therefore, we conclude that mode 1 is the UHIC mode extracted from DMD. The spatial structure of mode 1 resembled that of the time-averaged structure (Figure 3c). In this mode, the east-west striation was observed. Mode 4 is a decaying mode, with high wind speed areas near the domain's east and west edges. In the vertical cross-section, a sign-reversed component is observed at the outer edge of the UHIC. Since this mode has a low frequency (\(f_{4}=0.01\) min\({}^{-1}\)), it represents the expansion of the UHIC. The spatial pattern of mode 1 becomes clearer (i.e., the convergence region expands) because this mode decays with time. Mode 6 has a lower frequency than that of a typical thermal (\(f_{6}=0.038\) min\({}^{-1}\)). In this mode, we can observe the striated structures similar to those in converged winds in mode 1. This result can be regarded as thermals deformed by UHIC or UHIC deformed by thermals. The presence of spatial patterns, such as mode 6 suggests that both UHIC and thermals coexist while deforming the structure of each other. The deformation in this study means that the spatial structure of thermals changed from a random cells-like structure to a roll vortex-like structure.
Figure 5: The spatial patterns of dynamic modes of horizontal (westerly) wind at \(z=125\) m: Top–left: Mode 1, bottom left: Mode 6, top right: Mode 4, and bottom right: Mode 16; the large panels show horizontal cross-sections, and the small panels below the horizontal cross-sections show the vertical cross-sections. \(x,y\), and \(z\) axes indicate east–west, north–south, and vertical axes, respectively.
(striated) structure (referring to, for example, [PERSON] & [PERSON], 1989). Additionally, since the frequency of deformed thermals is smaller than that of the standard (undeformed) thermals, it is possible that some modulation (change in frequency) has been occurred. The spatial pattern of mode 16 (\(f_{16}=0.11\) min\({}^{-1}\)) shows finer structures than those of mode 6. It should be mentioned that the result at the altitude of \(z=37.5\) m shows no significant differences compared to that of \(z=125\) m (the figure is shown in the supplement, Figures S1 and S2). However, there are small differences in some modes. In horizontal wind modes, the cell patterns near the east and west edges of the domain are more pronounced compared to the result of \(z=125\) m in mode 4 and mode 6. In vertical wind modes, the strength of the upwelling existing over the center of the urban area became weaker. These differences are possibly caused by the difference of spatio-temporal difference of turbulences. Generally, the spatial scale of turbulence becomes small near the (ground) surface.
Figures 6 and 7 show the DMD scores for vertical wind and the horizontal cross-sections of the four modes plotted in red in Figure 6, respectively. Here, the four red points indicate the modes focused on in this study, the same as in Figure 4. Mode 1 is not oscillating and is decaying. The spatial pattern characteristics are similar to those of UHIC, and a clear line-shaped upwelling component can be observed above the urban area. Additionally, several upwelling branches are observed orthogonally to the line-shaped upwelling above the urban area. Therefore, mode 1 partly includes structures created by thermals. In other words, it can be said that the thermals merged above the urban area and formed a line-shaped upwelling. This result supports the previous finding by [PERSON] et al. (2013). Modes 10 and 14 are oscillation modes at frequencies lower than that of a typical thermal, similar to mode 6 in the horizontal wind component. Mode 14 is one of the most clearly decaying modes among the modes with similar frequencies. The characteristics of these modes are similar to those of the striated structure of UHIC modes. The reason why the decaying pattern cannot be observed clearly in east-west edge is that the thermals exist in this area are not affected (deformed) by UHIC. Thus, the characteristics such as frequency are different from that of thermals that exists near the urban area. Mode 18 has a frequency close to the lifetime of thermals (\(\sim\)0.1 min\({}^{-1}\)). Perturbations with fine spatial structures are extracted in this mode.
The results above show that the striated structure observed in the UHIC mode is deformation caused by thermals. In that case, what do the low-frequency decaying modes represent? The spatiotemporal cross-sectionpresented by [PERSON] et al. (2013) shows a line-shaped upwelling for a long period (several hours), during which it merges and forms a strong upwelling above the urban area. In other words, thermals became line-shaped upwelling and existed for a specific period. Therefore, these deformed thermals can be observed in low-frequency decaying and UHIC modes. Therefore, the low-frequency decaying modes represent the thermals that UHIC deformed.
## 4 Summary
This study applied a modal decomposition technique called DMD to a flow field where UHIC and thermals existed. DMD focuses on the temporal change in flow fields by decomposing the field based on a linear system. This study investigated how UHIC and thermals coexist based on temporal flow changes. The UHIC was extracted as a time-invariant mode that converges toward the city in the lower levels, similar to features generally described in the literature. The unique feature is that this mode exhibited a striated structure. This feature has not been described well in previous studies. All other modes were oscillating and decaying. We also extracted some modes with frequencies lower than the typical lifetime of thermals (approximately 0.1 min\({}^{-1}\)). One mode with a frequency of 0.02-0.05 min\({}^{-1}\) exhibited striated structures similar to those observed in the UHIC mode. Considering the previous findings that thermals showed stripe-like
Figure 7: The spatial patterns of the dynamic modes of vertical wind at \(z=125\) m; Top–left: Mode 1, bottom left: Mode 14, top right: Mode 10, and bottom right: Mode 18; the large panels show horizontal cross-sections and the small panels below the horizontal cross-sections show the vertical cross-sections.
structures when UHIC presents, these low-frequency modes can be considered thermals that form striated structures in the UHIC mode. Therefore, the low-frequency modes (indicating thermals) form the striated structures observed in the UHIC mode, whereas the thermals changed their shape into a stripe-like structure due to UHIC. Furthermore, the modes with frequencies similar to the thermal lifetime (approximately 0.1 min\({}^{-1}\)) show fine structures.
We also applied DMD to the vertical wind. All modes were time-decaying. The mode with the lowest decaying rate did not oscillate, where a line-shaped upwelling was observed above the city. Some upwelling branches orthogonal to this line-shaped upwelling were also observed in this mode. These results indicate that the advected thermals merge and form a line-shaped upwelling, a feature of UHIC. Focusing on the modes with similar frequency to those in the horizontal wind case, we also observed deformed thermals and finer structures in the horizontal wind cases. UHIC and thermals coexist and change their shapes through low-frequency modes. The modes with frequencies of approximately 0.02-0.05 min\({}^{-1}\) typically indicate this deformation. This study reinforces the existing perspectives by discussing the spatial patterns of the flow field and the corresponding frequency obtained using DMD. The difference of horizontal and vertical wind modes can be seen in, for example, mode 1 of each direction. Both modes indicated the UHIC characteristics, but not decaying in horizontal, but weakly decaying in vertical wind. Also, the high-frequency modes in horizontal wind tend to decay more than that of vertical wind. The present study shows that two thermally driven circulations, UHIC and thermals, possibly interact. This perspective will be important for more realistic flow simulations using the multi-scale modeling technique, which has attracted in recent years. When coupling the numerical models that reproduce phenomena at different spatio-temporal scales (i.e., coupling RANS and LES models), considering the interactions pointed out in the present study can help improve the simulation accuracy.
We listed the remaining issues of this study. One is the quantification of the interaction of UHIC and thermals using spectral analysis and metrics such as amplitude modulation correlation coefficient. Using such metric, we can discuss whether this interaction is symmetric from the perspective of information transfer. It should be noted that the DMD assumes the temporal change of field as a linear system. The influence of nonlinear process on the analysis should be discussed in the future study.
## Author Contributions
**[PERSON]:** Conceptualization; methodology; formal analysis; visualization; writing - original draft; writing - review and editing. **[PERSON]:** Writing - review and editing; formal analysis; methodology. **[PERSON]:** Supervision; writing - review and editing; funding acquisition.
## Acknowledgements
This work was supported by MEXT Promotion of Development of a Joint Usage/Research System Project: Coalition of Universities for Research Excellence Program (CURE) Grant Number JPMXP1323015474, JSPS KAKENHI Grant Numbers JP21K03656, JP22H03653, and 23H04483.
## Conflict of Interest Statement
The authors declare no conflicts of interest.
## Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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## Supporting Information
Additional supporting information can be found online in the Supporting Information section at the end of this article.
**How to cite this article:** [PERSON] et al. (2024) [PERSON] (2024). Separating urban heat island circulation and convective cells through dynamic mode decomposition. _Atmospheric Science Letters_, 25(12), e1279. _[[https://doi.org/10.1002/asl.1279_](https://doi.org/10.1002/asl.1279_)]([https://doi.org/10.1002/asl.1279_](https://doi.org/10.1002/asl.1279_)) | wiley | Separating urban heat island circulation and convective cells through dynamic mode decomposition | Takuto Sato, Hideitsu Hino, Hiroyuki Kusaka | https://doi.org/10.1002/asl.1279 | 2,024 | CC-BY |
wiley/fb284435_868c_45d6_a39e_3a6c29e8c54f.md | et al., 2008; [PERSON], 1965, 1967; [PERSON] et al., 2001; [PERSON] et al., 2017). Previous studies have explored the relationship among pollen source, dispersal and its driving forces in the vertical zones of different mountains in the world, but little research has been done in biodiversity hotspots. In particular, the lack of atmospheric reanalysis data prevents us from understanding the pollen dispersal mechanisms in mountainous areas.
The Hengduan Mountains are located on the southeastern edge of the Tibetan Plateau. They are one of the global biodiversity hotspots ([PERSON], 2016), and the region has the highest richness of vascular plant and endemic species in the Pan-Tibetan Highlands (comprising Tibetan Plateau, Himalaya, Hengduan Mountains and Mountains of Central Asia) ([PERSON] et al., 2022). In this region, few studies have dealt with the driving forces behind pollen dispersal, so many questions remain ([PERSON] et al., 2013; [PERSON] et al., 2009, 2011; [PERSON] et al., 2017). By analyzing a series of surface soil samples at different altitudes in the Hengduan Mountains (Figure 1), this study elucidates the pollen dispersal mechanisms in combination with atmospheric reanalysis data. The paper provides a background for the reconstruction of past vegetation, plant diversity, and climate change in the Hengduan Mountains and similar montane ecosystems around the world.
## 2 Materials and Methods
### Study Site
Jade Dragon Snow Mountain (27\({}^{\circ}\)10\({}^{\prime}\)-27\({}^{\circ}\)40\({}^{\prime}\)N, 100\({}^{\circ}\)10\({}^{\circ}\)-100\({}^{\circ}\)20\({}^{\prime}\)E) is located in Lijiang, Yunnan Province, Southwest China. It is the core area of the Hengduan Mountains orientated northeast-to-southwest, and is bounded by the Jinsha River in the west and Lijiang Basin in the south. The main peak, Shanzidou, reaches 5,596 m above sea level. The local vegetation displays an obvious vertical zonation. From 2,400 to 3,100 m, the vegetation is dominated by warm temperate coniferous forest (mainly _Pinus yumamenis_ Francis).) with a dry and warm habitat. The summer cloud line is about 3,100 m. Between 3,100 and 3,900 m, subalpine cold temperate coniferous forest (mainly _Abies foresiti_ Coltm.-Rog., _Abies georgei_ Orr, _Picea likiangensis_ (Franch.) [PERSON], and _Larix potantii_ var. _macrocarpa_ [PERSON]. [PERSON] ex [PERSON], [PERSON] and [PERSON]) exists with colder and wetter weather. About 3,900 m is the tree line. From 3,900 to 4,900 m, the vegetation consists of alpine shrubs and herbs (mainly _Rhododendon_, _Carex_). Around 4,900 m is the snow line, and above this is the permafrost snow belt (WGYV, 1987; [PERSON], 2022). The study site is influenced by a subtropical monsoon climate, with warm and humid summers and cool and dry winters. In summer, the weather is controlled by strong prevailing south-westerlies of the Indian summer monsoon, with more than 70% of the annual precipitation falling from May to September. In winter, it is mainly affected by the southern branch of the westerlies and the Asian winter monsoon (AWM), resulting in less precipitation ([PERSON] et al., 2006).
Figure 1: Location of the study site. (a) The red triangle shows the study site. The yellow (eastern slope of the Jade Dragon Snow Mountain) and green (Lugu Lake) circles represent the previous researches in the Hengduan Mountains ([PERSON] et al., 2013; [PERSON] et al., 2009). The lines with arrows indicate monsoons and atmospheric circulation systems around the study area, including Asian winter monsoon (AWM), East Asian summer monsoon (ESM), Indian summer monsoon (ISM) and Westerlies. (b) The topographic map of the sampling sites, located in Haligu (HLG), Wenhai (WH) and Yushuizhai (YSZ) on the southern slope of the Jade Dragon Snow Mountain. Maps were downloaded from ArcGIS Online Basemaps (www.arcgis.com). Boundary of the Hengduan Mountains is based on [PERSON] et al. (2022).
### Sampling and Pollen Analysis
In July 2022, 37 surface soil samples were collected from different elevations on the southern slope of the Jade Dragon Snow Mountain (Table S1 in Supporting Information S1). For pollen analysis, five g of each sample were weighed, boiled with distilled water, sieved and centrifuged before heavy liquid flotation ([PERSON] & [PERSON], 1999; [PERSON] et al., 1991). Pollen samples were fixed in glycerine jelly after electrolysis, using a mixture of acetic anhydride and concentrated sulfuric acid (9:1) ([PERSON], 1960). Pollen grains and spores were observed under a Leica DM 4000 light microscope and a Hitachi S-4800 Field Emission Scanning Electron Microscope at the Institute of Botany, Chinese Academy of Sciences, Beijing. Identification was performed by comparison with modern pollen slides and monographs (IB-CAS, 1976; IBSCIB-CAS, 1982; [PERSON] et al., 2016; [PERSON] et al., 1995). At least 500 pollen grains and spores were counted in each sample (terrestrial plant pollen more than 300 grains). The pollen relative abundance (RA) of a taxon was calculated by the equation: RA = (\(u/N\)) \(\times\) 100%, where \(n\) is the pollen number of a particular taxon and N represents the total pollen number of all taxa combined in the pool of samples. Tilia 1.7.16 was employed to create a pollen RA diagram and constrained cluster analysis (CONISS) was used to distinguish the pollen zones (PZ).
### Ordination Analysis
The ordination technique can be utilized to explore the relationships between pollen assemblages and climate-environmental factors. In this study, 15 terrestrial pollen taxa with a RA greater than 2% in at least one sample were selected for analysis. Historical climate data from 1970 to 2000 were downloaded from www.worldclim.org. Using ArcGIS Pro 3.0, three climate factors-annual mean temperature (Tem), annual precipitation (Pre), and annual mean wind speed (Win)-were extracted based on the latitude and longitude of the sampling sites. Additionally, the elevation of each site was included in the analysis. Ordination analysis was performed in R (version 4.4.1) with vegan package 2.6-8 ([PERSON] et al., 2024). To determine whether to use a unimodal or linear method in this study, we first conducted a detrended correspondence analysis. The results indicated that the gradient lengths of the first four axes are all less than 3, suggesting that the linear method would be appropriate for handling these data ([PERSON], 2003). Consequently, redundancy analysis (RDA) was selected for the analysis, and the data were standardized prior to performing the ordination.
### Global Atmospheric Reanalysis Data
To demonstrate atmospheric conditions, we used the Japanese 55-Year Reanalysis (JRA-55) that provides the assimilated atmospheric data at 6-hourly intervals at a spatial resolution of 1.25 deg longitude/latitude ([PERSON] et al., 2015). JRA-55 has been shown to capture well the low-level winds and their diurnal cycles over the Tibetan Plateau and surrounding areas ([PERSON], 2020).
## 3 Results
### Corresponding Relationship Between Pollen Assemblages and Modern Vegetation
A total of 19,679 spores and pollen grains were identified and were assigned to 51 taxa (including 7 families of lycophytes and pteridophytes, 3 genera of gymnosperms, 27 families and 14 genera of angiosperms), showing a high degree of taxonomic diversity (Table S2 and Figures S1-S6 in Supporting Information S1). Based on the CONISS of the RA of all taxa, the pollen diagram was divided into five distinct PZ (Figure S7 in Supporting Information S1). The features of each zone are described as follows:
PZ I (2.673 m) is characterized by the highest RA of _Pinus_ (mean RA: \(\sim\)89.9%). PZ II (3,060 m) is dominated by _Pinus_ (65.3%), followed by increasing herbs (12.2%) and ferns (10.3%). PZ III (3,200-3,400 m) shows a high frequency of _Pinus_ (86.3%) and an increase in _Quercus_ (6.1%). PZ IV (3,400-3,600 m) displays a significant increase in _Quercus_ (47.5%) and Ericaceae (6.4%), accompanied by a decrease in _Pinus_ (33.4%). Compared with PZ IV, PZ V (3,600-3,900 m) shows an increase in herbs (PZ IV: 3.3%, PZ V: 13.1%) and a decrease in trees and shrubs (PZ IV: 95.2%, PZ V: 84.7%). The dominant pollen taxa in PZ V are _Pinus_ (53.4%), _Quercus_ (13.2%), Ericaceae (5.8%), Polygonaceae (5.1%) and Ranunculaceae (3.6%). According to the dominant taxa of all PZ and modern vegetation (Figure 2), the pollen assemblages of PZ I and PZ II reflect the pine forest dominated by _Pinus_, which corresponds to the modern vegetation of pine forest (mainly _Pinus_ _yunnanenensis_). The pollen assemblages of PZ III and PZ IV indicate a needle and broad-leaved mixed forest (mainly _Pinus_, _Quercus_ and Ericaceae),which is consistent with the modern vegetation of coniferous and sclerophyllous oak mixed forest. The pollen assemblage of PZ V implies a coniferous and broad-leaved mixed forest with abundant herbs (mainly _Pinus_, _Abies_, _Quercus_, Ericaceae, Polygonaceae and Ranunculaceae), which is in sharp contrast to the modern vegetation of subalpine scrub and meadow.
The pollen grains from surface soil samples are divided into the two major pollination syndromes of seed plants (anemophilous and entomophilous) (Table S2 and Figure S7 in Supporting Information S1). The mean RA of anemophilous pollen is as high as 88.2% (of the total pollen number), mainly consisting of _Abies_, _Pinus_, _Tsuga_, _Almus_, _Betula_, _Quercus_, _Artemisia_, Chenopodaceae and Cyperaceae. On the contrary, the mean RA of entomophilous pollen is low (8.5%), consisting of Ericaceae, Rosaceae, Asteraceae, Polygonaceae and Ranunculaceae. In the warm temperate coniferous forest and needle and broad-leaved mixed forest, dominant taxa are primarily anemophilous trees (such as _Pinus yumanensis_ and evergreen sclerophyllous oaks) with pollen productivity, whereas the entomophilous shrubs and herbs (such as Ericaceae and Ranunculaceae) have low pollen productivity. Thus the RA of anemophilous arboreal pollen far exceeds that of entomophilous pollen from the surface soil in the two vegetation types. In the subalpine scrub and meadow, the number and abundance of entomophilous pollen significantly increase (such as Ericaceae, Asteraceae, Polygonaceae and Ranunculaceae), with the highest representation among the three vegetation types. However, the anemophilous pollen such as _Pinus_ (53.4%) and _Almus_ (3.5%) are also found in the samples of subalpine scrub and meadow, showing that these pollen grains are exotic.
### Relationship Between Pollen Assemblages and Climate-Environmental Factors
The RDA results show that the cumulative proportion explained by the first and second axes accounts for 26.7% of the pollen assemblages variables (with 16.2% and 10.5%, respectively) (Figure S8 in Supporting Information S1). In terms of the relationships between pollen taxa and climate-environmental factors (Figure S8a in
Figure 2: Schematic diagram showing the corresponding relationship between pollen assemblages and modern vegetation. (a) The mean relative abundance of palymoorphs in each zone and the schematic diagram of vertical vegetation zones in this study. (b)-(f) Photos of modern vegetation landscapes (provided by [PERSON]).
Supporting Information S1), _Pinus_ shows a positive correlation with annual mean temperature, while Polygonaceae and Fabaceae have a positive correlation with annual precipitation. Additionally, Polygonaceae, _Alnus_, _Betula_, _Quercus_, Rosaceae and Ranunculaceae are positively correlated with annual mean wind speed and elevation. According to the ordination of sampling sites along with climate-environmental factors (Figure S8b in Supporting Information S1), PZ I, PZ II, and PZ III, which are situated at lower elevations (below 3,400 m), have higher annual mean temperatures. In contrast, PZ IV and PZ V, located at higher altitudes (above 3,400 m), experience greater annual mean wind speed. Furthermore, PZ II and PZ V receive more annual precipitation.
### Seasonal Change and Diurnal Variations of Low-Level Winds
In order to explore the driving mechanisms of pollen dispersal in different vertical vegetation zones, we used JRA-55 to show the 20 years seasonal change of the average 850 hPa streamlines over the Tibetan Plateau and surrounding areas (Figure 3). The study site is primarily influenced by the southern branch of the westrelies in winter (DJF: December, January, February) and spring (MAM: March, April, May), the southwesterly monsoon from the Indian Ocean in summer (JIA: June, July, August), and the East AWM in autumn (SON: September, October, November) (Figures 3a-3d). On a local scale, the wind field over the Jade Dragon Snow Mountain remains uniform with prevailing sounder winds throughout the whole year (Figures 3e-3h). Figure 4 shows the apparent diurnal variation of the wind field over the Jade Dragon Snow Mountain, that is, the deviation after removing the daily average. The diurnal deviation of local flow field in the vertical section of the Jade Dragon Snow Mountain in the direction of east to west (100 degE) and south to north (27 degN) is characterized by the thermally-driven mountain-valley circulation. From no evening (06 UTC, 12 UTC), the upslope flow along the slopes is evident (Figures 4a, 4b, 4e, and 4f). There is significant downslope flow from the night until the next morning (18 UTC, 00 UTC) (Figures 4c, 4d, 4g, and 4h).
## 4 Discussion
Pollen analysis of surface soil samples from three vegetation zones in the region shows that the dominant taxa in the pollen assemblages of warm temperate coniferous forest and needle- and broad-leaved mixed forest are consistent with those of the modern vegetation. However, due to the influence of exotic pollen grains (e.g., _Pinus_, _Alnus_, _Tsuga_ and _Juglans_), the pollen assemblage of subalpine scrub and meadow does not faithfully reflect the composition and dominant taxa of the actual vegetation. Four exotic pollen types were found in the samples of this vegetation zone (above 3,600 m), including _Pinus_ (mean RA 53.4%), _Alnus_ (3.5%), _Tsuga_ (1.1%), and _Juglans_ (0.5%). Their parent plants are anemophilous, and their upper limits of distribution in southwestern China are 3,500, 3,600, 3,500 and 3,300 m, respectively ([PERSON] et al., 1999; [PERSON] et al., 2007). Therefore, these pollen types were transported to the sampling sites by anaidic winds. Such phenomena have also been reported by previous studies. For example, a large amount of _Pinus_ pollen (82.1%-91.7%) was though in moss samples from subalpine rhododendron scrub (3,900-4,100 m) on the eastern slope of the Jade Dragon Snow Mountain ([PERSON] et al., 2009). Abundant coniferous pollen (_Pinus_ 43%, _Picea_ 16% and _Abies_ 2%) were also found in the surface sediment samples of lakes and wetlands above the tree line (3,500 m) in the mountainous region of Colorado, USA (Fall, 1992a). Plenty anemophilous pollen (such as _Dacrylium cupressinum_ Sol. ex G.Forst. and _Nothofagus_) from low altitudes was preserved in the surface moss samples of subalpine and alpine regions in the South Island of New Zealand, while the modern vegetation is dominated by entomophilous herbs (such as _Celmisia_, _Olearia coenssoi_ Hook.f. and _Dracophylllam longifolium_ ([PERSON] and G.Forst.) [PERSON] and [PERSON].) ([PERSON], 1970). In addition, a few studies on pollen downslope transport have been reported, which means pollen appeared at elevations below the distribution of their parent plants ([PERSON], 1992b; [PERSON] et al., 2013; [PERSON] et al., 2009). For instance, _Betula_ pollen (mean RA 0.2%-1.5%) were found in lake bottom sediments, bark and surface soil samples from 2,684 to 2,755 m at Lugu Lake, Southwest China, while the parent plants grow at an altitude of 2,800-3,400 m in the lake region ([PERSON] & [PERSON], 1989; [PERSON] et al., 2013).
The RDA plots show three major types of exotic pollen taxa: _Pinus_, _Alnus_, _Tsuqa_ (_Juglans_ was excluded from the RDA analysis due to its RA being less than 2% across all samples). _Pinus_ is primarily found in lower elevation sites (PZ I, PZ II and PZ III) and exhibits a positive correlation with annual mean temperature, which is consistent with the distribution of its parent plants. _Alnus_ and _Tsuga_ are mainly observed in higher elevation sites (PZ IV and PZ V), with relatively high RA in PZ V. However, their parent plants do not exist in this vegetation zone. The ordination analysis suggests that these two pollen types may be positively correlated with wind speed. Previous studies have shown that wind and precipitation probably are the primary factors influencing pollen dispersal Figure 3: (a)–(d) The 20 years average 850 hPa flow chart around the Tibetan Plateau in general and (e)–(h) the Jade Dragon Snow Mountain in particular, representing monsoon circulation systems on a large scale.
Figure 4: (a)–(d) The diurnal deviations of the flow field in a vertical section around the Jade Dragon Snow Mountain in an east-west direction (100\({}^{o}\)E) and (g)–(h) south-north direction (22\({}^{o}\)N), representing the local mountain-valley circulation. The red shows the upward movement, while the blue represents the downward movement.
([PERSON] et al., 2013; [PERSON], 1980; [PERSON], 1990; [PERSON] et al., 2008; [PERSON], 1965, 1967; [PERSON] et al., 2001; [PERSON] et al., 2011; [PERSON] et al., 2017). For example, a study of modern pollen deposition suggests that strong westerlies and heavy rainfall resulted in a large amount of exotic Podocarpaceae pollen being deposited above the tree line in the Main Divide area of the South Island in New Zealand ([PERSON], 1990). Another study of modern pollen from surface lake sediments revealed that arboreal pollen (such as _Pinus_, _Picea_, _Abies_, _Betula_ and _Juglans_) from lower elevations were carried to subalpine and alpine lakes by upslope transport in Southwest China ([PERSON] et al., 2011). A large number of _Picea_ pollen were found in surface soil samples of subalpine scrb and meadow in the eastern Tibetan Plateau, and the data of local topography, wind speed and wind direction showed that the strong northwest upslope wind probably carried these pollen to the region ([PERSON] et al., 2017).
Influenced by biological characteristics of plants, weather, wind speed, turbulence and other factors, the diurnal variation of pollen concentration of different plants present individual idiosyncrasies in the air ([PERSON] et al., 2001). However, the diurnal variation pattern of the total pollen concentration is higher during the daytime and lower at night ([PERSON] & [PERSON], 2009). Research suggests that air pollen concentration is significantly correlated with temperature and relative humidity ([PERSON] et al., 2016; [PERSON] et al., 2010). The increasing temperature and decreasing relative humidity during the daytime are conducive to anther dehiscence and pollen dispersal, while low temperature and high humidity at night promote pollen deposition on the soil ([PERSON] et al., 2008). The atmospheric reanalysis data of our research indicates that southerly winds prevail throughout the year in the study area, accompanied by significant diurnal wind variations of mountain-valley circulation (Figures 3 and 4). In addition, March to June is the flowering season of anemophilous trees. Therefore, arboreal pollen grains are easily carried to the high altitude vegetation zone (such as scrub and meadow) by southerly winds and daytime upslope flow (Figure S9a in Supporting Information S1). Only a few pollen grains are transported to an altitude below their parent plants by nighttime katabatic winds (Figure S9b in Supporting Information S1), because by then most of the pollen had settled out of the atmosphere. Moreover, the canopy and trunks of trees growing at lower altitudes have a strong filtering effect ([PERSON], 1967), which limits the dispersal of pollen in the forest and excludes the exotic pollen. In this case, the dominant taxa of the pollen assemblages reflect the actual composition of the vegetation (e.g., _Pinus_), with only a few pollen being transported to a lower altitude by the wind and run-off. On the other hand, the subalpine scrub and meadow at higher altitudes is relatively open, mainly composed of entomophilous plants (such as Ericaceae, Ranunculaceae and Polygonaceae) with low pollen productivity. These pollen with low representation in the surface soil are deposited almost in situ. Thus the pollen assemblage is more susceptible to the influence of the anemophilous tree pollen transported from lower altitudes (e.g., _Pinus_, _Alnus_, and _Tsuga_).
Based on the investigation of the modern depositional process of surface soil pollen in different vertical vegetation zones in the Hengduan Mountains, the following three suggestions are proposed for the investigation of similar montane ecosystems around the world: (a) Consider the pollen source when interpreting pollen assemblages in high altitude areas, especially the possibility of anemophilous pollen being transported from lower to higher elevations. (b) The composition of the local vegetation should be investigated in detail, including the pollination syndrome of the dominant taxa. The interpretation of pollen assemblages should be based on the local vegetation. (c) In the reconstruction of past vegetation, plant diversity and climate change in montane ecosystems, pollen upslope and downslope movement probably also existed, which could complicate the reconstruction of the vegetation physiology at that time. Although the modern investigation of pollen deposition processes is unable to completely clarify the vegetation in the past, it could provide guidelines for paleecological research and provide data for the quantitative reconstruction of the paleoclimate.
## 5 Conclusions
By undertaking pollen analysis of surface soil samples in the vertical vegetation zones of the Hengduan Mountains, southwestern China, we investigated the corresponding relationship between pollen assemblages of surface soil samples and modern vegetation at different altitudes. The results show that pollen assemblages in the temperate coniferous forest and coniferous and sclerophyllous oak mixed forest correspond well with the dominant taxa in the modern vegetation. The former is dominated by _Pinus_ pollen, while the latter is dominated by _Pinus_, _Quercus_ and Ericaceae pollen. However, the pollen assemblage in subalpine scrub and meadows is dominated by _Pinus_, _Quercus_, Ericaceae and _Abies_ pollen, which demonstrates that the assemblage is inconsistent with the local vegetation. The atmospheric reanalysis data suggest that southerly wind prevails in this area with obvious diurnal wind variations associated with mountain-valley circulation. Strong upslope flow in daytime carries plenty of anemophilous arboreal pollen (such as _Pinus_ and _Alnus_) from low altitudes to the subalpine scrub and meadows, overriding the number and abundance of entomophilous pollen in the surface soil samples. This phenomenon could complicate the reconstruction of past vegetation, plant diversity and climate change. Our research provides new insight into the study of modern pollen depositional processes, and reveals the driving mechanisms of pollen dispersal in the Hengduan Mountains.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
The atmospheric data at 6-hourly intervals are provided by the Japanese 55-Year Reanalysis (JRA-55) ([PERSON] et al., 2015) and are available for download at [[https://search.diasip.net/en/dataset/JRA55](https://search.diasip.net/en/dataset/JRA55)]([https://search.diasip.net/en/dataset/JRA55](https://search.diasip.net/en/dataset/JRA55)). The datasets of sampling information, pollen relative abundance and major palynomorph pictures involved in this study are available at Zenodo ([PERSON] & [PERSON], 2024).
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wiley/fb17fe56_0846_4514_b49f_5fe298d6783e.md | # Geochemistry, Geophysics, Geosystems
Forentation Waters Delineate Diverse Hydrogeologic Conditions at a Plate Scale: Eastern Flank of the Juan de Fuca Ridge
[PERSON]
[PERSON]
C College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Moss Landing, CA, USA, \"Department of Oceanography, University of Hawaii, Honolulu, HI, USA, \"Earth and Planetary Sciences, University of California, Santa Cruz, Santa Cruz, CA, USA, \"Moss Landing Marine Laboratory, Moss Landing, CA, USA
[PERSON]
C College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Moss Landing, CA, USA, \"Department of Oceanography, University of Hawaii, Honolulu, HI, USA, \"Earth and Planetary Sciences, University of California, Santa Cruz, Santa Cruz, CA, USA, \"Moss Landing Marine Laboratory, Moss Landing, CA, USA
[PERSON]
C College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Moss Landing, CA, USA, \"Department of Oceanography, University of Hawaii, Honolulu, HI, USA, \"Earth and Planetary Sciences, University of California, Santa Cruz, Santa Cruz, CA, USA, \"Moss Landing Marine Laboratory, Moss Landing, CA, USA
[PERSON] College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Moss Landing, CA, USA, \"Department of Oceanography, University of Hawaii, Honolulu, HI, USA, \"Earth and Planetary Sciences, University of California, Santa Cruz, Santa Cruz, CA, USA, \"Moss Landing Marine Laboratory, Moss Landing, CA, USA
###### Abstract
The chemical composition of formation waters within the upper basaltic crust were calculated or measured at 24 sites on the northwest portion of the Juan de Fuca (JDF) Plate using data from sediment pore waters, scientific boreholes, and seafloor springs. Formation waters differ in composition across this ridge-flank region because of variations in water-rock reactions and residence times, exchange rates with overlying sediment pore waters, and microbial processes along flow paths. We interpret spatial variations in the solute composition of formation waters to resolve areas that are geochemically distinct or similar, lateral trends that result from water transport, areas where water-rock reactions in the deeper crust are apparent, and sites of seawater recharge and formation water discharge. We provide evidence for large-scale lateral flow associated with two (mostly) buried basement ridges on \(\sim\)1.4 and \(\sim\)3.5 Ma seafloor, which are subparallel to the JDF spreading axis to the west. Between these two ridges, where the seafloor and the sediment-basement interface are relatively flat, formation waters have undergone extensive exchange with overlying sediment pore waters, consistent with a long residence time. Basalic outcrops provide sites of seawater recharge and hydrothermal discharge, sometimes through the same feature, highlighting the heterogeneous nature of hydrogeologic conditions and processes. This work provides a blueprint for future plate-scale studies to assess, for example, geologic controls of crustal age, spreading rate, and sedimentation on subsurface hydrologic patterns.
16 AUG 2022
Accepted 1 NOV 2022
## 1 Introduction
Hydrothermal systems within the oceanic crust extract 20% of the Earth's heat loss from the solid Earth and affect biogeochemical cycles in the ocean (e.g., [PERSON], 1996; [PERSON], 2013; [PERSON] et al., 1980). Most of this heat loss occurs on mid-ocean ridge flanks far from spreading centers, where hydrothermal fluids are cool (\(<\)20 degC) ([PERSON], 2002). Because the volumetric flow rate of crustal formation waters (referred to herein as \"formation waters\") that discharge at cool temperatures on ridge flanks is comparable to that of the global river discharge to the ocean, even a small compositional change in seawater circulating through the crust can impact oceanic chemical budgets ([PERSON], [PERSON], et al., 2003; [PERSON] et al., 2017). Such chemical changes can result from seawater-basal reactions, diffusive exchange with overlying sediment pore waters, and microbial metabolic activity ([PERSON] & [PERSON], 2010). Because both diffusion to and from the sedimentary pore waters and metabolisms of microbes in the subsurface basaltic crust on ridge flanks are slow ([PERSON], [PERSON], et al., 2013), these processes have the greatest impact on the composition of formation waters mainly when their residencetime is sufficiently long (hundreds to thousands of years) ([PERSON] et al., 2020). Nevertheless, the role of sediment pore waters can be significant in some settings and for some solutes ([PERSON] & [PERSON], 2019). In contrast, when the residence time of circulating seawater is short, chemical changes are dominated by seawater-basalt reactions mainly as a function of reaction temperature (e.g., [PERSON], 2010; [PERSON], [PERSON], et al., 2013; [PERSON], 1979). Thus, given systematic differences in the chemical composition of formation waters in the volcanic ocean crust on ridge flanks, we can identify regions that are connected or isolated from each other, dominated by reactions or subject to mixing of different water types, or subject to evolutionary changes during transport as a consequence of water-rock, sediment, and microbial processes.
The northern Juan de Fuca (JDF) Plate, herein referred to as the \"JFR Flank\" and located offshore of North America, is unique in providing enough chemical data for formation waters across a wide region, including closely spaced samples, to characterize plate-scale subsurface hydrologic processes (Figure 1). We have compiled two decades of chemical data, supplemented with unpublished results, from 24 locations in this 10\({}^{4}\) km\({}^{2}\) region and determined the chemical composition of formation waters in upper basaltic crust from chemical gradients in sediment pore waters and from direct measurements of formation waters recovered from springs and borehole observatories. We compare the composition of formation waters from sites separated by kilometers to tens of kilometers, with the goal of determining which sites appear to be hydrologically connected and which appear to be isolated. For sites that appear to be connected, we assess whether trends in the composition of formation waters indicate lateral subs seafloor directions and rates. We are particularly interested in determining the relative influences of water-rock reactions, microbial metabolic processes, and diffusive exchange with sedimentary pore waters as formation waters flow from one site to the next (e.g., Hulme & Wheat, 2019). Because each of these three processes affect the composition of formation waters in distinct chemical ways, we can use systematic differences in the chemical composition of formation waters to infer (a) lateral pathways for subsurface flow, (b) compartmentalization on scales of kilometers, (c) where deeper water circulation within the crust may occur, (d) where lateral transport is \"sluggish\" resulting in diffusive fluxes to/from sediment pore waters that are consequently more important that advective fluxes within the basaltic crust, and (e) locations where seawater may recharge rapidly. In aggregate, formation water data provide a conceptual basis for inferring the nature of seawater flow within this ridge-flank environment; in addition, lessons learned from this area could be applicable to other regions where the geologic fabric includes basement outcrops, ridges, and seamounts, the latter of which number 10\({}^{4}\) to 10\({}^{5}\) worldwide ([PERSON] & [PERSON], 2007; [PERSON] et al., 2010).
## 2 Geologic and Hydrologic Setting
The JDF Plate is located in the northeast Pacific Ocean and is bounded by the JDF Ridge to the west (29 mm/yr spreading half rate; [PERSON], 2002), the Cascadia Subduction Zone to the east, the Sovanco Transform Fault to the north, and the Blanco Transform Fault to the south ([PERSON] et al., 1986) (Figure 1a). The bathymetry displays substantial relief along the northern and southern sections of the plate and to the west near the spreading axis where sediment is thin or absent ([PERSON] et al., 2005). Seafloor in the middle of the plate is generally smoother, with occasional NE-SW trending ridges that are roughly parallel to the spreading axis and that sometimes outcrop through the sediment plain ([PERSON], 1995; [PERSON] et al., 1999, 2005) (Figure 1b). Sediment is generally thicker to the east, where the plate is older and closer to the continental margin and composed of hemi-pelagic mud and turbidites that accumulated rapidly during sea-level low stands in the Pleistocene ([PERSON] et al., 2005).
Volcanic crust from the spreading axis to about 0.7 Ma is sparsely sedimented and basaltic exposures are common. Here young, exposed crust provides vast areas for potential seawater recharge and discharge, and faults and the broader crustal fabric likely influence subsurface pathways. Within such areas of thin sediment and extensive bare basalt it is difficult to locate sites of spring discharge, because temperatures are cool, the residence time of formation waters is short, and chemical anomalies in discharging waters are likely to be analytically indistinguishable from bottom seawater (e.g., [PERSON] et al., 2019; [PERSON] et al., 1997). To date, no sites of seawater discharge have been located on <0.7 Ma JFR flank crust, but low heat flux values near areas where sediment cover is absent or patchy suggest that advective heat extraction is common ([PERSON] et al., 1992; [PERSON] et al., 2006).
Seismic reflection and swath-map data reveal modest basement relief from 0.7 to 1.2 Ma ([PERSON] et al., 2005). The youngest buried basement ridge (\"First Ridge\") is located on \(\sim\)1.4 Ma crust (Figure 1b). Two additional, primarily buried, ridges with greater relief, are located on \(\sim\)3.5 and \(\sim\)3.7 Ma crust (\"Second Ridge\"). Such ridgeslikely formed by off-axis axis tectonics and volcanism, resulting in linear features oriented sub-parallel to the spreading center to the west ([PERSON] et al., 1998). There are multiple basement outcrops on Second Ridge, which connects the underlying crust to the overlying ocean, facilitating the exchange of bottom seawater and formation waters ([PERSON] et al., 1992; [PERSON] et al., 2003; [PERSON] et al., 2006; [PERSON] et al., 1998). Although sediment is much less permeable than basalt, near basaltic exposures, where sediment is thin, formation waters can seep slowly (mm yr\({}^{-1}\) to cm yr\({}^{-1}\)) from the sediment (e.g., [PERSON] et al., 1992; [PERSON] et al., 2002; [PERSON], [PERSON], et al., 2004; [PERSON], 1994).
On the eastern flank of the JDF Ridge, as on ridge flanks more generally where there is extensive sediment cover, the exchange of seawater and formation waters is limited. Exposures (e.g., seamounts, outcrops, and fracture zones) constrain subsurface flow paths, patterns, and rates as manifested by systematic variations in measured heat flux and formation water compositions, and reproduced with numerical simulations (e.g., [PERSON] et al., 2003; [PERSON] et al., 2006; [PERSON] et al., 2018; [PERSON] et al., 2000, 2019; [PERSON] et al., 2016). Underlying geologic structure and crustal fabric also help to guide flow across lateral distances of tens of meters to kilometers or more (e.g., [PERSON] et al., 2000). For example, Baby Bare has fault-exposures that are tens of meters long and oriented with the spreading axis to the west ([PERSON] et al., 2000). Such features, including one linear feature with <1 m of sediment on the up-thrusted footwall and similar sediment thickness on the down-thrust block, are hydrologically active, with the rate of pore water seepage decreasing with distance from the headwall ([PERSON], [PERSON], et al., 2004).
Figure 1.— (a) The Juan de Fuca Plate is located in the northeast Pacific Ocean off the coast of the United States of America. The plate is bounded by a spreading axis to the west, the Cascadia Subduction Zone to the east, the Sovanco Transform Fault to the north and the Blanco Transform Fault to the south ([PERSON] et al., 1986). The white box and circles represent the area of the larger map and the sample locations. (b) Magnesium concentrations in formation waters were determined for 24 sites. Eleven locations are scientific drilling sites (ODP Sites 1023–1032 and IODP Sites 1301). Another 11 sites (two with multiple distinctions) are on or adjacent basement highs, most of which (the Bares) are isolated outcrops that penetrate through turbidities and hemipagic clay (Baby, Mama [south and north], Papa, Wuzza, Zona, Grizzly [also IODP Site U1363], Grimini, Isita, and Tedby Bares, north and south First Ridge, and Rattelasek Ridge). Magnesium concentrations, which are color coded to the brown-yellow scale, are generally lower to the east where temperatures in basaltic crust are higher. Figure made with GeoMapApp (www.geomapapp.org)/CC BY 4.0, with basemap updated from [PERSON] et al. (2009). Approximate basement ages are based on magnetic anomalies ([PERSON] et al., 1982).
## 3 Methods
### Published Data
Ten Ocean Drilling Program (ODP) sites (Sites 1023-1032) were drilled and cored through sediment as part of Leg 168, along a transect perpendicular to the spreading axis, with crustal ages of 0.9-3.6 Myr (Table 1, Figure 1) ([PERSON] et al., 1997). This transect forms the foundation for the remaining 14 sites that were sampled, all of which targeted potential sites of formation water discharge or were drilled into basaltic basement and instrumented (Integrated Ocean Drilling Program [IODP] Sites 1301, 1362, and 1363). Additional sites with previously published sediment pore water data include basement boreholes drilled during IODP Expeditions 301 and 327 (Sites U1301, U1362, and U1363; [PERSON], [PERSON], et al., 2011; [PERSON], [PERSON], et al., 2005) and samples collected on or adjacent to basement outcrops that penetrate seafloor sediments, including three efflores located near the eastern end of the original ODP transect (Papa Bare, Mama Bare, and Baby Bare; e.g., [PERSON] et al., 1992; [PERSON] et al., 1998). The collection and analysis of sediment pore waters used the same analytical techniques as described below for previously unpublished data, with minor exceptions as noted. Pore water chemical data from ODP Leg 168 were extracted from recovered sediment while being exposed to the atmosphere ([PERSON] et al., 1997; [PERSON] et al., 1999; [PERSON] et al., 2001; [PERSON] et al., 2000). In contrast, a nitrogen-filled glove bag was used on IODP Exp. 301 (Site 1301; [PERSON], [PERSON], et al., 2005; [PERSON] et al., 2008; [PERSON] et al., 2010) and IODP Exp. 327 (IODP Site U1363 near Grizzly Bare; [PERSON], [PERSON], et al., 2011; [PERSON] et al., 2013) to extract pore waters.
Holes at five drilling sites (1024, 1025, 1026, 1027, and U1301) were cased through the sediment section and into upper basaltic basement ([PERSON] et al., 1997; [PERSON], [PERSON], et al., 2005). Holes at Sites 1025, 1026, and U1301 were drilled into crust that is naturally over-pressured, resulting in the discharge of formation waters at the seafloor (e.g., [PERSON], [PERSON], et al., 2004; [PERSON] et al., 2003, 2012; [PERSON] et al., 2012, 2014; [PERSON] et al., 2013). Samples of formation waters were also collected in Walden-Weiss titanium samplers from discharging waters at Sites 1025 and 1026 and at Baby Bare ([PERSON] et al., 2001; [PERSON] et al., 1998; [PERSON] et al., 1998; [PERSON], [PERSON], et al., 2003; [PERSON], 2000; [PERSON], [PERSON], et al., 2003; [PERSON] et al., 2002, 2010). Other cased boreholes (ODP Sites 1024 and 1027 and IODP Site 1301) were instrumented with continuous fluid samplers (OsmoSamplers; [PERSON] et al., 2004; [PERSON] et al., 2006; [PERSON] et al., 2011), sensors, and microbial experiments (e.g., [PERSON] et al., 2016; [PERSON] et al., 2011; [PERSON] et al., 2019; [PERSON] et al., 2011), allowing assessment of changes in the composition of formation waters following drilling as hydrologic systems rebounded chemically ([PERSON], [PERSON], et al., 2003; [PERSON], et al., 2010, 2020).
Pore water data from the basal sediments collected on ODP Leg 168 (ODP Sites 1023, 1027-1032) and IODP Site U1383 (Grizzly Bare) were used to calculate the concentration of formation waters by extrapolating chemical-depth trends from the deepest five or 10 pore water samples to the sediment-basalt interface (e.g., [PERSON] et al., 1999; Hulme & Wheat, 2019; [PERSON] et al., 2000, 2013) (Figure 2b). However, some ions (e.g., Mn and Fe) are highly reactive near the sediment-basement interface; thus, concentration gradients were constrained by fewer data (e.g., Hulme & Wheat, 2019). Such extrapolations are consistent with measured water compositions from borehole and spring water samples (ODP Sites 1024, 1025, 1026, 1027, 1301, and Baby Bare) (e.g., [PERSON], [PERSON], et al., 2004).
IODP Holes U1362A and U1362B ([PERSON], [PERSON], et al., 2011), which were located between IODP Hole 1301a and ODP Hole 1026B (the latter two span a total distance of 1.1 km), were not included in this compilation because formation waters remain contaminated with waters pumped into the formation even 9 years after drilling operations ceased. For example, in May 2019, elevated Cs (which was used as part of a cross-hole tracer experiment) concentrations exceeded 20 nmol/kg in discharging borehole water, relative to uncontaminated formation water with \(\sim\)8 nmol Cs/kg along this portion of the basaltic basement ([PERSON], 2019).
### New Data
#### 3.2.1 RetroFlux Expedition: Sample Collection and Chemical Analysis
Ninety-three sediment cores (piston and gravity) were collected during the RetroFlux expedition (R/V _[PERSON]_. _[PERSON]_ expedition TT-198), which surveyed the JFR Flink after ODP Leg 168 and prior to IODP Expedition 301 (Figure 1, Figures S1 and S2 in Supporting Information S1, and Table S1 in Supporting Information S2). Targets for these cores included thin sediment near and on basaltic outcrops (with samples collected from nearand on Grizzly Bare, Grimin' Bare, Papa Bare, Zona Bare, and Teddy Bare) and features that could be or have been basaltic outcrops (Wuzza Bare, Isita Bare, and Rattlesnake Ridge). Some of these features were illustrated and described in earlier geophysical studies ([PERSON] et al., 1992; [PERSON] et al., 2006).
First Ridge (Figure 1) was targeted for coring during TT-198 close to ODP Sites 1030 and 1031, in an effort to map the extent of pore water seepage through sediment with the goal of resolving the composition of formation waters at different distances along and away from the underlying geologic features. First Ridge was thought initially to have been formed by simple abyssal hill faulting but was later interpreted to have resulted from ridge offset and propagation ([PERSON] et al., 2008). Sediments are >100 m thick to the east and west of First Ridge, and thin to \(\sim\)40 m near Sites 1030 and 1031 ([PERSON] et al., 2005; [PERSON] et al., 2005). Heat flow data and sediment pore water profiles on and around First Ridge indicate temperatures \(\sim\)30\({}^{\circ}\)C to 40\({}^{\circ}\)C at the sediment-basement interface, significantly warmer than sites to the west, and the highest pore water seepage occurs along ridge edges, perhaps associated with faults that penetrate upper crustal rocks (Giambalvo
Figure 2: Chemical results from pore and spring waters from multiple sites (locations in Figure 1). (a) Depth profiles of the concentration of Mg concentrations in pore waters are shown for each location cored during TT198 (RetroFlux Expedition). The asymptote, when it exists, provides a measure for the concentration in the upward seepage formation water (Table 1). (b) Concentrations of Mg are plotted versus distance above the sediment-basement interface for each of the 10 sites.
et al., 2002; [PERSON] et al., 2006; [PERSON], [PERSON], et al., 2004). Upward seepage from First Ridge basement rocks is likely supported by recharge through nearby volcanic outcrops, with bulk permeability in basement consistent with that determined from nearby boreholes, \(\sim\)10\({}^{-13}\) to 10\({}^{-11}\) m\({}^{2}\)([PERSON] et al., 2002).
During TT-198 a 3.5 kHz pinger was used to position the core close to the edge of the basement outcrops to collect samples as close as possible to the limit of sediment cover. Upon recovery cores were sectioned and split. Some cores were placed in nitrogen-filled glove bags for sediment removal into acid-washed centrifuge tubes. Other sediments were placed directly into acid-washed centrifuge tubes from split cores. Centrifuge tubes were cooled to \(\sim\)4\({}^{\circ}\)C before pore waters were extracted by centrifugation. Pore waters were filtered (0.45 micron) and stored in hot acid-washed, high-density, polyethylene (HDPE) bottles. A total of 841 pore water samples were extracted and analyzed (Table S2 in Supporting Information S2).
Pore waters were analyzed at sea for (a) alkalinity by potentiometric titration with 0.1N hydrochloric acid; pH was measurement as part of this procedure, (b) chlorinity and Ca by potentiometric titration with silver nitrate and EGTA, respectively, (c) Mg by colorimetric titration with EDTA, and (d) nitrate and phosphate by colorimetry ([PERSON] et al., 1986; [PERSON] et al., 1994). Samples were analyzed onshore for the major, minor, and some trace ions using standard inductively coupled plasma optical emission spectrometry (ICPOES) and inductively coupled plasma mass spectrometry (ICPMS) techniques ([PERSON] et al., 2008; [PERSON] et al., 2017).
Pore water data from the RetroFlux (TT-198) expedition and Mama Bare were used to determine the composition of the formation waters based on the average asymptotic concentration in cores where the flow rate was \(>\)1 cm y\({}^{-1}\) (see below for estimate of flow rate) (Figure 2a).
#### 3.2.2 Zona Bare: Sample Collection and Analysis
Zona Bare outcrop was discovered by the fortuitous collection of swath bathymmetric data during a transit across the area ([PERSON] et al., 2006; [PERSON] et al., 2005) and was first visited on a single dive from the DSV _Ahvin_ and later sampled on a dive with the remotely operated vehicle (ROV) _[PERSON]_ (AT26-03; J2-718). During this ROV dive, we collected two sediment \"push\" cores and six spring samples from a site that was actively discharging formation water with temperatures up to 16.7\({}^{\circ}\)C. Samples from the two sediment cores were processed within a nitrogen-filled glove bag, centrifuged, filtered, and aliquoted as noted above. Sediments in the coring location were then excavated with the ROV to encourage more rapid discharge (a similar approach was used on Baby Bare with DSR/V _[PERSON]_; [PERSON] et al., 1998). Discharging spring waters were sampled with commercial 100-ml, animal-use HDPE syringes and 200 ml manipulator-activated, syringe-based samplers made of glass and titanium (e.g., [PERSON] et al., 2017). While direct sampling of springs helps to avoid artifacts associated with pore water samples, syringe sampling of spring waters inevitably results in some entrainment of bottom seawater, leading to the dilution of formation (spring) water (Figures 2c and 2d).
Pore waters and spring water samples were analyzed ashore. Chlorinity was determined potentiometrically by titration with silver nitrate and the major and minor ions were analyzed using standard ICPOES an ICPMS techniques as noted above (e.g., [PERSON] et al., 2017).
### Model to Constrain the Composition of Formation Waters Using Pore Water Chemical Profiles
We used systematic differences in pore water chemical profiles to determine the rate and direction of pore water seepage through the sediment and constrain the composition of formation waters that flow from underlying volcanic rock (e.g., [PERSON], 1995; [PERSON] & [PERSON], 1994). We used a simplified one-dimensional transport (advection-diffusion) equation ([PERSON], 1980) because we use the seepage velocity only as a gauge for the quality of our estimate for the composition of the formation water; faster upflow generally provides a better estimate for the composition of the formation water in upper basement. This model was further simplified by assuming a constant temperature and formation factor and/or porosity with depth, which is appropriate for the short cores that were collected, typically \(<\)3 m in length.
Given the boundary conditions
\(C\) (\(z=0\)) = \(C_{0}\), where \(C_{0}\) is the concentration of bottom seawater
and
\(C\) (\(z=z_{\text{deep}}\)) = \(C_{\text{deep}}\), where \(z_{\text{deep}}\) is the deepest sample analyzed and \(C_{\text{deep}}\) is the concentration at that depth, then \[C=C_{0}+A\left(\exp\left[v\,z\,/\,D_{z}\right]-1\right), \tag{1}\]
\[A=\left(C_{\mathrm{chop}}-C_{0}\right)\,/\left(\exp(vz_{\mathrm{chop}}/D_{z} \right)\,-1\]
where \(v\) is velocity and \(Ds\) is the sediment diffusion coefficient that is a function of the solute, temperature, and formation factor ([PERSON], 1979). For simplicity, we assume the formation factor is a function of porosity alone ([PERSON], 1979). On the basis of this model, a chemical concentration reaches an asymptote with depth if the upflow is sufficiently fast or the cored section is sufficiently deep. Thus, the composition in the formation water that seeps upward through the sediment can be calculated from the average value of the asymptote concentrations ([PERSON] & [PERSON], 1994). This analysis generally works for most ions if the upward seepage rate is >1 cm y\({}^{-1}\), as applied below (Table 1, Figure 2a). However, this analysis does not work as well for reactive solutes, like dissolved silicon, except at much faster seepage speeds. For such ions a reaction component is required (e.g., [PERSON] & [PERSON], 1994); however, such analysis is beyond the scope of this contribution, which focuses on a generalized model of plate-scale crustal hydrologic systems.
## 4 Results and Discussion
### Overview of Data and Interpretation
Chemical compositions of pore waters are listed in Tables S2 and S3 in Supporting Information S2 and chemical data for calculating the spring composition at Zona Bare are listed in Table S4 in Supporting Information S2. Mg concentrations, which represent one of many solutes that were analyzed, in formation waters from the 24 sites are plotted on a bathymmetric map (Figure 1, Table 1). In general concentrations of Mg are near the value in bottom seawater to the west. There is a general trend of decreasing Mg concentrations and increasing temperature in upper basaltic crust to the east (e.g., [PERSON] et al., 1999), with the exception of data from First Ridge, which has anomalously low Mg concentrations given the calculated temperature in upper basaltic crust.
Spatial patterns and trends for different reactive solutes are broadly consistent (Figures S3-S21 in Supporting Information S1), but there are important exceptions that constrain where crustal regions are isolated hydrogeologically, and where trends in the composition of formation waters indicate large-scale, lateral subsurface flow patterns. Primary processes that can help to explain observed patterns in formation water compositions include water-rock reactions, diffusive exchange with overlying sediment pore waters, and microbial metabolic process (the latter occurring in both basement rocks and in the overlying sediment). For example, the chlorinity and the concentration of sulfate in formation waters are key tracers (Figure 3). On ridge flanks, higher chlorinity values may result from the hydration of clay minerals and/or elevated chlorinity in bottom seawater during recent glacial periods (e.g., [PERSON], 1985). In contrast, there is no known source of sulfate in this setting, and temperatures are too cool (at most 64\({}^{\circ}\)C in this region) for gypsum saturation and microbial metabolic processes that would reduce sulfate within basalt are sluggish at best ([PERSON] et al., 2013). However, sulfate decreases in formation waters as a result of diffusive losses to the overlying sediment pore waters where it is reduced. Thus in this ridge flank setting, chlorinity is expected to increase along a lateral flow path and concentrations of sulfate are expected to decrease.
Figure 3: Chlorinity (a) and sulfate (b) color-coded concentrations in formation waters at 24 sites on the eastern flank of the Juan de Fuca Ridge. White dashed arrows indicate general monotonic trends indicating lateral flow in the upper volcanic crust, and dotted gold lines indicate potential boundaries between dissimilar compositional trends. In general, sulfate concentrations and chlorinity values remain near the bottom seawater concentration to the south and west. Systematic differences are noted in north-south trends and allow one to discern lateral transport patterns and assess the length-scale of compartmentalization in the transport of formation waters.
Another example is the complicated thermal effect on the concentrations of Ca in formation waters (Figure S4 in Supporting Information S1). At low temperatures (<20\({}^{\circ}\)C) Ca in formations waters does not readily form secondary minerals resulting from basaltic weathering (e.g., Fisher & Wheat, 2010). As bottom seawater (\(\sim\)2\({}^{\circ}\)C) warms, dissolved Ca concentrations can decrease with increasing temperature by precipitation of CaCO\({}_{3}\), which exhibits retrograde solubility, and from carbon that is released from basalt and dissolved in the formation water ([PERSON] et al., 2004; [PERSON] et al., 2019). Thus, at temperatures <20\({}^{\circ}\)C Ca concentrations can be less than that in bottom seawater, but at warmer temperatures Mg-Ca exchange with secondary clay minerals and zeolites is prevalent, producing Ca concentrations in excess of bottom seawater values. Measured alkalinities of these waters are much less than in bottom seawater, again because of CaCO\({}_{3}\) precipitation in veins. Even with Mg nearly removed from solution, dissolved Ca concentrations continue to rise in formation waters, now in exchange for Na. Thus, Ca concentrations in formation waters are a gauge of thermal conditions within the reaction zone.
Likewise, other solutes show concentration patterns that are affected by subsurface processes (Figures S5-S21 in Supporting Information S1). While such complexities in reaction and transport may be difficult to discern on an element-by-element basis, we use a range of solutes and their subsurface exchange mechanisms to elucidate flow conditions within discrete hydrologic regions of the JFR Flank. In the rest of this section, we present spatial differences in the composition of formation waters and discuss the significance of these observations for ridge-flank hydrogeology. We begin with discussion of large-scale, lateral water transport, then discuss evidence for compartmentalization, deeper circulation of formation waters, areas within which the flow of formation waters seems to be especially slow, leading to long-term isolation, and finally to the heterogeneity of recharge of seawater and discharge formation water.
### Evidence for Lateral Flow Along Strike
#### 4.2.1 Second Ridge
There is a systematic difference in the chemical composition of formation waters from Baby Bare to the northern side of Mama Bare, including Sites 1301 and 1026 and the southern side of Mama Bare along Second Ridge ([PERSON] & [PERSON], 2019; [PERSON] et al., 2000). This chemical difference was reproduced with a transport-reaction model in which seawater recharge occurs at Grizly Bare to the south, consistent with thermal and chemical data ([PERSON] et al., 2003; [PERSON] et al., 2006; [PERSON] et al., 2013). Direct evidence for this flow stems from an experiment in which chemical tracers were injected into one borehole and monitored at other boreholes along Second Ridge ([PERSON], [PERSON], et al., 2011; [PERSON] et al., 2016). Along this flow path diffusive exchange with sediment pore waters contributes significantly to the composition of the formation water for some solutes, under current thermal and flow conditions ([PERSON] & [PERSON], 2019). For example, concentrations of sulfate, K, and Y decrease along the Baby-Mama Bare transect as a result of diffusive losses to sediment pore waters, whereas concentrations of dissolved Li, Cs, ammonium, Mn, and Mo increase in formation waters.
The inferred flow path from south to north is probably guided by the structural fabric of the volcanic crust, as expressed with the bathymmetric trend that is defined by basement ridges, abyssal hill faulting, and smaller-scale features. For \(\sim\)14 km in the Baby-Mama Bare region, the basaltic ridge is well defined. It is less well defined for a 50-km segment between Grizly Bare and Baby Bare (Figure 4a; [PERSON] et al., 2005). Forty-five km to the north of Mama Bare lies Zona Bare. The composition of formation water at Zona Bare is generally consistent with the Baby-Mama Bare trend for many solutes ([PERSON], 2019). Using model parameters described by [PERSON] and [PERSON] (2019), for example, sulfate and potassium data generally fall on a linear trend with distance from Grizly Bare, consistent with the continued loss of both solutes to the overlying pore water (Figure 4b). Other solute data (e.g., not shown Mo, Rb, Li, and Mn) also indicate consistent trends, collectively suggesting a component of large-scale flow from Grizly Bare to Zona Bare. Numerical simulations show how some of the recharge occurring at Grizly Bare could flow north past Baby Bare, including discharge at 10s of kg/s at Zona Bare, without disrupting the Grizly Bare-to-Baby Bare flow system ([PERSON] et al., 2016).
Not all of the chemical data from Zona Bare fit the trends associated with the Baby-Mama Bare transect, requiring additional processes that influences solute concentrations. For example, the chlorinity of the formation water at Zona Bare is less than that of bottom seawater (Figures 3a and 4b, Table 1), whereas chlorinities along the Baby-Mama transect are 1.4%-2.5% greater than in bottom seawater. These latter data are consistent with a source of chlorinity from the overlying sediment pore water ([PERSON], 2019), where higher chlorinitycould result from the hydration of clay minerals and elevated chlorinity in bottom seawater during recent glacial periods (e.g., [PERSON], 1985). By contrast, the chlorinity at Zona Bare is 3.2% less than the value in present-day bottom seawater, which is perplexing.
This low chlorinity result was duplicated during two expeditions that used three sampling methods (gravity cores--RetroFlux in 2000; push cores and spring samples--_Jason 2_ dives in 2013). Pore water chlorinity i.e., lower than bottom seawater in other settings has been attributed to (a) addition of water from dehydration of the crust in subduction zones (e.g., [PERSON] et al., 1990), (b) dissolution of methane hydrates (e.g., [PERSON] et al., 2004), and (c) discharge of continental groundwater into the ocean ([PERSON], 2010). Extensive seismic coverage afforded by the [PERSON] et al. (2005) survey did not image a bottom-simulating reflector, which would indicate the presence of gas hydrates. Additionally, Zona Bear is \(\sim\)100 km west of the subduction zone, so freshening from continental sources seems unlikely. The most likely cause for the lower chlorinities and Na concentrations is from clay dehydration. Such dehydration is possible given the temperature in the upper basaltic crust at this location is \(\sim\)64\({}^{\circ}\)C and is likely to be greater at depth and in nearby areas where there is thicker sediment, increasing the temperature at the sediment-basement interface. The temperature range for the transition from opal-A to opal-CT is 30\({}^{\circ}\)C-80\({}^{\circ}\)C, and for smectite to illite 50\({}^{\circ}\)C to 150\({}^{\circ}\)C ([PERSON], 1990), the latter would also impact K concentrations. Dehydration of deep sediments that occurs near the basement surface could contribute to formation waters in the volcanic crust, particularly if flow were facilitated by off-axis faulting or a buried volcanic edifice
Rattlesnake Ridge also lies to the north of the Baby-Mama Bare transect. Two cores were collected here, but the lowest Mg concentration measured (39.5 mmol/kg) was 80% of that in seawater, indicating a very slow seepage speed (0.05 cm yr\({}^{-1}\), assuming a nearly depleted concentration at depth) and consequent dilution with bottom seawater (Table 1). Chlorinity and sulfate concentrations were estimated based on a regression with Mg and extrapolated to 3 mmol Mg/kg. These estimates are consistent with the continued flow of formation water from Mama Bare to the Rattlesnake Ridge. However, the ridge has a lower heat flow than the surrounding region and the thermal regime is dominantly conductive, neither of which are consistent with discharge ([PERSON] et al., 2006). Seismic and swathmap data suggest a lack of basaltic outcrops associated with Rattlesnake Ridge, which would limit exchange between seawater and formation water; nevertheless, it is possible that some portion of the ridge is exposed or there are small outcrops nearby, as high-resolution data are incomplete in this area. Based on its low
Figure 4.— (a) Locations where the chemical compositions of the formation waters were determined in the Second Ridge area are superimposed on the basaltic relief, which is covered everywhere by sediment except for areas marked in white (modified from [PERSON] et al., 2005). Grizly Bare is located \(\sim\)52 km south of Baby Bare, whereas Zona Bare is located 56 km north of Baby Bare (locations shown in Figure 1). (b) Solute concentrations of formation waters along the transect from Grizly Bare in the south to Zona Bare in the north. Lines are calculated for uniform flow rates by accounting for observed diffusive exchange with the overlying sediment pore waters (modified from Hulme and Wheat (2019)). Black boxes resent data from extending from Baby Bare to the north side of Mama Bare (Table 1). Other locations in the Second Ridge area are shown as different shapes and colors, as marked. Bottom seawater is represented by a square on the \(Y\)-axis intercept (distance = 0 km from Grizly Bare).
projected Ca concentration, low temperature relative to the regional temperature in upper basement, relatively high (albeit below the bottom seawater value) sulfate concentration, and low conductive heat flow, sediment cores from Rattlesnake Ridge could be near a site of seawater recharge, as discussed in more detail below (e.g., [PERSON] et al., 2013).
In summary, seawater recharges into the upper basaltic crust at Grizzly Bare and flows northward along the ridge defined by Baby-Mama Bares and farther north to Zona Bare, a linear distance of \(\sim\)110 km. Along the flow path, crustal formation waters discharge naturally at Baby, Mama and Zona Bare (Figure 5). The freshening of the formation water that was observed at Zona Bare is small (3.2%) and does not significantly impact the concentrations for most solutes, many of which have analytical uncertainties of \(\sim\)2%.
#### 4.2.2 First Ridge
Many of the 26 cores that were recovered in this area were intended to elucidate patterns of pore water flow through sediments overlying subseafloor faults and acoustic washouts ([PERSON] et al., 2002; [PERSON], [PERSON], et al., 2004; [PERSON] et al., 1999) (Figure 6b). Here the temperature in upper basaltic basement is \(\sim\)40\({}^{\circ}\)C ([PERSON] et al., 1999; [PERSON] et al., 2006). There were systematic variations in the composition of formation waters from First Ridge South to ODP Site 1031 to ODP Site 1030 to First Ridge North. Most of the chemical differences along this transect are not monotonic and are typically within a \(\sim\)2% error, which is typical of most analytical techniques that were used (Table 1). The exceptions are sulfate and phosphate, both of which generally decrease to the south (Figures S15 and S20 in Supporting Information S1). The sulfate data are consistent with lateral flow from north to south. Alkalinity data generally decreases southward and Ca increases southward, both consistent with subsurface flow southward (Figures S4 and S17 in Supporting Information S1). Measured heat flux and the calculated temperature in upper basement also rise from north to south, similarly
Figure 5: Color-coded strontium concentrations in formation waters at 24 sites on the eastern flank of the Juan de Fuca Ridge. Arrows denote direction of subsurface flow inferred from compositional changes in formation water relative to seafloor topology and crustal features with the exception of the arrow at 1024, which is based on heat flow considerations ([PERSON] et al., 2006). White circles identify sites and likely sites of seawater recharge. Red circles highlight discharge at known springs and likely discharge at the southern end of First Ridge. The yellow circle between First and Second Ridge denotes an area where the flow of formation water has a long residence time, consistent with sluggish lateral flow. Inset. The Sr versus Ca plot highlights the effect of diffusive exchange with the overlying Sr-rich pore waters. Black open squares denote waters that are “typical” of seawater-basal dominated conditions consistent with temperatures at the sediment basement interface. Red open diamonds represent data from First Ridge inferred to be affected by reaction at higher temperatures and subsequent conductive cooling. Blue filled diamonds represent sites of inferred seawater recharge or near areas with seawater recharge. Purple diamonds represent Papa and Zona Bares, both overprinted by a freshened source. Brown circles represent sites in the zone with a long residence time.
greater chemical alteration (e.g., Mg; Fisher & Wheat, 2010). Furthermore, sediment at Sites 1023-1025 host microbial sulfate reduction ([PERSON] et al., 2001), whereas sulfate concentrations in formation waters at Sites 1023-1025 are similar to bottom seawater, implying diffusive fluxes of sulfate to overlying pore waters is small compared with lateral transport in upper basaltic crust (Figure 3b). Given that the diffusion of sulfate along the Second Ridge has a measurable effect on the concentration of sulfate in formation waters, seawater transport within basement in the 1023-1025 area must be more rapid and/or the distance from the seawater source must be shorter such that the cumulative effect of sulfate loss to the overlying pore waters is below detection. This is consistent with inferred flow paths between outcrops present to the north and south of the Site 1023 to 1025 transect (Figures 1 and 5).
### Hydrogeologically Isolated Crustal Regions
In the examples above, we illustrated patterns of consistent changes in fluid composition, leading to interpretations of water flow in a single direction. Subseafloor water pathways in models of homogeneous upper basaltic crust also show a strong monotonic pattern of transport between sites of recharge and discharge, but also show flow vectors in a multitude of directions associated with local convection ([PERSON] et al., 2018; [PERSON] et al., 2016). However, the Sr data (Figure 5) indicate that flow paths are not well connected, resulting in the compartmentalization of subsurface hydrologic flow patters on a range of scales.
Five kilometers to the east of Second Ridge, upon which Baby-Mama Bare lie, another primarily buried ridge exists upon which Papa Bare s lies (Figure 4a). Wuzza Bare lies between these two ridges but is chemically more closely linked to the more eastern ridge upon which Papa Bare resides. ODP Site 1027 was drilled between these two ridges. Given the close proximity of these sites, one might expect that formation waters from Site 1027, Wuzza Bare, and Papa Bare would be compositionally similar and show a similar south-to-north change in composition like formation waters sampled along the transect from Grizzly Bare to Mama Bare. Instead, the formation waters that discharge from Papa Bare are distinct from Baby-Mama Bare transect to the west and those from Wuzza Bare and Site 1027 (Table 1); however, data form Site 1027 is uncertain because of the potential influence of an intrusive sill above (e.g., Wheat, [PERSON], et al., 2003).
Concentrations of Ca and B in formation waters at Papa Bare are the highest sampled to date on the JFR Flank; the concentration of B is almost twice the values from along the Baby-Mama Bare transect (Table 1, Figures S4 and S12 in Supporting Information S1). Similarly, concentrations of Li, K, and Rb at Papa Bare are the lowest of any we found from the JFR Flank (Figures S7, S9 and S10 in Supporting Information S1), and Sr concentrations at Papa Bare are lower than those along the Baby-Mama Bare trend (Figure 5). Sulfate concentrations in formation waters at Papa Bare are 7-8 mmol/kg less than values along the Baby-Mama Transect (Figure 3). Lastly, Na concentrations (Figure S8 in Supporting Information S1) and chlorinity (Figure 3) at Papa Bear are lower (1.7%) than bottom seawater, but in the range of values between those for the Baby-Mama transect and Zona Bare. Based on these systematic differences, we conclude that formation waters from Papa Bare have not mixed with those along the Baby-Mama Bare transect. For example, chlorinity and Li concentrations at Papa Bare are less than those along the Baby-Mama transect, yet along this transect the chlorinity and Li values increase. Similarly, if the high B concentration at Papa Bare impacted the Baby-Mama Bare transect, it would increase the B concentration along the transect, contrary to observations.
Like the Baby-Mama Bare transect, we argue for a south-to-north flow of formation water that feeds Papa Bare and may continue northward toward Zona Bare. This interpretation takes into account the composition of formation waters from Wuzza Bare, which are only slightly different than those on the Baby-Mama Bare transect (Table 1, Figure 4b). We suggest that formation waters flow from the south and reach Wuzza Bare with similar transport-reaction processes, then continue north to Papa Bare, where different processes affect the composition in ways that are distinctly different from \"typical\" sediment diagenetic and basalt weathering processes. Flow could conceivably continue to the north to Zona Bare, which has lower sulfate and chlorinity concentrations, but this scenario would require additional reactions such as the removal of Ca and B from formation waters that we consider unlikely. Flow in the opposite direction from Zona to Papa Bare can be ruled out because there is no mechanism in a ridge flank setting away from the axis that adds sulfate to formation water; however, S can be added to circulating fluids in young crust that is open to seawater circulation (e.g., [PERSON] et al., 1994).
Site 1027 lies between the Baby-Mama Bare and Papa Bare ridges and has over 600 m of sediment deposited upon basaltic basement and an overlying sill (Figure 4a, Table 1). The composition of the formation water is similar in some ways to that on the Baby-Mama Bare transect, although differences are observed in those elements that typically show sampling artifacts from deep-sea drilling ([PERSON] et al., 1992). Borehole waters were collected from a CORK at this site; however, such waters were influenced by inputs from the sill and sediment that overlies basaltic basement, thus the composition of the formation water is mixed with sill and sediment pore water ([PERSON], [PERSON], et al., 2003). Nevertheless, these data illustrate that flow on this ridge flank can be compartmentalized on the scale of kilometers.
Another example of compartmentalized flow is illustrated with data from Isita Bare, which lies about 4 km west of the Baby-Mama Bare transect (Figure 4a, Table 1). The composition of the formation water at this site is distinctly different and reflects more of a sediment component. We discuss this result in more detail below (Section 4.5) but point to it here to draw a contrast with formation waters from the Baby-Mama Bare transect. This contrast and the lack of a significant difference between Wuzza and Baby Bares waters further support active flow to Wuzza Bare that is similar to that supplied to Baby Bare.
Another measure of compartmentalized subseafloor seawater pathways is the difference in the composition of formation waters at ODP Sites 1030 and 1028, which are only 8 km apart. Systematic differences in the composition of formation waters at both sites preclude formation waters flowing from one hole to the other (Table 1). For example, sulfate concentrations prohibit flow from Site 1028 to 1030 because there is no known source of sulfate in this crustal setting (Figure 3). Likewise, the flow from ODP Site 1030 to 1028 is precluded because there is no mechanism to add Mg to the formation water to raise its concentration from 5.5 to 15.9 mmol Mg/kg as observed (Figure 1).
Results presented above illustrate that flow within shallow basement of this ridge flank is commonly compartmentalized. Even sites that are <4-5 km apart may not be part of the same hydrologic regime. Yet, given an appropriate fault-controlled crustal fabric, flow within the basaltic crust can be continuous on a scale of 50-100 km (e.g., [PERSON] et al., 1991; [PERSON] et al., 2003). We conclude that there is a general flow from the south that splits along the Baby-Mama Bare ridge and perhaps along the ridge underlying Papa Bare, where additional inputs affect the composition of formation water at Papa Bare (and potentially Wazza Bare and Site 1027). Flow from Second Ridge could lead toward Zona Bare to the north, but this is a less likely scenario for formation waters at Papa Bare. All of these waters are clearly distinct from those sampled at Isita Bare to the west, defining the lateral (cross-flow) limit of connection for south-to-north flow documented here.
### Formation Waters Impacted by Reactions at Depth
There are general trends in the global data set for calculated and measured compositions of formation waters on ridge flanks as a function of temperature in upper basaltic crust ([PERSON] et al., 1999; Fisher & Wheat, 2010; Mottl & Wheat, 1994; [PERSON], [PERSON], et al., 2003). Such trends suggest that water-rock reactions at a given temperature dominate seawater composition; however, the global record, and the one from the JDF Flank, show variations that do not follow these general trends. For example, at First Ridge, magnesium concentrations in formation waters show little change in concentrations up to \(\sim\)20\({}^{\circ}\)C, then decrease linearly with temperature until near depletion at 60\({}^{\circ}\)C (Figure 6a). However, there are a number of data that fall below this trend, indicating that in some locations more Mg is removed than expected for the temperature in upper basaltic basement. Data from First Ridge fall within this category (red open diamonds in Figure 6a).
The estimated temperature at the sediment basement interface along First Ridge was determined by measurements in Holes 1030/1031 and by extrapolating thermal gradients from the upper 4 m of the sediment column to the depth of the sediment-basement interface ([PERSON] et al., 1999; [PERSON] et al., 2006). Temperatures in the upper basement are 40\({}^{\circ}\)C-42\({}^{\circ}\)C, yet concentrations of Mg are low (<4 mmol/kg), similar to those from Second Ridge and the Baby-Mama Bare transect with reaction temperature of \(\sim\)64\({}^{\circ}\)C. Concentrations of Ca and chlorinarity are likewise higher than expected for a 40\({}^{\circ}\)C formation water and concentrations of alkalinity and the Na/Cl molar ratio are lower than expected (Figure 6). Each of the observed concentrations is consistent with those from the Baby-Mama Bare transect. We suggest that these formation waters penetrated deeper into the crust where they were warmed and reacted at temperatures \(\sim\)64\({}^{\circ}\)C. The depth of penetration require to reach \(\sim\)64\({}^{\circ}\)C has not been documented at this site, but may only require the penetration of a few hundred meters of basaltic crust, remaining in the extrusive portion of the crust (e.g., [PERSON] et al., 2002; [PERSON] et al., 2006; [PERSON] et al., 2004; [PERSON], [PERSON], et al., 2004). These warmed and altered formation waters then ascended to upper basement where conductive cooling during transport altered the original solute-to-heat ratios. Such changes in the ratio of solute concentration to heat ratios are common in most seafloor hydrothermal systems (e.g., [PERSON] et al., 1979; [PERSON], [PERSON], et al., 2004, 2017).
One possible pathway for deeper circulation at this site is a high-angle fault associated with abyssal hill topography or ridge propagation along the west side of First Ridge (e.g., [PERSON] et al., 2005) (Figure 6b). Additional seismic work on the JDF flank reveal deep (6-7 km) faults that extend to the Moho discontinuity, with brittle deformation extending as far as 200 km westward of the trench, potentially impacting sampled sites ([PERSON] et al., 2009). Furthermore, this region appears to be in the wake of a propagator trace, with an increase in the layer 2A velocity occurring at First Ridge ([PERSON] et al., 2008). Fault-bounded abyssal hills are common features on ridge flanks (e.g., [PERSON] et al., 2005; [PERSON] et al., 1996; [PERSON] et al., 1997), and it seems likely that some of these faults could provide high-permeability pathways to the deeper crust, with limited flow permitted across the fault plane and/or in parts of faults that are sealed with secondary minerals ([PERSON] et al., 1996; [PERSON], 2002; [PERSON] & [PERSON], 1996). Nevertheless, in this case, deeper-sourced and warmed waters cool during ascent from depth and \"weep\" at the seafloor after passing though much lower-permeable sediment that is sufficiently thick to thwart significant discharge ([PERSON], [PERSON], & [PERSON], 2004) Given the heterogenous nature of oceanic crust and the global data set referred to above, formations waters that penetrate beyond the upper several hundred meters of permeable basalt may not be anomalous.
### Sediment Dominated Formation Waters
If the lateral transport of formation waters through the upper crust is sufficiently rapid, diffusive sources/sink from overlying sediment will have little influence on the composition of the formation water (e.g., [PERSON], [PERSON], et al., 2013; [PERSON] & [PERSON], 2008). However, if the lateral transport of formation waters is sufficiently slow, or if there is vigorous local mixing in an isolated crustal region, diffusive exchange with the overlying pore water can measurably impact the composition of the seawater-derived, formation water ([PERSON], 2019; [PERSON] et al., 2020). Along the Baby-Mama Bare transect at Second Ridge, Cl, Ba, Sr, Cs, Mo, Mn, Fe, Co, ammonium, and Zn each have a sediment pore water contribution to the formation water that results in either a net flux to the ocean or a net flux to the ocean and basaltic crust ([PERSON], 2019). We examined these solutes in formation waters from the JFR Flank to determine which solutes are good proxies for pore water input and long residence times for formation waters in upper basaltic basement. Note that long residence times can occur for formation waters that are relatively stagnant, and for formation waters that are convecting vigorously in permeable volcanic crust, but are isolated below less permeable sediments.
Many of the elements listed above were not measured at every site, but some were analyzed from enough sites to be the basis for interpretations (Table 1). For example, there is a clear difference in Sr concentrations at ODP Sites 1028, 1029, and 1032 and Isita Bare compared to those from First Ridge and Second Ridge (Figures 5 and 7a). In this area between the First Ridge and Second Ridge, there is relatively little basement relief and notable absence of basement outcrops that would allow relatively easy exchange of bottom seawater and formation waters (Figure 1). Seafloor heat flow in this region matches lithospheric predictions, on average, meaning there is no thermal evidence for advective heat extraction, but there could still be significant lateral movement of heat as a result of vigorous mixing confined to the volcanic crust ([PERSON] et al., 1992, 1999; [PERSON] et al., 2006). Elevated concentrations of Sr generally coincide with higher concentrations of Li and lower concentrations of sulfate (Figures 7b and 7c). Sulfate can be consumed by microbial sulfate reduction in the overlying sediment (e.g., [PERSON], 2019; [PERSON] et al., 2000). Low NaCl molar ratios and low concentrations of K, Rb, and B are generally observed at these four locations as well (Figures S9, S10, S12 and S14 in Supporting Information S1).
Although a number of potential pore water solutes could affect the composition of formation waters in a hydrologic system with slow flow, Sr data provide the best measure for a long residence time for formation waters in
Figure 7: Solute concentrations in formation waters from the JFR Flank plotted versus Mg concentration. Black open squares denote waters that are “typical” of conditions dominated by seawater-basal reactions, consistent with temperatures at the sediment basement interface. Symbols are the same as in Figure 5.
warm ridge flank settings (20 degC-70 degC) because of its relatively high concentration in pore waters globally. Sulfate, Li, and other alkali metal data provide confirmation. For lower temperature hydrothermal systems (<20 degC), dissolved oxygen and nitrate may be better proxies for the extent of solute exchange between the upper basaltic crust and overlying sediment, which defines the residence time for formation waters (e.g., Orcutt, [PERSON], et al., 2013; [PERSON] et al., 2020).
### Recharge
Similar to formation water discharge, seawater recharge is facilitated by permeable basaltic outcrops that enhance connections between the ocean and the underlying volcanic crust. While discharging waters on ridge flanks can leave visual cues, such as shimmering water, staining, microbial mats, and/or vent organisms ([PERSON] et al., 2018; [PERSON] et al., 1998), there are no visual cues of seawater recharge. The most direct way of determining where seawater recharge occurs is through systematic mapping of formation water trends (to infer flow directions) and measuring variations in heat flux values along seismic lines adjacent to basaltic outcrops ([PERSON] et al., 2003; [PERSON] et al., 2006; [PERSON] & [PERSON], 2007). Pore water chemical profiles can provide additional information on the rate of recharge and the extent of local mixing ([PERSON] et al., 2013), although sediment permeability is so low that most crustal recharge occurs through rock outcrops ([PERSON], [PERSON], & [PERSON], 2004; [PERSON], [PERSON], et al., 2004).
Sediment pore water from eight gravity cores collected on and adjacent to Grizzly Bare show a depletion in Mg of \(\sim\)6 mmol/kg and an increases in Ca \(\sim\)6 mmol/kg relative to bottom seawater. These differences were recorded at a depth of 1.3 m below the seafloor in thin sediment (RetroFlux GC9) collected on the summit of Grizzly Bare, an outcrop that rises 650 m above the sediment plain. Pore water chemical profiles from this location did not indicate seepage. Given the thin, cool sediments on the summit, such chemical differences are consistent with input from a formation water that has experienced higher temperatures, tens of degrees warmer than the near bottom seawater temperatures associated with this sediment core. Similar to ODP Sites 1030 and 1031, there is a decoupling of heat content and water composition, where heat is lost conductively during ascent from depth whereas the water composition remains consistent with higher temperature alteration. Likewise, pore waters from five holes drilled at Site U1363 on the northeast flank of Grizzly Bare also show complex flow patterns of formation water and the potential for mixing and discharge of altered seawater from Grizzly Bare ([PERSON] et al., 2013). Estimated water compositions at the sediment-basement interface from borehole data near Grizzly Bare are consistent with mixing between bottom seawater and altered formation waters with a composition similar to waters that discharge from Baby Bare, \(\sim\)50 km to the north. For some solutes, this trend is impacted by a sedimentary component from diffusive exchange with overlying pore water. However, these pore water compositional data are consistent with flow both away from and toward the outcrop along different radial profiles, as inferred from heat flow surveys ([PERSON] et al., 2006) and simulated with numerical models ([PERSON] et al., 2016). Thus, large outcrops can be sites of both recharge and discharge. In this area of seawater recharge, primary channels through which water, heat, and solutes move through the crust remain poorly constrained by sampling at a small number of locations.
Two seismic profiles and heat flow profiles were collected near Grimin' Bare, a basaltic outcrop northwest of Grizzly Bare and south of the sluggish flow area ([PERSON] et al., 2006) (Figure 1). Grimin' Bare rises about 250 m above the sediment plain. Heat flow values away from this outcrop are consistent with lithospheric cooling models, and calculated temperatures for the sediment-basement interface of \(\sim\)64 degC. However, heat flow on the west side of the outcrop is locally elevated, indicative of upflow of warm formation waters. Data from the east side of Grimin' Bare are ambiguous, but this profile is complicated by the collapse of the eastern third of the orifice, as indicated from bathymmetric and seismic reflection data ([PERSON] et al., 2006). Fourteen sediment cores were recovered from this outcrop, many along the NE fault where the slide propagated. Pore waters from these cores show a range of composition-depth profiles (Figure 8). Two of these profiles are consistent with upward seepage of water containing 33 mmol Mg/kg and 26.9 mmol sulfate/kg (Figures 8a and 8b). One profile may indicate seawater recharge. The other profiles show major solute concentrations that do not change with depth. Given the geologic setting, regional conditions, and the likely thinness of the sediment, such uniform seawater concentration-depth profiles suggest seawater recharge, perhaps through nearby outcrops and not the sedimented areas that were cored.
As noted above, two of the Grimin' Bare concentration-depth profiles change from bottom seawater concentrations and reach asymptotic values at depth, consistent with upward seepage of formation waters (Figure 8). The asymptotic values for Mg and Ca are more consistent with a 35\({}^{\circ}\)C formation water than altered seawater at 64\({}^{\circ}\)C, while the Ca-Mg trend points to a reasonable Ca concentration (55 mmol/kg) for the nearly depleted Mg concentration (3 mmol/kg) that is expected for a 60\({}^{\circ}\)C altered seawater. However, the alkalinity-Mg trend points to a negative alkalinity (\(-\)1.7 mmol/kg) for the same depleted Mg concentration (3 mmol/kg). Negative alkalinities do not occur in ridge-flank settings, indicating that this water is not a simple mixture of a 60\({}^{\circ}\)C-65\({}^{\circ}\)C formation water with bottom seawater. Instead, these water compositions are consistent with a lower temperature of \"equilibration\" within the crust. Because the sulfate concentration (27.5 mmol/kg) is little altered from bottom seawater (28.1 mmol/kg) there is not a significant sediment pore water component, implying that the residence time of the water in basaltic basement at this cored sited is likely short. Pore water data from these two cores suggest that we cored a cooler (35\({}^{\circ}\)C) formation water that is surrounded by a deeper, warmer and more altered formation water. Given that these two cores were collected on the northeast portion of the outcrop, near the seamount failure plain, it is possible that flow patterns and mixing of waters are related to the complex structure of the underlying edifice. Locations of seawater recharge are difficult to pinpoint and potential seawater recharge at Rattlesnake Ridge, the outcrops north of the First Ridge, Teddy Bare, Grizzly Bare and Grimini' Bares indicate that water transport within the upper basaltic crust remain unclear.
## 5 Summary and Conclusions
The composition of formation waters from 24 locations across 10\({}^{4}\) km\({}^{2}\) on the eastern flank of the JDF Ridge help to delineate; regions that are hydrologically connected or isolated, lateral flow paths of formation water (including suspected sites of hydrothermal recharge), regions where there is evidence for limited or no exchange of formation water with the ocean, and areas within which formation waters may circulate more deeply than the uppermost volcanic crust. Variations in the composition of formation waters are influenced by water-rock reactions, microbial metabolic activity, and diffusional exchange with overlying sediment pore waters. Because the upper permeable basaltic crust is heterogeneous, flow pathways can be complex, but some trends point to large-scale flow patterns. For example, systematic differences in the composition of formation waters indicate flow from north to south within the crust along First Ridge, and flow from south to north within the crust along Second Ridge. Such flow along basement ridges and other bathymetric highs are likely regulated by the crustal fabric and faulting associated with ridge-flank formation and tectonic evolution. Yet, adjacent crust just a few kilometers away may not experience this flow.
Figure 8: Pore water solute data from sediment gravity cores collected on Grimini’ Bare during TT-198. (a) Mg and sulfate data are plotted as a function of depth. Mg data imply discharge of formation waters at speeds of 1–5 cm/yr (red and brownish squares). One core indicates recharge at a rate of 0.1 cm/yr (Blue squares). Sulfate data indicate that formation waters are little changed from the bottom seawater concentrations of 28.1 mmol/kg. (b) Ca and alkalinity data are plotted versus Mg to highlight extrapolated values from a best-fit line. Symbols are the same as in panel (a).
We have identified several potential sources for seawater recharge, and two sites (Baby Bare and Zona Bare) with natural springs that discharge formation waters. The latter are small (<100 m high) basement highs that penetrate thick sediments that cover most of the volcanic crust in this region. Baby Bare appears to be a location where formation waters only discharge--no areas of seawater recharge were located on Baby Bare ([PERSON], [PERSON], et al., 2004). Zona Bare is also a site of ridge-flank discharge, but there may be recharge nearby Rattlesnake Ridge. Sites of discharge may be associated with underlying faults in several locations, including Baby Bare, First Ridge, and Grimini Bare. Larger outcrops Grizzly Bare and Grimini Bare appear to be locations of both recharge and discharge. In the case of Grimini' Bare a range of crustal water compositions may discharge from the outcrop. By contrast, where there are few outcrops and no significant faulting, the flow of formation water within the upper basaltic basement may be sluggish or there can be vigorous flow within isolated crustal regions, leading to a long residence time for formation waters. A long residence time is characterized by altered formation waters that are significantly affected by diffusive exchange with overlying sediment pore water.
The nature of flow patterns, rates, and pathways in the upper volcanic crust is arguably better known on the eastern flank of the JDF Ridge than anywhere else on the seafloor of Earth's ocean. The young, warm, and heavily sedimented crust of the JDF Flank is easily accessible from ports along the west coast of North America, and remains an intriguing region for resolving coupled geochemical, geothermal, microbial, and hydrologic processes. The combination of crustal properties in the upper basaltic crust produces formation waters that can be highly altered, which makes it relatively easy to detect differences that result from water-rock reactions, microbial metabolic processes, and diffusional exchange with overlying sediment pore waters. However, the JDF Flank is anomalous relative to most ridge flanks because of its young age and deep burial of volcanic rocks (e.g., [PERSON] et al., 2012) and proximity to a subduction zone where plate deformation may enhance faulting and subsurface flow ([PERSON] et al., 2008). Most young mid-ocean ridge flanks are relatively bare of sediment and so have cooler (<20\({}^{\circ}\)C) temperatures in upper basement, resulting in shorter residence times for circulating seawater and slower reaction rates with crustal basalt, leading to more subtle changes from the composition of seawater (e.g., [PERSON] et al., 2018; [PERSON] & Dunk, 2010; [PERSON] et al., 2017, 2020). Additional work is needed across a range of ridge flank conditions to resolve typical processes and the global influence of plate-scale hydrothermal flows.
## Data Availability Statement
New data (coring locations and chemical analyses of seawater) used in this study are available and open sourced at zenodo via [[https://doi.org/10.5281/zenodo.7232817](https://doi.org/10.5281/zenodo.7232817)]([https://doi.org/10.5281/zenodo.7232817](https://doi.org/10.5281/zenodo.7232817)).
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wiley/fb1f94e0_cb43_40a0_89a6_5ae039bc150c.md | # Geophysical Research Letters
A New Method for Eliminating Dust Effects When Quantifying the Light Absorption Properties of Brown Carbon
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]
###### Abstract
Accurate quantification of the absorption properties of brown carbon (BrC) aerosols is crucial to assess the Earth-atmosphere radiative impacts of BrC. However, the BrC absorption properties were often misestimated in field observations, due to neglecting the contribution of dust absorption. This study solved this problem by coupling a method for calculating the dust concentration into the traditional model for quantifying BrC absorption. The results show that dust absorption was up to 16.8% of the sum of BrC and dust absorption in northwestern China. The potential contribution of dust to the sum of BrC and dust absorption was significantly higher in the Asia-located studies (0.4%-16.8%) than in the Americas-located (<1.2%) and Europe-located (<2.3%) studies. This work underscores the necessity of eliminating the negative effect of dust in BrC quantitative model. It prompts us to revisit the BrC absorption properties resolved by previous studies, especially in dust-influenced areas such as Asia.
Key Words.:A New Method for Eliminating Dust Effects When Quantifying the Light Absorption Properties of Brown Carbon
* [1][PERSON]. [PERSON], [PERSON], X.
absorption coefficients into BC and non-BC (NBC) in this method. The NBC absorption coefficients is considered as the BrC absorption coefficients after neglecting dust absorption. Aerosol chemistry measurement techniques have driven the subsequent development of the method. [PERSON] et al. (2018) considered three BrC components as the contributing sources to the NBC absorption coefficients and separated the NBC absorption coefficients into three BrC components via the multiple linear regression (MLR) method. This algorithm proposed by [PERSON] et al. (2018) has now been widely used worldwide because of its advantages in separating the absorption coefficients of individual BrC components ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2021). The studies applying this algorithm (Figure 1 and Text S1 in Supporting Information S1) reveal that biomass combustion-related OA and secondary OA (SOA) are the most significant contributors to NBC absorption at 370 nm worldwide. The algorithm effectively advances the understanding of BrC absorption properties in the academic community, and it has much room for advancement in the future as well. However, the algorithm still suffers from an unresolved but important problem, which is the difficulty in separating dust and BrC absorption. Ignoring possible dust absorption and treating NBC absorption coefficients as BrC absorption coefficients is the response in almost all studies, even though they mostly acknowledge the presence of dust (Text S2 in Supporting Information S1). This may assign the absorption caused by dust to BrC, thus incorrectly assessing the radiative effects of BrC.
This study aims to optimize this algorithm by solving the problem of separating between BrC and dust absorption, thus achieving an accurate quantification of the BrC absorption properties. We first presented a method to calculate the dust mass concentrations using aerosol size distributions, then the dust mass concentrations were introduced into MLR analysis, thus solving the challenge of separating the absorption properties of dust and BrC components. Our findings underscore the necessity of including dust in NBC absorption modeling, particularly in northwestern Chinese regions where dust presence is notable. Therefore, it is necessary to revisit the BrC absorption properties quantified in previous observations.
## 2 Materials and Methods
### Sampling Site and Instruments
The Semi-Arid Climate and Environment Observatory of Lanzhou University (SACOL) (35\({}^{\circ}\)57\({}^{\prime}\)N, 104\({}^{\circ}\)08\({}^{\prime}\)E, 1,965.8 m a.s.l.) is a rural site in the Chinese Loess Plateau, representing the background in the semi-arid region of
Figure 1: Contributions of different brown carbon (BrC) components to the non-BC (NBC) absorption coefficient at 370 or 405 nm calculated via the multiple linear regression method in different studies ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2021). Full names of BrC components: BBOA, biomass burning organic aerosol; LO-BBOA, less-oxidized BBOA; MO-BBOA, more-oxidized BBOA; HOA, hydrocarbon-like OA; O-HOA, oxygenated HOA; COA, cooking OA; ECOA, coal combustion OA; NOA, nitrogen-containing OA; and SOA, secondary OA. Detailed calculation of NBC absorption coefficient and SOA was in Text S1 in Supporting Information S1.
northwest China (Figure S1 in Supporting Information S1) ([PERSON] et al., 2008). The SACOL site suffers from anthropogenic aerosol pollution (e.g., BC and BrC), which is most severe during the winter ([PERSON] et al., 2022; [PERSON] et al., 2022). The dust aerosols emitted from desert sources, such as the Taklamakan and Gobi deserts, are frequently transported to the SACOL site during the spring and winter ([PERSON] et al., 2015). It can be found that the SACOL site during the winter is a natural experimental field for studying BrC and dust absorption.
A situ field campaign was conducted in winter 2018-2019 (7 December 2018 to 6 January 2019) at the SACOL site. An aerodynamic particle size spectrometer (APS; model 3321, TSI) measured the number particle size distribution (PSD) in range of 0.5-20 \(\mu\)m. A tapered element oscillating microbalance machine (TEOM; Model RP-1400A, Thermo) measured the PM\({}_{2.5}\) (particulate matter with a diameter less than 2.5 \(\mu\)m) mass concentration. An AE31 endiometer (Model AE31, Magee Scientific) measured the PM\({}_{2.5}\) absorption coefficients (\(b_{\rm mb}\)) at 370, 470, 520, 590, 660, 880, and 950 nm. Three OA components in non-refractory PM\({}_{1}\) (particulate matter with a diameter less than 1 \(\mu\)m) were identified based on the high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS; Aerodyne) data, including biomass burning OA (BBOA), coal combustion OA (CCOA), and oxygenated OA (OOA) ([PERSON] et al., 2022). Times of all instrument data were adjusted to China Standard Time (UTC+8) and 1 hr time resolution.
### Data Processing
#### 2.2.1 Calculation of Dust Mass Concentration in PM\({}_{2.5}\)
The root cause for the difficulty in separating BrC and dust absorption is the lack of dust information. Therefore, a method for calculating dust mass concentration using APS data was proposed in this study. First, the number PSD observed by APS was converted to mass PSD with the spherical particle assumption. Note that APS is good at capturing the PSD shape but is not designed for fully quantitative measurements, so the mass PSD needs to be corrected. Therefore, the mass PSD was corrected using the TEOM-observed PM\({}_{2.5}\) mass concentration. The strong correlation (\(R^{2}=0.72\)) between the TEOM-observed PM\({}_{2.5}\) and the corrected APS-reconstructed PM\({}_{2.5}\) proved the reliability of the APS data (Figure 2a). Finally, the corrected mass PSD was decomposed into two modes using multi-modal fitting (Figure 2b). The mode 1 was the mass PSD of anthropogenic aerosol and the mode 2 was the mass PSD of dust aerosol (The contribution of sea salt aerosol does not need to be considered because the SACOL site is far from the ocean.). The dust mass PSD in the size range of 0-2.5 \(\mu\)m was integrated to obtain the dust mass concentration in PM\({}_{2.5}\). The detailed processing of the APS data is in Text S3 in Supporting Information S1.
#### 2.2.2 Calculation of BC and NBC Absorption Coefficients
The asthalometer data processor ([[https://zenodo.org/record/832403](https://zenodo.org/record/832403)]([https://zenodo.org/record/832403](https://zenodo.org/record/832403))) with [PERSON]'s algorithm was applied to correct the AE31 data ([PERSON] et al., 2003; [PERSON] et al., 2018). The following equation is used in the
Figure 2: (a) Correlation between the tapered element oscillating microbalance machine (TEOM)-observed PM\({}_{2.5}\) concentration and the corrected aerodynamic particle size spectrometer (APS)-reconstructed PM\({}_{2.5}\) concentration. (b) Average corrected mass PSDs. The gray bars indicate the original mass particle size distributions (PSDs) observed by APS. The mode 1 (blue line) and mode 2 (brown line) indicate the fitted mass PSDs of anthropogenic and dust aerosols, respectively.
[PERSON]'s algorithm to convert the aerosol light attenuation coefficient (\(b_{\text{\tiny{ATN}}}\)) collected at the filter fiber to the aerosol light absorption coefficient (\(b_{\text{\tiny{abs}}}\)) in the atmosphere:
\[b_{\text{\tiny{abs,NBC}}}=\frac{b_{\text{\tiny{ATN}}}}{C_{\text{ref}}\times R( \text{ATN})} \tag{1}\]
where \(C_{\text{ref}}\) is a parameter to correct multiple scattering of the light beam at the filter fiber, \(R(\text{ATN})\) is a function of attenuation to correct the particle loading effect. \(R(\text{ATN})\) is used to adjust the continuity of \(b_{\text{\tiny{abs}}}\) and has little effect on \(b_{\text{\tiny{abs}}}\) but \(C_{\text{ref}}\), which depends on the filter material and aerosol composition ([PERSON] et al., 2015; [PERSON] et al., 2003), can significantly affects the magnitude of \(b_{\text{\tiny{abs}}}\). Based on the range of \(C_{\text{ref}}\) reported by [PERSON] et al. (2010), we used \(C_{\text{ref}}\) = 2.80 and 4.57 for quartz filter fiber to represent the upper and lower limits of \(b_{\text{\tiny{abs}}}\) at all wavelengths in this study.
Aerosol absorption Angstrom exponent (AAE) reflects the wavelength dependence of \(b_{\text{\tiny{abs}}}\) expressed as:
\[\text{AAE}=-\text{ln}\left(\frac{b_{\text{\tiny{abs}}}(\lambda_{1})}{b_{\text {\tiny{abs}}}(\lambda_{2})}\right)/\text{ln}\left(\frac{\lambda_{1}}{\lambda_{2 }}\right) \tag{2}\]
where \(b_{\text{\tiny{abs}}}(\lambda)\) is the \(b_{\text{\tiny{abs}}}\) at the wavelength of \(\lambda_{1}\) = 370 nm and \(\lambda_{2}\) = 880 nm were taken for AAE of total aerosol and BC, \(\lambda_{1}\) = 370 nm and \(\lambda_{2}\) = 660 nm were taken for AAE of BrC.
BC has a strong absorption at all wavelengths, whereas NBC absorption is negligible at near-infrared wavelengths. Therefore, it is assumed that \(b_{\text{\tiny{abs}}}\) at 880 nm, which is abbreviated as \(b_{\text{\tiny{abs}}}\) (880), was only contributed by BC and that \(\text{AAE}_{\text{BC}}\) was a constant ([PERSON] et al., 2018). The NBC absorption coefficient (\(b_{\text{\tiny{abs,NBC}}}\)) at the wavelength of \(\lambda\) was obtained as follows:
\[b_{\text{\tiny{abs,NBC}}}(\lambda) =b_{\text{\tiny{abs}}}(\lambda)-b_{\text{\tiny{abs,BC}}}(\lambda)\] \[=b_{\text{\tiny{abs}}}(\lambda)-b_{\text{\tiny{abs}}}(880)\times \left(\frac{880}{\lambda}\right)^{\text{AAE}_{\text{BC}}} \tag{3}\]
\(\text{AAE}_{\text{BC}}\) = 1 was taken in most studies, but recent studies have suggested that there may be significant uncertainty in the \(\text{AAE}_{\text{BC}}\)([PERSON], 2010; [PERSON] et al., 2020). To estimate the effect of \(\text{AAE}_{\text{BC}}\), the results with \(\text{AAE}_{\text{BC}}\) from 0.8 to 1.2 were calculated.
#### 2.2.3 Calculation of Multiple Linear Regression
The \(R^{2}\) between BBOA, CCOA, and dust and \(b_{\text{\tiny{abs,NBC}}}\) (370) were approximately 0.4, 0.8, and 0.2 (Figure S6 in Supporting Information S1), respectively, suggesting that they were potential contributors to NBC absorption. Note that OOA had no light-absorbing capacity and was not added to the MLR analysis because there was no correlation between OOA and \(b_{\text{\tiny{abs,NBC}}}\) (370).
MLR method was used to resolve the mass absorption coefficient (MAC) of each absorbing species (\(\text{m}^{2}\cdot\text{g}^{-1}\)). Three MLR schemes (called T1, T2, and T3 schemes, respectively) were established. T1 scheme is an optimized MLR scheme with dust added. BBOA, CCOA, and dust were potential contributors to NBC absorption in T1 scheme. T2 scheme is a traditional MLR scheme without an intercept. Only BBOA and CCOA were potential contributors to NBC absorption in T2 scheme. T3 scheme is a traditional MLR scheme with an intercept. BBOA, CCOA, and intercept were considered potential contributors to NBC absorption in T3 scheme. The regression models of three MLR schemes were as follows:
\[\text{T1}:b_{\text{\tiny{abs,NBC}}}(\lambda)=a\times[\text{BBOA}]+b\times[ \text{CCOA}]+c\times[\text{Dust}] \tag{4a}\] \[\text{T2}:b_{\text{\tiny{abs,NBC}}}(\lambda)=a\times[\text{BBOA}]+b\times[ \text{CCOA}]\] (4b) \[\text{T3}:b_{\text{\tiny{abs,NBC}}}(\lambda)=a\times[\text{BBOA}]+b\times[ \text{CCOA}]+\text{intercept} \tag{4c}\]In the above equations, [BBOA], [CCOA], and [Dust] indicate the mass concentrations of BBOA, CCOA, and dust, respectively. \(a\), \(b\), and \(c\) are regression coefficients and their physical significance is the MACs of BBOA, CCOA, and dust, respectively, at the wavelength of \(l\). The physical significance of intercept is the unconsidered NBC absorption contributor. The intercept can be considered as dust absorption coefficient if the dust and OA components are completely decoupled in the MLR calculation, which will be discussed in Section 3.3. The MLR results of T1, T2, and T3 schemes have been examined and are considered robust (Figure S7 in Supporting Information S1).
Notably, the particle sizes for \(b_{\text{abs,NBC}}\) and dust mass concentration were PM\({}_{2.5}\), whereas the particle sizes for BBOA and CCOA mass concentrations were PM\({}_{1}\). Although the organic matter is usually mainly present in PM\({}_{1}\), there is still a little organic matter in range of 1-2.5 um ([PERSON] et al., 2016; [PERSON] et al., 2016). Therefore, the mass concentrations of BBOA and CCOA in PM\({}_{1}\) might be slightly lower than those in PM\({}_{2.5}\), which might lead to a slight overestimation of the MACs of BBOA and CCOA in the MLR analysis.
## 3 Results and Discussion
### Overview of BC and NBC Absorption
This study focused on aerosol absorption at 370 nm because of its high signal-to-noise ratio. The average total \(b_{\text{abs}}\) (370) was 61.2 (37.5) Mm\({}^{-1}\) for \(C_{\text{ref}}\) = 2.80 (4.57) (Figure S8 in Supporting Information S1). AAE of total aerosols was mainly distributed in the range of 1.0-2.2, and the highest frequency was found in the range of 1.4-1.5. The AAE\({}_{\text{BC}}\) is usually around 1, so the AAE much greater than 1 indicated the presence of both NBC and BC aerosol. The contributions of the NBC to \(b_{\text{abs}}\) (370) were 49%, 39%, and 29%, which were higher than the results at most sites worldwide (Figure S9 in Supporting Information S1), when AAE\({}_{\text{BC}}\) = 0.8, 1.0, and 1.2, respectively. It highlighted the importance of NBC absorption on the radiation balance of the Earth-atmosphere system at the SACOL site. It also implied that the SACOL site was well suited for conducting studies on BrC and dust absorption.
### Overview of Absorbing Species
The average mass concentrations of BBOA and CCOA were 1.6 and 3.8 \(\text{\mu g}\cdot\text{m}^{-3}\), respectively. The average mass concentration of dust was 11.7 \(\text{pg}\cdot\text{m}^{-3}\), which was \(\sim\)8 and \(\sim\)3 times higher than those of BBOA and CCOA, respectively. Three average trajectories clusters (i.e., C1, C2, and C3) were calculated by the 72-hr backward trajectories at 500 m (Text S4 and Figure S10 in Supporting Information S1). C1, which accounted for 62% of the trajectories, came from the Tengerer Desert. C2 passed through the northeastern Tibetan Plateau and explained 28% of the trajectories. C3, which accounted for 10% of the trajectories, originated from the southern Taklamakana Desert and passed through the northern Tibetan Plateau. The relative mass contribution of CCOA, BBOA, and dust corresponding to C1, C2, and C3 were similar, indicating that there was almost no long-range transported CCOA, BBOA, and dust during the observation period. Bivariate polar plots (Figure S11 in Supporting Information S1) showed that there were significant regional transported CCOA from the west and south and BBOA from the southeast, which were emitted from Lanzhou and Dingxi city ([PERSON] et al., 2022). The distribution of dust was homogeneous in the bivariate polar plots, indicating the dust was a regional background aerosol.
### Multiple Linear Regression Analysis
The MLR results for three schemes are shown in Figure 3. The results of T1 scheme with AAE\({}_{\text{AC}}\) = 1 were discussed in this paragraph. CCOA was the strongest light-absorbing NBC species with a MAC of 2.67-4.36 m\({}^{2}\): g\({}^{-1}\) at 370 nm (The lower and upper limits of MAC indicated \(C_{\text{ref}}\) = 4.57 and 2.80, respectively.). CCOA was the largest contributor to \(b_{\text{abs,NBC}}\) (69.7% at 370 nm). Strong CCOA absorption was also found at the Chinese Xianghe site in winter 2017-2018 Q. [PERSON] et al., 2019), implying that the radiative effects of absorbing aerosols emitted from winter coal combustion need special attention in China. BBOA had the second highest MAC (1.24-2.03 m\({}^{2}\cdot\text{g}^{-1}\)) at 370 nm and contributed to 13.4% of \(b_{\text{abs,NBC}}\) (370). The MAC of dust at 370 nm (0.21-0.34 m\({}^{2}\cdot\text{g}^{-1}\)) in this study was very close to the MAC of PM\({}_{2.5}\) dust at 375 nm (0.20 \(\pm\) 0.03 m\({}^{2}\cdot\text{g}^{-1}\)) in the Chinese Gobi Desert ([PERSON] et al., 2017). Although the MAC of dust is much lower than the MAC of BBOA, the contribution of dust to \(b_{\text{abs,NBC}}\) (370) (16.8%) was slightly higher than that of BBOA because of the high dust concentration. [PERSON] et al. (2018) quantified a dust MAC of 0.014 m\({}^{2}\cdot\text{g}^{-1}\) at 637 nm at the Zhangye site, which was dominated by fresh dust ([PERSON] et al., 2018), much lower than the dust MAC of 0.05-0.08 m\({}^{2}\cdot\text{g}^{-1}\)at 637 nm in this study. This difference is attributed to the enhanced dust absorption capacity at the SACOL site due to the mixing of dust with anthropogenic pollutants ([PERSON] et al., 2018). \(C_{\rm{ref}}\) did not affect the contribution of absorbing species to NBC absorption, but AAE\({}_{\rm{BC}}\) significantly affected the assignment of \(b_{\rm{abs,NDC}}\) (370) to absorbing species. An increase in the contribution of CCOA to \(b_{\rm{abs,NDC}}\) (370) from 62.9% to 80.5% when AAE\({}_{\rm{BC}}\) increased from 0.8 to 1.2 was found. The contribution of BBOA and dust to \(b_{\rm{abs,NDC}}\) (370) decreased from 14.4% and 22.7% to 11.0% and 8.5% when AAE\({}_{\rm{BC}}\) increased from 0.8 to 1.2. Therefore, caution should be maintained when selecting AAE\({}_{\rm{BC}}\).
The results of T1 scheme were taken as a baseline to assess the estimation biases in the results of the other schemes. In the T2 scheme (Figure 3d), the absorption coefficients of CCOA and BBOA at 370 nm were all overestimated due to the dust absorption was forced to be assigned to CCOA and BBOA. The evaluation biases of CCOA and BBOA decreased from 20.3% and 69.2% to 6.0% and 32.9% when AAE\({}_{\rm{BC}}\) increased from 0.8 to 1.2. In the T3 scheme (Figure 3e), the estimation biases of CCOA and BBOA were not sensitive to AAE\({}_{\rm{BC}}\) and were stable at approximately \(-3\)% and \(-4\)%, respectively. It suggested an improvement in the results for the BrC components with the addition of the intercept.
Theoretically, the intercept can be equated to dust absorption coefficient if the absorption of the dust and BrC components are completely decoupled. However, this does not hold true in practical calculations because the intercept in the T3 scheme was always greater than the dust absorption coefficient in the T1 scheme (Figure 3e). The bias of intercept increased continuously with the increase of AAE\({}_{\rm{BC}}\) when AAE\({}_{\rm{BC}}\)\(\leq\) 1.14; after AAE\({}_{\rm{BC}}\)\(>\) 1.14, the bias of intercept decreased slightly with increasing AAE\({}_{\rm{BC}}\) and then increased again. It is deduced that the main reason is the lack of constraints from the dust mass concentration in T3 scheme, resulting in the absorption of dust and BrC components not being completely decoupled, so that a part of the absorption coefficients belonging to the BrC component was also included in the intercept. Another possible explanation is that there were still some absorptive aerosol components that cannot be measured by current observation methods, and the absorption coefficients of these unknown components were classified in the intercept by the MLR method. Based on the above analysis, the intercept cannot be simply equated to the dust absorption coefficient. The physical significance of the intercept may include the dust absorption coefficient, the noise generated by the incomplete decoupling, and the absorption coefficients of unknown components. This was also supported by the calculation result in Section 3.4 that the potential contribution of dust to the \(b_{\rm{abs,NDC}}\) was lower than the
Figure 3: Contributions of different absorbing aerosol species to the \(b_{\rm{abs,NDC}}\) at 370 nm as a function of absorption Ångström exponent of BC (AAE\({}_{\rm{BC}}\)) in (a) T1, (b) T2, and (c) T3 schemes. Estimation bias of absorption contributions as a function of AAE\({}_{\rm{BC}}\) for (d) T2 and (e) T3 schemes relative to T1 scheme.
contribution of the intercept in the studies at the Delhi (16% vs. 1.6%-3.3%) and Amazonia (2.8% vs. 0.6%-1.2%) sites, as well as at the SACOL site.
In summary, the MAC of the BrC components resolved by the MLR with an intercept (i.e., T3 scheme) is closer to that resolved by the T1 scheme. Therefore, it is recommended to add an intercept to the MLR analysis if dust concentration information cannot be obtained due to limited observations. In addition, not only the research data in this study can be applied to this optimized MLR algorithm. For example, the organic components observed by an HR-ToF-AMS can be replaced by the organic matter measured by an organic carbon/elemental carbon analyzer ([PERSON] et al., 2020). The dust mass concentration can also be reconstructed using the mass concentration of aerosol metal elements ([PERSON] et al., 2021; [PERSON] et al., 2021). It is believed that the radiative effects of global BC, BrC, and dust aerosols can be better constrained if the algorithm in this study is extended and applied to globally accumulated aerosol chemistry and absorption data.
### Potential Dust Absorption Contributions From Previous Studies
We used the results resolved at the SACOL site to reassess the results at the other studies in Figure 1 in order to provide suggestions for future studies. We used the dust MACs of 0.21-0.34 m\({}^{2}\). g\({}^{-1}\) at 370 nm from this study as the upper and lower limits of the dust MACs, and used in situ observation data and Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2) reanalysis data to acquire the surface dust mass concentrations, and finally quantified the potential contributions of the dust to the NBC absorption coefficient in these studies (Figure 4). The detailed calculation is shown in Text S5 in Supporting Information S1.
The ratio of dust to organic aerosol mass concentrations (abbreviated as dust/OA) in PM\({}_{2.5}\) was used as an indicator of the degree of dust dominance. Most of the Americas-located and Europe-located studies had dust/OA values below 0.1, except for the study at the Athens site (0.27), which is close to the African dust region, indicating that the influence of dust was weaker in the Americas and Europe. The studies at the SACOL, Everest, Xianghe, and Delhi sites had dust/OA values as high as 0.28-1.04 because of the frequent exposure to Asian dust ([PERSON] et al., 2010; [PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON] et al., 2024), and these four sites are categorized as Asian dust influenced sites. The contributions of dust to the \(b_{\mathrm{abs,NBC}}\) were below 1.2% in the studies at the Fresno (405 nm) and Amazonia (370 nm) sites. The contributions of dust to the \(b_{\mathrm{abs,NBC}}\) at 370 nm were 1.4%-2.3% and 1.2%-1.9%, respectively, in the studies at the Athens and Greater Paris sites. Overall, there was almost no contribution of dust to the \(b_{\mathrm{abs,NBC}}\) in the Americas-located and Europe-located studies. The contributions of dust to the \(b_{\mathrm{abs,NBC}}\) at 370 nm were much higher in almost all Asia-located studies than in the Americas-located and Europe-located studies, while the contributions at the Asian-located studies were highly correlated with the observed particle sizes. The PM\({}_{2.5}\) particle sizes used in the studies at the SACOL, Gomolangma, Guangzhou, and Singapore sites corresponded to high contributions. Among the Asia-located studies, the contribution at the SACOL site (16.8% at AAE\({}_{\mathrm{EC}}\) = 1.0) was the highest, followed by the Gomolangma site (8.1%-13.1%). The studies at the Guangzhou site (5.6%-9.1%) and Singapore site (3.8%-6.1%) also exhibited high dust absorption contributions, although they were weakly affected by Asian dust. [PERSON] et al. (2022) quantified the contribution of dust to methanol-soluble BrC absorption in Guangzhou in the winter to be 10.9%, which was similar to the results in this study (5.6%-9.1%). Meanwhile, The PM\({}_{1}\) particle sizes in the studies at the Xianghe site and Delhi site were used. The contributions of dust to the \(b_{\mathrm{abs,NBC}}\) at the Xianghe site (0.4%-0.8%) and Delhi site (1.6%-3.3%) were the lowest among the Asia-located studies, even though they are located in the Asian dust influenced areas. This phenomenon is attributed to the selection of the observed particle size. The ratio of organic concentration in PM\({}_{1}\) and PM\({}_{2.5}\) is usually approximately 60%-80% ([PERSON] et al., 2012; [PERSON] et al., 2022), much higher than the ratio of dust concentration in PM\({}_{1}\) and PM\({}_{2.5}\) (0.16-0.20 in Text S5 in Supporting Information S1). PM\({}_{1}\) particle size can retain BrC particles and remove dust particles as much as possible, thus minimizing the effect of dust absorption.
In summary, the contribution of dust to the NBC absorption are much higher in the Asia-located studies (except at the Xianghe site) than in the Americas-located and Europe-located studies. The natural reason for this situation is the high background dust concentration in Asia. The technical reason is the use of PM\({}_{2.5}\) particle size at most Asia-located studies. These two reasons together lead to the non-negligible contribution of dust to NBC absorption in the Asia-located studies. Considering that dust aerosols are important not only in the Asian dust influenced areas but also in the Middle East, Northern Africa, and Central Australia (Figure 4a), it is necessary to revisit the BrC absorption properties at these dust-influenced areas resolved by previous studies. It should also be realized that the impact of dust absorption in the Americas, Europe, the Pacific Islands, and Southern Africa may be limited because of low background dust concentrations. We strongly suggest that BrC absorption studies in these dust-influenced areas should apply the improved algorithm in this study or select PM\({}_{1}\) particle size to exclude dust absorption as much as possible.
## 4 Conclusions
The absorption properties of BrC are critical for the accurate assessment of the impact of BrC on the Earth-atmosphere radiation balance in models. However, the quantified BrC absorption properties are subject to large errors due to the current inability to separate BrC and dust absorption in field observations. To solve this problem, we coupled the traditional MLR algorithm and the method of calculating dust mass concentration, and successfully separated the BrC and dust absorption properties at the SACOL site. The dust absorption was up to
Figure 4: (a) Spatial distribution of average surface dust concentration in PM\({}_{2.5}\) (colorbar) during 2017–2021 from MERRA-2 reanalysis data and the positions of sites (yellow dots) where the multiple linear regression method had been applied. (b) Potential contributions of dust to the non-BC absorption coefficient at 370 or 405 nm (brown bar) and the ratio of the dust to organic aerosol mass concentration in PM\({}_{2.5}\) (green dot) at these sites. The upper and lower ends of the brown bars indicate the upper and lower limits of the potential contribution, while the solid and striped bars indicate that the particle sizes are PM\({}_{1}\) and PM\({}_{2.5}\), respectively.
16.8% of NBC absorption at the SACOL site, emphasizing the non-negligible influence of dust when quantifying BrC absorption properties. We evaluated the results in other studies around the world and showed that the potential contribution of dust to non-black carbon absorption is much higher in the Asia-located studies (0.4%-16.8%) than in the Americas-located studies (<1.2%) and European studies (<2.3%). It suggests that the BrC absorption properties in the Asia-located studies resolved by previous studies are likely to be overestimated and need to be reexamined. Higher background dust concentrations and more frequent selection of PM\({}_{2.5}\) particle size are both natural and technical reasons for the higher dust absorption contributions in the Asia-located studies. We strongly recommend that future BrC studies in dust-influenced areas, including Asia, the Middle East, North Africa, and Central Australia, use the improved algorithm in this study or select PM, particle size to exclude as much as possible the effect of dust absorption.
## Data Availability Statement
The data at the SACOL site is available from [PERSON] et al. (2024). The MERRA-2 data (GMAO, 2015) is available from the National Aeronautics and Space Administration (registration required for access). The IMPROVE data ([PERSON] et al., 1994) is available from the Interagency Monitoring of Protected Visual Environments (registration required for access).
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* [PERSON] et al. (2021) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2021). Black Carbon and secondary brown carbon, the dominant light absorption and direct radiative contributions of the atmospheric aerosols over the Tibetan Plateau. _Geophysical Research Letters_, _48_(11), e2021 GL092524. [[https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) gl092524]([https://doi.org/10.1029/2021](https://doi.org/10.1029/2021) gl092524) | wiley | A New Method for Eliminating Dust Effects When Quantifying the Light Absorption Properties of Brown Carbon | Chenguang Tang, Pengfei Tian, Xinghua Zhang, Yingjing Lin, Xianjie Cao, Jiening Liang, Yan Ren, Jiayun Li, Jianzhong Xu, Lei Zhang, Tao Deng, Xuejiao Deng | https://doi.org/10.1029/2023gl102875 | 2,024 | CC-BY |
wiley/fb11de5d_03f0_4c7a_897a_465cab1bf01d.md | [PERSON] et al., 2000), but whether they originate in the lower mantle, and the extent to which they are purely thermal or thermochemical in nature is debated (e.g., [PERSON] et al., 2012; [PERSON], 2017).
In west Africa, the Cameroon Volcanic Line (CVL) is a linear volcanic chain stradling the continent-ocean boundary. Initially explained in the context of traditional plume-plate interactions, leading to inclusion with global deep-mantle hotspot catalogs ([PERSON] et al., 2003; [PERSON] & [PERSON], 2015), the CVLs lack of age progression has given rise to numerous subsequent alternative formation hypotheses. Such hypotheses include small-scale convection (e.g., [PERSON] & [PERSON], 2000; [PERSON] et al., 2011), shear zone reactivation (e.g., [PERSON], 1988), lithospheric delamination (e.g., [PERSON] et al., 2014; [PERSON] et al., 2012), and inflow of material from Ethiopia/Afar (e.g., [PERSON] & [PERSON], 1998). Whether CVL magmatism requires any contribution from the lower mantle is therefore uncertain.
Elsewhere, Madagascar Cenozoic magmatism has been postulated to arise from decompression melting associated with regional uplift, lithospheric thinning and intracontinental rifting with limited contributions from subplate thermal anomalies (e.g., [PERSON] et al., 2017; [PERSON] et al., 2016). However influx of plume material below the northern magmatic province specifically, has previously been suggested ([PERSON], 1998). Below recent magmatism in central Madagascar, the presence of thermal anomalies that may extend below the shallow mantle (>200 km) is unresolved (e.g., Cucciniello
Figure 1.— (a) Red/orange/yellow circles indicate P410s/PP410s/PKF410s piercing points; 947 seismograph stations are shown as blue triangles. Inset globe shows 2,778 unique earthquakes used for three RF data sets using the same colors. (b) Quaternary volcanoes and Cenozoic volcanic provinces shown with respect to the main geological features. White dashed circles: the Ethiopian (EP) and Kenyan (KP) topographic plateaus. AF, Afar; CM, Central Madagascar magmatism; CO, Comoros Islands, CVL, Cameroon Volcanic Line; MER, Main Ethiopia Rift; TD, Turkana depression; WRB/ERR, western/eastern rift branches of southern East African Rift (EAR).
et al., 2017; [PERSON] et al., 2017) because seismic station coverage has only recently expanded (e.g., [PERSON] et al., 2012; [PERSON] et al., 2011), meaning body wave constraints capable of resolving this issue are presently lacking.
Africa's deep mantle structure is characterized by the African Superplume (e.g., [PERSON] et al., 2002; [PERSON] et al., 2007). This broad, \(>\)500 km wide inclined upwelling appears to rise from the Large Low Velocity Province (LLVP) on the core-mantle boundary below southern Africa, reaching upper mantle depths somewhere below the East African Rift System (e.g., [PERSON], 2016; [PERSON] et al., 2011). This feature has been imaged frequently by seismic tomography (e.g., [PERSON] et al., 2008; [PERSON] et al., 1999, 2011), however more recent high resolution studies indicate the presence of multiple upwellings with a variety of depth extents (e.g., [PERSON] et al., 2021; [PERSON], 2011; [PERSON] et al., 2015). Tomographic images often suffer along-rappath smearing, underestimation of anomaly amplitudes, and are typically inadequate to allow discrimination between the competing effects of thermal and compositional variation on seismic wavespeed in the sublithospheric mantle. Consequently tomographic models have not been able to robustly constrain the thermochemical contribution to magmatism from mid-to-lower mantle depths (e.g., [PERSON] et al., 2015; [PERSON] et al., 2021; [PERSON] et al., 2019; [PERSON] et al., 2017; [PERSON] et al., 2010).
Petrological evidence for high \({}^{3}\)He/\({}^{4}\)He ratios in Ethiopia specifically (up to R/Rae=20), presents clear evidence for a deep mantle contribution to East African Cenozoic magmatism (e.g., [PERSON] et al., 1996; [PERSON] et al., 2006). More recent studies have presented elevated helium isotopic ratios observed in the southern East African Rift as evidence for a common lower mantle source for all East African magmatism ([PERSON] et al., 2014; [PERSON] et al., 2011). However, the relative proximity of proposed mantle upwellings (e.g., [PERSON] et al., 1998; [PERSON] et al., 2000), limited depth resolution, variable sampling strategies, and lithospheric contamination (e.g., [PERSON] et al., 2013; [PERSON], [PERSON], et al., 2006) limit the capability of such studies to conclusively decipher between competing models of African mantle upwellings ([PERSON], 2017). A high resolution, continent-wide investigation capable of constraining thermochemical contributions to African magmatism from below the upper mantle is therefore required.
Thermochemical conditions control the depth at which mantle materials undergo phases changes (e.g., [PERSON] et al., 2008), which cause seismic impedance contrasts of varying amplitude (e.g., [PERSON] & [PERSON], 1994; [PERSON] et al., 2018; [PERSON] & [PERSON], 1996). Compositional variations may also give rise to further phase transitions not predicted within a well-mixed, pyrotilic composition (e.g., [PERSON] et al., 2005; [PERSON] et al., 2010). Upon encountering impedance contrasts, seismic energy can convert from P-to-s and vice versa. Processing of seismic waveforms to extract receiver functions (RFs) highlights these conversions in the seismogram, and when stacked appropriately can elucidate the depth at which phase transitions occur. RFs, processed to target mantle transition zone (MTZ) depths and below, can therefore be used to probe the thermal and compositional impact of heterogeneous upwelling below Africa.
Regional studies of the African MTZ are legion (e.g., [PERSON] et al., 2006; [PERSON] et al., 2002; [PERSON] et al., 2019; [PERSON] et al., 2000; [PERSON] et al., 2011) and have been revisited periodically as new networks have been deployed. Continent-wide studies are scarce and primarily focus on single station stacks from few permanent observatory sites (e.g., [PERSON] & [PERSON], 2013). RF studies often show conflicting results, in part due to variable and/or inadequate time-to-depth corrections applied based on 1D radial Earth models or relative arrival-time tomographic models. Here we present a continent-wide compilation of P-to-s RFs (obtained from P, PP, and PKP phases) recorded at 947 publicly available African seismograph stations from 1990 to 2019 (Figure 1). We capitalize on the recent high-resolution absolute arrival-time P-wavespeed tomographic model for Africa of [PERSON] et al. (2021) to convert our RFs from time-to-depth, and compare against results from four other S-wavespeed models. This consistent continent-wide data processing approach enables us to compare MTZ discontinuity topography beneath regions of mantle upwellings across Africa. We consider whether RF data can provide evidence in support of multiple mantle plumes below the East African Rift System, and specifically if these upwellings manifest as two thermochemically distinct regions at MTZ depths and below. We also interrogate our continental RF data set for insights into the nature of mantle upwellings below magmatism in Madagascar and Cameroon.
### Mantle Discontinuities, Causes, and Topography
Important to investigating the variable impact of upwellings on mantle discontinuity structure below the African continent is an understanding of seismically observable diagnostics of mantle thermochemical heterogeneity sampled by RF techniques. While comprehensive reviews can be found in [PERSON] (1994), [PERSON] (2000), [PERSON] et al. (2013), and [PERSON] (2016), here we briefly summarize the characteristics and causal mechanisms of mantle discontinuities in the depth range \(\sim\)350-1,200 km. The dominant mineralogical component of mantle rock is olivine, making up 40%-60%. The most abrupt phase changes in the olivine system are expressed as the upper and lower discontinuities of the mantle transition zone at \(\sim\)410 km depth, where olivine transitions to wadsleyite, and at \(\sim\)660 km where ringwoodite transitions to bridamine and ferropericlase. We refer to these transition depths as 4410 and d660 respectively and their converted phases by phase names bounding the discontinuity depth from which they are converted (e.g., P410s, PP660s). The transition from wadsleyite to ringwoodite \(\sim\)520 km is thought to be more gradational and is only intermittently observed ([PERSON], 2001; [PERSON], 2013).
The olivine to wadsleyite transition at \(\sim\)410 km displays a positive Clapeyron slope such that the transition occurs at greater depth in regions of higher temperature, and promotes mass transfer (e.g., [PERSON], 1995). Clapeyron slope estimates center on \(\sim\)+3.0 MPa/K (e.g., [PERSON], 1994), but literature values can vary (\(\sim\)+1.5 to +4.0 MPa/K; [PERSON] et al., 1989; [PERSON] et al., 2004). In MTZ RF analyses, the P410s conversion typically manifests as a single peak arrival, but variations in transition sharpness/impedance contrast (reflected in signal peak broadness) can be affected by composition (including water content) and temperature (e.g., [PERSON] et al., 2018; Heffrich & Wood, 1996).
The lower MTZ phase transition is typically dominated by the transition from ringwoodite to bridgamine and ferropericlase at \(\sim\)660 km. It displays a negative Clapeyron slope of \(-\)2.5 MPa/K (e.g., [PERSON] et al., 2014) on average, although a range of values have been proposed (\(-\)0.5 to \(-\)3.9 MPa/K: [PERSON] et al., 2015; [PERSON] et al., 2005). The transition is thought to impede mass transfer, perhaps leading to ponding of warm upwellings and stagnation of downgoing slabs (e.g., [PERSON] et al., 1992; [PERSON] & [PERSON], 2011). However, a significant proportion of the upper mantle and MTZ may be composed of majorite garnet, which undergoes a transition to bridgamine in the depth interval \(\sim\)640-750 km. Garnet is thought to be particularly stable in warm and basaltic environments ([PERSON] et al., 2008). The majorite transition is described by a positive Clapeyron slope of \(\sim\)+1.3 MPa/K and therefore promotes mass transfer ([PERSON], 2002). Due to competing effects of both the olivine and garnet transitions, the d660 discontinuity may display greater topography and complexity than the d410, sometimes manifesting as two peaks within RFs (e.g., [PERSON] & [PERSON], 2008). Consequently, it also possesses powerful diagnostic potential for both temperature and compositional variation, particularly within upwellings ([PERSON], 2007; [PERSON] et al., 2016).
Despite the typically well-mixed nature of the mid-to-lower mantle, within the depth interval 800-1,200 km, impedance contrasts have been observed by multiple seismic methods ([PERSON] et al., 2017; [PERSON], 2016; [PERSON] et al., 2018). These discontinuities likely result from heterogeneity introduced by downgoing slabs or upwelling plumes, often linked to the presence of an entrained basaltic component ([PERSON] et al., 2017; [PERSON], 2016). A number of phase transitions within subducted material have been proposed, yet only a transition from stishovite to post-stishovite (e.g., [PERSON] et al., 2010) can occur outside of subduction settings. Therefore this phase transition has been invoked to explain observations of converted arrivals from mid-mantle depths below Iceland ([PERSON] et al., 2017) and southern Africa (e.g., [PERSON] et al., 2010). Intermittent observations of mid-mantle discontinuity structure can therefore be indicative of chemically distinct plume material, or small-scale entrained heterogeneity from a chemically distinct deep source. The mineral physics and seismological contributions discussed above provide the framework within which to interpret mantle upwellings and associated processes causing heterogeneous discontinuity structure below the African plate.
### Previous Geophysical Observations of African Mantle Discontinuities
The African continent is the ideal locale to study mantle upwellings because it has remained largely free of collisional tectonics for over 550 Myr ([PERSON], 2004). Underlying subducted slabs are therefore largely restricted to the lower-most mantle (e.g., [PERSON], 2000). Furthermore, the relatively stationary nature ofthe African plate since 30 Ma ([PERSON] & [PERSON], 1986; [PERSON] et al., 2015) presents the opportunity to investigate the uncertain role of directly underlying mantle thermochemical anomalies in the formation of up-lifted plateaus, rift and flood basalt related magmatism in the east (e.g., [PERSON] et al., 2003, 2008; [PERSON], 2017), the enigmatic CVL in the west (e.g., [PERSON], 1998; [PERSON] & [PERSON], 2000; [PERSON] et al., 2012), and volcanic provinces of Madagascar (e.g., [PERSON] et al., 2017).
Because sampling of African mantle discontinuity structure by reflected phases is piecemeal by nature (e.g., [PERSON] & [PERSON], 2013; [PERSON] et al., 2019), previous discontinuity observations are primarily derived from converted seismic phases. Prior African broad-scale converted phase studies utilized single station RF stacks. For example, [PERSON] and [PERSON] (2013) found intermittent observations of the wadsleyite to ring-woodite transition at \(\sim\)520 km depth with little correlation with thermal or compositional proxies. Meanwhile, [PERSON] et al. (2008) observed little correlation between MTZ thickness and sites of upwelling mantle across Africa.
A number of RF studies have focused on the MTZ structure below the northern East African Rift, centered around Ethiopia and Afar. [PERSON] et al. (2000) used single station RF stacks to propose a normal MTZ thickness below Afar, suggesting that any small positive thermal anomaly (100-150 K) is isolated in the upper mantle. By contrast, [PERSON] et al. (2006) imaged an uplifted d660 by \(\sim\)20-30 km below the eastern Ethiopian plateau but average values below the northwestern Ethiopian plateau, instead suggesting that a thermal anomaly of \(\sim\)300 K restricted to central and eastern Ethiopia may extend below 660 km. [PERSON] et al. (2011) revealed a regionally depressed 4410 by 30-40 km below the Main Ethiopian Rift (MER) and Afar indicating a positive thermal anomaly of \(\sim\)250 K in the MTZ. This study also observed variable d660 depths and interpreted these in light of compositional variations; Olivine-dominant below Afar, and garnet dominant below the MER. More recent MTZ studies imaged largely average MTZ thicknesses in Afar and central Ethiopia suggesting minimal thermal perturbations ([PERSON], [PERSON], et al., 2016; [PERSON] et al., 2015). These studies focused on local heterogeneity to invoke a stable melt layer caused by hydrous upwelling directly above the d410 in Afar ([PERSON] et al., 2015) and 20 km of MTZ thinning as evidence for a lower mantle plume stem isolated to below the western Ethiopian plateau ([PERSON], [PERSON], et al., 2016).
In the southern East African Rift, a thinned MTZ (30-40 km) and associated 200-300 K anomaly below the eastern rift branch is often interpreted as evidence for active upwelling from deeper mantle ([PERSON] & [PERSON], 2013; [PERSON] et al., 2000; [PERSON] et al., 2017). Normal thickness MTZ below the western rift branch and Tanzanian craton is inconsistent with present-day thermal anomalies rooted at/below the MTZ (e.g., [PERSON] et al., 2017). A significantly depressed d410 beneath rifts in Kenya and northern Tanzania (30-40 km) combined with a pervasively depressed d660, was interpreted as evidence for a warm, garnet dominant MTZ by [PERSON] et al. (2009). [PERSON] and [PERSON] (2013) suggested that processing RFs using 3D time-to-depth corrections leads to improved d660 depths compared to previous results, instead citing an uplifted d660 as compelling evidence for a connection of the African Superlump through the MTZ in this region.
Below southern Africa, while some small-scale discontinuity heterogeneity has been proposed (e.g., [PERSON], 2004; [PERSON] et al., 2009), a consensus is emerging that there is minimal thermal perturbation of the MTZ below cratonic regions and the most southerly African rifts ([PERSON] et al., 2002; [PERSON], [PERSON], et al., 2016; [PERSON] et al., 2018; [PERSON] et al., 2015). Elsewhere below the Cameroon Volcanic Line, [PERSON] et al. (2011) used MTZ RFs to suggest that thermal anomalies associated with magmatism are isolated to the upper mantle.
Particularly below regions of African Cenozoic magmatism, where reliable 3D time-to-depth corrections are paramount, quantitative comparisons between previous studies are hindered by the variable methodological approaches used in time-to-depth corrections and RF stacking, limited exploration of uncertainties in discontinuity depths and a lack of published data sets available electronically. We address these issues by applying a consistent, reproducible data processing approach at the continental-scale which facilitates quantitative interrogation of discontinuity depths and make our codes, data set and results available electronically. Furthermore, we allow more smoothing in our stacking procedure than previous regional studies, taking an approach to map and interpret broader-scale features away from the edges of our data coverage. Because previous studies lack agreement on the nature of the d660 discontinuity across Africa, we pay particular attention to this discontinuity in our study.
## 2 Data and Methods
### P-to-s RFs
Upon encountering an impedance contrast, seismic energy undergoes partial conversions from P-to-s and vice versa. We refer to the P-to-s conversions from the MTZ discontinuities as P410s and P660s. Pds phases are delayed with respect to the direct-P phase arrival due to slower S-wave propagation above the discontinuity. In the absence of dipping interfaces and significant anisotropy, Pds arrivals can be enhanced through deconvolution of the vertical from the radial seismogram producing RFs. This process removes the effect of the seismic source, instrument response and source side structure, with the resulting time series representing Earth structure along the raypath beneath the seismometer. RFs can subsequently be stacked to further enhance arrivals. We calculate RFs using the time domain iterative deconvolution method of [PERSON] (1999) using up to 200 Gaussian pulses of a user defined width. This is initially set to 5 s (i.e., a maximum frequency of 0.2 Hz), but we also explore the effect of increasing maximum frequency in later analysis.
### Seismic Data Processing
Our data download, processing and analysis is conducted using ObsPy ([PERSON] et al., 2010). Seismic data were sourced from the Incorporated Research Institutions for Seismology (IRIS), GeoForschungZentrum datacenter (GEOFON), French national datacenter (RESIF), and Institut de Physique du Globe de Paris datacenter (IPGP). Due to the lack of proximal tectonic environments generating large magnitude earthquakes over a broad backazimuthal range required for RF analysis, we extend our data coverage by calculating RFs not just from direct-P phases but also from PP and PKP phases. We use minimum earthquake magnitudes of 5.0 \(M_{\rm{w}}\), 6.2 \(M_{\rm{w}}\), and 6.2 \(M_{\rm{w}}\) at epicentral distance ranges of 30\({}^{\rm{o}}\)-90\({}^{\rm{o}}\), 100\({}^{\rm{o}}\)-130\({}^{\rm{o}}\), and 145\({}^{\rm{o}}\)-155\({}^{\rm{o}}\) for P, PP, and PKP RFs, respectively. We consider phases recorded at stations throughout Africa active in the time period 1990-2019.
Initially raw data are windowed from 25 s before, to 150 s after, the direct phase arrival, filtered from 0.01-0.2 Hz and RFs with a 0.2 Hz maximum frequency are calculated. The quality control (QC) steps detailed below are used to assess this initial data set. RFs that pass QC criteria are recomputed using a range of higher maximum frequencies (0.5-0.9 Hz), which are re-assessed against the same QC to check that RFs also pass at the higher frequency. We follow the strict QC procedures adopted by [PERSON] and [PERSON] (2016) but make a few minor adaptations. We exclude RFs in which the direct phase arrival does not occur within 2 s of zero (implying poor correlation between radial and vertical seismograms) and that when reconvolved with the vertical component reproduce less than 60% of the radial component seismogram. RFs are also removed in which pre- and post-peak amplitudes are greater than 40% and 70% of the direct phase arrival amplitude respectively. Lastly we impose signal-to-noise ratio (SNR) constraints on the vertical (SNR\(>\)2.5) and radial (SNR\(>\)1.75) component seismograms used in RF calculation. We define SNR as \(\frac{A_{signal}}{A_{noise}}\). \(A_{signal}\) is the root-mean squared amplitude for a 60 s window beginning at the direct phase arrival time using the ak135 reference model ([PERSON] et al., 1995). We include a preceding 5 s buffer and define \(A_{noise}\) as the root-mean squared amplitude for a 60 s window beginning 65 s before the predicted direct phase arrival time. Due to the strict nature of this automated QC procedure and the prevalence of sub-optimally deployed temporary networks yielding low SNR waveforms across Africa, we also employ a visual data inspection. Those vertical and radial component data that only failed QC through the SNR constraint are visually inspected when SNR values are greater than 1.25 for both components which resulted in the recovery of a further 2,971 good Pds, PPs, and PKPds RFs.
Figures S1-S3 show stacks of Pds, PPds, and PKPds RFs sorted by epicentral distance. Abundant interference from upper mantle and core diffracted phases with converted phases from MTZ discontinuities is visible at the limits of our initial epicentral distance ranges. We therefore further restrict the data used in subsequent stacking procedures to the ranges 40\({}^{\rm{o}}\)-90\({}^{\rm{o}}\), 100\({}^{\rm{o}}\)-125\({}^{\rm{o}}\), and 145\({}^{\rm{o}}\)-150\({}^{\rm{o}}\) for the Pds, PPds, and PKPds data sets respectively. This process yields 15,020 Pds RFs, 12,713 Pds RFs, and 741 PKPds RFs (28,474 RFs in total) from 2,778 unique events recorded at 947 stations across Africa. Where appropriate, we alsoutilize RF stacking in the slowness domain to differentiate between multiples and conversions which have shallower and steeper incidence angles respectively, compared to the direct phase. Slowness stacks for the entire data set and for the five notable sub-regions across Africa can be found in Figures S4 and S5.
### Time-to-Depth Corrections
At a given epicentral distance, the travel-time difference between the direct phase and P-to-s converted phases depends on the depth to the discontinuity and the wavespeed difference between the P and S phases above it. To extract discontinuity depths from delay times of converted phases, we must assume a mantle wavespeed structure. Previous African MTZ RF studies primarily used 1D reference Earth models such as ak135 ([PERSON] et al., 1995) or regional relative arrival-time tomographic models that place no constraint on the background mean velocity structure. Without adequately accounting for 3D absolute wavespeed structure, reliable interpretations from MTZ studies are restricted to MTZ thickness, typically less influenced by overlying velocities than absolute discontinuity depths. Conversely insights into both the thermal and chemical nature of the MTZ can be obtained by interpreting the behavior of the d410 and d660 separately. We therefore seek reliable absolute discontinuity depths, necessitating consideration of 3D absolute wavespeed structure.
Here, we compute time-to-depth corrections using the 1D radial model ak135 (Figures S6-S8) and five 3D mantle absolute wavespeed models. We utilize the most up-to-date P- and S-wavespeed models for Africa (AFRP20 and AF2019: [PERSON] et al., 2021; [PERSON] et al., 2020). Both AFRP20 and AF2019 are parameterized globally to 2660 km depth and specifically improve resolution beneath Africa by including data from temporary deployments across the continent. We also test three recent global S-wavespeed models (SL2013 SV, SEMUCB-WM1 and SGLOBerani: [PERSON] et al., 2015; [PERSON], 2014; [PERSON], 2013). We calculate estimated S-wavespeed anomalies for the AFRP20 model by using the relationship \(\delta V_{s}=\delta V_{r}\times\) (depth/2,891 + 2) and use the inverse relationship to calculate estimated P-wavespeed anomalies for S-wavespeed models. Our 3D depth corrections account for station elevations and the continental crust appropriate for each tomographic model. We use the results from the five 3D time-to-depth corrections to quantitatively assess the uncertainties in MTZ discontinuity depths (Figures S9-S13).
### Common Conversion Point Stacking
Raypath backazimuthal variation facilitates sampling of the MTZ over a broad area beneath a seismograph station (\(\sim\)500 km radius). Converted ray piercing points at 410 km depth for our African data set are shown in Figure 1. We employ the common conversion point stacking method of [PERSON] (1997) to account for the spread of conversion points beneath each station and enhance converted phase amplitudes. We define a grid of points spaced 0.5\({}^{\circ}\) in latitude and longitude and 2 km in depth throughout our study region (36\({}^{\circ}\)S-27\({}^{\circ}\)N, 0\({}^{\circ}\)E-52\({}^{\circ}\)E 60-1,300 km depth). RF energy is back-propagated along raypaths and stacked into proximal grid points at distances within two-times the Fresnel-zone half width (\(\Delta^{\text{HW}}\)) from the raypath using a normalized cubic spline weighting function defined by [PERSON] et al. (2011). The Fresnel zone half width is defined as:
\[\Delta^{HW}=\sqrt{\left(\frac{\lambda}{3}+z\right)^{2}-z^{2}} \tag{1}\]
where \(\lambda\) is the wavelength of a 10 s shear wave and \(z\) is depth. Summed stacking weights and the standard error are tracked throughout the grid volume and are subsequently used to normalize stacked amplitudes and highlight poorly constrained regions within the grid (following [PERSON] & [PERSON], 2016). Figure S6 shows the data coverage through the final summed stacking weights in the grid at 410 and 660 km depth. We can expect to constrain discontinuities in regions where the summed weight is above 2 and amplitudes are greater than twice the standard error from the mean. Given these criteria, depths of peak amplitudes within the CCP stacks are picked in the ranges 370-450 km and 620-700 km to highlight converted phases arriving from mantle transition zone depths. We limit our presentation of CCP stacking results to these regions shown on map plots and highlight picked depths as yellow dashes in cross sections plots (Figures 2-6). We refer to 3D time-to-depth corrected CCP stacks based on the tomographic model used as AFRP20-CCP, AF2019-CCP, SL2013-CCP, SEMUCB-CCP and SGLOBErani-CCP throughout the manuscript. In the Supplementary Material, following [PERSON] et al. (2019), we quantitatively assess the observed topography in the different 3D time-to-depth corrected CCP stacks (Figures S14-S17) as well as a stack for ak135 (ak135-CCP). Strong positive correlation between MTZ discontinuity topography typically indicates inadequate account of upper mantle wavespeed structure, which is expected to vary significantly below Africa (e.g., [PERSON] et al., 2021; [PERSON] et al., 2020). AFRP20-CCP achieves the best statistical performance of the resulting depths and is most similar to the average of the five 3D time-to-depth corrected CCP stacks (Figures S9-S12), so is the primary focus of results and interpretations below.
## 3 Results
### MTZ Topography and Thickness
African MTZ discontinuity topography and thickness from AFRP20-CCP is explored in maps (Figures 2 and 3) and cross section (Figure 4). By using five 3D tomographic models for time-to-depth corrections, we can isolate robust features of our CCP stacks, independent of the tomographic model used (Figure 5, Figures S9 and S10) and derive regional uncertainty estimates from the standard deviation of the d410 depth, d660 depth and MTZ thickness (Figures S11 and S12). The average uncertainties across Africa are 4.3, 6.8, and 3.9 km for d410 depth, d660 depth, and MTZ thickness, respectively. We highlight regions where AFRP20-CCP differs significantly from the average values across the five 3D time-to-depth corrected CCP stacks. We present discontinuity depths using a discrete color scales of 5 km for all map plots in line with quantitative uncertainties.
Below Ethiopia (ETH), the regional d410 depth is depressed at \(\sim\)417 \(\pm\) 5.0 km with maximum depths of \(\sim\)420-435 km below the Main Ethiopian Rift (MER), adjacent rift flanks and Afar (Figures 2 and 4). Western ETH displays normal d410 and d660 depths. Regional d660 depths in AFRP20-CCP are \(\sim\)657 \(\pm\) 7.2 km, yet below the MER and eastward, d660 depths are \(\sim\)645-655 km. However, the average d660 depths across the five 3D time-to-depth corrected CCP stacks favors a depressed d660 in the southeast (Figures S10-S11). ETH shows a regional MTZ thickness of \(\sim\)240 \(\pm\) 3.4 km with strongest thinning of \(\sim\)25-30 km below
Figure 2: Maps of d410 (a) and d660 (b) discontinuity depths within AFRP20-CCP using RF data containing maximum frequencies of 0.2 Hz. Regions are shown only where stacking weight is greater than 2 (Figure S6) and relative amplitude is greater than two standard error. Regional discontinuity depths are presented for the five regions outlined in white boxes throughout the manuscript. CAM, Cameroon; EAR, East African Rift; ETH, Ethiopia; MAD, Madagascar; SAF, Southern Africa.
Afar, the MER, adjacent rift flanks and in the southwest, while the northwestern Ethiopian plateau shows normal MTZ thickness (Figures 3 and 5). Below the southern East African Rift (EAR), AFRP20-CCP shows a depressed regional d410 of \(\sim\)421 \(\pm\) 4.1 km depth with maximum depressions of \(>\)30 km in the northeast (Figures 2 and 4). The regional d660 depth below EAR is also depressed at \(\sim\)667 \(\pm\) 5.8 km, with much of the region exhibiting \(\sim\)10 km depression of the d660. EAR displays a regional MTZ thickness of \(\sim\)244 \(\pm\) 3.0 km with the strongest zones of thinning (\(>\)20 km) confined to the northeast (Figures 3 and 5).
Below southern Africa (SAF), the regional d410 depth is \(\sim\)407 \(\pm\) 3.9 km, while the regional d660 depth in AFRP20-CCP of \(\sim\)663 \(\pm\) 6.4 km (Figures 2 and 4) differs significantly from the average across five 30 time-to-depth corrected CCP stacks of \(\sim\)653 km (Figures S10 and S11). MTZ thickness is \(\sim\)256 \(\pm\) 5.1 km below SAF. Madagascar (MAD) shows depressed regional d410 and d660 depths of \(\sim\)415 \(\pm\) 5.8 km and \(\sim\)669 \(\pm\) 10.5 km respectively (Figure 2), however stacking amplitude loss, incoherency, or error increases toward the north likely contributing to significant uncertainty, particularly in d660 depths (Figures S10 and S11). MAD displays some apparent thinning of the MTZ (\(>\)10 km) below the southern, central and northern zones (Figures 3 and 5). None of the six CCP stacks show a coherently stacked d410 below Cameroon (CAM: Figure 2, Figure S9). AFRP20-CCP shows a regional d660 depth of \(\sim\)671 \(\pm\) 7.7 km below CAM (Figure 2) but differs significantly from the average across the five 3D time-to-depth corrected CCP stacks of \(\sim\)658 km (Figures S10 and S11).
Figure 6 and Figures S18 and S19 explore the sensitivity of d410 and d660 depths to RF maximum frequency. Across Africa, d410 depths are largely insensitive to RF frequency content (Figure S18). Below EAR, the d660 peak splits toward higher frequencies, causing variability in d660 depth picks. Maximum amplitude peaks in \(F_{\rm max}\) = 0.2 Hz stacks show depths of greater than 665 km (Figure 6--A). At higher frequency, the maximum amplitude peak is the shallower of the two peaks, resulting in picks at depths of less than 660 km (Figure 6--B), while the marginally weaker peak occurs at depths around \(\sim\)680 km (Figure 6). Below ETH 4660 depths do not exhibit significant sensitivity to RF maximum frequency because the depth to the maximum converted phase amplitude is consistently less than 660 km (Figure 6). Indeed the regional d660 depth for ETH at 0.2 and 0.9 Hz maximum frequency is \(\sim\)657 km, while beneath EAR regional d660 depths decrease from 667 to 661 km with increasing maximum RF frequency.
### Mid-Mantle Observations
We further interrogate AFRP20-CCP for mid-mantle conversions, selecting peak amplitudes in the depth range 960-1,100 km (Figure 7), based on the abundance of scatters previously observed away from subduction zone settings at these depths (e.g., [PERSON] et al., 2017; [PERSON], 2016). Because low amplitude seismic conversions from mid-mantle depths often suffer interference from multiplets, we assess whether observed peaks in AFRP20-CCP are robust by returning to the RF data themselves to compute 15 local depth and slowness stacks for both Pds and PPds data sets (Figures S20-S29). Only well-sampled regions are chosen to maximize the data within each local stack that indicate similar discontinuity depths. Following [PERSON] et al. (2017), we adopt a traffic-light system indicating our confidence that a seismic conversion represents mid-mantle structure rather that an interfering multiple, where red indicates low confidence, yellow indicates medium confidence, and green indicates high confidence. Our approach focuses on confirming the identification of mid-mantle conversions; we cannot confirm or deny the presence of mid-mantle conversions away from good data coverage.
Figure 3.— Map of mantle transition zone (MTZ) thickness (d660 - 4410) within AFRP20-CCP (Figure 2). Violet lines: outlines of Archean cartons. TC, Tanzania carton. Black triangles: Quaternary volcanoes. Regions are shown only where both d660 and d410 converted arrivals are significant. Regional acronyms as in Figure 2. GM, Global mean.
Robust conversions appear below EAR at a depth of \(\sim\)1,025 km and below southern Africa at \(\sim\)1,056 km (R8, R15--Figure 7). The corresponding high confidence Pds depth and slowness stack for region R8 is shown in Figure 8. EAR hosts a number of other regions with possible observations at 1,018-1,080 km depth (R5, R6, R7, R9, R10). We note that in our broader regional stacks (Figures S4 and S5), the EAR stack including 2,902 RFs is the only stack to indicate a robust mid-mantle conversion, suggesting a discontinuity might be more widespread here. Possible mid-mantle conversions may also exist in R3, R12, and R13 below ETH and MAD respectively. Elsewhere, although positive amplitude peaks exist in AFRP20-CCP above two standard error, these are more likely the result of multiples from shallow structure (see slowness stacks in Figures S20-S29).
## 4 Discussion
### Robustness of Discontinuity Depths
Significant differences in discontinuity depths between 3D time-to-depth corrected CCP stacks, computed using identical RF data (i.e., the same maximum frequency content), result directly from the 3D tomographic corrections applied, and are the primary source of uncertainty in our MTZ discontinuity depths. 3D time-to-depth corrections are further influenced by our imposed relationship between \(\delta V_{s}\) and \(\delta V_{v}\), variable data coverage, resolving power, and inherent sampling differences between shear and compressional wavesped tomographic models. Straightforward assessment of uncertainties in tomographic models is challenging. However, tomographic models typically underestimate wavespeed anomaly amplitudes leading to under correction of discontinuity depths in time-to-depth corrections. In this instance, discontinuities are not shifted shallow/deep enough so appear deeper/shallower than their true depth (see detail in Supplementary Material and Figures S14-S17). Quantitative analysis (see Supplementary Material) shows that our 3D time-to-depth corrections within CCP stacks remove a large degree of the correlated discontinuity topography present in ak135-CCP, where both MTZ discontinuities are strongly uplifted below SAF and strongly depressed below EAR and ETH (Figures S9 and S10). Before interpreting discontinuity topography, we discuss the extent of under-or-over correction, and quantitatively consider the reliability of our discontinuity depth results.
Figure 4: Along the profile (a), waveform cross-sections (up to 0.2 Hz) through AFPR20-CCP (b) and AF2019-CCP (c). Yellow ticks: depths of maximum amplitudes of MTZ discontinuities within regions where peaks are significant. Strong negative peaks in the MTZ often result from coherent stacking of surface multiples. d660 depths within AFRP20-CCP (solid) and AF2019-CCP (dashed) are shown below (d). EAR, East African Rit; ETH, Ethiopia; SAF, Southern Africa.
Because previous studies in southern Africa find little thermal MTZ perturbation (e.g., [PERSON] et al., 2002; [PERSON] & [PERSON], 2013; [PERSON] et al., 2018) below cool cratonic lithosphere (e.g., [PERSON] et al., 2021; [PERSON] et al., 2020), we can test under-or-over correction of MTZ topography within 3D time-to-depth corrected CCP stacks beneath SAF and extend these inferences throughout other well sampled regions of Africa. For example, within AF2019-CCP, similar to ak135-CCP, regional d410 and d660 depths (\(\sim\)399 and \(\sim\)645 km) are uplifted below SAF, and are therefore likely under corrected in this region (Figure 4, Figures S9 and S10). Conversely in AFRP20-CCP, uplifted regional d410, but the slightly depressed regional d660 below SAF (\(\sim\)407 and \(\sim\)663 km) suggests that d410 depths are under corrected while the d660 depths may be slightly over corrected. These inferences are consistent with damped least squares tomographic models constrained predominantly by shallowly penetrating shear waves in AF2019 resulting in lateral smearing, and deep diving compressional waves in AFRP20 resulting in vertical smearing ([PERSON] et al., 2021; [PERSON] et al., 2020).
3D time-to-depth corrections, in regions where the upper mantle wavespeed is slow, shift apparent MTZ discontinuity depths shallower (e.g., Figure S14). Accounting for potential under correction of d410 depths in both AFRP20-CCP and AF2019-CCP would reduce the depression of the d410 below EAR and ETH. For the d660, accounting for under correction within AF2019-CCP and slight over correction within AFRP20-CCP leads to convergence of depth estimates (improved similarity across Figures 4b-4d, Figure S10), showing a depressed d660 beneath EAR and an uplifted d660 beneath ETH. Because the regional d660 discontinuity depths derived from the average of the five 3D time-to-depth corrected CCP stacks below ETH and EAR are slightly uplifted and depressed respectively (658.6 and 665.8 km), this observation is likely robust rather than an artifact of our 3D wavespeed corrections. Additionally, under correction of the d410 and over correction of the d660 could result in artificial MTZ thinning below areas of warm upper mantle anomalies.
Figure 5: Maps of mantle transition zone (MTZ) thickness (d660–d410) within a k135-CCP (a), AFRP20-CCP (b), AF2019-CCP (c), SL2013-CCP (d), SEMUCB-CCP (e), SGLOBErani-CCP (f). Regions are shown only where both d660 and 4410 converted arrivals are significant. The corresponding plots for d410 and d660 depth as well as the mean and standard deviation d410 and d660 depths derived from the five 3D time-to-depth corrected CCP stacks are included in the Supplementary Material (Figures S9–S12), Violet lines: outlines of Archean cartons. TC: Tanzania carton. Black triangles: Quaternary volcanoes. CAM, Cameroon; EAR, East African Rift; ETH, Ethiopia; MAD, Madagascar; SAF, Southern Africa.
However, the normal MTZ thickness observed below the northwest Ethiopian plateau provides confidence that this effect is negligible below well instrumented regions.
The imposed relationship between \(\delta V_{s}\) and \(\delta V_{p}\) anomalies used in time-to-depth correction may also be a significant source of error, particularly in regions of highly heterogeneous upper mantle structure. One such region is the Main Ethiopian Rift (MER), in which a significant portion of the crust and upper mantle is melt rich (e.g., [PERSON] et al., 2010; [PERSON] et al., 2005). S-wavespeeds are significantly more sensitive to the surface of the mantle.
Figure 6.— Along the profile (a), waveform cross-sections through AFRP20-CCP of increasing maximum RF frequency from 0.2–0.9 Hz (b–e). Yellow ticks: depths of maximum amplitudes of MTZ discontinuities where peaks are significant. Magenta ellipses (A, B) highlight specific features referred to in the text, d660 depth comparison (f) within AFRP20-CCP of increasing maximum frequency (\(F_{\rm max}=0.2\) Hz: black, \(F_{\rm max}=0.5\)–0.9 Hz gray lines, dark to light). The yellow region highlights the difference between d660 depth using RF \(F_{\rm max}=0.2\) and 0.9 Hz. EAR, East African Rift; ETH, Ethiopia.
tive to the presence of melt than P-wavespeeds (e.g., [PERSON] & [PERSON], 2000). Consequently when using the AFRP20 tomographic model, the imposed conversion to \(\delta V_{S}\) anomalies does not capture the full extent of slow S-wavespeed anomaly amplitudes observed along the MER in high resolution upper mantle studies (\(\delta V_{S}\approx-11\%\); [PERSON] et al., 2019; [PERSON] et al., 2016). Here, shallow mantle \(\delta V_{S}\) anomalies are \(\approx\)2.7\(\times\) the highest \(\delta V_{P}\) anomaly in AFRP20. We estimate a melt rich upper 120 km below the MER may cause a further depression of up to 9 km on MTZ discontinuities. True discontinuity depths below the MER may therefore be shallower than imaged in AFRP20-CCP. While, melt is confined to a narrow region below the MER (e.g., [PERSON] et al., 2016), our two Fresnel-zone half width smoothing criteria during CCP-stacking means this source of uncertainty may have a broader footprint at MTZ discontinuity depths. In the relatively melt poor southern EAR ([PERSON], 2020), we expect this source of error to be less significant. Consequently, considering the distribution of melt in the upper mantle further supports the observed variable behavior of the d660 between ETH and EAR.
Furthermore, in the lower lithosphere of the Tanzanian craton (\(\geq\)90-135 km depth), AFRP20 shows P-wavespeed anomalies are slow ([PERSON] et al., 2021), while S-wavespeed anomalies remain fast to significantly greater depth (\(\sim\)175 km e.g., [PERSON] et al., 2012; [PERSON] et al., 2019; [PERSON] et al., 2003). If \(\delta V_{S}\) and \(\delta V_{P}\) anomalies are anti-correlated in this region, our assumed scaling between them breaks down. However the resulting estimated uncertainty is less than the vertical resolution (2 km) of our CCP stacks when using the AF2019 tomographic model ([PERSON] et al., 2020).
To minimize the impact of data noise in our CCP stacks, we limit our interpretations to broad regional features, rather than shorter wavelength features at the edge of data coverage. To avoid miss-identification of maximum amplitude peak in a given depth interval which may not be derived from the true discontinuity depth, we only report discontinuity depths from the low frequency stacks (up to 0.2 Hz) that do not exhibit double peaked arrivals. In the cases where high frequency stacks exhibit a double peaked nature, we take the utmost care when interpreting discontinuity depths.
### MTZ Discontinuity Structure Below Africa
#### 4.2.1 African MTZ Thickness
Our results show a strong correlation exists between locations of African Cenozoic magmatism and a locally thinned MTZ, particularly beneath ETH and EAR (Figures 3 and 5), in contrast with results from the broad-scale study of [PERSON] et al. (2008). Extending our observed correlation to regions at the edge of our data coverage across Cameroon, northern Madagascar, southwest ETH and western EAR may be less robust however (see Sections 4.2.4 and 4.2.5, Figures S11 and S12). MTZ thinning of \(\sim\)25-30 km occurs below Afar and extends to the southwest below the MER and adjacent rift flanks, while the northwestern Ethiopian plateau is not underlain by a significantly thinned MTZ. Our results conflict with previous RF studies that suggest MTZ thinning is restricted to beneath the northwestern Ethiopian plateau ([PERSON], [PERSON], et al., 2016), the MTZ thickens toward the southwest ([PERSON] et al., 2011), or observe little MTZ thinning throughout ETH ([PERSON] et al., 2000; [PERSON] et al., 2015). Only the work of [PERSON] et al. (2011) and [PERSON] et al. (2015) consider the impact of 3D absolute wavespeed heterogeneity on discontinuity depths beneath ETH (using the tomographic model of [PERSON] et al., 2006). However, our results migrated from time-to-depth using five different tomographic models show broad agreement beneath ETH (Figure 5).
Figure 7.— Map of mid-mantle observations in AFRP20-CCP (up to 0.2 Hz). Colored regions highlight depths of significant peaks at mid-mantle depths 960–1.100 km. Labeled regions are outlined based on confidence of a true Pfs/Pfs conversion within the CCP stack based on slowness analysis (see example in Figure 8). High confidence result: green, intermediate yellow, low: red. Dashed blue regions show location of previous mid-mantle discontinuities observed using using PTP precursors [PERSON] et al. (1995—A) and using SKSdp phases [PERSON] et al. (2010—B). Gray dashed lines mark the \(\delta V_{P}=-0.5\%\) contour in the AFRP20 tomographic model ([PERSON] et al., 2021).
MTZ thinning of \(>\)20 km also underlies northeastern EAR although magmatism occurs significantly offset to the east of the thinned MTZ (Figures 3 and 5). Because strong cratonic lithosphere may extend beyond the mapped surficial Archean terranes (e.g., Figure 3), this offset may indicate deflection of upwelling material around the Tananzanian craton ([PERSON] & [PERSON], 2013). Our results broadly agree with previous studies that have suggested MTZ thinning below northeast Tanzania and the eastern rift branch of the EAR reflects active upwelling while the lack of distinct thinning on western rift shows upwelling is likely to be more passive ([PERSON] & [PERSON], 2013; [PERSON] et al., 2000; [PERSON] et al., 2017). MTZ thinning largely underlying Cenozoic magmatism in Afar, the MER and Kenyan eastern rift branch implies that magmatism is influenced by processes at MTZ depths or below. Elsewhere, below SAF, the average MTZ thickness across the five 3D time-to-depth corrected CCP stacks corroborates previous results ([PERSON] et al., 2002; [PERSON], [PERSON], et al., 2016; [PERSON] et al., 2018; [PERSON] et al., 2015) indicating little MTZ thickness perturbation beneath this region but is subject to significant uncertainty (Figure S12).
#### 4.2.2 African MTZ Temperature
Given robust MTZ discontinuity depths, MTZ temperature anomalies can be estimated using d410, d660 depths and MTZ thickness (e.g., [PERSON] et al., 2008). We favor estimates based on d410 depths and MTZ thickness because d660 depths are sensitive to both temperature and composition (e.g., [PERSON] et al., 2006). Similarity between d410 depth and MTZ thickness derived temperature anomaly estimates indicates regional d410 depths obtained from 3D tomographic corrections are reliable, thermal anomalies traverse the MTZ, and the d660 is not controlled by the garnet transition, that is, a prolific composition dominates. We calculate temperature estimates based on the depth to the maximum amplitude peak observed for both MTZ discontinuities within AFRP20-CCP for the lowest maximum frequency (up to 0.2 Hz), because thermal anomaly estimates based on higher maximum frequency CCP stacks yield variations over unrealistically short length-scales. While the absolute value and range of thermal anomaly estimates is highly sensitive to the Clapeyron slopes used to calculate them, the spatial pattern remains unchanged (in Figure 9, we assume average values: \(\delta P/\delta T_{\rm d410}=3.0\) MPa/K and \(\delta P/\delta T_{\rm d400}=-2.5\) MPa/K following [PERSON], 1994; [PERSON] et al., 2014). Analysis presented in Section 4.1 suggests that these thermal anomaly estimates are likely to represent an upper bound, because not all 3D wavespeed-induced topography may have been removed. By propagating a maximum regional d410 depth uncertainty of \(\sim\)5.8 km (in CAM, MAD) through the relationships used to estimate temperature anomalies, we anticipate uncertainties of \(<67\) K using average Clapeyron slope values. The most sensitive Clapeyron slope would yield maximum uncertainties of \(>130\) K.
In ETH, peak MTZ thermal anomalies below the MER and adjacent rift flanks are \(\sim\)100-150 K across both estimates, while below Afar, peak thermal anomalies vary from \(\sim\)150-275 K (Figure 9). The median MTZ
Figure 8: Depth (a) and slowness (b) stack for 163 Pds RFS whose piercing points at 1,000 km depth fall within R8 (see Figure 7). RF max frequency is 0.2 Hz. (a) Depth stack amplitudes are multiplied by five and 20 below 150 and 900 km, respectively. Depth conversion uses the AFRP20 tomographic model ([PERSON] et al., 2021). The depth of high amplitude positive peaks at and below MTZ depths are labeled. (b) Predicted converted Pds arrivals have negative slowness (solid line), multiples have positive slowness (dashed line) w.r.t. direct-P phase. The number of RFS included in the stack is given in the upper left. A positive high confidence amplitude conversion is observed on the predicted slowness line at \(\sim\)106 s (violet dashed circle).
thermal anomaly across ETH is slightly elevated ranging from \(\sim\)60-76 K. Further south beneath EAR, median thermal anomalies are significantly higher when using the d410 estimate (\(\sim\)122 K) compared to the MTZ thickness proxy (\(\sim\)35 K). Correspondingly, MTZ thicknesses predict a maximum thermal anomaly of \(\sim\)175 K in this region while the d410 depths predict \(>\)425 K. The differences between the two predictions may suggest the d660 in EAR is affected by non-olivine phase transitions (discussed further in the next Section). Evidence from our five CPC stacks and their corresponding 3D wavespeed models indicates that these observed differences are not likely the result of inaccurate 3D time-to-depth correction or thermal anomalies that do not traverse the MTZ. Median regional MTZ thermal anomalies for SAF are approximately equal across both estimates (Figure 9). We hesitate to interpret thermal anomalies in CAM and MAD where data coverage and thus results are highly variable.
Figure 9 shows that maximum MTZ temperature anomalies reside beneath EAR and are significantly higher than those below ETH. Previous studies of the southern East African Rift consistently reveal a 200-350 K thermal anomaly below the eastern rift branch ([PERSON] et al., 2009; [PERSON] & [PERSON], 2013; [PERSON] et al., 2000; [PERSON] et al., 2017) corroborated by our results. Meanwhile in Ethiopia previous studies do not provide a consensus on MTZ thermal anomalies because average MTZ thicknesses imaged by [PERSON] et al. (2000), [PERSON] et al. (2015), and [PERSON], [PERSON], et al. (2016) below Afar and central Ethiopia suggest minimal thermal perturbations, while [PERSON] et al. (2006) and [PERSON] et al. (2011) suggest significantly greater thermal perturbations of \(\sim\)250-300 K below central/eastern Ethiopia and Afar. We suggest that our observation of higher thermal anomalies in the MTZ below EAR compared to ETH is robust because both the d410 is deeper and MTZ thinner in EAR, compared to ETH, across the five 3D time-to-depth corrected CCP stacks (Figures S11 and S12). At shallower depths, however, periodically determined temperature estimates show the modest maximum temperature peak resides below ETH (+140 K at present beneath Afar: [PERSON] et al., 2012), and the slowest absolute upper mantle seismic wavespeeds (e.g., [PERSON] et al., 2021) exist below the MER and adjacent western Ethiopian plateau. In Section 4.4, we explore whether this anti-correlation between the location of highest temperatures in the East African upper mantle compared to the MTZ could be explained by additional heating of the Ethiopian upper mantle or a lateral influx of warm material to the Ethiopian upper mantle.
Figure 9: Maps of estimated temperature anomalies within the mantle transition zone (MTZ) derived from AFRP20-CCF (Figures 2 and 3). Discontinuity depths are converted to pressure using PREM ([PERSON], 1981). (a) Temperature anomaly derived from d410 depths. We assume the temperature anomaly where d410 depth equals 410 km is zero. We assume an average value for the d410 Clapeyron slope of \(\delta\mathcal{P}/ST_{\text{d40}}=3.0\) MPa/K ([PERSON], 1994). (b) Temperature anomaly derived from MTZ thickness. We assume the temperature anomaly is zero where MTZ thickness is 250 km. We use the same Clapeyron slope for the d410 as in (a) and an average 4660 Clapeyron slope of \(\delta\mathcal{P}/ST_{\text{d40}}=-2.5\) MPa/K ([PERSON] et al., 2014) for the olivine transition. WEF: Western Ethiopian plateau, other regional acronyms as in Figure 2.
#### 4.2.3 East African MTZ Composition
The depressed d410 underlain by an uplifted, frequency insensitive d660 below the MER and eastward (>10 km: Figures 2, 4, and 6), indicates a warm MTZ dominated by phase transitions within the olivine system. Approximately average d660 depths below the adjacent western Ethiopian plateau indicate that the lower MTZ lacks significant thermal or compositional heterogeneity here (Figure 2). Both of these observations from AFRP20-CCP agree with prior work of [PERSON] et al. (2006). Unlike [PERSON] et al. (2011), we do not observe any evidence for deepening of d660 depths to the southwest beneath ETH across the five 3D time-to-depth corrected CCP stacks (Figures S11 and S12), and therefore do not interpret any compositional heterogeneity here.
Below EAR, the d410 depression of up to 30 km (Figures 2 and 4), underlain by a depressed d660 at lower frequencies (>10 km: Figure 6--A) with double-peaked arrivals at higher frequencies (Figure 6--B), is consistent with a majorite garnet transition around the d660 (e.g., [PERSON] et al., 2006). The observed behavior of the d660, particularly at lower frequencies, agrees with prior work using RFs and reflected phase observations in EAR ([PERSON] & [PERSON], 2013; [PERSON] et al., 2009). While [PERSON] and [PERSON] (2013) used 3D time-to-depth corrections from a relative arrival-time tomographic model to image an uplifted d660 in EAR, we suggest that depression of d660 in EAR is robust because it is consistently imaged across our five 3D time-to-depth corrected CCP stacks utilizing absolute wavespeed tomographic models (Figures S10 and S11). The majorite garnet transition is expected to occur in anomalously warm regions ([PERSON], 2002), corroborating the greater depression of the d410 observed below EAR than below ETH (Figures 2 and 4). Both d660 depression (e.g., [PERSON] et al., 2016) and double-peaked arrivals (e.g., [PERSON], 2008) have been interpreted as garnet signatures within upwellings elsewhere. Within Section 4.4, we investigate whether these two regions of differing MTZ behavior may indicate two mantle upwellings of distinct thermochemical nature lie beneath the East African Rift System.
#### 4.2.4 Cameroon
The regional depth stack for Cameroon shows a weak converted arrival from the d410 (Figure S4). In the CCP stacks beneath Cameroon, the stacked d410 converted arrival is patchy and incoherent (Figure 2, Figure S9), despite >500 piercing points sampling 410 and 660 km depths, reasonable stacking weights (e.g., Figure 1, Figure S6) and the ability to account for backazimuthal discontinuity topographic variations. This is all the more striking, as the d660 converted arrival has high amplitudes in depth, slowness and CCP stacks (Figure 2, Figures S4 and S10). However median d660 depths vary widely (649-671 km: Figures S10 and S11) and exhibit significant uncertainty, likely reflecting poorly resolved upper mantle wavespeeds away from dense seismic station coverage. Consequently, we hesitate to interpret broad-scale d410 and d660 patterns beneath Cameroon.
The small coastal region, below which both d410 and d660 depths are reported, shows an apparently thinned MTZ by 20-30 km (Figures 3, 5, and 10, Figure S12), collocated with the most recent magmatism along the CVL at Mount Cameroon ([PERSON], 1985) and the region of uncertain d660 depth observed by [PERSON] et al. (2011). High frequency CCP stack cross sections (Figure 10f--A) indicate double peaked behavior around both the d410 and d660 here, meaning multiple arrivals may interfere to produce depressions of both d410 and d660 in the low frequency stack (Figure 10e). Notably, very low positive d410 converted arrival amplitudes are often found below strong negative peaks (Figures 10b and 10e--B), but overlying negative arrivals do not appear to overprint any positive arrivals from the d410 within higher frequency stacks (Figures 10c and 10f). It remains unclear from slowness stacking whether these negative arrivals are multiples or conversions (Figure S4).
The normal amplitudes observed for the d660 converted arrival suggest the weak d410 converted arrival amplitudes are not due to incoherent stacking due to poor time-to-depth corrections. More appealing explanations for low d410 converted arrival amplitudes include a gradational discontinuity, incoherent stacking induced by short-wavelength discontinuity topography, or a low impedance contrast. A water-rich MTZ (e.g., [PERSON] et al., 2018) or basaltic accumulation (e.g., [PERSON] et al., 2019) have recently been invoked to explain decreased d410 impedance contrasts yet mechanisms to achieve this below the CVL are likely to require a lower mantle contribution. [PERSON] et al. (2011) found little evidence ofMTZ thinning along the CVL, so favored a upper mantle thermal convection cell, adjacent to the Congo craton, as a causal mechanism for CVL magmatism. Regional tomographic models also do not support a low wavespeed anomaly across the MTZ ([PERSON] et al., 2015; [PERSON] et al., 2010), yet continental and global scale images do not rule out a lower mantle contribution to magmatism (e.g., [PERSON] et al., 2021; [PERSON] et al., 2019; [PERSON] & [PERSON], 2015). The complex 4410 and d660 behavior exhibited below Cameroon in this study is also not easily reconciled with a causal mechanism for the CVL solely isolated in the upper mantle, but improved data coverage in the region is required to draw more definite conclusions.
Figure 10: Waveform cross-sections through AFRF20-CCP in Cameroon (a and d) and Madagascar (g and b) using maximum RF frequencies of 0.2 Hz (b, e, h, and k) and 0.5 Hz (c, f, i, and l). Yellow ticks: depths of maximum amplitudes of significant d660 and d410 converted arrivals. Magenta ellipses (A, B, C) highlight specific features referred to in the text.
#### 4.2.5 Madagascar
As far as we have been able to determine, this study is the first to illuminate MTZ discontinuity structure below Madagascar using converted phases. AFRF20-CCP reveals depressed median d410 and d660 depths with moderate MTZ thinning (\(\sim\)415, \(\sim\)669, \(\sim\)246 km, respectively; Figures 2, 3, and 10). Rather than interpret d410 depression and MTZ thinning at the northern and southern tips of Madagascar, we focus on central Madagascar where AFRF20 displays adequate upper mantle horizontal resolution ([PERSON] et al., 2021) and high-quality RF data coverage is good (Figure 10, Figure S6).
Below central Madagascar, we observe a depression of both d410 and d660 (\(\sim\)10-15 km) centered at \(\sim\)17-19\({}^{\circ}\)S (Figures 2, 3, and 10--C). MTZ thinning and depression of both d410 and d660 in central Madagascar is observed across the majority of our five 3D time-to-depth corrected CCP stacks (Figure 5, Figures S9 and S10) although this region exhibits moderate uncertainties (Figures S11 and S12). Similarly to EAR, depression of the d410 and d660 may indicate a warm upwelling crossing the MTZ in which the d660 is dominated by the garnet transition (e.g., [PERSON], 2002), rather than the olivine transition. This is consistent with a relatively narrow slow wavespeed anomaly extending to \(>\)1,000 km depth within AFRF20 ([PERSON] et al., 2021). While this may imply that central Madagascar Cenozoic magmatism is underlain by a mantle upwelling sourced below the MTZ, a significant thermal anomaly is not necessary to explain central Madagascar magmatism from a geochemical perspective ([PERSON] et al., 2017).
### Implications of Mid-Mantle Discontinuity Observations
Depth and slowness stacks indicate that EAR is underlain by several potential mid-mantle discontinuities, the most robust of which is observed at \(\sim\)1,025 km depth in region R8 (Figures 7 and 8, Figures S5, S20-S29). Mid-mantle discontinuities below EAR are in a similar region to those identified using PP' precursors ([PERSON] et al., 1995). The region coincides with distinct slow wavespeeds within AFRF20 ([PERSON] et al., 2021) at \(\sim\)1,000 km depth, which is the likely the mid-mantle expression of the African Superplume (Figure 7). Slow wavespeeds also correlate with intermediate confidence discontinuity observations below ETH and MAD at mid-mantle depths (regions R3, R12, R13).
SAF is also underlain by a high confidence result (R15), proximal to mid-mantle discontinuities previously identified using SKSdp RFs ([PERSON] et al., 2010). However R15 does not correlate with slow wavespeeds at 800-1,200 km depth in AFRF20 ([PERSON] et al., 2021), perhaps indicating other causal mechanisms beyond upwelling anomalous material need to be considered. Although the top of the African LLVP may underlie southern Africa, its is likely limited to below \(\sim\)1,500 km depth (e.g., [PERSON] & [PERSON], 2016; [PERSON] et al., 2011).
Several studies have suggested that the presence of mid-mantle discontinuities requires a basaltic component (e.g., [PERSON] et al., 2017; [PERSON], 2016), since phase changes are not predicted within a pyrolitic composition at mid-mantle depths (e.g., [PERSON] et al., 2005). To explain observations below both subduction zones and regions of active upwelling, such as EAR and Iceland (e.g., [PERSON] et al., 2017), chemical heterogeneity may be introduced to the mid-mantle by recycled basaltic crust that remains differentiated at the core mantle boundary, before subsequent entrainment within upwelling. Alternatively, upwellings may sample primordial material within LLVPs ([PERSON] et al., 2007) introducing small-scale chemical heterogeneity to mid-mantle depths.
Association of high confidence mid-mantle discontinuities below EAR likely indicative of chemical heterogeneity associated with slow wavespeeds of the African Superplume (e.g., [PERSON] et al., 2021; [PERSON] et al., 2011) corroborates previous studies ([PERSON] et al., 2002; [PERSON] et al., 2007) that suggest the African Superplume is a thermochemical feature. East African magmatism may therefore be underlain by a basalt enriched or primordial chemically distinct upwelling. Slow mid-mantle wavespeeds demarcating a second whole mantle upwelling that reaches the lower mantle below the Indian Ocean ([PERSON] et al., 2021), distal from the African Superplume, are collocated with intermediate to low confidence mid-mantle discontinuity observations beneath ETH. Therefore, an upwelling below ETH is not required to contain a chemically distinct component based on this mid-mantle criterion.
### Implications for East African Magmatism
Although substantial debate has centered around the number of plumes that contribute to East African magmatism (e.g., [PERSON], [PERSON], et al., 2006; [PERSON] et al., 1998; [PERSON] et al., 2012; [PERSON] et al., 2000; [PERSON], 2017), recent results point toward the contribution of two whole mantle plumes ([PERSON] et al., 2021): a subvertical slow wavespeed anomaly that extends eastward from the upper mantle below ETH to the lower mantle below the Indian Ocean and the African Superplume that extends southwestward from the upper mantle below the EAR to the lower mantle below southern Africa. Our RFs provide compelling evidence for a strong thermochemical upwelling below EAR likely associated with the African Superplume (Figure 11). By comparison, upwelling below central/eastern ETH is likely to be purely thermal in nature, exhibiting lower peak temperatures at MTZ depths. RF results alone are insufficient to independently confirm the two whole-mantle plume hypothesis due to relative proximity of upwellings at transition zone depths ([PERSON] et al., 2021) and reduction in data coverage below the Turkana depression separating the two distinct regions of MTZ behavior (Figure S6). However, a single broad plume is hard to reconcile with available RF evidence because a mechanism to heat the lower transition zone below ETH without introducing a chemical perturbation from elsewhere is required. Both the garnet transition, dominant around the d660 in EAR and overlying d410 are predicted to promote mass transfer ([PERSON], 1994; [PERSON], 2002) so ponding of hot material is not expected around MTZ depths, in agreement with available tomographic evidence (e.g., [PERSON] et al., 2021). Furthermore, lateral spreading of thermal anomalies within the transition zone is unlikely based on global observations ([PERSON] & [PERSON], 2008).
The nature of the d660 and mid-mantle discontinuities sampled here support the view that East African geochemical anomalies sourced in the deep mantle are likely transported to the surface via the basalt enriched African Superplume (e.g., [PERSON], [PERSON], et al., 2006). This upwelling likely taps the African LLVP (e.g., [PERSON], 2016) and crosses the MTZ below EAR (e.g., [PERSON] et al., 2021). Entrainment of high \({}^{3}\)He/\({}^{4}\)He ratios (R/Ra=20 in Ethiopia: [PERSON] et al., 2014; [PERSON] et al., 2011; [PERSON] et al., 1996; [PERSON] et al., 2006) within a basalt enriched African Superplume is consistent with the developing consensus that only the most buoyant upwellings facilitate transport of primordial helium signatures to the surface ([PERSON] et al., 2017; [PERSON] et al., 2015). This may be sourced from LLVPs in the lower mantle that likely host both recycled basalt and primordial helium signatures ([PERSON] et al., 2016; [PERSON] et al., 2019). The lack of significant along-rift variability in basalt isotopic ratios (e.g., [PERSON] et al., 2014; [PERSON] et al., 2011) suggests that Superplume material spreads throughout the East African upper mantle ([PERSON], 2020).
Figure 11.— Schematic summary of our favored interpretation along the profile shown in the inset map, including observed high confidence mid-mantle discontinuity topography (thick dashed line), and interpreted anomalous LLVP composition in the southern upwelling below EAR (black flacks). Upwelling below ETH, is likely to be purely thermal in nature and is routed further east in the lower mantle, but is projected onto the profile for illustration. Topographies on the surface, base of the lithosphere, and mantle discontinuities are exaggerated and not to scale. CMB, core-mantle boundary. EAR, East African Rifi; ETH, Ethiopia; LLVP, Large Low Velocity Province; MTZ; Mantle Transition Zone; SAF, Southern Africa.
Consequently, significantly reduced seismic wavespeeds ([PERSON] et al., 2021) and modestly elevated petrologically determined thermal anomalies ([PERSON] et al., 2012) below ETH compared to EAR, are challenging to explain by along-rift upper mantle compositional variation. Our results combined with those of [PERSON] et al. (2021) suggest compositionally anomalous material is presently not transported to the Ethiopian upper mantle directly from below because Ethiopia is underlain by a purely thermal anomaly likely sourced away from LLVPs in the lower mantle (Figure 11). Although Superlump material may be pervasive throughout the East African upper mantle, in Ethiopia specifically, conditions for mantle melting, rifting and highly anomalous upper mantle wavespeeds may be enhanced by the additional contribution of a purely thermal plume directly below. Proximal plumes of varying nature (e.g., [PERSON], 2005) are therefore responsible for the complex East African upper mantle thermochemical signatures.
## 5 Conclusions
Using Pds, PPds, and PKFds RFs, we present continent-wide observations of seismic discontinuity structure beneath Africa at mantle transition zone depths and below. We exploit a new high-resolution absolute P-wavespeed tomographic model for the African continent ([PERSON] et al., 2021) to migrate the RFs in our common conversion point stacks, and compare against results from four other S-wavespeed models.
A thin transition zone is seen beneath the majority of Cenozoic magmatism along the East African Rift, although some offset occurs and can be explained by interactions between upwellings and overriding stable mantle lithosphere. Our observations imply that East African Rift magmatism is influenced by processes at or below transition zone depths. The Main Ethiopian Rift and adjacent rift flanks are underlain by a depressed d410 (>10 km) while the uplifted d660 (\(\sim\)10 km) is offset eastward, indicating a positive thermal anomaly in the Ethiopian transition zone. Below the eastern branch of the southern East African Rift, depression of the d410 of up to 30 km suggests a stronger thermal anomaly. Here, a regionally depressed (\(\sim\)10 km) d660 showing frequency dependent splitting and robust mid-mantle discontinuities at \(\sim\)1,025 km depth indicate an anomalous composition. Our observations combined with slow wavespeeds illuminated by [PERSON] et al. (2021) suggest a hot, chemically distinct upwelling beneath the southern East African Rift, likely sourced from within the African LLVP. Meanwhile Ethiopian rift magmatism is underlain by a purely thermal upwelling, sourced away from the African LLVP. Variations in East African upper mantle seismic wavespeeds and petrologically determined temperature estimates can be reconciled with along-rift geochemical trends if the confluence of a dominant thermochemical African Superlump spreading in the upper mantle, with a purely thermal upwelling centered below Ethiopia is considered.
A patchy, incoherent d410 is underlain by a broadly coherent d660 below Cameroon. The complex d410 behavior, perhaps resulting from a regionally lowered impedance contrast, may suggest a causal mechanism for the Cameroon Volcanic Line not isolated to the upper mantle. Depression of MTZ discontinuities below central Madagascar collocated with tomographically imaged slow wavespeeds extending to \(\sim\)1,000 km depth may reflect eastwards diversion of chemically distinct African Superlump material. However, a direct causal link to Cenozoic Madagascar magmatism remains uncertain.
## Data Availability Statement
All Seismic data used are freely available from the Incorporated Research Institutions for Seismology ([[https://ds.iris.edu/ds/nodes/dmc/](https://ds.iris.edu/ds/nodes/dmc/)]([https://ds.iris.edu/ds/nodes/dmc/](https://ds.iris.edu/ds/nodes/dmc/))), GeoForschungZentrum ([[http://geofon.gfz-potsdam.de/](http://geofon.gfz-potsdam.de/)]([http://geofon.gfz-potsdam.de/](http://geofon.gfz-potsdam.de/))), French national ([[http://seismology.resif.fr/](http://seismology.resif.fr/)]([http://seismology.resif.fr/](http://seismology.resif.fr/))), and Institut de Physique du Globe de Paris ([[http://geoscope.ipsp.fr/index.php/en/](http://geoscope.ipsp.fr/index.php/en/)]([http://geoscope.ipsp.fr/index.php/en/](http://geoscope.ipsp.fr/index.php/en/))) datacenters. Temporary seismograph network codes (with FDSN registered DOI numbers) used to supplement permanent global and national networks include: 1C: [PERSON] and [PERSON] (2011), 2H: [PERSON] and [PERSON] (2009), 4H: [PERSON] and [PERSON] (2011b), 5H: [PERSON] and [PERSON] (2011a), 6A: [PERSON] et al. (2010), 7C: [PERSON] et al. (2014), 8A: [PERSON] (2015), AF: Penn State University (2004), NR: Utrecht University (UU Netherlands) (1983), XA: [PERSON] (1997), XB: [PERSON] and [PERSON] (2005), XD: [PERSON] and [PERSON] (1994), XI: [PERSON] (2000), XX: [PERSON] and [PERSON] (2012), XV: [PERSON] et al. (2011), XW: [PERSON] et al. (2009), YA: [PERSON] (2012), YI: [PERSON] and [PERSON] (2010), YQ: [PERSON] and [PERSON] (2013), YV: [PERSON] and [PERSON] (2012), YY: [PERSON] (2013), ZE: [PERSON] (2007), ZE: [PERSON] et al. (2012), ZF: [PERSON] et al. (2015), ZK: [PERSON] (2009), ZP: [PERSON] (2007), ZS: [PERSON].
et al. (2007), ZV: [PERSON] and [PERSON] (2014). These data were subsequently processed using IRIS products and Obspy ([PERSON] et al., 2010). Figures were plotted using matplotlib ([[https://matplotlib.org/3.1.1/index.html](https://matplotlib.org/3.1.1/index.html)]([https://matplotlib.org/3.1.1/index.html](https://matplotlib.org/3.1.1/index.html))) and the Generic Mapping Tools ([[https://www.generic-mapping-tools.org/](https://www.generic-mapping-tools.org/)]([https://www.generic-mapping-tools.org/](https://www.generic-mapping-tools.org/))). MTZ discontinuity depth values obtained in this study are available as a Supplementary Text file that accompanies this manuscript (_[PERSON]_and_[PERSON]_Africa_RFs_MTZ_depths.txt_). SMURFPy (Seismological Methods Utilizing Receiver Functions in Python3) data processing routines are available at [[https://doi.org/10.5281/zenodo.4337258](https://doi.org/10.5281/zenodo.4337258)]([https://doi.org/10.5281/zenodo.4337258](https://doi.org/10.5281/zenodo.4337258)).
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wiley/fae0b996_9d2f_40fa_bba6_d6ed2c18d7f1.md | Alpine greening deciphered by forest stand and structure dynamics in advancing treelines of the southwestern European Alps
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON] & [PERSON]
###### Abstract
Multidecadal time series of satellite observations, such as those from Landsat, offer the possibility to study trends in vegetation greenness at unprecedented spatial and temporal scales. Alpine ecosystems have exhibited large increases in vegetation greenness as seen from space; nevertheless, the ecological processes underlying alpine greening have rarely been investigated. Here, we used a unique dataset of forest stand and structure characteristics derived from manually orthorectified high-resolution diachronic images (1983 and 2018), dendrochronology and LiDAR analysis to decipher the ecological processes underlying alpine greening in the southwestern French Alps, formerly identified as a hot-spot of greening at the scale of the European Alps by previous studies. We found that most of the alpine greening in this area can be attributed to forest dynamics, including forest ingrowth and treeline upward shift. Furthermore, we showed that the magnitude of the greening was highest in pixels/areas where trees were first established at the beginning of the Landsat time series in the mid-80s corresponding to a specific forest successional stage. In these pixels, we observe that trees from the first wave of establishment have grown between 1984 and 2023, while over the same period, younger trees established in forest gaps, leading to increases in both vertical and horizontal vegetation cover. This study provides an in-depth description of the causal relationship between forest dynamics and greening, providing a unique example of how ecological processes translate into radiometric signals, while also paving the way for the study of large-scale treeline dynamics using satellite remote sensing.
1 Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNSS, LPCA, F-38000, Grenoble, France
2 Parc National du Mercantour, 23 Rue d'Italie, 06000, Nice, France
3 Department of Geography, University of Bonn, Mackenheimer Allee 166, D-53115, Bonn, Germany
## 1 Introduction
Alpine ecosystems, here defined as high-elevation habitats within and above treeline, have undergone particularly fast warming in recent decades ([PERSON] et al., 2015, 2022), triggering diverse and extensive vegetation responses, with already tangible consequences on biodiversity and ecosystem services. This includes an increased cover of gramoids ([PERSON] et al., 2018) and species richness in high summits ([PERSON] et al., 2023; [PERSON] et al., 2012; [PERSON] et al., 2020; [PERSON] et al., 2018; [PERSON] et al., 2012), shifts in phenological phases ([PERSON] et al., 2021), colonization of recently deglaciated areas ([PERSON] et al., 2008; [PERSON] et al., 2010; [PERSON] et al., 2016), screens and grasslands by shrubs and trees ([PERSON] et al., 2007; [PERSON] et al., 2004; [PERSON] et al., 2018; [PERSON], [PERSON], et al., 2008), increased shrub growth ([PERSON] et al., 2021, 2023) and treeline upward shifts ([PERSON] et al., 2010; [PERSON] et al., 2014; [PERSON] et al., 2007). Most studies on the dynamics of alpine plants relied on resurvey methods in real-time ([PERSON] et al., 2012; [PERSON] et al., 2018) or a space-for-time approach ([PERSON] et al., 2018). For woody vegetation, dynamics are generally assessed by diachronic aerial photography comparison ([PERSON] et al., 2010; [PERSON] et al., 2014; [PERSON] et al., 2007), dendrometry([PERSON] et al., 2003) or dendrochronology ([PERSON] et al., 2022). Alpine vegetation dynamics have only more recently been studied using remote sensing techniques ([PERSON] et al., 2017; [PERSON] et al., 2021, 2024; [PERSON] et al., 2023; [PERSON] et al., 2022).
In the vast toolkit of plant ecology research, satellite remote sensing stands out due to its temporal resolution (up to daily), historical depth (spanning up to 40 years) and comprehensive spatial coverage (up to global). For decades, trends in spectral proxies of vegetation cover--most of the time referred to as 'greening' (positive) or 'browning' (negative trends)--have been used to document biotic response to environmental changes across multiple scales and have facilitated a holistic understanding of eco-systems when combined with other classical methods ([PERSON], 2013; [PERSON] et al., 2018; [PERSON] et al., 2014). However, measured reflectances and derived indices and trends are subject to biases ([PERSON] et al., 2024; [PERSON] et al., 2014; [PERSON] et al., 2016). Inconsistencies arise from various sources (such as radiometric or geometric irregularities over time) that must be accounted for to isolate the vegetation signal. In addition, translating radiometric signals into ecological information remains a complex task ([PERSON] et al., 2020). Although vegetation indices simplify the complexity of plant life into a single dimension, and while recently developed vegetation indices (such as NIRv or kernel Normalised Difference Vegetation Index, kNDVI) offer closer ties to biophysical parameters ([PERSON] et al., 2021), they still lack in explaining ecological processes. Attributing greening to ecological processes therefore remains a major challenge as it opens avenues to decipher the drivers and subsequent consequences of greening on other ecosystem components. This path, from the correction of the measurement and resulting metrics to the ecological interpretation, requires careful application of corrective methods to build confidence in greening estimates and the use of additional high-resolution datasets to compare the distribution of greening with underlying ecological processes.
In the French Alps, the pioneering study from [PERSON] et al. (2017) used long-term changes in annual maximum NDVI derived from Landsat and MODIS imagery to identify the most significant increases in annual maximum NDVI in mountains. In this lineage, [PERSON] et al. (2021) demonstrated that north-exposed vegetation was more prone to greening compared to south-exposed slopes in the European Alps, a finding later confirmed by [PERSON] et al. (2022). [PERSON] et al. (2023) confirm these results on a global scale, showing that colder and wetter polar-facing slopes responded more positively to warming than equatorial-facing slopes. While the above-mentioned studies progressively refine our understanding of the greening of alpine ecosystems, none of them addressed the underlying ecological process. To bridge this knowledge gap, this paper aims to decipher the spatial distribution of greening trends and underlying ecological processes in a large watershed of the Southwestern European Alps previously identified as a greening hotspot ([PERSON] et al., 2021). For that purpose, we (1) produced a robust estimate of Landsat-based greening from 1984 to 2023 based on the state-of-the-art corrective and statistical methods, from which we (2) analysed the spatial variability of greening along gradients of elevation and slope (mesotopographic gradients). Then, by compiling a unique dataset of forest stands (tree count changes and age estimates) and structure (tree maximum height and forest vertical complexity) characteristics obtained from combined diachronic high-resolution (20 cm) aerial images, high-definition LiDAR point cloud and tree-ring analysis, we (3) investigate forest dynamics, that is forest ingrowth and treeline upward shift, and its spatial relation with greening.
## Data and Methods
### Study area and methods
The study area encompasses the watershed of the Col de la Cayolle (Mercantour National Park, southern French Alps, Fig. 1). According to the Strahler classification, this watershed includes five first-order catchment areas, with a total geodetic area of 64 km\({}^{2}\). Elevation ranges from 1720 m up to 3051 m a.s.l at the Mont Pelat. However, we limited our analyses to surfaces above 2000 m to focus on vegetation within and above the treeline. Above this elevation, forest stands are dominated by _Larix decidua_. Within this study area, we gathered four independent datasets from which we derive five metrics including the (i) Landsat time series of annual maximum kNDVI from 1984 to 2023 (_greening_), (ii) the spatial distribution of tree individuals in 1983 and 2018 (with the absolute difference referred to as _tree count changes_) obtained the photo-interpretation of a high-resolution image, (iii) _tree age estimates_ derived from dendrochronological analyses from trees sampled across three of the five watersheds along an elevational gradient and (iv) forest structure metrics (_local maximum height_ and _local tree height variability_) obtained using high-definition LiDAR point cloud. The procedure developed to produce these metrics of interest is schematized in Figure 2 and described in detail in the next sections.
### Landsat-based greening and significance estimates
We utilized all Tier 1 data available from our study site from 1984 to 2023 in Landsat Collection 2 provided by
the U.S. Geological Survey (USGS) and hosted on Google Earth Engine (GEE). The Tier 1 data products analysed include surface reflectance from Landsat 5 Thematic Mapper (TM), Landsat 7 Enhanced Thematic Mapper + (ETM+) and Landsat 8 Operational Land Imager (OLI). We exclusively chose images with an average cloud cover of less than 80%, as scenes with high cloud cover can compromise the accuracy of geometric calibration, particularly for the months of June, July and August. The C Version of Function of Mask (CFmask) was applied to categorize each pixel as clear (land/water), snow, cloud, adjacent to cloud or cloud shadow ([PERSON] et al., 2015; [PERSON] and [PERSON], 2012). Pixels affected by snow, cloud, adjacent to cloud or cloud shadow were excluded from the analysis. Angular effects arising from variation in viewing and solar geometry throughout the Landsat time series have been identified as a significant source of variation in retrieved directional reflectance, independent from ground-related changes ([PERSON] et al., 2015). Correcting for these effects is crucial due to the variability in the sun-surface sensor geometry, described as the Bidirectional Reflectance Distribution Function (BRDF), at the time of acquisition, which varies both spatially and temporally. [PERSON] et al. (2016) introduced a comprehensive method using a fixed set of parameters based on the RossThick-LiSparse BRDF model ([PERSON] et al., 2002). This method enables the normalization of the entire LTS to nadir (0 deg viewing zenith angle) and a constant solar zenith angle, reducing BRDF-related variations in reflectance. Our correction implementation involved the use of global coefficients and an optimal, normalized solar zenith angle set constant per location ([PERSON] et al., 2016). We performed cross-sensor calibration to correct for systematic radiometric discrepancies in red and near-infrared bands among Landsat 5 TM, 7 ETM+ and 8 OLI satellites using [PERSON] et al. (2023) methods and coefficients from [PERSON] et al. (2024) that were obtained for European temperate mountains. We computed the kNDVI for every cloud and snow free images available ([PERSON] et al., 2021) using the formula:
Figure 2: Schematic description of material and methods employed in this analysis following the four sections used in the text. Red text represents the five main variables extracted from our study site using different methods.
\[\text{kNDVI}=\tan\,h\,\left(\left(\frac{\text{NIR}-\text{Red}}{2\sigma}\right)2\right)\]
where \(\sigma\) represents the pixel-wise sensitivity of the index to sparsely/densely vegetated regions computed as \(\sigma=0.5\times(\text{NIR}+\text{Red})\) and tanh the hyperbolic tangent function. We tracked kNDVI trajectories between 1984 and 2023 by computing the annual maximum during the growing season. [PERSON] et al. (2020) demonstrated that NDVI-max estimates are dependent on the number of observations during the growing season. [PERSON] et al. (2024) showed that, because Landsat observations increase over the time series, the dependence of NDVImax on sampling frequency can lead to an overestimation of greening. [PERSON] et al. (2020) showed that this sampling bias can be partially corrected by modelling phenology on a pixel-by-pixel basis and adjusting the estimates of NDVImax based on mean phenology. Hence, we applied phenological modelling to adjust kNDVI values before computing kNDVImax. We relied on the Harmonic Analysis of Time Series (HANTS) reconstruction method as used by [PERSON] et al. (2024). This procedure was only applied on kNDVI observations with values higher than 0.15 to eliminate unregulated pixels as the correction relies on phenological modelling. This processing allowed us to derive a robust annual kNDVImax series for our study site. To obtain slope and \(P\)-value estimates pixel-wise, we used an autoregressive model to derive temporally uncorrelated trends from 1984 to 2023 ([PERSON] et al., 2021). The autoregressive model available in the'remotePARTS' R package ([PERSON] et al., 2021) is preferred over the commonly used Theil-Sen estimator because it considers temporal autocorrelation in time series.
### Forest stands characteristics from photo interpretation and dendrochronology
Data on forest stands were obtained from two sources, (i) photointerpretation of tree individuals at the beginning and end of the Landsat time series (40 years apart) and (ii) extensive sampling and age estimation based on tree-ring counting (Fig. 2).
To pinpoint the precise locations of tree individuals in the recent period, we utilized the orthorectified version of the \(\copyright\) BD ORTHO Coloured Infra-red image from 2018, available in Lambert-93 (EPSG:2154) projection, which was already orthorectified and georeferenced. For the earlier period (i.e. 1983), we mosaicked infra-red coloured aerial images downloaded at remoterletemps.fr. These images correspond to a unique acquisition campaign in June 1983. We manually geo-referenced and oriented nine historical aerial images. Following [PERSON] (2020), we orthorectified and georeferenced each image using ArcGIS Pro software (Esri, 3.2.0), specifically employing the spline transformation method with the 2018 image as a reference. The spline method is a true rubber-sheeting method that ensures that all control points in the reference map are geo-referenced to the exact coordinates provided for these locations. This method was preferred over parametric approaches, which require the interior and exterior parameters, as the nine images were distorted in various ways due to inconsistent view angles and high variations in elevation. Additionally, it gains substantial advantages from the abundance of available control points. For each of the nine images, we followed the same three-step procedure: (1) 10-50 features providing stable and easily identifiable reference points in 1983 and 2018, such as roads, topographic features or houses were used as a reference to align the orthorectified imagery accurately; (2) up to 150 control points per image were added, starting at the edges and moving progressively toward the centre of the image. This method ensures excellent accuracy and the most consistent possible error across the entire image but requires a large amount of operator time; (3) overlapping areas between adjacent images were finally used to adjust the georeferencing, in accordance with the reference image. Since Root Mean Square Errors are not computable with the spline transformation method due to the exact placement of control points, we visually validated the orthorectification and georeferencing steps by superimposing processed images. Once geo-referenced, the average spatial resolution of 1983 images was 40 cm.
Tree individuals were manually photo-interpreted from processed images on ArcGIS Pro software (Esri, 3.2.0) for the two dates. The study area was divided into \(1\times 1\,\text{km}\) squares with each square photo-interpreted one at a time. Points that have already been photo-interpreted were systematically displayed on the screen during photo-interpretation so that double counting was hardly possible. To minimize operator biases, photo-interpretation was primarily conducted by a single observer ([PERSON]), with contributions from B.N. Manual photo interpretation is a time-consuming process and can lead to variations due to training biases. To ensure consistent photo interpretation quality across our study area, the areas that were photo-interpreted initially were reviewed a second time by the primary interpreter only ([PERSON]). Errors related to double mouse clicking were identified during the photo-interpretation process and corrected. In addition, we calculated the exact coordinates of each point and removed duplicated values. This diachronic analysis of high-resolution aerial images allowed us to obtain a precise and exhaustive trajectory of tree individuals in our study area over the Landsat acquisition period. We summarized the distribution of tree individuals by counting the number of trees per Landsat pixel (\(30\times 30\,\text{m}\)), which we refer to as 'tree count'.
To enhance the temporal resolution of the tree dynamic, we complemented the diachronic analysis with dendrochronological analysis. Sampling campaigns were conducted over 3 years (2021, 2022 and 2023), targeting larch trees across five elevational transects. The transects extend from the dense forest stand located \(\sim\) 2000 m a.s.l. to the highest tree individuals (\(\sim\) 2700 m). They were positioned to cross patches with intense greening, to account for varying exposure, slope and grazing influences, in the different watersheds of our study site. We systematically sampled the dominant trees at regular intervals along the elevation gradient. Increment cores were extracted from 532 trees using a Pressler increment borer. To precisely estimate tree age, cores were taken as close as possible to the soil surface. All collected samples were air-dried, mounted and prepared following standard dendrochronological procedures described by [PERSON] (2002). They were subsequently scanned at 2400 DPI using an Epson 10000 XL Scanner. Tree-ring width series were produced measuring the rings on the high-resolution images using the program CooRecorder, and visual cross-dating was undertaken on CDendro 7.6 software ([PERSON], 2013). The pith offset, that is, the number of rings from the pith to the last cross-dated ring, was estimated using the \"DistanceToPith\" tool in CooRecorder, based on the concentric circles method. While a significant path offset may lead to an underestimation of ages in older individuals, we anticipate minimal bias given the predominantly young age and limited diameter of the majority of sampled trees.
## 3 Forest structure from dense LIDAR
Data on forest structure were obtained for the end of the Landsat time series from the high-density point clouds IGN LiDAR HD from the French lidar High-Density (LiDAR HD) campaign ([[https://geoservices.ign.fr/lidarhd](https://geoservices.ign.fr/lidarhd)]([https://geoservices.ign.fr/lidarhd](https://geoservices.ign.fr/lidarhd))) collected in summer 2021 over our study site. Across our study site, the average point density is 26.4 points/m\({}^{2}\), with 24 pulses/m\({}^{2}\) and a total of 5.55 billion points covering the entire watershed. The point cloud was processed using the 'lidR' R package ([PERSON] et al., 2020). As a first step, we normalized point height using Delaunay triangulation for spatial interpolation with default parameters. Next, we constructed a canopy height model (CHM) using a normalized point cloud through the points-to-raster method with default parameters. Finally, we extracted the apex tree height for each of the individuals identified through photointerpretation on the 2018 aerial image (Forest stands characteristics from photo interpretation and dendrochronology Section).
For each Landsat pixel (30 x 30 m), we extracted two metrics representing the forest structure in recent years: (1) the local maximum height and (2) the local tree height variability. The latter is calculated as the normalized difference between the ninth and the first quantile of the tree height distribution within each Landsat pixel (Fig. 2). This index tends to be closer to one when there is a greater difference between the smallest and tallest tree heights within a pixel, and closer to zero when this difference is lower. It represents the homogeneity of forest structure within each pixel. We preferred using a quantile instead of a simple standard deviation as it is less sensitive to extreme values. As the data is only available for the year 2021, it is interpreted as an indicator of the forest structure at the end of the Landsat time series.
## 4 Statistical analysis
We performed three distinct analyses corresponding to (1) detection, (2) attribution and (3) ecological interpretation of the greening signal.
1. We explored the distribution of Landsat greening direction and magnitude across mesotopographic gradients defined by elevation data obtained from the 25 m EU-DEM ([[https://land.copernicus.eu/imagery-in-situ/eu-dem/](https://land.copernicus.eu/imagery-in-situ/eu-dem/)]([https://land.copernicus.eu/imagery-in-situ/eu-dem/](https://land.copernicus.eu/imagery-in-situ/eu-dem/))) and Diurnal Anisotropic Heat Index (DAH) resampled on Landsat grid using bilinear interpolation. The DAH index approximates the anisotropic heating of the land surface due to radiation ([PERSON] and [PERSON], 2009). We computed DAH as cos(amax-\(a\))\(\times\) arctan(\(b\)), where \(a\) is the aspect, \(b\) is the slope and the parameter amax corresponds to the aspect with the maximum total heat surplus. We used the default amax value of 202.5\({}^{\circ}\) in SAGA 7.8.2. Values closer to \(-1\) have low radiation energy (steep north-exposed slopes) while values closer to +1 have high radiation energy throughout the day (steep south-exposed slopes). Values around 0 represent flat surfaces.
2. We explored the attribution of greening to ecological processes by comparing greening to changes in tree count within similar mesotopographic gradients. For this purpose, we split Landsat pixels showing significant greening (\(P<\) 0.05) into those attributed (with changes in tree count) and those not attributed (without tree count changes, including the absence of tree in both periods) to forest dynamics.
3. We deciphered patterns of greening attributed to forest dynamics using tree count changes, tree age estimates and forest structure metrics (local maximum height and normalized variability). To achieve this goal, we (Spatial distribution and attribution of greening Section) examined the distribution of each variable along elevation. Next, we (Causal relationships between greening, forest stands and structure dynamics Section)implemented two random forest analyses and partial dependence plots to identify the best predictors of greening. For the first analysis, we built a pixel-based random forest using only tree count changes, local maximum height and local maximum normalized variability as predictors of greening to maximize the number of samples used. The second analysis involved building a sample-based random forest where we extracted greening, tree count changes, local maximum height and local maximum normalized variability at the location of dendrochronological samples. This allowed us to include tree age estimates in our analysis. Variance explained and variables importance presented in the results section are derived from this second model. We computed each random forest 100 times by randomly selecting two-thirds of the dataset to obtain uncertainty estimates. Partial dependence plots were generated to assess how greening trends varied across the range of the predictor while holding all other predictors at their average value. We computed the quantiles of greening values, elevation and proportion for each category of pixel including non-significant pixels, significant greening, significant greening attributed to forest expansion and significant greening not attributed to forest expansion. All the analyses were performed using the randomForest, caret and pdp R packages ([PERSON], 2017; [PERSON] et al., 2023; [PERSON] and [PERSON], 2002). Finally, we present a synthetic view of the relationships between greening and advancing treelines.
## Results
### Spatial distribution and attribution of greening
We observed high variability in the spatial distribution of greening magnitude (Fig. 3A) with the highest magnitudes observed on north-exposed slopes between 2100 and 2300 m (0.005 kNDVImax/year, Fig. 3B). In total, 61.5% of the watershed area above 2000 m, shows significant greening (\(P<0.05\)), although with pronounced spatial disparities (Fig. 3C and D). On north-exposed slopes between 2100 and 2300 m, nearly 100% of the pixels exhibited significant positive greening (Fig. 3D), whereas this percentage decreases to 60% between 2300 and 2700 m. By contrast, on south-exposed slopes, the proportion of pixels showing significant greening is higher above (60%) than below (45%) 2400 m (Fig. 3D). The number of tree individuals more than doubled over the Landsat acquisition period with 140 210 trees identified in 1983 compared to 355 011 in 2018 (Fig. 4A). Increases in tree individual count were observed for all elevation and exposition in the watershed, but with a maximum between 2100 and 2300 m, mainly on north-exposed slopes (Fig. 4B). Based on the presence/absence of tree count changes, we attributed significant greening to either 'forest dynamics' or 'other ecological processes'. Across the entire watershed, we found that 56% of significant greening coincided with an increasing number of identified trees, while greening was attributed to other ecological processes for 44% of the pixels. (Fig. 5A). Along mesotopographic gradients, the proportion of greening attributed to forest dynamics reaches 90% in north-exposed slopes of the subalpine belt (between 2000 and 2300 m above sea level) compared to 70% in south-exposed slopes at similar elevations (Fig. 5B). Between 2400 and 2500 m, this proportion decreases to 30%, and it is nearly absent above 2500 m (Fig. 5B).
### Causal relationships between greening, forest stands and structure dynamics
The distribution of tree count changes shows a maximum between 2150 and 2250 m coinciding with local maximum tree recruitment mostly occurring between 1980 and 1990 (Fig. 6A). The oldest tree individuals measured were established around the year 1985 at an elevation of 2150 m. Progressively between 2150 and 2300 m, the establishment year changes from 1985 to 2000. Above 2300 m, all trees sampled were found to have been established around the year 2005 (Fig. 6A). The local maximum tree height progressively decreases from 16 m at 2000 m to 2 m at 2600 m. At around 2200 m, the highest tree height is approximately 10 m (Fig. 6B). The local tree height normalized variability slightly peaks around 2000 m with the lowest variability observed above 2350 m and moderate variability under 2100 m (Fig. 6B). As previously shown in Figure 3, greening is peaking around 2200 m (Fig. 6C).
The random forest model including the four predictor variables explains 74.30% of the variance in greening. Tree count changes were the most important variable in explaining these trends, followed by local tree maximum height, local tree height variability and establishment year, in decreasing order of importance. We used partial dependence plots to explore the relationship between each variable and greening while removing the effect of other predictors. Greening shows progressive increase, ranging from 0.0031 NDVI/year when there are no changes in tree count to 0.0045 NDVI/year in areas with the highest tree count change between 1983 and 2018 (Fig. 7A). Trees recruited between 1980 and 1990 exhibit consistently high greening at 0.00425 NDVI/year, whereas younger trees recruited after 2005 show lower trends at 0.00375 NDVI/year but with greater variability (Fig. 7B). Greening is highest for stands dominated by tree of moderate height around 15 m (0.0045 NDVI/year), moderate for taller trees around 30 m (0.0037 NDVI/year) and lower for smaller trees around 5 m (0.003 NDVI/year) (Fig. 7C). Greening peaks when local tree height variability is highest, 0.00385 NDVI/year compared to 0.00325 NDVI/year for low local tree height variability (Fig. 7D). To summarize, our findings indicate that greening is tightly associated with forest stands dominated by 30-40 years-old trees, exhibiting high variability in tree height (around a median of 15 m) and having undergone a strong increase of the number of trees in the last four decades (Fig. 8). We found that pixels exhibiting significant greening not attributed to forest expansion had greening values of 0.0017 NDVI/year [0.0011/0.0025] compared to 0.0031 NDVI/year [0.0021/0.0045] for those attributed to forest expansion. Within greening pixels attributed to forest expansion, we found high variability among pixels with the highest values reaching 0.0056 NDVI/year [0.0038/0.0076] for pixels corresponding to forest stands dominated by 30-40 years-old trees, high variability in tree
Figure 3: (A) Distribution of Landsat-based greening trends over our study site. (B) Distribution of average greening trends along gradients of elevation and aspect for all pixels in the study site. Cells in white have less than 10 pixels and are not shown. (C) Percentage of significant positive trends over the whole area. (D) Distribution of the percentage of significant positive trends along elevation and aspect gradients for all pixels in the study site.
height and high increase in tree count number (Table 1). In older and younger stands, greening values were around 0.003 NDVI/year [0.0025/0.0046].
## Discussion
Studies on plant dynamics using satellite imagery often face challenges in interpreting results ecologically. This paper addresses these challenges by developing a statistically robust method to estimate greening (Fig. 3) and comparing it with datasets describing trajectories of forest stands and structure (Fig. 2). Previous studies have identified the south-western European Alps, especially the sparsely vegetated north-facing subalpine areas around 2200 m, as greening hotspots ([PERSON] et al., 2021; [PERSON] et al., 2022). We found similar patterns over the Cayolle watershed (Fig. 3), indicating that our study site is representative of this hotspot. We found that the spatial variability of greening is mostly driven by forest dynamics (Fig. 4), with more than half of the greening attributed to changes in tree count over the watershed, and almost all of it for subalpine north-exposed (Fig. 5). This indicates that the dynamics of the advancing treeline are the primary cause of the observed intensified greening in this area. By mobilizing a unique assemblage of datasets on tree count changes, age and forest structure (Figs. 2 and 6), we identified the specific moment, within the forest successful stage, that coincides with the highest greening magnitudes (Fig. 7). This corresponds to an intermediate stage of advancing treelines, with stands composed of 40 years old, tall trees and ongoing closure of clearings by younger individuals (Fig. 8). The contributions of this paper are threefold: (1) forest dynamics are the predominant factor contributing to greening in the south-western Alps; (2) for a given stage of forest succession, the greening peaks occurs when the vertical growth of the early established trees coincides with the closure of clearings by younger individuals leading to a notable expansion of both vertical and horizontal vegetation cover; (3) greening is a reliable indicator for monitoring forest dynamics across extensive geographical scales and over prolonged periods, potentially spanning decades.
## Attributing alpine greening to ecological processes
This detailed analysis of how satellites capture ecological processes is conceptually part of the approach to move beyond the diagnostic of change (production of greening maps and identification of hotspots and spatial patterns) toward the attribution to underlying ecological processes. In a given area, several ecological processes can take place simultaneously, all potentially resulting in an increase in NDVI of comparable magnitude. However, the drivers of these processes and the consequences can vary greatly. We demonstrate that within the study area, forest dynamics account for the majority of the greening, although in certain locations, particularly at higher elevations, more than half, or even all, of the greening is attributed to other ecological processes (Fig. 5B).
Figure 4: (A) Number of photo-interpreted trees along elevation for 1983 and 2018. (B) Distribution of absolute tree count changes between 1983 and 2018 along gradients of elevation and DAH.
For example, we have identified a summit grassland around 2600 m which was degraded in 1983 but has since recovered by 2018 (Fig. 5C). This grassland, historically used as a sheep resting place before the return of wolves in the late 1990s, shows high greening rates, reaching up to 0.008 NDVI/year, surpassing the average greening observed in the 2018 (Fig. 5C). This suggests that the average greening observed in the 2018 (Fig. 5C) is not a good indicator of the presence of a
advancing treelines at lower elevations. Similarly, in a wider alpine context, several studies confirm that distinct ecological processes could be reflected in a closely related radiometric signal. [PERSON] et al. (2023) thus linked intense greening (up to 0.004 NDVI/year) to increases in plant species richness attributed to the upward migration of competitive species on high-elevation nunataks of Mont-Blanc. In proglacial margins, [PERSON] et al. (2023) attributed the high magnitude of greening (up to a maximum of 0.01 NDVI/year) to the opening of new surfaces for colonization and slope stabilization following deglaciation ([PERSON] et al., 2023). Large-scale studies such as those of [PERSON] et al. (2021) or [PERSON] et al. (2022) in the European Alps encompass numerous ecological processes. However, there is no doubt that the variables driving these ecological processes differ from one another. Failure to consider these processes independently
Figure 6: Distribution of (A) forest stands (tree count changes and tree recruitment year), (B) forest structure (local tree height variability and maximum) variables and (C) greening variable along elevation gradients for fuels exhibiting significant greening attributed to tree trajectories. Solid and dashed lines represent the median, and quantile 25 and 75 values respectively obtained from quantile Generalized Additive Models (qGAM).
necessarily results in oversimplification and may lead to misinterpretation of both causes and consequences of the greening complexity ([PERSON] et al., 2020).
### Temporality of satellite observations in advancing treelines
Forest development typically follows successional stages that have been widely discussed and theorized ([PERSON] and [PERSON], 1996), leading to variations in tree count, age, height or structure complexity over space and time ([PERSON] et al., 2011). Along the elevational gradient, we identified several stages including mature stands comprising multi(centennial)-old tall trees with moderate structural complexity and limited changes in tree count at lower elevations (Fig. 6). On the other hand, high elevations stands are in a pioneering stage, characterized by young and small trees, sparsely distributed and with limited height variations.
Figure 7.: Partial dependence plots of predictor variables in a Random Forest regression model. Solid and dashed lines represent the median, and quantile 25 and 75 values respectively obtained by recomputing the analysis using randomly 66% of the dataset each time.
In the central portion of the gradient, larch forest typically represents an intermediate stage with 40-year-old tall trees and the ongoing closure of clearings by younger individuals, resulting in high complexity in forest structures (Fig. 6). Among those stages, greening is found to be the highest in areas currently exhibiting the intermediate stage (Fig. 7). This suggests that Landsat-based accounts of greening peaked when the initial establishment occurred \(\sim\) 40 years ago, at the beginning of the Landsat time series. Consequently, other greening estimates based on sensors such as MODIS would fail to capture this peak. During this period, trees from the initial wave of establishment have increased in height and the density of the understory strata has risen (Fig. 8), corresponding to both increased horizontal and vertical vegetation cover ([PERSON] et al., 2011). In this context, we can reasonably hypothesize that older stands below 2100 m a.s.l. represent a post-greening stage, which would have been identified as a greening hotspot in an earlier time window. Conversely, we expect higher-elevation grasslands undergoing initial establishment to show increased greening magnitude in the coming decades, assuming favourable environmental conditions persist (Fig. 8). Landsat-based greening is measured between 1984 and 2023, representing a snapshot within the true but unknown temporal scale at which ecological processes unfold. Consequently, the sensitivity of remote sensing measurements significantly relies on the kinetics of the underlying processes, and whether they generate a sufficiently significant signal during this limited 40-year observation period. In the European Alps, landscapes have been shaped by human activity for thousands of years ([PERSON] et al., 2014; [PERSON] et al., 2017). In the southern French Alps, the earliest stone structures associated with pastoralism, dating to ca. 2500 BC, are found at elevations between 2100 and 2400 m ([PERSON], 2015) presupposing forest clearance designed to create more suitable pasture. These practices have continued throughout the Holocene with varying intensity ([PERSON] et al., 2014). After a period of expansion following the Black Death, the French forest contracted almost continuously, reaching a minimum in the early 19 th century, followed by an increase in forest cover up to the present ([PERSON] et al., 1999; [PERSON]
Figure 8: Link between forest successful stage and forest stands and structure characteristics and its translation into greening. four forest successful stages are distinguished with the main processes of forest in growth and expansion underlined. Greening magnitude is interpreted in light of the transition between forest successful stages (and corresponding changes in vegetation cover), suggesting the existence of pre-greening, greening and post-greening stages in the context of advancing treelines.
et al., 2010; [PERSON] & [PERSON], 2011). Landsat-based greening and associated forest expansion over the last four decades hence only capture the most recent moment of this multi-centennial trajectory.
## 4 Greening as a proxy for shifting treelines
One of the most striking ongoing ecological trajectories in alpine ecosystems worldwide is the upward shift of treelines ([PERSON] et al., 2008; [PERSON] et al., 2009; [PERSON] et al., 2011). This phenomenon is an extensively observed ecological trend in the European Alps ([PERSON] et al., 2024), with well-documented case studies in the central Austrian and Italian Alps ([PERSON] & [PERSON], 2020; [PERSON] et al., 2007), Switzerland ([PERSON] et al., 2007; [PERSON], [PERSON], et al., 2008) and France ([PERSON], 2001). Similar trends are reported in neighbouring mountain ranges including the Pyrenees ([PERSON] et al., 2018; [PERSON] & [PERSON], 2004), the Apennines ([PERSON] et al., 2023; [PERSON] et al., 2018) and the Carpathians ([PERSON] & [PERSON], 2020). Despite extensive studies, the spatial variability in the magnitude of treeline changes remains puzzling with contrasting kinetics of treeline trajectories observed in the European Alps ([PERSON] et al., 2017). In particular, the interactions between the factors driving treeline shifts, such as climate, topography, species distribution and geomorphological activity, remain unclear. Most studies exploring treeline shift have relied on repeated field surveys, diachronic series of maps or photographs or dendrochronology, thus limiting the surface area from which conclusions can be drawn. Using greening as a proxy for advancing treelines offers a simplified and scalable approach ([PERSON] et al., 2023; [PERSON] et al., 2020). This perspective partly aligns with the results of [PERSON] et al. (2018) who explored the distribution of Landsat-based greening along forest structure gradients and observed faster changes at the cotone compared to closed forest and open lands. Similarly, [PERSON] and [PERSON] (2022) tracked greening along gradients of tree cover density at the Boreal biome scale and found a signal consistent with a poleward biome shift. Yet, both studies relied on spatial co-occurrence rather than causal evidence, leading to results that have sparked controversy due to discrepancies with field studies ([PERSON], 2022). This calls for an improved understanding of how advancing treelines translate into greening signals.
Here, we address this knowledge gap by providing a better understanding of how the population and structural trajectory of an advancing treeline influence the magnitude of greening. Our results not only confirm the validity of greening as a proxy for advancing treelines but also enable exploration of their large-scale drivers. Additionally, while we are considering greening as a single monotonic trend over the last four decades, tracking interannual variability of maximum NDVI might highlight non-linear trajectories of forest expansion ([PERSON] et al., 2022). This is significant as forest expansion might have occurred at an irregular rate during this period considering that warming mostly occurred in the 1990s. Furthermore, the reappearance of wolves in the 1990s ([PERSON], 2005) led to changes in sheep practices, which potentially influenced the treeline movement ([PERSON] et al., 2004). Beyond greening, studying the temporal variability of NDVImax trends could improve our understanding of the intertwined effects of climate and land-use change over the last four decades.
## 5 Limits of datasets and analysis
In this study, we mobilized four independent datasets to characterize stand and forest structure, each with its limitations and inaccuracies. Diachronic analysis of aerial
\begin{table}
\begin{tabular}{l c c c} \hline \hline & \multicolumn{2}{c}{Greening} & & \\ & values (NDVI) & Proportion & Elevation \\ Pixel categories & year) & (\%) & (m) \\ \hline Non-significant (\(P\!>\!0.01\)) & 0.0005 & 51 & 2499 \\ & [0.0001] & & [2376] \\ Significant greening & 0.0024 & 49 & 2364 \\ (\(P\!<\!0.01\)) & [0.0015/ & & [2224/ \\ & 0.0036] & & 2517] \\ Significant greening & 0.0031 & 56 & 2268 \\ attributed to forest & [0.0021/ & & [2152/ \\ expansion & 0.0045] & & 2369] \\ Pre-greening stage & 0.0035 & 37 & 2306 \\ & [0.0025/ & & [2239/ \\ & 0.0047] & & 2360] \\ Greening stage & 0.0056 & 37 & 2193 \\ & [0.0038/ & & [2133/ \\ & 0.0076] & & 2257] \\ Post-greening stage & 0.0032 & 26 & 2085 \\ & [0.0024/ & & [2044/ \\ & 0.0044] & & 2134] \\ Significant greening not & 0.0017 & 44 & 2525 \\ attributed to forest & [0.0011/ & & [2395/ \\ expansion & 0.0025] & & 2613] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of greening values and proportion of greening pixels. Non-significant and significant pixels correspond to pixels with a \(P\!>\!0.01\) and \(P\!<\!0.01\), respectively, with the proportion being relative to the entire study area. Significant greening attributed, or not, to forest, expansion corresponds to pixels exhibiting significant greening (\(P\!<\!0.01\)) and with changes, or no changes, in tree count between the two periods. Within greening pixels attributed to forest expansion, we distinguished the three stages (pre-greening, greening and post-greening) described in Figure 8. Values correspond to the median and first and third quantiles.
photographs has been used to study treeline movement by either image classification approach ([PERSON] et al., 2014; [PERSON] et al., 2018) or manual and machine-based photo interpretation of tree individuals ([PERSON] et al., 2016). Our photointerpretation was conducted manually on two sets of images with differing spatial resolution, radiometric quality and taken, at different times of day. We found that our ability to identify smaller trees and differentiate them from larger bushes depended significantly on the shade cast by the tree. During field sampling, we realized that trees smaller than 1 m 50 were not identifiable on the 2018 images, with this threshold likely being slightly higher on older images, leading to overestimation of tree count changes between both periods. This bias could limit our interpretation of the association between greening and forest succession (Fig. 8), as we cannot confirm that trees newly present in 2018 were not simply small and undetectable in 1983.
Nevertheless, our analysis also relied on tree dating by coring at the base to determine the date of recruitment (Fig. 2). This approach allows us to quantify the age gradient along greening and altitude with confidence (Fig. 6), although the absolute age of the trees is probably slightly underestimated due to pith missing during the scoring process ([PERSON], 2001) and our sampling only covers a limited part of our study site (Fig. 1). Similarly, the forest structure metrics we relied on are simplified proxies. Based on our LiDAR dataset, with an average point of 26.4 points/m\({}^{2}\), we could not compute more accurate metrics such as the Vertical Complexity Index ([PERSON] et al., 2011) as in [PERSON] et al. (2023). Additionally, forest structure metrics were computed at the Landsat-pixel scale (30 m) to match other data, but this scale might not be ideal for capturing forest structural diversity ([PERSON] et al., 2023).
Despite these limitations, we are confident that our study provides a detailed interpretation of greening in ecological terms. However, transposing these findings to other mountain regions remains challenging. The advancement of the treeline at our study site is particularly rapid and consists entirely of Larch trees, known for their pioneering capacity due to rapid growth, short time between germination and sexual maturity and anemochorous seeds ([PERSON], 1953). The sensitivity of the remote sensing measurements significantly relies on the kinetics of the underlying process, and whether it generates a sufficiently significant signal during the 40-year observation period. For example, we cannot assert that the widely studied _Pinus uncinata_ advancing treeline will produce a similar signal, given its much longer reproduction times and spread by zoochory. Additionally, considering the current elevation of the _P. uncinata_ treeline at around 2000 m, climatic control on forest expansion is expected to be limited ([PERSON] et al., 2007). Further studies in different contexts, including other treeline-forming tree species, varying rates of expansion and at different elevations or latitudes, particularly closer to the climatic treeline, are needed to better understand the complex link between the radiometric signal and advancing treelines.
## Conclusion
In this study, we quantified Landsat-based greening over the last four decades in a large watershed of the Southwestern Alps, an area identified as a hotspot of greening at the scale of the European Alps. Using a heterogeneous and multidisciplinary dataset compiled for a single area, we demonstrated that more than half of significant greening in the watershed is attributed to forest dynamics, though there is considerable variation in greening magnitude within advancing treelines. Greening is found to be particularly high when the initial establishment occurred at the beginning of the Landsat time series; During the observation period, this first wave of recruitment has grown while the understory strata have been re-colonized by other trees, leading to increased horizontal and vertical vegetation cover. These new findings provide valuable insights into the ecological processes underlying alpine greening and offer an opportunity to study treeline dynamics at a large scale using greening as a proxy.
## Acknowledgements
The authors are particularly grateful to the Parc National du Mercantour for their support, authorization and helpful discussion during fieldwork. [PERSON] acknowledges a CNRS doctoral scholarship. This work received funding from the ANR project TOP (LIFE16 CCA/IT/000060) and the Zone Atelier Alpes project HERITAGE. This research has been supported by the Agence Nationale de la Recherche (project TOP, Trajectories of agPO-Pastoral systems in mountains, grant no. ANR-20-CE32-0002). LECA acknowledges the Agence Nationale de la Recherche (grant nos. Labex OSUGe02020 and IA-10-LABX-0056).
## Author Contributions
[PERSON] designed the methodology, conducted the remote sensing analysis and wrote the original draft. [PERSON] conducted the dendrology and contributed to photo-interpretation. [PERSON], [PERSON] and [PERSON] participated in the analysis and manuscript editing. [PERSON] organized and participated in the fieldwork.
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wiley/faf683b1_8545_4faa_bf7d_4db85d7868c0.md | # IGR Oceans
Research Article
at Nantucket Island
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
[PERSON]
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 19731, USA
###### Abstract
The relative contributions of local and remote wind stress and air-sea buoyancy forcing to sea-level variations along the East Coast of the United States are not well quantified, hindering the understanding of sea-level predictability there. Here, we use an adjoint sensitivity analysis together with an Estimating the Circulation and Climate of the Ocean (ECCO) ocean state estimate to establish the causality of interannual variations in Nantucket dynamic sea level. Wind forcing explains 67% of the Nantucket interannual sea-level variance, while wind and buoyancy forcing together explain 97% of the variance. Wind stress contribution is near-local, primarily from the New England shelf northeast of Nantucket. We disprove a previous hypothesis about Labrador Sea wind stress being an important driver of Nantucket sea-level variations. Buoyancy forcing, as important as wind stress in some years, includes local contributions as well as remote contributions from the subpolar North Atlantic that influence Nantucket sea level a few years later. Our rigorous adjoint-based analysis corroborates previous correlation-based studies indicating that sea-level variations in the subpolar gyre and along the United States northeast coast can both be influenced by subpolar buoyancy forcing. Forward perturbation experiments further indicate remote buoyancy forcing affects Nantucket sea level mostly through slow advective processes, although coastally trapped waves can cause rapid Nantucket sea level response within a few weeks.
Footnote †: footnoteinfo]Footnote : footnotemark:
## Plain Language Summary
The change in the rate of sea-level rise (SLR) in the northeast coast of the United States in the past few decades was 3-4 times higher than that of the global-mean SLR. The magnitude of interannual sea-level variation in this region is even larger than the long-term change over the last few decades. The causes of interannual sea-level variation there are not well understood, limiting the knowledge of sea-level predictability. This study identifies the causality of interannual variations of sea level near Nantucket Island with wind and buoyancy forcing. The latter is the combination of air-sea heat and freshwater fluxes. These forcings together affect sea level. We employ a method to separate the contributions of wind and buoyancy forcings, both near and away from Nantucket, on Nantucket sea level. Wind contribution is primarily near-local, from regions northeast of Nantucket along the New England shelf. Local and remote buoyancy forcing contributions are overall smaller than wind contributions, but can be comparable to wind contributions in some years. In particular, buoyancy forcing from the subpolar North Atlantic can affect Nantucket sea level a few years later, providing a source of predictability for Nantucket sea level.
## 1 Introduction
The northeast coast of the United States (US) is a densely-populated region with enhanced sea level rise (SLR) relative to the global mean ([PERSON] et al., 2012). Many processes contribute to sea-level change in this region ([PERSON] et al., 2019; [PERSON] et al., 2019 and references therein). Quantifying the relative contributions of these different processes to past sea-level change can improve the reliability of future SLR predictions.
The magnitude of interannual sea-level variations in the northeast US is large compared to the long-term secular trend over the last few decades ([PERSON] et al., 2013). For example, [PERSON] et al. (2015) reported an extreme sea-level variation during 2009-2010 that was equivalent to approximately 30 years of global-mean SLR. In addition to having large magnitudes, interannual sea-level variations in the region are also coherent from Cape
## 2 Model and Methodology
Because seasonal-to-decadal sea-level variations are coherent north of Cape Matteras from Mid-Atlantic Right to GoM (Figure S1 or see [PERSON] et al., 2013), we choose to use sea level at Nantucket Island as a proxy for sea level along the entire US northeast coast. Nantucket is also the approximate geographic center of the US northeast coast region. The model grid cell that we define as \"Nantucket\" is at 41.4\"N, 70.5\"W, with 20-m model water depth.
We focus on interannual sea-level variations during 1992-2015 and use the global, data-constrained ECCO Version 4 Release 3 (hereafter ECCO V4r3) ocean and sea-ice estimate ([PERSON] et al., 2015; [PERSON] et al., 2017). As there is no surface atmospheric pressure loading in the ECCO V4r3 solution, sea level in this study refers to ocean dynamic sea level without the inverse barometer (IB) effect. The IB effect accounts for 25% of interannual variance of total sea level along the US northeast coast ([PERSON] & [PERSON], 2015).
The ECCO state estimates are obtained by fitting the Massachusetts Institute of Technology general circulation model (MITgcm) to satellite and in-situ ocean and sea-ice observations using an adjoint-based optimization method. The model's first-guess surface boundary conditions, initial conditions, and mixing parameters are iteratively adjusted to minimize the model-data differences in a least-squares sense. The time-trajectory of the optimized, free-running model can be entirely ascribed to first principles, namely, satisfying the physics described by the model equations. Covering the period 1992-2015, the ECCO V4r3 solution has a nominal 1\({}^{\circ}\) horizontal grid spacing and 50 vertical levels with thickness varying from 10 m near the surface to 456.5 m at a maximum depth of 6,134.5 m. The model uses a rescaled vertical coordinate z*, a non-linear free surface, and real freshwater flux boundary condition. They help the numerical model accurately account for the mass and density contributions to sea level by material exchanges through the ocean surface ([PERSON] et al., 2008; [PERSON] et al., 2015). Numerous studies have used various ECCO products to investigate changes in sea level (e.g., [PERSON] and [PERSON], 2015; [PERSON] et al., 2021), temperature and salinity (e.g., [PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] and [PERSON], 2018), and other oceanic physical properties. A comprehensive list of ECCO-related publications can be found at [[https://ecco-group.org/publications.htm](https://ecco-group.org/publications.htm)]([https://ecco-group.org/publications.htm](https://ecco-group.org/publications.htm)).
To quantify the relative contribution of different forcing from different locations to Nantucket sea-level variations, we employ the method of adjoint gradient decomposition ([PERSON] et al., 2015) whereby a quantity of interest (objective function), Nantucket sea level in this case, is expanded linearly in terms of its causal elements using the ECCO adjoint model. While the original ECCO V4r3 solution uses time-evolving atmospheric state and bulk formulae to calculate the individual air-sea heat and freshwater flux terms (e.g., sensible and latent heat flux, evaporation), this study employs a \"flux-forced\" version of the ocean model forced wind prescribed zonal and meridional wind stress (TAUU and TAUV), net heat flux (QNET), and net freshwater flux (EmPmBf) of V4r3 that allows the influences of different forcing mechanisms to be more readily quantified ([PERSON] et al., 2021).
We run the ECCO adjoint model backward in time to calculate the adjoint sensitivities of Nantucket sea level with respect to these four air-sea fluxes as a function of location and lead time. Specifically, sensitivities are calculated using monthly-mean Nantucket sea level in December 2015 as the objective function, thus allowing the computation of adjoint sensitivities to forINGS with the longest possible lead time over the 1992-2015 ECCO V4r3 period. The resultant set of adjoint sensitivities quantifies the linear response of Nantucket sea level to unit positive perturbations in each forcing as a function of location and lead time. We make a reasonable approximation that the adjoint sensitivities are independent from ocean state and therefore stationary in time, following previous studies (e.g., [PERSON] et al., 2011; [PERSON] et al., 2021; [PERSON] et al., 2016; [PERSON] and [PERSON], 2019; [PERSON] et al., 2014).
Figure 1 shows adjoint sensitivities of Nantucket sea level to heat flux, freshwater flux, zonal and meridional wind stress at various forcing lead times. The values have been normalized by the maximum sensitivity value in the region (number specified on each panel) and are thus non-dimensional. The heat and freshwater flux sensitivities at 1-year lead time are mostly from the Scotian Shelf that is not very far from Nantucket Island. As the lead time increases, the largest sensitivities occur in regions farther away, for example, from the subpolar North Atlantic with forcing lead times of 2-3 years and south of Iceland at year 5. In contrast, the wind stress sensitivities are dominated by local features and even going back further in time, the largest sensitivities are still not very far from Nantucket Island.
To reconstruct Nantucket sea-level anomaly (SLA) at a target time, \(t\), the adjoint sensitivities are convolved with the anomalies of each forcing with respect to its time mean. Mathematically, Nantucket SLA, \(J\), is reconstructed by the following equation:
\[J(t)\approx\sum_{i}\sum_{i}\sum_{\Delta t}\frac{\partial J}{\partial F_{i}(s, \Delta t)}\delta F_{i}(s,t-\Delta t) \tag{1}\]
where \(\frac{\Delta t}{\partial F_{i}(s,t-\Delta t)}\) is the adjoint sensitivity of Nantucket SLA to forcing \(F_{i}\) at lead time \(\Delta t\) and location \(s\); and \(\delta F_{i}(s,t-\Delta t)\) is the anomaly of forcing \(F_{i}\) at some prior time \(t-\Delta t\) (i.e., target time minus lead time).
Using Equation 1, one can reconstruct Nantucket SLA time series by aggregating the cumulative contributions of all forcings through all lead time and space. To gain insight into the contributions of particular forcings to the overall sea-level variation, we analyze the individual elements of Equation 1. In fact, this is the basis for us to decipher the relative contributions of different forcings as well as local versus remote forcings. See [PERSON] et al. (2007, 2015, 2021) for details regarding the methodology of the decomposition and reconstruction to determine causal mechanisms.
Unless otherwise specified, the study is based on 13-month low-pass-filtered monthly sea-level time series, referenced to its global and 1992-2015 time means, with the seasonal cycle and a linear trend removed so as to focus on regional interannual variations. We show that the convolution-based sea-level reconstruction reproduces most of the interannual sea-level variance at Nantucket estimated by ECCO. We then decompose the reconstructed Nantucket sea-level variations into individual forcing contributions or regional contributions.
## 3 Adjoint-Based Reconstruction of Nantucket Sea Level
Figure 2a compares interannual variations of Nantucket sea level estimated by ECCO (blue) to tide-gauge data (gray) and the estimate from the Archiving, Validation and Interpretation of Satellite Oceanographic (AVISO) merged-altimetry gridded product (black). Both tide-gauge data and AVISO have been corrected for the 1B effect and are referenced to global-mean sea level from AVISO. The tide-gauge SLA are very similar to the AVISO SLA even though the latter have been spatially averaged onto the ECCO grid closest to Nantucket. While ECCO estimate overall resembles these observations (correlation coefficient \(r\) = 0.79 and 0.80, respectively), there are some notable mismatches, for example, during 1997 and 2013. These mismatches are likely due to limitations in the ECCO V4r3 model (e.g., coarse grid resolution and representation of coastal processes), because the tide-gauge data is more similar to AVISO (\(r\) = 0.93) despite some notable difference between them. The reconstructed Nantucket sea level (orange) explains approximately 89% of the interannual variance of the ECCO estimate (blue). This indicates that the assumptions involved in the adjoint-based reconstruction (e.g., stationary linear response) are reasonable. Accounting for the dependence of adjoint sensitivities on seasonally varying ocean state
Figure 1: Nantucket sea-level sensitivity to heat flux (a)–(d), freshwater flux (e)–(h), zonal (i)–(l) and meridional wind stress (m)–(p) at various forcing lead times (indicated by legends) computed by integrating the ECCO adjoint model backward in time. The circle indicates the location near Nantucket Island where the objective function is defined. For each panel, the values of the sensitivities have been normalized by the maximum magnitude of sensitivities in the region (shown in legends) and are thus non-dimensional. Positive sensitivity value at a location means that a positive perturbation to the forcing at that location for the particular lead time will increase Nantucket sea level at the terminal time (time 0). The sign convention for the forcing itself is positive for downward heat flux (W m\({}^{-2}\)) and freshwater flux (kg m\({}^{-2}\) s\({}^{-1}\)), eastward and northward wind stress (N m\({}^{-5}\)). Longer lead times are shown for the sea-level sensitivities to heat and freshwater fluxes because of the longer time scales of their evolutions.
(e.g., [PERSON] et al., 2014) may increase the variance explained beyond 89%, but at much higher computational cost because it requires 11 more multi-decadal adjoint sensitivity runs.
Having established that Equation 1 can reconstruct most of the interannual variability of Nantucket sea level represented in ECCO, we next quantify the contributions by wind stress and buoyancy forcings (Figure 2b). Wind stress (dashed) is the largest contributor, explaining 67% of the interannual variance of the reconstructed Nantucket sea level. This confirms previous studies suggesting that wind forcing is the dominant contributor to sea-level variations along the US northeast coast ([PERSON] et al., 2013; [PERSON] et al., 2016, 2019; [PERSON], 2015; [PERSON] et al., 2014). A prominent example is during 2009-2010 when the 5-cm increase of sea level is almost completely due to wind forcing. [PERSON] et al. (2015) found that the increase of sea level along the US northeast coast during 2009-2010 is consistent with the northeaesterly wind stress anomaly during the same period that causes anomalous onshore Ekman transport.
Although sizable, buoyancy forcing contribution (dotted) does not formally explain much variance of the overall interannual variation of Nantucket sea level during the 1992-2015 period (\(-\)1%). However, the difference in variance explained by the total reconstruction (89%) and wind stress contribution (67%) is largely due to buoyancy forcing which can be as important as wind stress during certain years. For example, during 2010-2013 wind stress causes a 5-cm decrease of sea level, but it is offset by a 3-cm increase of sea level due to buoyancy forcing (inset on the right of Figure 2b). During 1999-2002, the 3-cm increase of sea level due to wind stress is offset by a 4-cm decrease due to buoyancy forcing (inset on the left of Figure 2b). Buoyancy forcing also appears to be more important at lower frequencies than wind forcing. The reconstructions by wind and buoyancy forcings have partial compensation with weak but significant anticorrelation (\(r=-0.26\)). Note that the explained variances by individual forcing contributions are not additive because forcings may covary. Such covariation makes it difficult
Figure 2: (a) Nantucket SLA from tide gauge (gray), AVISO (black), ECCO (blue), and adjoint-based sea-level reconstruction (orange) using both wind stress and buoyancy forcings plus the contribution of adjustment to initial state. The number (89%) in the legend is the percentage variance of ECCO SLA (blue) explained by the total reconstructed SLA (orange). (b) The total reconstructed SLA (orange; same as in panel (a)) and individual reconstruction using wind stress (dashed), buoyancy forcing (dotted), and the contribution of adjustment to initial state (purple). The numbers are the percentage variance of the total reconstructed SLA (orange) explained by each of these three factors. The two insets show reconstructed SLA for 1999–2002 and 2010–2013. All time series are 13-month low-pass-filtered with the respective mean seasonal cycle and linear trend removed. The curves are referenced to their corresponding time mean, except that those in the insets are relative to January 1999 and January 2010, respectively. Units are in cm.
to separate the forcing contributions using traditional covariance-based analyses (e.g., regression). A negative explained variance of one variable by another occurs when they are anticorrelated or the ratio of the latter's standard deviation (\(\sigma\)) to the former's is twice larger than \(r\)(see [PERSON] et al., 2015). Table 1 lists \(\sigma\) of reconstructed sea-level and \(r\) between total reconstruction and the reconstructions by individual forcings. The fact that wind stress and buoyancy forcing together explain 97% of the variance of Nantucket sea level even though buoyancy forcing alone does not explain any interannual variance suggests the importance of buoyancy forcing.
The contribution of the anomalies in the initial condition (purple in Figure 2b) quantifies the effect of sea-level adjustment to the initial state of the ECCO model that is independent from the effects of subsequent forcings. The initial condition's contribution is obtained by taking the difference between the ECCO solution and the same simulation in which the model's initial conditions are replaced by its 1992-2015 time-mean ocean state. The variance explained by the initial state is close to zero and mostly affects sea level before 2000.
## 4 Local and Remote Forcing Contributions
We further investigate the local and remote contributions of wind and buoyancy forcings. By excluding the spatial summation in Equation 1, we obtain the contribution of a forcing at each location to Nantucket sea level. We then compute the fraction of Nantucket interannual sea-level variance explained by reconstructed SLA using wind stress or buoyancy forcing at each location. The resultant maps, referred to as the forcing influence maps, are shown in Figure 3. Similar to adjoint sensitivities of wind stress (Figure 1), wind stress contribution (Figure 3a) is seen to be mainly local, with the largest contribution from the GoM and Scotian Shelf northeast of Nantucket. Moreover, wind stress contribution is largely confined to the shelf and almost entirely northeast of Nantucket. Outside the large and positive local influence region, there is little contribution by wind stress.
Buoyancy forcing, on the other hand, has contributions covering a much broader region northeast of Nantucket, including remote areas in the subpolar North Atlantic (Figure 3b). There is a local positive contribution from the GoM and Scotian Shelf. In the subpolar region, there are positive remote contributions by buoyancy forcing over the Labrador Sea, the western subpolar gyre, and the southeastern Greenland Shelf. There are also weak positive contributions farther upstream along the eastern coasts of the Atlantic Ocean and Nordic Seas. Values of negative variance explained are found for buoyancy forcing from the eastern subpolar gyre, the continental slopes of Grand Banks and Flemish Cap, and the Gulf of St. Lawrence. There are also noticeable negative values of explained
\begin{table}
\begin{tabular}{l c c} Reconstruction & \(\sigma\) & \(r\) \\ \hline Total & 1.94 & 1 \\ Wind & 1.88 & 0.83 \\ Buoyancy & 1.19 & 0.30 \\ \hline \end{tabular}
\end{table}
Table 1: _Standard Deviation (\(\sigma\); in cm) of Reconstructed Nantucket Sea Level and Correlation Coefficient (\(r\)) Between Total Reconstruction and the Reconstruction Using an Individual Forcing_
Figure 3: Fractions of variance of the total reconstructed Nantucket interannual SLA explained by reconstructed SLA using (a) wind stress and (b) buoyancy forcing per unit area (km\({}^{-2}\)) at each location. Contours are isobaths of 200, 700, and 2,000 m (dark gray).
variance from the Labrador and Newfoundland shelves that are sandwiched between positive values from the Labrador Sea and coastal regions.
[PERSON] et al. (2017) identified a strong correlation between decadal changes of steric height in the subpolar North Atlantic and the sea level along the US northeast coast. The region with large contribution of remote buoyancy forcing identified in our study is roughly over the same region where they found good correlation between subpolar steric height and sea level along the US northeast coast. Our results corroborate their hypothesis that sea-level variations in the subpolar gyre and the US northeast coast can both be influenced by subpolar buoyancy forcing, with our results demonstrating this causality. Our results also suggest that subpolar buoyancy forcing explains only 10% of the interannual variance of Nantucket sea level.
The contributions from local and remote forcings can be quantified by the variance of the total reconstructed SLA explained by each forcing from various forcing regions (defined in Table 2 and Figure 4; Table 2 also has other statistics, \(\sigma\) and \(r\)). Here the local forcing region is defined as the GoM with depths shallower than 2,000 m. We also consider a larger regional forcing box, encompassing the smaller local forcing box as well as the Mid-Atlantic Right to the south and the Scotian Shelf to the north. Any contributions outside the regional forcing box are considered as remote forcing contributions.
Table 2 summarizes the variance of the total reconstructed SLA explained by wind and buoyancy forcings from the various regions defined above. For winds, the GoM (local forcing region) is the main contributor, explaining about 48% of the variance of the total reconstructed Nantucket sea level. The regional wind contributions from the GoM, Mid-Atlantic Bight, and Scotian Shelf account for 66% of the variance. Remote winds explain about 27% of the variance, smaller than the local and regional wind contributions. In contrast, remote buoyancy forcing contribution is larger than local buoyancy forcing contribution, explaining 8.5% and 2.6% of the variance of the total reconstructed SLA respectively. Our causal analysis indicates that local wind stress is the main contributor to sea level change along the US northeast coast.
Figure 5 shows the reconstructed sea-level time series using wind stress (Figure 5a) and buoyancy forcing (Figure 5b) from various forcing regions (Table 2). The numbers in the figure legend are the variance of the reconstructed SLA using wind stress (Figure 5a) and buoyancy forcing (Figure 5b) explained by the reconstruction from each forcing region. For wind stress, the local forcing box explains 58% of the variance of the wind reconstruction, more than that of the remote forcing region (49%). That the local wind contribution is larger than the remote wind contribution is consistent with what is shown in Table 2. The wind stress contribution from the Labrador Sea is
\begin{table}
\begin{tabular}{l l c c} \hline Forcing & Region name & Description & Explained variance (\(\sigma\); \(r\)) \\ \hline Wind & Local (Gulf of Maine) & 71\({}^{\circ}\)–66\({}^{\circ}\)W, 40\({}^{\circ}\)–45\({}^{\circ}\)N, 0–2,000 m & 48\% (0.84;0.77) \\ & Regional & 80\({}^{\circ}\)–60\({}^{\circ}\)W, 35\({}^{\circ}\)–45\({}^{\circ}\)N, 0–2,000 m & 66\% (1.3;0.83) \\ & Remote & All areas outside the regional forcing box & 27\% (0.87;0.53) \\ & Labrador Sea & 65\({}^{\circ}\)–45\({}^{\circ}\)W, 50\({}^{\circ}\)–70\({}^{\circ}\)N & \(-\)15\% (0.46;-0.19) \\ Buoyancy & Local (Gulf of Maine) & 71\({}^{\circ}\)–66\({}^{\circ}\)W, 40\({}^{\circ}\)–45\({}^{\circ}\)N, 0–2,000 m & 2.6\% (0.54;0.19) \\ & Regional & 80\({}^{\circ}\)–60\({}^{\circ}\)W, 35\({}^{\circ}\)–45\({}^{\circ}\)N, 0–2,000 m & 2.7\% (0.58;0.20) \\ & Remote & All areas outside the regional forcing box & 8.5\% (0.79;0.31) \\ & Labrador Sea & 65\({}^{\circ}\)–45\({}^{\circ}\)W, 50\({}^{\circ}\)–70\({}^{\circ}\)N & 0.0\% (0.48;0.12) \\ \hline \end{tabular} _Note. The standard deviation (\(\sigma\)) of total reconstructed SLA is 1.9 cm. The numbers in parenthesis are the standard deviation (cm) of the reconstruction by a particular forcing from a specified region and the correlation coefficient (\(\sigma\)) between the total and specific reconstructed SLA._
\end{table}
Table 2_Percentage Variance of Total Reconstructed SLA Explained by the Reconstructed SLA Using Wind Stress and Baoyancy Forcing From Various Forcing Regions_
Figure 4.— Forcing regions shown in a map of the correlation coefficient between the monthly-mean AVISO SLA near Nantucket Island (denoted as X) and that at each grid point. See Table 2 for definitions of the forcing regions. The remote forcing region is defined as all areas outside the regional forcing box (in blue). The dashed oval is a schematic illustration of the subpolar gyre and its counterclockwise circulation (as designated by the arrow on its perimeter). The two straight arrows are schematic illustrations of the Labrador Current and shelf break currents. Contours are isobaths of 200, 700, and 2,000 m (dark gray). The sea level is the same as used in Figure S1.
negative (\(-4.2\%\)). Also, the magnitude of reconstructed SLA from wind stress over the Labrador Sea is small (the largest being about 1 cm) compared with the 4-cm magnitude of that using wind stress from all regions. Reconstructed SLA using wind stress from the Labrador Sea is uncorrelated to that from all forcing regions (\(r\) being close to zero). The lack of wind stress contribution from the Labrador Sea found in this study differs from what was hypothesized by [PERSON] et al. (2013) based on the anticorrelation of wind stress curl in the Labrador Sea with North-America coastal sea level. The ECCO wind stress curl is indeed significantly anticorrelated with Nantucket sea level (\(r=-0.46\)), similar to [PERSON] et al. (2013). However, our causal analysis presented above shows that Labrador Sea wind stress curl is not an important driver of sea-level variation along the US northeast coast.
For reconstructed SLA using buoyancy forcing, local and remote forcings explain 53% and 76% of the variance, respectively. That the remote buoyancy forcing is larger than the local buoyancy forcing is also consistent with what the explained variance of the total reconstructed SLA indicates (Table 2).
## 5 Enhanced Buoyancy Contribution During 2010-2013 and 1999-2002
While wind contribution is generally larger than the buoyancy forcing contribution, the latter can be as important as the former in some years (Figure 2b), most notably during 2010-2013 and 1999-2002. Here, we further investigate where the buoyancy contribution came from during the two time periods. The contributions of local and remote buoyancy forcing for 2010-2013 and 1999-2002 are illustrated in the insets of Figure 5b, where the time series are the same as the curves in Figure 5b but with the anomalies computed relative to January 2010 and January 1999, respectively.
For 2010-2013, there was about 3-cm of SLR from 2010 to early 2012. The main contributor is from the Labrador Sea and starts in 2010. There was a record low of ocean heat loss in the Labrador Sea during 2008-2010,
Figure 5: Reconstructed SLAs (cm) using a particular forcing in a specific forcing region for (a) wind stress and (b) buoyancy forcing. The individual curves are reconstructed SLAs from the globe (blue), local (dashed), remote (dotted), regional (red), and Labrador Sea (purple) forcing regions. See text and Table 2 for definitions of the forcing regions. The numbers are percentage explained variance of reconstructed SLA using a particular forcing over a specific region. The insets show reconstructed SLAs for 1999–2002 and 2010–2013. Also shown in the inset is the sum (black) of reconstructed SLAs from the local forcing box (dashed) and Labrador Sea (purple). All curves are relative to the corresponding time mean, except that those in the insets are relative to January 1999 and January 2010.
which would create a positive sea-level change along the US northeast coast ([PERSON] et al., 2015). Adjoint sensitivities (Figures 0(a)-0(h)) and a forward perturbation experiment later in the study (Section 6.1.1) indicate that a perturbation of buoyancy forcing in the Labrador Sea takes 2-3 years to affect Nantucket sea level. Therefore, the record low of ocean heat loss in the Labrador Sea during 2008-2010 is expected to cause a sea-level rise near Nantucket during 2010-2012.
The buoyancy forcing contribution from the Labrador Sea peaks in mid-2011. However, the local buoyancy forcing contribution starts to increase around the same time and extends through the first half of 2012. The local contribution seems to be caused by the marine heat wave event during 2011-2012 that generated a record warm sea surface temperature (SST) not seen in past 150 years ([PERSON] et al., 2014, 2015). Local buoyancy forcing causes about 1-cm increase in Nantucket sea level and is almost completely due to heat flux forcing (not shown), consistent with the impact of the marine heat wave event.
There is also another event during 1999-2002 when reconstructed SLA due to buoyancy decreases by more than 4 cm. The buoyancy forcing from the GoM and Scotian Shelf causes about 1.9 cm decrease, while the remote buoyancy forcing from the Grand Banks, Labrador Sea and the subpolar gyre caused about 1.3-cm decrease.
The results in this section suggest that Nantucket sea level may be partly predictable a couple years into the future in some years. The forcing influence map (Figure 2(b)) and the sensitivity maps due to heat and freshwater fluxes (Figures 0(a)-0(h)) illustrate where and when buoyancy forcing affects the interannual variations of Nantucket sea level. In particular, the remote buoyancy forcing from the subpolar North Atlantic, especially the large positive influence region (red color in Figure 2(b)), can have a significant effect on Nantucket sea level a few years later.
## 6 Perturbation Experiments
To investigate how forcing affects Nantucket sea level, we further conduct forward forcing perturbation experiments similar to [PERSON] et al. (2015). Analysis of the forward model evolutions in response to the selected forcing perturbations sheds light on the associated oceanic processes and time scales. We present results related to remote buoyancy forcing in Section 6.1 and wind stress in Section 6.2. Note that the forcing perturbation experiments described in this section do not use the bulk-formula forcing formulation. The bulk formulae act to \"restore\" the surface ocean to a certain value based on atmospheric states, which presumably would make the buoyancy anomalies dampen away more quickly. Future efforts investigating potential impact of using the bulk-formula methodology on evolution of the perturbed ocean state would be of interest.
### Remote Buoyancy Forcing
The buoyancy forcing influence map (Figure 2(b)) provides a guidance for the forcing perturbations. Here we conducted three forward model sensitivity experiments by perturbing the remote buoyancy forcing in the subpolar gyre south of Greenland (Section 6.1.1), along the continental shelf in the Labrador Sea (Section 6.1.2), and near the Flemish Cap (Section 6.1.3). The buoyancy forcing in the first two regions is associated with relatively large positive variance explained for Nantucket sea level, while that in the third region is associated with negative variance explained.
#### 6.1.1 Subpolar North Atlantic
We perturb the heat flux in the subpolar North Atlantic (Figure 5(a)) where there are large positive contributions by remote buoyancy forcing, specifically, the deep ocean (>2,000 m) between 65\({}^{\circ}\)-45\({}^{\circ}\)W and 50\({}^{\circ}\)-60\({}^{\circ}\)N that has explained variance of Nantucket sea level larger than \(2.5\times 10^{-7}\) km\({}^{-2}\) (see Figure 2(b)). The prescribed heat flux perturbation increases linearly over the course of one week reaching a maximum magnitude of 5 W m\({}^{-2}\) at 12 Z of 9 December 1992, and then decreases linearly to zero over the course of one week.
The monthly-mean perturbed SLA, computed as the sea level difference between the perturbed run and the reference run (i.e., ECCO V4\(\pi\)3), indicates that the positive heat flux perturbation creates an initial SLA that is predominantly positive due to local thermosteric effect. The positive anomaly first rotates counterclockwise while spreading to a larger region of the subpolar gyre due to the effect of the circulation. Figure 5(b) shows SLA about 1 month after the initial heat flux perturbation is applied. The dominant feature is a region of large positive anomaly (red color) not very far away from the region with initial heat flux perturbation. There are small positive SLAs in distant regions such as Hudson Bay and a large swath of continental shelves along the east coast of North America. Although not visibly noticeable from the map, the time series of perturbed Nantucket SLA suggests that very weak signals can actually reach Nantucket within 1 month (cyan curve in Figure 7). This quick Nantucket sea-level response to the heat flux perturbation in the subpolar North Atlantic is likely due to coastally trapped waves with typical speeds around 2-3 m s\({}^{-1}\) at high latitudes that would take a few weeks to propagate from the perturbed subpolar North Atlantic to reach Nantucket ([PERSON] et al., 1998; also see Figure 1 of [PERSON] et al., 2019).
Figure 6.— (a) Mask (in red) for a 2-week heat flux perturbation centered at 12Z, 9 December 1992 that is applied in the subpolar North Atlantic (see text). (b)–(f) The resultant monthly-average SLA (m) in January 1993 (b), March 1994 (c), April 1995 (d), November 1996 (e), and January 1999 (f). Nantucket is denoted by X.
Figure 7.— Time series of monthly-mean perturbed SLA (\(\times 10^{-3}\) cm) at Nantucket for heat flux perturbation applied to the subpolar North Atlantic Ocean (cyan), over the continental slope of the Labrador Sea (orange), and over Flemish Cap (green). Dots correspond to the time instances for panels (b)–(f) of Figures 6, 8 and 9.
While coastally trapped waves can cause rapid sea level variations thousands of kilometers away (e.g., [PERSON] & Marshall, 2002; [PERSON] et al., 2008), the majority of the positive SLA due to positive heat flux perturbation in the subpolar North Atlantic reaches Nantucket via what appears to be slow advective processes during 1994-1996. After moving westward reaching the continental slope in a month (Figure 6b), the SLA further spreads southward, likely via the Labrador Current. In about 15 months, the anomaly reaches the Grand Banks (Figure 6c). The SLA further spreads southwestward along the shelf. The perturbed SLA at Nantucket reaches the maximum response in about 2 years (Figure 6d), remaining around the same magnitude for about 1 year (Figure 7) and then gradually decaying thereafter (Figures 6e and 6f). The adjustment of SLA by the slow advective process is similar to what was found by [PERSON] and [PERSON] (1996) using a simple shallow-water model.
#### 6.1.2 Continental Slope
We conduct a second experiment over the continental shelf in the Labrador Sea where explained variance is also large (Figure 3b). The same perturbation as in the first experiment is applied to the region between 65\({}^{\circ}\)-55\({}^{\circ}\)W and 60\({}^{\circ}\)-70\({}^{\circ}\)N where the values of explained variance in Figure 3b are larger than \(2.5\times 10^{-7}\) km\({}^{-2}\) (Figure 8a).
The positive heat flux perturbation creates positive SLA that quickly spreads to the shelf (Figure 8b), moves southward (Figure 8c), and further expands to the shelf and the subpolar North Atlantic (Figures 8d-8f). SLA at Nantucket (orange curve in Figure 7) reaches a plateau in about 1 year (December 1993) and stays on approximately the same magnitude for about 18 months (through June 1995). The anomaly further increases to the peak in September 1995 and then reduces over time. The perturbed SLA at Nantucket reaches a plateau in 1 year in this experiment as opposed to be 2 years in the first experiment because the perturbed heat flux in this experiment, being over the continental slope, is closer to the Labrador Current that carries the perturbed sea level signal.
#### 6.1.3 Flemish Cap
We also conduct a third experiment on Flemish Cap where explained variance is negative. The same perturbation to heat flux is applied over Flemish Cap where the explained variance in Figure 3b is smaller than \(-2\times 10^{-7}\) km\({}^{-2}\) (Figure 9a).
As in the other two experiments, the positive heat flux perturbation first generates positive SLA. In 1 month, the positive SLA propagates northeastward (away from Nantucket) and barely has any effect on Nantucket sea level
Figure 8: Same as Figure 6, but for the continental shelf of the Labrador Sea. (a) Mask (in red). (b)–(f) The resultant monthly-average SLA (m) in January 1993 (b), December 1993 (c), September 1995 (d), November 1996 (e), and January 1999 (f).
(Figure 9b). It subsequently spreads to a larger area to the northeast while rotating counterclockwise (Figure 9c) and gradually occupies the whole subpolar North Atlantic and Nordic Seas (Figures 9d and 9e). After 2 years, the positive sea level signal starts affecting Nantucket sea level (Figures 9e and 9f). Time series of the perturbed SLA at Nantucket shows very small values for over 2 years after the heat flux perturbation was applied (green curve in Figure 7). Nantucket SLA eventually increases and reaches its maximum after 5 years, much longer than the other two experiments. The negative explained variance near Flemish Cap (Figure 3b) thus can be attributed to the much longer time scales of the anomaly as it travels and dissipates around the subpolar gyre, thereby causing a response of Nantucket sea level that is not coherent with the dominant interannual signal at Nantucket.
### Wind Stress
Sensitivities to wind stress also show some interesting patterns. For instance, there is a dipole pattern for meridional wind stress over George Banks (Figure 1p). We explore it by conducting similar perturbation experiments to meridional wind stress over the western (Figure 10a) and eastern (Figure 10d) Grand Banks, respectively. The perturbated regions were chosen where the normalized sensitivities over the Grand Banks (Figure 1p) are larger than 0.27 and less than \(-\)0.34 for the two experiments. Same as in the previous three experiments, a positive perturbation with a maximum magnitude of 0.05 N m\({}^{-2}\) is applied over a 2-week period in December 1992.
The two perturbations initially generate SLAs with opposite signs, likely because Ekman transport due to perturbation in meridional wind stress moves water toward and away from the shallow region of Grand Banks, respectively (Figures 10b and 10e). The anomaly quickly propagates counterclockwise along the shelf as coastally trapped waves, with SLA at Nantucket reaching its maximum within 1-2 months (Figure 10g). The anomaly dissipates more rapidly than in the three heat flux perturbation experiments (compare Figure 10g vs. Figure 7). Although the majority of SLA dissipates quickly, some small SLA persists for a long time, probably propagating via higher-mode coastally trapped waves and through advective-diffusive processes. Figures 10c and 10f show SLA 3 years after the initial perturbation. SLA now occupies the whole North Atlantic with a maximum magnitude three orders smaller than that of the initial SLA. SLAs at Nantucket are positive and negative for the two experiments, consistent with the dipole pattern in the sensitivity map (Figure 1p).
Figure 9: Same as Figure 6, but for Flemish Cap (see text). (a) Mask (in red). (b)–(f) The resultant monthly-average SLA (m) in January 1993 (b), March 1994 (c), April 1995 (d), November 1996 (e), and January 1999 (f).
## 7 Concluding Remarks
We conducted a causal analysis to quantify the impacts of local and remote atmospheric forcings on interannual variations of Nantucket sea level. We first reconstructed Nantucket sea-level variations through the convolution of forcing anomalies with sea-level sensitivities to forcings computed using the adjoint of the ECCO model. We then decomposed the convolution into contributions by local and remote wind and buoyancy forcings. Wind forcing explains 67% of the Nantucket interannual sea-level variance, while wind and buoyancy forcing together explain 97% of the variance.
Wind stress contribution is mainly local, from the GoM and Scotian Shelf northeast of Nantucket. Wind stress from the GoM alone explains 48% of the Nantucket sea-level variance. If regional wind stress from the Mid-Atlantic Bight to the south and the Scotian Shelf to the north are included, the explained variance increases to 66%. Remote wind stress from outside the three aforementioned regions explains only 27% of the interannual variance of Nantucket sea level.
Remote buoyancy forcing explains 8.5% of Nantucket interannual sea-level variance, larger than the 2.6% variance explained by local buoyancy forcing. Although buoyancy forcing contribution is overall smaller than wind
Figure 10: Same as Figure 6, but for perturbations applied to meridional wind stress over (a)–(c) western and (d)–(f) eastern Grand Banks, respectively. Panels (a) and (d) are the mask, while the other maps are SLAs (m). (g) Respective time series of SLA at Nantucket, same as in Figure 7.
contribution, it can be comparable to wind contribution in some years (e.g., 1999-2002 and 2010-2013). Remote buoyancy forcing from the subpolar North Atlantic can significantly influence Nantucket sea level a few years later, providing a source of predictability for Nantucket sea-level variations. Forward perturbation experiments indicate that the remote buoyancy forcing affects the Nantucket sea level mainly via slow advective ocean processes, although coastally trapped waves can cause rapid Nantucket sea level response in a few weeks.
The results of our causality analysis (a) confirm the dominant contribution of local winds suggested by most previous studies that were based on correlation analysis or simplified models, (b) validate a hypothesis that subpolar-gyre buoyancy forcing plays a role in sea-level variations along the US northeast coast, and (c) nullify a correlation-based hypothesis that winds over the Labrador Sea are an important driver of sea-level variation along the US northeast coast. Our results about the relative contributions of different forcings and regions also provide useful information to evaluate climate models and to improve statistical or machine-learning methods for sea-level prediction for the US northeast coast.
Future investigations beyond this study include forcing contributions to Nantucket sea-level variations on decadal-and-longer time scales, the effect of adjoint-sensitivity dependence on the seasonally varying ocean state, and similarity and difference in forcing mechanisms for sea-level variations in the US southeast coast (e.g., [PERSON] et al., 2019) and those in the US northeast coast. Future effort using ECCO Version 4 Release 4, which has air-pressure loading forcing, and its adjoint would allow the inclusion of surface pressure effect in the attribution analysis.
## Data Availability Statement
This study uses the following data: ECCO V4r3 ([[https://ecco.jpl.nasa.gov/drive/files/Version4/Release3](https://ecco.jpl.nasa.gov/drive/files/Version4/Release3)]([https://ecco.jpl.nasa.gov/drive/files/Version4/Release3](https://ecco.jpl.nasa.gov/drive/files/Version4/Release3))), tide gauge ([[https://www.psmsl.org/data/obtaining/rfr.monthly.data/1111.frdata](https://www.psmsl.org/data/obtaining/rfr.monthly.data/1111.frdata)]([https://www.psmsl.org/data/obtaining/rfr.monthly.data/1111.frdata](https://www.psmsl.org/data/obtaining/rfr.monthly.data/1111.frdata))), and AVISO ([[https://resources.marine.coopernicus.eu/product-detail/SEALEVEL_GLO_PHY_1_4_MY_008_047/INFORMATION](https://resources.marine.coopernicus.eu/product-detail/SEALEVEL_GLO_PHY_1_4_MY_008_047/INFORMATION)]([https://resources.marine.coopernicus.eu/product-detail/SEALEVEL_GLO_PHY_1_4_MY_008_047/INFORMATION](https://resources.marine.coopernicus.eu/product-detail/SEALEVEL_GLO_PHY_1_4_MY_008_047/INFORMATION))). The adjoint sensitivity, forcing, and reconstruction script can be found at [[https://ecco.jpl.nasa.gov/drive/files/Version4/Release3/other/research/Nantucket_sea_level](https://ecco.jpl.nasa.gov/drive/files/Version4/Release3/other/research/Nantucket_sea_level)]([https://ecco.jpl.nasa.gov/drive/files/Version4/Release3/other/research/Nantucket_sea_level](https://ecco.jpl.nasa.gov/drive/files/Version4/Release3/other/research/Nantucket_sea_level)).
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* Ponte & Pte | wiley | Local and Remote Forcing of Interannual Sea‐Level Variability at Nantucket Island | Ou Wang, Tong Lee, Christopher G. Piecuch, Ichiro Fukumori, Ian Fenty, Thomas Frederikse, Dimitris Menemenlis, Rui M. Ponte, Hong Zhang | https://doi.org/10.1029/2021jc018275 | 2,022 | CC-BY |
wiley/fb0538a5_a293_4417_b528_9465412a82c9.md | # Geophysical Research Letters+
Footnote †: The authors. Geophysical Research Letters published by Wiley Periodicals LLC on behalf of American Geophysical Union.
In Situ Observations of Magnetic Reconnection Caused by the Interactions of Two Dipolarization Fronts [PERSON]
1 School of Electronic Information, Hubei Laojia Laboratory, Wuhan University, Wuhan, China, 2 School of Physics and Electronic Engineering, Hubei University of Arts and Science, Xiangyang, China1
[PERSON]
1 School of Electronic Information, Hubei Laojia Laboratory, Wuhan University, Wuhan, China, 2 School of Physics and Electronic Engineering, Hubei University of Arts and Science, Xiangyang, China1
###### Abstract
Using high-resolution data from the Magnetospheric Multiscale mission, an electron-only reconnection current sheet is found between two successive dipolarization fronts (DFs). The electron-only reconnection occurs between the northward component of the magnetic field of the flux pileup region (FPR) of the first DF (DF1) and the southward component of the magnetic dip of the second DF (DF2). The faster DF2 compresses the FPR of DF1, which constitutes an anti-parallel topology and reduces the thickness of the current sheet. Further analysis shows that the current sheet is unstable to the electron tearing instability, which may power the onset of the reconnection. Our results suggest that these two DFs may merge into one by the reconnection, which sheds light on the evolution of DFs during their earthward propagation.
Magnetic reconnection, releasing magnetic energy and energizing plasmas, are believed to be responsible for the explosive phenomena in space. Though reconnection has been investigated for decades, the onset of reconnection is elusive. Dipolarization fronts (DFs), important carriers in the transportation of mass, magnetic flux, and energy in the magnetotail, can be generated by reconnections and will integrate into the geomagnetic field at last. The generation of DFs and dynamics at DFs are thoroughly probed by simulations and observations. However, the evolution of DFs during their earthward propagation is rarely inspected. In this work, we present an observation of an electron-only reconnection between two successive DFs. The latter DF compresses the former DF and reduces the thickness of the current sheet between them. Inside the reconnection current sheet, electron tearing instability is unstable, which may power the reconnection. By reconnection, these two DFs may merge. Our observations can improve our understanding of the evolution of DFs in the magnetotail.
Research Letter
10.1029/2024 GL109685
## 1 Introduction
Magnetic reconnection, which can effectively convert energy from the magnetic field to the particles, is an explosive physical process in space, astrophysical, and laboratory plasmas. And it is thought to be responsible for many explosive phenomena such as supernova ejections, solar flare, geomagnetic substorm, and so on. The terrestrial magnetosphere, capable of in situ observations, is an ideal laboratory to explore the dynamics of magnetic reconnection. Magnetic reconnection in the terrestrial magnetotail has been widely observed ([PERSON] et al., 2010; [PERSON] et al., 2020; [PERSON] et al., 2018, 2022, 2023; [PERSON] et al., 2019, 2022; [PERSON] et al., 2001; [PERSON] et al., 2003; [PERSON] et al., 2018), and it is crucial for energy release and mass and magnetic flux transport in the magnetotail.
The onset of reconnection requires magnetic energy dissipation, which can be caused by the inverse electron Landau resonance due to electron tearing instability in the collisionless plasma ([PERSON] et al., 1966; [PERSON], 2015). For a current sheet with strictly anti-parallel field lines across the sheet, the growth rate for the collisionless tearing instability can significantly increase as the half-thickness of the current sheet approaches ion scales ([PERSON] et al., 1995; [PERSON], 2015; [PERSON] et al., 1991; [PERSON], 1974). However, a minor component (\(\sim\)10% of the anti-parallel magnetic field) normal to the current sheet (\(B_{\rm normal}\)) can restrain the electron Landau resonance and stabilize this instability ([PERSON] et al., 1995; [PERSON], 1979; [PERSON], 1976; [PERSON] et al., 1991; [PERSON], 1974). In the terrestrial magnetotail, the curved topology of the magnetic field can give such a \(B_{\rm normal}\) component and prevent spontaneous reconnection. Thus, how to reduce the \(B_{\rm normal}\) and bypass the stabilization threshold is vital to the onset of reconnection in the magnetotail.
Dipolarization fronts (DFs), ion-scale discontinuities separating the hot and tenuous high-speed plasmas from the cold and dense ambient plasmas, are important in transporting mass, energy, and magnetic flux from themagnetotail to the Earth (e.g., [PERSON] et al., 2011; [PERSON] et al., 2019; [PERSON] et al., 2024; [PERSON] et al., 2009). The typical features of a DF include an abrupt increase of \(B_{\rm z}\) within a short duration, a decrease in plasma density, and earthward plasma flow (e.g., [PERSON] et al., 2009). Abundant dynamic processes are found at and around DFs, such as sub-structures at DFs ([PERSON] et al., 2012; [PERSON] et al., 2020; [PERSON] et al., 2014), plasma waves and instabilities ([PERSON] et al., 2012; [PERSON], [PERSON], et al., 2015; [PERSON] et al., 2019; Pritchett & Coroniti, 2010; [PERSON] et al., 2022; [PERSON] et al., 2009; [PERSON], [PERSON], et al., 2014), energy conversion ([PERSON] et al., 2013; [PERSON], [PERSON], et al., 2015; [PERSON] et al., 2024; [PERSON] et al., 2019), and electron acceleration ([PERSON] et al., 2011; [PERSON] et al., 2023; [PERSON] et al., 2018; [PERSON]. [PERSON] et al., 2022).
A magnetic dip is usually found ahead of a DF (e.g., [PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2013, 2015; [PERSON] et al., 2016; [PERSON], [PERSON], et al., 2014), and the generation mechanism of the magnetic dip is under debate. [PERSON] et al. (2015) found that the redistribution of the cross-tail current caused by the plasma pressure gradient ahead of the DF combined with the duskward current at the DF can lead to the magnetic dip. [PERSON], [PERSON], et al. (2014) simulated that earthward and downward secondary current carried by reflected ions can cause the magnetic dip prior to the arrival of DFs. Using 3D global hybrid simulation, [PERSON] et al. (2015) explained the DFs as earthward propagating flux ropes. By reconnection between southward \(B_{\rm z}\) and northward geomagnetic field, the erosion of the southward magnetic flux of the flux ropes results in the DFs with magnetic dips ([PERSON] et al., 2003; [PERSON] et al., 2015).
DFs can be generated by magnetic reconnection ([PERSON] et al., 2013; [PERSON] et al., 2009). As DFs approach the Earth, the magnitude of the magnetic field reduces, and the energy carried by the earthward plasma flow transfers into the thermal energy and compression of the magnetic field ([PERSON] et al., 2008). However, how the DFs evolve during their earthward movement is rarely investigated.
In this work, we present in situ observation of an electron-only reconnection by the Magnetospheric Multiscale (MMS) mission between the northward flux pileup region (FPR) of the former DF and the southward magnetic dip of the latter DF. The latter DF moves faster than the former DF, compressing the current sheet between them. The electron tearing instability is found to be unstable in this current sheet, which may power the reconnection between these two DFs. We deduce that these two DFs may merge through the reconnection. Our observations reveal the possible evolution of DFs during their propagation in the magnetotail.
## 2 Observations
The data used in this work are from the MMS. The Fluxgate Magnetometer ([PERSON] et al., 2016) records the 3-D magnetic field of 128 Hz in burst mode. The Electric Double Probes ([PERSON] et al., 2016; [PERSON] et al., 2016) give the 3-D electric field of 8,192 Hz in burst mode. The Fast Plasma Investigation ([PERSON] et al., 2016) provides the plasma moments and 3-D plasma distribution functions, where electrons' data are sampled once every 30 ms in burst mode, and ions' data are sampled once every 150 ms in burst mode.
Figure 1 shows an overview of two successive DFs observed by MMS2 in the terrestrial magnetotail from 10:03:03 to 10:03:55 UT on 2 June 2017, when MMS2 was located at [\(-\)17.0, \(-\)5.5, 2.0] Earth radii (\(R_{\rm E}\)) in geocentric solar magnetospheric (GSM) coordinate system. During this interval, the spectra of ions and electrons are mainly concentrated on the energy range from several to tens keV (Figures 1a and 1b). Combined with the high temperature of electrons (Figure 1g) and large plasma \(\beta\) (larger than 0.5, red dashed line in Figure 1j), one can deduce that MMS was in the plasma sheet ([PERSON] et al., 2006). From \(\sim\)10:03:17 to \(\sim\)10:03:24.9 UT, \(B_{\rm z}\) increases sharply (Figure 1c), \(N_{\rm e}\) decreases (Figure 1e), and plasmas flow earthward (Figures 1d and 1j), which are features of a DF (dubbed DF1, [PERSON] et al., 2012; [PERSON] et al., 2002; [PERSON] et al., 2009). Then, \(B_{\rm z}\) continuously increases (Figure 1c) and \(N_{\rm e}\) decreases (Figure 1e) from \(\sim\)10:03:43.4 to \(\sim\)10:03:48.9 UT, which suggests another DF (entitled DF2). \(T_{\rm e}\) shows clear enhancement at DF1 and DF2, and the maximum of \(T_{\rm e}\) at the FPR (also called dipolarizing flux bundles) of DF1 is larger than that of DF2 and FPR2 (Figure 1g), which means that DF1 and DF2 are not one single DF. DF2 has a negative \(B_{\rm z}\) dip at the leading edge (Figure 1c). Timing analysis ([PERSON] et al., 1983) are performed on \(B_{\rm z}\) from 10:03:22.03 to 10:03:24.05 UT and from 10:03:43.47 to 10:03:48.41 UT, and the average motion velocity of DF1 and DF2 are \(\mathbf{V}_{\rm DF1}=233\times[0.95,-0.24,-0.22]\) km/s and \(\mathbf{V}_{\rm DF2}=513\times[0.76,-0.49,-0.43]\) km/s (GSM), which indicates that DF2 moves faster than DF1. At the end of the FPR of the DF1, an unambiguous current sheet is detected (Figure 1h, as marked by the red shade), in which the current is mainly contributed by electrons (Figure 1f).
Figure 2 shows the details of the current sheet in a local boundary normal (LMN) coordinate system. The LMN coordinate system is determined by the minimum variance analysis ([PERSON], [PERSON], 1998) on the magnetic field from 10:03:40.76 to 10:03:43.04 UT, and the results are \(\mathbf{L}=[-0.13,\,0.14,\,0.98]\), \(\mathbf{M}=[0.48,\,-0.86,\,0.18]\), and \(\mathbf{N}=[0.87,\,0.50,\,0.05]\) in GSM coordinates. The ratio of the maximum eigenvalue to the median one is 12.3, and the ratio of the median eigenvalue to the minimum one is 18.3, implying that the LMN coordinate system is reliable. A current sheet (the maximum of \(J_{\rm L}\) and \(J_{\rm M}\) are 30 nA/m\({}^{2}\) and 73 nA/m\({}^{2}\), respectively) is observed from \(\sim\)10:03:41.44 to 10:03:42.14 UT (Figure 2). Timing analysis is performed on \(B_{s}\) from 10:03:41.29
Figure 1: MMS2’s observations of dipolarization fronts (DFs) in the terrestrial magnetotail. (a) Ion and (b) electron omnidirectional differential flux; (c) magnetic field; (d) ion velocity; (e) electron density; (f) electron velocity; (g) electron temperature; (h) current density calculated by plasma moments \(\mathbf{J}=n\mathbf{\langle V_{\rm L}-V_{\rm J}\rangle}\); (i) plasma beta, the red dashed line is 0.5. The bars on the top mark different parts, in which “BG” stands for the background plasmas, “DF1” stands for the first dipolarization front, “FPR1” stands for the flux pileup region of the first dipolarization front, “DF2” stands for the second dipolarization front, and “FPR2” stands for the flux pileup region of the second dipolarization front. The red shade stands for the current sheet. All data are from MMS2 and presented in geocentric solar magnetospheric coordinates.
to 10:03:42.24 UT, and the average result is 470 \(\times\) [0.84, 0.50, 0.24] km/s (GSM). Then, the thickness of the current sheet is estimated as 329 km, that is, \(\sim\)0.6 \(d_{\rm J}\) or \(\sim\)27.7 \(d_{\rm J}\) (where \(d_{\rm J}\)\(\sim\) 509 km and \(d_{\rm J}\)\(\sim\) 11.9 km are ion and electron inertial length calculated with the average \(N_{\rm i}\) = 0.2 cm\({}^{-3}\) at the two sides of the current sheet from 10:03:41.2 to 10:03:41.44 UT and from 10:03:42.14 to 10:03:42.5 UT), indicating that this current sheet belongs to a sub-ion-scale structure. Ion flow is large but nearly unchanged during the crossing of the current sheet (the maximum change of \(V_{\rm i}\) is less than 0.1 \(V_{\rm A}\), \(V_{\rm A}\)\(\sim\) 288 km/s is the ion Alfven speed derived from the average plasma parameters \(|B_{\rm H}|\) = 5.9 nT and \(N_{\rm i}\) = 0.2 cm\({}^{-3}\) at the two sides of the current sheet from 10:03:41.2 to 10:03:41.44 UT and from 10:03:42.14 to 10:03:42.5 UT, Figure 2c). Considering that the background flow is strong, it is simpler and clearer to remove the background flow in the electron velocity and convective term in the electric field to investigate the local processes. \(V_{\rm d}\), and \(V_{\rm ext}\) are mainly negative in the current sheet, and the maximum of \(V_{\rm ext}\) and \(V_{\rm ext}\) are \(-\)849 km/s and \(-\)2,025 km/s (Figure 2e), which are much larger than the ion Alfven speed \(V_{\rm A}\). Thus, they are super-ion-Alfvenic electron jets. Along with the negative \(V_{\rm ext}\), \(B_{\rm H}\) changes from positive to negative (Figure 2a). \(B_{\rm M}\) stays positive and it has a negative to positive perturbation relative to a guide field \(\sim\)6.8 nT (estimated by \(B_{\rm M}\) at \(B_{\rm L}\) reversal) \(\sim\)0.8 \(B_{\rm B}\) (\(B_{\rm 0}\)\(\sim\) 8.7 nT is the average asymptotic magnetic field at the two sides of the current sheet from 10:03:41.2 to 10:03:41.44 UT and from 10:03:42.14 to 10:03:42.5 UT, Figures 2a and 2b), which is consistent with Hall magnetic field of the guide field reconnection (e.g., [PERSON], 2001). \(B_{\rm N}\)
Figure 2.— Detailed observations of the electron-only reconnection in the thin current sheet by MMS2 in LMN coordinates. (a) \(L\), \(N\) components, and the magnitude of the magnetic field; (b) \(M\) component of the magnetic field; (c) ion velocity; (d) electron density; (e) electron velocity with background flow removed (\(V_{\rm e}-V_{\rm i}\)); (f) current density calculated by plasma moments; (g) electric field in the ion frame; (h) \(L\) components of ion perpendicular velocity, \(\mathbf{E}\times\mathbf{B}\) drift velocity, and electron perpendicular velocity; (i) energy conversion rate \(\mathbf{J}\cdot\mathbf{E}^{\prime}\), where \(\mathbf{E}^{\prime}=\mathbf{E}+V_{\rm e}\times\mathbf{B}\); (j) a sketch of the crossing of the reconnection current sheet.
negatively enhances (Figure 1(a)), which is consistent with the crossing of one side of the outflow. \(N\) component of the electric field in the ion frame changes from negative to positive (Figure 1(g)), which is the Hall electric field. Therefore, the current sheet is reconnecting. \(L\) components of \(\mathbf{V}_{\text{\text{\text{LL}}}}\) and \(\mathbf{V}_{\text{\text{\text{LL}}}}\) deviate significantly from that of \(\mathbf{V}_{\text{\text{\text{LL}}}\text{\text{\text{\text{R}}}}}\) (Figure 1(h)), which implies that both ions and electrons are demagnetized. Besides, there is intense energy conversion from the fields to the plasmas in the current sheet (\(\mathbf{J}\cdot\mathbf{E}^{\prime}\) with a maximum of 68 pW/m\({}^{3}\), Figure 1(j)), which is on the same order as the reconnections in the magnetotail ([PERSON] et al., 2018; [PERSON] et al., 2018). Two negative \(\mathbf{J}\cdot\mathbf{E}^{\prime}\) peaks are found next to the positive one, which is consistent with the observations and simulations with a _N_-direction dominated, one-side crossing of the reconnection current sheet ([PERSON] et al., 2018; [PERSON] et al., 2018). According to the super-ion-Alfvenic electron jets, electron demagnetization, and noteworthy \(\mathbf{J}\cdot\mathbf{E}^{\prime}\), one can deduce that MMS detected an electron diffusion region (EDR, e.g., [PERSON] et al., 2019). It is worth noting that \(\mathbf{V}_{\text{\text{\text{L}}}}\) is steady in the current sheet (Figure 1(c)). Neither ion outflow nor ion inflow is observed, indicating ions do not respond to the reconnection process. Thus, the reconnection observed here is an electron-only reconnection, as reported in the magnetosheath and magnetotail ([PERSON] et al., 2018; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2018).
Electron-only reconnection is a novel type of reconnection in which ions do not respond to the process of reconnection, which is very different from the traditional reconnection where both ions and electrons participate in the reconnection. Electron-only reconnection, first reported in the magnetosheath ([PERSON] et al., 2018), has been observed in the magnetotail ([PERSON] et al., 2018; [PERSON], [PERSON], et al., 2020). However, the properties of the electron-only reconnection in the magnetotail are different from those in the magnetosheath. In the magnetosheath, electron-only reconnection occurs in the electron-scale current sheet and can persist relatively long. The spatial scale of the reconnection is confined to a small region so that ions do not respond to the reconnection process ([PERSON] et al., 2018; [PERSON] et al., 2021; [PERSON] et al., 2022). However, observations and simulations have proved that the electron-only reconnection in the magnetotail is a short-lived transition phase from the quiet current sheet to the traditional reconnection, and it can only exist for several ion cyclotron periods ([PERSON] et al., 2021, 2022; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2022; [PERSON] et al., 2020). Besides, the thickness of the electron-only reconnection current sheet in the magnetotail can vary from electron scale to ion scale ([PERSON] et al., 2022; [PERSON], [PERSON], et al., 2020), which can be larger than that in the magnetosheath. \(N_{\text{\text{\text{e}}}}\) enhances in the current sheet (Figure 1(d)), which is consistent with the electron-only reconnection reported in the magnetotail and simulations ([PERSON] et al., 2022; [PERSON], [PERSON], et al., 2020). On the contrary, \(N_{\text{\text{\text{e}}}}\) is depleted in the traditional reconnection ([PERSON] et al., 2018). In general, we propose that MMS encountered a guide field electron-only reconnection event without ion coupling ([PERSON] et al., 2021; [PERSON] et al., 2018) between two DFs. The inferred trajectory of MMS crossing the reconnection current sheet is shown in Figure 1(j).
The normal direction of the electron-only reconnection current sheet is earthward and duskward directed ([0.87, 0.50, 0.05], GSM), and the electron outflow is mainly in the negative \(\mathbf{Z}\) direction in GSM coordinates, which is very different from the standard magnetic reconnection expected in the magnetotail (normal direction of the reconnection current sheet is oriented in the \(\pm\mathbf{Z}\) direction and outflow is oriented in the \(\pm\mathbf{X}\) direction in GSM coordinates, e.g., [PERSON] et al., 2018). This difference may indicate the dynamics in this reconnection current sheet and the onset of the reconnection is particular.
## 3 Discussions
3D simulations suggest that the DF can be a place for secondary reconnection ([PERSON] et al., 2015). However, how can the secondary reconnection be initiated? The magnetotail's neutral sheet can be unstable to electron tearing instability, in which the electron Landau resonance can provide the dissipation required to initiate reconnection ([PERSON] et al., 1966). However, a normal component (i.e., \(B_{\text{z}}\) in GSM coordinates) caused by the curved magnetic field lines in the magnetotail can stabilize the electron tearing instability in a current sheet in the \(x\)-\(y\) plane ([PERSON] & [PERSON], 1976) and prevent the onset of reconnection. For the event observed here, the current sheet lies mainly in the \(y\)-\(z\) plane. Thus, the current sheet is a tilted current sheet. The tilted current sheet makes \(B_{\text{z}}\) a component in the plane of the current sheet and may allow electron tearing instability to occur spontaneously. The growth rate of the tearing mode can significantly enhance when the current sheet thins (e.g., [PERSON] et al., 1995; [PERSON], 2015; [PERSON] et al., 1991; [PERSON], 1974), and the orientation of the X-line is tended to be the direction of the fastest growth rate of the tearing mode (e.g., [PERSON] et al., 2018). However, the reconnection is 3-D. The magnetic fields on two sides of the boundary layer can shear at an arbitrary angle \(\mathbf{\phi}\) (see details in [PERSON] et al., 2018). As long as the antiparallel magnetic components can be found in a plane, reconnection can occur on this plane. Thus, the choice of the plane is not only ([PERSON] et al., 2018). Considering that the X-line is perpendicular to the reconnection plane, determining the reconnection plane is equivalent to determining the orientation of the X-line. Based on the simulations (e.g., [PERSON] et al., 2018), if the orientation of the X-line is in the range determined by the magnetic field on the current sheet's two sides, there is always a plane where antiparallel components can be found, and the growth rate of the tearing mode can be positive ([PERSON] et al., 2018). In other words, determining the range of the growth of the tearing mode is equivalent to determining the orientation of the X-line. Thus, based on the theory, simulations, and observations ([PERSON] et al., 2011; [PERSON] et al., 2013, 2018; [PERSON] et al., 2022), the unstable range of the tearing mode instability can be approximately determined with the magnetic field on the current sheet's two sides (the cyan and magenta arrows in Figure 3). As long as the orientation of the X-line lies in the unstable range, the tearing mode can be unstable, and reconnection may occur. In simulations, the orientation of the X-line can be determined by the magnitude of the current density with all information in the simulation box known ([PERSON] et al., 2018). However, it is impossible to do so in observations, where only a slice of the 3-D reconnection is observed. In a rigorous LMN coordinate system where the reconnection plane is perfectly in the LN plane, the orientation of the X-line is in the M direction and the current is only in the M direction at the X-line. However, the orientation of the X-line can be tilted from the M direction in observations due to the difficulty of determining the perfect reconnection plane. In the EDR, which contains the X-line, \(V_{\rm{eff}}\) is the dominant component, \(V_{\rm{eff}}\), is weaker, and \(V_{\rm{eff}}\) is negligible compared to \(V_{\rm{eff}}\) and \(V_{\rm{eff}}\) (e.g., [PERSON] et al., 2018), which is also the case in our event. Thus, for a reconnection in a LMN coordinates with M direction tilted from the X-line orientation, we can approximately use current density in the LM plane to infer the orientation of the X-line (i.e., the orientation of the fastest growth of the tearing mode). In our event, the magnetic field used to determine the unstable range of the tearing instability are the average values on the current sheet's two sides. \(B_{\rm{L1}}\) and \(B_{\rm{M1}}\) are the average values from 10:03:40 to 10:03:40 to 10:03:40.9 UT, and \(B_{\rm{L2}}\) and \(B_{\rm{M2}}\) are the average values from 10:03:42.2 to 10:03:43.2 UT. The currents in Figure 3 are acquired from 10:03:41.44 to 10:03:42.14 UT. Most of the currents in the current sheet observed by MMS are well inside the unstable range (coral shade in Figure 3), suggesting that this current sheet is dominated by tearing instability. Moreover, the thickness of the current sheet is sub-ion-scale. Hence, under the compression of DF2, electron tearing instability may develop in the current sheet and trigger the electron-only reconnection therein. Besides, this electron-only reconnection may not develop into an ion-coupled reconnection due to the compression of DFs limiting the scale of the current sheet. However, it is interesting to discuss what will happen if the electron-only reconnection evolves into an ion-coupled one. The electron-only reconnection is regarded as the early stage of the ion-coupled reconnection (e.g., [PERSON] et al., 2021, 2022; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2022; [PERSON] et al., 2020). Thus, electron-only reconnection will occur first if two DFs reconnect. If the electron-only reconnection evolves into an ion-coupled one, the reconnection between DFs can be faster due to the much larger energy conversion rate (\(\mathbf{J}\cdot\mathbf{E}^{\prime}\)) of the ion-coupled reconnection than the electron-only reconnection (e.g., [PERSON] et al., 2022). However, the total energy released by the reconnection will not change because the magnetic energy stored in the magnetic dip is the same. Besides, ions will be energized if the reconnection between two DFs is an ion-coupled reconnection.
Both DFs have negative dips ahead of them (Figure 1c). It is said that the magnetic dip ahead of a DF can be formed by reconnection between a flux rope and the geomagnetic field (e.g., [PERSON] et al., 2015; [PERSON] et al., 2018; [PERSON] et al., 2003; [PERSON] et al., 2015) or the downward current ([PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON], [PERSON], et al., 2014). Dawnward currents are found near the dip regions of DF1 and DF2 (Figure 1h). But the duskward currents dominate. Besides, the dawnward currents are mainly carried by electrons rather than ions (Figures 1d, 1f, and 1h, e.g., [PERSON] et al., 2015). And the precursor signature such as increases of \(V_{\rm{ls}}\) ahead of DFs (e.g., [PERSON] et al., 2015) are not found (Figure 1d). Thus, the magnetic dips are not caused by the dawnward current here (e.g., [PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON], [PERSON], et al., 2014). \(B_{\rm{y}}\) component is not dominated at both DFs (Figure 1c). However, the \(N_{\rm{e}}\) minorly increases at the reversals of \(B_{\rm{z}}\) from the dips to the DFs
Figure 3.— The current density of the reconnection current sheet in the \(L\)–\(M\) plane. The colorful dots represent the current density observed by different Magnetospheric Multiscale mission. The magenta and cyan arrows are the average magnetic field on the two sides of the reconnecting current sheet, which define the unstable range of the tearing instability predicted by the theory (as shown by the coral shade).
(Figure 1e), which means the magnetic dips may be a remnant signature of the erosion of a plasmoid without a strong core field (e.g., [PERSON] et al., 2015; [PERSON], [PERSON], et al., 2020).
DFs and flux ropes can be generated by magnetic reconnection. As the counterpart of the DFs, flux ropes can host complicated evolution during their movement, such as coalescing with other flux ropes by reconnection (e.g., [PERSON] et al., 2016; [PERSON] et al., 2017). Then, it is reasonable to ask whether DFs have similar processes as flux ropes coalescing. In our event, two successive DFs interact with each other through reconnection between the southward component of the magnetic dip of DF2 and the northward component of the FPR of DF1. With the proceeding of reconnection, the southward component of the magnetic dip of DF2 will be dissipated. When the dip is totally dissipated, the DF2 may integrate into DF1 due to the compression of the faster plasma flow behind DF2 (Figure 1d). Magnetic dips are usually accompanied with DFs (e.g., [PERSON] et al., 2015) and multiple DFs have also been reported (e.g., [PERSON] et al., 2009). Thus, the reconnections between DFs may be common. A single DF in the magnetotail can be the result of the coalescence of two or even more DFs. And the multiple DFs can be coalescing. However, more data are needed to be surveyed because the reconnections between DFs are transient compared to the time of the motion of the DFs.
## 4 Summary
In summary, an electron-only reconnection is identified in a tilted current sheet between two successive DFs. Both DFs have negative magnetic dips ahead of them, and the reconnection happens between the magnetic field of the FPR of DF1 and the magnetic field of the dip region of DF2. The faster DF2 compresses the FPR of DF1, which constitutes an anti-parallel topology and reduces the thickness of the tilted current sheet. In the tilted current sheet, the \(B_{x}\) caused by the curved topology of the magnetotail is a component in the plane, which can circumvent the stabilization effect of electron tearing instability. The electron tearing instability is unstable in the tilted current sheet, which may power the onset of the electron-only reconnection between two DFs. The successive DFs may merge into one DF eventually due to the reconnection and the faster plasma flow behind DF2. Our observations fill the gap of the evolution of the DFs between their generation and their ultimate fate of integrating into the geomagnetic field.
## Data Availability Statement
Magnetospheric Multiscale (MMS) data used in this work are publicly available from the MMS Science Data Center ([[https://lasp.colorado.edu/mms/sdc/public/about/browse-wrapper/](https://lasp.colorado.edu/mms/sdc/public/about/browse-wrapper/)]([https://lasp.colorado.edu/mms/sdc/public/about/browse-wrapper/](https://lasp.colorado.edu/mms/sdc/public/about/browse-wrapper/))).
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* [PERSON] et al. (2013) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2013). Current structures associated with dipolarization fronts. _Journal of Geophysical Research-Space Physics_, 178(11), 6908-6908. [[https://doi.org/10.1002/2013](https://doi.org/10.1002/2013) ja01920]([https://doi.org/10.1002/2013](https://doi.org/10.1002/2013) ja01920)
* [PERSON] et al. (2022) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] (2022). Direct evidence of interchange instabilities at dipolarization fronts. _Journal of Geophysical Research-Space Physics_, 12(10), 02022A03008. [[https://doi.org/10.1029/2022A030085](https://doi.org/10.1029/2022A030085)]([https://doi.org/10.1029/2022A030085](https://doi.org/10.1029/2022A030085))
* [PERSON] et al. (2016) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2016). Electromagnetic disturbances observed near the dip region ahead of dipolarization front. _Geophysical Research Letters_, 47(3), 3026-3043. [[https://doi.org/10.1002/2016608033](https://doi.org/10.1002/2016608033)]([https://doi.org/10.1002/2016608033](https://doi.org/10.1002/2016608033))
* [PERSON] et al. (2019) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2019).
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2019). Observations of an electron diffusion region in symmetric reconnected with weak guide field. _The Astrophysical Journal_, 8701, 34. [[https://doi.org/10.3847/1538-4357/asf16f](https://doi.org/10.3847/1538-4357/asf16f)]([https://doi.org/10.3847/1538-4357/asf16f](https://doi.org/10.3847/1538-4357/asf16f))
* [PERSON] et al. (2014) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2014). Observations of large-amplitude magnetosonic waves at depolarization fronts. _Journal of Geophysical Research: Space Physics_, 119(4), 4335-4347. [[https://doi.org/10.1002/20149019796](https://doi.org/10.1002/20149019796)]([https://doi.org/10.1002/20149019796](https://doi.org/10.1002/20149019796))
* [PERSON] et al. (2014) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2014). On the origin of pressure and magnetic perturbations ahead of depolarization fronts. _Journal of Geophysical Research: Space Physics_, 119(1), 211-220. [[https://doi.org/10.1002/2013](https://doi.org/10.1002/2013) ja019394]([https://doi.org/10.1002/2013](https://doi.org/10.1002/2013) ja019394) | wiley | In Situ Observations of Magnetic Reconnection Caused by the Interactions of Two Dipolarization Fronts | K. Jiang, S. Y. Huang, Y. Y. Wei, Z. G. Yuan, Q. Y. Xiong, S. B. Xu, J. Zhang | https://doi.org/10.1029/2024gl109685 | 2,024 | CC-BY |
wiley/fad80e63_7e1a_4f0b_93f7_2e9836375ea8.md | would raise the water pressure in rock joints as well as the swelling in clayous rocks, or enable dissolution or leaching, that freeze-thaw would raise the pressure in cracks from the ice formation, as well as cause a loss of cohesion from the melt, while thermal stresses could cause daily to yearly cycles of thermal expansion ([PERSON] et al., 2016). Quantifying the contributions of each of these meteorological processes toward the rock mass alteration is a complex task, as constraints accumulate until failure ([PERSON], 2017), thus making direct comparisons difficult.
The role of weathering in the development of rock mass instabilities is thus hard to quantify, especially in the context of frail sedimentary rocks such as flysch ([PERSON] & [PERSON], 2014). In such a geological setting, the differential weathering between the softer rocks and the more competent units leaves the slope vulnerable to multiple modes of failure, such as toppling, sliding, or rockfalls ([PERSON] & [PERSON], 2013; [PERSON] et al., 2022). To understand the role of meteorological variations on the development of rock cliff instabilities, studies tackling this problem in such a geological context have quantified either rock alteration of selected rock segments using extensometers ([PERSON] & [PERSON], 2023b), or rockfall volume using time-lapse LIDAR ([PERSON] & [PERSON], 2023a).
In [PERSON] and [PERSON] (2023b), the authors have installed extensometers on flysch walls overhanging major road segments in the Haute-Gaspesie region, located in eastern Quebec, Canada. With these instruments, the authors aimed to study the impact of the differential weathering between the different rock sequences on the progressive failure of the sandstone layers. They were able to measure the toppling of the sandstone blocks caused by the compression of the siltstone layers. Their measurements highlight the fatigue caused by the shrink-swell behavior of the siltstone, linked to variations in water content caused by rainfall or melt, as well as the irreversible deformation in the sandstone layers caused by freeze-thaw cycles, linked to the expansion of water in cracks and pores. In [PERSON] and [PERSON] (2023a), the authors have used time-lapse LIDAR to generate consecutive surface models of rock cliffs in the Haute-Gaspesie region. By subtracting the different surfaces, they were able to compute a time series of rockfall volume, enabling the determination of rockfall occurrence as well as rockfall magnitude. By coupling their measurements with weather data, they were also able to identify meteorological conditions responsible for increasing the frequency of low-magnitude rockfalls (winter freeze-thaw cycles and moderate rainfall) as well as large-magnitude rockfalls (spring thaw and high-intensity rainfall). Both these methods come with their trade-off. Using extensometers can provide key insights into the alteration of localized rock segments with dense temporal measurements. On the other hand, repeated LIDAR surveys can measure centimetric surface deformation, but at the cost of a greatly reduced temporal density.
To address these weaknesses and complement rock wall monitoring, many authors have proposed to use passive seismic monitoring (PSM) systems ([PERSON] et al., 2011; [PERSON] et al., 2008; [PERSON] et al., 2019; [PERSON], [PERSON], et al., 2017; [PERSON] & [PERSON], 2011; [PERSON] et al., 2017). The processes precursory to rockfalls as well as the rockfalls themselves generate detectable seismic events, making PSM a viable tool to study rockfall hazards and their link to meteorological occurrence in addition to building an early warning system ([PERSON] et al., 2018; [PERSON] et al., 2016; [PERSON] et al., 2015). Typical use of PSM in such a framework is similar to global seismology and earthquake surveillance ([PERSON] & [PERSON], 2010). It implies the use of an event-detection algorithm, triggered when the seismic amplitudes are multiple times greater than the ambient noise ([PERSON] & [PERSON], 2016). The rate of occurrence of seismic events is often analyzed and linked to meteorological variations, such as rainfall amounts. Analysis of the seismic waveforms is necessary to distinguish the different signals of interest, such as local or global earthquakes as well as anthropogenic noise. For example, [PERSON] and [PERSON] (2010) have installed a seismic network to monitor a rockslide in the French Alps. After detecting, interpreting, and discriminating relevant seismic events, they were able to provide a sense of how rainfall affects rockfall amounts as well as the accelerations in the rockslide's displacements. Depending on the instrument configuration and the number of sensors, the spatial localization of the seismic source is possible. Work from [PERSON] and [PERSON] (2011), located on the same site in the French Alps, showed how rockfall events and microseismic tremors can be located using simple velocity models. The authors were able to compute the trajectory of a rockfall as it hit the rock face, as well as locate micrometors beneath the surface, linked to the development of larger mass movements.
Besides, machine learning has recently become increasingly used in all areas of seismology, including natural hazards monitoring. Machine learning can help in dealing with noisy environments, for example, in more densely populated areas, as well as when processing large data sets. Typical uses of machine learning in seismology are event detection ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] & [PERSON], 2019) and classification ([PERSON], [PERSON], et al., 2017; [PERSON] et al., 2023; [PERSON] et al., 2017). Most of the studies use supervised learning, where the arrival time or the origin of the seismic events are known and (often) manually labeled. However, other studies rely on unsupervised learning, where events with similar statistical properties are grouped (or clustered) together. In the latter case, a low-dimensional projection (or embedding) of the detected seismic signals is typically computed with feature engineering ([PERSON] et al., 2011; [PERSON] et al., 2017; [PERSON] et al., 2020) or deep learning ([PERSON] et al., 2021; [PERSON] et al., 2023). A clustering algorithm can then be used to group signals that are close to each other in the embedded space. Since the mechanisms causing the events in the different clusters are not known, an in-depth analysis of the occurrence of the events in each cluster must be performed to allow their interpretation, linking meteorological variations to the occurrence of each different type of seismic event.
In this study, we aim to use the latter approach to analyze seismic data acquired on a rock cliff located in eastern Canada to detect and classify rockfall events, as well as to understand the link between meteorological variations and seismic activity associated with rockfall, ultimately paving the way for the development of a surveillance tool. The proposed method uses very sensitive _Short-Time Average over Long-Time Average_ (STA-LTA) windows ([PERSON] & [PERSON], 2016) to build a large catalog of unlabeled seismic events. For each detected event, we compute 85 features synthesizing various seismic properties that represent the envelope, the frequency content, polarization attributes, and correlation between the geophones installed within the network. We use Gaussian Mixture Models (GMM) ([PERSON], 2020), to partition the collected data set into three different clusters. To interpret their physical origins, we analyze their different properties, such as the daily temporal distribution of their occurrence, as well as the _P_-wave polarization distribution. Furthermore, a regression analysis is made where the rate of occurrence of every type of signal is the target variable. With multiple meteorological features as the explanatory variables, this analysis aims to associate the different clusters with physical processes.
## 2 Study Site
The Haute-Gaspesie region is located in the northeastern part of the Appalachian geological province and is mainly characterized by Ordovician sedimentary rocks. Within an approximately 70 km long extension that includes the study area, the main regional road has multiple sections landlocked between the Saint-Laurent River and tall rock walls, reaching up to 100 m in some sectors (Figure 1a). As a result, the road is exposed to multiple natural hazards, such as coastal erosion or flooding ([PERSON] et al., 2019), snow avalanches ([PERSON] et al., 2011) and ice falls ([PERSON] et al., 2017), as well as debris flows ([PERSON] et al., 2015) and rockfalls ([PERSON] & [PERSON], 2023, 2023b). The rock cliffs are made of highly fractured Ordovician flysch, sedimentary sequences of sandstone, mudstone, and pelagic shale ([PERSON], 1971; [PERSON], 1969) and are highly unstable due to differential weathering ([PERSON] et al., 2022). More specifically, as the sandstone layers exhibit a much higher resistance to weathering than the mudrock layers, the latter retreats much faster, creating a progressively larger overhang of the sandstone. This increases tensile stresses until the sandstone layers eventually fail and fall ([PERSON] et al., 2022). The study site is located around 2 km west of the village of Gros-Morne, in the province of Quebec, Canada. The 65 m-high rock face is almost vertical (80-85\({}^{\circ}\)) ([PERSON] & [PERSON], 2023b). The cliff is facing north-northwest (340\({}^{\circ}\)), thus receiving little solar exposure. The main bedding plane shows a strike and dip of 100\({}^{\circ}\) and 10\({}^{\circ}\) respectively with many orthogonal joints. The rock wall overlooks a talus with a slope of around 38\({}^{\circ}\), 40 m in height, formed of sandstone blocks and mudstone flakes. The region is under a humid, continental climate. Between 1991 and 2020, the maximum and minimum average temperatures were 16.3 and \(-9.2^{\circ}\)C in July and January respectively ([PERSON], 2023b).
## 3 Methodology
### Data Collection
Multiple instruments were installed on the rock wall near Gros-Morne, approximately 20 m from the top of the rock face (Figures 1a-1c). Precipitation data were also collected at a nearby weather station, located 21 km west of the site. A synthesis of the instruments is presented in Table 1. We redirect the reader to [PERSON] and [PERSON] (2023b) for further information on the installation of the instruments. In 2020, three triaxial geophones were installed in boreholes drilled perpendicularly to the wall within thick enough sandstone layers. Each geophone is an in-house assembly made with three HG-6 HS sensors (HGS India) having a cutoff frequency of 4.5 Hz and a sensitivity of 79 V/(m/s) \(\pm\) 5%, mounted inside a custom 3D printed case and sealed in a rigid ABS tube. Eachgeophone was inserted 60 cm deep into a borehole and cemented with fast-setting cement. The geophones were connected to Pegasus loggers (Nanometrics) that were continuously recording at a sampling frequency of 1 kHz and were powered by a 28 Ah 12 V battery maintained with a solar panel and a Maximum Power Point Tracker (MPPT) regulator, as shown by the simplified sketch in Figure 1d. The data were retrieved periodically from the field and stored on a local server for further processing. The geophones were installed in close proximity (<10 m) mainly due to the preliminary nature of the study, where the aim was to gather initial data to inform future research. The chosen configuration allowed for a feasible setup under the constraints of roped work on the rock cliff. Additionally, the proximity to the already installed weather station facilitated the installation of the power source. It should be noted that power problems occurring between October 2020 and July 2021 caused three major interruptions in data acquisition.
\begin{table}
\begin{tabular}{l c c c c} \hline \hline Instrument & Precision & Datalogger & Sampling period & Specifications \\ \hline GeoPrecision 915 MHz thermistor string & \(\pm\) 0.01\({}^{\circ}\)C & Minlogger M-LogSW & 15 min & Eleven probes installed at 30 cm intervals up to 3 m. \\ Onset S-WSET-B wind speed and direction & \(\pm\) 1.1 m/s and sensor & HOBO Microstation & 15 min & – \\ OTT Pluvio\({}^{2}\) & \(\pm\) 0.05 mm & Campbell CR1000 & 15 min & Installed 21 km west of the site. \\ HG-6 HS geophone & \(\pm\) 79.9 V/m/s & Nanometrics Pegasus & 1 ms & Three 3C geophones installed \(\sim\)60 cm within the rock face. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Synthesis of the Instruments Installed on and Near the Site
Figure 1: Study site. (a) Gros-Mome location. The yellow shading highlights the \(\sim\)70 km section of the road at risk of rockfalls. (b) Drone photograph of the studied rock cliff and its surroundings. (c) Data collection at the meteorological station, showing the flysch layers. (d) Schematic of the installed geophones.
### Event Detection
The first data processing step consists of building a catalog of seismic recordings that encompass events triggered by a wide range of mechanisms. This is achieved using the _Short-Time Average over Long-Time Average_ (STA-LTA), which consists of computing the ratio between two moving average windows of different lengths (short and long) on seismic traces ([PERSON], 2016). While the shorter moving window encapsulates temporally local amplitude variations, the longer moving window records ambient noise levels. For a trace \(\mathbf{x}\) of length \(n\), this can be defined by
\[\frac{\text{STA}}{\text{LTA}}(\mathbf{x},n_{\text{S}},n_{\text{L}})=\frac{1/n_{ \text{S}}\sum_{i=\text{cat}-n_{\text{S}}}^{\text{a}}\text{CF}(x_{i})}{1/n_{ \text{L}}\sum_{i=\text{cat}-n_{\text{cat}}}^{\text{a}}\text{CF}(x_{i})}, \tag{1}\]
where \(n_{\text{S}}\) and \(n_{\text{L}}\) are the lengths of the short and long moving windows respectively, and CF(\(\mathbf{x}\)) is a characteristic function of the trace. While many characteristic functions exist, a popular one for triaxial component geophones is the sum of the absolute values of every component
\[\text{CF}(\mathbf{x})=|\mathbf{x}_{\text{N}}|+|\mathbf{x}_{\text{E}}|+|\mathbf{x}_{\text{z}}|, \tag{2}\]
where N, E, and z denote the north, east, and vertical components respectively. With this definition, a seismic event is triggered when the STA-LTA ratio is raised over a given threshold \(\tau_{\text{m}}\). The event is recorded until the ratio reaches another threshold \(\tau_{\text{cat}}\). This method needs a delicate parametrization and trial-and-error is needed unless a labeled data set exists. While we have video footage of a few controlled rockfall experiments, finding optimal STA-LTA parameters proved difficult. Therefore, we decided to use very sensitive parameters, detecting as many events as possible, with the goal of discriminating events in a subsequent step. Besides, using multiple STA-LTA filters helps in detecting wider ranges of seismic events ([PERSON] et al., 2024). We therefore performed event detection using two STA-LTA pairs: 1 and 60 s, as well as 2.5 and 60 s, both using values of 10 and 2 for \(\tau_{\text{m}}\) and \(\tau_{\text{cat}}\). Those short and long window pairs were found to be adequate for detecting a broad range of seismic events.
Since the geophones in the network are close to each other, delays in \(P\)-wave arrival are very small, and each detected event is therefore considered synchronous. As a result, an event in the catalog is constituted by the waveforms recorded at the three 3 C geophones, for nonoverlapping STA-LTA detections at any of the geophones. Finally, to account for the possibility that rockfall events can cause multiple seismic events in close succession, detected seismic events closer than 3 s are joined together. Our preliminary testing also revealed that applying a 50 Hz highpass filter helped some of the noise caused by either the nearby shore or the roads located above and under the cliff. The highpass filter effectively works as a means to record weaker, local seismicity. After detection, each trace in the catalog is stored in its raw form, without the high-pass filter. Implementation of STA-LTA and event detection is done through the obspy library ([PERSON] et al., 2010).
### Event Classification
Next, events are classified using Gaussian Mixtures Models (GMM) ([PERSON], 2020). This requires computing features that synthesize various properties of the signal, which is done following the approach proposed by [PERSON] et al. (2017). A total of 85 features are computed (Table 2), grouped into four categories of properties:
* the envelope,
* the spectrum,
* \(P\)-wave polarization, and
* correlation in the geophone network.
Details on how the features are computed are shown in Appendix A.
Since our network contains three triaxial geophones, each event has nine associated traces. For the first two categories (envelope and spectrum), the values are computed on the trace with the highest signal-to-noise ratio (SNR), computed as the ratio between the maximum absolute value in a trace and its standard deviation. The latter two categories of seismic features (polarization and network correlation) depend on all three components of the entire geophone network. Finally, the resulting data set is standardized using Z-score normalization and analyzed
\begin{table}
\begin{tabular}{l l l} \hline \hline Variable & Category & Description \\ \hline abscorAVG & Correlation & Average absolute value from the correlation matrix \\ abscorMAX & Correlation & Maximum absolute value from the correlation matrix \\ abscorMED & Correlation & Median absolute value from the correlation matrix \\ abscorMIN & Correlation & Minimum absolute value from the correlation matrix \\ abscorRANGE & Correlation & Difference between maximum and minimum absolute value from the correlation matrix \\ abscorSTD & Correlation & Standard deviation of the correlation matrix’s absolute values \\ corrAVG & Correlation & Average correlation of the correlation matrix \\ corrMAX & Correlation & Maximum correlation of the correlation matrix \\ corrMED & Correlation & Median correlation of the correlation matrix \\ corrMIN & Correlation & Minimum correlation of the correlation matrix \\ corrRANGE & Correlation & Difference between maximum and minimum correlation of the correlation matrix \\ corrSTD & Correlation & Standard deviation from the correlation matrix \\ DUR & Envelope & Logarithm of the duration of the recorded signal \\ ENERGY BP a-b & Envelope & Logarithm of the energy from the envelope with a bandpass signal from a to b Hz. \\ & & Computed with slices of 50 Hz, from 1 to 499. \\ ENERGY BS a-b & Envelope & Logarithm of the energy from the envelope with a bandstop signal from a to b Hz. \\ & & Computed with slices of 50 Hz, from 1 to 499. \\ envAREA & Envelope & Logarithm of the area under the signal envelope. \\ envAVG & Envelope & The average amplitude of the signal envelope. \\ KURT & Envelope & The kurtosis of the signal envelope. \\ envMAX & Envelope & Logarithm of the maximum amplitude of the signal envelope. \\ NPEAKS & Envelope & The number of peaks in the signal. \\ SKEW & Envelope & Skew from the signal envelope. \\ KURT BP a-b & Envelope & Kurtosis from the envelope with a bandpass signal from a to b Hz. Computed with slices of 50 Hz, from 1 to 499. \\ KURT BS a-b & Envelope & Kurtosis from the envelope with a bandstop signal from a to b Hz. Computed with slices of 50 Hz, from 1 to 499. \\ & & Logarithm of the time until the signal maximum amplitude. \\ RISETIME & Envelope & Logarithm of the time until the signal maximum amplitude. \\ SNR & Envelope & Strongest signal-to-noise ratio of the signals. \\ MEAN BEARING & Polarization & Mean azimuth of the waveform from the three geophones (Flinn, 1965). \\ MEAN PLANARTITY & Polarization & Mean planarity from the three geophones (Flinn, 1965). \\ MEAN PLUNGE & Polarization & Mean plunge from the three geophones (Flinn, 1965). \\ MEAN RECTILINEARTITY & Polarization & Mean rectilinearity from the three geophones. \\ PLANE DIP & Polarization & Dip of the plane of best fit containing the three geophones. \\ PLANE STRIKE & Polarization & Strike of the plane of best fit containing the three geophones. \\ R VALUE & Polarization & Measure of similarity between the polarization of the three geophones ([PERSON], 1959). \\ VAR PLANARTITY & Polarization & Variance of the planarity between the three geophones. \\ VAR RECTILINEARITY & Polarization & Variance of the rectilinearity between the three geophones. \\ dtARGMAX & Spectrum & Frequency at which the amplitude spectrum is maximal \\ dtRAVG & Spectrum & Logarithm of the average of the amplitude spectrum \\ dtRENERGY z-b & Spectrum & Logarithm of the energy between a and b of Nyquist frequency. Computed in slices of a tenth, from 0 to 1. \\ dtMAX & Spectrum & Logarithm of the maximum amplitude of the signal spectra \\ \hline \hline \end{tabular}
\end{table}
Table 2: Features Used in the Clustering and Their Computationthrough principal component analysis (PCA) ([PERSON], 2020). Partitioning of the reprojected data set is then made through GMM, using the Expectation-Maximization (EM) algorithm to compute the mean vectors \(\boldsymbol{\mu}_{i}\) and covariance matrices \(\mathbf{\Sigma}_{i}\) optimizing the partitioning of the data set in \(k\) clusters. The implementation of both PCA and GMM is made using the sklearn library ([PERSON] et al., 2011). The Bayesian information criterion (BIC) is an intuitive metric when used with GMMs. For a model \(M\) and observed data \(X\), it is defined as
\[\text{BIC}(M|X)=-2\log\bigl{(}\rho\bigl{(}X|M,\hat{\theta}\bigr{)}\bigr{)}+K_{M }\,\log(N), \tag{3}\]
where \(p\bigl{(}X|M,\hat{\theta}\bigr{)}\) is the likelihood of the data given a model \(M\) with \(K_{M}\) parameters \(\hat{\theta}\) and \(N\) observations. By computing the BIC for various numbers of clusters, an optimal value of \(k\) can be chosen through an elbow-curve analysis ([PERSON] et al., 2011).
### Regression Analysis
To physically interpret the discrimination made by the GMM, the rate of occurrence of seismic events in every cluster is compared to different meteorological variables (see Table 1) through a regression exercise. We assume that the rate of occurrence of the different clusters can be explained by meteorological changes. For example, it has been observed that the rate of occurrence of rockfalls is closely linked to meteorological variations, such as rainfall or freeze-thaw events ([PERSON] et al., 2016). We thus use features computed from the available meteorological time series to predict the rate of occurrence of the events of the different clusters and analyze the importance of the different input features. Because the sampling period of the seismic data is much lower than for the meteorological variables (respectively 1 ms and 15 min), we count the number of seismic events in bins of 15 min to allow the comparison. Further complexities emerge from the temporal dimension of this problem, which are tackled in the following ways. First, the meteorological variables vary smoothly over time while seismic events occur in short, discrete bursts, thus resulting in very poor temporal continuity. To compare the non-smooth rate of occurrence of seismic events to the meteorological time series, the \(\log_{10}\) of the rate of occurrence is smoothed using a moving average filter. The averaging window size has a significant impact on the results, and the selected window value was chosen after trial and error. A window that is too short results in a challenging problem for the regressors, as cluster occurrences may still show poor temporal continuity compared to meteorological variations. Conversely, a window that is too long averages out the signal, potentially leading to the inference of constant values. A moving window of half a day appears to yield a good balance in capturing both short-term variations and long-term trends in cluster occurrence. Furthermore, variations in meteorological variables can induce a delayed response from the rock cliff. To mitigate this effect, we compute multiple statistical moments in mobile windows of different sizes, similar to the method proposed by [PERSON] et al. (2021). More specifically, we compute the moving average and standard deviation for moving windows of 1 hour, 1 day, and 1 week. We use the data from those moving windows in a classical regression exercise, where the time-averaged meteorological data now serve as input variables to predict cluster occurrence. The moving windows are implemented using the pandas library ([PERSON] et al., 2011). Another hypothesis is that the sampled meteorological variables are co-linear. It is then necessary to use statistical tools to deal with the complexities brought by the multicollinearity of the meteorological variables. Decision tree-based models are resilient to multicollinear features due to their ability to select the most informative features at every split, their use of multiple weak learners in an ensemble, and their non-parametric nature ([PERSON], 2001). For this reason, the following decision tree-based regressors were used: Random Forests Regression, Gradient Boosting Regression, and XGBoost ([PERSON] & [PERSON], 2016), all easily integrable through the scikit-learn environment ([PERSON] et al., 2011).
\begin{table}
\begin{tabular}{l c c} \hline Variable & Category & Description \\ \hline dtNPEAKS & Spectrum & Numbers of peaks from the signal spectra \\ dtHVAR & Spectrum & Logarithm of the variance of the amplitude spectrum \\ \hline \end{tabular} _Note._ Logarithm Used in the Computation of Features is \(\log_{10}\).
\end{table}
Table 2: ContinuedEach method was tested in a typical machine learning fashion with a \(k\)-fold validation and a training-test data set ([PERSON] & [PERSON], 2016). To account for the temporal nature of the data, both training and testing data were consecutive in time. Testing data are 3 days long and taken every 2 weeks. This training and testing scheme was used to avoid data leakage ([PERSON] et al., 2011), common in the inference of temporal and spatial data where variables are correlated through time (or space). A grid search was also run to seek the best results that can be achieved with the testing data. This step was also implemented using the sklearn library ([PERSON] et al., 2011). SHAP values are used to interpret the results with one consistent method across all regressors ([PERSON] & [PERSON], 2014). Initially introduced in game theory, SHAP values aim to explain the importance of variables while staying model-agnostic. A particularity of SHAP values is that, for a model involving \(m\) features and \(n\) observations, SHAP values are organized in a \(n\times m\) matrix. For a given observation \(i\), it can be intuitively described as the contribution from an independent feature \(j\) on the target value. A feature with a positive value for a given observation means that the feature increased the prediction outcome, while, on the contrary, a negative value contributed to lowering it. The distribution of SHAP values amongst the different input features is ultimately analyzed. To simplify this analysis when many features are present, it is common to reduce the analysis to only the mean absolute value of all observations, which means that for an input variable \(j\), the resulting effective SHAP value is
\[\text{SHAP}_{j}^{*}=\frac{1}{n}\sum_{i=1}^{n}|\text{SHAP}_{i,i}|. \tag{4}\]
SHAP value analysis is implemented using the SHAP library ([PERSON] et al., 2020). Finally, to simplify the analysis, meteorological variables were limited to the following:
1. Temperature at the surface and 30, 60, and 90 cm depths,
2. Temperature gradient at 15, 75, and 135 cm depths,
3. Precipitation,
4. Wind speed and orientation.
We do little feature engineering on the meteorological variables apart from computing the northern and the eastern wind speed components, respectively noted \(\text{wind}_{N}\) and \(\text{wind}_{E}\). Finally, the analyzed period contains missing data. To account for this, the data were split into three consecutive sequences.
1. 2020-07-11 to 2020-10-06,
2. 2021-01-28 to 2021-06-05 and
3. 2021-06-23 to 2021-09-14.
## 4 Results
### Event Catalog, Clustering, and Preliminary Classification
Controlled rockfall tests were filmed on video to assess typical rockfall waveforms at the site. Figure 2 shows a sandstone block that was manually detached, its position at two moments during the fall, with the seismic waveforms recorded at the same time. Figures 1(a) and 1(b) show the seismic signal recorded at the vertical component of one geophone and the corresponding spectrogram as well as the triggered STA-LTA window. Detaching the rock causes two events of low amplitude (<0.5 mm/s) between 6 and 8 s (Figure 1(c)). The first impact occurs at around 10 s (Figure 1(d)). As the rock fell for around half a meter before the first impact, low amplitudes (\(\sim\)2 mm/s) are recorded, but frequencies up to 200 Hz are reached, causing triggering by the detection algorithm. The second impact (Figure 1(e)) at around 11 s is of much larger amplitude (>10 mm/s), as the rock had time to gain more energy. The large block is followed by smaller sandstone blocks as well as mudstone flakes, causing multiple arrivals of smaller amplitude. We recorded a third impact of the main block (not shown in the pictures of Figure 1(a) as it was not captured well by the camera) in the talus a little before 14 s. This one is of much lower amplitude (<2 mm/s) and frequency content (<50 Hz), the impact being attenuated by the looser material within the talus. The red shading in Figure 1(b) shows the portion of the signal detected by the STA-LTA detector defined previously. The initial toppling was not detected, as well as the main block reaching the talus, which illustrates a limitation of the approach. While initially thought to be due to the application of a highpass filter, this behavior is attributed to the length of the STA-LTA windows. Increasing the length of the shorter windows could help in detecting the entire rockfall as one single event, at the cost of being less sensible to smaller local amplitude variations. Conversely, a shorter long window could potentially detect every individual rockfall, at the cost of being more sensible to noise. We have kept the selected parameters as a balance between the two considerations. With this method, we found that around 75,000 valid signals were detected over 465 days.
After computing features for the detected signals, the clustering was made on the 25 first components of the PCA reprojected data set (Figure 3a). The 25 first components account for about 95\(\%\) of the variance in the data, effectively reducing the number of dimensions in the clustering problem from 85 to 25. Using the first two components for visualization, the raw reprojected data reveal at least two clusters of similar shape and slightly different orientation, as well as great variance in PCA\({}_{2}\). Choosing an appropriate number of clusters is not a trivial problem - some authors propose to use an elbow-curve analysis, computing a clustering metric (such as the BIC defined above) for a varying number of clusters. The BIC curve obtained with our data, shown in Figure 3b, indicates that any number of clusters from three to six would be appropriate. We chose to work with three clusters, based on the hypothesis that three types of signals can be registered on the cliff, either linked to anthropogenic activity, rock falls, or pre-failure deformation. Restricting the number of clusters to three is admittedly a crude approximation of the range of possible seismic activity at the cliff. Many different types of mass movements exist and each of them might have its seismic signature ([PERSON] et al., 2011; [PERSON] et al., 2008; [PERSON] et al., 2017), and a large variety of meteorological phenomenons can also generate seismic noise, such as rainfall or wind ([PERSON] et al., 2022; [PERSON] et al., 2005; [PERSON] et al., 2022; [PERSON] et al., 2017). However, this simplification aims only to facilitate the analysis and link the signals to a physical interpretation. From here on, the naming convention referring to the clusters 0, 1, and 2 shown in Figure 4b is adopted. Figure 5 shows the 10 normalized waveforms closest to the centroids of each cluster as well as the Welch periodograms ([PERSON], 1967). The waveforms representative of Cluster 0 show steep increases in amplitudes, with one or multiple arrivals. Frequency content is also quite high, showing energy well above 150 Hz. Cluster 1 and 2 appear noisier, showing diffuse or multiple arrivals. Frequency content is also lower, mostly contained under 100 Hz apart from a few cases in Cluster 1.
Figure 3.— Principal component analysis of the seismic events catalog and performance of the clustering for different numbers of clusters.
(a) Explained variance of the seismic events data set as a function of the number of principal components. The 25 first components explain 95\(\%\) of the variance in the data. (b) Bayesian Information Criterion from the Gaussian Mixture Models as a function of the number of clusters.
Figure 2.— Controlled rockfall test. (a) Spectrogram, (b) and trace of the vertical component from geophone 00368 capturing the signature of a rockfall. (c, d, and e) show the different stages of the rockfall, respectively the toppling, as well as the first and second impact. The third impact, in the talus, is not shown as it was not captured well on video.
Finally, Figure 6 shows the distribution of some intuitive features for the three clusters, potentially helping the interpretation of their physical origins. Events from Cluster 0 and 1 generally have more energy at higher frequencies (> 150 Hz), while events from Cluster 2 are stronger at lower frequencies (< 150 Hz). Events from Cluster 2 also show the strongest rectilinearity and planarity, as well as being generally more correlated across the geophone network. Cluster 0 typically has short, clear signals, shown by the lowest durations and highest signal-to-noise ratios. It is also characterized by much lower rise times, also shown by the steep amplitude increase in the typical signals (Figure 5). Finally, events from Cluster 1 show weaker amplitudes, as shown by the _Env. max_ attribute.
### Spatio-Temporal Distribution Analysis
Benefiting from the geophones in the network having three components, a polarization analysis of the different waveforms was performed to gain insights into the spatial distribution of the source of the signals. Results of the analysis are shown in Figure 7a. For each event, the plunge and bearing are computed with [PERSON]'s method ([PERSON], 1965) for each geophone. The metrics \(\kappa\)([PERSON], 2007) and \(R\)([PERSON], 1953) provide a measure of dispersion, akin to the standard deviation for normal distributions. However, they grow inversely with dispersion, that is, the larger the number, the smaller the spread, where \(\kappa\) converges toward infinity and \(R\) converges to 1.
The polarization analysis results for Clusters 0 and 1 show that their distributions are more spread out than the distribution of Cluster 2. Indeed, the latter has different overall plunge and bearing, as well as larger values of \(\kappa\) and \(R\). However, the polarization from geophone 00380 stands apart from geophones 00368 and 00400, which is suspected to be due to a poor electrical connection of the eastern component, causing sporadically invalid traces. However, it is still clear, from geophones 00368 and 00400 alone, that the polarization attributes of Cluster 2 stand out. Clusters 0 and 1 have sub-vertical orientation and show a slight trend toward the northeastern quadrant, while Cluster 2 is more focussed. This bimodal orientation in clusters 0 and 1 could be caused by misclassification of the GMM where the data overlap (Figure 4b). Interpretation is greatly helped by plotting the daily occurrence distribution for each group (Figure 7b). Although Clusters 0 and 1 have quasiuniform temporal distributions, it is clear that the events of Cluster 2 occur mainly during daytime.
### Regression Analysis and Meteorological Variable Importance
We used the regressors defined in Section 3.4 (Random Forests Regression, Gradient Boosting Regression, and XGBoost) to associate the occurrence of the seismic events of the different clusters with meteorological variations. A grid search was conducted to optimize the testing scores, and the resulting parameters are detailed in Appendix B. Visually, it appears that days with a high count in Cluster 0 (Figure 8e) correlate with stronger precipitations in early September 2020 (Figure 8a) and some thawing events in April 2021 (Figure 8b). The regression analysis serves to quantify these relationships more rigorously.
Figure 4: The seismic event data set reprojected along the first two principal components. (a) Log\({}_{10}\) density amongst the two first principal components of the event catalog. (b) The location and covariance of the three clusters detected by the Gaussian mixtures.
Figure 5: Ten waveforms closest to the centroids of each cluster computed by the GMM. Left: Normalized amplitudes. Right: Normalized periodograms, computed with the method of [PERSON] (1967).
For each regressor, the \(R^{2}\) score
\[R^{2}=1-\frac{\sum_{i=0}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{\sum_{i=0}^{n} \left(y_{i}-\hat{y}\right)^{2}} \tag{5}\]
was computed for both training and testing data. The \(R^{2}\) score is a measure of the goodness of fit of a model ([PERSON] et al., 2011), ranging from 0 to 1 in linear regression. A value of 1 means that the modeled data \(\hat{y}\) are perfectly estimating the observed data. **y**. A value of 0 means that the model is as good as the mean observed data \(\hat{y}\). We compute the \(R^{2}\) score for every split, both in training and testing. The average \(R^{2}\) scores in training and testing for the prediction of the different regressors are quite different, as shown in Table 3.
In training, each regressor performs relatively well, some even showing high \(R^{2}\) (>0.80). It is however of no interest to look at the contribution of the different input features if the model cannot generalize. Thus, a good score is needed in testing. For the latter, the \(R^{2}\) scores are much lower, often an indication of overfitting. It might be possible that the grid search did not find an optimal combination of parameters for the regressors, resulting in imbalanced training and testing scores. The test scores are, however, within an arbitrarily tolerable range--the
Figure 6: Boxplots showing the normalized distributions of a few selected variables for the three clusters. The rectangles show the first and third quartiles respectively, while the lines extend to 1.5 times the interquartile range above and below these quartiles.
goal here is not to build accurate prediction tools, but to have a grasp on the meteorological variables needed to predict the occurrence of the different types of seismic events. The scores for the prediction of Cluster 0 are the worst overall, while the other two have similar results. To help interpret the contribution of input features in the next section, we weight the SHAP values according to the testing performance of each regressor and present the result in Figure 9.
## 5 Discussion
### Cluster Interpretation
The typical waveforms of Cluster 0, shown in Figure 5a, are similar to those of rockfall impacts ([PERSON] et al., 2011; [PERSON] et al., 2008; [PERSON] et al., 2017). The rockfall test was also detected and classified as an event of Cluster 0. The spread-out spatial distribution and uniform temporal distribution observed for this cluster, illustrated in Figure 7, is an indicator that the events of this cluster are linked to the geomorphological dynamics of the cliff. Inspection of the meteorological variables that are significant in the regression analysis corroborates this idea. For instance, seismic activity linked to rockfall events is likely correlated to rainfall and thawing events, as rockfall occurrence greatly increases with rainfall and thaw ([PERSON] et al., 2016). Surface temperature variations on a short timescale as well as deep temperature and temperature gradients on longer timescales are all strongly indicative of events of Cluster 0. We also find that rain events on longer timescales are important. Higher mean rain over a week is indicative of large amounts of cumulative precipitation, while higher weekly rain standard deviation is a sign of isolated rain events. The typical waveforms of Cluster 0, paired with the important meteorological variables, hint that events in that group are linked to rockfall activity. The poorer performance of
Figure 7: Spatial and temporal distribution of the occurrence of the seismic events for each cluster. (a) Polarization analysis for each geophone and each cluster. (b) Daily temporal distribution of each cluster.
the regressors in the prediction of the occurrence of this cluster relative to Clusters 1 and 2 is also interesting. We hypothesize that while the simplification of using three clusters eases the interpretation, it might result in gathering signals with different physical source mechanisms in Cluster 0, restricting the regressor's ability to generalize to unseen data. It is also possible that better feature engineering of the meteorological variables, such as a freeze-thaw index or better rain attributes, might have yielded improved results.
The typical waveforms of events in Cluster 1 have lower amplitudes and frequency content, making interpretation challenging from the waveform alone. However, like Cluster 0, spread-out spatial and uniform temporal distributions (Figure 7b) suggest that events in Cluster 1 are not associated with anthropogenic activity. The regression analysis shows that the important variables are linked to wind speed and wind orientation variations on shorter timescales. To investigate if the occurrence of events of Cluster 1 could be linked to strong winds, the frequency content of 15-min-long seismic time series recorded during varying wind speed and precipitation conditions is examined (Figure 10). Typical Power Spectral Density (PSD) during periods without rain nor wind (Figure 10a) shows almost white noise with average power below \(10^{-7}\) (mm/s)\({}^{2}\)/Hz, while the PSD with strong rain and strong wind (Figure 10c) is orders of magnitude higher, with values well above \(10^{-6}\) (mm/s)\({}^{2}\)/Hz. The PSD for the 50 typical events of each cluster (Figures 10d-10f) was also computed. Cluster 1 shows the PSD closer to what is observed during periods with strong rain and strong winds, corroborating the hypothesis that they are related. It is also interesting to note that the testing scores of the different regressors are the best for this cluster, hinting at a simpler phenomenon: wind hitting the rock cliff.
The analysis of the spatio-temporal distribution of the occurrence of seismic events in Cluster 2 (Figure 7) shows that they are likely linked to anthropogenic activity, mainly attributed to the passage of cars above and below the cliff. The occurrence of events on this cluster, being almost exclusively between 7 am. and 9 pm., along with a tightly distributed polarization, indicates
Figure 8: Time series of meteorological data and seismic events occurrence. (a) Daily precipitation. (b) Horizontal temperature profile within the rock cliff. (c and d) Daily wind speed and direction. (e, f, and g) Daily count for events in cluster 0, 1, and 2 respectively. The gray shading highlights the periods with a power outage. The green shading shows the consecutive time series used for the regression analysis. The red shading shows where we have valid seismic data but lack the meteorological data to use in the regression.
\begin{table}
\begin{tabular}{l c c c} \hline \hline & Random forests & Gradient boosting & XGBoost \\ \hline Cluster 0 & 0.33/0.10 & 0.75/0.21 & 0.73/0.23 \\ Cluster 1 & 0.60/0.53 & 0.86/0.65 & 0.89/0.64 \\ Cluster 2 & 0.41/0.24 & 0.73/0.40 & 0.83/0.35 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Training/Testing \(R^{2}\) for the Different Regressorsthat the seismic sources are artificial. The meteorological variables related to Cluster 2 should then also vary on a daily timescale and be indicative of the time of the day, as is human activity. The most important feature, temperature gradients at the surface and on an hourly time scale, captures this dynamic well - it is a good indicator of whether the rock face is heating or cooling as the temperature rises or diminishes, thus being a good proxy of the time of the day. Intuitively, one could think that surface temperatures would be the best indicator for this, where warmer or colder temperatures would directly be linked to daytime or nighttime. However, surface temperatures also vary greatly seasonally and thus cannot be used alone to infer the time of the day. This could explain why surface temperatures on a daily timescale are only the third most important variable in forecasting the occurrence of events from Cluster 2. Furthermore, the testing scores from the different regressors are all quite poor for this cluster. This could potentially be explained by the fact that while anthropic activity varies greatly with the time of the day, it varies less according to other meteorological variables.
### Shortcomings
Although we have provided a physical interpretation for the three clusters found through the proposed methodology, further work is needed to better understand the physical origin of the underlying events. It may seem that the main weakness of this work is that the chosen number of clusters greatly hinders the ability to differentiate the different mechanisms generating the seismic events. While using three clusters does provide additional simplicity in the interpretation, events of different origins might be grouped in the same cluster. Defining an appropriate number of clusters to be used in such an analysis has been a long-standing problem ([PERSON] et al., 2011). The
Figure 10: Probability density function of the seismic power spectra for continuous 15-min sequences of panel (a) no rain and no wind, (b) strong rains with weak winds and (c) strong rain and strong winds. (d, e, and f) show the Probability density function for Cluster 0, 1, and 2 respectively.
Figure 9: Importance of the first 10 variables in the prediction for every cluster and regressors as computed by SHAP values, ranked by weighted mean importance. The absolute SHAP values are scaled between 0 and 1 to be compared throughout. (a, b, and c) are the important variables for the prediction of Clusters 0, 1, and 2 respectively.
BIC curve (Figure 2(b)) shows that three clusters could be insufficient. However, tests have shown that using more clusters only resulted in a subdivision of Cluster 2, which we had little interest in analyzing further since its occurrence was linked to anthropogenic activity. Computing more seismic features might help in discriminating different signatures in the seismic signals. Recent research has shown that deep learning might help in that regard ([PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2023). However, it is also possible that other clustering algorithms might suit this problem better, like hierarchical clustering ([PERSON] and [PERSON], 2012) where differences within clusters can be analyzed.
Another shortcoming is the fact that the analysis of the spatial distribution of the events is limited by the design of the network (close proximity of the geophones). This pilot study however can aim to better prepare subsequent work. Mainly, the use of a larger number of seismic sensors distributed over a larger domain would allow locating the hypocenter of the seismic events ([PERSON] and [PERSON], 2011). The analysis of the distribution of the waveform properties would be greatly complemented by the spatial distribution of the sources, adding further dimensions to the clustering.
Furthermore, the use of the STA-LTA event detection algorithm biases the study by restricting the analysis to seismic events exhibiting amplitudes well above the noise level. Studies have shown that seismic events of low amplitude, with waveforms typically undetected by algorithms such as STA-LTA, tend to occur before rockfalls or landslides ([PERSON] et al., 2023; [PERSON] et al., 2020). In these studies, the researchers analyze the entirety of the traces with deep scattering networks, making use of the large seismic data sets available. Coupling such an approach with the location of seismic events could prove useful in the monitoring and understanding of natural hazards.
Finally, the regression analysis adopted in this work struggles to explain complicated phenomena, as shown by the poor testing scores. Using multiple co-linear variables makes explaining causal phenomena between the input and target variables difficult. Furthermore, linking the occurrence of the different clusters to meteorological variations is made difficult by the discrete nature of the clustering, potentially oversimplifying the studied phenomena. Adding on the idea that one could analyze the entirety of the traces (e.g., using deep learning approaches), it would be interesting to analyze the variations of a continuous, low-dimensional embedding of the seismic traces instead of discrete, clustered data.
## 6 Conclusion
The aim of the presented clustering methodology is to discriminate different types of seismic signals and attempt to provide a physical interpretation of their origins. The clustering demonstrates that it is possible to discriminate natural and anthropogenic signals, as shown by the clear non-uniformity of the spatial and temporal distribution of the seismic events. Furthermore, the regression analysis lets us rank different meteorological variables by importance in the prediction of the frequency of occurrence for each type of seismic event. The differences in the ranking of the meteorological variables corroborate the hypothesis that events of the three clusters have different origins and help explain the different seismogenic sources. The regression analysis suggests that events of Cluster 0 can be associated with rainfall and thawing events, which are typically linked to rockfalls. This, combined with the fact that the typical signals from this cluster exhibit an envelope and frequency content similar to observed rockfall events, indicates that Cluster 0 can indeed be linked to rockfall activity. While the results that are achieved using the proposed methodology are promising, the latter is limited by numerous factors and opens the door to multiple avenues for future research. As discussed in the previous section, the fixed number of clusters hinders the analysis. It would be interesting to analyze in detail the impact of a larger number of clusters, as well as different clustering algorithms. Furthermore, the methodology requires the computation of pre-determined seismic features and manual feature engineering for creating a low-dimensional space to analyze the waveforms. Research has shown that deep learning can help in building this embedding space, with either autoencoders ([PERSON] et al., 2021; [PERSON] et al., 2023) or deep scattering networks ([PERSON] et al., 2023; [PERSON] et al., 2020; [PERSON] et al., 2022). Moreover, the use of automatic detection algorithms, such as STA-LTA, combined with the use of bandpass filters biases the types of events that are detected. Analyzing the entirety of the traces would likely give insight into the occurrence of typically undetected lower amplitude signals. Such signals could be linked to initial toppling or progressive failure before a rockfall. Finally, a larger number of geophones would allow to locate the hypocenter of the seismic events. The spatial distribution of the origin of the different seismic events would provide additional helpful information to the clustering and characterization of the seismicity.
## Appendix A Feature Computation
Details about the computation of the features presented in Table 2 are presented in the following. Many of the features are inspired by [PERSON] et al. (2017). While we have implemented the feature computation, we also refer the reader to [PERSON] et al. (2021), who provide an obspy integrated approach.
### Correlation Computation
For \(n\) vectors \(\mathbf{x}_{1}\) to \(\mathbf{x}_{n}\) of length \(m\), the covariance matrix is
\[\mathbf{\Sigma}=\begin{bmatrix}\sigma_{x_{1},x_{2}}&\sigma_{x_{1},x_{2}}&\cdots& \sigma_{x_{1},x_{n}}\\ \sigma_{x_{2},x_{2}}&\sigma_{x_{2},x_{2}}&\cdots&\sigma_{x_{2},x_{n}}\\ \vdots&\vdots&\ddots&\vdots\\ \sigma_{x_{n},x_{1}}&\sigma_{x_{n},x_{2}}&\cdots&\sigma_{x_{n},x_{n}}\\ \end{bmatrix}, \tag{10}\]
where \(\sigma_{x_{n},x_{j}}\) is the pairwise covariance between the two vectors \(\mathbf{x}_{i}\), \(\mathbf{x}_{j}\), defined as
\[\sigma_{x_{i},x_{j}}=\frac{1}{m-1}\sum_{i=1}^{m}(x_{i}-\overline{x_{i}})\left( x_{i_{k}}-\overline{x_{j}}\right). \tag{11}\]
For any detected event, we compute the covariance matrix \(\mathbf{\Sigma}\) of the nine recorded traces from the three triaxial geophones in the network. We thus obtain a cross-correlation matrix \(\mathbf{\Sigma}\) of size \((9,9)\). Different metrics are computed using \(\mathbf{\Sigma}\), such as the maximum, minimum, average, standard deviation, and median value, as well as the range of spanned values (i.e., maximum - minimum). We also compute the same metrics on the absolute values of this matrix, that is, \(|\mathbf{\Sigma}|\).
### Polarization Attributes
We follow the definitions given by [PERSON] (1988) for computing polarization attributes. For a three-component seismic sensor, the covariance matrix within a time window can be computed as
\[\mathbf{\Sigma}=\begin{bmatrix}\sigma_{x,x}&\sigma_{x,n}&\sigma_{x,n}\\ \sigma_{x,x}&\sigma_{x,n}&\sigma_{x,n}\\ \sigma_{x,n}&\sigma_{x,n}&\sigma_{x,n}\\ \end{bmatrix} \tag{12}\]
where indices \(e,n\), and \(z\) refer to the three components, and \(\sigma_{x,n}\) is, for instance, the covariance of the vertical and north components. Geometrically, the covariance matrix \(\mathbf{\Sigma}\) can be thought of as the coefficients of the polarization ellipsoid ([PERSON], 1988). The principal axes of this ellipsoid, found through singular value decomposition, are represented by the eigenvalues \(\lambda\) and the eigenvectors \(\mathbf{u}_{1}\), \(\mathbf{u}_{2}\) and \(\mathbf{u}_{3}\). Once these values are computed, many polarization features can be determined. In this work, we used the rectilinearity
\[R=1-\frac{\lambda_{2}+\lambda_{3}}{2\lambda_{1}}, \tag{13}\]
the planarity
\[P=1-\frac{2\lambda_{3}}{\lambda_{1}+\lambda_{2}} \tag{14}\]
and
\[\phi=\cos^{-1}|u_{11}|. \tag{11}\]
The sign(\(x\)) function is introduced by [PERSON] (1988) to ensure there is no 180\({}^{\circ}\) ambiguity by only taking the positive vertical component of \(\mathbf{u_{1}}\). We compute polarization features on a per-geophone basis and some are synthesizing their distribution across the network. We also compute a value of dispersion \(R_{f}\) between the different azimuth and incidence determined for every seismic sensor ([PERSON], 1953). For \(n\) vectors \(\mathbf{x}_{1}\) to \(\mathbf{x}_{m}\), \(R_{f}\) is computed as the averaged norm of the summed, normalized vectors
\[R_{f}=\frac{1}{n}\left\|\sum_{n=1}^{n}\frac{\mathbf{x}_{i}}{|\mathbf{x}_{i}|_{k}} \right\|_{2}. \tag{12}\]
One can see that for \(n\) identical vectors \(\mathbf{x}_{i}\), \(R_{f}=1\), while opposite vectors would yield \(R_{f}=0\)([PERSON], 1953).
### Waveform Attributes
We compute a large number of features representative of the recorded waveforms. The signal-to-noise ratio (SNR) is computed for the nine recorded traces as the ratio between the trace maximum value and its standard deviation:
\[\text{SNR}(\mathbf{x})=\frac{x_{\text{max}}}{\sigma_{x}}. \tag{13}\]
We select the trace with the highest SNR for computing the features. We initially compute the skew and the kurtosis, respectively computed with the biased sampled third and fourth moments:
\[\bar{\mu}_{3}=\frac{m_{3}}{m_{2}^{3/2}} \tag{14}\]
and
\[\bar{\mu}_{4}=\frac{m_{4}}{m_{2}^{3}} \tag{15}\]
where the \(k\)th moment is defined as:
\[m_{i}=\frac{1}{n}\sum_{n=1}^{n}(x_{i}-\bar{x})^{k}. \tag{16}\]
We also compute the analytic signal (or envelope) of the selected waveform by taking the absolute value of the Hilbert transform, that is, \(|H(\mathbf{x})|\). On this envelope, the average and maximum amplitude as well as the area under the curve (with trapezoidal integration) are computed. Other features computed are the rise time, namely the time it takes for the envelope to reach its maximum value, and the duration of the signal. Furthermore, we also compute the energy and the kurtosis from the waveform between different frequency bands. As the sampling frequency is 1 kHz, we compute, in frequency intervals of 50 Hz, properties contained within the signal after applying either a bandpass or a bandstop filter. We do so for frequencies 0-50 Hz, 50-100 Hz, and so on. The energy \(E\) is computed using the filtered waveform as the sum of the squared discrete values, that is,\[E(\mathbf{x})=\sum_{i=1}^{m}x_{i}^{2} \tag{13}\]
### Spectral Attributes
Finally, we compute features related to the frequency content of the selected waveform. The amplitude spectra are computed from the discrete Fourier transform, that is, \(|\mathbf{X}^{2}|=|F(\mathbf{x})|^{2}\). Also computed are the average amplitude, maximum value, and variance as well as the frequency of maximum amplitude. Furthermore, the energy between different frequency bands of 50 Hz is computed, summing similarly to that of Equation 13, however only taking samples between the selected frequencies.
## Appendix B Parameters of the Regressors
A grid search was conducted for every regressor in order to obtain the best testing scores. The parameters are the following:
* Random Forests
* Max depth: 30
* Number of estimators: 250
* Minimum samples per leaf: 0.05
* Minimum samples per split: 0.05
* Maximum features: Square root of total number of features
* Gradient Boosting
* Maximum depth: 10
* Number of estimators: 250
* Minimum samples per leaf: 0.05
* Minimum samples per split: 0.005
* Maximum features: Square root of total number of features
* Learning rate: 0.05
* Subsample: 0.6
* Maximum depth: 15
* Number of estimators: 250
* Learning rate: 0.05
* Subsample: 0.3
* Minimum child weight: 5
## Appendix C Data Availability Statement
The seismic data used in this study are available through the Borealis Data repository ([PERSON], 2024). The codes and the meteorological data used to generate the results as well as Figures 4 and 9 are stored on GitHub ([PERSON], 2024).
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wiley/fad867fb_7e9e_48c8_9516_62840f90a353.md | # JGR Space Physics
Research Article
10.1029/2024 JA032639
Kay Points
High-latitude lower thermospheric temperature response to geomagnetic activity depends on magnetic local time and magnetic latitude
Above 100 km, strong and weak (or even negative) responses occur in the dusk and dawn sectors, respectively
The results agree with earlier theoretical predictions, highlighting the importance of storm-induced vertical wind and Joule heating
[PERSON]
High-latitude lower thermospheric temperature response to geomagnetic activity depends on magnetic local time and magnetic latitude
Above 100 km, strong and weak (or even negative) responses occur in the dusk and dawn sectors, respectively
The results agree with earlier theoretical predictions, highlighting the importance of storm-induced vertical wind and Joule heating
###### Abstract
The magnetosphere-ionosphere-thermosphere system is externally driven by the energy input from the solar wind. A part of the solar wind energy deposited in the magnetosphere during geomagnetically active periods dissipates into the thermosphere. Previous studies have reported temperature perturbations in the lower thermosphere during geomagnetic storms. The present study aims to assess the climatological spatial pattern of the lower thermospheric response to geomagnetic activity at high latitudes based on 21 years of temperature measurements by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument onboard the TIMED (Thermosphere Ionospheric Mesosphere Energetics and Dynamics) satellite and their comparison with the recently developed half-hourly geomagnetic activity index Hp30. The temperature response to geomagnetic activity, evaluated at different seasons and altitudes, is better organized in magnetic coordinates than in geographic coordinates. At 110 km, the temperature increases with Hp30 at all magnetic local times, but with a prominent dusk-dawn asymmetry in the magnitude. That is, the temperature variation per unit Hp30 is larger in the dusk sector than in the dawn sector. At 106 km, the response in the dawn sector is further reduced or even negative. These results provide observational evidence to support earlier theoretical predictions; according to which, both storm-induced vertical wind and Joule heating contribute to the temperature increase in the dusk sector, while in the dawn sector, the vertical wind acts to cool the air and thus counteracts Joule heating.
Key Words.:10.10.
Some studies have focused on temperature perturbations in the mesosphere and lower thermosphere during geomagnetically active periods. [PERSON] et al. (2007) showed an increase in high-latitude temperature by \(\sim\)10 K at 85 km following the geomagnetic storm in January 2005, based on Microwave Limb Sounder (MLS) measurements from the Aura satellite. [PERSON] et al. (2007) reported a temperature reduction of \(\sim\)25 K at 90 km as observed by the meteor radar at Andenes (69\({}^{\circ}\)N, 16\({}^{\circ}\)E) during the geomagnetic storm in October 2003. [PERSON] et al. (2010) analyzed temperature measurements from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite and found that the temperature at 100-120 km is enhanced during periods of elevated geomagnetic activity. [PERSON] et al. (2015) used Na lidar observations at Fort Collins (41\({}^{\circ}\)N, 105\({}^{\circ}\)W) and noted temperature enhancements above 100 km during the geomagnetic storms in April 2002, November 2004, and May 2005. In one of the cases (November 2004), cooling was observed between 98 and 103 km. Using Aura/ MLS measurements, [PERSON] (2017) showed an increase in the polar temperature during the November 2004 geomagnetic storm, but at a mesospheric altitude of \(\sim\)77 km. The author noted that the temperature variation could be due to the concurrent change in the polar vortex rather than the geomagnetic storm. [PERSON] et al. (2018) examined the lower thermospheric response to the geomagnetic storm in March 2013 using temperature data from TIMED/SABER. They noted that a temperature rise occurs 12-36 hr after geomagnetic disturbances depending on latitude and altitude. [PERSON] et al. (2022) investigated temperature perturbations from TIMED/SABER during the geomagnetic storm in September 2017, pointing out that there is a north-south asymmetry in the temperature response in the lower thermosphere. [PERSON] et al. (2021), also using TIMED/SABER data, performed a superposed epoch analysis of temperature perturbations at 94-110 km over more than 100 geomagnetic storms. It was demonstrated that a temperature enhancement occurs following the storm onset and its magnitude tends to be larger at higher latitudes and altitudes. [PERSON] et al. (2018, 2023) used a numerical model to examine temperature perturbations in the lower thermosphere under geomagnetically active conditions. The results predicted that the temperature response at high latitudes strongly depends on local time ([PERSON] et al., 2023), which is yet to be experimentally verified.
We present in Figure 1 examples of the lower thermospheric temperature response to geomagnetic activity at high latitudes for selected months, including cases for both the Northern (a, c, and e) and Southern (b, d, and f) Hemispheres. These examples encapsulate our current understanding of temporal characteristics of the lower thermospheric temperature response to geomagnetic activity. Each panel (a)-(f) displays, from top to bottom, the Dist index ([PERSON], 1964; [PERSON] & [PERSON], 1991), Hp30 index ([PERSON] et al., 2022), and high-latitude temperature measurements from TIMED/SABER (described later in more detail). Dist is an hourly geomagnetic activity index often used as a measure of geomagnetic storm activity. Hp30 represents the level of planetary geomagnetic activity, similar to the more commonly used 3-hourly geomagnetic activity index Kp ([PERSON] et al., 2021) but with a higher temporal resolution of 30 min. The TIMED/SABER temperature measurements were averaged temporally over a 48-hr period and spatially over the region poleward of 60\({}^{\circ}\) magnetic latitude of the Quasi-Dipole coordinate system ([PERSON] et al., 2010; [PERSON] & [PERSON], 2017; [PERSON], 1995b). The temporal smoothing was used to avoid gaps in the data. It is noted that different scale ranges are adopted in different panels. Figure 1 demonstrates that the high-latitude temperature above \(\sim\)100 km tends to increase during geomagnetically active periods (i.e., periods with decreasing Dst and increasing Hp30). This is consistent with findings in the previous studies mentioned above. Figure 1, however, does not provide information about the spatial structure of temperature perturbations. In the present study, we further explore the TIMED/SABER temperature measurements for the spatial characterization of the lower thermospheric response to geomagnetic activity. The main objective is to determine the climatological patterns of the high-latitude temperature response, taking into account their dependence on magnetic local time, magnetic latitude, season, and altitude, which has not been achieved in previous work.
## 2 Data and Method of Analysis
SABER is a broadband radiometer onboard NASA's TIMED satellite ([PERSON] et al., 2023; [PERSON] et al., 1999). SABER measures carbon dioxide (CO\({}_{2}\)) infrared emission at 15 um from the Earth's limb to derive atmospheric temperature. The algorithm to retrieve temperature in the mesosphere and lower thermosphere is described in [PERSON] et al. (2001). We use the latest version (v2.0) of the TIMED/SABER temperature data for the height range of 70-110 km. The SABER temperature measurements extend over the 21-year period from January 2002 to December 2023 corresponding to almost two entire solar cycles. Figure 2a displays daily values of the 10.7 cmFigure 1.— Monthly plots of (top) the Dst index, (middle) HP30 index and (bottom) TIMED/SABER temperature measurements in the lower thermosphere (90–110 km) at high magnetic latitudes (poleward of 60” Quasi-Dipole latitude) for (a) June 2012, (b) December 2011, (c) October 2006, (d) April 2006, (e) February 2015 and (f) August 2003, illustrating the geomagnetic activity effect on the high-latitude lower thermospheric temperature in the Northern Hemisphere (a, c, e) and Southern Hemisphere (b, d, f). A 48-hr moving average is applied to the temperature data for temporal smoothing. Note that different panels use different scale ranges.
solar radio flux (\(F_{10.7}\); [PERSON], 2013), which is a proxy for solar radiation heating to the upper atmosphere (e.g., [PERSON] et al., 2014).
The TIMED spacecraft is in a circular polar orbit with a 74.1\({}^{\circ}\) inclination at an altitude of 625 km. SABER views 90\({}^{\circ}\) to the right of the traveling direction of the spacecraft. The location of the SABER tangent point varies along the orbit from 52\({}^{\circ}\)S to 83\({}^{\circ}\)N for the north viewing yaw mode of the spacecraft, and 83\({}^{\circ}\)S to 52\({}^{\circ}\)N for the south viewing yaw mode. A north viewing mode lasts for \(\sim\)60 days, and then the spacecraft turns to its south viewing mode for another \(\sim\)60 days. During each 60-day yaw cycle, SABER samples temperature from all local times at any given latitude (except for a few hours around local noon). The yaw maneuver takes place on nearly the same dates for each year. Consequently, SABER temperature measurements from the northern-hemisphere high latitudes are concentrated around June (local summer), October (equinox) and February (local winter), while the measurements from the southern-hemisphere high latitudes are concentrated around December (local summer), April (equinox) and August (local winter). This is illustrated in Figure 2b, which shows the number of high-latitude measurements for each calendar day. The three seasonal groups of data (i.e., local summer, equinox, and local winter) in each hemisphere are analyzed separately.
[PERSON] et al. (2008) and [PERSON] et al. (2008) presented detailed error analyses for the v1.07 TIMED/SABER temperature data. Random errors in individual temperature measurements are 1.8 K at 80 km, 3.6 K at 90 km, 6.7 K at 100 km, and 15.0 K at 110 km, while systematic errors are 1.4 K at 80 km, 4.0 K at 90 km, 5.0 K at 100 km, and 25.0 K at 110 km for typical midlatitude conditions. Uncertainties may be larger under polar summer conditions. These error estimates are valid for the v2.0 data that are employed for the present study, as there are no changes in v2.0 relative to v1.07 that would influence precision. The random errors are unlikely to have any visible impact on our results presented in this paper, because as will be detailed below, our statistical analysis
Figure 2.— (a) Daily values of the 10.7 cm solar radio flux (\(F_{10.7}\)) during January 2002–December 2023. (b) The number of TIMED/SABER measurements at high magnetic latitudes (poleward of 60\({}^{\circ}\) Quasi-Dipole latitude) in the (red) Northern and (blue) Southern Hemispheres for each calendar day. Three seasonal groups are visible for each hemisphere: the data around June (local summer), October (equinox) and February (local winter) for the Northern Hemisphere, and the data around December (local summer), April (equinox) and August (local winter) for the Southern Hemisphere.
always involves a large number of independent temperature measurements (\(N>500\)), which reduces the uncertainty that propagates from individual measurements to the final climatological results by \(\sim\)\(\frac{1}{N^{\prime}}\)
The TIMED/SABER data were binned according to magnetic local time (MLT) and magnetic latitude (MLAT) in the Quasi-Dipole coordinate system. MLT is an angle, given in units of hours, between the magnetic longitude of the location of interest and the magnetic longitude of the anti-solar point. As mentioned earlier, the main cause of lower thermospheric disturbances during geomagnetic storms is Joule heating. Since electric fields (**E**) and currents **(J)** in the ionosphere are strongly controlled by the geomagnetic field ([PERSON], 1995a), the spatial pattern of Joule heating (**J-E**) is better organized in magnetic coordinates than in geographic coordinates. A convention is to describe Joule heating as a function of MLT and MLAT (e.g., [PERSON] et al., 2018; [PERSON] et al., 2024; [PERSON], 2005). [PERSON] et al. (2013) showed that when temperature data are sorted in geographic coordinates, high-latitude lower thermospheric temperature exhibits a prominent longitudinal asymmetry due to the longitudinal asymmetry of Joule heating in geographic coordinates.
A total of 262 equal-area bins were deployed in the region poleward of 52\({}^{\circ}\) MLAT. This achieves the spatial resolution of approximately 450 km. Figure 3 depicts the number of available TIMED/SABER measurements (\(N\)) in each MLT-MLAT bin for the (a-c) Northern and (d-f) Southern Hemispheres for different seasonal groups. The bins with \(N\leq 500\) are highlighted by light purple, which are excluded from the statistical analysis. Aside from those, \(N\) typically falls between 1000 and 1500. It may be noted that in the Northern Hemisphere, the data are concentrated around the high-latitude midnight sector, while in the Southern Hemisphere, the data distribution is more uniform. The difference between the two hemispheres arises from the fact that the magnetic pole in the Southern Hemisphere is more displaced from the Earth's rotation axis than in the Northern Hemisphere.
Figure 3.— Sample number of TIMED/SABER measurements in each magnetic local time (MLT)–magnetic latitude (MLAT) bin in the (a–c) Northern and (d–f) Southern Hemispheres for (a, d) local summer, (b, e) equinox and (c, f) local winter.
The effect of solar radiation heating on the lower thermospheric temperature was evaluated using the \(F_{10.7}\) index. The lower thermospheric temperature is known to vary linearly with the \(F_{10.7}\) index, and this linear dependence can be represented by a linear regression model (e.g., [PERSON] et al., 2014):
\[T_{m}=a+b\cdot F_{10.7}. \tag{1}\]
The coefficients \(a\) and \(b\) were determined in the least squares sense using the temperature measurements obtained during geomagnetically quiet periods, which are defined here as Hg30 \(<\) 2. The difference between observed (\(T_{o}\)) and modeled (\(T_{m}\)) temperatures (i.e., \(\Delta T=T_{o}-T_{m}\)) was used for the evaluation of the geomagnetic activity effect. A weak correlation was found between \(\Delta T\) and Hg30 with the correlation coefficients between \(-\)0.15 and \(+\)0.45 at 110 km. It was found that the correlation between \(\Delta T\) and Hg30 is generally higher than the correlation between \(\Delta T\) and \(-\)Dst, and the correlation between \(\Delta T\) and ap30. ap30 is a half-hourly geomagnetic activity index, which is similar to Hp30 but linearly scaled with ground magnetic field perturbations ([PERSON] et al., 2022). When the correlation between \(\Delta T\) and Hp30 is significant (\(p<\) 0.05), the linear dependence of \(\Delta T\) on Hp30 was evaluated by fitting a linear regression model. We examine the behavior of the regression coefficient (i.e., the slope of the regression line), which represents the temperature variation per unit Hp30, or the sensitivity of temperature to geomagnetic activity.
## 3 Results and Discussion
Figure 4 shows the background quiet-time temperature \(T_{m}\) (see Equation 1) at 110 km for \(F_{10.7}\) = 100 solar flux unit (sfu = \(10^{-22}\) W m\({}^{-2}\) Hz\({}^{-1}\)). The high-latitude temperature is higher during local summer than during other seasons in both hemispheres. This is expected from the seasonal variation of solar radiation heating. During
Figure 4: Distribution of the background quiet-time temperature \(T_{m}\) (see Equation 1) at 110 km for the 10.7 cm solar radio flux (\(F_{10.7}\)) at 100 solar flux unit (sfu = \(10^{-22}\) W m\({}^{-2}\) Hz\({}^{-1}\)) as a function of magnetic local time (MLT) and magnetic latitude (MLAT) in Quasi-Dipole coordinates in the (a–c) Northern and (d–f) Southern Hemispheres for (a, d) local summer, (b, e) equinox and (c, f) local winter. See main text for the derivation of \(T_{m}\) from TIMED/SABER measurements.
local summer, the temperature is highest in the polar region not only due to solar radiation but also due to wave-induced dynamics ([PERSON], 2012). To give a more complete picture, Figure S1 in Supporting Information S1 shows height profiles of \(T_{\rm{m}}\) at the magnetic pole for different seasons. In Figure 4, it is interesting that the Southern-Hemisphere temperature is higher during local winter (August) than during equinox (April) by 15-25 K, while the Northern-Hemisphere temperature tends to be lower during local winter (February) than during equinox (October). In either case, the temperature difference between local winter and equinox is within the systematic error in the data. The primary sources of the systematic error are atomic oxygen (O) and CO\({}_{2}\). The retrieval of v2.0 TIMED/SABER temperature involves daily mean values of O from the MSISE-00 empirical model ([PERSON] et al., 2002) and monthly mean values of CO\({}_{2}\) from the WACCM model ([PERSON] et al., 2007). Systematic errors in v2.0 TIMED/SABER temperature are then dependent on the accurate representation of seasonal variation of O and CO\({}_{2}\) in these models.
Figure 5 depicts the MLT-MLAT distribution of the regression coefficient at 110 km, representing the sensitivity of \(\Delta T\) to Hp30. The MLT-MLAT bins with a \"\(\times\)\" mark indicate lack of significant correlation between \(\Delta T\) and Hp30. The results show that the overall high-latitude temperature response is positive at 110 km, indicating an increase in temperature with increasing Hp30. This is as anticipated from Figure 1. For a typical geomagnetic storm in which Hp30 increases from 2 to 6, the sensitivity value of 10 corresponds to a temperature enhancement by 40 K. The sensitivity of temperature to geomagnetic activity is relatively high and low in the dusk and dawn sectors, respectively. This is the case in all seasons in both hemispheres, and is most evident during local summer. The highest response during the local summer is probably due to enhanced Joule heating in the summer hemisphere compared to winter ([PERSON] et al., 1983). Similar results can be obtained using Dst instead of Hp30, which
Figure 5.— TIMED/SABER temperature variation \(\Delta T\) at 110 km per unit value of the geomagnetic activity index Hp30, representing the sensitivity of temperature to geomagnetic activity, as a function of magnetic local time (MLT) and magnetic latitude (MLAT) in Quasi-Dipole coordinates in the (a–c) Northern and (d–f) Southern Hemispheres for (a, d) local summer, (b, e) equinox and (c, f) local winter. The bins with a “\(\times\)” mark indicate lack of significant correlation (\(p<0.05\)) between \(\Delta T\) and Hp30.
are presented in Figure S2 in Supporting Information S1. We noted that the temperature response to geomagnetic activity is better organized in MLT and MLAT than in local solar time (LST) and geographic latitude (LAT). Figure S3 in Supporting Information S1 is the same as Figure 5 but in LST and LAT. The results are as expected from the fact that Joule heating, which is the primary source of the energy input to drive lower thermospheric disturbances during geomagnetically active periods, is controlled by the electric field and current, which are organized in magnetic coordinates.
Figure 6 shows the temperature response to geomagnetic activity at lower altitudes (106, 100, and 94 km) for local summer. At 106 and 100 km, the response in the dawn sector is further reduced or even negative (i.e., cooling). At 94 km, the temperature response to geomagnetic activity is no longer significant in most bins. The results for equinox and local winter can be found in Figures S4 and S5 in Supporting Information S1, respectively.
Figure 7 accounts for a delay in the temperature response to Hp30 at 110 km during local summer. The introduction of a one-hour delay in Hp30 (Figures 7a and 7d) yields results similar to those without a delay (Figures 5a and 5d). The MLT-MLAT pattern is also similar when a 10-hr delay is introduced (Figures 7b and 7e) but with an increased response in the dawn sector. These results suggest that the response time depends on MLT and MLAT. The overall temperature response is reduced with a time lag of 20 hr (Figures 7c and 7f). Figure 8 further illustrates how the temperature response to Hp30 depends on a time lag in different MLT sectors (as indicated in the bottom row). In the dusk sector (Figures 8a and 8d), the temperature response is largest with a time lag of 1 hour, and it slowly decreases with additional time lag. In the midnight sector (Figures 8b and 8e), the maximum temperature response occurs with a time lag of several hours, and in the dawn sector (Figures 8c and 8f), the temperature response reaches its maximum later but within 24 hr. These results suggest that the temperature variation first occurs in the
Figure 6.— (a–c) Same as Figure 5a but at (a) 106 km, (b) 100 km, and (c) 94 km. (d–f) Same as Figure 5d but at (a) 106 km, (b) 100 km, and (c) 94 km.
dusk sector in response to elevated Hp30, and it gradually extends to the midnight and dawn sectors on a time scale of hours to a day. Figures S6 and S7 in Supporting Information S1 present the same variables as Figure 8 except for equinox and local winter, respectively. A comparison of Figure 8, Figures S6 and S7 in Supporting Information S1 suggests that the response characteristics are different depending on the season and hemisphere.
The previous modeling work by [PERSON] et al. (2018, 2023) provides valuable insight into the mechanism behind the observed positive and negative response of the high-latitude lower thermospheric temperature to geomagnetic activity (Figure 6). [PERSON] et al. (2018, 2023) used the Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIME-GCM; [PERSON], 1994) to study the mechanism for temperature perturbations in the lower thermosphere during geomagnetic storms. In TIME-GCM, the rate of temperature change is calculated by solving the thermodynamic equation. [PERSON] et al. (2018, 2023) evaluated the importance of individual terms in the thermodynamic equation to identify the processes that dominate temperature perturbations. [PERSON] et al. (2023), focusing on high latitudes, demonstrated that temperature perturbations in the lower thermosphere (100-110 km) are mainly due to Joule heating, adiabatic heating/cooling and vertical heat advection. Other heating mechanisms such as particle heating make only minor contributions. Adiabatic heating/cooling and vertical heat advection are both associated with changes in the vertical wind induced by storm-time Joule heating. Since the temperature in the lower thermosphere increases with height (see Figure S1 in Supporting Information S1), vertical heat advection due to upward and downward winds leads to a decrease and increase of temperature, respectively. At the same time, upward and downward winds lead to adiabatic cooling and heating, respectively. Therefore, the observed positive response of the lower thermospheric temperature at high latitudes can be associated with Joule heating and/or storm-induced downward wind, while the negative response can be
Figure 7.— (a–c) Same as Figure 5a but incorporating a time lag of (a) 1 hour, (b) 10 hr, and (c) 20 hr. (d–f) Same as Figure 5d but incorporating a time lag of (d) 1 hour, (e) 10 hr, and (f) 20 hr.
associated with upward wind. It should be noted that the Earth's rotation and horizontal advection can displace temperature perturbations from the regions of heating and cooling. Thus, for example, the region of the maximum negative temperature response may not be collocated with the maximum upward wind.
[PERSON] et al. (2023) also showed that the relative importance of Joule heating, adiabatic heating/cooling and vertical advection at high latitudes depends on local time. That is, in the dust sector, both Joule heating and downward wind contribute to an increase in temperature, while in the dawn sector, upward wind leads to a decrease in temperature.
Figure 8.— TIMED/SABER temperature variation \(\Delta T\) at 110 km per unit value of the geomagnetic activity index H\({}_{2}\)30, representing the sensitivity of temperature to geomagnetic activity, plotted as a function of time lag, for the (a, d) dust sector, (b, e) midnight sector, and (c, f) dawn sector in the (a–c) Northern and (d–f) Southern Hemispheres during local summer. Magnetic local time (MLT) and magnetic latitude (MLAT) ranges for the dusk, midnight and dawn sectors are indicated in the bottom panels.
temperature. Our results based on the analysis of TIMED/SABER temperature observations reveal a dusk-dawn asymmetry (Figures 5 and 6) similar to the TIME-GCM predictions by [PERSON] et al. (2023), providing observational and statistical evidence to support the role of both storm-induced vertical wind and Joule heating. We note that in a recent study, [PERSON] et al. (2024) also presented observations to support dusk-dawn asymmetry of the high-latitude lower thermospheric temperature response to geomagnetic storms, in alignment with the present work.
[PERSON] et al. (2015) addressed the mechanism by which local-time variations in the vertical wind and temperature are produced in the high-latitude lower thermosphere during geomagnetically active periods. In general, the vertical wind arises from the divergence/convergence of horizontal winds due to the requirement of mass conservation. During geomagnetic storms, ion drag plays an important role for the neutral dynamics in the high-latitude lower thermosphere (e.g., [PERSON] and [PERSON], 1984). The ion drag is composed of two parts: Pedersen drag and Hall drag. The Pedersen drag acts mainly in the direction perpendicular to the electric field and thus tends to be rotational. The Hall drag, on the other hand, acts at a right angle to the Pedersen drag and thus tends to be divergent or convergent. Since the high-latitude electric field, along with other relevant parameters, varies with MLT (e.g., [PERSON] et al., 2024), the ion drag is also MLT dependent. [PERSON] et al. (2015) numerically demonstrated that the Hall drag is primarily responsible for the local-time dependent response of the vertical wind and temperature to geomagnetic activity in the high-latitude lower thermosphere.
Our results reveal that the response time depends on MLT and MLAT (Figures 7 and 8). This is in qualitative agreement with the model predictions by [PERSON] et al. (2018), which showed that the temperature variation first occurs in the nighttime high latitudes and later at lower latitudes and other local times. The delayed response may be partly explained by the fact that it takes hours until the storm-induced large-scale circulation is established. Besides, the response time of several hours in the midnight and dawn sectors may be partly due to Earth's rotation. For instance, temperature perturbations in the dusk sector may be observed in the dawn sector 12 hr later. The better understanding of the delayed temperature response to geomagnetic activity in the high-latitude lower thermosphere can benefit from more modeling and observational studies.
## 4 Summary and Conclusions
This study statistically examined the response of the high-latitude lower thermosphere to geomagnetic activity based on 21 years of temperature measurements from TIMED/SABER. The temperature response was quantified using the recently developed half-hourly geomagnetic activity index Hp30. Temperature perturbations were derived by first evaluating background quiet-time climatologies at different magnetic local times, magnetic latitudes, seasons and altitudes, and then subtracting them from corresponding measurements. The linear dependence of temperature perturbations on Hp30 was evaluated and used as a measure of the geomagnetic activity effect on temperature. The primary results are summarized as follows:
1. The lower thermospheric temperature response to geomagnetic activity at 100-110 km is better organized in magnetic coordinates than in geographic coordinates (Figure 5 and Figure S3 in Supporting Information S1).
2. At 110 km, temperature increases with increasing geomagnetic activity (Figures 1 and 5 and Figure S2 in Supporting Information S1). The temperature response is more pronounced during local summer than during equinox and local winter, probably due to enhanced Joule heating.
3. The temperature response at 110 km is relatively strong and weak in the dusk and dawn sectors, respectively (Figure 5). At 106 and 100 km, the temperature response in the dawn sector can be negative, indicating cooling during geomagnetically active periods (Figure 7). The dusk-dawn asymmetry in the temperature response to geomagnetic activity agrees with the previous model predictions by [PERSON] et al. (2023). According to their TIME-GCM simulation results, both Joule heating and downward wind contribute to temperature enhancement in the dusk sector, while in the dawn sector, cooling by upward wind counteracts the Joule heating effect.
4. The maximum response to geomagnetic activity occurs 1-24 hr after an increase in geomagnetic activity, depending on magnetic local time, magnetic latitude, season and hemisphere (Figures 7 and 8, Figures S6 and S7 in Supporting Information S1). This is in qualitative agreement with the TIME-GCM results by [PERSON] et al. (2018), which predicted that the temperature variation initially occurs in the nighttime high latitudes and then spread to other local times at lower latitudes. The delayed response may be partly due to the slow development of the storm-induced large-scale circulation and may also be partly due to Earth's rotation. More studies on the storm-induced circulation in the high-latitude lower thermosphere and complex time lags observed in the temperature response are warranted.
## Data Availability Statement
The TIMED/SABER temperature data (v2.0) utilized in this study are available at the SABER project data server in SABER Team (2021). The Hpo indices including Hp30 used in this study are available at the GFZ website in [PERSON] et al. (2022). Daily values of the \(F_{10,7}\) index is available at the website in Space Weather Canada (2021). The Dst index is available at the website of the World Data Center (WDC) for Geomagnetism, Kyoto in [PERSON] et al. (2015).
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wiley/fad6e765_278e_4789_b056_de20e2f70343.md | ###### Abstract
A A
anvil strengthening the mesoscale downdraft ([PERSON] et al., 1988; [PERSON] and [PERSON], 1995), and melting crystals enhancing the negative buoyancy of the cold pool ([PERSON] and [PERSON], 1988; [PERSON] and [PERSON], 1979). Ice generated in the leading convective line is transported rearward to compose a large fraction of the stratiform precipitation, with both regions separated by a transition zone characterized by a relative minimum in radar reflectivity ([PERSON] and [PERSON], 1991, 1993; [PERSON] and [PERSON], 1994; [PERSON] and [PERSON], 1988; [PERSON] and [PERSON], 1987; [PERSON] and [PERSON], 1985; [PERSON] and [PERSON], 1995). There are several hypotheses on the mechanisms generating this reflectivity trough: ice crystal sublimation ([PERSON] and [PERSON], 1991), lack of aggregation ([PERSON] and [PERSON], 1993), suppressed crystal growth by downdrafts ([PERSON] and [PERSON], 1994), and crystal size sorting in which the heavier particles fall out in the convective region and the lighter, smaller particles are transported rearward ([PERSON] et al., 2018; [PERSON] and [PERSON], 1994; [PERSON] and [PERSON], 1988; [PERSON] and [PERSON], 1987). The fallout pattern of ice particles also impacts the intensity and across-line extent of the trailing stratiform precipitation ([PERSON] and [PERSON], 1987; [PERSON] and [PERSON], 1985), and without the rearward transport of ice from the convective cells, little to no precipitation would reach the surface in the stratiform region ([PERSON], 1994; [PERSON] and [PERSON], 1988; [PERSON] and [PERSON], 1987; [PERSON] and [PERSON], 1989). The varied results of these and other studies demonstrate that the structure of squall lines in numerical model simulations is sensitive to the microphysics parameterizations used ([PERSON] et al., 2009, 2012, 2015; [PERSON] and [PERSON], 2012; [PERSON] and [PERSON], 1988; [PERSON] and [PERSON], 1989; [PERSON] and [PERSON], 1995). This sensitivity reveals the need to better determine fundamental controls on squall line precipitation features for their accurate representation by numerical models.
In numerical model simulations, most microphysics schemes represent small-scale ice processes using an Eulerian method to track the collective properties of a group of particles advecting through each grid box of the domain. Specifically, bulk microphysics schemes make implicit and explicit assumptions about how ice crystal properties (e.g., shape, density, fall speed) are distributed with respect to some measure of size. This Eulerian framework effectively averages these properties so that individual particle characteristics are lost, often resulting in erroneous, varied simulations of a given storm (e.g., [PERSON] et al., 2015). Numerical models are only now beginning to include microphysical methods that track the collective changes to the physical properties of ice crystals. These particle property schemes have been developed for both bulk (i.e., [PERSON] et al., 2017; [PERSON] and [PERSON], 2015) and bin ([PERSON] et al., 2021) applications. However, the lifecycle of an ice crystal's properties is known to depend on the specific paths traced by the crystal through a cloudy atmosphere. [PERSON] (2008) has estimated that the great diversity in observed snow crystals is due to the heterogeneity of the trajectories traced by the crystals in clouds, suggesting that accurate modeling of ice populations requires Lagrangian modeling.
Lagrangian trajectory modeling provides a way to examine the diversity and evolution of ice particle properties by tracking the specific growth pathways taken by individual crystals, which is not possible in Eulerian frameworks. Lagrangian modeling has not yet been used on particle property schemes even though Lagrangian methods are perfectly suited to the task. Modeling the simultaneous transport and growth of individual ice crystals is challenging and computationally expensive, though recent \"super-particle\" Lagrangian methods are promising (e.g., [PERSON] et al., 2019; [PERSON] et al., 2020). The advantage of a Lagrangian approach is a more explicit representation of ice crystal growth processes, the accompanying crystal structural changes, and their interaction with the larger-scale cloud structure, which are all needed for studying cloud systems and improving bulk microphysics schemes.
Lagrangian particle trajectory studies have been used to examine the growth and transport of hydrometors in a variety of cloud types. Numerous studies have conducted trajectory calculations on hailstones to understand storm controls on hailstone size and fallout location (e.g., [PERSON] and [PERSON], 1976; [PERSON], 1983; [PERSON] and [PERSON], 2020; [PERSON] et al., 1990; [PERSON], 1983; [PERSON] and [PERSON], 1987; [PERSON] et al., 2005). Similarly, liquid droplet trajectories have been analyzed in tropical cyclones ([PERSON] et al., 2017), cloud mergers ([PERSON] and [PERSON], 1996), maritime clouds ([PERSON] et al., 1999), arctic clouds ([PERSON] et al., 2000), and marine stratocumulus ([PERSON] and [PERSON], 2005). [PERSON] and [PERSON] (2019) computed snowflake trajectories in mesoscale snowbands to understand the mechanisms determining horizontal distributions of snowfall, and [PERSON] et al. (2018) computed trajectories of ice crystals detrained from deep tropical convection into the avail. In comparison, there is a relative lack of ice crystal trajectory studies on squall lines. Past studies utilized Doppler radar observations to estimate ice particle trajectories in squall lines ([PERSON] and [PERSON], 1991, 1993; [PERSON] and [PERSON], 1994), but they lacked detailed information about the evolution of particle properties. [PERSON] and [PERSON]. (1995) briefly examined ice particle trajectories in a 2D model simulation of a squall line, but the particle growth trajectories were not the focus of their study.
The current study presents a novel ice crystal trajectory growth (ICTG) model that is used to examine ice processes and their impacts on squall line structure. Our ICTG model simultaneously grows and advects ice crystals in three-dimensional space, tracks physical changes of individual particles, and incorporates recent laboratory-based parameterizations of ice-vapor deposition ([PERSON] et al., 2019; [PERSON] & [PERSON], 2014) and riming ([PERSON] & [PERSON], 2015). The goals of this study are: (a) To introduce the new ICTG model, (b) To test the model's ability to accurately capture the spatial distribution and properties of ice particles in a simulated squall line in the context of past studies, and (c) To gain insight on how variability in an ice particle's initial size and location impacts the particle's trajectory, its evolution, and the squall line's precipitation structure. The remainder of this paper is organized as follows: Section 2 presents a description of the ICTG model, Section 3 describes how we employ the model to study squall lines, Section 4 and 5 show results from 2D and 3D ICTG simulations, and the conclusions are in Section 6.
## 2 Ice Crystal Trajectory Growth Model Description
### Model Overview
The ICTG model in the current study was developed to capture the natural evolution of ice crystal properties throughout their growth life cycle and learn how the crystal's evolution contributes to the microphysical structure of organized cloud systems. The model simultaneously grows and advects ice crystals by using the thermodynamic and kinematic output from 3D numerical model simulations. The model operates in a Lagrangian framework by tracking the steady-state thermodynamic conditions that each crystal experiences and calculating the resultant evolving particle properties (e.g., axis lengths, effective density, fall speed). The ICTG model runs completely offline and therefore does not produce any dynamic or thermodynamic feedbacks with the 3D simulation. All of the particles captured by the ICTG model are in the ice phase only, so from here on, the words \"particle\" and \"crystal\" will be used interchangeably.
The ICTG model is initialized with user-specified particle sizes, aspect ratios, densities, and locations in the domain. Then, over small, user-specified time steps (\(<\)20 s; see [PERSON] et al. (2013)), each particle's evolution from vapor deposition, sublimation, and riming of cloud droplets is calculated. The model calculates each ice particle's evolution individually, and it does not include melting, aggregation, or secondary ice production. Although aggregation is an important ice growth process in stratiform clouds, in this study we only use the ICTG model for proof-of-concept simulations to test the sensitivity of the results to changes in the crystal's initial size (see Section 3 for a description of how we employ the ICTG model in this study). After the particle's growth is calculated, the fall speed is updated, and the particle is advected some distance for each time step. The trajectory model uses first-order upwind advection, in which the velocity vector assigned to each particle comes from the nearest grid point at each time step. The particle's horizontal velocity is assumed to equal that of the horizontal wind, and the particle's vertical velocity is the difference between the vertical wind and the fall speed. Each particle is advected until it reaches the melting level or until its mass completely sublimates.
### Vapor Deposition
Ice crystals can grow by vapor deposition to precipitation-sized particles with shapes determined by surface attachment kinetics that depend on the temperature and ice supersaturation. At temperatures above \(-20^{o}\)C, crystal shapes generally fall into one of two primary habits: planar or columnar. Planar crystals usually have their major dimension parallel to the basal (hexagonal) facet, whereas columnar crystals have their major dimension parallel to the prism (rectangular) facet. The classical hexagonal and prism structure of single crystalline ice suggests describing crystal size in terms of at least two dimensions referenced to the basal and prism facets. We define these dimensions as \(c\), which is half the maximum distance along the prism facet, and \(a\), which is half the maximum distance along the basal facet. Crystal shape is represented by oblate (planar) and prolate (columnar) spheroids, which allows us to describe crystal shapes with two dimensions instead of one. The crystal's aspect ratio, defined as \(\phi=cla\), is used to distinguish the habit, where 0 \(<\phi<1\) indicates an planar crystal, \(\phi>1\) indicates a columnar crystal, and \(\phi=1\) indicates an isometric crystal. The rate at which each facet grows determines the crystal's habit, and the growth rate of a facet depends on the gas-phase vapor and thermal fluxes in combination with surface attachment processes. To refer to the crystal size, we use an equivalent volume spherical diameter, defined as \(d=2\left(a^{2}c\right)^{1/3}\)([PERSON] et al., 2013).
#### 2.2.1 Vapor Deposition Mass Growth Rate
In order for ice crystals to grow, vapor molecules must first adsorb onto the crystal surface and then find an attachment site. Steps in the crystal surface provide the attachment sites, and at least two mechanisms are known to govern the density of steps. Permanent screw dislocations are a continual source of surface steps, providing numerous attachment sites for adsorbed vapor molecules. In the absence of dislocations, two-dimensional nucleation produces surface steps and this mechanism has a strong supersaturation dependence. Since the surface mechanisms that control step formation and propagation are not well understood, surface attachment processes are usually modeled with growth efficiencies. The efficiency with which vapor molecules can incorporate into the ice lattice is given by a deposition coefficient \(\alpha\), where a value of unity means perfect incorporation. We use the parametric form of \(\alpha\) proposed by [PERSON] and [PERSON] (1996):
\[\alpha\left(s_{\text{surf}},T\right)=\left(\frac{s_{\text{surf}}}{s_{\text{ blur}}}\right)^{n}\tanh\left[\left(\frac{s_{\text{charf}}}{s_{\text{surf}}} \right)^{n}\right], \tag{1}\]
Where \(s_{\text{surf}}\) is the surface supersaturation, \(s_{\text{charf}}\) is the characteristic supersaturation, and \(m\) is an adjustable parameter that determines the crystal growth mechanism. Growth by permanent dislocations occurs for \(m=1\)([PERSON] et al., 1951), and growth by 2D nucleation occurs for \(10\leq m\leq 30\)([PERSON], 1996). Ice crystal growth is not largely a function of \(m\) once \(m>10\), though notable differences in the crystal semi-axis length (\(\sim\)800 \(\mu\)m) can occur at \(-15^{\circ}\)C when growing crystals for 15 min via permanent dislocations versus 2D nucleation ([PERSON] et al., 2019; [PERSON] & [PERSON], 2014). For the simulations in this study, we follow [PERSON] and [PERSON] (2015) and set \(m\) to 15, corresponding to growth by 2D nucleation, which is necessary to realistically produce thin ice crystals such as dendrites ([PERSON], 1982; [PERSON] et al., 2019; [PERSON], 1996).
The capacitance model has traditionally been used to calculate the ice crystal mass growth rate from vapor deposition. Although the capacitance model assumes a rough crystal surface and perfectly efficient growth, to better approximate the growth of real crystals, we instead use the model of [PERSON] and [PERSON] (2014) that combines the capacitance model with a model for surface attachment through steps. [PERSON] and [PERSON] (2014)'s model approximates faceted crystals as spheroids and includes axis-dependent attachment kinetics. In their model, the mass growth rate of an ice crystal from vapor deposition is
\[\left(\frac{d\,m_{i}}{dt}\right)_{\text{deposition}}=4\pi C(a,c)s_{i}\left[\frac{1}{D _{r}^{*}}+\frac{\rho_{\text{eq}}l_{i}}{K_{T}^{*}T}\left(\frac{l_{i}}{R_{i}T}- 1\right)\right]^{-1}, \tag{2}\]
where \(C\) is the capacitance, \(s_{i}\) is the ambient ice supersaturation, \(\rho_{\text{eq}}\) is the equilibrium vapor density at the ambient temperature \(T\), \(l_{i}\) is the enthalpy of sublimation, \(R_{i}\) is the gas constant for water vapor. The variables \(D_{r}^{*}\) and \(K_{T}^{*}\) include impacts from attachment kinetics on each facet, and they take the following forms:
\[D_{r}^{*}=\frac{2}{3}\frac{f_{r}D_{r}}{\left(\frac{4\,D_{r}}{a_{r}a_{r}}\frac {c}{a_{r}}+\frac{c}{c_{\text{A}}}\right)}+\frac{1}{3}\frac{f_{r}D_{r}}{\left( \frac{4\,D_{r}}{a_{r}a_{r}a_{r}}\frac{c}{a^{2}}+\frac{c}{c_{\text{A}}}\right)}, \tag{3}\]
\[K_{T}^{*}=\frac{2}{3}\frac{f_{T}K_{T}}{\left(\frac{4\,D_{r}}{\pi_{r}a_{r}a_{r} ^{*}a_{r}}\frac{c}{a_{r}}+\frac{c}{c_{\text{A}}}\right)}+\frac{1}{3}\frac{f_{ T}K_{T}}{\left(\frac{4\,D_{r}}{\pi_{r}a_{r}a_{r}a_{r}a_{r}}\frac{c}{a^{2}}+\frac{c}{c_{ \text{A}}}\right)}, \tag{4}\]
where \(C_{\text{A}}\) is the capacitance a small distance \(\Delta\) above the crystal's surface, \(D_{r}\) is the vapor diffusivity of air, \(K_{T}\) is the thermal conductivity of air, \(f_{i}\) and \(f_{T}\) are the ventilation coefficients for vapor diffusion and thermal conduction, \(c_{p}\) is the specific heat capacity of air at constant pressure, \(\rho_{z}\) is the air density, and \(\bar{c}_{v}\) and \(\bar{c}_{v}\) are the mean molecular speeds of water vapor and air molecules, respectively. Note that Equation 3 also contains deposition coefficients for each axis of the crystal, \(\alpha_{a}\) and \(\alpha_{r}\), which control the efficiency with which each facet grows. In Equation 4, \(\alpha_{T,a}\) and \(\alpha_{r,c}\) are the thermal accommodation coefficients for each axis. We set both \(\alpha_{T,a}\) and \(\alpha_{r,c}\) to unity in the ICTG model, following [PERSON] and [PERSON] (1999).
#### 2.2.2 Aspect Ratio and Density Evolution From Vapor Deposition
The aspect ratio of an ice crystal evolves through differences in \(\alpha_{\rm z}\) and \(\alpha_{\rm z}\), which have the functional form of Equation 1. Differences between their magnitudes come from \(s_{\rm dur}\) and \(s_{\rm surf}\), which is calculated above each axis (see [PERSON] and [PERSON] (2014), pg. 378). Aspect ratio evolution follows the hypothesis from [PERSON] and [PERSON] (1996), which states that the ratio of the axis growth rates is equal to the ratio of the deposition coefficients for each axis, \(\Gamma(T)\):
\[\frac{dc}{da}=\frac{\alpha_{\rm z}(\Gamma)}{\alpha_{\rm z}(\Gamma)}=\Gamma( \Gamma). \tag{5}\]
We use this hypothesis because it is consistent with growth of faceted ice with steps nucleated at the crystal edges ([PERSON] et al., 2019).
At high ice supersaturations, secondary ice crystal habits such as dendrites, hollowed features, and rosettes can develop. Such secondary habits are not explicitly represented in microphysical models. These features are represented through a deposition density (\(\rho_{\rm ap}\)) that accounts for the branches and hollows that occur in real crystals ([PERSON] & [PERSON], 1994):
\[\rho_{\rm ap}=917\exp\left[\frac{-3\max\left(\Delta\rho_{\rm z}-0.05,0\right) }{\Gamma(\Gamma)}\right]. \tag{6}\]
Here, \(\rho_{\rm ap}\) depends only on the temperature and the vapor density excess above the equilibrium value (\(\Delta\rho_{\rm z}=\rho_{\rm x}-\rho_{\rm ap}\)). We add the deposition density to the particle effective density by using volume-weighting:
\[\rho_{\rm z,2}=\rho_{\rm z,3}\left(\frac{V_{\rm z,1}}{V_{\rm z,2}}\right)+\rho _{\rm ap}\left(1-\frac{V_{\rm z,1}}{V_{\rm z,2}}\right), \tag{7}\]
Where \(\rho_{\rm z,1}\) (\(\rho_{\rm z,2}\)) and \(V_{\rm z,1}\) (\(V_{\rm z,2}\)) are the ice crystal effective density and volume before (after) one time step. During periods of sublimation, the aspect ratio is assumed to remain constant, which has been documented in laboratory measurements ([PERSON], 1998).
#### 2.2.3 Ventilation
Once an ice crystal becomes large enough to appreciably fall, it can amplify the thermal and vapor fluxes around it, which can enhance the particle's growth rate through ventilation. In the ICTG model, we assume that ventilation only occurs as a result of the crystal's vertical falling motion and neglect ventilation from the crystal's horizontal motion. From [PERSON] (1976), the ventilation coefficient for vapor diffusion is given by
\[f_{\rm z}=a_{1}+a_{2}\Big{(}N_{\rm sch}^{1/3}N_{\rm fr}^{1/2}\Big{)}^{b}, \tag{8}\]
where \(a_{1}\), \(a_{2}\), and \(b\) are constants, \(N_{\rm sch}\) is the Reynolds number of the ice crystal, and \(N_{\rm sch}\) is the Schmidt number of water vapor. Reynolds numbers are calculated using the Reynolds number-Best number power law relationship from [PERSON] (1996). We use power law coefficients with dependencies on a particle's projected cross-sectional area and mass-diameter relation such that the coefficients are general for all ice types ([PERSON], 2005). The ventilation coefficient for thermal diffusion follows a similar functional form:
\[f_{\rm T}=a_{1}+a_{2}\Big{(}N_{\rm fr}^{1/3}N_{\rm fr}^{1/2}\Big{)}^{b}, \tag{9}\]
where \(a_{1}\), \(a_{2}\), and \(b\) are constants, and \(N_{\rm fr}\) is the Prandtl number of air.
### Riming
Riming is the process of an ice crystal collecting supercooled liquid droplets that freeze onto the crystal surface, which can drastically increase the crystal's mass and fall speed while only mildly increasing its maximum dimension. Riming in the ICTG model is only from collection of cloud droplets and is based largely on [PERSON] and [PERSON] (2015), who developed a method to capture the evolving aspect ratio of ice crystals during timing. The following is a brief summary of their riming model, with slight adjustments made in the ICTG model.
#### 2.3.1 Riming Mass Growth Rate
The mass growth rate of an ice crystal from riming is given by
\[\left(\frac{dm_{i}}{dt}\right)_{simus}=\sum_{r_{i}}\ E_{il}A_{g}|v_{i}-v_{i}|m_{i}n _{i}, \tag{10}\]
where \(E_{il}\) is the efficiency with which the ice crystal collects cloud droplets of radius \(r_{p}\). \(A_{g}\) is the combined geometric cross-sectional area of the crystal and droplet, \(v_{i}\) is the fall speed of the ice crystal, and \(v_{p}\), \(m_{p}\) and \(n_{i}\) are the fall speed, mass, and number concentration of a cloud droplet of radius \(r_{p}\) respectively. In Equation 10, crystals are assumed to fall with their major axis perpendicular to their fall direction. The cloud droplets are assumed to follow a log-normal distribution with 200 size bins, and the distribution is calculated from the cloud droplet mass and number mixing ratios output from the 3D numerical model simulation. Because the fall speeds of cloud droplets are generally much smaller than those of precipitating ice crystals, the cloud droplet fall speed in Equation 10 can be neglected. Depending on the crystal habit, different collision efficiencies are calculated. Spherical collision efficiencies are from [PERSON] and [PERSON] (1974), plate efficiencies are from [PERSON] (1980), and columnar efficiencies are based on a modified spherical efficiency developed in [PERSON] and [PERSON] (2015).
#### 2.3.2 Aspect Ratio Evolution From Riming
[PERSON] (1982) found that riming acts to primarily increase the minor axis of an ice crystal with little changes to the major axis length. So as ice crystals become heavily armed, they lose their initial shape. Once their underlying crystal shape is no longer discernible, they are considered to be graupel, which has an aspect ratio of approximately 0.8 ([PERSON], 1992; [PERSON], 1978). Given these factors, [PERSON] and [PERSON] (2015) only add time to the minor axis and allow crystals to rime with an evolving aspect ratio until it reaches a limiting value, with plates riming to an aspect ratio of 0.8 and columns to an aspect ratio of 1.25 (the inverse of 0.8). Once these limiting values are reached, the aspect ratio remains constant thereafter, provided that growth only occurs by riming. Note that in the ICTG model, the ice crystal aspect ratios can evolve freely after these limiting values are reached if the crystals are advected into regions with no liquid cloud water but continue to undergo vapor growth.
In the ICTG model, we compute the density of the rime mass following [PERSON] (1962):
\[\rho_{\rm time}=0.11\left(\frac{-r_{t}v_{i}}{T}\right)^{0.76}, \tag{11}\]
where \(r_{t}\) is the radius of the ice crystal. The rime density is added to the full crystal density using volume-weighting. Limits are imposed on the full crystal density (whether it is undergoing riming and vapor growth or vapor growth only in a given time step), with a lower limit of 50 kg m\({}^{-3}\) and an upper limit of 917 kg m\({}^{-3}\). The lower limit has been used to approximate the density of thin dendrites ([PERSON] et al., 2014).
### Fall Speeds
Ice crystals in the ICTG model are initialized as stationary with 0 m s\({}^{-1}\) fall speed. After the first time step, ice crystals fall at terminal velocity. Terminal velocities are computed following [PERSON] (1996):
\[v_{T}=\frac{N_{R}n_{i}}{\rho_{a}}\frac{1}{L}. \tag{12}\]
Here, \(n_{a}\) is the dynamic viscosity of air, \(\rho_{a}\) is the air density, and \(L\) is a characteristic length of the ice crystal. [PERSON] (1992) determined that \(L=2\sqrt{ac}\) for columns, \(L=2a\) for plates, and \(L=2r\) for spheres. This characteristic length scale allows the fall speed to be habit-dependent and assumes the crystals fall with their major axis perpendicular to their fall direction.
## 3 Simulation Design
### 3D Quasi-Idealized Squall Line Simulation Setup
To test the performance of the ICTG model, this study uses output from the ARW configuration of the Weather Research and Forecasting (WRF) Model, version 4.1.2 ([PERSON] et al., 2019), which is a non-hydrostatic,fully compressible model. We use WRF to simulate a three-dimensional quasi-idealized squall line based on a leading-convective, trailing-stratiform squall line that tracked through central Oklahoma on 19 June 2007. This particular case has also been used to examine electrification and test microphysics and dynamics parameterizations in squall lines in previous studies ([PERSON] et al., 2018; [PERSON] et al., 2010; [PERSON], 2014; [PERSON] et al., 2012, 2015).
We use the same simulation setup as [PERSON] et al. (2015), except that we use the aerosol-aware microphysics scheme from [PERSON] and [PERSON] (2014). Radiation, boundary layer physics, and surface fluxes are turned off for simplicity. The domain is \(612\times 122\) km with a horizontal grid spacing of 1 km. The domain has 100 vertical levels with a top at 25 km, and Rayleigh damping is applied to the top 5 km. The bottom and top boundaries are rigid, the zonal (across-line) boundaries are periodic, and the meridional (along-line) boundaries are open.
The squall line is initialized with a combined sounding from Lamont, Oklahoma beneath 700 hPa and Norman, Oklahoma above 700 hPa at 0000 UTC that was smoothed using a 1-2-1 moving average ([PERSON] et al., 2015). The initial environmental wind shear is 12 m s\({}^{-1}\) from 0 to 5 km altitude in the across-line direction and 0 m s\({}^{-1}\) in the along-line direction. Convection initiates from forced horizontal convergence at the surface and domain center that decreases with height for the first hour. Additional details on the simulation setup are found in [PERSON] et al. (2015). The model is run with a 2.5-s time step and reaches a quasi-steady state by hour 6. At hour 6, the simulated squall line is a mature storm with a distinct low-reflectivity transition zone, an upshear-tilted convective updraft, and a broad, mesoscale updraft in the stratiform region (Figure 1). The convective region is defined as the region with a maximum in line-average reflectivity from \(x=260\)-\(300\) km, the transition zone as the region with a relative minimum from \(x=240\) to \(260\) km, and the stratiform region as the region with a relative maximum from \(x=190\) to \(240\) km.
We interpolate the vertical dimension of the 3D WRF simulation to Cartesian coordinates with 0.25-km vertical grid spacing, and use output from the simulation at hour 6 for the ICTG model. Therefore, the thermodynamic and kinematic fields from the WRF simulation that are ingested into the ICTG model are static in time. Because
Figure 1.— (a) Plan view of simulated reflectivity at 6 hr and 0.5 km altitude using the Thompson-aerosol microphysics scheme ([PERSON], 2014). Line-average (b) reflectivity, (c) vertical velocity, with positive values indicating upward motion, and (d) across-line velocity, with positive values indicating near-to-front flow.
the ICTG model does not provide feedbacks to the WRF simulation, the thermodynamics, microphysics, and dynamics from the WRF simulation do not evolve in response to particle growth in the ICTG model.
### Initializing the ICTG Model
The ICTG simulations assume crystals are growing from frozen cloud or drizzle drops initiated in the leading convective edge of the squall line. This reasoning is based on the squall line's thermodynamic and precipitation structure, in which considerable rain and cloud water are present above the melting level in the convective line under highly ice-supersaturated conditions (Figures 2a-2d). Additionally, above 6 km, the convective region contains a sharp vertical increase in snow and cloud ice mixing ratios and a decrease in cloud droplet and rain mixing ratios, indicating ongoing freezing of liquid droplets (Figures 2e and 2f). Given the presence of copious ice particles in this region, it is reasonable to assume that supercooled droplets are freezing by immersion freezing and contact nucleation and are subsequently growing into larger ice particles. It is worth noting that this ice nucleation method is used merely as a way to select reasonable initial crystal sizes. Ice crystals will certainly also form through deposition nucleation, but these crystals will be initially small and of similar size to crystals formed from small cloud drops.
We simulate 3D ice crystal trajectories using the full 3D WRF output, and we also simulate 2D ice crystal trajectories using an along-line average of the WRF output across the y-dimension of the domain. To decide where to initialize the ice crystals, we define a set of criteria based on the line-average temperature (Figure 2b) and vertical velocity (Figure 1c). Crystals are initialized above the maximum updraft within the temperature range of \(-10\) to \(-24^{\circ}\)C, which is conducive to ice crystal nucleation and growth from frozen cloud droplets ([PERSON], 1972). In the across-line direction, crystals are initialized 10 km ahead to 20 km rearward of the line-average maximum updraft. These criteria yield an ice crystal initialization domain with vertical limits of 5.75-7.75 km and across-line limits of 267-297 km. Ice crystals are initialized every 1 km horizontally and every 0.25 km vertically. This choice of initial particle placement results in 30,969 total ice crystal trajectories calculated in a single 3D simulation. For a given 2D simulation, 279 total trajectories are calculated.
Ice crystals are initialized as spheres with a density of 917 kg m\({}^{-3}\). We focus on four different initial crystal sizes for both the 2D and 3D simulations. These initial sizes were chosen based on the cloud droplet and raindrop size
Figure 2: The shading indicates line-average (a) supersaturation with respect to ice, (b) temperature, and mass mixing ratio for (c) cloud droplets, (d) rain, (e) cloud ice, (f) snow, and (g) graupel. In all panels, the line-average reflectivity is contoured in black at 10, 20, 30, and 50 dBZ. The cyan contour is the line-average 0\({}^{\circ}\)C isotherm, and the magenta square outlines the crystal initialization domain.
distributions within the crystal initialization domain (Figure 3). These distributions do not vary considerably with height, so the initialization domain-average distribution is used to determine initial crystal sizes. Two initial sizes were chosen to be the 50 th percentiles of the domain-average cloud droplet and rain drop size distributions (based on number of drops). These diameters are \(d=0.04\) and 0.1 mm, respectively, which represent cloud- and drizzle-sized particles. The cloud droplet size distribution was calculated using the non-zero average cloud mass and number mixing ratios in the 3D crystal initialization domain. An inverse exponential size distribution was calculated for rain, which is the distribution type used in the Thompson-aerosol microphysics scheme ([PERSON], 2014). We removed part of the raindrop distribution at diameters less than 0.05 mm as this size range is typically within the range of cloud droplet sizes (Figure 3). The 50 th percentile of the raindrop size distribution was then calculated. The diameter that we select to separate the cloud droplets from the precipitation-sized particles is somewhat arbitrary, as there is no specific size that delineates between these particles.
To examine additional variability in realistic growth trajectories, larger initial particle sizes were also chosen: \(d=0.5\) mm (drizzle/raindrop size) and 1 mm (raindrop size). Trajectories from other interim sizes (0.01, 0.07, 0.3, 0.7 mm) were also examined and are briefly discussed, but we determined that the aforementioned four initial sizes best capture the largest variations in particle properties and trajectories. As shown in Table 1, the four main trajectory simulations are named according to their dimensional size (2D or 3D) and their initial particle size (cloud, drizzle, drizzle/rain, rain). Both the 2D and 3D trajectory simulations are integrated with a 15-s time step for a maximum of 6 hr. The simulations are stopped sooner if the particle sublimates to extinction or reaches 4.5 km altitude (just above the melting level) before 6 hr.
## 4 2D Ice Crystal Trajectory Simulations
### Ensemble of Trajectories
To test the ICTG model, we first examine the trajectory patterns from the four main 2D ice crystal trajectory simulations (Table 1), with interim particle sizes added for completeness. Shown in Figure 4, the 2D simulations have distinctly different particle trajectory patterns, which vary according to the initial crystal diameters. The majority of the smaller crystals (\(d\leq 0.1\) mm) are transported rearward into the trailing stratiform region. These crystals also end up in the leading anvil, but only crystals initially smaller than 0.07 mm are light enough to be transported to the trailing anvil. The particles larger than 0.3 mm are too heavy to be lofed rearward to the stratiform region and instead reach the melting level either in the transition zone or the leading convective line. Only the largest particles (\(d\geq 0.7\) mm) reach the melting level in the leading convective line, consistent with the greater reflectivity values in this region. In all of the simulations, particles initiated in the highly ice-subsaturated front edge
\begin{table}
\begin{tabular}{l l l l l} \hline & \(d=0.04\) mm & \(d=0.1\) mm & \(d=0.5\) mm & \(d=1\) mm \\ \hline
2D & SIM2D-CL & SIM2D-DRZ & SIM2D-DRZRA & SIM2D-RA \\
3D & SIM3D-CL & SIM3D-DRZ & SIM3D-DRZRA & SIM3D-RA \\ \hline \end{tabular}
\end{table}
Table 1: Simulation Names for the Four 2D and 3D Simulations of Focus in This Study
Figure 3: (a) The horizontally averaged log-normal cloud droplet size distribution at every 0.5 km in altitude in the crystal initialization domain. The vertically and horizontally averaged distribution over the full crystal initialization domain is indicated by the dotted black line. (b) As in (a), but for the raindrop size distribution. The vertical black lines in both panels indicate the initial particle sizes used for the trajectory simulations.
indicating the same trajectory patterns but more clearly showing the highly trafficked regions and the spatial spread in trajectories. In SIM2D-CL (Figure 4b), the particle trajectories are organized according to their initial position relative to the convective updraft. The particles initiated rearward of the updraft (dark blue trajectories in Figure 4b) between 7.25 and 7.75 km altitude are most likely to be transported into the forward and rear anvils. Many of these particles have not yet reached the melting level after 6 hr of ICTG model integration, consistent with the trajectory retrieval in ([PERSON] & [PERSON], 1994), which found that particles in the trailing anvil had the longest trajectory times. Their slower fall speeds suggest that they have fall speeds nearly balanced by the weak mesoscale updraft in the stratiform region (cf. Figure 1c). The updraft-rewarted particles initiated between 5.75 and 7.25 km altitude are transported directly rearward and approach the melting level near the rear end of the stratiform region between \(x=185\) and 215 km. These trajectories have some spread that may be due to their different initial altitudes. Higher altitude particles have longer interaction with the mesoscale updraft, thus prolonging the time that they remain lofted while being transported rearward. These results are consistent with previous studies that found that ice crystals falling into the stratiform region originated from immediately rearward of the convective updraft at mid-to upper levels ([PERSON] & [PERSON], 1991, 1993; [PERSON] & [PERSON], 1994; [PERSON] & [PERSON], 1995).
For the SIM2D-CL particles initiated within the updraft (green and yellow trajectories in Figure 4b), there are two distinct trajectory regimes. Particles initiated between 7.25 and 7.75 km altitude are transported to the forward anvil where they sublimate to extinction, and particles initiated between 5.75 and 7.25 km are lofted upward and then transported rearward, where they reach the melting level in the trailing stratiform region. This second regime of particles reaches the melting level at the same location as many updraft-rewarted particles, but these particles do not have similar trajectories; rather, the updraft-centered particles follow a more straight-line, diagonal path to the stratiform region, suggesting that they have larger fall speeds earlier in their trajectories or that they encounter downdrafts or weaker updrafts in the transition zone. The maximum in trajectory density near \(z=6\) km
Figure 5.— Shading represents the trajectory density (number of times a particle passes over each grid box non-consecutively) for the 2D simulations (a) SIM2D-CL, (b) SIM2D-DRZ, (c) SIM2D-DRZRA, and (d) SIM2D-RA. Black contours are line-average reflectivity factor at 10, 20, 30 and 50 dBZ, and gray contours are line-average vertical velocity at 0.5, 1, 2, and 4 m s\({}^{-1}\). The colored lines are representative trajectories in a given simulation, and the black dot at the end of the trajectory is the particles’s final position above the melting level. The gray square outlines the crystal initialization domain.
and \(x\) = 240 km marks the overlap of updraft-rewarward and updraft-centered trajectories, as shown by the two representative trajectories in Figure 5a. Finally, the SIM2D-CL particles initiated forward of the updraft (orange and red trajectories in Figure 4b) sublimate to extinction either immediately or after following an elliptical path to the forward anvil.
The trajectories in SIM2D-DRZ (Figure 4d) are nearly similar to those in SIM2D-CL with a few exceptions. One difference is that the updraft-rewarward particles (dark blue trajectories) are now too heavy to be lifted by the mesoscale updraft into the anvils; instead, all of the particles reach the melting level in the stratiform region, slightly forward of the particles in SIM2D-CL. The relatively larger fall speeds in SIM2D-DRZ cause some of the particles initiated at lower altitudes to fall immediately into subsaturated air and sublimate to extinction just above the melting level at \(x\) = 225 km. These sublimated particles yield a gap in the trajectories between the updraft-rewarward particles (dark blue trajectories) and the updraft-centered particles (yellow trajectories). A second gap in trajectories reaching the melting level appears at the transition zone (\(x\) = 240-260 km), though this gap results from a smaller group of quickly falling particles in the leading line due to their accelerated growth aloft. An example trajectory from this group of particles is shown in Figure 5b.
The trajectories of particles from SIM2D-DRZRA (Figure 4f) and SIM2D-RA (Figure 4h) have little dependence on the initial particle location. The majority of the particles approach the melting level toward the rear end of the convective reflectivity tower, with the SIM2D-DRZRA particles traveling farther rearward than the heavier SIM2D-RA particles. This finding is consistent with past studies asserting the importance of particle size sorting in generating the reflectivity structure of the squall line. In both SIM2D-DRZRA and SIM2D-RA, the updraft-forward particles (red trajectories in Figures 4f and 4h) initiated in subsaturated air are lofted up to 2 km by the convective updraft and travel farther than the updraft-centered and updraft-rewarward particles, suggesting that their mass was reduced by partial sublimation. The overall result is a downward and rearward-extending maximum in trajectory density for both simulations (Figures 5c and 5d). The reduced trajectory density in the transition zone is consistent with the reduced snow and graugel mixing ratios in this region (cf. Figures 2f and 2g). Notably, some SIM2D-RA trajectories ending in the transition zone sublimate to extinction after prolonged periods in ice-subsaturated air (Figure 4h). The observed locations of widespread particle sublimation (underneath the leading anvil, above the stratiform melting level, in the transition zone) in all of the simulations are consistent with the locations identified in [PERSON] (1994) and [PERSON] et al. (2018).
### Representative Trajectories
The Lagrangian framework of the ICTG model allows us to learn how the particle properties evolve in response to their varied trajectories through different regions of the storm with different growth conditions. The representative trajectories shown in Figure 5 were selected to best represent common trajectory patterns that result in notable differences in the particle evolution and final particle properties. The five representative particles are named according to their simulation and initial size: P2D-CL1, P2D-CL2, P2D-DRZ, P2D-DRZRA, P2D-RA. In Figure 6, we examine time series of the environmental conditions and microphysical processes that give rise to each representative particle's properties. The goal is to understand the role of various microphysical processes in producing the modeled evolution of the representative particles.
The P2D-CL1 and P2D-CL2 trajectories exemplify the two types of paths that the smaller particles (\(d\)\(\lesssim\) 0.1 mm) follow toward the stratiform melting level. Particle P2D-CL1 is lofted by the updraft during the first 0.5 hr (Figures 6h and 6j). During this time, it is situated in strongly ice-supersaturated air (\(s\), up to 0.18, Figure 6d) and abundant cloud water (Figure 6f) in the convective updraft, but it only experiences minimal riming due to its low collection efficiency (Figure 6e). Around 0.25 hr, the particle's density begins to stabilize around 760 kg m\({}^{-3}\) as it travels away from the abundant liquid cloud water (Figure 6f) in the convective zone. From 0.5 to 1.5 hr, the particle passes through the transition zone, where the ice-supersaturation remains near zero (Figure 6d), and the particle's diameter and mass (Figures 6a and 6c) remain relatively small (\(<\)0.25 mm and \(<\)0.02 mg, respectively). Just before reaching the stratiform melting level at 1.5 hr, the majority of the particle sublimates (due to ice-sub-saturation), and its diameter shrinks by 0.16 mm.
In contrast, the updraft-rewarward Particle P2D-CL2 has a different evolution. This particle does not experience an initial increase in size because it is initiated in nearly unsaturated air and low cloud water content (thus limited riming). This particle experiences moderate supersaturations (\(s_{i}\) \(<\) 0.08) throughout its entire trajectory,yet becomes 0.85-mm larger and 0.35-mg heavier than Particle P2D-CL1. As shown in Figure 6b, p2D-CL2 remains mostly in the planar crystal temperature range (\(-8\) to \(-22^{\circ}\)C), and this is consistent with the particle's oblate aspect ratio evolution (Figure 6i). At 1.25 hr, this particle's density decreases to 675 kg m\({}^{-3}\) once the particle reaches the mesoscale updraft. Because the particle is unimmed, this density reduction is associated with dendritic growth (i.e., branching). Branching is further confirmed by the increasing ice supersaturation and steady air temperatures near \(-16^{\circ}\)C, which falls in the dendritic growth temperature range (\(-12\) to \(-18^{\circ}\)C). On the other hand, Particle P2D-CL1 did not experience significant dendritic growth because it quickly passed through the appropriate temperature range (near \(-15^{\circ}\)C) which had low supersaturations. Although the current iteration of the ICTG model does not include aggregation, the diversity of particles being transported into the stratiform region supports the likelihood of aggregating particles through mechanical interlocking of ice crystal branches. This finding implicitly supports past work associating the enhanced vapor deposition in the mesoscale updraft with a large prevalence of aggregates composed primarily of dendrites ([PERSON] & Houze, 1994; [PERSON] & Houze, 1979; [PERSON] & Heymsfield, 1989). While aggregation is beyond the scope of the present study, future trajectory modeling studies will examine the effects of aggregation.
Because SIM2D-CL and SIM2D-DRZ have similar trajectory patterns, the next representative particle, P2D-DRZ, was chosen to be distinct from the previous two representative trajectories; thus, it does not follow the maximum trajectory density. Particle P2D-DRZ is initialized toward the front edge of the convective updraft and experiences an initial decrease in density to 375 kg m\({}^{-3}\) during the first 0.1 hr, owing to light timing in the updraft. From 0.1 to 0.5 hr, ice-spersaturated conditions lead to light vapor deposition. From 0.5 to 3 hr, the particle's fluctuating density evolution suggests there are competing effects from timing and vapor deposition. From 2 to 3 hr, the particle actually passes through the convective updraft a second time, as seen by the trajectory loop (Figure 5b), vertical velocity (Figure 6h), and particle height (Figure 6j). Between 1.5 and 2.5 hr, timing dominates the relatively small growth in the particle's mass. After 2.5 hr, the particle continues to time, but its growth is dominated by vapor deposition (Figure 6d), as indicated by the increasing particle density and the final particle mass (\(\sim\)0.125 mg) being much larger than the accumulated time mass (\(\sim\)0.015 mg). This accelerated growth aloft results in the particle becoming too heavy for the updraft to support at 2.8 hr, resulting in a fast, 0.5-hr descent to the melting level at the rear end of the convective line.
Figure 6.— Time series of particle (a,c,e,g,i,j) equivalent diameter, mass, accumulated time mass, effective density, aspect ratio, and height for the representative particles shown in Figure 5 (b,d,f,h) ambient temperature, ice supersaturation, cloud water mixing ratio, and vertical velocity. The black dots at the end of each line is the value at the crystal’s final position.
Particle P2D-DRZRA and P2D-RA are both initiated at the same location as Particle P2D-CL1, yet they have considerably different trajectories due to their larger size. Instead of being lofed by the updraft, the particles immediately fall through the updraft, resulting in their shorter trajectory times (0.55 hr for P2D-DRZRA, 0.25 hr for P2D-RA). Their larger size also enables significant accumulations of prime mass. Particle P2D-DRZRA has a larger reduction in density (by 200 kg m\({}^{-3}\)) than Particle P2D-RA because the smaller initial size of P2D-DRZRA makes it more susceptible to density changes from mining. During the first half of its trajectory, Particle P2D-DRZRA experiences less-supersations up to 0.09 in the planar crystal temperature range and thus simultaneously grows by vapor deposition into an oblate shape (Figure 6i). During the second half of its trajectory, conditions are ice-subsaturated down to \(-\)0.1, and Particle P2D-DRZRA sublimates during its descent to the melting level to nearly its initial size and mass at 0.5 mm and 0.06 mg, respectively. Despite riming, the strongly ice-subsaturated conditions down to \(-\)0.15 result in Particle P2D-RA sublimating to a smaller diameter (0.95 mm) and mass (0.4 mg) than it initially had.
We also tested the sensitivity of the 2D trajectories to a decrease in the initial density to 500 kg m\({}^{-3}\) for larger (\(\geq\)0.5 mm) crystals (not shown), and found that the trajectories shifted rearward by 6-12 km and residence times increased by \(\sim\)7 min. Overall, the particle properties remained similar to those with initial densities of 917 kg m\({}^{-3}\).
## 5 3D Ice Crystal Trajectory Simulations
In this section, we expand our trajectory analysis to use the full three-dimensional output from the WRF simulation. This approach will introduce along-line variability in the trajectories and provide insight on how the storm's along-line variability impacts the spatial distribution of ice crystals and their properties. Moreover, the 3D trajectory simulations will show that the ICTG model can be utilized on 3D output.
### Representative Trajectories
Figure 7 shows the trajectory density from the 3D simulations and select representative trajectories with the same starting positions as those in Figure 5. The representative particles are named with the same convention as those in the 2D simulations. Overall, the trajectory density patterns are similar to those from the 2D trajectories which were computed using a line-average of the squall line's structure. One notable difference is that the trajectory densities in SIM3D-DRZRA and SIM3D-RA extend up to 12 km altitude in the convective region, as opposed to 8 km altitude in SIM2D-DRZRA and SIM2D-RA, owing to the stronger updrafts in the 3D simulations, which become weaker when averaged for the 2D representation of the flow. The representative trajectories in all four simulations are also similar to their 2D counterparts, with the exception of P3D-DRZ, which travels a maximum of 12 km in the along-line direction (Figure 8a). However, the majority of the particles in all 3D simulations are not advected an along-line distance greater than 5 km (Figure 8b). In fact, the majority of the larger particles (\(\geq\)0.5 mm) are advected no greater than 0.5 km in the along-line direction. These results show that the 2D simulations using line-averaged thermodynamic and kinematic fields maintain the salient trajectory patterns of fully 3D particle transport. We now examine whether this averaging also maintains comparable particle growth signals.
Figure 9 shows the time series of the representative particle properties from the 3D simulations. Particles P3D-CL1 and P3D-CL2 both show similar properties as the corresponding particles in the 2D simulations: P3D-CL1 ends up 0.9-mm smaller and 0.6-mg lighter than P3D-CL2 upon reaching the melting level. Although the first 0.75 hr of P3D-CL1's trajectory are in ice-supersaturated conditions, the temperatures are also extremely low (\(<\)\(-\)25\({}^{\circ}\)C), which slows vapor deposition growth rates. Even after the particle descends beneath 8 km into higher subfreezing temperatures (\(t\) = 1 hr), particle growth remains inhibited, now by supersaturation values that are near zero. The particle ends up with an aspect ratio \(>\)1, indicating a columnar crystal. A columnar crystal occurs here because Particle P3D-CL1 is immediately lofed \(\sim\)1 km higher than Particle P2D-CL1 by the stronger convective updraft in the 3D simulation. These higher altitudes are in the columnar temperature regime (\(<\)\(-\)22\({}^{\circ}\)C). Afterward, Particle P3D-CL1 enters the transition zone where potential growth into other habits is inhibited by the fluctuating levels above and below ice saturation.
In contrast, Particle P3D-CL2 grows to be larger and heavier than P3D-CL1. P3D-CL2 grows into a planar crystal with an extremely low aspect ratio (down to 0.05), and it begins branching once it reaches the stratiform mesoscale updraft at \(t\) = 1.25 hr, as shown by the corresponding diameter increase, density decrease, and temperature Figure 8: (a) Representative trajectories from Figure 7, but in three dimensions. Their horizontal projections are plotted onto the along-line/across-line plane, as well as the reflectivity at 0.5 km altitude. The gray rectangle outlines the across- and along-line limits of the ice crystal initialization domain. (b) Normalized frequency of the maximum along-line distance traveled by ice crystals during their trajectories. Normalized frequency is defined as count of particles with a given maximum along-line distance divided by the maximum count for that simulation.
Figure 7: As in Figure 5, but for the 3D simulations.
of \(-16^{\circ}\)C (within the dendritic growth temperature range). The particle continues to quickly grow thereafter as it encounters persistent ice-supersaturated conditions provided by the mesoscale updraft, reaching the melting level with a final diameter of 1.15 mm and a final mass of 0.6 mg. This result agrees well with past modeling and observational studies remarking on the faster deposition growth of ice particles within the mesoscale updraft of the trailing stratiform region ([PERSON], 1994; [PERSON], 1987).
Particle P3D-DRZ grows to be the third largest 3D representative particle, with a final diameter of 1 mm upon reaching the melting level. It becomes 0.13-mg heavier than its 2D counterpart, with most of its mass acquired by a combination of riming and vapor deposition when the particle is in warmer temperatures below 7 km (at \(t\) = 0.5 and 1.2 hr). Particle P3D-DRZ ends up oblate (in contrast to the slightly prolate P2D-DRZ), owing to reduced growth of P3D-DRZ while it is at higher altitudes in the columnar temperature regime (\(<\)\(-22^{\circ}\)C).
Particles P3D-DRZRA and P3D-RA are both initially lofted \(\sim\)0.5 km by the stronger convective updrafts in the 3D simulations instead of immediately falling downward as their 2D counterparts did. They quickly rime while in the convective updrafts and then approach the melting level in the leading line instead of being transported to the stratiform region. Similar to their 2D counterparts, both particles have trajectory times between 0.25 and 0.5 hr and partially sublimate upon quickly falling into ice-subsaturated air above the melting level. However, the stronger subaurations in the 3D simulation causes more of Particle P3D-RA's mass to sublimate than that of Particle P2D-RA, where P3D-RA has a 0.35-mg mass reduction at the end of its trajectory, in contrast to the 0.13-mg reduction for P2D-RA.
Thus far, the ICTG model has demonstrated the ability to realistically track the locations and changes of evolving ice crystals in the simulated storm. Differences in the particle properties were shown to depend on their initial size and location, which is consistent with past observational and modeling studies. The 2D and 3D simulations produce similar bulk trajectory patterns, but the properties of the cloud- and drizzle-sized particles in the 3D simulations are generally more extreme in magnitude than those from the 2D simulations. At appropriate temperatures, the more extreme supersaturations in the 3D simulations help generate considerably larger particles than in the 2D simulations, but there are also comparable regions of extreme subsaturation in the 3D simulations that can produce smaller particles through greater sublimation. The similarity between the 2D and 3D trajectory patterns likely arose due to a balanced interaction between the particle's fall speed and the simulated vertical and
Figure 9: As in Figure 6, but for the 3D simulations.
across-line wind speeds; the faster winds and more extreme particle growth in the 3D simulations balanced each other in the same way as the slower winds (due to line averaging) and less extreme particle growth in the 2D simulations. The ICTG model has thus demonstrated its versatility across different source model configurations.
### Particle Recycling in the Convective Updraft
A small group of particles with a distinct trajectory type in both 2D and 3D simulations grew to significant sizes, some even larger than the selected representative particles. The updraft-forward upper-level particles from Figures 4a-4d, as well as Particles P2D-DRZ (Figure 5b) and P3D-DRZ (Figure 7b), all had elliptical trajectories with repeated passes through the convective updraft. We now explore the impact of these repeated passes (that we call particle recycling) on a particle's final properties upon reaching the melting level.
Figure 10 shows select particle trajectories from SIM3D-CL and SIM3D-DRZRA that have particle recycling patterns. Both particles make multiple passes through an updraft-downdraft couplet between 8 and 10 km altitude before reaching the melting level within the convective line. During these repeated passes, the particles grow by both vapor deposition and riming, as supported by the multiple peaks in ice supersaturation and cloud liquid water (Figures 10d and 10f) occurring at the same time as small increases in the particle diameter, mass, and accumulated time mass (Figures 10c-10g). In these examples, the collected time mass is an order of magnitude greater than that of the representative particles in Figure 9. Due to its larger size, the particle from SIM3D-DRZRA has a larger collision efficiency and accretes more cloud droplets than the smaller particle from SIM3D-CL. The fastest increase in both particles' mass occurs during their final descent toward the melting level, when the particles
Figure 10: Representative trajectories showing particle recycling in the (a) SIM3D-CL and (b) SIM3D-DRZRA simulations. Cross sections of vertical velocity (shading) and reflectivity (black contours at 30 and 40 dBZ) are shown at \(y=15\) km in (a) and \(y=19\) km in (b) to match the initial along-line position of each particle and show the kinematic conditions contributing to their recycling trajectories. The gray box outlines the crystal initialization domain. Panels (c)–(h) show time series of the ice crystal properties and environmental conditions over the particle’s trajectory, with the line colors corresponding to the trajectories in (a) and (b).
quickly collect time (at \(t\) = 2.4 hr for SIM3D-CL, \(t\) = 1.2 hr for SIM3D-DRZRA), yielding a final mass of 2.8 and 1.5 mg, respectively. With repeated passes through the vertical velocity couplet, the particles have more time to grow (via vapor deposition) large enough to considerably collect cloud droplets once they fall into the higher temperatures below. It is worth noting, however, that riming only contributes to \(\sim\)20% of their total mass prior to partially sublimating at the end of their trajectory; the other \(\sim\)80% is from vapor deposition.
### Bulk Particle Properties
We now examine the final properties of all particles from the SIM3D-CL and SIM3D-DRZRA simulations. These two simulations were chosen because they yield distinctly different final particle properties and have initial crystal sizes that are represented in the cloud and raindrop size distributions (cf. Figure 3). Figures 11 and 12 show the line-average final particle properties based on their initial locations in the crystal initialization domain, excluding particles that sublimate to extinction. This examination provides a more holistic analysis of the bulk particle properties than is possible by examining only select representative particle trajectories.
In SIM3D-CL (Figure 11), there are two initialization regions with particles that grow considerably larger and heavier than the rest: ahead of the convective updraft near 7.5 km altitude and rearward of the updraft near 6.75 km. Nearly all of the updraft-rewarted particles (\(x\) < 277 km) grow exclusively by vapor deposition and have a larger density (700 kg m\({}^{-3}\), Figure 11d) and lower aspect ratio (<0.6, Figure 11e), likely related to their lack of riming (Figure 11c). The largest (\(\geq\)0.9 mm) and heaviest (\(\geq\)0.6 mg) updraft-rewarted particles are most similar to Particle P3D-CL2 (cf. Figure 7a), which travels directly rearward to the stratiform region and undergoes dendritic growth. In contrast, the relatively smaller updraft-rewarted particles initialized near 7.5 km altitude are transported to higher altitudes, into the leading and trailing anvils, where the lower temperatures and higher characteristic supersaturations produce slower vapor deposition growth rates. This group of particles also has the longest trajectory times (>2 hr, Figure 11f), in agreement with the 2D simulations, which show that the particles entering the anvil regions do not complete their trajectories after 6 hr. The updraft-rewarted particles initialized near 6 km do not grow as large as those initiated near 6.75 km due to prolonged exposure to ice-subsaturated air.
Figure 11.— (a) The average final equivalent diameter of the crystals that did not completely sublimate, plotted on the crystals’ initial position, using data from SIM3D-CL. Black contours are line-average supersaturation with respect to ice, and white contours are line-average vertical motion at the 0.5, 1, 2, and 4 m s\({}^{-1}\) levels (b)–(f) As in (a), but for final mass, accumulatedrime mass, final particle density, final aspect ratio, and total trajectory time. Total trajectory time is the time it takes the crystal to reach the melting level or 6 hr, whichever comes first.
The updraft-centered particles (277 \(<\) \(x\) \(<\) 290 km) are the smallest (\(\sim\)0.4 mm) and lightest (\(<\)0.1 mg) of all of the particles. The updraft-centered particles initiated above 7 km mostly travel into the leading anvil region and experience slowed growth. The particles initiated below 7 km have trajectories similar to Particle P3D-CL1 (cf. Figure 7a), whose growth is limited by low supersaturation and sub-saturation in the transition zone.
Most of the updraft-forward particles (_x_ \(>\) 290 km) sublimate to extinction (not shown), but of those that remain, they grow relatively large. Their relatively large size (\(\geq\)0.9 mm), mass (\(\geq\)0.4 mg), and accumulated time mass (\(\geq\)0.1 mg) suggest that these particles undergo recycling, consistent with the initial locations of the individual particles in Figure 10 and Particle P3D-DRZ. The aspect ratio of these particles is near 0.8, and their density is between 400 and 500 kg m\({}^{-3}\), suggesting that these particles have become small, graupel-like particles that reach the melting level in the convective line, in agreement with the spatial distribution of the graupel mixing ratio (cf. Figure 2g).
For the bulk particle characteristics of SIM3D-DRZRA (Figure 12), a gradient in the final particle properties occurs across the convective updraft. On average, the updraft-rewarward particles (_x_ \(<\) 277 km) generally end up smaller (\(<\)0.6 mm), lighter (\(<\)0.1 mg), and denser (\(>\)700 kg m\({}^{-3}\)) than the remaining particles due to growth at low supersaturation and limited cloud water. These particles are initially too heavy for the convective updrafts to considerably left them into regions favorable for prolonged deposition or timing growth and thus do not grow as large or heavy as the initially smaller, updraft-rewarward particles from SIM3D-CL. This finding is consistent with ([PERSON] & [PERSON], 1994), who found greater growth of smaller ice particles (relative to larger particles) initialized at upper levels rearward of the convective updraft in their 2D model. As a result, these larger updraft-rewarward particles follow quasi-straight paths down to the melting level, similar to Particle P3D-DRZRA. The particles initiated below 6.5 km generally have aspect ratios \(>\)1 as a result of them falling to lower altitudes and into a temperature range favorable for columnar growth (\(-\)8 to \(-\)3\({}^{\circ}\)C). This finding also agrees with ([PERSON] & [PERSON], 1994), who found that needles were produced near 5.5 km altitude in their squall line simulation.
The updraft-forward particles (_x_ \(>\) 290 km) grow relatively larger. Given that these particles are initiated in subsaturated air, they partially sublimate before reaching the convective updrafts. This early sublimation allows the updrafts to increase the particles' residence time in ice-supersaturated air and the probability of them coming into contact with supercooled liquid cloud droplets. The majority of the updraft-forward particles have a reduced
Figure 12.— As in Figure 11, but for SIM3D-DRZRA.
density between 450 and 550 kg m\({}^{-3}\), suggesting that they have some degree of riming or branching. Similar to SIM3D-CL, the particles initiated above 6.75 km have an increased size (\(\geq\)0.9 mm) and mass (\(\geq\)0.5 mg), though the particles from SIM3D-DRZRA have larger masses and collect more rim than the corresponding particles in SIM3D-CL. These particles are also likely graupel-like particles that resulted from recycling multiple times through the convective updraft. Their initial location, relatively large accumulated rime mass, and longer trajectory time suggest that they are similar to the recycling trajectory from SIM3D-DRZRA in Figure 10b.
The distinct differences in final particle properties between SIM3D-CL and SIM3D-DRZRA collectively show that capturing size-dependent evolution of crystal properties is important for simulating the microphysics in squall lines. Smaller particles ejected from the convective line have longer trajectories and are more likely to branch, have reduced densities, and end up in the upper parts of the cloud. In contrast, initially larger particles are more likely to heavily rime, have less spread in their trajectories, and reach the melting level sooner and closer to the convective line. Particle densities and fall speeds can have impacts on the kinematics through precipitation loading, and differences in the spread of trajectories hold implications for the latent heating structure of the storm. These notable differences in particle properties and transport highlight the importance of capturing accurate ice initialization in simulated squall lines.
## 6 Conclusions
This study introduces a novel ICTG model and evaluates its performance on a quasi-idealized WRF simulation of a leading-convective, trailing-stratiform squall line. The ICTG model includes recent laboratory-based parameterizations of ice crystal growth via vapor deposition and riming, as well as ice crystal decay via sublimation. The ICTG model tracks the trajectories of individual ice particles in space and allows the properties of those particles to evolve naturally based on their environment. By following the specific growth pathways taken by the ice crystals, the ICTG model simulates ice crystal characteristics within a squall line in a way not possible with Eulerian bulk microphysical models. The Eulerian modeling framework effectively averages the particle properties of a given ice crystal population, while the Lagrangian modeling framework maintains and tracks the evolving characteristics of individual particles throughout each particle's lifetime. This Lagrangian approach is important because ice crystals can develop a large diversity in crystal forms that affect their subsequent growth, fall speeds, and collection rates. Indeed, [PERSON] (2008) has estimated that the heterogeneity in ice crystal trajectories accounts for much of the estimated diversity in snowfall. Our modeling framework is designed to explore this diversity in ice crystal evolution and examine how such variety determines the microphysical properties of cold cloud systems.
Our analysis focused on 2D and 3D simulations of ice crystals initialized in the leading convective updraft of a squall line with diameters of 0.04, 0.1, 0.5, and 1 mm. In both the 2D and 3D simulations, the ICTG model was capable of producing an ice crystal trajectory pattern with particle properties that were consistent with past observational studies and the overall reflectivity structure of the simulated squall line. The particles with smaller initial diameters (\(d\leq 0.1\) mm) had trajectories that were generally organized by their initial across-line position relative to the convective updraft. Those smaller particles initiated immediately rearward of the updraft were transported to the stratiform region where they grew rapidly via vapor deposition in the supersaturated mesoscale updraft. These particles became the largest in diameter (\(\geq\)0.9 mm) and mass (\(\geq\)0.6 mg), while simultaneously evolving into secondary habits, consistent with past studies identifying increased dendritic growth in the stratiform region. The smaller particles initiated within the convective updraft ended up in the leading anvil or in the trailing stratiform region; these particles did not grow as large as the updraft-rearward particles, owing to their limited interaction with the mesoscale updraft. In contrast, the initially larger particles (\(d\geq 0.5\) mm) fell through the convective updraft and followed quasi-straight paths down toward the melting level, regardless of their initial position relative to the convective updraft. Their shorter trajectories in mostly subsaturated air resulted in these particles having a final mass 0.4-mg less than that of the initially smaller particles. In all of the simulations, the particles initiated along the front edge of the convective updraft were most likely to rime and reach the melting level closer to the convective line. Of these rimed particles, those initiated above 7.5 km became large (\(d\geq 0.9\) mm) graupel-like particles, owing to repeated passes through the convective updraft.
These results show that initially small particles (\(d\lesssim 0.1\) mm) can grow large either by vapor deposition when transported to the stratiform region or via recycling in the convective updraft, whereas initially larger particles(\(d\geq 0.5\) mm) with faster fall speeds have limited time and growth potential and thus remain primarily in the convective region. The ICTG model's production of varied particle trajectories based on size is consistent with past modeling and observational studies documenting size sorting of ice particles ejected from the leading convective line. One potential result of this size sorting is the commonly observed minimum reflectivity zone between the leading line and stratiform precipitation regions.
The above findings collectively reveal the importance of mining and vapor deposition in organizing ice particles in leading-line, trailing-stratiform squall lines. The ICTG model neglected aggregation and secondary ice production, yet produced a spatial distribution of ice particles in agreement with the simulated precipitation pattern. The ICTG model's production of realistic particle properties suggests that the model can be used to infer particle growth mechanisms in squall lines and other storm systems. This is a much-needed analysis because understanding the ice transport and growth in these systems at a basic level can improve forecasts of these storms as well as quantitative precipitation estimation.
Although the ICTG model is still under development, future use of the model can guide bulk microphysics scheme development. Differences between particle properties produced by the ICTG model versus Eulerian numerical models can reveal which assumptions and microphysical processes may be contributing to inaccuracies in precipitation features produced by bulk microphysics schemes. The Lagrangian nature of the ICTG model can provide further information on which regions of a storm bulk microphysics schemes struggle to reproduce and can identify the microphysical processes most responsible for potential inaccuracies. These comparisons can improve the microphysics of operational forecast models, leading to better forecasts of storm evolution as well as quantitative precipitation estimation. Future work will involve the addition of aggregation to the model, accounting for variations in particle number concentrations, and testing the robustness of the results using squall line simulations with different microphysics schemes.
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wiley/facf4d18_55e7_4d39_8b2e_8b7f9f4a6373.md | Identifying Three-Dimensional Radiative Patterns Associated With Early Tropical Cyclone Intensification
[PERSON], [PERSON], and [PERSON].
###### Abstract
Cloud radiative feedback impacts early tropical cyclone (TC) intensification, but limitations in existing diagnostic frameworks make them unsuitable for studying asymmetric or transient radiative heating. We propose a linear Variational Encoder-Decoder (VED) framework to learn the hidden relationship between radiative anomalies and the surface intensification of realistic simulated TCs. The uncertainty of the VED model identifies periods when radiation has more importance for intensification. A close examination of the radiative pattern extracted by the VED model from a 20-member ensemble simulation on Typhoon Haiyan shows that longwave forcing from inner core deep convection and shallow clouds downshear contribute to intensification, with deep convection in the downshear-left quadrant having the most impact overall on the intensification of that TC. Our work demonstrates that machine learning can aid the discovery of thermodynamic-kinematic relationships without relying on axisymmetric or deterministic assumptions, paving the way for the objective discovery of processes leading to TC intensification in realistic conditions.
Key Words.:TCS, keyword keyword
## 2 Data
### Convection-Permitting Hindcasts of Two Tropical Cyclones
We analyze a 20-member set of WRF Version 4.3.1 (Skamarock, 2008) ensemble hindcast simulations of Typhoon Haiyan (2013) and a small set of simulations of Hurricane Maria (2017), ran at a convective-permitting resolution (3 km). The same set of simulations for Maria in [PERSON] et al. (2020) is analyzed to evaluate if ML models can learn the same physical conclusion in that paper - disabling Cloud Radiative Feedback (CRF) disrupts tropical cyclogenesis. This set of simulations includes one Control (CTRL) experiment and 4 \"no-CRF\" sensitivity simulations. \"No-CRF\" simulations are produced by running the CTRL restart files at different times, albeit setting all hydmeteor terms in the longwave and shortwave schemes to be zero. The CTRL simulation was initialized from GEFS analysis and integrated from 14 September 2017, 1200 UTC to 20 September 2017, 1200 UTC. Readers are referred to [PERSON] et al. (2020) for more details regarding the setup of the Maria experiments.
We use the Haiyan ensemble simulations to analyze the role of CRF in realistic conditions, that is, without the no-CRF experiments. These simulations are constructed by dynamically downscaling the National Center for Environmental Prediction's Global Ensemble Forecast System (GEFS) ensemble member outputs. The primary source of variability in the ensemble comes from the interaction between convection and slight variability in the GEFS synoptic conditions. The Haiyan WRF simulations are integrated from 1 November 2013, 00 UTC to 8 November 2013, 00 UTC, with a two-nested, 15-3 km horizontal grid spacing fixed model domain. The inner domain is around 3,600 x 2,200 km in size. Radiation is treated with the Rapid Radiative Transfer Model for GCMs (RRTMG; [PERSON] et al., 2008), and microphysics is treated using the Thompson and Eidhammer scheme ([PERSON] and [PERSON], 2014). Other model physics are configured identically to the Maria simulations. The model contains 55 stretched vertical levels and is topped at 10 hPa. These simulations are assigned integer labels from 0 to 19. All simulations produce outputs at an hourly interval; these outputs are post-processed into a TC-relative framework by tracking the local maxima in 700 hPa absolute vertical vorticity, spatially smoothed with a 1.5-degree boxcar filter, and temporally filtered with a three-point Gaussian filter to remove noise.
For Haiyan, while we use all the data for training and evaluation, we keep the analysis tractable by focusing on two ensemble members: Member 2, which intensifies at a quicker rate, and Member 11, which intensifies at a slower rate.
### Cross-Validation Strategy
Following best machine learning practices, we divide the data into training, validation, and test sets. Evaluating model skills on data unseen during training ensures good prediction skills for out-of-sample data. This section discusses how we perform the data splitting.
Since ensemble simulations and sensitivity experiments can be treated as different realizations of the same physical system responding to slightly different forcing, we opt for a data-splitting strategy based on ensemble member labels (Haiyan) and experiment labels (Maria).
For Haiyan, we use 80% of the ensemble outputs (16 experiments) for training, and 20% of the data (4 experiments) for validation and testing. Two experiments that are not strongly correlated to the other experiments are left out at first to create an independent test set; the remaining 18 experiments are partitioned into training and validation subsets by randomly generating a list of two numbers between 1 and 20; the two numbers are then used as references to separate the validation set from the training set. This data-splitting procedure is repeated 40 times to create 40 different sets of training data, which enables evaluations of the model variability associated with the choice of data split. Our test set is truly independent because the two test experiments are never used in the training or validation set for all data splits.
We slightly altered the data-splitting strategy for Maria due to a lack of samples. The Control (CTRL) simulation is always included in the training set because it has the most samples and represents how the TC evolves in realistic conditions where CRF always exists. The \"NCRF-36h\" experiment is used as the test data set amongst the four remaining sensitivity experiments because the storm intensity changes in that experiment depart most from the CTRL simulation. We randomly split the other experiments into a portion that is merged into the training set (2 experiments) and the other portion for model validation (1 experiment). The cross-validation strategy for Maria yields three different data splits to test the ability of the trained ML models to depict the counterfactual scenario of TC evolution without cloud radiative feedback (CRF).
## 3 Methodology
### Machine Learning Framework
Our analysis leverages machine learning (ML) to identify radiative spatial features relevant to TC intensification from WRF output. We adopt an interpretable, stochastic linear VED model to discover such features. Latent heating is not used as an input because it is treated as an internal response to external forcings such as radiation in the moist static energy variance budget ([PERSON], 2022; [PERSON] and [PERSON], 2014). A schematic diagram of our framework is provided in Figure 1. The framework is divided into two parts: a learned encoder and a learned decoder for TC surface intensity predictions. The learned encoder distills radiative information relevant to TC intensity predictability into a limited number of structures. We constrain the number of extracted structures (one per variable in our case) to maximize interpretability and avoid model overfitting. The encoder incorporates Principal Component Analysis (PCA) to compress three-dimensional WRF longwave radiation and shortwave radiation outputs into multiple low-dimensional PCs, each representing the time evolution of a particular radiative anomaly pattern. The PCA reduces the complexity of the data from three-dimensional volumes to 1D time series. The encoder distills knowledge by combining the PCs into traceable compressed representations based on skillful TC intensity forecasts. The scalar output of the encoder is the projection of the radiation structures of individual samples onto the learned time-invariant structures, which roughly represents the spatial similarity between the two structures. We use these scalars to predict the 24-hr, forward-facing \(\left(V_{t+2\lambda}-V_{t}\right)\) intensification of TC surface intensity with a linear decoder. A lead time of 24 hr is commonly used for short-term intensity predictions ([PERSON], 2007). All models presented herein are implemented and trained with the PyTorch deep learning library ([PERSON] et al., 2019). As shown in Section 3.2, the linear VED framework can be considered a combination of different multiple linear regression (MLR) equations. Training an ML model involves using an iterative procedure called \"stochastic gradient descent\" (SGD) to progressively optimize the weights and biases of the different MLR equations. The SGD procedure for all models is performed with the Adam Optimizer. Whether or not an ML model can reach an optimal solution depends on the \"learning rate,\" the step at which the SGD procedure proceeds, and a well-designed loss function. Loss functions are quantifiable measurements that are tied to the optimization process. An example of this is optimizing a model by minimizing a loss function like the mean squared error (MSE) between model predictions and observations. The VED architecture requires a specialized loss function for optimization. The VED architecture can be considered a generalized form of the Variational Autoencoder (VAE) architecture that uses different input-output pairs. Thus, the loss function used to optimize the VED model has the same structure as that commonly used for VAEs:
\[\text{VEDloss}=\
u\text{Reconstruction Loss}+(1-\
u)\text{KLloss}, \tag{1}\]
where \(\
u\in[0,1]\) is the weight of the reconstruction loss in the overall VED loss. The reconstruction loss measures how well the model predicts the output (a simple mean absolute error in our case), whereas the KL loss constrains the distribution of the latent space. We use an annealing strategy to train the VED models. The models are first
Figure 1: The interpretable linear VED framework proposed in this study combines a pattern-finding encoder and a decoder for tropical cyclone intensification rate prediction. The first linear layer in the encoder modules combines different radiation structural information in the PCs into the time evolutions of the mean structures and uncertainty structures. A random sampling of the normal distributions with mean and log variances conditioned on the inputs introduces uncertainty to a decoder module that predicts the 24-hr surface wind intensification prediction. There is flexibility in the choice of the decoder architecture, from simple multiple linear regressors to a complex nonlinear Artificial Neural Network. Optimization of model weights with loss functions tries to minimize the absolute error between the truth and the predictions from the decoder based on the learned patterns.
optimized with only the reconstruction loss. We will then continue training the best model with the smallest reconstruction loss with different \(\
u\) to optimize the prediction spread. The \"learning rate\" and \(\
u\) are model hyperparameters - parameters that define the architecture of an ML model and its training. The best sets of hyperparameters for different data splits are found with the Optuna hyperparameter tuning framework ([PERSON] et al., 2019).
Various aspects of the proposed framework will be elaborated upon in this section. First, we demonstrate that the extracted patterns and their contributions to the VED predictions can be mathematically defined, ensuring full interpretability (Section 3.2). Second, we describe methods to incorporate uncertainty quantification in the framework (Section 3.3), which is critical in physical discovery (e.g., for Section 4.2). Finally, we present the metrics used in this work to evaluate prediction skills (Section 3.4).
### Mathematical Construction of the Interpretable VED Models
As a whole, the main objective of the proposed VED model can be described by a simple equation:
\[\underbrace{\left(dV_{\text{surf}}\right)}_{\text{Interstinction}}=b+\underbrace{a _{\text{Lw}}\cdot X_{\text{Lw}}}_{\text{Longwave contribution}}+\underbrace{a_{\text{SW}}\cdot X_{\text{SW}}}_{\text{ Shortwave contribution}} \tag{2}\]
where the prediction target is the temporal change in maximum tangential mean surface winds (\(V_{\text{surf}}\)) in units of m/s. Radiative contributions to the prediction are proportional to linear regression coefficients \(a_{\text{Lw}}\) and \(a_{\text{SW}}\) (in units of m.s\({}^{-1}\).K\({}^{-1}\)). The intercept term (\(b\); units in m/s\({}^{2}\)) in the equation can be thought of as the intensification's expected value over the training set (positive in our case). Intensification rates predictions can be calculated from the sum of radiative contributions (\(X_{\text{Lw}},X_{\text{SW}}\)) that are sampled from normal distributions \(\mathcal{N}\), with learned means (\(\mu_{\text{Lw}},\mu_{\text{SW}}\)) and variance (\(\sigma_{\text{Lw}}^{2},\sigma_{\text{SW}}^{2}\)) calculated from learned logarithmic standard deviations (\(\log\)\(a_{\text{Lw}}^{2}\). log\(\sigma_{\text{SW}}^{2}\)):
\[X_{\text{Lw}}\sim\mathcal{N}\big{(}\mu_{\text{Lw}},\sigma_{\text{Lw}}^{2}\big{)},\;X_{\text{SW}}\sim\mathcal{N}\big{(}\mu_{\text{SW}},\sigma_{\text{SW}}^{2} \big{)} \tag{3}\]
These four statistical moments are constructed with the learned weights and biases in the VED encoder module, and we will show that the conditional means \(\mu_{\text{Lw}}\) and \(\mu_{\text{SW}}\) can be interpreted as projections of the longwave and shortwave fields onto data-driven, three-dimensional patterns. We will further show that the linear regression coefficient and intercept term can be defined with the learned weights and biases for both the encoder and decoder modules.
#### 3.2.1 Encoder
As mentioned previously, Principal Component Analysis (PCA) extracts information from the WRF raw fields. The PCA linearly transforms input physical fields (\(X_{i}\)) into combinations of orthogonal singular (PCA) spatial modes (\(\Pi_{\text{X}}(z,r,\theta)\)), and their corresponding time evolution (PC loadings time series; \(PC_{\text{X}}(t)\)):
\[X_{i}(t,z,r,\theta)-\overline{X_{i}(t,z,r,\theta)}=\sum_{i=1}^{N}PC_{\text{X} }(t)\Pi_{\text{X}}(z,r,\theta), \tag{4}\]
where \(N\) is the number of retained PCA modes. Instead of the raw field, different loadings \(PC_{\text{X}}(t)\), which represents the time evolution of different radiative spatial modes, are used as inputs to the VED. These \(PC_{\text{X}}(t)\) time series are standardized to have a mean of 0 and a variance of 1 to avoid high variance in the regression weights:
\[\widetilde{PC}_{\text{X}}(t)=\frac{PC_{\text{X}}(t)-\overline{PC_{\text{X}}( t)}}{\sigma_{PC_{\text{X}}(t)}}, \tag{5}\]
where \(\overline{PC_{\text{X}}}\) and \(\sigma_{PC_{\text{X}}(t)}\) are the mean and standard deviation of the PC loadings, calculated over the training set.
The second task of the encoder is to combine different PCA modes for longwave radiation and shortwave radiation into two scalars representing the projection of radiation structures onto time-invariant \"mean structures\" (\(\Pi_{LW,u},\Pi_{SW,u}\)) and two scalars representing the projection onto \"logarithmic variance structures\" (\(\Pi_{LW,u_{\text{log}}^{2}},\Pi_{SW,\text{log}^{2}}\)). These four projection scalars (encoder output) are the linear combinations of the standardized PC loadings (Equation 5),
\[\begin{split}\mu_{LW}&=\ b_{1,LW,u}+\sum_{i=1}^{n_{ \text{max}}}a_{1,LW,u_{i}}\times\widetilde{PC}_{LW,i},\\ \text{log}\sigma_{LW}^{2}&=\ b_{1,LW,\text{log}^{2} }+\sum_{i=1}^{n_{\text{max}}}a_{1,LW,\text{log}^{2},i}\times\widetilde{PC}_{LW,i},\\ \mu_{SW}&=\ b_{1,SW,u}+\sum_{i=1}^{n_{\text{max}}}a_{1, SW,u_{i}}\times\widetilde{PC}_{SW,i},\\ \text{log}\sigma_{SW}^{2}&=\ b_{1,SW,\text{log}^{2} }+\sum_{i=1}^{n_{\text{max}}}a_{1,SW,\text{log}^{2},i}\times\widetilde{RT}_{ SW,i}.\end{split} \tag{6}\]
In these equations, terms with \(a\) and \(b\) represent the learned weights and biases in the VED framework, respectively. The subscripts in these terms have different options highlighting different aspects of the framework: \"1\" and \"2\" represent learned weights and biases in the encoder module and the decoder module; \"LW\" and \"SW\" represent the physical variables these coefficients are associated with (longwave and shortwave radiation). Finally, \(\mu\) and \(\text{log}\sigma^{2}\) indicate the specific branch these coefficients are in within the VED framework (mean structure and uncertainty structure).
From Equation 2, the scalars defined in Equation 6 will be used to construct normal distributions \(\mathcal{N}(\mu,\text{log}\sigma^{2})\) for longwave and shortwave radiation. Each time the VED model is run, two scalars will be randomly sampled from the two normal distributions and used as inputs in the prediction equation (Equation 2). We could quantify the uncertainty of the prediction of TC intensification rates by running the model multiple times with the same inputs.
#### 3.2.2 Interpreting the Encoding as a Scaled Projection
In addition to guiding how to combine the different PC modes, the learned encoder weights can also be used to obtain the 3-D spatial patterns corresponding to the four scalars (Equation 6),
\[\begin{split}\Pi_{\mu,LW}&=\ \lambda_{LW,u}\sum_{i=1}^{n_{ \text{max}}}a_{1,LW,u_{i}}\times\Pi_{LW,i},\\ \Pi_{\gamma\text{SW}}&=\ \lambda_{SW,u}\sum_{i=1}^{n_{ \text{max}}}a_{1,SW,u_{i}}\times\Pi_{SW,i},\\ \Pi_{\text{log}\gamma\text{LW}}&=\ \lambda_{LW,\text{log}^{2} }\sum_{i=1}^{n_{\text{max}}}a_{1,LW,\text{log}^{2},i}\times\Pi_{LW,i},\\ \Pi_{\text{log}\gamma\text{SW}}&=\ \lambda_{SW,\text{log}^{2} }\sum_{i=1}^{n_{\text{max}}}a_{1,SW,\text{log}^{2},i}\times\Pi_{SW,i},\end{split} \tag{7}\]
where \(\lambda\) represents scaling factors that ensure the extracted patterns have a norm of 1. The full mathematical deviation of this constant is shown in Appendix A.
But how are the scalars (Equation 6) and the spatial patterns (Equation 7) related? In this section, we show that the scalars are scaled projections of raw fields onto the time-invariant patterns. We first introduce an inner product that will help us reinterpret the encoder module:
\[\left\langle PC_{X_{1}}|PC_{X_{2}}\right\rangle_{X_{2}}=\sum_{i=1}^{N}PC_{X_{1}} ^{\prime}PC_{X_{2}}^{\prime}, \tag{8}\]where the \(X_{3}\) subscript indicates that the inner product and the projection are defined with respect to the \(X_{3}\) variable for which the PC decomposition and orthogonal modes are calculated. Using this notation, the longwave conditional mean scalar (\(\mu_{\text{LW}}\)) can be expressed as the projection of the spatiotemporal longwave heating field onto \(\Pi_{\mu,\text{LW}}\):
\[\underbrace{\mu_{\text{LW}}(t)}_{\text{Conditional Mean}}=\left\langle\underbrace{ \text{LW}^{\prime}(x,y,z,t)}_{\text{Longwave Heating Assembly}}\right| \underbrace{\Pi_{\text{LW},\mu}(x,y,z)}_{\text{Dust-Driven Pattern}}\right\rangle_{LW}. \tag{9}\]
Indeed, the PC loadings (\(PC_{i,\Pi_{\text{LW}},\text{ev}},PC_{i,\Pi_{\text{LW}},\text{ev}},PC_{i,\Pi_{ \text{LW}},\text{ev}},PC_{i,\Pi_{\text{LW}},\text{ev}}\)) of the learned mean (\(\Pi_{\mu,\text{LW}}\), \(\Pi_{\text{LSW}}\)) and standard deviation (\(\Pi_{\text{log}^{2}\mu_{\text{LW}}}\), \(\Pi_{\text{log}^{2}\mu_{\text{SW}}}\)) obey the following equations:
\[\begin{split}\left\langle\mu_{LW}=\left\langle LW^{\prime}\ \mid\Pi_{\mu,\text{LW}}\right\rangle_{LW}& =\sum_{i=1}^{n_{\text{ev}}}PC_{i,LW}\times PC_{i,\Pi_{\text{LW}},\text{ev}}\\ \log\sigma_{LW}^{2}=\left\langle LW^{\prime}\ \mid\Pi_{\text{ log}^{2}\mu_{\text{LW}}}\right\rangle_{LW}&=\sum_{i=1}^{n_{ \text{ev}}}PC_{i,\text{LW}}\times PC_{i,\Pi_{\text{LW}},\text{ev}}\\ \mu_{\text{SW}}=\left\langle SW^{\prime}\ \mid\Pi_{\text{SW}} \right\rangle_{SW}&=\sum_{i=1}^{n_{\text{ev}}}PC_{i,SW}\times PC _{i,\Pi_{\text{LW}},\text{ev}}\\ \log\sigma_{SW}^{2}=\left\langle SW^{\prime}\ \mid\Pi_{\text{ log}^{2}\mu_{\text{SW}}}\right\rangle_{SW}&=\sum_{i=1}^{n_{ \text{ev}}}PC_{i,SW}\times PC_{i,\Pi_{\text{LW}},\text{ev}}.\end{split} \tag{10}\]
allowing us to interpret the conditional moments (\(\mu_{LW},\mu_{\text{SW}},\text{log}\sigma_{LW}^{2},\text{log}\sigma_{SW}^{2}\)) as projections of raw radiative heating fields onto stationary patterns. Using this projection notation, Equation 2 may be rewritten as:
\[\begin{split}\underbrace{\left(\frac{dV^{\prime}_{\text{LW}}}{ dt}\right)_{\text{2 nd}}}_{\text{Interification}}&=\underbrace{a_{LW}\mathcal{N}\big{(}\left\langle LW \right|\Pi_{\mu,\text{LW}}\right\rangle_{LW},\,c_{LW}e^{dev_{LW}\left\langle LW \right|\Pi_{\text{log}^{2}\mu_{\text{LW}}^{2}}\right\rangle_{\text{ex}}} \big{)}}_{\text{Longwave consumption}}\\ &\quad+\underbrace{a_{\text{SW}}\mathcal{N}\big{(}\left\langle SW \right|\Pi_{\text{SW}}\right\rangle_{\text{SW}},\,c_{\text{SW}}e^{dev_{LW} \left\langle SW\right|\Pi_{\text{log}^{2}\mu_{\text{SW}}^{2}}\right\rangle_{ \text{SW}}}\big{)}}_{\text{Shortwave contribution}}\\ &\quad+b,\end{split} \tag{11}\]
where the \(c_{LW}\), \(c_{\text{SW}}\), \(d_{LW}\), and \(d_{\text{SW}}\) are constants involved when expanding the variance terms. The definitions of these terms are provided in the next section.
#### 3.2.3 Effective Weights and Biases in the Prediction Equation
In this section, we will define several terms that are left undefined in previous sections. These undefined terms include the \"effective weights\" and bias terms in Equation 2, the scaling factor in Equation 6, and the four variance constants terms in Equation 11. The exact deviation steps for these terms can be found in Appendix A.
The \"effective weights\" terms can be obtained by factoring out the constant terms in the normal distributions after expanding Equation 2 with Equations 5 and 6.
The effective weight of the longwave contribution to TC intensification is,
\[a_{LW}=|a_{2,LW}|\sqrt{\sum_{i=1}^{n_{\text{LW}}}\frac{a_{1,LW,\mu,i}^{2}}{ \sigma(PC_{i,LW})^{2}}}, \tag{12}\]
whereas the effective weight of the shortwave contribution is \[a_{SW}=|a_{2,SW}|\sqrt{\sum_{i=d}^{n_{SW}}_{i=d}a_{1,SW,a_{i},i}\frac{PC_{i,SW}}{ \sigma(PC_{i,SW})^{2}}} \tag{13}\]
The overall model bias (\(b\)), which can be thought of as the intensification's expected value over the training set (positive in our case), can be obtained by substituting Equation 2 with Equations 5 and 6 and isolating constant terms that are not in the normal distributions:
\[\begin{split} b&=b_{2}+a_{2,LW}\left(b_{1,LW,a}- \sum_{i=d}^{n_{SW}}\frac{a_{1,LW,a_{i}}\overline{PC_{i,LW}}}{\sigma(PC_{i,LW})} \right)\\ &+a_{2,SW}\left(b_{1,SW,a}-\sum_{i=d}^{n_{SW}}\frac{a_{1,SW,a_{i}} \overline{PC_{i,SW}}}{\sigma(PC_{i,SW})}\right).\end{split} \tag{14}\]
This term will be referred to as \"persistence baseline\" in the subsequent sections. Physically, this term can be considered as the main contribution of non-radiative processes to the intensification of all training TCs.
The scaling factors for the four extracted patterns are mathematically derived by (a) combining Equations 2, 5, and 6, (b) building upon the equivalence of Equation 11 and the output equation from (a), and (c) assuming the norms (squared) of the structures to be 1. For the mean longwave structure, the scaling factor is,
\[\lambda=\left[|a_{2,LW}|\sqrt{\sum_{i=d}^{n_{SW}}_{i=d}a_{1,LW,a_{i},i}\over \sigma(PC_{i,LW})^{2}}\right]^{-1}. \tag{15}\]
\(\lambda\) for the other scalars can be similarly defined by substituting the encoder weights and PC loading time series with those corresponding to the shortwave radiation and the logarithmic variance structures.
Finally, algebraic manipulations allow us to mathematically define the four constants involved in the variance calculation (\(c_{LW},c_{SW},d_{LW},d_{SW}\)) :
\[c_{LW}=\sqrt{\frac{|a_{2,LW}|}{a_{LW}}}\text{exp}\left(b_{1,LW,\text{log}^{ 2}}-\sum_{i=d}^{n_{SW}}a_{1,LW,\text{log}^{2},i}\frac{PC_{i,LW}}{\sigma(PC_{ i,LW})}\right), \tag{16}\]
\[c_{SW}=\sqrt{\frac{|a_{2,SW}|}{a_{SW}}}\text{exp}\left(b_{1,SW,\text{log}^{2} }-\sum_{i=d}^{n_{SW}}a_{1,SW,\text{log}^{2},i}\frac{PC_{i,SW}}{\sigma(PC_{i, SW})}\right), \tag{17}\]
\[d_{LW}=\sqrt{\sum_{i=d}^{n_{SW}}_{i=d}a_{1,LW,\text{log}^{2},i}\over\sigma(PC _{i,LW})^{2}}, \tag{18}\]
\[d_{SW}=\sqrt{\sum_{i=d}^{n_{SW}}_{i=d}a_{1,SW,\text{log}^{2},i}\over\sigma(PC _{i,SW})^{2}}. \tag{19}\]
In the prediction equation, positive longwave contributions to surface wind intensification arise when the values sampled from \(\mathcal{N}(\mu_{\text{LW}},\sigma_{\text{LW}})\) are greater than zero. Positive longwave contributions will lead to intensification quicker than the training set reference (\(b\)), and vice versa. A quicker intensification occurs when the spatial distribution of longwave anomaly relative to the training average projects strongly onto \(\Pi_{\text{LW}}\). In contrast, smaller intensification rates correspond to cases in which longwave anomalies and \(\Pi_{\text{LW},\mu}\) are orthogonal to each other. Similar logic can be applied to the shortwave contributions.
### Uncertainty Quantifications for Physical Insights
By setting up a normal distribution based on the learned \(\mu\) and log\(\sigma^{2}\)([PERSON] & Welling, 2013), the proposed VED enables uncertainty quantification (UQ) for both the extracted structures and the intensification predictions. This section touches upon how we may use VED uncertainty for physical insights.
The ML models are more trustworthy when they provide the full distribution of possible extracted structures and prediction outcomes. The full distributions yield uncertainty information that can be reliably interpreted, which is crucial when we use data-driven techniques to discover new physical processes. For example, we can use prediction uncertainties to assess the relevance of radiation with time. In contrast, uncertainties in the latent structures highlight specific areas in the structure to focus on in future work for scientific discovery.
One of the potential limitations in the current VED setup, especially when applying to the tropical cyclogenesis problem, is that we predict intensification with only the longwave and shortwave radiation information. It is likely that all pathways to tropical cyclone genesis and intensification are not included in this underdetermined system. We adopted this strategy because we are in a low sample regime, which necessitates restricting the input to avoid overfitting. However, the restricted nature of the model creatively yields physical understanding. Specifically, we argue that the temporal evolutions of model spread and error reveal the changes in the relevance of radiative feedback with time. Large spread and errors should arise when the system is undetermined and requires information from non-radiatively-coupled variables for reliable intensification predictions. These are periods where non-radiative processes are more important predictors of TC intensification. In contrast, we expect smaller model errors and spread when radiative heating is strongly coupled to intensification.
### Evaluating the Trained Probabilistic Models
The trained VED models are evaluated with two criteria--good mean prediction skills and a well-calibrated uncertainty in the model outputs. We sample the model spread by running each model 30 times and aggregating the 30 model predictions. A suite of stochastic and determinative performance metrics are used to assess the quality of the model. Two stochastic metrics are evaluated: the Continuous Ranked Probability Score (CRPS score) and the Spread-skill reliability (SSREL) value ([PERSON] et al., 2023).
The CRPS score compares the Cumulative Distribution Function (CDF) of the probabilistic forecasts against the observations; it is also a generalization of the deterministic mean absolute error (MAE) metric for probabilistic models:
\[\text{CRPS}\big{(}F,y_{pred}\big{)}=\int_{-\infty}^{\infty}\big{[}F\big{(}y_{ pred}\big{)}-\mathcal{H}\big{(}y_{pred}-y_{true}\big{)}\big{]}^{2}dy_{pred}, \tag{20}\]
where \(F\) represents the CDF of the model predictions, \(\mathcal{H}\) is the Heaviside step function applied to the difference between the truth \(\big{(}y_{true}\big{)}\) and one prediction \(\big{(}y_{pred}\big{)}\) sampled from the full distribution. A well-calibrated model should have as small a CRPS score as possible.
The SSREL value ([PERSON] et al., 2023) measures the quality of a binned spread-skill plot--an assessment of the statistical consistency of a probabilistic model ([PERSON] et al., 2013). A statistically consistent model, sampled from the same distribution as the truth, should have its spread closely match its error. If the spread-skill curve of a model deviates from the 1-1 line, the model is either under-dispersive (overconfident) or over-dispersive (underconfident). The SSREL value measures weighted distances between the model curve and the 1-1 line:
\[\text{SSREL}=\sum_{k=1}^{K}\frac{N_{k}}{N}\big{[}\text{RMSE}_{k}-\overline{ \text{SD}_{k}}\big{]}, \tag{21}\]
where \(K\) is the number of bins, \(N_{k}\) is the number of samples in a bin, \(N\) is the total number of samples, \(\text{RMSE}_{k}\) is the root-mean-square-error of the model predictions for samples within the bin, SD is the standard deviation of the model predictions. A perfectly calibrated model will have an SSREL value of 0. We report two metrics for the mean deterministic skills: the mean absolute error (MAE) and root mean squared error (RMSE).
## 4 Results
An advantage of our proposed model architecture is that it simultaneously extracts structures relevant to 24-hr intensification rates and the uncertainties in the predictions. Here, we explore using this information to understand (a) how we can use ML to identify temporal periods where radiation is an important driver of intensification, (b) the relevance of axisymmetric radiation to intensification, (c) whether asymmetric radiation exerts influence on intensification, and (d) whether we can show this influence with simple perturbation experiments.
### Choosing the Best VED Model and Comparison With the Best Baseline Model
It is important to present evidence that the proposed VED model achieves better probabilistic skills than the traditional baseline. Here, we compare the best VED model to a simple Principal Component Regression baseline (description in Appendix B). The best VED model is chosen objectively based on the CRPS and SSREL scores. Figure 2 shows the minimum and median CRPS scores for all trained Haiyan VED and baseline models with different hyperparameters on the validation set. We also substitute the fully linear prediction layer in the baseline model with feed-forward neural networks with different depths to evaluate the responses of prediction skills to nonlinearity.
Adding nonlinearity degrades the median CRPS scores for most baseline models (Figures 1(a) and 1(c)), which justifies keeping the model fully linear. The shape of the CRPS score curves for the baseline models (Figures 1(a) and 1(c)) suggests the existence of an optimal range of **dropout rates** for better generalizability. For the VED models, a \(\lambda\) that is too small, that is, too large a KL loss during training deteriorates prediction skills.
The CRPS score comparison above establishes optimal ranges for the **dropout rates** (the baseline models) and \(\lambda\) (the VED models). The best models for comparison are determined by calculating the SSREL scores for all models trained with these optimal coefficients. The spread-skill plot for the best baseline and VED models (Figure 2) provides a strong justification for using the VED model in our study. Specifically, the spread-skill curve of the VED model is much shorter than the baseline one, which indicates the VED predictions are more accurate. Compared to the best baseline model, the best VED model better captures the peaks in the training data set and removes the large biases in early intensification rates seen in the baseline predictions on the test set. Based on these comparisons, we conclude that the VED model is superior to the baseline model for our research task.
Figure 2: The mean Continuous Ranked Probability Score scores (left column) and the spread-skill diagrams (right column) show that the trained Variational Encoder-Decoder (VED) models outperform the trained baseline models with different dropout rates and degrees of nonlinearity in the prediction equation (”nonlin:3” represents baseline model with three nonlinear layers in the decoder). Comparing the best fully linear baseline model for Haiyan and Maria (brown lines in panel b and d; **dropout rates** of 0.3 and 0.1 respectively) and the mean performance of the VED model with the best SSREL score shows that the VED model makes fewer mistakes in its predictions and is generally more well-calibrated than the best baseline model. A well-calibrated model means that most points on the model’s spread-skill curve are as close to the 1-1 line (gray lines in panels (b, d)) as possible.
For Maria, the best VED model performs similarly to the best baseline model in terms of the minimum CRPS score (Figure 2c). The uncertainty for both the best baseline model and best VED model are well calibrated. However, the VED model is again preferable for Maria because of the smaller prediction errors (Figure 2d).
Interestingly, the benefit of the VED model compared to the baseline model seems to scale to the sample size. The VED model always overperforms the baseline for the Haiyan ensemble case with a larger sample size (Table 1), whereas the VED model mostly only overperforms the baseline in probabilistic metrics for the Maria simulations (Table 2). A potential explanation for worse VED skills for Maria is that the more complex model (VED) overfits the training data in cases with low sample size.
### Prominence of Radiative Feedbacks in the Early Intensification Phase
#### 4.2.1 Identifying Periods of Radiatively Driven Intensification
By construction, our simple VED model predicts TC intensification exclusively from radiative heating, overlooking significant contributions from surface fluxes and wind-induced surface heat exchange ([PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2016). Recent modeling studies (e.g., [PERSON] et al., 2020; [PERSON] and [PERSON], 2018) suggest that radiative heating could be less critical to TC intensification beyond the initial genesis or spin-up stage.
To investigate whether this holds in our case studies, we use the VED model to _identify periods when radiative feedbacks dominate TC intensification_. Instances with significant model errors or uncertainties are times when radiative heating alone cannot predict TC intensification. In contrast, instances with accurate predictions and minimal uncertainty are likely times when radiative heating is dominant.
Our VED's capability to distinguish radiative heating-dominated stages is crucial for reliability assessment and scientific discovery. Figure 3 presents the mean prediction and prediction spread of the best-calibrated VED models for Haiyan and Maria. For Maria, the probabilistic ML models replicate the intensification rate reduction in CRF mechanism-denial experiments (Figure 3a). Decomposing predicted intensification into longwave and shortwave contributions (Figure 3b) shows that the slower intensification in the mechanism-denial experiments is primarily attributable to the longwave component. This result is reassuring as it identifies the longwave component of CRF as the main contributor to the early intensification of TCs, consistent with the \"cloud greenhouse effect\" framework in [PERSON] et al. (2020). However, the model underestimated the intensification rate at the latter stage of the NCRF-60h TC's life cycle, possibly due to unaccounted non-radiative processes like the surface fluxes feedback (e.g., [PERSON] and [PERSON], 2016). Furthermore, the model assigned a smaller weight to the shortwave channel in the linear prediction equation for Maria (Figure 3b), resulting in a shortwave contribution close to zero. We believe the model has learned the strong effect of disabling CRF in the sensitivity experiments and its impact on intensification, which manifests mainly in the longwave channel. The shortwave contribution is larger in the realistic Haiyan ensemble simulations (Figure 3d).
For Haiyan, where CRF always exists, we compare the VED predictions for a high intensification rate Haiyan ensemble member (Member 2) to those for a slow intensification member (Member 11) to assess the role of radiation in realistic conditions (Figure 3c). Increased bias (Figure 3c) and wider uncertainty range (Figure 3e) for Member 2 predictions in the latter part of the TC's life cycle shows the limitation of the VED model to understand the mature phase of TC intensification. The prediction distribution for samples taken during the high uncertainty phase is close to the training data distribution (prior), implying the need for non-radiative inputs to adequately constrain the probabilistic predictions and reduce overall model bias. In contrast, the model
\begin{table}
\begin{tabular}{l l l l l} \hline Experiment & Metric & Training & Validation & Test \\ \hline VED & CRPS & **2.83** (3.35) & **1.65** (4.69) & **2.86** (3.73) \\ & SSREL & **1.31** (2.61) & **0.33** (3.54) & **1.03** (2.44) \\ & RMSE & **4.52** (5.34) & **2.61** (6.99) & **4.83** (5.95) \\ & MAE & **3.67** (4.25) & **2.15** (5.76) & **3.75** (4.74) \\ Baseline & CRPS & 3.23 (3.48) & 2.26 (4.83) & 3.45 (3.90) \\ & SSREL & 1.89 (2.45) & 0.67 (4.19) & 1.17 (2.76) \\ & RMSE & 5.35 (5.68) & 3.67 (7.17) & 5.54 (6.09) \\ & MAE & 4.28 (4.56) & 2.96 (6.00) & 4.31 (4.93) \\ \hline \end{tabular} _Note._ Also shown in the table is the median of the prediction skills distribution of all trained models with different hyperparameter settings (numbers in brackets). All values in the table are multiplied by \(10^{5}\) for readability. The best model is indicated with bolded numbers.
\end{table}
Table 1: Prediction Skills of the Best VED and the Best Baseline Model on the Haiyan Ensemble
\begin{table}
\begin{tabular}{l l l l l} \hline Experiment & Metric & Training & Validation & Test \\ \hline VED & CRPS & 1.76 (5.88) & **2.28** (7.78) & **1.39** (5.26) \\ & SSREL & 0.59 (3.51) & **0.80** (4.33) & **0.33** (2.95) \\ & RMSE & 3.74 (9.27) & 3.93 (10.12) & **2.21** (7.32) \\ & MAE & 2.21 (7.95) & 3.20 (9.95) & **1.74** (7.08) \\ Baseline & CRPS & **1.16** (2.32) & 2.39 (3.46) & 2.32 (2.60) \\ & SSREL & **0.36** (1.62) & 0.88 (3.28) & 1.68 (2.21) \\ & RMSE & **2.46** (4.57) & **3.57** (6.22) & 3.54 (3.84) \\ & MAE & **2.03** (3.21) & **3.13** (4.85) & 3.22 (3.51) \\ \hline \end{tabular} _Note._ The bold values in the table is to highlight the type of model that has the best performance evaluated with different metrics.
\end{table}
Table 2: Prediction Skills of the Best VED and the Best Baseline Model on the Maria Experimentspredictions for samples taken from the early intensification phase of Member 2 are accurate, indicating predictability from the radiative heating fields.
Comparing linear decompositions of VED predictions (Figure 3d) reveals that lower intensification rates for Member 11 (Hours 10-20) are due to reduced longwave contribution. Positive longwave contribution in Member 2 leads to a faster intensification rate beyond the persistence baseline (overall model bias). In the next section, we analyze the radiation structures in the two ensemble members to provide physical interpretations of how differences in radiative heating structures might explain the differing intensification rates of the two ensemble members.
#### 4.2.2 Qualitative Agreement With Existing Diagnostic Tools
In the previous section, we claimed that transitioning from an accurate, low-uncertainty regime to an inaccurate, high-uncertainty regime in the VED predictions can be understood as separating periods where radiation is more critical from non-radiative processes are more important. Here, we use well-established budget analysis tools to evaluate the extent to which the claim is valid.
Figure 3: Decomposing tropical cyclone intensification predictions for Maria and Haiyan shows longwave radiative heating’s link to early intensity differences. We present mean Variational Encoder-Decoder (VED) surface intensification predictions (dashed for Maria (a) from three WRF simulations and for Haiyan (c) from two ensemble members, with actual rates of intensity change (thick). The shadings in the left columns illustrate the range of possible VED predictions given the same inputs using a Monte Carlo approach. Panels (b) and (d) show longwave and shortwave radiation contributions to the mean VED predictions. Zooming in on Haiyan Member 2, Panel (e) compares the evolution of VED uncertainty associated with longwave radiation (purple) against two Moist Static Energy (MSE) variance sources (blue and brown). In [PERSON]’s mechanism-denial experiment and the early phase of Haiyan, the model associates the difference between a quickly intensifying tropical cyclone and a slowly intensifying one with longwave radiation. The vertical dashed lines in panel (e) show the two-stage behavior in the longwave MSE variance source term (black) and similar behavior in VED prediction uncertainties (purple). The time lag between the two methods is shown in panel (e; black arrow).
We can analyze the cyclogenesis process with the Frozen Moist Static Energy Spatial Variance Budget ([PERSON] and [PERSON], 2020; [PERSON] and [PERSON], 2018; [PERSON] and [PERSON], 2014):
\[\frac{1}{2}\frac{\partial\text{var}\hat{h}}{\partial t}=\frac{\overline{\hat{h }^{\prime}}\overline{\hat{h}^{\prime}}\overline{\hat{h}^{\prime}}+\overline{ \hat{h}^{\prime}}\overline{\hat{h}^{\prime}}}{\text{SEP Contribution}}+\underbrace{ \overline{\hat{h}^{\prime}}\overline{\text{NetLW}^{\prime}}+\overline{\hat{h}^ {\prime}}\overline{\text{NetSW}^{\prime}}}_{\text{Radiative Contribution}}-\overline{ \
abla_{h}\cdot\overline{\hat{u}^{\prime}}\hat{h}}, \tag{22}\]
where varf is the spatial variance of vertically integrated moist static energy (MSE), and SEF (the Surface Enthalpy Flux) is the sum of LHF (the Latent Heat Flux) and SHF (the Sensible Heat Flux). The radiative contribution consists of net column longwave radiative flux convergence (NetLW) and net column shortwave radiative flux convergence (NetSW). Primes indicate anomalies relative to the mean of the spatial domain, represented by overlines. MSE spatial variance source terms are obtained by spatially averaging all terms on the right-hand side of Equation 22. We perform the spatial averaging from 0 to 600 km from the TC center. The MSE variance summarizes the spatial distribution of frozen MSE surrounding a developing tropical cyclone, with the biggest contribution coming from moisture ([PERSON], 2022). Since tropical cyclogenesis shares similarities with rotating convective self-aggregation, TCs form as the TC thermodynamics transition to an aggregated state, characterized by a compact moisture blob surrounded by drier air (positive \(\partial_{t}\)varf\(\hat{h}\), e.g., [PERSON] and [PERSON], 2020; [PERSON] and [PERSON], 2018). From Equation 22, the source terms for the MSE variance are the covariance between the existing MSE anomalies and different flux anomalies. Creating positive MSE variance anomalies necessitates spatially aligned anomalies. For example, positive radiative contribution to MSE variance may arise from warm longwave heating anomalies in the high energy TC inner core or cool radiative anomalies in the drier TC surroundings ([PERSON], 2015). Inward moisture transport from radiatively driven secondary circulations (in-up-out circulations; e.g., [PERSON], 2015; [PERSON] et al., 2020; [PERSON] et al., 2020) can enhance MSE variance by redistributing moisture toward the TC center.
Figure 2(e) compares the time evolution of the radiation and surface enthalpy flux MSE variance source terms and the time evolution of the learned logarithmic variance structure for the longwave channel (\(\log^{2}_{LW}\)). The advection term is not considered due to the coarse temporal resolution of the saved WRF outputs. Focusing on Haiyan member 2, the contribution from NetLW to the overall MSE variance budget is initially comparable to the contribution from SEF but becomes less important toward the end of the time series. This behavior is consistent with the expected increase in prominence of surface fluxes feedback ([PERSON]; [PERSON], 1986; [PERSON] and [PERSON], 1987; [PERSON] and [PERSON], 2016) after the initial genesis stage. Consistent with the MSE variance budget analysis, we see two distinct phases in the \(\log^{2}_{LW}\) time series, one with smaller values before 20 hr (fewer prediction uncertainties) and one with larger values after 20 hr (more prediction uncertainties). It is encouraging that the NetLW term and \(\log^{2}_{LW}\) time series have a two-stage behavior as it ensures that the ML model is trustworthy and has learned physically meaningful relationships.
A notable caveat to the above discussion is that our ML framework predicts TC kinematic changes, whereas the MSE variance budget measures thermodynamical changes. This distinction potentially explains a 5-hr time lag between the decrease in longwave contribution to MSE variance and the increase in ML prediction uncertainties. The idea that thermodynamic forcing precedes kinematic changes can be supported by Figure 2 in [PERSON] et al. (2020), where TC surface intensification occurs 12-24 hr after the drop in SEF contributions. The analysis in [PERSON] (2017) also shows that strong moist entropy forcing precedes the genesis time of idealized axisymmetric TCs. Finally, airborne observations suggest that the TC core becomes and remains close to saturation for some time before the build-up of storm circulations ([PERSON] and [PERSON], 2019).
### Axisymmetric Results: The Dominance of Upper-Level Longwave Radiation
The proposed framework's physical interpretability relies on the model predictions and the extracted structures. In the following sections, we progressively highlight different aspects of the extracted structures to show how they can clarify the role of radiation in TC intensification. We start by analyzing the azimuthal mean of VED-extracted structures to illustrate how spatial gradients in radiative anomalies affect TCs. We obtain these structures by multiplying the PCA spatial modes and the trained encoder weights.
#### 4.3.1 Maria
In the case of the Maria simulations (Figure 4), the VED model extracts a \(\mu_{LW}\) pattern with an upper-level longwave anomaly dipole and a shallow cloud radiative signal near the surface (Figure 4c). The anomaly fields are defined with respect to the training mean. In other words, it shows how the radiative heating structure of a sample deviates from the mean of all training samples. This way of defining the anomaly also eliminates the need to recalculate the PCs for individual experiments. To demonstrate how the learned \(\Pi_{\mu,\text{LW}}\) (Figure 4c) encodes physical knowledge, we compare Hour 80 from the Maria CTRL simulation (Figures 4a and 4b) to a sample taken from the same time in the NCRF-36h experiment (Figures 4d and 4e). The VED framework predicts higher surface intensification rates for the CTRL sample due to positive \(\mu_{LW}\). In contrast, the NCRF-36h sample has a lower predicted intensification rate due to negative \(\mu_{LW}\). Comparing Figures 4b and 4c, we see that a positive \(\mu_{LW}\) arises when the anomaly field is spatially distributed in the same way as \(\Pi_{\mu,\text{LW}}\). In the raw longwave radiation field (Figure 4a), the positive \(\mu_{LW}\) of the CTRL sample corresponds to the concentration of strong longwave cooling near the cloud top (i in Figure 4a) and heating near the TC center (ii in Figure 4a). In contrast, the negative \(\mu_{LW}\) in the mechanism denial example features a lowered and weakened longwave cooling and the absence of heating near the TC center; both contribute to a weaker simulated TC. From the Maria example, we demonstrate that combining the sign of the projection (\(\mu_{LW}\)) and the raw fields provides valuable information on why NCRF-36h TC fails to intensify. The next section uses \(\mu_{LW}\) to understand why two Haiyan ensemble members have different intensification rates during their organization phases.
#### 4.3.2 Haiyan
The azimuthal mean of \(\mu_{LW}\) for Haiyan (Figure 5c) exhibits a vertical dipole pattern around 200 hPa and a shallow vertical dipole at 900 hPa, reflecting broad anvil clouds in the outer core and shallow clouds in the inner core. We compare samples from two members: Member 2, with a significant positive \(\mu_{LW}\) (larger predicted intensification rate), and Member 11, with a small \(\mu_{LW}\) (smaller predicted intensification rate). In the Member 2 sample, positive \(\mu_{LW}\) indicates weakening of the upper-level longwave dipole between 50 and 300 km from the TC center and a vertically expanded upper-level longwave heating near the TC center (i in Figure 5a), along with a more prominent 900 hPa shallow cloud radiative dipole (ii in Figure 5a). These longwave patterns may indicate deep convective development, rising outflow height near the TC center, destabilized inner core upper-level thermal stratification, and enhanced shallow cloud frequency. Colder upper tropospheric temperatures and higher outflow layers have been shown to boost TC intensity. Following balanced dynamics ([PERSON], 1952; [PERSON], 2009), upper-level radiative cooling triggers secondary circulations that accelerate surface tangential winds in idealized TCs ([PERSON] et al., 2019). From an energetic perspective, rising outflow layers enhance the thermal efficiency of a TC heat engine, resulting in a stronger TC ([PERSON], 2013; [PERSON] et al., 2014). While
Figure 4: The learned data-driven structure for the mean longwave prediction (\(\Pi_{\mu,\text{LW}}\): c) for Maria shows a prominent upper-level longwave anomaly dipole. A sample from Hour 80 of the CTRL simulation (a–b), which is predicted by the machine learning model to have a high intensification rate because of a positive projection of \(LW^{\prime}\) (b; perturbation compared to the training mean) onto \(\Pi_{\mu,\text{LW}}\) (c). We contrast the CTRL sample with another sample taken at the same hour from the NCRF-36h simulation (d–e), which is predicted to have a negative intensification rate due to a negative projection of \(LW^{\prime}\) (e) onto \(\Pi_{\mu,\text{LW}}\). The two samples illustrate the physical meaning of the projections: a positive projection (red arrows) occurs when the \(LW^{\prime}\) is similarly spatially to \(\Pi_{\mu,\text{LW}}\), whereas a negative projection occurs when the \(LW^{\prime}\) is opposite in sign to \(\Pi_{\mu,\text{LW}}\).
shallow clouds are suggested to assist cyclogenesis by moistening the lower troposphere and spinning up the near-surface circulation ([PERSON], 2014), our VED model analysis implies their effect on the overall TC intensification is relatively minor. Decomposing the model prediction by vertical level (description in Appendix C) suggests that the shallow cloud contribution to intensification is between two and one order of magnitude smaller than the upper-level radiative contribution (Figure 7b). These findings corroborate those from idealized simulations (e.g., Kilroy, 2021).
### Asymmetric Radiative Heating Favors Tropical Cyclone Intensification
Here, we show that some asymmetric longwave radiative anomaly structures are potential predictors for intensification. The linear combinations of PC longwave eigenvectors yield a complex, spatially asymmetric, three-dimensional radiative heating pattern (Figures 6a and 6b). The \(\Pi_{\text{d,LW}}\) cross sections at 1,000 hPa (Figures 6a) and 100 hPa (Figure 6b) both exhibit distinct wavenumber-1 asymmetry, with a shallow cloud radiative signature at 1,000 hPa (i. in Figure 6a; downshear right quadrant) distributed upwind of the deep convective signature at 100 hPa (ii. in Figure 6b; downshear left quadrant). Considering how the secondary circulations associated with CRF may intensify tangential winds and spin up surface cyclones ([PERSON] et al., 2020), we postulate that any positive longwave contribution to Member 2 surface winds should be distributed mainly in the TC's northern half. We validate this with the surface wind intensification from Hour 16 to 40 (Figure 6c), which shows the effect of a positive \(\mu_{LW}\). The surface wind acceleration is indeed broader over the TC's northern half, with the strongest acceleration located downwind of the downshear left positive upper-level \(\Pi_{\text{d,LW}}\) with minimal uncertainty. The spatial correlation between surface wind acceleration and \(\Pi_{\text{d,LW}}\) supports the hypothesis that upper-level wavenumber-1 longwave heating anomaly contributes positively to surface intensification. While shallow clouds have a minor contribution to the overall TC intensification (Section 4.2), the shallow cloud radiative signature (i in Figure 6a) still coincides spatially with the intensifying _local_ winds in the downshear right quadrant.
To identify which mesoscale anomalies in \(\Pi_{\text{d,LW}}\) are most unambiguously correlated to intensification, we create standard deviation maps from the ten best-performing models \(\Pi_{\text{d,LW}}\) structures (Figures 6d and 6e). Low standard deviations suggest that the ML models consistently find the exact relationship between mesoscale anomalies and intensification in a specific area. We should prioritize such areas in our analysis. Using the deviation maps at 100 hPa (Figure 6e), we conclude that the 100 hPa \(\Pi_{\text{d,LW}}\) positive anomaly in the downshear left quadrant (i in Figure 6a) is unambiguously related to intensification (low uncertainty). Asymmetric deep convection is typically located in the downshear quadrants of sheared TCs (e.g., [PERSON] et al., 2024; [PERSON] et al., 2024). In
Figure 5: The learned data-driven structure for the mean longwave prediction (\(\Pi_{\text{L,LW}}\); (c) for Haiyan shows the spatial distribution of \(LW^{\prime}\) that is most correlated with early tropical cyclone (TC) intensification. The example that is predicted to have a high intensification rate (a, b) is taken from Hour 15 of Member 2, whereas the predicted low intensification rate (d, e) example is taken from Hour 17 of Member 11. The Member \(2\,LW^{\prime}\) example has a strong positive projection (red arrows) onto \(\Pi_{\text{d,LW}}\) (c), which is indicative of concentrated inner-core deep convection (200 hPa longwave anomaly dipole within 100 km of TC center) in the raw azimuthal-averaged LW. Additionally, the Member 2 example also features shallow clouds in the outer core (900 hPa anomaly dipole between 100 and 300 km from the TC center; (b). Both the inner-core deep convection and outer-core shallow cloud signatures are weaker in the Member 11 example, which leads to a lower predicted intensification rate (blue arrow).
contrast, the upper-level anomalies in the upshear quadrants have more uncertainty. The higher uncertainty in these quadrants may reflect non-shear mechanisms not directly related to intensification on precipitation asymmetry, such as TC movement ([PERSON] et al., 2022). Finally, the 1,000 hPa deviation map (Figure 6d) shows model consistency in depicting a cold LW anomaly at the TC center and a shallow cloud signature in the context, the upper-level anomalies in the upshear quadrants have more uncertainty. The higher uncertainty in these quadrants may reflect non-shear mechanisms not directly related to intensification on precipitation asymmetry, such as TC movement ([PERSON] et al., 2022). Finally, the 1,000 hPa deviation map (Figure 6f) shows model consistency in depicting a cold LW anomaly at the TC center and a shallow cloud signature in the context, the upper-level anomalies in the upshear quadrants have more uncertainty. The higher uncertainty in these quadrants may reflect non-shear mechanisms not directly related to intensification on precipitation asymmetry, such as TC movement ([PERSON] et al., 2022). Finally, the 1,000 hPa deviation map (Figure 6f) shows model consistency in depicting a cold LW anomaly at the TC center and a shallow cloud signature in the context.
Figure 6: The spatial cross-sections of the best-performing model’s mean longwave pattern \(\Pi_{\mu LW}\) at (a) 1,000 hPa and (b) 100 hPa both exhibit substantial wavenumber-1 asymmetry in the inner core (0–200 km from the tropical cyclone center). The trustworthiness of individual anomaly areas in \(\Pi_{\mu LW}\) is assessed by the standard deviation of the 10 best models’ \(\Pi_{\mu LW}\) at (c) 1,000 hPa and (d) 100 hPa. We highlight two longwave anomalies that are trustworthy (small \(\Pi_{\mu LW,\
u}\)): a low-level shallow cloud signature (i in panel (a)) and the deep convection downwind of the shallow cloud signature (ii in panel (b)). We compare (c) the 24-hr surface wind intensification associated with the Member 2 example in Figures 5a and 5b show a strong spatial correlation between the broad surface wind intensification (iii in panel (c)) and the upper-level longwave anomaly signature (ii in panel (b)).
Figure 7: Providing the trained machine learning (ML) models with perturbed inputs gives us the first hints as to how the tropical cyclones might behave in a true intervention setting. Panel (a) shows how perturbating the H\({}_{24W}\) (red dots and squares) changes the longwave contribution to the ML prediction (red line) compared to perturbing the same sample with an axisymmetric version of \(\Pi_{\mu LW}\) (blue dots and squares). Panel (b) shows that upper-level anomalies (100 hPa; dashed red) contributes more to the overall longwave contribution (red line) than the lower tropospheric anomalies (1,000 hPa; dashed dotted red).
downshear right quadrant (i in Figure 5(a)). A high standard deviation in the boundary between the two areas indicates uncertainty in the spatial extent of these signatures across models (Figure 5(d)).
Considering these results, the longwave anomaly signature associated with deep convection in the downshear left quadrant is the feature that has the strongest correlation to surface intensification. Widespread inner core convective development near and slightly downwind of the upper-level longwave anomalies (not shown) in the Haiyan Member two example points to a link between longwave anomalies, secondary circulations, and deep convective development, which also facilitate the axisymmetrization of TC structures - an indicator of TC genesis ([PERSON] et al., 2004) and intensification ([PERSON] et al., 2017).
## 5 Discussion
### Complementing Physics-Based Budget Analysis With Machine Learning Diagnostics
This section briefly discusses how the proposed ML-based method complements existing physics-based diagnostic methods. The first category of physics-based diagnostic methods is budget equations. Budget equations are attractive in that each term in the equation has a well-defined physical meaning; the equations suitable for the tropical cyclogenesis problem include the moist static energy variance budget ([PERSON] and [PERSON], 2014), horizontal momentum budget ([PERSON] et al., 2018), kinetic energy budget ([PERSON] et al., 2016), and available potential energy budget ([PERSON] and [PERSON], 2018). One disadvantage of budget analyses for our problem is that they do not directly predict surface intensification from thermal forcing. The MSE variance budget calculates the spatial variance in MSE (a thermodynamic term), whereas the horizontal momentum equation lacks a thermal source term. There is no direct equation that links the MSE variance and TC intensity, even though a statistical correlation exists between the two ([PERSON], 2022). While it is possible to get physical insights by comparing the thermodynamic and kinematic budget terms side-by-side, such analyses are qualitative, not quantitative. Another disadvantage common to all budget analysis methods is that they rely on variables not typically included in simulation output lists. It is well-known that these budgets are hard to close _post-hoc_ ([PERSON] et al., 2020), that is, calculating the budget terms with typical model outputs, especially if the model outputs are stored infrequently. A better option is to estimate those terms directly in the model (online). However, this requires rerunning pre-existing large cloud-resolving simulation data sets with the online calculation of budget terms (e.g., [PERSON] et al., 2019), which is often computationally prohibitive. Hence, our ML framework complements physics-based budgets by (a) establishing quantitative relationships between thermodynamic forcing and kinematic changes and (b) relaxing the data requirements in temporal frequency and online budget calculations.
The second category of physics-based diagnostics used in tropical cyclogenesis studies is the Sawyer-Eliassen Equation (SEQ; [PERSON] and [PERSON], 2009). Given a thermodynamic forcing, the SEQ outputs a streamfunction representing the balanced circulation induced by said heating. While this method links thermodynamics and kinematics, the physical assumptions used to derive the SEQ (hydrostatic, thermal wind balance) mean that the thermal forcing needs to be averaged over a long period of time. Additionally, the SEQ only provides the 2D solutions for azimuthally averaged 2D thermal forcing in radius-height coordinates, which removes crucial spatial context. Finally, [PERSON] et al. (2009) noted that the balance solution substantially underestimates the boundary layer inflow, which is problematic for surface intensity assessments. While an unbalanced version of the SEQ exists ([PERSON] and [PERSON], 2023), the extended SEQ is still a 2D diagnostic framework. Following the above discussions, our ML method complements SEQ by allowing 3D thermal forcing as an input, which enables analyses of the effect of asymmetric thermal forcing on surface winds (Section 4.3).
Our ML framework extracts one time-invariant pattern per variable. The intensification rates predicted by the framework are linearly related to the spatial similarities between the radiative structures of individual samples and the extracted pattern. Our approach complements traditional composite analysis by removing subjectivity in the definition of composites. Finally, our framework highlights specific small-scale anomalies most relevant to information by enabling quantifiable assessments of each anomaly's contribution to ML predictions.
### Anticipating the Response of Tropical Cyclones to Radiative Perturbations
One of the main advantages of ML models compared to traditional physics-based models is that ML models are inexpensive to run once they are trained. We may leverage this characteristic of ML models for scientific discovery. Specifically, we may treat ML models as an efficient hypothesis generator and a framework for simple hypothesis testing.
We design a sensitivity experiment using the trained Haiyan models to understand whether the prominent wavenumber-1 structure in \(\mu_{LW}\) means that asymmetric longwave anomaly is more critical to intensification than axisymmetric ones. These questions are easily answerable by feeding the ML models with perturbed input, that is, synthetic structures. Here, we present the full definition of axisymmetric and asymmetric anomalies used in the intervention experiments.
Taking longwave radiation as an example, its mean contribution to the ML intensification forecast is proportional to \(\mu_{LW}(t)\) (Equation 9). We would like to show that adding an asymmetric pattern like \(\Pi_{JLW}\) causes the ML model to predict higher intensification rates than adding an axisymmetric pattern. In the asymmetric pattern experiment, we perturb the raw data in cartesian coordinates by adding the learned pattern to the training-mean longwave cooling field:
\[\overline{LW_{training}}\pm\Pi_{JLW}, \tag{23}\]
which tests the effect of adding or removing extra radiation to specific areas in the developing TC. For the case of the axisymmetric pattern experiment, we perturb the raw data with the azimuthal mean of the extracted \(\mu_{LW}\) pattern:
\[\overline{LW_{training}}\pm\Pi_{JLW}^{\#}, \tag{24}\]
where \(\gamma\) is a multiplication factor that ensures that both synthetic structures have the same spatial variance and \(\left({}^{\#}\right)\) is the azimuthal mean operator. Practically, every grid point in the axisymmetric synthetic structure is multiplied by the ratio between the standard deviation of the asymmetric and axisymmetric synthetic structure.
Feeding the VED with the new inputs perturbed by the synthetic asymmetric structure predicts higher longwave contributions to intensification during the early intensification stage. Conversely, the axisymmetric synthetic structure leads to a smaller response in the VED prediction (Figure 6(a)). VED predictions are only weakly sensitive to the synthetic perturbations later in the TC's life cycle. These results broadly agree with our conjecture that asymmetric longwave forcing leads to faster early TC intensification in the data-driven models.
## 6 Conclusion
Recent evidence (e.g., [PERSON] et al., 2020) highlights the significance of radiation in early TC development. However, the precise role of radiation in realistic TCs and whether asymmetric structures in radiation impact TCs differently from axisymmetric ones has remained underexplored. We fill this knowledge gap by employing a data-driven, interpretable, stochastic, machine learning model (VED) on convective-permitting simulations of two TCs to estimate the transfer function between 3D radiative patterns and surface wind intensification. We optimize the model architecture to enhance the likelihood of extracting physically meaningful patterns. This optimization involves (a) maximizing surface intensification prediction skills by optimally combining different asymmetric radiative patterns and (b) regressing to the unconditional distribution of intensification rates when radiation is uninformative. In both case studies, our model finds spatially coherent, physically meaningful radiation patterns from complex, high-dimensional simulation output data.
The VED architecture allows the quantification of uncertainties in both the model predictions and the extracted radiation patterns. We provide several examples where we leverage this information for scientific discovery. By intentionally making the model learn exclusively from radiation, the errors and uncertainties in ML predictions are quantifiable indicators of how relevant radiation is to TC intensification. Our findings reveal that longwave radiation exerts a larger influence on intensification than shortwave. The radiation is mostly only relevant in the early genesis phase (Section 4.2), consistent with the results from prior physical modeling experiments.
The ML model extracts three-dimensional structures in radiation and quantifies the effect of different radiative anomalies on intensification. Our results suggest that the combination of downshear left deep convective development in the inner core and low tropospheric shallow clouds in the downshear right quadrant may be used as valuable predictors for the rate of intensification during the TC genesis phase (Section 4.4). The deep convective and shallow cloud signals have a wavenumber-1 spatial asymmetry. Our VED model's linearity is useful here because we can, for example, decompose by vertical level to conclude that the upper-level radiative signal likely impacts the surface intensification the most. The VED-extracted three-dimensional longwave anomaly structure for Haiyan has a strong spatial correlation with the broader surface wind intensification in the northern quadrants, which is potentially helpful to highlight where longwave radiative anomalies should be distributed that can potentially yield the most impact on TC intensification.
We believe that the strength of the ML framework here lies in its simplicity. The entirely linear nature of the model ensures full interpretability and decomposability, providing clarity on how the model extracts structures from WRF outputs. Our case studies demonstrate the value of sacrificing some model performance for interpretability and how interpretability leads to scientific discovery. The simple linear VED models also show superior skills to the more complex ML models in low sample size regimes (Section 4.1). Our approach is a valuable addition to existing data-driven approaches for scientific exploration and is particularly useful in situations with limited training data. The architecture is flexible, allowing for an easy introduction of nonlinearity and making it adaptable to other prediction problems in more complex systems.
Looking ahead, interpretable ML architectures can potentially be used to (a) reveal the source of forecast spreads in ensemble model predictions for extreme winds, for example, by identifying the dominant uncertainty-adding circulation patterns, and (b) quantifying the impact of different physical variables on uncertainties in climate models. We can also adopt the framework to forecast the spin-up of local winds in different shear-relative quadrants for a clearer understanding of the role of radiation in the genesis of TCs. Finally, a logical next step to build trust in the ML model explanations is to use the learned structures for targeted sensitivity experiments with physics-based numerical models, which should clarify the causal relationship between these structures and TC intensification.
## Appendix A Derivation Steps for the Effective Weights, Biases, and Constants
This appendix presents the relevant steps to derive the Effective Weights and bias of the overall VED model (Sections 3.2 and 3.2.3), followed by the scaling factors and logarithmic variance constants.
We first focus on the model bias term. The decoding (prediction) module of the VED model can be mathematically expressed by:
\[\begin{split}\left(\frac{dV_{surf}}{dt}\right)_{2\text{thr}}& =\,a_{2,LW}\mathcal{N}\Big{(}\mu_{LW},e^{\text{loop}\mu_{LW}^{2} }\Big{)}\\ &+a_{2,NW}\mathcal{N}\Big{(}\mu_{SW},e^{\text{loop}\mu_{LW}^{2} }\Big{)}\\ &+b_{2}.\end{split} \tag{10}\]
We expand 10 with 5 and 6, the mean structure scalars \(\big{(}\mu_{LW},\,\mu_{SW}\big{)}\) in 10 becomes:
\[\begin{split}\mu_{LW}&=\,a_{2,LW}\Bigg{(}b_{1,LW, \mu}+\sum_{l=1}^{\infty_{LW}}\frac{a_{1,LW,\mu,\mu}}{\sigma(PC_{i,LW})}PC_{i,LW }-\sum_{l=1}^{\infty_{LW}}\frac{a_{1,LW,\mu}}{\sigma(PC_{i,LW})}\overline{PC _{i,LW}}\Bigg{)},\\ \mu_{SW}&=\,a_{2,NW}\Bigg{(}b_{1,SW,\mu}+\sum_{l=1} ^{\infty_{LW}}\frac{a_{1,SW,\mu}}{\sigma(PC_{i,SW})}PC_{i,SW}-\sum_{l=1}^{ \infty_{LW}}\frac{a_{1,SW,\mu}}{\sigma(PC_{i,SW})}\overline{PC_{i,SW}}\Bigg{)}.\end{split} \tag{11}\]
The overall bias (\(b\)) of the VED model is the sum of the first and third terms in Equation 11.
Comparing Equations 10, 10, and 11 shows that the non-constant terms (second on the right-hand side) in Equation 11 is equivalent to the projection of radiative anomaly onto the learned patterns (Equation 10). Using longwave mean structure as an example, we have:\[PC_{i,\parallel_{Lw,\alpha}}=\lambda\frac{a_{2,LW}a_{1,LW,\alpha,\lambda}}{\sigma( PC_{i,LW})},\] (A3)
where \(\lambda\) is the proportionality coefficient for the longwave mean structure. We now assume the norm of the data-driven structure to be 1:
\[1=\left\langle\Pi_{LW,\alpha}\mid\Pi_{LW}\right\rangle_{LW}\sum_{i=1}^{n_{LW} }PC_{i,\parallel_{Lw}}^{2}=\lambda^{2}a_{2,LW}^{2}\sum_{i=1}^{n_{LW}}\frac{a_ {1,LW,w,i}^{2}}{\sigma(PC_{i,LW})^{2}},\] (A4)
From Equation A4, the \(\lambda\) for longwave mean structure is:
\[\lambda_{LW,\alpha}=\left[\left|a_{2,LW}\right|\sqrt{\sum_{i=1}^{n_{LW}} \frac{a_{1,LW,\alpha,\lambda}^{2}}{\sigma(PC_{i,LW})^{2}}}\right]^{-1}.\] (A5)
The other three \(\lambda\) in the VED model can be obtained with a similar procedure.
We can rewrite Equation A1 with the definition of the mean structure scalars (Equation A2), Equation 6, and \(\lambda\) (Equation A5),
\[\begin{split}\left(\frac{dV_{surf}}{dt}\right)_{2\text{dtr}}=& \mathcal{N}\left(\frac{a_{2,LW}}{\lambda_{LW,\alpha}}\underbrace{\sum_{i=1}^ {n_{LW}}PC_{i,\parallel_{LW}}PC_{i,LW}}_{(LW)},\sqrt{a_{2,LW}}\,e^{\text{ dtr}\partial_{LW}^{2}}\right)\\ &+\mathcal{N}\left(\frac{a_{2,SW}}{\lambda_{SW,\alpha}}\underbrace {\sum_{i=1}^{n_{LW}}PC_{i,\parallel_{LW}}PC_{i,\parallel_{LW}}}_{(SW)}, \sqrt{a_{2,SW}}\,e^{\text{ dtr}\partial_{LW}^{2}}\right)\\ &+b\end{split}\] (A6)
To see how Equation A6 related to Equation 11, we factor out all constant terms from the normal distribution:
\[\begin{split}\left(\frac{dV_{surf}}{dt}\right)_{2\text{dtr}}=& \underbrace{\frac{a_{2,LW}}{\lambda_{LW,\alpha}}}_{a_{surf}}\mathcal{N} \left(\left\langle LW\middle|\Pi_{\alpha,LW}\right\rangle_{LW},\sqrt{\lambda_{ LW,\alpha}\left|a_{2,LW}\right|}\,e^{\text{ dtr}\partial_{LW}^{2}}\right)\\ &+\underbrace{\frac{a_{2,SW}}{\lambda_{SW,\alpha}}}_{a_{surf}} \mathcal{N}\left(\left\langle SW\middle|\Pi_{5,SW}\right\rangle_{SW},\sqrt{ \lambda_{SW,\alpha}\left|a_{2,SW}\right|}\,e^{\text{ dtr}\partial_{LW}^{2}}\right)\\ &+b,\end{split}\] (A7)
allowing us to identify the \"effective weights\" \(a_{LW}\) and \(a_{SW}\).
We now use the definition of the logarithmic variance in the model's first (projection) layer (6) to expand the logarithmic variance term of the normal distributions:
\[\sqrt{\lambda_{LW,\alpha}\left|a_{2,LW}\right|}\exp\bigl{(}\log\sigma_{LW}^{ 2}\bigr{)}=\sqrt{\lambda_{LW,\alpha}\left|a_{2,LW}\right|}\exp\left(b_{1,LW, \alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha, \alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha, \alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha, \alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha, \alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha,\alpha, \alpha,\alphaWe notice that parts of Equations 14 and 15 are constant, which means that we can simplify this equation further by defining variance prefactors for longwave radiation (\(c_{LW}\); Equation 16) and shortwave radiation (\(c_{SW}\); Equation 17).
\[c_{LW}=\sqrt{\lambda_{LW,\omega}|a_{2,LW}|}\exp\left(b_{1,LW,\text{ log}^{2}}-\sum_{l=1}^{n_{\text{LW}}}a_{1,LW,\text{log}^{2},l}\frac{\overline{ PC_{i,LW}}}{\sigma(PC_{i,LW})}\right), \tag{16}\] \[c_{SW}=\sqrt{\lambda_{SW,\omega}|a_{2,SW}|}\exp\left(b_{1,SW,\text {log}^{2}}-\sum_{l=1}^{n_{\text{LW}}}a_{1,SW,\text{log}^{2},l}\frac{\overline{ PC_{i,SW}}}{\sigma(PC_{i,SW})}\right), \tag{17}\]
Using the same reasoning as for the mean longwave structure (Equation 13), proportionality coefficient for the longwave logarithmic variance structure (\(\lambda_{LW,\text{log}^{2}}\)) for the PC loadings of the logarithmic variance structure:
\[PC_{i,\text{J1 log}^{2},\mu}=\lambda_{LW,\text{log}^{2}}\frac{a_{1,LW,\text{ log}^{2},l}}{\sigma(PC_{i,LW})}\Rightarrow\lambda_{LW,\text{log}^{2}}=\left( \sum_{l=1}^{n_{\text{LW}}}\frac{a_{1,LW,\text{log}^{2},l}^{2}}{\sigma(PC_{i,LW })^{2}}\right)^{-1/2}. \tag{18}\]
\[PC_{i,\text{J1 log}^{2},\mu}=\lambda_{LW,\text{log}^{2}}\frac{a_{1,SW,\text{ log}^{2},l}}{\sigma(PC_{i,SW})}\Rightarrow\lambda_{SW,\text{log}^{2}}=\left( \sum_{l=1}^{n_{\text{LW}}}\frac{a_{1,SW,\text{log}^{2},l}^{2}}{\sigma(PC_{i, SW})^{2}}\right)^{-1/2}. \tag{19}\]
For consistency with the mean structures, we transform the logarithmic variance term (Equations 14 and 15) using Equations 14, 15, 16, which yields:
\[c_{LW}\exp\left(\sum_{l=1}^{n_{\text{LW}}}\frac{a_{1,LW,\text{ log}^{2},l}\times PC_{i,LW}}{\sigma(PC_{i,LW})}\right)=c_{LW}\exp\left(\frac{1}{ \underbrace{\lambda_{LW,\text{log}^{2},l}}_{d_{\text{LW}}}}\times\langle LW \mid\Pi_{\text{log}^{2}_{LW}}\rangle_{LW}\right) \tag{20}\]
\[c_{SW}\exp\left(\sum_{l=1}^{n_{\text{LW}}}\frac{a_{1,SW,\text{log}^{2},l}\times PC _{i,SW}}{\sigma(PC_{i,SW})}\right)=c_{SW}\exp\left(\frac{1}{\underbrace{ \lambda_{SW,\text{log}^{2},l}}_{d_{\text{LW}}}}\times\langle SW\mid\Pi_{ \text{log}^{2}_{LW}}\rangle_{SW}\right) \tag{21}\]
## Appendix B Baseline: Principal Component Regression
We implement a simple two-layer linear regression model as a baseline to examine if the more complex VED architecture improves the overall prediction skills and provides a more well-calibrated prediction uncertainty. This baseline is analogous to a two-branch principal component regression (schematic diagram in Figure 16). The baseline model only extracts two structures from the longwave and shortwave radiation information. These structures are analogous to the \(\mu_{LW}\) and \(\mu_{SW}\) in the VED model. Rather than extracting the uncertainty structures and sampling them with the reparameterization trick, we introduce uncertainty in the baseline model using a dropout mechanism. The dropout mechanism zeroes out a random selection of input features, allowing the model to have uncertainties in both the structure layer level and the final prediction outputs. The amount of input features this operation drops is determined by a tunable **dropout rate** hyperparameter that ranges from 0 to 1.
## Appendix C Decomposition by Vertical Levels
We isolate the effect of heating anomalies at different vertical levels by setting all grid point values in the input data to zero, _except for those at the vertical level(s) of interest_.
For instance, if we are interested in the individual contributions of longwave radiative heating at 1,000 hPa and 100 hPa, we can separate the LW field into three distinct terms:\[LW=LW_{100}+LW_{1000}+LW_{200-900},\] (C1)
where \(LW_{100}\) (\(LW_{1000}\)) is the longwave field where all grid points except those at 100 (1,000) hPa are zeroed out, \(LW_{200-900}\) is the longwave field where grid points at 100 and 1,000 hPa are zeroed out.
Projecting the three components of the right-hand side of Equation C1 onto the longwave PC eigenvectors yields the same decomposition for the PC loadings:
\[\forall i\in[[1,n_{LW}]],\ PC_{i,LW}=PC_{i,LW_{min}}+PC_{i,LW_{min}}+PC_{i,LW _{500-m0}}\] (C2)
After standardization, Equation C2 can be separated into a constant part:
\[\underbrace{\left(\frac{\overline{PC_{i,LW_{min}}}+\overline{PC_{i,LW_{min}}} +\overline{PC_{i,LW_{min}}}}{\sigma(PC_{i,LW})}\right)}_{\overline{PC_{i,LW}}}\] (C3)
and a part that varies in time:
\[\underbrace{\left[\frac{PC_{i,LW_{min}}}{\sigma(PC_{i,LW})}+\frac{PC_{i,LW_{ min}}}{\sigma(PC_{i,LW})}+\frac{PC_{i,LW_{min}}}{\sigma(PC_{i,LW})}\right]}_{ \overline{PC_{i,LW}}}.\] (C4)
Substituting Equation C4 into Equation A6 and expanding the first term in Equation A6, we can decompose surface intensification into additive terms that match the longwave radiative heating field's decomposition of Equation C1.
\[\begin{split}\frac{dV_{inf,24}}{dt}&=\left(\frac{ dV_{LW,1000\mu_{0}}}{dt}+\frac{dV_{LW,200-1000\mu_{0}}}{dt}\right)\\ &\quad+\frac{dV_{SW,100-1000\mu_{0}}}{dt}+b,\end{split}\] (C5)where \(\frac{d^{(V_{\text{rec},\text{num}})}}{dt}\) quantifies how radiation anomalies at 100 hPa affect the surface intensification. Figure C1 shows an example of how we use this decomposition technique to illustrate the contributions of longwave radiative anomalies at different vertical levels to Haiyan Member 2.
## Data Availability Statement
The code used to train the neural networks and to produce all figures of this manuscript is hosted on Github ([[https://github.com/freddy0218/2024_TCG_VED](https://github.com/freddy0218/2024_TCG_VED)]([https://github.com/freddy0218/2024_TCG_VED](https://github.com/freddy0218/2024_TCG_VED))) and stored in a DOI-assigned public repository (Tam, 2024a). The processed PC time series data and trained models are archived on a separate, DOI-assigned public repository (Tam, 2024b). The post-processed longwave and shortwave WRF radiation fields for the two Haiyan ensemble members are also included in the archive for recreating the results shown in Figures 3 and 5. All WRF namnist settings files to recreate the WRF simulations used in this study are archived in a separate repository (Ruppert, 2024) with postprocessing scripts. The PyTorch ([PERSON] et al., 2019) framework is used to train all the machine learning models in this manuscript. The binary files of PyTorch are available for installation via the Anaconda platform. The Optuna optimization tool can be accessed on [[https://github.com/optuna/optuna](https://github.com/optuna/optuna)]([https://github.com/optuna/optuna](https://github.com/optuna/optuna)). We provide a short Jupyter tutorial with the minimal steps required to use the trained models to get the intensification rate predictions and the extracted mean longwave structure. This file can be assessed from the repository (Tam, 2024b) (minimalexample.ipynb).
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wiley/fa9d3109_4455_4c4b_925a_c1ece25a26ed.md | # Geochemistry, Geophysics, Geosystems
Iridium Communications Satellite Constellation Data for Study of Earth's Magnetic Field
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abrupt changes in the external magnetospheric currents (e.g., magnetopause and ring currents) may be present, though this has not yet been extensively documented ([PERSON] et al., 2015). Crustal fields are \"permanent\" on geologic time scales shorter than crustal formation and circulation (technic) and are useful as magnetic imprint markers. These crustal fields are best resolved in satellite observations at the lowest attainable orbit altitudes (\(\sim\)300-400 km) as the depth is comparatively shallow (\(<\)10 km) and the horizontal length scales are small (1-500 km).
Precise characterization of the main magnetic field, actively generated internally by the dynamo together with contributions from remanent magnetization of the crust, is important for many government, commercial, and scientific users (cf. [PERSON] & [PERSON], 2018) motivating continuous maintenance of the World Magnetic Model (WMM) by the National Centers for Environmental Information ([PERSON] et al., 2020) and the International Geomagnetic Reference Field (IGRF) and Definitive Geomagnetic Reference Field models (e.g. [PERSON] et al., 2021) under the analyses of the International Association of Geomagnetism and Aeronomy. The interaction of the magnetized solar wind with the Earth's magnetic field produces various current systems and the resulting magnetic signals on the ground and at satellites in low-Earth orbit (LEO, cf. [PERSON] et al., 2017) must be considered for precise study of the internally generated field (cf. [PERSON] & [PERSON], 2009; [PERSON] et al., 2017; [PERSON] & [PERSON], 2017). In addition, the dynamical interaction of neutral thermospheric winds with plasma populations in the ionosphere drives currents, and hence magnetic fields, that must be considered in analyses of ground and LEO magnetometer observations (e.g., [PERSON] & [PERSON], 2017). The range of spatial distributions and temporal variations of external sources complicates studies of the main field and makes precise characterization of the global field a challenging inversion problem (cf. [PERSON] et al., 2018).
Variations in the magnetic field of the Earth arise from changes in the fluid outer core (cf. [PERSON] et al., 2010). Recently the magnetic pole motions have accelerated such that linear extrapolation for the field secular variation is not sufficient to meet operation requirements for main field models and intermediate model releases have been necessary (cf. [PERSON] & [PERSON], 2018; [PERSON], 2019). Scientific interests in sub-decadal time scales of main field variations is growing as well. Processes occurring at these time scales relate to the nature and characteristics of geomagnetic jerks, their spatial scales, global distribution, and prevalence to inform and constrain the core fluid dynamics from which they arise ([PERSON] et al., 2002; [PERSON] et al., 2013; [PERSON] et al., 2010). Similarly, waves in the magnetic field have also been inferred ([PERSON] & [PERSON], 2019; [PERSON] et al., 2016; [PERSON] et al., 2015) and diagnosing the wavelengths and group speeds are key to determining their origins. There is therefore considerable practical and fundamental scientific interest in augmenting present capabilities to measure Earth's field on sub-decadal and even sub-annual time scales.
To date the most accurate and reliable results for the main field have been obtained using combinations of data from globally distributed ground magnetic observatories and precision magnetic field measurements from satellites in LEO. The first precise LEO magnetic mapping mission, combining precision scalar and vector magnetic field measurements with precision attitude sensors, was MAGSAT, conducted in 1979 and 1980 ([PERSON] et al., 1982). After a hiatus of nearly two decades, this was followed by missions using precise magnetic mapping instrumentation (i.e., scalar and vector magnetometers with precision attitude sensors co-located with the vector magnetometer) including the Oersted satellite launched in early 1999, the CHAMP satellite launched in July of 2000, and SAC-C launched in November 2000 (cf. [PERSON] et al., 2010). Most recently the set of three Swarm satellites were launched in November 2013 ([PERSON] et al., 2013, 2016). The Swarm mission conducts multi-point precision magnetic field mapping, and they remain operational with an expected lifetime to at least 2024. Recent derivations of the main field from Swarm yield high-resolution maps of the crustal field and magnetic potential representations of the core field, and can resolve time scales as short as about 6 months ([PERSON] et al., 2016).
The central challenge of precise global magnetic mapping from LEO is that the satellite observations are obtained along one or two orbital planes in inertial space. Separating internal, ionospheric, and magnetospheric induction sources requires accounting for each of these contributions. Because of orbital precession, polar LEO orbits span all local times in approximately 6 months depending on the precise inclination. This coverage makes global mapping somewhat challenging for time scales shorter than about 6 months without convolving local time period signals with seasonal variations. Notwithstanding these challenges, powerful inversion techniques have been developed to simultaneously account for all of these contributions(cf. [PERSON] et al., 2018). These state-of-the-art techniques have yielded remarkable advances including unprecedented characterization of the ocean induction fields.
Nonetheless, the inversions remain under-determined and are subject to substantial covariance among the large number of parameters (>10,000) used in the fits. Such inversions always benefit from additional observations and it is therefore of interest to explore avenues to augment the available database. The development and launches of commercial satellite constellations into LEO for communications began in the late 1990s and offer an opportunity for unprecedented orbital coverage over the Earth. While these constellations were not designed to support science-grade magnetic field measurements, the satellites in these constellations that carry commercial magnetometers may still offer real benefit for Earth's main field science. In this study, we consider whether magnetic field data acquired from the Iridium Communications satellite constellation might provide another set of observational constraints for main field characterization. This constellation consists of 66 satellites in the communication network and additional on-orbit spares, all in near polar (86\({}^{\circ}\) inclination), 780 km altitude orbits. The Iridium Communications satellites launched in 1997-1998 (Block 1) and replaced by the Iridium NEXT constellation (2017-2019) carry engineering magnetometers to support satellite operations. Moreover, the Iridium orbits are distributed over six orbit planes, 11 satellites in each plane, spaced evenly in longitude by 30\({}^{\circ}\). Thus, the constellation provides dense global coverage of all latitudes and longitudes in as short a time as two hours.
Magnetometer data from the Block 1 Iridium satellites were first used for science analysis to study the Birkeland field-aligned currents which generate magnetic signals above the ionosphere as great as \(\sim\)2,000 nT ([PERSON] et al., 2000; [PERSON] et al., 2001) and more recently for the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) under which the data transmission to the ground was increased 10-100-fold to allow measurement of the large-scale Birkeland currents every 10 min ([PERSON] et al., 2014, 2018; [PERSON] et al., 2012; [PERSON] et al., 2020).
Although the data from the body-mounted Iridium magnetometers are of substantially lower quality than acquired from precision instruments, non-science magnetometer data can be calibrated using orbital data to contribute to Earth main field studies (cf. [PERSON] et al., 2020). For satellite constellations in particular, the continuous global coverage of all local times and number of observations warrants an assessment of the potential utility of these data for the characterization of Earth's magnetic field. The comparatively high altitude and low resolution imply that the data are unlikely to contribute to understanding of the crustal field, but the crustal field has been found to be largely static and has been extensively analyzed (cf. [PERSON] et al., 2010; [PERSON] et al., 2017). The Iridium data therefore are most applicable for specifying the external field and in studies of the dynamics of the field originating from the core. Motivated by the prospects for such unprecedented global coverage in magnetic field observations, we use magnetic field data from the Iridium Communications constellation originally acquired and processed for AMPERE to assess whether useful, independent information on Earth's main field can be extracted. The AMPERE data from Block 1 give one sample every 19.44 s (\(\sim\)1.2\({}^{\circ}\) along track spacing) and the constellation's configuration achieves global sampling with \(\sim\)2.25\({}^{\circ}\) longitude separation mapping the globe every 2 h.
In this study, we present an initial analysis and data reduction of the Block 1, original, Iridium magnetometer data from January 2010 to November 2015 to identify artifacts and erroneous signals in the data and to quantify the characteristics of the core field that might be resolved using these observations. Section 2 provides a detailed description of the magnetic field data and processing developed for AMPERE, as well as the modification of the standard AMPERE data processing for main field studies. Section 3 discusses the selection of geomagnetically quiet intervals for analysis. Section 4 presents the analysis of these data for Earth's field together with initial global maps. Detailed analyses yielding time series of spherical harmonics for January 2010 to November 2015 are given in Section 5. The results are summarized and opportunities for applications are discussed in Section 6.
## 2 Opportunity of Iridium Magnetic Field Observations
The satellites constituting the Iridium Communications network are illustrated in Figure 1. The 66 satellites in Iridium network orbits are distributed over six orbit planes, with 11 satellites in each plane. The orbit planes are evenly spaced in longitude by 30\({}^{\circ}\) and the satellites within each plane are also evenly spaced along the orbit track, corresponding to 9-min (33\({}^{\circ}\) orbit angle) separations in \(\sim\)100-min period orbits. Additional satellites in each orbit plane serve as on-orbit spares.
The first generation of Iridium satellites, denoted as Block 1, were launched starting in 1997 and continued to operate until 2019, after launch of the constellation of Iridium NEXT satellites was completed. The avionics systems of both the Block 1 and NEXT Iridium satellites include a vector magnetometer. Each of the Block 1 Iridium satellites carried an Ithaco IM-103 vector fluxgate magnetometer as part of the attitude control system. The magnetometers had intrinsic noise below 0.1 nT/\(\sqrt{\text{Hz}}\) at 1 Hz, absolute accuracy of 0.5% of full scale, and linearity to 1 part in 10\({}^{\circ}\). They were read out every 90 ms with 30-nT digitization on board for closed-loop attitude control. The flight software system was initially configured only to support downlink rates for engineering monitoring, \(\sim\)200 s between samples corresponding to \(\sim\)12\({}^{\circ}\) in latitude.
Although the Iridium avionics magnetometers have digitization, sampling cadence, and performance substantially coarser than typical science instrumentation (cf. [PERSON], 2002), they provide resolution sufficient to detect signals of Earth's Birkeland currents that are typically \(\sim\)300 nT and up to 2,000 nT, with a signal to noise ratio of about 10 ([PERSON] et al., 2000). It is worth noting that the original detection and studies of Earth's Birkeland currents were conducted using the attitude magnetometer on the Triad satellite (cf. [PERSON] & [PERSON], 1976), so the application of utility magnetometers for science has been well demonstrated. However, the coverage afforded by the Iridium Communications constellation enables a dramatic advance in understanding the dynamics of Birkeland currents.
To take advantage of the global-scale, continuous coverage provided by the Iridium constellation configuration, the AMPERE data set was developed ([PERSON] et al., 2000; 2014; [PERSON] et al., 2001). This required new flight software to be implemented on the Iridium Block 1 satellites to downlink magnetic field samples at 19.44 s (standard rate) or 2.16 s (high rate) intervals from every satellite in the communications network. Test data were acquired starting in October 2009, and complete AMPERE data were collected beginning January 1, 2010 and have continued to the present.
Processing to produce AMPERE data was developed to ingest, merge, and correct magnetometer data and attitude estimates from each individual satellite to yield time series and gridded maps of de-trended, inter-calibrated magnetic field perturbations reflecting signatures of field-aligned, Birkeland, currents flowing between the ionosphere and magnetosphere (cf. [PERSON] et al., 2020 for details on inversion techniques for AMPERE). Available AMPERE data spans January 2010 through September 2017. The NEXT magnetometer data are being calibrated and processing for science products is in process. The present analysis uses AMPERE data from the Iridium Block 1 satellites from 2010 to 2015.
The global coverage of the magnetic field observations from the Iridium Communications constellation is dramatically different from prior LEO observations of Earth's magnetic field (cf. [PERSON] et al., 2010, 2013, 2016). In the nine minutes between successive Iridium satellite passage over a given geographic latitude, the Earth rotates 2.3\({}^{\circ}\). In 2 h, the Earth rotates 30\({}^{\circ}\), so that all longitudes pass under one of the Iridium constellation orbit planes. The sampling interval of 19.44 s corresponds to an along track distance of 1.16\({}^{\circ}\) around the orbit, corresponding to the approximate maximum latitude spacing in the near-polar orbits at the equator. Thus, in as little as two hours the observations blanket the Earth with magnetic field samples spaced by 2.3\({}^{\circ}\) in longitude and 1.2\({}^{\circ}\) in latitude between 86.4\({}^{\circ}\)S and 86.4\({}^{\circ}\)N. This coverage also spans all local times with 2-h spacing so that the external current sources are simultaneously tracked and their effects effectively averaged in local time at every geographic longitude over 1 day.
Figure 1.— Schematic depiction of Block 1 Iridium Communications satellite communications network configuration in low Earth orbit at 780 km altitude and 86\({}^{\circ}\) inclination. The satellites are configured in six orbit planes with 11 satellites in each plane constituting the communication network from which magnetometer data were acquired for Active Magnetosphere and Planetary Electrodynamics Response Experiment beginning January 1, 2010. The light blue solid lines are the orbit planes and the yellow dashed lines depict the radio links between orbit planes.
The motivation to increase the magnetic field data returned from the Iridium satellites was to track and study the dynamics of Birkeland currents reflecting the solar wind-magnetosphere interaction (cf. [PERSON] et al., 2018; [PERSON] et al., 2017). During development of AMPERE science data processing, discrepancies between geographically registered magnetic field data and the IGRF-11 main field model ([PERSON], [PERSON], et al., 2010) were noted but not analyzed in detail since the objective for AMPERE was to remove main field signals to extract the Birkeland current signatures. The simple expedient of a one-quarter orbit period high-pass filter was used to remove remaining residuals (cf. [PERSON] et al., 2000). Discrepancies between polar cap filtered observations during geomagnetic active times, however, indicate that this approach is not ideal (cf. [PERSON] et al., 2014) and motivated re-examination of the main field signals in the AMPERE data. The extensive coverage of the data allowed examination of consistency in patterns in departures from IGRF-11 over days, months, and years. There was a surprisingly consistent evolution of the global patterns given the low expectations for the instrumentation stability and accuracy. This result motivated a systematic study to assess whether these data could provide a novel means of monitoring changes in the core-generated field.
## 3 AMPERE Data Processing and Science Products Overview
The AMPERE data processing flow is presented to set the context for its application to main field characterization. It is useful to consider some examples of AMPERE results from geomagnetically active and quiet conditions to illustrate the character of the Iridium Block 1 data and the data processing and calibration processes applied to these data. One key aspect of the rapid coverage over the entire Earth that Iridium provides is the opportunity to identify data intervals for conditions with the lowest possible contributions from magnetospheric and ionospheric currents driven by interaction with the solar wind.
On the Iridium Block 1 satellites the magnetic field data were used as one input to the attitude determination process and were calibrated using uploaded tables to enable this on-board closed-loop process. The target attitude knowledge accuracy was \(\sim\)0.1\({}^{\circ}\), sufficient to maintain the inter-satellite communication links upon which the network depended. To specify the scale of the uncertainty that the attitude accuracy implies, we note that a 0.1\({}^{\circ}\) attitude error corresponds to an error in the magnetic field measurement of 80 nT perpendicular to the field direction at the altitude of the Iridium satellites. The accuracies needed for auroral science are higher than those required for on-board operations, so post-processing calibrations were used to improve the estimates of the observed field for AMPERE science ([PERSON] et al., 2000). The attitude and measurement accuracies for study of Earth's magnetic field and the variations in the core-generated field are substantially more stringent than the requirements for AMPERE, necessitating additional processing and analysis to identify artifacts in the data and determine signals most reliably attributed to the main field.
It turns out that the errors in the data are randomly distributed and it is only because the constellation provides a large number of observations that one can determine the mean values to greater precision than the uncertainty of the individual samples. Below we adopt a grid in latitude and longitude with bins extending 9\({}^{\circ}\) in longitude and 9\({}^{\circ}\) in latitude for a total of 800 bins. In one day, the 66 Iridium satellites returned, on an average, 4,440 samples from each space vehicle (SV) for a total of 293,000 measurements distributed over all latitudes and longitudes, so the number of samples in each 9\({}^{\circ}\)\(\times\) 9\({}^{\circ}\) bin is \(\sim\)360. The statistical error in the mean of measurements with uncertainties of 80 nT is therefore a factor of 20 lower, or \(\sim\)4 nT. This estimate illustrates how the quantity of data returned and the dense coverage provided by the constellation compensate both for the attitude knowledge accuracy and the coarse digitization. This initial estimate is borne out in the analysis and statistics presented below.
The magnetometer post-processing calibration requires determination of 12 different parameters related to the orientations of the three sensing axes (six angles), three offsets or zero levels, and three gain adjustment factors (cf. [PERSON] et al., 2019 and references therein). For nonspinning spacecraft in LEO, approaches have been developed to costimate a nonlinear solution for these parameters together with core model coefficients (cf. [PERSON] et al., 2020). For AMPERE, we adopted a simpler, linear approach to deriving calibrated perturbations relative to a reference model from the reported observations. This was used to derive the perturbation inputs to the science product processing described in detail by [PERSON] et al. (2020).
The AMPERE pre-processing proceeds as follows. First, we write **B\({}_{\text{SC}}(t)\)** to denote the data returned by the magnetometer in spacecraft coordinates (SC) at the time \(t\), converted to engineering units using a preliminary scale factor. Spacecraft coordinates are defined as \(+X\) in the body direction that is nominally ram facing, \(+Z\) as the body direction nominally nadir, and \(+Y\) in the body direction nominally in the orbit normal direction. The spacecraft and magnetometer coordinates are identical to within mounting and internal magnetometer orientation designs. Departures of the body orientation from these nominal directions are provided in the attitude data in terms of roll, pitch, and yaw angles and these angles are used in transforming between body (magnetometer) coordinates and geophysical systems. The scale factors for Block 1 analysis are those applied on-board the satellite at the time of acquisition. The reference model for Earth's main field in geographic coordinates is written as \(\mathbf{B}_{\text{modo-GEO}}\). In this paper, the reference model is IGRF-11 evaluated at the satellite location of each measurement with a constant secular variation ([PERSON], [PERSON], et al., 2010), but we refer to this with the general term \"model\" since the analysis can use any reference model. The next step in the analysis is to evaluate the reference model at the location and date-time of each magnetometer sample, denoted \(\mathbf{B}_{\text{model-GEO}}(\mathbf{r}(t),\,t)\), where \(\mathbf{r}(t)\) is the location of the satellite at the time \(t\). Using the spacecraft attitude, denoted as a four-element quaternion, \(\mathbf{q}(t)\), we construct a rotation matrix from GEO coordinates into the SC frame, denoted \(\mathbf{A}_{\text{GEO-SC}}(\mathbf{q}(t))\). We then transform the reference model into the SC frame
\[\mathbf{B}_{\text{model-GC}}\left(\mathbf{r}(t),\mathbf{q}(t),t\right)= \Delta_{\text{GEO-SC}}\left(\mathbf{q}(t)\right)\cdot\mathbf{B}_{\text{model-GEO }}\left(\mathbf{r}(t),t\right), \tag{1}\]
and calculate the residual between the observed field and the model in the SC frame
\[\Delta\mathbf{B}_{\text{SC}}\left(t\right)=\mathbf{B}_{\text{SC}}\left(t \right)-\mathbf{B}_{\text{model-SC}}\left(\mathbf{r}(t),\mathbf{q}(t),t\right). \tag{2}\]
Note that because the magnetometer and spacecraft coordinates are identical, an additional rotation from the SC frame into the magnetometer frame is not needed. The calibration is then derived by fitting each component of \(\Delta\mathbf{B}_{\text{SC}}(t)\) to the model field using linear regression. We use an entire day of data to determine best fits to \(\Delta\mathbf{B}_{\text{SC}}(t)\) in the form
\[\Delta\mathbf{B}_{\text{SC-fit}}\left(t\right)=\mathbf{B}_{0}+\mathbf{\frac{M }{\text{ }}}\cdot\mathbf{B}_{\text{model-SC}}\left(\mathbf{r}(t),\mathbf{q}(t),t\right) \tag{3}\]
where the offset vector, \(\mathbf{B}_{0}\) and matrix, \(\mathbf{M}\), are constants for each day. We do not require that these values be the same between different days. The fit can be obtained in closed form since it is a simple linear fit, so it is a fast calculation, which is not an insignificant consideration when processing data from up to 75 satellites. The residual magnetic field signal that cannot be expressed in terms of linear correlations to the reference model is then
\[\delta\mathbf{B}_{\text{SC}}\left(t\right)=\Delta\mathbf{B}_{\text{SC}}\left( t\right)-\Delta\mathbf{B}_{\text{SC-fit}}\left(t\right). \tag{4}\]
To see how this relates to a calibration applied to the \(\mathbf{B}_{\text{SC}}(t)\) to obtain a best estimate for a calibrated \(\mathbf{B}_{\text{SC}}(t)\), we expand Equation 4 to
\[\delta\mathbf{B}_{\text{SC}}\left(t\right)=\mathbf{B}_{\text{SC}}\left(t \right)-\left\{\mathbf{B}_{0}+\left(\mathbf{\frac{1}{\text{ }}}+\mathbf{M}\right)\cdot\mathbf{B}_{\text{model-SC}}\left(\mathbf{r}(t), \mathbf{q}(t),t\right)\right\}, \tag{5}\]
where \(\mathbf{\frac{1}{\text{ }}}\) is the identity matrix. Given that the residual, \(\delta\mathbf{B}_{\text{SC}}(t)\) has minimum standard deviation for this form of the calibration, the conversion from \(\mathbf{B}_{\text{SC}}(t)\) to calibrated data \(\mathbf{B}_{\text{SC}}(t)\) is given by
\[\mathbf{B}_{\text{SC}}^{{}^{\prime}}\left(t\right)=\left(\mathbf{\frac{1}{ \text{ }}}+\mathbf{\frac{M}{\text{ }}}\right)^{-1}\cdot\left(\mathbf{B}_{\text{SC}}\left(t\right)-\mathbf{B}_{0 }\right). \tag{6}\]
Written this way, it is clear that \(\mathbf{B}_{0}\) is the offset vector and \(\left(\text{I}+\text{M}\right)^{-1}\) is the calibration matrix. The matrix elements can be expressed in terms of transformations to orthogonalize the sensing axes, rotate from the effective magnetometer frame into the spacecraft frame, and to apply gain corrections to each axis to yield a true vector (cf. [PERSON] et al., 2019). Note however that any signals related to sensor or electronics cross-talk between axes is not distinguished from orthogonality corrections so the interpretation of the calibration matrix is to some extent ambiguous. Because it is more efficient and hence faster, while preserving the information given by a nonlinear inversion for the orthogonalization parameters that determine the matrix, we leave the calibration in the matrix form since our only interest is in transforming to the best estimate true vector field measurement.
Results showing the sequence in processing from \(\mathbf{B}_{\text{SC}}\) to \(\Delta\mathbf{B}_{\text{SC}}\) to \(\delta\mathbf{B}_{\text{SC}}\) for May, 2010 and Iridium Satellite Vehicle 30, denoted SV030, are shown in Figure 2 for the entire day. To more clearly see features of the data at each step in the processing, a subset of the data is shown in Figure 3 for the first four hours of the day. Figures 2 and 3 also show the filtered \(\mathbf{5B}_{\text{SC}}\) that are used as the inputs to subsequent AMPERE science processing. Comparing the \(\mathbf{B}_{\text{SC}}\) data with the residuals, \(\mathbf{\Delta B}_{\text{SC}}\), there are clear orbit period signals with amplitudes of about 1%-2% of the original signal. The calibration reduces the residuals to less than about 100-200 nT amplitude, making the Birkeland current signatures much more prominent as spikes in the \(\delta\mathbf{B}_{\text{SC}}\) time series (denoted as \(\mathbf{\hat{B}}\)), especially in the cross-track or Y component. Signals having periods roughly half to one quarter of the orbit period remain in the \(\mathbf{\delta B}_{\text{SC}}\) time series, and with a source for these signals not initially identified. To extract the Birkeland current signals more clearly, we therefore applied a 25-min period high pass filter to \(\mathbf{\delta B}_{\text{SC}}\). The filtered result is shown in the bottom row as \(\mathbf{\delta B}_{\text{filtered}}\). The filtering reduced the baseline residuals by about a factor of two without obviously distorting the Birkeland current signals. This allowed production of the first version of AMPERE science products ([PERSON] et al., 2001, 2020), which have been applied to a range of questions in auroral and magnetospheric science (cf. [PERSON] et al., 2018).
During active times when the auroral zones expand equatorward, as far as 40\({}^{\circ}\) colatitude, the 25-min period can be comparable to the time it takes a polar orbiting satellite to traverse the auroral zone. Substantial discrepancies between \(\mathbf{\delta B}_{\text{filtered}}\) data from near-conjunctions of Iridium satellites do occur ([PERSON] et al., 2014) that turn out to be due to distortions from this filter. Revisions to the processing are in development to eliminate the filtering step to mitigate this distortion. The data used here for study of the Earth's field are the \(\mathbf{\delta B}_{\text{SC}}\) before this filtering.
Figure 2: One day of data from Iridium Satellite Vehicle 30 (denoted SV030) in satellite body coordinates showing results at four stages of data processing. From left to right: the columns show the magnetic field components in the \(X\)-axis (along track in the ram direction, parallel to the satellite velocity, \(\mathbf{v}\), in magenta); \(Y\)-axis (cross track in the \(\mathbf{v}\times\mathbf{r}\) direction, in turquoise); and \(Z\)-axis (\(\text{nadir}\),\(-\mathbf{r}\) direction, in black). From top to bottom, the rows show: magnetometer readings converted to engineering units, \(\mathbf{B}_{\text{BC}}\); magnetic field residual after subtracting the IGRF-2010 model with secular variations (\(\mathbf{B}_{\text{decay}}\)), \(\mathbf{\Delta B}\); residual corrected for offsets, misalignment, and orientation using multi-linear regression between \(\mathbf{\Delta B}\) and \(\mathbf{B}_{\text{decay}}\), \(\mathbf{\delta B}_{\text{B}}\); the corrected residual after applying a high-pass filter with a cut-off period of 25 min (\(\sim\)1/4 of an orbit period), \(\mathbf{\delta B}_{\text{linear}}\).
The AMPERE products provide an important measure of geomagnetic disturbance and are used here to identify periods of particularly quiet conditions. It is therefore useful to discuss the AMPERE processing to illustrate the relationship between quiet conditions and the input data for the main field analysis. Examples of AMPERE products from two 10-min intervals during a geomagnetically active period on May, 2010 are shown in Figure 4, for 03:30-03:40 UT (top) and 12:00-12:10 UT (bottom). These data products and tools to generate graphics used here are available via the AMPERE web page ([[http://ampere.jhuapel.edu](http://ampere.jhuapel.edu)]([http://ampere.jhuapel.edu](http://ampere.jhuapel.edu))). This moderate geomagnetic storm was driven by an interplanetary magnetic cloud with a southward interplanetary magnetic field (IMF) of 13 nT. The auroral electric index, auroral electroject (AE), reached over 1,500 nT and the minimum equatorial storm disturbance index, \(D_{\rm{ss}}\) was near \(-\)60 nT. The horizontal filtered \(\delta\mathbf{B}_{\perp}\), is shown in the left panel by colored arrows. The center panels show the orthogonal function fit to \(\delta\mathbf{B}_{\perp}\), labeled \(\delta\mathbf{B}_{\perp,\rm{ss}}\), as described in [PERSON] et al. (2020). The anti-sunward magnetic perturbations in the dawn and dusk sectors associated with the Birkeland currents are clear, and the basic Region 1/Region 2 current polarities are evident (cf. [PERSON], 1976). Currents in the polar cap at latitudes \(>\)80\({}^{\circ}\) (in the 12:00-12:10 UT interval) are not considered reliable, as they result from discrepancies in the \(\delta\mathbf{B}_{\perp}\) near the orbit plane crossing point. Measurements near the orbit plane crossing point can exacerbate errors in the \(\delta\mathbf{B}_{\perp}\) owing to the small separations between tracks, resulting in spurious filamentary currents. Consistent with the bottom rows of Figures 2 and 3, the \(\delta\mathbf{B}_{\perp}\) equatorward of the Birkeland currents are below \(\sim\)100 nT in magnitude.
The total Birkeland current, \(I_{\rm{TRt}}\), is a convenient measure of the intensity of this high-latitude externally driven current system and is readily calculated from the AMPERE current density distributions. As described in [PERSON] et al. (2014), this calculation is done by setting a minimum current density magnitude, \(J_{r,\rm{au}}=0.16\)\(\mu\)A/m\({}^{2}\), and then separately integrating the upward and downward \(J\), whose magnitudes exceed
Figure 3: Magnetic field data from Iridium Satellite Vehicle 30 (SV030) for the first 4 h of May 24, 2010 in the same format as Figure 2, showing slightly more than two orbits of data. The residual signals in \(\delta\mathbf{B}\) show signals occurring over roughly an orbit period and twice an orbit period, most clearly in the along-track and cross-track components. Short-period spikes in the along and cross-track components most evident in the \(\delta\mathbf{B}_{\rm{Green}}\) time series at \(\sim\)00:08 UT, \(\sim\)01:00 UT, \(\sim\)01:45 UT, and \(\sim\)03:25 UT are due to Birkeland currents.
\(J_{\rm r,min}\) to obtain \(I_{\rm Up,h}\) and \(I_{\rm Down,h}\), where \"\(h\)\" is either N or S to indicate the polar hemisphere being integrated. The threshold magnitude \(J_{\rm r,min}\) was determined from the noise level in \(J\), during very quiet geomagnetic conditions and reflects the end-to-end noise in the data and AMPERE analysis process. The thresholding minimizes contributions from lower latitude noise spread over large areas which would otherwise be a significant contribution and thereby allows one to evaluate the integrals for \(I_{\rm Up,h}\) and \(I_{\rm Down,h}\) without imposing arbitrary latitude boundaries. The total current flowing in the Birkeland system is defined as
\[I_{\rm Tot,h}=\frac{1}{2}\Big{(}I_{\rm Up,h}-I_{\rm Down,h}\Big{)}, \tag{7}\]
and the net current as
\[I_{\rm Tot,h}=I_{\rm Up,h}+I_{\rm Down,h}. \tag{8}\]
The \(I_{\rm Up,h}\) and \(I_{\rm Down,h}\) for the 3:30-3:340 UT interval were 6.08 million Amperes (MA) and \(-\)6.12 MA, respectively, yielding an \(I_{\rm Net,N}\) of \(-\)0.04 MA. For the 12:00-12:10 UT interval \(I_{\rm Up,N}\) and \(I_{\rm Down,N}\) were 9.25 MA and \(-\)8.83 MA, and \(I_{\rm Net,N}\) was \(+\)0.42 MA, about 5% of \(I_{\rm Tot,N}\). The small \(I_{\rm Tot,N}\) values are taken in the AMPERE results as uncertainties in \(I_{\rm Tot,N}\). Inter-hemispheric currents that have been reported at low latitudes ([PERSON] et al., 2019) range up to 10 s of nA/m\({}^{2}\) and occur well equatorward of the auroral zones. Inter-hemispheric currents in the auroral zone Birkeland currents are thought to range between 0.1 and 0.4 \(\mu\)A/m\({}^{2}\)([PERSON] et al., 2014), comparable to the variability we find in \(I_{\rm Tot,h}\).
Figure 4: Example 10-min intervals of AMPERE processing steps and products from two intervals during geomagnetic activity on May 29, 2010, 03:30-03:40 UT (top) and 12:00–12:10 UT (bottom). Panels show the view looking down from above the north magnetic pole to 40\({}^{\rm m}\) magnetic latitude, with magnetic non and the top and dusk to the left (left) horizontal magnetic perturbations (\(\mathbf{\delta B}_{\perp}\)) along each orbit track, with arrows colored differently for different satellites in the direction of \(\mathbf{\delta B}_{\perp}\) and scaled by 50 nT; (middle) continuous fit to the \(\mathbf{\delta B}_{\perp}\) data (\(\mathbf{\delta B}_{\perp,\rm{td}}\)) using harmonic functions customized to be normalized over the latitude range shown and evaluated at every hour in local time and degree in latitude; (right) radial electric current density, \(J_{\rm e}\) calculated as \(\
abla\times\mathbf{\delta B}_{\perp}/\mu_{0}\), where red is upward (positive) \(J_{\rm e}\) blue is downward (negative) \(J_{\rm e}\) and the color saturation is set to 1 pA/m\({}^{2}\).
## 4 Quiet Day Selection
As illustrated in Figure 4, the coverage of the tridium constellation allows us to impose strict limits on geomagnetic activity to select intervals as free of external signals as possible. To illustrate how intervals of quiet geomagnetic activity were identified and quantified, Figure 5 shows the IMF observed by the Advanced Composition Explorer (ACE) spacecraft at the Sun-Earth Lagrange point 1 (L1) together with three sets of geomagnetic disturbance measures for an eight day interval in 2010, from May 22 nd through the 29 th, which includes the time intervals shown in Figure 4. The three components of the IMF in solar ecliptic coordinates are shown in Figure 5a color coded as light blue, turquoise, and magenta for \(B_{\rm{CXH}}\), \(B_{\rm{YZ,HZ}}\), and \(B_{\rm{Z,HZ}}\), respectively. The IMF magnitude (\(B_{\rm{IMF}}\)) and the negative of the magnitude (\(-B_{\rm{IMF}}\)) are shown in thick and thin black traces, respectively. The magnetic cloud that was responsible for the geomagnetic storm on the May 29, 2010 first arrived at L1 around 1800 UT on May 28, 2010 with peak negative \(B_{\rm{Z,HZ}}\) occurring between 0,300 and 1200 UT on the May 29, 2010.
The second, third, and fourth panels of Figure 5 shows the measures of geomagnetic disturbance used in this study for selection of \"quiet\" periods. Both the AE and H-index datasets are available from the Geomagnetic Data Service of the Kyoto World Data Center for Geomagnetism, Kyoto, Japan ([[http://wdc.kugi.kyoto-u.ac.jp/wdc/Sec3.html](http://wdc.kugi.kyoto-u.ac.jp/wdc/Sec3.html)]([http://wdc.kugi.kyoto-u.ac.jp/wdc/Sec3.html](http://wdc.kugi.kyoto-u.ac.jp/wdc/Sec3.html))). The AE index indicates high-latitude magnetic perturbations generally resulting from auroral electrojets, while the SymH and AsyH indices provide a proxy for equatorial magnetic perturbations related to enhancements in the Earth's ring current. The 24-h running averages of \(I_{\rm{IR,N}}\), \(I_{\rm{IR,N}}\), AE, SymH, and AsyH were used to construct a composite measure of geomagnetic activity. The IMF
Figure 5: Eight-day interval of the parameters and sliding 24-h averages used to identify geomagnetically quiet intervals, together with the interplanetary magnetic field (IMF) observed by the Advanced Composition Explorer spacecraft at the Earth-Sun Lagrange point 1 (L1). From top to bottom the panels show: (a) IMF data; (b) total Bireland currents (\(I_{\rm{Ao}}\)) in the northern (black) and southern (blue) hemisphere and their running 24-h averages together with the net current (magenta, torquoise, and gold lines, respectively); (c) auroral electroject index (black) and its running 24-h average (magenta); (d) symmetric (SymH) and asymmetric (AsyH) H-indices (black and blue, respectively) and their 24-h running averages (magenta and turquoise, respectively). Three of the quiet periods occurred during this interval and are indicated by the yellow boxes in the bottom three panels: May 22, 2010/12:00-May 23, 2010/12:00; May 23, 2010/21:00-May 24, 2010/21:00; and May 27, 2010/03:00-May 28, 2010/03:00.
data are shown here for context to illustrate that the active periods correspond to strongly southward IMF as expected, but these data are not needed for the quiet condition determination. The three 24-h intervals highlighted by light yellow rectangles in Figures (b)b-(d)d indicate a set of quiet intervals selected for analysis of the main field.
To select quiet 24-h periods, we first constructed normalized quantities from the disturbance measures shown in Figure 5. The running 24-h average of a quantity, g, is denoted by angle brackets, <g>. We calculated a total current from the 24-h averages
\[I_{\text{Tot}}=\langle I_{\text{Tot},N}\rangle+\langle I_{\text{Tot},S}\rangle. \tag{9}\]
Using both <\(I_{\text{Tot},N}\)> and <\(I_{\text{Tot},N}\)> rather than just one hemisphere has the advantage of muting seasonal influence on the Birkeland currents driven by polar ionospheric illumination variations. We also used both SymH and AsyH since these indices represent different sets of external currents: SymH primarily represents the symmetric ring current and symmetric magnetospheric compressions, while AsyH reflects the storm-time asymmetric ring current, at times with substantial contribution of from the cross-tail current. We therefore calculated
\[\text{H}=\left\lvert\langle\text{Sym}H\rangle\right\rvert+\left\lvert\langle \text{AsyH}\rangle\right\rvert, \tag{10}\]
to capture all of these effects. We then normalize the \(I_{\text{Tot}}\) <AE>, and \(H\) values by constructing z-distributions for each using 1 month of data to define the distributions. For example, from a month of \(I_{\text{Tot}}\) values we evaluated the average, \(m_{\text{Tot}}\) and the standard deviation, \(\sigma_{\text{Tot}}\) and calculated a normalized value as
\[V_{\text{tot}}=\frac{\left(I_{\text{Tot}}-m_{\text{Tot}}\right)}{\sigma_{T \text{tot}}}, \tag{11}\]
known as the z-score. This was similarly done for <AE> and \(H\) to obtain \(V_{\text{AE}}\) and \(V_{\text{T}}\), respectively. We then took the average of these three normalized disturbance parameters to derive a single composite disturbance parameter, \(Q\),
\[Q=\frac{\left(V_{\text{Tot}}+V_{\text{AE}}+V_{\text{H}}\right)}{3}, \tag{12}\]
which is positive (negative) for conditions that are more (less) disturbed than the average taking into account Birkeland currents, auroral electrojets, and ring current-tail-compression dynamics.
The time series for \(Q\) were then used to determine quiet 24-h intervals. We then identified the quietest seven periods in each month. This was done by finding the minimum \(Q\), logging it, removing all \(Q\)-values within this period, and then searching for a new minimum \(Q\) in the remaining data until seven non-overlapping 24-h periods were identified and logged. To ensure that there is at least some quiet data from every month, we also selected the three quietest periods in each month. Then, because not all months were equally quiet, we collected from the remaining periods, the 12 quietest ones for each quarter of the year centered on solstice or equinox months (i.e., November-January, February-April, May-July, August-October). Thereafter we selected the quietest four from these 12. Altogether, the above selection criteria yielded 263 quiet 24-h periods for January 2010 through November 2015. As of this writing, 8 months of lithium Block 1 magnetometer data during this span are not currently available. Hence, data for August and September 2013, June and July 2014, and November 2014 through February 2015 are not included in the analysis. For quarters with missing months, the number of additional quiet periods were reduced to two periods if only 2 months were available or one period if only one month was available. No quarter was devoid of data. The three quiet periods occurring during the interval marked in Figure 5 by the yellow boxes were May 22, 2010/12:00-May 23, 2010/12:00; May 23, 2010/21:00-May 24, 2010/21:00; and May 27, 2010/03:00-May 28, 2010/03:00. Table S1 in the supporting information lists all 263 intervals together with parameters used to derive the z-scores and the final values for \(Q\) for each interval. For one quiet interval, April 16, 2010 18:00-April 17, 2010 18:00, a complete 24-h interval of data was not available so it was not included in the subsequent analysis.
It is instructive to contrast these quiet periods with the moderate storm time interval shown in Figure 4. The examples of Figure 6, in the same format as Figure 4, are for May 23, 2010 at 02:00-02:10 UT (top) during the quietest interval of the 8-days span shown in Figure 5 and for May 27, 2010 at 12:00-12:10 UT (bottom) during the least quiet of the three identified quiet periods. The first interval exhibits a cluster of perturbations near noon around 80\({}^{\circ}\)N magnetic latitude, typical of Birkeland currents during northward IMF (cf. [PERSON] et al., 2008), but there are no systematic signals equatorward of \(\sim\)70\({}^{\circ}\)N magnetic latitude. The relatively small signals, \(<\)100 nT, at lower latitudes are typical for uncorrede, that is, unidentified, noise and variations consistent with vehicle attitude uncertainty. For the case of May 27, 2010 at 12:00-12:10 UT, there are evident R1/2 currents poleward of \(\sim\)67\({}^{\circ}\)N, at significantly higher latitudes than the active time currents in Figure 4 but with signals below \(\sim\)300 nT, which are less than \(\sim\)1/5 th of the more active time signals. This May 27, 2010 interval in Figure 6 represents the most active conditions included in the quiet interval database, while the May 23, 2010 case in Figure 6 is more typical of the quiet conditions for the database.
## 5 Data Pre-Processing for Earth's Main Field
The first step in pre-processing the calibrated Iridium data for study of Earth's main field is to transform the data into geographic coordinates and assess whether the data seem to be ordered by geographic location. The second step is to examine the distributions of the residuals to assess whether the errors appear to be random, and to evaluate their averages in suitable latitude-longitude ranges and estimate the errors in the means for each bin. The first indication that the Iridium constellation data may record useful information on Earth's main magnetic field was the presence of consistent patterns when plotting the residuals transformed to spherical geographic coordinates, \(\delta B_{t}\) (radial), \(\delta B_{b}\) (polar angle positive southward), and \(\delta B_{b}\) (azimuthal positive eastward), and registered in geographic latitude and longitude. Two examples of the residuals obtained from the two nearly consecutive quiet intervals shown in Figure 5 are shown in Figure 7. The plot shows all of the samples from every satellite, totaling \(\sim\)290,000 points, plotted as colored dots for
Figure 6: Example 10-min intervals of Active Magnetosphere and Planetary Electrodynamics Response Experiment products in the same format as Figure 4 from May 23, 2010 at 02:00-02:10 UT (top) during the quietest 24-h period in Figure 5 and May 27, 2010 at 12:00-12:10 UT (bottom) during the most active interval during the third quiet 24-h period in Figure 5.
May 22, 2010/12:00-May 23, 2010/12:00 on the left and May 23, 2010/21:00-May 24, 2010/21:00 on the right. One significant point to note is that the distributions of \(\delta\)**B** in Figure 7 are not a random mixture of positive and negative values but appear to be organized into coherent regions. For example, the \(\delta B_{\rm r}\) pattern for both quiet periods show several broad, 60\({}^{\circ}\)-wide longitude bands of positive values, one from \(-\)90\({}^{\circ}\) to \(-\)30\({}^{\circ}\)E and 0\({}^{\circ}\)-30\({}^{\circ}\)N latitude, another from 0\({}^{\circ}\) to 90\({}^{\circ}\)E and \(-\)45\({}^{\circ}\)-0\({}^{\circ}\)N, and a third from about 120\({}^{\circ}\)-180\({}^{\circ}\)E and 0\({}^{\circ}\)-60\({}^{\circ}\)N. The \(\delta B_{\rm b}\) distributions show a broad positive band in the southern hemisphere and a region of northward (negative) field from \(-\)90\({}^{\circ}\)E-0\({}^{\circ}\)E to 20\({}^{\circ}\)N-60\({}^{\circ}\)N. In addition, these general patterns are consistent between the two quiet periods. The signals that are the least consistent between the 2 days are at high latitudes, poleward of 70\({}^{\circ}\)N in \(\delta B_{\rm g}\) in the northern hemisphere, arising from the Birkeland current signals (cf. Figure 6).
Results from two additional consecutive quiet periods from November 2015 are shown in Figure 8. These intervals from November 21, 21/06:00-November 22, 2015/06:00 and November 22, 2015/06:00-November 23, 2015/06:00 exhibit larger residuals with clear patterns consistent between the 2 days, but ones that are quite different from the patterns shown in Figure 7. In \(\delta B_{\rm r}\) distributions there are three regions of positive residuals, one between 40\({}^{\circ}\)N-70\({}^{\circ}\)N and \(-\)180\({}^{\circ}\)E-90\({}^{\circ}\)E, a second centered on \(-\)45\({}^{\circ}\)E and 10\({}^{\circ}\)N spanning about 40\({}^{\circ}\) in longitude and latitude, and a third roughly 'U'-shaped region from 30\({}^{\circ}\)E to 180\({}^{\circ}\)E with a strongest band at about 50\({}^{\circ}\)S spanning 60\({}^{\circ}\)E-120\({}^{\circ}\)E. In the equatorial zone, 30\({}^{\circ}\)S-30\({}^{\circ}\)N, the \(\delta B_{\rm r}\) has a roughly 3-wave structure with longitude. The \(\delta B_{\rm b}\) distributions show intense positive residuals at high southern latitudes, poleward of 60\({}^{\circ}\)S from 30\({}^{\circ}\)E to 120\({}^{\circ}\)E, a broad zone of moderately positive residuals from \(-\)180\({}^{\circ}\)E to 0\({}^{\circ}\)E south of about 30\({}^{\circ}\)N, and an arc of negative \(\delta B_{\rm g}\) from \(\sim\)70\({}^{\circ}\)N at \(-\)180\({}^{\circ}\)E extending across 0\({}^{\circ}\)E at 60\({}^{\circ}\)N and to 20\({}^{\circ}\)S at 90\({}^{\circ}\)E. The slightly sinusoidal shaped high-latitude Birkeland current signatures are most evident
Figure 7.— Calibrated magnetic field residuals from all Iridium Block 1 satellites in geographic spherical coordinates versus geographic latitude and longitude for May 22, 2010/12:00–May 23, 2010/12:00 on the left and May 23, 2010/21:00–May 24, 2010/21:00 on the right. The panels show all of the samples from every satellite, \(\sim\)290,000 points, plotted as colored dots. From top to bottom the panels show \(\delta B_{\rm r}\), \(\delta B_{\rm b}\), and \(\delta B_{\rm g}\) all using the same color scale.
in the southern polar region in \(\delta B_{\rm p}\) poleward of 60\({}^{\circ}\)S, but \(\delta B_{\rm p}\) also exhibits a roughly wave-like pattern of residuals across all longitudes extending from about 30\({}^{\circ}\)S to 30\({}^{\circ}\)N. The peaks in the equatorial \(\delta B_{\rm p}\) residuals correspond roughly to midpoints between extrema in a similar 3-wave pattern in the \(\delta B_{\rm p}\). As with the pair of quiet intervals from May 2010, these two periods in November 2015 illustrate a highly coherent pattern in the \(\delta\)B when registered in geographic latitude and longitude, as well as a remarkable consistency between the two periods. The magnitudes of the residuals are substantially greater in November 2015 than they were in May 2010, indicating that the secular variation extrapolation from January 1, 2010 used in the IGRF-11 model may be departing more substantially in the later years. The remarkable feature of these examples is that these global maps were obtained in just a single day of observations and yield highly consistent results.
To assess the statistical uncertainties and confidence of the mean perturbations in the geographical patterns found in Figures 7 and 8, we first divided the observations into 20 latitude and 40 longitude bins, each 9\({}^{\circ}\) in latitude by 9\({}^{\circ}\) in longitude. The bin size is a trade-off between maximizing the statistics in each bin, which favors larger bins, and retaining enough spatial resolution to resolve wavelengths at least as short as the distance from the core to the satellite altitude. For Iridium altitude, the core is about 3,800 km below the satellites, and this wavelength corresponds to an azimuthal order of \(\sim\)12 at the equator. The 9\({}^{\circ}\times\)9\({}^{\circ}\) bin size allows a harmonic decomposition up to degree and order 20. Given the average number of samples obtained in one day by the 66 Iridium Block 1 satellites, a typical number of \(\sim\)360 samples comprise each latitude-longitude bin. All of the \(\delta\)B measurements within each bin are averaged for each quiet period. Because the Iridium satellites are in near polar orbits, the number of samples in each bin is nearly uniform with latitude even though the area of the bins decreases toward the poles. The bin averages for the May
Figure 8.— Calibrated magnetic field residuals from all Iridium Block 1 satellites in the same format as Figure 7 for November 21, 2015/06:00–November 22, 2015/06:00 on the left and November 22, 2015/06:00–November 23, 2015/06:00 on the right. As for Figure 7, but more evident here owing to the larger residual magnitudes, the dots are small enough that the white space between tracks of points are predominantly blank spaces between tracks of samples.
22-23, 2010 and May 23-24, 2010 quiet intervals are shown in Figure 9. Similarly, averages for November 21-22, 2015 and November 22-23, 2015 are shown in Figure 10. For both sets of quiet periods, the bin averages reveal that the patterns from the individual observations throughout the satellite orbits are consistently present in the means. The perturbation regions are also more clearly evident, and there is consistency, even in relatively small-scale features (i.e., below 20\({}^{\circ}\) in latitude and longitude), between successive days.
To assess the residual distributions relative to the means we examined the distribution of all residuals for individual quiet periods. As an example of this assessment, the distributions for all measurements of \(\delta B_{\rm p}\), \(\delta B_{\rm p}\), and \(\delta B_{\rm p}\) are shown for a quiet interval from November 21-22, 2015 in Figure 11. The Gaussian fit to each distribution very closely follows the actual data distribution, indicating that the data are primarily normally distributed. Similar Gaussian distributions are obtained when considering the averaged data within each latitude-longitude bin. The normal character of the distributions is consistent with a random error due to the attitude determination uncertainty of \(\sim\)80 nT. The standard deviations for each latitude-longitude bin for May 22, 2010/12.00-May 23, 2010/12.00 and for November 21, 2015/06:00-November 22, 2015/06:00 are shown in Figure 12. The standard deviations within each bin range from about 40 to 100 nT with the highest
Figure 9: Global maps of averaged magnetic field residuals relative to IGRF-11 in geographic spherical coordinates from all Iridium Block 1 satellite observations in 9\({}^{\circ}\) by 9\({}^{\circ}\) latitude-longitude bins. Left panels show results for the 24-h quiet period starting at 12:00 UT on May 22, 2010 and the right panels show results for the 24-h quiet period immediately following, starting at 21:00 UT on May 23, 2010.
values in the polar latitudes (i.e., higher than \(\pm 60^{\circ}\)), corresponding to the auroral zones and so reflecting the variability of the natural signals there. For the 262 quiet day events with complete data, there were two days for which the standard deviation of the residuals were more than five times greater than all of the other days which was attributed to operations activities on the satellites. Excluding these 2 days from the data set leaves 260 quiet days with complete data and distributions comparable to those shown here.
For potential use in specifying the main field, the standard deviation of measurements in each bin is less important than the uncertainty of the mean. With about 350 points in each bin, the standard error in the mean is roughly a factor of 18 smaller than the standard deviation. Maps of the standard errors in the mean are shown in Figure 13 for the same two intervals and in the same format. The standard errors are generally below 3 nT for the May 2010 case and between 3 and 5 nT for the November 2015 case shown in Figure 12. The increase in the standard errors is primarily due to the fact that there were somewhat fewer satellites operating in fine attitude control mode as the Block 1 satellites were experiencing degraded performance of some subsystems, and hence there were somewhat fewer magnetic field measurements in the analysis.
Figure 10: Global maps of averaged magnetic field residuals in the same format as Figure 9. Left panels show results for the 24-h quiet period starting at 06:00 UT on November 21, 2015 and the right panels show results for the next 24-h quiet period, starting at 06:00 UT on November 22, 015.
\[a_{\text{int}}=\sqrt{\frac{\left(2l+1\right)\left(l-m\right)!}{2\pi\left(l+m\right)!}}\quad\text{for }m>0. \tag{16b}\]
The convenience of Equation 15 is that it allows one to calculate the coefficients contributing to the patterns of the residuals directly from convolution integrals. Given the maps for \(\delta B_{\text{\tiny{(}}}\),\(\phi\),\(\tau\),\(\iota\)), \(\delta B_{\text{\tiny{(}}}\),\(\phi\),\(\tau\),\(\iota\)), and \(\delta B_{\text{\tiny{(}}}\),\(\phi\),\(\iota\)) for each quiet interval, denoted \(l_{\text{\tiny{t}}}\), the harmonic coefficients for each pattern are given by
\[\mathbf{c}_{\text{\tiny{in}}}\left(t_{\text{\tiny{t}}}\right)=\frac{2\pi}{ \int\limits_{0}^{2\pi}d\phi\sum\limits_{0}^{\pi}\left(\theta\right)d\theta \,\mathbf{B}\left(\theta,\phi,t_{\text{\tiny{t}}}\right)a_{\text{\tiny{in}}}P _{\text{\tiny{in}}}\left(\cos\theta\right)}{\cos\left(m\phi\right)} \tag{17a}\] \[\mathbf{s}_{\text{\tiny{in}}}\left(t_{\text{\tiny{t}}}\right)=\frac{2\pi}{ \int\limits_{0}^{2\pi}d\phi\sum\limits_{0}^{\pi}\left(\theta\right)d\theta \mathbf{B}\left(\theta,\phi,t_{\text{\tiny{t}}}\right)a_{\text{\tiny{in}}}P _{\text{\tiny{in}}}\left(\cos\theta\right)}{\sin\left(m\phi\right)}. \tag{17b}\]
Figure 13.— Standard error of the mean, \(\sigma_{\text{m}}\) of the averaged magnetic field residuals within each latitude-longitude bin for the May 22, 2010/12:00–May 23, 2010/12:00 (left panels) and May 21, 2015/06:00–May 22, 2015/06:00 quiet intervals (right panels). The standard error value for each component for both quiet periods is indicated by the color scale.
These integrals were evaluated by summing the average \(\delta\mathbf{B}\) in each 9\({}^{\circ}\) by 9\({}^{\circ}\) bin multiplied by the spherical harmonic evaluated at the bin center latitude and longitude and multiplied by the bin solid angle. The integrals are evaluated using a discrete sum which was checked with a unity argument in the integrand which yielded 4\(\pi\) to within 0.1%. The coefficient values are mostly below 10 nT and all below \(\sim\)50 nT, so the errors in the coefficients are typically less than 0.01 nT and all less than 0.05 nT. The convolution also assumes that all of the data are from the same spherical shell, which is not strictly true. The Iridium satellites are in slightly eccentric orbits: The maximum and minimum altitudes differ from the mean by 9 km, a difference in geocentric distance of 0.13%. For the low degree coefficients for which the amplitudes reach 50 nT, this leads to errors not larger than \(\sim\)0.2 nT. For \(l=13\), the maximum error from the spherical shell approximation increases to 1.9% but the coefficients are all below 5 nT so the errors in the results are below 0.1 nT. The bin angular sizes allow for evaluation of coefficients up to degree and order 20, but the time series in the coefficients above degree 13 did not exhibit systematic trends above the noise level in the results over the 5 years analyzed here.
The coefficients given by these convolution integrals are the coefficients of the expansion of the patterns in each component in terms of spherical harmonics and must be distinguished from the conventional Gauss coefficients that are used to express the Earth's field in IGRF, WMM, and other main field models. Neither a radial dependence nor constraints that the coefficients in Equation 17a and 17b correspond to physical solutions for Earth's field are implied. For instance, there is no constraint that the \(\mathbf{c}_{\mathrm{in}}(t_{\mathrm{i}})\) be zero, which allows for identification of spurious signals in the results. The \(\mathbf{c}_{\mathrm{in}}(t_{\mathrm{i}})\) and \(\mathbf{s}_{\mathrm{in}}(t_{\mathrm{i}})\) are a convenient way to represent the patterns for each quiet period and allow us to examine the time variation of the coefficients to identify systematic behavior of different angular and temporal scales. From the time series of the coefficients, artifacts in the data set can be pinpointed and removed from the \(\mathbf{c}_{\mathrm{in}}(t_{\mathrm{i}})\) and \(\mathbf{s}_{\mathrm{in}}(t_{\mathrm{i}})\). Revised maps of field perturbations, from which unphysical artifacts are subtracted can also be reconstructed.
As an example, the time series of \(\mathbf{c}_{\mathrm{in}}(t_{\mathrm{i}})\) and \(\mathbf{s}_{\mathrm{in}}(t_{\mathrm{i}})\) for \(l=2\) over the entire span of the quiet interval data are shown in Figure 14. The figure also shows the \(\mathbf{c}_{\mathrm{in}}\) time series with gray lines and open circles. Because \(\mathbf{c}_{\mathrm{in}}\) corresponds to a magnetic charge it is clearly unphysical and we use the time series of \(\mathbf{c}_{\mathrm{in},20}\) as one indicator of artifacts in the signals. One of the most striking features of the time series are annual and shorter period (\(\sim\)8 months) variations in the coefficient amplitudes, primarily in the \(m=0\) coefficients. The annual signal is most clear in the \(\mathbf{c}_{\mathrm{2,20}}\) (black dots and lines in Figure 14f) (Note that hereinafter we omit the \"\((t_{\mathrm{i}})\)\" for simplicity although the time series is always implied.) The shorter period, 8-months signal, is clearest in \(\mathbf{c}_{\mathrm{2,20}}\) (black dots and lines in Figure 14b). We note that the \(\mathbf{s}_{\mathrm{in}}\) are identically zero by definition. Other non-zero coefficients indicate variations at similar periods, for example \(\mathbf{c}_{\mathrm{2,20}}\), \(s_{\mathrm{-21}}\), \(\mathbf{s}_{\mathrm{-21}}\), and \(\mathbf{c}_{\mathrm{4,22}}\). Other coefficients show very little of these periodicities and exhibit slower trends, indicative of departures from secular variation, for example in \(\mathbf{c}_{\mathrm{2,20}}\), \(s_{\mathrm{-21}}\), \(\mathbf{s}_{\mathrm{-22}}\), \(\mathbf{c}_{\mathrm{4,22}}\), and \(\mathbf{s}_{\mathrm{-22}}\). The amplitudes of the slow variations and of the periodic signals are all on the order of \(\sim\)10-80 nT, down to levels below the magnetometer digitization of 30 nT, consistent with the several nT statistical errors of the means of the average field in each latitude-longitude bin.
The 12-month period suggests a variation in magnetometer response with season, that is, with mean solar exposure around the orbit. The 86\({}^{\circ}\) inclination orbits have an 8-month local time precession period, so that this is the periodicity in the local time of orbital ascending/descending mode. The 8-months period variation in \(\mathbf{c}_{\mathrm{2,20}}\) suggests that there is a bias in the magnetometer response with the solar illumination history around the orbit and this is confirmed by a very similar signal in \(\mathbf{c}_{\mathrm{2,20}}\). A possible contribution to this bias is the temperature calibration for the magnetometers, which was applied in Iridium pre-processing on board the satellites. However, we found no systematic variation of the \(\delta\mathbf{B}_{\mathrm{SC}}\) with magnetometer temperature, consistent with the correct application of this calibration. Nonetheless, a response with the annual and precession periods is evident in many coefficients and might be related to temperature gradients at the magnetometer or other dynamic thermal characteristics of the vehicles. With the data available at this time it is not possible to fully diagnose what causes these signals, but the correlation with the 8-months orbit and 12-months seasonal periods imply that these signals are most likely artifacts, and in an abundance of caution we treat them as such. That artifacts are present in the data was clear as the \(\mathbf{c}_{\mathrm{in},20}\) were not identically zero. Particularly for \(\mathbf{c}_{\mathrm{r,60}}\), the \(\mathbf{c}_{\mathrm{0}}\) have amplitudes and periods comparable to those of Figure 12.
The presence of a monopole signal may seem alarming at first, although one must remember that the convolution approach applies no physical constraints on the coefficients. In fact, the \(l=0\) terms are useful diagnostics. The \(c_{r,n0}\) signals are attributed to offsets in \(\delta B_{s,\mathrm{SC}}\): Since the spacecraft fly maintaining a nadir orientation, the \(r\)-component is always radial and hence an error in the zero level will appear in \(c_{r,n0}\). It is worth noting that the calibration approach which identifies the zero levels from the time series data can give a spurious baseline since the convolution integral of Equation 16 for \(l=0\) is essentially a mean, weighted by the solid angle since \(Y_{\mathrm{o}0}\) is a constant. Hence, the time series analysis for the offsets and \(c_{r,n0}\) are actually different, and this accounts for the residual artifact in \(c_{r,n0}\) arising from time variations in the zero level around the orbit. If the instrument zero levels were constant, the time series offset would be correct and the convolution results would be zero. This information therefore serves as a diagnostic of these orbit variation artifacts.
The \(c_{r,n0}\) and any other signals at \(12\)- or \(8\)-months periods and their harmonics are considered as artifacts and were removed as follows. Great care was used in preparing the time series of the \(\mathbf{e}_{\mathrm{in}}\) and \(\mathbf{s}_{\mathrm{in}}\) for spectral analysis with the objective to notch filter only the frequencies of the orbital period artifacts and then reconstruct the time series without disturbing the slower trends or introducing distortions from windowing. The
Figure 14.— Time series of the spherical harmonic coefficients \(\mathbf{e}_{\mathrm{in}}(t_{0})\) and \(\mathbf{s}_{\mathrm{in}}(t_{0})\) for \(l=2\). Top panel (a) shows the total power in nT\({}^{3}\) summed over \(m=0,1\), and \(2\) for all components (black), \(r\) only (magenta), \(\theta\) only (turquoise), and \(\phi\) only (gray). The bottom six panels show in order from top: \(c_{\mathrm{in}}\), \(c_{\mathrm{in}}\) (b and c), \(c_{\mathrm{in}}\), \(c_{\mathrm{in}}\), \(c_{\mathrm{in}}\) (d and e), and \(c_{\mathrm{in}}\), \(c_{\mathrm{in}}\) (f and g). The color coding in the bottom six panels are black for \(m=0\), dark red for \(m=1\), and lighter red for \(m=2\). Panel 2 also shows the \(l=0\) cosine coefficient, \(c_{\mathrm{in}}\) in gray, which is an unphysical.
first step was to detrend the time series by fitting them with a fifth order polynomial fit and then subtracting this fit. This same fit was added back in to preserve these non-periodic trends after removing the periodic signal artifacts. The second step was to construct longer time series from the detrended \(\mathbf{c}_{\text{in}}\) and \(\mathbf{s}_{\text{in}}\) by reflecting the original time series about the first and last time sample. We denote the span of the original time series as \(T_{\text{attr}}\). This yielded a pseudo time series that is three times longer than the original but which could be windowed, notch filtered, and inverted back to a time series without applying any windowing distortion to the original time series in the center third of the new pseudo time series. The mirroring ensures that the extension of the original time series did not introduce discontinuities that would have generated artificial harmonic series in the Fourier transforms. An example of this mirrored pseudo time series is shown in the top red trace of Figure 15, for \(c_{\text{,20}}\).
The first step in the Fourier analysis was the application of the fast Fourier transform (FFT) window shown by the gray trace in the top of Figure 15. The ends of the window are half-cosines extending \(0.8T_{\text{data}}\) from the ends. The center of the window is constant at \(1\) from \(-0.2T_{\text{data}}\) to \(1.2T_{\text{data}}\). The data multiplied by this window function are shown by the blue trace in Figure 15. This windowed time series was then converted into a continuous, evenly sampled time series by interpolating to a 3-h spaced time series, corresponding to the smallest time increment in the original quiet interval selection (cf. Section 4 above). The resulting windowed and oversampled data was then transformed using an FFT. To produce the \"notch\" filter, the Fourier coefficients nearest the 12-months and 8-months periods and their harmonics (up to the sixth harmonic), along with one frequency bin above and below those nearest bins, were set to zero. The notched transform was then inverted to obtain the filtered residual signal shown by the light green trace in Figure 15. The fraction of frequency bins notched in this way was less than 10% of the number of frequencies, so that the fraction of true signal removed was not larger than 10% even though the contamination signal is much larger than this. In addition, the notched Fourier coefficients were extracted and transformed to the time domain to construct a time series of this artifact signal. The thick, black trace labeled \"Notch filt.\" in Figure 15 shows the time series of the signal that was removed. The signal in the \(c_{\text{,20}}\) at the 8- and 12-months periods and harmonics is a large fraction of the original signal, but for the majority of the \(\mathbf{c}_{\text{in}}\) and \(\mathbf{s}_{\text{in}}\) the notch filtered signal is much smaller.
Figure 15.— Correction analysis sequence for \(c_{\text{,20}}\). Vertical gray lines indicate the time span of the original input data (i.e., 0–2,190 days from January 1, 2010). From top to bottom the traces show: detrended and mirrored time series (red, “Input \(c_{\text{in}}\)”) together with the custom time window function (gray, “FFT Window”); windowed extended time series data (blue, “Windowed”) and notch filter signal (black, “Notch filt.”); time series with notch filtering applied, i.e., the residual between the blue and black traces (light green, “Filter residual”) and the linear correlation with the \(c_{\text{,00}}\) time series where \(k\) is the slope fit coefficient (orange, “\(k\times\) filtered \(c_{\text{in}}\)”); net correction for the input time series (thin black line, “Net correction”); and the net signal with identified artifacts removed (dark green, “Corrected \(c_{\text{in}}\)”).
After notch filtering to remove artifacts related to orbital dynamics, the filtered residual \(\mathbf{c}_{in}\) and \(\mathbf{s}_{in}\) were compared to the filtered residual \(c_{r,no}\). To do this comparison, the same filtering process was first applied to the \(c_{r,no}\), and where the residual signals in the filtered \(c_{r,no}\) were considered to be erroneous as well. We then evaluated and subtracted from the filtered \(\mathbf{c}_{in}\) and \(\mathbf{s}_{in}\) the linear correlation between the filtered \(c_{r,no}\) and the filtered \(\mathbf{c}_{in}\) and \(\mathbf{s}_{in}\) where the slope of the linear fit is denoted by \"\(k\)\" in Figure 15. This subtracted signal for \(c_{r,no}\) is shown by the orange trace overlaid on the light green filter residual signal in Figure 15. This resulting signal shows that a substantial fraction even of the filtered signal in this case was highly correlated with the filtered \(c_{r,no}\). The total correction, arising from the sum of the notch filter signal with the correlated \(\mathbf{c}_{r,no}\) signal, is shown by the thin black trace Figure 15, labeled \"Net correction\". The final corrected time series of \(c_{r,no}\) with this correction subtracted is shown in the bottom dark green trace, labeled as \"Corrected \(\mathbf{c}_{r,no}\)\".
The corrected \(\mathbf{c}_{in}\) and \(\mathbf{s}_{in}\) resampled at the dates of the original data and to which the long-term trends have been added back in (removed before frequency analysis and notch filtering), are denoted by a prime as \(\mathbf{c}_{in}\)\" and \(\mathbf{s}_{in}\)\". The \(\mathbf{c}_{in}\)\" and \(\mathbf{s}_{in}\)\" for \(l=2\) are shown in Figure 16 using the same format as Figure 14. The most prominent features of these corrected time series are now the slow trends evident in the power (Figure 16a), with the largest slow variation in \(s_{r,2}\)\", and also present in most of the coefficient time series. The noisiest
Figure 16: Time series of the filtered spherical harmonic coefficients \(\mathbf{c}_{in}\)/(\(t\)) and \(\mathbf{s}_{in}\)/(\(t\)) for \(l=2\) after applying the notch and \(c_{r,no}\) correlation corrections, in the same format as Figure 14.
time series are \(c_{\text{Lo},z^{\prime}}\) and \(s_{\text{Lo},z^{\prime}}\) which exhibit \(\sim\)40 and \(\sim\)20 nT peak-to-peak variations, respectively, between just a few samples. These variations are likely spurious but not corrected with the process implemented, as these signals did not display any clear periodicities and so were not clearly attributable to any particular source. The other time series have peak-to-peak noise levels of between 5 and 20 nT which we consider the limit of the present Iridium Block 1 data and the processing described here. The long-term trends appear to be well resolved and the rapid variations between successive quiet periods could be mitigated with modest low pass filtering to resolve variations on time scales as short as 1 or 2 months.
To assess how much artifact signals contribute to the patterns of the \(\mathbf{\delta}\mathbf{\text{B}}\) shown in Figures 7-10, we used the \(\mathbf{c}_{\text{in}^{\prime}}\) and \(\mathbf{s}_{\text{in}^{\prime}}\) up through \(l=13\) to reconstruct the \(\mathbf{\delta}\mathbf{\text{B}}\) maps. The results of the reconstructed \(\mathbf{\delta}\mathbf{\text{B}}\) maps from the \(\mathbf{c}_{\text{in}}\) and \(\mathbf{s}_{\text{in}^{\prime}}\) before artifact correction, are shown in the left hand columns of Figures 17 and 18 for May 23, 2010/21:00-May 24, 2010/21:00 and November 21, 2015/06:00-November 22, 2015/06:00, respectively. The reconstructed \(\mathbf{\delta}\mathbf{\text{B}}\) maps agree very closely with the maps of the binned averages (Figure 9 right hand column and Figure 10 left hand column). The reconstructed \(\mathbf{\delta}\mathbf{\text{B}}\) maps from the \(\mathbf{c}_{\text{in}^{\prime}}\) and \(\mathbf{s}_{\text{in}^{\prime}}\), after artifact correction, are shown in the center columns of Figures 17 and 18. In both cases, the filtered coefficient results retain the patterns in the original binned data with relatively small changes. For example, for the May 23-24, 2010 case near 10\({}^{\circ}\)N-30\({}^{\circ}\)N latitude there is a positive \(\delta_{R}\) signal across all longitudes which is not discernible in the filtered map. Thus, the obvious periodicities in some of the \(\mathbf{c}_{\text{in}}\) and \(\mathbf{s}_{\text{in}^{\prime}}\) were not significant contributors to the original coherence in the geographically registered residuals relative to IGRF-11.
To check whether the Iridium results are consistent with independent models, we subtracted the IGRF-11 model from the CHAOS 7.4 model ([PERSON] et al., 2020; [[https://doi.org/10.5281/zenodo.352398](https://doi.org/10.5281/zenodo.352398)]([https://doi.org/10.5281/zenodo.352398](https://doi.org/10.5281/zenodo.352398))), both at 780 km altitude. These results are shown in the right hand columns of Figures 17 and 18. Considering the
Figure 17.— Magnetic field residuals relative to International Geomagnetic Reference Field (IGRF-11) reconstructed from the spherical harmonic coefficient time series and of the CHAOS 7.4 model relative to IGRF-11 versus geographic latitude and longitude for the quiet period of May 23, 2010/21:00 UT to May 24, 2010/21:00 UT. The columns show the original spherical harmonic fit on the left, the filtered spherical harmonic results in the center, and the residual of CHAOS 7.4 relative to IGRF-11 on the right. From top to bottom the rows show maps for the \(\mathbf{\delta}\mathbf{\text{B}}_{R}\), \(\mathbf{\delta}\mathbf{\text{B}}_{\text{in}}\) and \(\mathbf{\delta}\mathbf{\text{B}}_{\text{in}}\) magnetic field components.
November 2015 case first, all three components of the field have similar patterns in the Iridium and CHAOS 7.4 residuals. The linear regression coefficient for \(\delta B\), between the corrected Iridium and CHAOS 7.4 residuals is 0.82. The standard deviations of the Iridium residuals are 52, 31, and 36 nT for \(r,\delta\), and \(\phi\), respectively, while for the CHAOS 7.4 residuals the standard deviations are 59, 36, and 40 nT, for \(r,\delta\), and \(\phi\), respectively. For May 2010, the correspondence between the corrected Iridium residuals and the CHAOS 7.4 residuals is not as strong. The linear regression coefficient for \(\delta B\), is lower, 0.41, and the standard deviations in \(\delta\)B are also different: for the corrected Iridium residuals they are 34, 24, and 19 nT, for \(r,\delta\), and \(\phi\), respectively, whereas for the CHAOS 7.4 residuals they are 17, 11, and 10 nT, \(r,\delta\), and \(\phi\), respectively. To compare the change from May 2010 to November 2015 we took the difference in residuals, the November 2015 residuals minus those from May 2010. The statistics of the changes in \(\delta\)B residuals are similar, with standard deviations in \(r,\delta\), and \(\phi\), respectively, of 43, 29, and 33 nT from Iridium and 46, 27, and 32 nT for CHAOS 7.4. The Iridium and CHAOS 7.4 changes in \(\delta\)B are well correlated with linear regression coefficients of 0.89, 0.48, and 0.78 for \(r,\delta\), and \(\phi\), respectively. The standard deviations in the Iridium residuals minus the CHAOS 7.4 residuals are 21, 29, and 22 nT, in \(r,\delta\), and \(\phi\), respectively. Over the 5.5-year baseline, this suggests that the annual variations agree on average to \(\sim\)5 nT/yr at the 1-sigma level.
To compare the evolution of residual patterns over the 6-year interval analyzed, Figure 19 shows maps of the \(\delta B_{\rm s}\) corresponding to the top center and right panels of Figures 17 and 18, for six dates close to August 1 separated by one year. The correlation between the \(\delta B_{\rm s}\) patterns is generally high and increases over time although there are some systematic differences. Both Iridium and CHAOS have prominent positive \(\delta B_{\rm s}\) features near \(-60^{\circ}\) lon. near the equator and near \(+60^{\circ}\) lon. and \(-45^{\circ}\) lat., although this feature is not initially as strong in the CHAOS-derived maps as in the Iridium residuals. These two positive \(\delta B_{\rm s}\) features are separated by a band of negative \(\delta B_{\rm s}\) extending from \(-20^{\circ}\) lon. to \(-60^{\circ}\) lat. to the equator and \(0^{\circ}\)lon. in the CHAOS maps for all years, but they are nearly contiguous positive \(\delta B_{\rm s}\) regions in the Iridium results until 2014. Both patterns show the development of a positive \(\delta B_{\rm s}\) feature between \(-180^{\circ}\) and \(-120^{\circ}\) lon. between \(50^{\circ}\) and
Figure 18.— Magnetic field residuals relative to International Geomagnetic Reference Field (IGRF-11) reconstructed from the spherical harmonic coefficient time series and of CHAOS 7.4 for November 21, 2015/06:00 UT to November 22, 2015/06:00 UT in the same format as Figure 17.
80\({}^{\circ}\) lat., although it is a bit narrower in latitude in the Iridium results. This feature is present in all of the CHAOS maps but not initially in the Iridium results. The prominent negative \(\delta B\), feature near 100\({}^{\circ}\) lon. and extending between \(-\)20\({}^{\circ}\) and \(+\)45\({}^{\circ}\) lat. develops in both sets of residuals. Initially, the Iridium results have a double peaked \(\delta B_{t}\) feature centered near 145\({}^{\circ}\) lon. between the equator and 70\({}^{\circ}\) lat. which is not present in the CHAOS residuals but by August 2014 this feature in the Iridium patterns has merged with the positive \(\delta B_{t}\) region at more southern latitudes to form a shape similar to the CHAOS residuals in the southeastern positive \(\delta B_{t}\) feature. The results for \(\delta B_{b}\) and \(\delta B_{b}\) are presented in Figures S1 and S2 in the supporting information and exhibit essentially the same high degree of correspondence.
## 7 Discussion and Conclusions
Analysis of magnetometer data from the Iridium Communications Block 1 satellites revealed coherent signatures and distributions in the departures of the calibrated observations relative to the IGRF-11 model when registered in geographic coordinates. Although there are substantial standard deviations (up to \(\sim\)80 nT) in the localized latitude-longitude ranges used for the field mapping analysis (9\({}^{\circ}\) latitude by 9\({}^{\circ}\) longitude solid angle bins), the values are consistent with uncertainties in the Iridium Block 1 attitude determination system. The magnetic field residuals form Gaussian distributions consistent with a random error in the data. The large number of measurements in each solid angle bin afforded by the constellation in one day (\(\sim\)350 independent measurements) therefore imply standard errors in the mean of 2-4 nT, possibly low enough to yield information about Earth's main magnetic field. This level of sensitivity is sufficient for detecting secular variations and geomagnetic jerks related to variations in the magnetic field at the Earth's
Figure 19: Maps of the radial component magnetic residuals, \(\delta B_{t}\), relative to International Geomagnetic Reference Field (IGRF-11) from the filtered spherical harmonic coefficient time series and of CHAOS 7.4 minus IGRF-11 for six different quiet days, one for each year from 2010 to 2015. Dates were chosen to be close to 1 August of each year so the interval between successive maps is approximately 1 year. The Iridium results are shown in the first and third columns (”Filtered SH-Fit”) and the CHAOS 7.4 results in the second and fourth columns (\"CHAO5.7.4 - IGRF 11\"). The Iridium and CHAOS 7.4 results are shown side-by side for each date in columns one and two for July 19, 2010, August 2, 2011, and July 31, 2012, and in columns three and four for July 21, 2013, August 10, 2014, and July 19, 2015. Corresponding figures for the polar and azimuthal components, \(\delta B_{t}\) and \(\delta B_{b}\) are provided in the supporting information.
core-mantle boundary. The Iridium Block 1 constellation data therefore offer the promise of revealing the global behavior of Earth's field on time scales shorter than ever before resolved.
The global coverage allows a tight constraint on geomagnetically quiet periods, yielding 260 very quiet 24-h intervals from the full data set used for this study, spanning from January 2010 to November 2015. To study the time behavior of the magnetic field patterns, the patterns from the quiet data set were convolved with spherical harmonic orthogonal functions to directly calculate the cosine and sine harmonic function coefficients. The time series of these coefficients were then used to assess the time dependence of each component of the signal. This revealed both gradual variations in the field, indicative of a discrepancy in the predicted and actual secular variation of the field as well as a gradual acceleration of the field relative to a secular variation, and shorter period variations matching annual and orbit local time precession periods. The precession and seasonal signals are attributed to artifacts in the magnetic field data arising from thermal gradients or other unidentified magnetic contaminations. Fourier analysis of the spherical harmonic coefficients allowed quantification and removal of these signals, as well as identification of components proportional to unphysical magnetic signals (i.e., the monopole term in the harmonic expansion). After removal of all of these artifacts, the patterns in the magnetic maps retained the basic features initially found in the original, registered data, indicating that these basic patterns are not readily associated with artificial signals. Because of the global nature of the observations, it is difficult to attribute the persistent geographically fixed patterns to external current systems.
The resultant reconstructed maps of perturbations over the 260 quiet intervals are a potential resource for study of the dynamics of Earth's magnetic field. The series of maps are essentially time series of magnetic field residuals at 800 virtual geomagnetic observatories (cf. [PERSON] & [PERSON], 2006; [PERSON] & [PERSON], 2007) albeit at an irregularly spaced set of quiet days. These time series represent what we consider to be the best data product of the Block 1 Iridium magnetic field data for core field science. There are various potential values of this novel data product. First, it is an independent estimation of Earth's field that does not use the regularization techniques employed in other studies. Second, it provides global maps of the field on much shorter time scales than previously possible. Third, it can augment standard techniques for co-estimating the field as an additional regularization constraint, thereby potentially enhancing standard techniques for deriving the changes in Earth's core field.
There are of course limitations with this data set owing to the fact that the Iridium Block 1 instrumentation and spacecraft were never designed for high-precision science applications. Very importantly, the approach as described here does not provide an estimate of the field intensity but yields only the shape of the field relative to the mean intensity of the model field used for the calibration step in the analysis. A coestimation analysis might potentially overcome this limitation, but the stability of the magnetometer calibration is a major challenge as the magnetometers are not thermally stable or precisely calibrated instruments. Moreover, on-board calibrations were changed throughout the lifetime of the Block 1 satellites to update operational performance, but these calibration records are not complete. The corrections applied in this analysis subsume these calibration updates and do not provide a record of calibration stability. Additionally, artifact analysis performed in this study suggests that orbit variations in the temperature and/or thermal environment remained after the application of the pre-flight temperature calibration. However, analysis of the residual correlation with temperature indicated that there was no remaining signature of temperature dependence, and so the thermal environment behavior possibly contributing to artifacts in the data set may be due to some other effect such as a temperature gradient. As seen in comparisons between the original, binned magnetic field residuals and the corrected, reconstructed residuals, the consistency of the patterns, independent of the set of satellites in different local times, points to a real, natural source for the coherency in the patterns rather than artifacts in the analysis.
Even with these substantial limitations in mind, the global nature of the observations and persistent consistency of the patterns suggest that future analyses with these data may prove valuable. First, the residual maps derived here can be compared against other main field estimates such as WMM, IGRF-2015, or CHAOS-7 and later generations of the CHAOS model. Comparison of the residuals from these models vis-a-vis IGRF-11 may provide insight into whether the present derived data products afford new useful information. Independent of these comparisons, the short cadence and global coverage of the data product lends itself naturally to the study of the more rapid variations of the core-generated field, such as geomagnetic jerks.
The data set is particularly attractive for this application as it provides the first opportunity to characterize the global distribution of jerk signals to assess their temporal and spatial signatures independently.
Iridium NEXT data being collected for the continuation of the AMPERE data set are presently in the calibration development phase, but the higher precision of the attitude sensors on the NEXT satellites suggest that the uncertainty due to attitude knowledge errors may be substantially lower. An assessment of the Iridium NEXT data for potential application to the continued study of the geomagnetic field is therefore future work that may be of great utility.
## Data Availability Statement
The data and data products used for this study are posted via the AMPERE facility server via [[http://ampere.jhuapl.edu](http://ampere.jhuapl.edu)]([http://ampere.jhuapl.edu](http://ampere.jhuapl.edu)) and include the Iridium residuals relative to IGRF-11 as well as the vector magnetic residuals corresponding to the 800 virtual geomagnetic observatories for each of the 260 24-h quiet intervals generated for the study.
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* [PERSON] and [PERSON] (2017) [PERSON], & [PERSON] [PERSON] (2017). Sq and EBJ-A review on the daily variation of the geomagnetic field caused by ionospheric dynamo currents. _Space Science Reviews_, 206, 299-405. [[https://doi.org/10.1007/s11214-016-0282-z](https://doi.org/10.1007/s11214-016-0282-z)]([https://doi.org/10.1007/s11214-016-0282-z](https://doi.org/10.1007/s11214-016-0282-z)) | wiley | Iridium Communications Satellite Constellation Data for Study of Earth's Magnetic Field | Brian J. Anderson, Regupathi Angappan, Ankit Barik, Sarah K. Vines, Sabine Stanley, Pietro N. Bernasconi, Haje Korth, Robin J. Barnes | https://doi.org/10.1029/2020gc009515 | 2,021 | CC-BY |
wiley/fac5306c_54c1_46e6_9d58_1450451fe7ca.md | # Geophysical Research Letters+
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly cited.
Footnote †: This is an open access article under the terms of the Creative Commons Attribution Attribution License, which permits, distribution and reproduction in any medium, provided the original work is properly.
## 2 Data Sets
We combined multiple remote sensing methods, including satellite altimetry, optical sensors, and meteorological satellite products. Additionally, we utilized in situ data, such as water level and precipitation gauges. These complementary data sets provide spatially dense measurements and continuous time series, offering a robust and reliable approach to flood monitoring and management of the Porto Alegre metropolitan region. To assess the impact of the flood, we also incorporated socioeconomic indicators, including the social vulnerability index, the total population count, and the vulnerable population by human development zone (Defined by the Brazilian institute for applied economic research, IPEA in portuguese, as geographic regions delineated based on key socio-economic indicators, such as income levels, access to education, and healthcare outcomes).
We used the Sentinel-2 and SWOT data sets for flood extension and volume analysis. Specifically, we used Sentinel-2 data (European Space Agency, 2021) from Bands B2 (blue), B3 (green), B4 (red), and the Scene Classification Map (SCL). The spatial resolution of 10 m for the Bands and 20 m for the SCL. High-density pixel cloud data from the SWOT mission (SWOT, 2024) were accessed via _EarthAccess_ Python package ([PERSON] et al., 2024). For the SWOT data, we retained only pixels with a water fraction above 0.1 that were classified as open water, water near land, or dark water.
SWOT pixel cloud data are already corrected for instrument calibrations and signal propagation delays due to the ionosphere and the dry and wet components of the troposphere, as well as crossover calibration (JPL, 2024). We additionally subtracted model-based estimates of tides (solid Earth, load, and pole), as well as the geoid, to provide a baseline for interpreting water height data.
The water level and precipitation data sets from HIDROWEB, a tool provided by Brazil's National Water Agency, were also analyzed for two gauge stations in the study area: _Cais Maud C6_ and _Terminal CATSUL Guaiba_(Agencia Nacional de Aguas, 2024). These in situ measurements provided valuable information on temporal water level variations and were used to verify the accuracy of the SWOT water level data for that event.
We also incorporated the OPERA Land Surface Disturbance Alert from the Harmonized Landsat Sentinel-2 (HLS) Version 1 data set to assess vegetation disturbances in the Porto Alegre metropolitan region. This data set, accessed through the _EarthAccess_ Python package ([PERSON] et al., 2024), provides vegetation disturbance alerts with a 30-m spatial resolution. By analyzing the vegetation disturbance index, we identified areas where vegetation cover decreased, which is crucial to understanding the impacts of the flood on local crops and ecosystems.
To analyze the terrain characteristics of the study area and estimate anomalies in water depth in combination with SWOT measurements, we utilized the Forest And Buildings removed Copernicus Digital Elevation Model (FABDEM). The FABDEM is a global elevation map that removes building and tree height biases from the Copernicus GLO 30 Digital Elevation Model ([PERSON] et al., 2024). The data is available at one arc-second grid spacing (approximately 30 m at the equator).
For large-scale atmospheric analysis, we used the half-degree hourly global _reanalysis_ Modern-Era Retrospective analysis for Research and Applications 2 (MERRA-2, Global Modeling and Assimilation Office, 2015), including air temperature, total precipitable water vapor and geopotential height at 500 hPa. Additionally, half-hourly precipitation data at 0.1-degree resolution from the Integrated Multi-satellite Retrievals for Global Precipitation Measurements (IMERG) data set ([PERSON] et al., 2019) were utilized. Sentinel-2, MERRA-2, FABDEM, and IMERG data were processed and accessed via Google Earth Engine using the _geemap_ Python package ([PERSON], 2020).
For our analysis of extreme events, we obtained precipitation data from the Meteorological Database (BDMEP), which is maintained by the Brazilian National Institute of Meteorology (INMET) and can be accessed at [[https://bdmep.inmet.gov.br/](https://bdmep.inmet.gov.br/)]([https://bdmep.inmet.gov.br/](https://bdmep.inmet.gov.br/)). We specifically selected precipitation records from both conventional and automatic meteorological stations in the state of Rio Grande do Sul. Additionally, we utilized the ENSO 3.4 monthly index, obtained from the NOAA Physical Sciences Laboratory (PSL) at [[https://psl.noaa.gov/data/correlation/nina34](https://psl.noaa.gov/data/correlation/nina34)]([https://psl.noaa.gov/data/correlation/nina34](https://psl.noaa.gov/data/correlation/nina34)). anom.data, to examine potential climatic influences on this extensive flood.
Furthermore, we estimated the extent of the floods by combining the SCL water classification data with a shapefile of an interactive map developed by the Institute of Hydraulic Research (IPH) of the Federal University of Rio Grande do Sul (UFRGS) (Instituto de Pesquisas Hidraulicas, 2024). This map was previously evaluated against field survey data as reported in a technical note published by IPH ([PERSON] et al., 2024). Finally, socio-economic indicators were sourced from the Social Vulnerability Atlas provided by the Institute of Applied Economic Research (Instituto de Pesquisa Economica Aplicada, 2024). The social vulnerability index considers factors such as urban infrastructure, human capital, and income.
## 3 Large-Scale Atmospheric Conditions
A combination of rare atmospheric conditions drove this unprecedented flood event. Central and southeastern Brazil endured an intense heat wave, with temperatures exceeding the median by over 6\({}^{\circ}\)C for April and May (Figure 0(a)). The extreme temperatures persisted for 10 days above the top 10% of historical records (24 April to 5 May). This event was accompanied by a notable negative anomaly in precipitable water vapor, with levels falling below 10 kg m\({}^{-2}\) in the southeastern and parts of northeast Brazil, falling below the 20 th percentile for the same period (Figure 0(b)). Adding to these factors is the South American Low-Level Jet (SALLJ, [PERSON] et al., 2004), which acts as a robust moisture corridor, transporting significant amounts of water vapor from the Amazon region to the south of Brazil (Figure 0(b)).
A negative temperature anomaly south of the study region indicated the northeastward propagation of an atmospheric cold front. This front may have been blocked by the air mass of the prevailing heat wave, leading to intense and localized precipitation in southern Brazil (Figure 1d). The average precipitation levels were around 3 mm h\({}^{-1}\), exceeding the 90 th percentile for April and May.
We adopted a methodology based on [PERSON] et al. (2019) to investigate the potential presence of atmospheric blocking. This approach accounts for the effect of planetary vorticity by scaling the anomalous geopotential height at 500 hPa with a latitude-dependent factor, \(\frac{\sin(\mathrm{G}^{2})}{\sin(\mathrm{dust})}\), and identifying periods where the adjusted value exceeds 100 m for more than 10 consecutive days ([PERSON], 1983). To reduce the influence of short-term variability, we applied this method to a 5-day running-averaged time series, which detected a persistent blocking event during the May 2024 flood (red polygon in Figure 1c.) We also tested the method's sensitivity and found that the blocking pattern remained consistent across running averages ranging from 3 to 27 days.
The analysis of daily atmospheric snapshots, as illustrated in Figure 1, underscores the persistence of the features described in this study (For more details, refer to the video in the Supporting Information S1). In particular, the observed atmospheric blocking pattern, dominated by a high-pressure system, closely resembles the phenomenon documented by [PERSON] et al. (2019), which is generated by a stationary Rossby wave triggered by the Madden-Julian Oscillation (MJO). Such blocking events are generally associated with extreme drought conditions in some locations and heavy precipitation in others, and they contribute to approximately 60% of marine heatwaves in the region. In the current case, the blocking shifted northward, positioned near the edge of the South American Low-Level Jet. This shift facilitated the transport of substantial precipitable water vapor to the study area, resulting in extreme drought and a heatwave in central Brazil, as well as intense, localized rainfall in southern Brazil.
The Climate Prediction Center's report for MJO conditions in May 2024 further underscores the role of the MJO in shaping these atmospheric conditions (Climate Prediction Center, 2024). According to the report, the RMM
Figure 1: (a) 10-m air temperature anomaly, (b) precipitable water vapor anomaly, (c) anomalous height at 500 hPa and winds, and (d) mean precipitation. The anomalies are relative to the median for Apr and May. (a–c) MERRA-2 reanalysis data; (d) IMERG satellite product data. The Brazilian state of Rio Grande do Sul is highlighted in yellow. The gray arrow in panel represents the South American Low Level Jet (SALLL). The red polygon in panel depicts the region of atmospheric blocking. Diagonal hatching indicates values above the 90 th percentile, and cross-hatching indicates values below the 20 th percentile. Values are averaged over the time range of the event (26 April to 6 May 2024). Percentiles are computed for each grid point for April and May across the entire 40-year time range of MERRA-2 data and the 24-year time range of IMERG data.
based (Principal Components) MJO index showed a notable increase in amplitude around 26 April, indicating a strengthened MJO over the Indian Ocean, which subsequently propagated eastward toward the Maritime Continent through early May. During this phase, strong upper-level anticyclonic flow was observed across South America, contributing to the atmospheric blocking that stalled the cold front, which was responsible for intense rainfall over southern Brazil. Notably, the MJO's position tends to shift northward from early April to late May as it transitions into a boreal summer pattern ([PERSON] & [PERSON], 2004). The northward shift could explain the differing outcomes compared to those observed by [PERSON] et al. (2019) for the austral summer.
## 4 Extreme Events and Contributing Factors
Between the 67 meteorological stations distributed throughout Rio Grande do Sul state, the average total precipitation from 27 April to 6 May 2024, was 304 mm (Figure 2a), above the 90% range of historical extreme events of the region. In some regions, the total rainfall exceeded 650 mm, particularly in the municipalities of _Bento Goncalves_ and _Soledade_ (the two dark circles in Figure 2a). Satellite-based IMERG data effectively captures this anomalous precipitation pattern, closely reflecting the observations from meteorological stations and reaffirming its value in tracking extreme rainfall events across the region.
To contextualize this event within the historical record, we analyzed daily precipitation data for each station, focusing on extreme events that lasted more than 3 consecutive days. For each event, we calculated the total accumulated precipitation and the duration in days. Our analysis of historical extreme events is conducted using data aggregated from all stations distributed throughout the state of Rio Grande do Sul, which mitigates the impact of data quality issues that may exist for individual stations in the INMET operational weather network. The median total rainfall for all extreme events since 1960 was approximately 100 mm, with a typical 10%-90% range of 50-188 mm (Figure 2b). Although rare, events with total precipitation exceeding 250 mm (the 98 th percentile) were identified, though none exceeded 380 mm. The May 2024 event stands out as an extreme outlier in the historical record, with more than five meteorological stations reporting rainfall exceeding 380 mm.
This 9-day event contributed approximately 20% (with a range of 5%-40%) of the median total annual precipitation, underscoring the exceptional nature of the event. During such a short period, the unusually high accumulation increased the risk of flooding and other hydrological hazards in affected areas. Our analysis revealed that
Figure 2: (a) Map of Rio Grande do Sul state (yellow line) showing accumulated precipitation (in mm) across 67 INMET meteorological stations (diamonds) and IMERG (filled contours) between 27 April and 6 May 2024. The red square depicts the metropolitan region of Porto Alegre. (b) Time series of total rainfall for events lasting more than 3 days at the stations over time, with the red line indicating the 6-month median of total rainfall. Gray shading represents the 10%-90% spread of the data, and black dots represent extreme events (>250 mm, approximately the 95 th percentile). ENSO 3.2 index is plotted in the right \(y\)-axis.
98% of the extreme events registered since 1960 lasted less than 7 days, emphasizing the rarity of prolonged rainfall in this region. Only three events, including the one in May 2024, persisted for more than 8 days. The other two previous events occurred in January 2019 and June 1972, which are confirmed through records from FloodList ([PERSON], 2019) and historic newspapers (Jornal do Brasil, 1972).
Approximately 45% of the extreme rain events occurred during the late autumn and early winter (April to July), while 43% occurred between September and December. [PERSON] et al. (2019) reported that the majority of floods in this region tend to occur during the winter months (defined in their study as July-August-September). This suggests that factors beyond seasonal precipitation patterns may play a significant role in driving extreme flood events. These factors likely include previous hydrologic and land-use conditions, as well as specific storm characteristics, such as storm geometry, spatial extent, and intensity. Moreover, extreme flooding events are often influenced by a combination of variables and do not necessarily correlate directly with extreme rainfall alone ([PERSON] et al., 2018).
While the El Nino-Southern Oscillation (ENSO) is primarily a Pacific phenomenon, its influence extends to the Atlantic, where warmer sea surface temperatures (SSTs) can shape large-scale atmospheric conditions ([PERSON], 2006). In southern Brazil, extreme precipitation events tend to cluster during El Nino years, suggesting a potential long-term link between ENSO and such occurrences. An analysis of historical data indicates that 67% of extreme events since 1960 occurred during El Nino years, while only 17% occurred during La Nina years. This finding suggests that El Nino creates more favorable conditions for extreme precipitation in the region.
To further investigate this relationship, we constructed monthly precipitation composites for different ENSO phases, incorporating data from all meteorological stations (Figure 2c). La Nina events are generally associated with weak negative precipitation anomalies, typically less than 50 mm per month (Figure 2c). In contrast, El Nino events have a more pronounced impact, with positive anomalies often exceeding 50 mm when the ENSO 3.4 index surpasses 1.0. During intense El Nino events, characterized by an ENSO 3.4 index exceeding 2.0, monthly precipitation anomalies can reach up to 100 mm, particularly from October to December. The composite analysis clearly highlights that El Nino increases the likelihood of rain events.
In summary, the May 2024 flood appears to have resulted from a unique convergence of factors. While El Nino conditions tend to increase the amount of rainfall throughout the year, the synoptic conditions associated with the MJO contributed to atmospheric blocking and elevated local temperatures that delayed the progression of the cold front. Future studies should explore whether combined signals from the MJO and ENSO could enhance predictive capabilities for flood-prone regions in southern Brazil.
## 5 Flood Extent and Volume
Understanding the spatial extent and volume of floodwaters is critical for assessing the impact on both natural and human-modified landscapes. To capture conditions before the flood event, we calculated the median of all Sentinel-2 images taken between 1 March and 15 April 2024, with less than 5% cloud cover. This pre-event composite provides a clear baseline of the region's typical (austral summer and fall) conditions. For the flood event, a single Sentinel-2 image from 6 May 2024, was used to assess the extent and impact of the flooding.
The comparison between the pre- and post-flood conditions vividly illustrates the extensive flooding and the subsequent deposition of sediments within the region (Figures 3a and 3b). In the pre-flood image, water bodies are contained within their usual channels, as depicted by the blue lines. However, the post-flood image shows a dramatic change, with large areas inundated and marked by an orange hue, likely indicating a high sediment load carried by the floodwaters. This dispersal of sediments is particularly evident in regions adjacent to river systems, where floodwater has overflowed. The scale bar highlights that the flood's effects extended over several kilometers from the river basin, transforming not only previously green and vegetated areas but also urban zones and croplands into sediment-laden floodplanes. The red outlines help delineate the flood's extent, underscoring the widespread impact. In the short term, the accumulation of sediment in these areas can lead to increased siltation, which can clog waterways, affect navigation, and damage infrastructure ([PERSON], 2010; [PERSON] and [PERSON], 2020; [PERSON] et al., 2023). In addition, altered flow patterns can impact aquatic habitats, leading to changes in species distribution and water quality. The heavy sediment load can also strain water treatment facilities and complicate flood response efforts.
Although these true-color composites provide a clear two-dimensional view of the flood extent, they lack depth information. The latter could be crucial for inferring the water volume, a key parameter for engineering assessments and flood management. To investigate the water depth anomaly, we employed a straightforward but robust methodology with the potential for refinement in future research. We first compared SWOT water-level measurements against two gauge stations within the study area (Figure 3c). The time series from the gauge stations reveal the floods rapid intensification, with water levels surging from a pre-flood baseline of 1 m to over 4 m within days. The northernmost station (CAIS MAUA C6) recorded even higher peaks (5 m), demonstrating the expected upstream gradient in such severe floods. We then computed median SWOT values within a 30-m radius of each station and adjusted the SWOT reference level to match the gauges by subtracting the small 28 cm average offset. The resulting SWOT time series closely mirrored the in situ observations, exhibiting the same pattern of rise of the water level with an average error of only 20 cm and 98% of the Pearson correlation coefficient. This underscores the precision of SWOT measurements in assessing flood events of this magnitude.
Figure 3: (a) Pre-flood Sentinel-2 true color composite showing typical water distribution near Porto Alegre, Brazil (15 April 2024). (b) Post-flood Sentinel-2 composite (6 May 2024) showing extensive flooding. Orange areas indicate inundation with significant sediment deposition near rivers. (c) Water level time series at two gauge stations (_CAIS MAUA C6_ and _TERINICAL CATSUL GU/BA_) illustrating the rapid rise in water levels. Stars represent median SWOT water levels: thick stars denote pass 533, other stars pass 492. Gray dashed lines indicate snapshots for pre- and post-flood water depth anomaly maps (panels, d, e). (d) Pre-flood Sentinel-2 composite with water depth anomaly from SWOT and FABDEM outputs. Blue lines show permanent water channels from land-cover data. (e) Post-flood water depth map (6 May 2024), with areas exceeding 5 m near rivers. Red and blue stars in (d, e) mark gauge station locations.
Next, we objectively map SWOT water heights on a 30-m grid throughout the study area and derived water depth anomalies using the FABDEM topography data (Figures 3d and 3e). The correlation length scale for the objective mapping was set to 10 km, estimated a priori based on the spatial patterns observed in the SWOT water height data. To reduce the computational burden, we randomly selected 66,000 pixels -- equivalent to the number of interpolated grid cells -- from the SWOT data for the objective mapping. We repeated the mapping with different randomly chosen pixels and 20% fewer and 20% more pixels, observing no significant changes in the final interpolated field. Additionally, the final interpolated field was compared with the spatial pattern from the pre-interpolated pixels, confirming strong consistency between the two. We identified that approximately 1.6% of the grid cells exhibited negative water depth anomalies during this process. These cells were excluded and interpolated linearly from the surrounding points to ensure data continuity.
The deepest inundation (> 5 m) is clustered near river channels, delineating immediate floodplains and wetlands. We also observed an upstream gradient in water depth, with greater volumes accumulating in the northern and western regions. Moderate depths (2-4 m) affected some of the hardest-hit urban areas north of Porto Alegre. However, the most extensive flooding occurred in the relatively shallow cropland plains adjacent to the Jacui River. The total water volume difference between 6 May and 15 April reached a staggering 1.5 billion cubic meters, emphasizing the intensity of the flood in this region. For context, this is enough water to supply New York City for more than a year (396 days, see Supporting Information S1 for details).
## 6 Flood Impacts
The interplay between land cover, vegetation disturbance, and social vulnerability is a key factor in understanding the impacts of environmental hazards such as this flood. Our estimates show that approximately 54% of the croplands and about 25% of the urban areas were flooded (Figure 4a). Most of the croplands in this region are rice plains, which are usually located in the floodplain of the river (see Supporting Information S1 for details, Governo de Estado do Rio Grande do Sul, 2022). The post-flood vegetation disturbance (Figure 4b) highlights the persistent impacts on vegetation and croplands, with disturbances categorized by severity. The flood-affected area includes significant patches of severe disturbance (>50%) in red, concentrated near water bodies and mainly affecting wetlands, croplands, and grasslands. Lesser disturbances (<50%) are scattered around the periphery, mainly impacting nearby croplands, reflecting a gradient of flood intensity. For urban areas, practically the entire municipality of Eldorado do Sul, the northern part of Porto Alegre, and large areas in the north of Porto Alegre, such as Canoas, were affected. Although the description of the flood impact in terms of land use is important for assessing the immediate physical and economic damage, we expanded the analysis of the urban areas by also exploring the socioeconomic aspects.
Among other socioeconomic variables, the IPEA data set (Instituto de Pesquisa Economica Aplicada, 2024) provides information about the total population and the fraction of the population classified as socially vulnerable for each human development zone. We estimated the vulnerable population affected by the flood by assuming a homogeneous distribution of the population within each human development zone. Specifically, we multiplied the total population by the fraction of the population classified as socially vulnerable and then by the fraction of the area affected by the flood (Figure 4c).
The majority of the vulnerable population affected by the flood in the study area is located in the northern part of Porto Alegre, within the Canoas municipality (Figure 4c). Additionally, there is a significant concentration of vulnerable population in the central part of the study area, particularly in the Santa Rita neighborhood of the Guaiba municipality. Six of the affected human development zones each have more than 3,000 people in social vulnerability. In total, despite the social profile of the affected population not differing significantly from the average, about 67,000 of affected individuals in the study area are classified as socially vulnerable, which represents about 16% of the total affected. Socially vulnerable groups are considered the least resilient segment of the population, and they typically face greater difficulties in recovering from flood impacts due to limited financial resources, weaker social support networks, and fewer opportunities for recovery ([PERSON], 2017; [PERSON] et al., 2022; [PERSON] et al., 2023).
## 7 Discussion and Conclusions
Although this study is only an initial analysis of the flood's effects on land use areas and on vulnerable populations, we were able to identify some clear patterns. The land use analysis revealed extensive impacts on crops,particularly rice plains, which are consumed locally and exported within Brazil and globally (Argus Media, 2024; FeedNavigator, 2024; Governo do Estado do Rio Grande do Sul, 2022). This highlights how the impacts of extreme weather events, when combined with social and infrastructure factors, can produce far-reaching consequences that extend beyond the directly affected areas, influencing both national and international food security.
Although there were no significant differences between the social profile of the affected population and the broader study area, the fact that \(\sim\)67,000 socially vulnerable individuals were impacted, according to the IPEA data set, underscores the potential for such events to exacerbate social inequality, particularly in the Global South. This aligns with the findings of previous studies that demonstrate that vulnerable populations often bear the brunt of climate-related disasters ([PERSON], 2016; EPA, 2021; [PERSON], 2016; [PERSON] et al., 2023; [PERSON], 2003; [PERSON], 2017; [PERSON] et al., 2022; [PERSON] et al., 2021; [PERSON] et al., 2019). More work is clearly needed to refine the land cover and socio-economic metrics and expand the analysis to provide a more comprehensive understanding of the flood's impact.
These observations of local vulnerability are further complicated by the influence of large-scale climate events, such as ENSO. Over the past year, we have witnessed the fourth-most powerful El Nino on record, yet uncertainty remains regarding how ENSO may evolve in future climate scenarios. Recent studies predict that stronger El Ninos could occur more frequently ([PERSON] et al., 2014; [PERSON] et al., 2024; [PERSON] et al., 2024; [PERSON] et al., 2024), potentially followed by more consecutive La N\(\tilde{\text{n}}\)as events ([PERSON] et al., 2023). If future extreme weather events coincide with El Nino years, the impacts could be even more devastating, particularly in regions like this one that are already vulnerable to such events.
While the extreme rainfall during the May 2024 event was due to large-scale atmospheric conditions, particularly the blocking of a cold front, the floods in the Metropolitan Region of Porto Alegre were exacerbated by local infrastructure vulnerabilities. The collapse of some floodgates on the dikes surrounding Porto Alegre near Guaiba
Figure 4: Maps of the study region showing (a) land use, (b) post-flood vegetation disturbance (26 May), and (c) estimated affected vulnerable population by human development zones, with the flood-affected area indicated by black, white, and red lines, respectively.
River played a critical role in allowing floodwaters to enter the city (check Supporting Information S1 for details). These dikes were originally constructed after the great flood of 1941 to protect the city, but the lack of proper maintenance over the years led to the failure of some of the floodgates. This highlights the compounding effect of intense rainfall and poorly maintained infrastructure, demonstrating that extreme weather events alone may not fully explain the scale of the disaster.
Our historical analysis clearly shows that the May 2024 event was a significant outlier in the record, with no discernible trend in the frequency of similar extreme events in the region. This underscores the need for further investigation into the drivers and impacts of such anomalies. While this study provides a foundational understanding, additional research and modeling experiments are necessary to determine whether the region is likely to experience more events of this magnitude in the future.
In addition to the immediate impacts of flooding, floodwater drainage introduces significant secondary challenges ([PERSON] et al., 2016). Runoff carries large volumes of mud and debris downstream, depositing sediment in lower river areas, river mouths, and coastal zones. This influx of sediment has the potential to alter the morphology of the local river, possibly changing the watercourse and disrupting the natural equilibrium. Over time, these changes may affect flood patterns, water availability, and the stability of ecosystems. Aquatic and terrestrial species that depend on stable water conditions could be particularly vulnerable.
The ongoing sedimentation and changes in river morphology also present challenges for water management. Infrastructure maintenance, ecosystem protection, and water management strategies must adapt to altered watercovourses and sediment flows ([PERSON] & [PERSON], 2023; [PERSON] et al., 2016). This will require comprehensive monitoring and proactive management to mitigate the impacts on both human and natural systems. Sustainable management of affected river and coastal systems will be essential in the face of these evolving challenges.
This study emphasizes the importance of applying high-resolution remote sensing technologies, such as Sentinel-2 and SWOT, to monitor long-term changes in flood-affected areas. Specifically, SWOT or other radar altimeters have the added value of not being strongly influenced by cloud coverage, which can limit the use of optical sensors like Sentinel-2 for flood and extreme precipitation events. This work provides an initial, straightforward approach to obtaining floodwater levels from SWOT measurements, which can be perfected for future investigations. Continued monitoring is crucial for assessing the persistence and evolution of flood impacts, evaluating the effectiveness of flood management strategies, and adjusting response measures. Expanding this research approach to other flood-prone regions will be critical, especially as climate change is expected to increase the frequency and intensity of flooding events ([PERSON] et al., 2023). With this multi-sensor approach, we can gain valuable insights into managing future flood risks and strengthening resilience to climate change worldwide.
## 8 Inclusion in Global Research
This research study examines the severe flood that struck southern Brazil in May 2024. Four of the authors are Brazilian nationals, having earned part of their academic degrees from several Brazilian institutions (University of Sao Paulo, Federal University of Ceara, Federal University of Rio Grande), the latter being located in the state affected by the flood. Notably, one of the authors has family members living in the region who were directly impacted by the disaster. While the Brazilian authors are early career scientists currently expanding their professional paths outside of Brazil, they continue to maintain strong collaborative ties with Brazilian institutions.
Given these connections, we acknowledge the significant role of our local knowledge and networks in conducting this research. Our study relied on satellite data provided by international agencies and did not involve field data collection or direct collaboration with local researchers or communities within Brazil. However, we recognize the importance of equitable research practices and the need to respect and acknowledge the contributions and impacts on the affected communities.
We affirm that all ethical considerations related to the use of satellite data have been adhered to, and no permits or local authorizations were required for the data utilized. We appreciate the assistance and support from local institutions and individuals who indirectly contributed to our understanding of the flood event through their previous work and ongoing research efforts.
## Data Availability Statement
Open science is a crucial component of this study, ensuring that the research process is transparent, reproducible, and accessible to the broader scientific community. By providing access to the code, data, and processing methods used in this study, our goal is to facilitate collaboration and foster advances in the field. The computational code developed and used in this study is made available via Simoes-Sousa (2024a). This repository contains all scripts used for data access, processing, analysis, and figure generation to assist users in reproducing the results and adapting the methods for future research. All data used in this study are publicly available, ensuring transparency in our research methodology. In addition, we have archived the specific data subsets and processed data used in our analyses on Zenodo, available via Simoes-Sousa (2024b). This includes curated data sets derived from the original sources, as well as processed files that reflect the transformations applied during the study.
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* Institute de Pesquisa Economica Agricado. (2024). Atlas du vuzmuldalleled social [Dataset]. [[https://iv.ipa.gov.br/index.php/view1111/pa24/en111/pa24.php/view1111/pa24](https://iv.ipa.gov.br/index.php/view1111/pa24/en111/pa24.php/view1111/pa24)]([https://iv.ipa.gov.br/index.php/view1111/pa24/en111/pa24.php/view1111/pa24](https://iv.ipa.gov.br/index.php/view1111/pa24/en111/pa24.php/view1111/pa24)).
* [PERSON] et al. (2021) [PERSON], [PERSON], & [PERSON] (2021). Data analysis reveals that extreme events have increased the flood simulations in the Taquir River's Valley, southern Brazil. Latin American Data in Science, 1(1), 16-25. [[https://doi.org/10.53805/stds.v11.20](https://doi.org/10.53805/stds.v11.20)]([https://doi.org/10.53805/stds.v11.20](https://doi.org/10.53805/stds.v11.20))
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* [PERSON] et al. (2022) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2022). Urban flood-related remote sensing: Research trends, gaps and opportunities. _Remote Sensing_, 14(21), 5005. [[https://doi.org/10.3390/ts14215505](https://doi.org/10.3390/ts14215505)]([https://doi.org/10.3390/ts14215505](https://doi.org/10.3390/ts14215505)) | wiley | The May 2024 Flood Disaster in Southern Brazil: Causes, Impacts, and SWOT‐Based Volume Estimation | Iury T. Simoes‐Sousa, Carolina M. L. Camargo, Juliana Tavora, Agata Piffer‐Braga, J. Thomas Farrar, Tamlin M. Pavelsky | https://doi.org/10.1029/2024gl112442 | 2,025 | CC-BY |
wiley/fa7fb998_4a39_48d9_8fe3_0bb0bebee183.md | # Reviews of Geophysics'
Manuscript
10.1029/2020 RG000728
Amazon Hydrology From Space: Scientific Advances and Future Challenges
[PERSON]
10.1029/2020 RG000728
[PERSON]
1 Laboratoire d'Etudes en Geophysique et Oceanographie Spatiales (LEGOS), Universite Toulouse, IRD, CNRS, CNES, UPS, Toulouse, France, University of Brasilia (UnB), Institute of Geosciences, Brasilia, Brazil, \"Federal University of Rio Grande do Sul (UFRGS), Institute of Hydraulic Research, Porto Alegre, Brazil,\" University of Grenoble Alpes, IRD, CNRS, Grenoble INP, Institut des Geosciences de l'Environnement (IGE, UMR 5001), Grenoble, France, \"University of California Santa Barbara, Earth Research Institute, Santa Barbara, CA, USA, \"Hydro Matters, Le Faget, France, \"Instrumentation Lab for Aquatic Systems (LabISA), Earth Observation Coordination of National Institute for Space Research (INPE), Sao Jose dos Campos, Brazil, \"Laboratoire d'Etudes du Rayonnement et de la Matiere en Astrophysique et Atmospheres, Paris, France, \"Federal University of Vicosa (UFV), Vicosa, Brazil,\" \"Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Potsdam, Germany, \"Mamirata Institute for Sustainable Development, Tefe, Brazil,\" Departamento de Odenemimento Territorialy Construccion, Universidad Nacional Agarita La Molina (UNALM), Lima, Peru, \"Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
###### Abstract
As the largest river basin on Earth, the Amazon is of major importance to the world's climate and water resources. Over the past decades, advances in satellite-based remote sensing (RS) have brought our understanding of its terrestrial water cycle and the associated hydrological processes to a new era. Here, we review major studies and the various techniques using satellite RS in the Amazon. We show how RS played a major role in supporting new research and key findings regarding the Amazon water cycle, and how the region became a laboratory for groundbreaking investigations of new satellite retrievals and analyses. At the basin-scale, the understanding of several hydrological processes was only possible with the advent of RS observations, such as the characterization of \"rainfall hotspots\" in the Andes-Amazon transition, evapotranspiration rates, and variations of surface waters and groundwater storage. These results strongly contribute to the recent advances of hydrological models and to our new understanding of the Amazon water budget and aquatic environments. In the context of upcoming hydrology-oriented satellite missions, which will offer the opportunity for new synergies and new observations with finer space-time resolution, this review aims to guide future research agenda toward integrated monitoring and understanding of the Amazon water from space. Integrated multidisciplinary studies, fostered by international collaborations, set up future directions to tackle the great challenges the Amazon is currently facing, from climate change to increased anthropogenic pressure.
The Amazon basin is the largest river basin in the world, characterized by complex hydrological processes that connect high rates of precipitation, extensive floodplains, dense tropical forests, complex topography, and large variations in freshwater storage and discharge. It plays a key role in the water, energy, and carbon cycles and interacts with the global climate system. Earth observations have played a major role in supporting research in Amazon hydrology, and the characterization of several hydrological processes was only possible with the help of remote sensing data. The basin is now facing great risk under current climate change and increased anthropogenic pressure and the resulting environmental alterations require a better understanding of the overall basin's water cycle across scales. We review the strengths and limitations of observations from satellites in the context of the current and upcoming hydrology-oriented satellite missions, and we make recommendations for improving satellite observations of the Amazon basin water cycle, along with an interdisciplinary and stepwise approach to guide research for the next decades.
## 1 Introduction
The Amazon River basin is a major hydrological system (\(\sim\)6 million km\({}^{2}\)) with diverse rivers, floodplains, and wetlands ([PERSON] et al., 2011; [PERSON] et al., 2019, Figure 1). It spans seven countries and hosts four of the 10 largest rivers in the world, namely the Solimoes-Amazonas, Madeira, Negro, and Japura rivers (Figure 2). It receives high annual rainfall (\(\sim\)2,200 mm year\({}^{-1}\), [PERSON] & [PERSON], 2018; [PERSON] et al., 2009) and around 30%-40% of the precipitation in the basin is recycled by local evapotranspiration ([PERSON] & [PERSON], 1994; [PERSON] et al., 1979; [PERSON], [PERSON], & [PERSON], 2013) providing moisture to southern parts of South America. The Amazon River flows into the Atlantic Ocean with an average annual discharge of \(206\times 10^{7}\) m\({}^{3}\)s\({}^{-1}\)([PERSON] et al., 2010), amounting to almost 20% of the total global freshwater reaching the ocean annually and exports a large number of sediments to the ocean (\(1.1\times 10^{9}\) tons per year; [PERSON] et al., 2020).
The high rates of precipitation, evapotranspiration and large variations in freshwater storage and river discharge make the Amazon basin a key player in the global climate system, with large contributions to the water, energy, and carbon cycles ([PERSON] et al., 2013; [PERSON] et al., 2021; [PERSON] et al., 2016). Amazon surface waters, for instance, are a major source and sink of carbon dioxide ([PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2013; [PERSON] et al., 2002) and the largest natural geographic source of methane in the tropics ([PERSON] et al., 2013; [PERSON] et al., 2004; [PERSON] et al., 2017; [PERSON] et al., 2013). Seasonal variations in the water contribute to the formation of tropical forests ([PERSON] et al., 2012), maintain high aquatic productivity ([PERSON], 2001) and biodiversity ([PERSON], 1997; [PERSON] et al., 2010), and influence fish distributions and fisheries yield ([PERSON] et al., 2010; [PERSON] et al., 2015; Figure 1). The Amazon hosts \(\sim\)40% of the world's tropical forest and \(\sim\)15% of global land biodiversity ([PERSON] et al., 2018). It is also the home of local people that rely on rivers as transportation corridors, and utilize these environments for their subsistence ([PERSON] et al., 1991; [PERSON] et al., 2020; [PERSON] et al., 2016). Amazon also serves the broader South American population in terms of energy, food, and other forest products.
The region is now facing risks under climate and anthropogenic changes, and changes in Amazon hydrology could have substantial impacts globally ([PERSON] et al., 2019). In the past decades, the basin experienced several intense climatic events, such as extreme droughs and floods, with no equivalent in the last 100 years ([PERSON] et al., 2018; [PERSON] & [PERSON], 2016). Severe droughs can lead to environmental disturbances, from increased fire occurrence ([PERSON] et al., 2008) to abrupt shifts in fish assemblages ([PERSON] et al., 2017). Moreover, the accumulated negative impacts of increased human interventions across the region, such as damming ([PERSON] et al., 2017; [PERSON] et al., 2017), deforestation ([PERSON] et al., 2020; [PERSON] et al., 2009; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2012), fires ([PERSON] et al., 2008; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2008), and mining ([PERSON] et al., 2019; [PERSON] et al., 2015), will possibly trigger major modifications that could affect the Amazon water cycle.
Characterizing and understanding the dynamics of the Amazon water cycle is of primary importance for climate and ecology research and for the management of water resources. Consequently, there is a need for comprehensive monitoring of the spatial-temporal dynamics of the Amazon water cycle components and how they interact with climate variability and anthropogenic pressure. In large and remote tropical watersheds such as the Amazon, in situ observational networks are difficult to operate and maintain, and remote sensing observations have brought opportunities for monitoring the various components of the water cycle, although many technical challenges still need to be overcome.
While the Amazon basin was in the spotlight of international scientific discussion during the last decades, the understanding of Amazon hydrology coevolved with another groundbreaking field: the remote sensing (RS) of the terrestrial water cycle. In this context, the Amazon basin has been an ideal natural laboratory for the seminal development of RS techniques with the advent of Earth observations (EO) and these advances have fostered the scientific understanding of Amazon hydrology, ecosystems, and environmental changes. For example, the first applications of altimeter and gravimetric satellites to characterize, respectively, surface water elevation ([PERSON] et al., 1990) and total water storage variations ([PERSON] et al., 2004) were performed in the basin due to its wide river and large spatial and temporal changes of freshwater. Pioneering RS applications also include microwave, synthetic-aperture radar (SAR), and interferometric mapping of large-scale flood inundation and characterization of sediment dynamics ([PERSON] et al., 2000;Figure 1: Amazon River basin diversity. (a) Moderate Resolution Imaging Spectroradiometer (MODIS) image of the central Amazon basin, characterized by large floodplains (Source: National Aeronautics and Space Administration [NASA] catalog; [[https://visibleearth.nasa.gov/images/62101/the-amazon-brazil/62104](https://visibleearth.nasa.gov/images/62101/the-amazon-brazil/62104)]([https://visibleearth.nasa.gov/images/62101/the-amazon-brazil/62104](https://visibleearth.nasa.gov/images/62101/the-amazon-brazil/62104))); (b) Sentinel-1 image of rivers and lakes of the upper Solmoes River (Source: ESA catalog; [[https://www.esa.int/ESA_Multimedia/Images/2020/09/Amazon_Riverk](https://www.esa.int/ESA_Multimedia/Images/2020/09/Amazon_Riverk)]([https://www.esa.int/ESA_Multimedia/Images/2020/09/Amazon_Riverk](https://www.esa.int/ESA_Multimedia/Images/2020/09/Amazon_Riverk))); (c) MODIS image showing the reduced cloud cover over water bodies (Source: NASA catalog; [[https://earthobservatory.nasa.gov/images/145649/mapping-the-amazon](https://earthobservatory.nasa.gov/images/145649/mapping-the-amazon)]([https://earthobservatory.nasa.gov/images/145649/mapping-the-amazon](https://earthobservatory.nasa.gov/images/145649/mapping-the-amazon))); (d) Aerial view of Branco River (Photo by [PERSON]); (e) Floodplain during the high water (Photo by [PERSON]); (f) Channel (Photo by [PERSON]); (g) Community at the river bank (Photo by [PERSON]); (h) Manatee (Photo by [PERSON]); (i) Arapaima (Piranucu) fish, the largest scaled freshwater fish in the world (Photo by [PERSON]).
[PERSON] et al., 2003; [PERSON] et al., 1993; [PERSON] et al., 1994). Since then, several applications using RS data have been carried out in other basins worldwide (e.g., [PERSON] et al., 2021). All these important developments have been done by a diverse community of scientists with different interests and views on the Amazon water cycle, and surprisingly, there is a lack of review analyzing the continuous growth of publications that make use of RS observations to study the hydrology of the region.
Here, we review the various achievements of more than three decades of scientific advances on the hydrology of the Amazon basin from RS (Figure 2), and present perspectives, currently fostered by an unprecedented availability of satellite observations and the upcoming launch of dedicated hydrology satellites, such as the Surface Water and Ocean Topography (SWOT) and the NASA-ISRO SAR mission (NISAR). This work reunited experts on RS of different hydrological processes of the Amazon basin to review specific topics and discuss paths toward scientific advances as well as the opportunities shaping this field for the next decades. Reviews account for variables of the hydrological cycle such as precipitation, evapotranspiration, surface water elevation, surface water extent, floodplain and river channels topography, water quality (e.g., estimation of sediments, chlorophyll, and dissolved organic matter), total water storage and groundwater storage that is presented in separate sections (Figure 2). Each section describes how the variable is retrieved from RS observations, presents the scientific advances that have been achieved from this information, as well as
Figure 2: Location of the Amazon basin in South America, and representation of the hydrological variables observed by remote sensing techniques, with the respective section numbers as addressed in this review.
various applications in the basin, and discusses future challenges. Then, four sections are dedicated to the integration of RS data in the fields of water budget closure, hydrological and hydraulic modeling, aquatic environments, and environmental changes over the Amazon. Section 7 summarizes the scientific advances, the knowledge gaps, and the research opportunities regarding Amazon hydrology and ecosystems, including the forthcoming satellite missions. It also presents how the lessons learned from Amazon experiences are benefiting other large river basins worldwide. The two final parts discuss how to move forward from the scientific advances toward basin-scale water resources planning and new environment monitoring tools, and highlight our recommendations that set forward the research agenda of Amazon hydrology from space for the coming decade.
## 2 Precipitation
Precipitation is a crucial component of the water cycle ([PERSON], 2008; [PERSON], [PERSON], et al., 2009; [PERSON], 1984; [PERSON], 2011), characterized by high spatial and temporal variability. In the Amazon basin, precipitation is related to complex interactions of various large-scale physical and dynamic processes as well as local features, which are responsible for the temporal and spatial distribution of precipitation ([PERSON], 1990). For instance, in addition to the orographic rains that occur in the transition between the Andes mountains and the Amazon, the substantial transpiration from the forest contributes to abundant water fluxes to the atmosphere, which eventually returns to the land as recycled precipitation and contributes up to around 30% of the basin's rainfall ([PERSON], 2006; [PERSON], 1994; [PERSON] et al., 2009; [PERSON], 1991; [PERSON] et al., 2018; [PERSON] et al., 2010; [PERSON] & [PERSON], 2019; [PERSON] et al., 2014). This contribution is normally presented as a convection process, which helps to maintain a climatological upper-level, large-scale circulation known as the Bolivian high ([PERSON], 1997; [PERSON], 1981), and together with other related precipitation patterns are affected by both global-scale phenomena (e.g., El Nino-Southern Oscillation [ENSO], Tropical Atlantic sea surface temperature [SSTemp]) and local forcing, such as land cover structures ([PERSON], 1988; [PERSON] et al., 2021; [PERSON] et al., 2008; [PERSON] et al., 2020; [PERSON] et al., 2006).
Mainly because of its large extent, precipitation regimes in the basin differ from one region to another in terms of the seasonal pattern (Figures 3c-3f), and on a more local scale, rainfall regimes are highly variable in space ([PERSON] et al., 2021; [PERSON] et al., 2009). Therefore, accurate and reliable rainfall measurements are crucial for the study of climate trends and variability, and also for the management of water resources and weather, climate, and hydrological forecasting in this region ([PERSON] et al., 2012; [PERSON] et al., 2017; [PERSON] et al., 2005).
Gauge observations are traditionally used to measure precipitation directly at the land surface ([PERSON], 2001), and various large-scale data sets at different scales have been developed from these in situ observations ([PERSON] et al., 2013; [PERSON] et al., 2017). However, in situ measurements have several drawbacks, such as incomplete cover over sparsely populated areas, a common feature of Amazonian countries, or in remote regions at high altitudes in the Andes ([PERSON] et al., 2020). In addition, the variability of rainfall means that the measurements from in situ stations are typically not representative of the surrounding areas, or maybe inaccurate ([PERSON] et al., 2017; [PERSON] et al., 1986). In the Amazon basin, for instance, rainfall stations are typically located in the cities, placed near to the main tributaries, and low density of stations is observed in tropical forests and in regions not accessible. Therefore, the low density of the rain gauge network and the lack of homogeneity in the time series prevent reliable monitoring using ground data ([PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON], [PERSON], et al., 2009; [PERSON] et al., 2002). Collecting complementary observations to in situ measurements is then fundamental to obtain an estimation of rainfall over the continent's surfaces ([PERSON] & [PERSON], 2011; [PERSON] & [PERSON], 2011; [PERSON] et al., 2014).
Satellite observations of precipitation have become available on a global scale in recent decades. These satellites mainly use infrared (IR) and microwave (MW) sensors to provide precipitation estimates using different techniques ([PERSON] & [PERSON], 2011). The sensors used to estimate precipitation can be classified in three categories ([PERSON], 2010): (a) visible/IR (VIS/IR) sensors on geostationary (GEO) and low Earth orbit (LEO) satellites, (b) passive MW (PMW) sensors on LEO satellites, and (c) active MW (AMW) sensors on LEO satellites. Imaging systems on GEO provide the rapid temporal update cycle needed to capture the Figure 3.— (a) Schematic representation of remote sensors for precipitation estimation onboard satellites. (b) Illustration of the VIS/IR and microwave coverage range for different cloud types. Precipitation climatology for (c) Annual, (d) Austral summer (DIF), and (e) Austral winter (JJA) from CHIRP v2 data set (1981–2020) at 5 km spatial resolution and HOP data set (1981–2009) ([PERSON] et al., 2016; [PERSON] et al., 2012) in small boxes at left-bottom at \(\sim\)100 km spatial resolution. (f) The annual regime for 11 large basins of the Amazon, based on HOP data sets (1981–2009) (bars) and the CHIRP based (1981–2020) in magenta lines. (g) Annual average negative (red scale) and positive (blue scale) bias of six precipitation RS-based and non-gauged-corrected products in the Amazon basin for the period 2000–2016, adapted from ([PERSON], [PERSON], et al., 2017).
growth and decay of precipitating cloud systems on a scale of several kilometers. Current systems provide rapid hourly updates in the VIS and IR spectrum, and for optically thick clouds the precipitation can be inferred from the energy reflected by the clouds and the temperature of the cloud top, respectively. MW-based imagers on board LEO satellites are better suited than IR sensors for quantitative measurements of precipitation due to the well-established physical connection between the upwelling radiation and the underlying cloud precipitation structure ([PERSON] et al., 2000; Figures 3a and 3b).
From these sensors, a diverse range of retrieval algorithms has been developed to estimate precipitation, which requires careful validation and provides information about their quality, limitations, and associated uncertainties. These algorithms are mainly divided into the so-called \"microwave-calibrated\" and \"morphing\" methods ([PERSON] et al., 2007; [PERSON] et al., 2004; [PERSON] et al., 2003; [PERSON] et al., 2004; [PERSON] et al., 2012). However, there are differences among these data sets due to shortcomings in the sources and in the generation of the products. Therefore, LEO MW, GEO VIS/IR, gauge-based, and reanalysis data have been blended together to take advantage of the inherent relative benefits of each type of sensor and product (Figure 3a). This can increase accuracy, coverage, spatial-temporal resolution, spatial homogeneity, and temporal continuity ([PERSON] et al., 1994; [PERSON] et al., 1995; [PERSON] et al., 2004; [PERSON] et al., 2007; [PERSON] et al., 2002; [PERSON] et al., 2004; [PERSON] et al., 1998; [PERSON] et al., 2003).
In terms of operationally available data sets, these include the Tropical Rainfall Measuring Mission (TRMM; [PERSON] et al., 2007), the Climate Hazards Group InfraRed Precipitation (CHIRP; [PERSON] et al., 2015), the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN; [PERSON] et al., 2015), Integrated Multi-satellite Retrievals for GPM (IMERG; [PERSON], [PERSON], & [PERSON], 2015; [PERSON], [PERSON], [PERSON], et al., 2015), Multi-Source Weighted-Ensemble Precipitation near-real-time (MSWEP-NRT; [PERSON] et al., 2018) and the Climate Prediction Center (CPC) morphing technique (CMORPH; [PERSON] et al., 2004) products, among others. Although an increasing number of precipitation data sets with higher spatial and temporal resolution has been constructed and compared directly or through the application of hydrological models, uncertainty and inconsistency are found among the different data sets ([PERSON] et al., 2018; [PERSON], [PERSON], et al., 2017; [PERSON] et al., 2008; [PERSON] et al., 2017; [PERSON] et al., 2018; [PERSON] et al., 2017). A summary of satellite-derived rainfall data sets currently available for the Amazon region is provided in Table 1.
Precipitation information based on RS has contributed substantially in the last decades to the understanding of key processes causing spatial and temporal variability of precipitation, as well as local and regional atmospheric processes related to precipitations. These global or quasi global data sets generally provide records of precipitation suitable for the climate and hydrological studies, such as hydrological reanalysis initiatives evaluated in the Amazon on regional (e.g., [PERSON] et al., 2017; [PERSON] et al., 2019) and global scales (e.g., [PERSON] et al., 2015; [PERSON] et al., 2004; [PERSON] et al., 2013). For instance, many studies have used satellite rainfall databases to force hydrological models. One of the first studies was done in the Tapajos River basin, one of the major tributaries of the Amazon basin, using TRMM precipitation estimates as input to a precipitation-runoff model ([PERSON] et al., 2008). In order to represent the interannual, intraseasonal (30-70 days, [PERSON], 1998) and multidecadal series in the Amazon, different research has been evaluated ([PERSON] et al., 2017). Satellite-based data sets were also used in water balance approaches to evaluate long-term trends ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2018) and monthly variations of runoff ([PERSON] & [PERSON], 2018). In addition, hydrological extreme events have been reported in the Amazon basin during the last decades, which has been possible by using satellite-based rainfall estimates ([PERSON] et al., 2018; [PERSON] et al., 2012, 2014; [PERSON] et al., 2021; [PERSON] et al., 2013; [PERSON] & [PERSON], 2016; [PERSON], [PERSON], [PERSON], & [PERSON], 2013; [PERSON] et al., 2012). Applications of precipitation databases to the understanding of the hydrologic cycle through modeling are described in Section 6.2.
However, due to inconsistencies between different databases, several evaluations of rainfall data sets were performed that consider the Amazon basin, from global evaluations (e.g., [PERSON] et al., 2018, [PERSON], [PERSON], et al., 2017; [PERSON], [PERSON], et al., 2017; [PERSON] et al., 2018), only Amazon (e.g., [PERSON] et al., 2020; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019) and in particular regions of Amazon (e.g., [PERSON] et al., 2020; [PERSON] & [PERSON], 2008; [PERSON] & [PERSON], 2017; [PERSON] et al., 2015; [PERSON] et al., 2011; [PERSON] et al., 2007; [PERSON]
local scale ([PERSON] et al., 2008; [PERSON] et al., 2019; [PERSON] et al., 2004). RS data helped to reveal that river breezes reduced rainfall over the Amazon water bodies (rivers and large reservoirs) through the use of TRMM ([PERSON], [PERSON], & [PERSON], 2011).
Changes in land cover can produce complex mesoscale circulation patterns, including the so-called \"deforestation breeze\" that can happen over small deforested patches but loses strength at deforestation scales of around 100 km ([PERSON] & [PERSON], 2015; [PERSON] et al., 2010). These deforestation-induced circulation patterns can significantly alter rainfall trends at different scales ([PERSON] et al., 2021). Rainfall patterns can also be affected from local to continental scales, with such changes being observed over the Amazon in recent decades ([PERSON] et al., 2011; [PERSON] et al., 2017; [PERSON] et al., 2019). The effects of deforestation on rainfall will be further discussed in Section 6.4.
Remotely sensed data have been used to evaluate the temporal variability on different time scales. For instance, spatial synoptic changes in rainfall patterns were evaluated using RS information due to the heterogeneous spatial distribution of weather stations and inconsistent temporal measurements of gauge data ([PERSON] et al., 2017; [PERSON] et al., 2018). Other studies on a daily scale focused on evaluating the performance of the TMPA V7, TMPA RT, CMORPH, and PERSIANN data sets to represent the precipitation concentration index during the period 2001-2009 ([PERSON] et al., 2019). This index is an indicator for temporal precipitation distribution. The authors concluded that the best products (CMORPH and TMPA V7) can be an alternative source of data to detect changes in daily precipitation concentration during dry or wet seasons in regions of the basin that experience extreme events.
Considering that one of the main characteristics of convection processes in tropical regions is their strong relationship with the diurnal cycle ([PERSON] & [PERSON], 1985; [PERSON] & [PERSON], 1984), pioneer studies were performed since the 1990s for the understanding of convective patterns in the Amazon basin. Based on 9 years (1983-1991) of data from GEO IR satellites (i.e., the B3 ISCCP product) with 3-hr temporal resolution, [PERSON] and [PERSON] (1997) documented several features of the diurnal march of the frequency of convective cloudiness. Data from SSM/I onboard the Defense Meteorological Satellite Program via application of the Goddard Profiling algorithm were also used to characterize the climatology (10-year) and the diurnal variability (6-year) of the rainfall in the basin ([PERSON] et al., 2000). [PERSON] et al. (2016) evaluated two GPM products in order to reproduce the diurnal cycle of precipitation in the central Amazon and obtained similar results to [PERSON] et al. (2004), who showed that rain tends to occur mainly during the afternoon in the central Amazon basin.
Rainfall information from RS has helped to identify the time of wet season beginning and ending ([PERSON] et al., 2017), which is especially important because the prolongation of the dry season increases the vulnerability of local ecosystems and agriculture to drought and fire events ([PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON] et al., 2011). One of the first RS-based assessments found that the onset of the Amazon wet season typically occurs within a single month ([PERSON] et al., 1989). [PERSON] et al. (1994) produced a regional precipitation climatology over the Amazon during the wet season (January-May) using three years of the twice daily Special Sensor Microwave/Imager (SSM/I) data. Changes in the seasonal cycle amplitude were also observed with the TRMM data ([PERSON] et al., 2020).
RS information supported important developments in the understanding of the processes governing the seasonality of rainfall in the Amazon basin. The availability of satellite-derived precipitation, OLR, and reanalysis allowed the description of the thermally-driven seasonal patterns that form the SAMS, which was previously not understood as a monsoon partly because it lacks the classical seasonal inversion of absolute zonal winds ([PERSON] & [PERSON], 1998). An uncommon characteristic of the monsoon over the Amazon elucidated by these RS products is that the onset of rains occurs before the southward migration of the ITCZ and that the Bolivian high-pressure zone characteristic of the SAMS is partly generated by the latent heat release from precipitation over the basin before the traditional monsoon onset ([PERSON] et al., 1999).
At seasonal to intraseasonal scales, OLR data from NOAA polar-orbiting satellites was used to identify the intensity and spatial features of the SACZ in the Brazilian Amazon region ([PERSON] et al., 2004). The SACZ is a northwest-southwest convection band that extends from the Amazon basin to the southeastern Atlantic Ocean, and its intensity and geographical distribution are associated with extreme rainfall events in the southern Amazon. At the intraseasonal scale, the large-scale Madden-Julian oscillation (MJO;[PERSON], 1994) has been established as the dominant mode of variability across the tropics, modulating the SACZ and other climatological features over the basin. [PERSON] et al. (2019) and [PERSON] et al. (2018) used OLR data as a proxy of convection to analyze the intraseasonal variability of precipitation in South America, and, in particular, [PERSON] and [PERSON] (2006) showed that the MJO is the main atmospheric mechanism of rainfall variability on intraseasonal timescales over the eastern Amazon during the wet season, which was confirmed through the use of rain gauge network by [PERSON] et al. (2019). Moreover, RS information has contributed to understanding the mechanisms of atmospheric circulation and rainfall data sets' performance of seasonal and intraseasonal precipitation data sets. For instance, in the Andes-Amazon transition region, particular atmospheric circulation patterns (CP) were described by [PERSON] et al. (2018), where particular meteorological situations are related to regional rainfall anomalies by using TRMM 3B42, TRMM 2A25 RP, and CHIRPS data sets.
Changes in the spatial and temporal distribution of rainfall in the Amazon basin may provide an indicator of climate variability and in turn are an indicator of hydrological variability, including extreme events, such as floods and droughts (e.g., [PERSON] et al., 2011; [PERSON] & [PERSON], 2016). Direct evaluation of these data sets have been done to assess the temporal evolution of rainfall through analysis of occurrence indexes such as the dry-day frequency and the wet-day frequency through the CHIRPS data set ([PERSON], [PERSON], et al., 2019); or the assessment of the trend in the length of the wet season in southern Amazon with the PERSIANN-CDR data set ([PERSON] et al., 2017). The interannual evolution of the hydrological processes, such as runoff coefficient, was evaluated through a water balance analysis by using the CHIRPS data set ([PERSON], [PERSON], et al., 2019). A similar approach, the long-term surface water balance over the Andes-Amazon strain, was performed by [PERSON] and [PERSON] (2018) through the use of in situ (precipitation from GPCC and runoff from HYBAM) and RS-based information (evapotranspiration from ORCHIDEE, GLEAM, MPI, and MOD16), which pointed out that failures and scarcity of information in the high Andes induce uncertainties and errors in the water budget. In addition, CHIRPS v2.0 was used to analyze precipitation anomalies for the identification of spatial patterns of drought over the basin related to the tropical Atlantic and Pacific SSTemp anomalies and different ENSO events ([PERSON] et al., 2019).
Rainfall estimations by RS since the 1980s in the Amazon basin have depicted more amounts of rain in the north, particularly during the wet season ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2018) and lower amounts in the south, particularly during the dry season ([PERSON], [PERSON], et al., 2019; [PERSON] et al., 2019). This north-south contrasting pattern is translated to the hydrological behavior of the main basins that show an intensification of the hydrological regime in the main course of the Amazon ([PERSON] et al., 2018; [PERSON], [PERSON], et al., 2009; [PERSON] et al., 2020).
Amazon characteristics pose unique challenges to satellite rainfall retrieval algorithms, both from IR and MW sensors, considering the contrast in terms of orography, climate, and changes in vegetative cover. For IR, challenges occur mainly for warm orographic rains (shown north of 10 degS), where fixed brightness temperature thresholds (cooler than warm orographic clouds) tend to underestimate rainfall amounts. This would be happening in the hot-spots regions in the Peruvian and Bolivian Andes-Amazon transition ([PERSON] et al., 2015). For the MW algorithms, rain overestimation comes from cold surfaces and ice over mountain tops which can be interpreted as precipitation ([PERSON] et al., 2011; [PERSON] et al., 2015).
Since satellite-based rainfall estimates are adjusted based on observations from rain gauges, the accuracy of estimated rainfall values can be increased. However, this requires a network of rain gauges with adequate spatial coverage in key areas of the Amazonia and high-quality records for proper calibration and validation. In the case of in situ stations, some aspects should be considered, for instance, that rainfall estimates are likely to be biased by river breeze at some times of the year, as meteorological stations are usually located near large rivers and close to most cities ([PERSON], [PERSON], et al., 2011; [PERSON] et al., 2019; [PERSON] et al., 2004).
Current satellite-borne radar missions, such as TRMM Precipitation Radar, CloudSat's Cloud Profiling Radar, or GPM Dual frequency Precipitation Radar, have low temporal resolution, therefore are unable to observe the short-time evolution of weather processes. To overcome this limitation, using only radars on LEO, it is necessary to have a constellation of them. In recent years nanoatellites (e.g., SmallSat or CubeSat platforms) have the capability to miniaturize, reduce cost and simultaneously preserve the fundamental requirements of their larger and more expensive peers. In this sense, RainCube is a potential technology demonstration mission to enable precipitation radar technologies on a low-cost platform ([PERSON] et al., 2019).
Ground-based radars can measure the vertical structure of rain since its structure depends on the type of rain, but with better temporal resolution than MW on board satellites ([PERSON] et al., 2020). A recent example is the operational algorithm RAdar INfrared Blending algorithm for Operational Weather monitoring, which merges ground radar network with VIS and IR images from satellites to provide rainfall patterns and intensity over Italy ([PERSON] et al., 2020). New methods have emerged that take advantage of the global cell phone network and its density to estimate rainfall intensities, mainly in urban areas, but which can also be used in regions with high topographical variability ([PERSON] et al., 2016; [PERSON] et al., 2013, 2016; [PERSON] et al., 2017), however, they have not yet been explored in the Amazon basin. In general, monthly and annual data sets are useful because they have an adequate agreement to the observations, but not with daily and much less sub-daily data.
## 3 Evapotranspiration
Evapotranspiration (ET) has considerable importance for the terrestrial climate system, providing moisture to the atmosphere, linking the water, energy, and carbon cycles ([PERSON] et al., 2017; [PERSON] et al., 2010), and driving precipitation and temperature at local and regional scales ([PERSON] et al., 2018). Studies have shown that around half of the precipitation in the Amazon basin is recycled by locals ET ([PERSON] et al., 1979; [PERSON], [PERSON], & [PERSON], 2013; [PERSON] et al., 2017). In addition, Amazon ET constitutes an important source of moisture for southeastern South America through atmospheric low-level (often referred to as \"flying rivers\"), providing around 70% of the precipitation in this region ([PERSON] et al., 2010; [PERSON], 2020). Especially during the dry season, Amazon ET seems to be more efficiently converted to precipitation in the La Plata River Basin than local ET ([PERSON] & [PERSON], 2014).
With the advent of satellite observations, ET has been estimated at multiple spatial and temporal scales. RS models to estimate ET can be divided into two main approaches: one based on surface energy balance (SEB) and another using physical equations. One well-known energy balance model is the Surface Energy Balance Algorithm for Land (SEBAL), proposed by [PERSON] (1995) to overcome most of the problems of the early surface energy balance models, which were suitable only for local scale due to their dependence on local measurements for calibration. Based on principles and methods adopted in SEBAL, [PERSON] et al. (2007) proposed the Mapping evapotranspiration at high Resolution with Internalized Calibration (METRIC) algorithm, including an internal calibration using Inverse Modeling at Extreme Conditions (CIMEC) and micrometeorological measurements to reduce computational biases inherent to energy models that use RS data ([PERSON] et al., 2007, 2011). Other surface energy balance models were also proposed to use RS data, such as Surface Energy Balance Index (SEBI; [PERSON] & [PERSON], 1993), Simplified Surface Energy Balance Index (S-SEBI; [PERSON] et al., 2000), and Surface Energy Balance System (SEBS; [PERSON] et al., 2001).
SEB algorithms are generally defined as \"One Source Surface Energy Balance\" models, since they do not distinguish between soil evaporation and canopy transpiration, whereas the land surface is treated as a big leaf and as a single uniform layer ([PERSON] et al., 2013; [PERSON] et al., 2016). In contrast, in the Two-Source Energy Balance (TSEB) models ([PERSON] & [PERSON], 1999; [PERSON] et al., 1995), the soil-vegetation system is approximated as a two-layer model, where the energy fluxes are partitioned into soil and vegetation components ([PERSON] et al., 1995). Based on the TSEB approach, the Atmosphere-Land Exchange Inverse model (ALEXI) was developed by [PERSON] et al. (1997), designed to represent land-atmosphere exchange over a wide range of land cover conditions. Both approaches rely on thermal RS data, using meteorological inputs as ancillary data ([PERSON] et al., 2016).
RS models based on physical equations are generally divided into Penman-Monteith and Priestley- Taylor equation-based approaches. [PERSON] (1948) was the first to formulate an equation to calculate evaporation based on a physical approach using two terms, an energy term related to radiation and an aerodynamic term related to the vapor pressure deficit and wind speed ([PERSON], 2012). While this equation represented open water evaporation, [PERSON] (1965) presented an extension by adding surface and aerodynamic resistances, and thus the equation became more consistent with an estimation of ET from vegetated surfaces, resulting in the well-known Penman-Monteith equation ([PERSON] & [PERSON], 2013). Based on this approach, the MOD16 algorithm was formulated by [PERSON] et al. (2007, 2011), previously proposed by [PERSON] et al. (2007), to calculate ET through the integrated use of global meteorological reanalysis and RS data from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor, including leaf area index (LAI), a fraction of absorbed photosynthetically active radiation (fPAR), albedo and land cover classification. [PERSON] et al. (2008) also proposed a similar ET algorithm based on this equation, the Penman-Monteith-Leuning (PML) using a simple biophysical model to calculate surface conductance from MODIS LAI. Another approach is the Priestley-Taylor equation ([PERSON] & [PERSON], 1972). This model uses an empirical parameter to simplify the Penman-Monteith approach, minimizing the uncertainties related to estimating aerodynamic and surface resistances. Based on this equation, [PERSON] et al. (2008) developed the JPL-PT model, and [PERSON] et al. (2011) proposed the Global Land-Surface Evaporation Amsterdam Model (GLEAM), designed to estimate daily terrestrial evaporative fluxes and the root-zone soil moisture using maximum observations derived from RS ([PERSON] et al., 2017). A summary of the main RS-based models to estimate ET in the South American tropics, with applications in the Amazon basin, is presented in Table 2.
RS-based ET models have improved our understanding of ET processes worldwide, allowing us to understand hydrological processes from local to large spatial and multiple temporal scales. Energy balance models have the advantage provide fine spatial resolution. These models can estimate human impacts on the energy and water cycles and on the land-surface interactions. However, since they are dependent on thermal RS data, they are generally restricted to clear-sky or cloud-free conditions, which is a major drawback, especially in tropical humid areas, such as the Amazon ([PERSON] et al., 2009). In addition, SEB models usually require the presence of hot and cold conditions in the satellite domain area. This requirement is a disadvantage since the selection of the hot and cold endmembers for internal calibration using the CIMEC process on RS images can generate subjective results, especially under wet regions such as the Amazon basin, where the selection of hot endmembers during both wet and dry seasons is a challenge ([PERSON] et al., 2017). Physically-based equations have the advantage to map ET at the high temporal resolution, enabling long-term and large-scale assessments of land-surface interactions. However, some limitations include the uncertainty in parameterizing physical processes, as surface resistance and conductance, and, therefore, some models are dependent on the use of look-up tables biome-properties ([PERSON] et al., 2013). Error propagation derived from meteorological forcing data is also an issue ([PERSON] et al., 2019; [PERSON] et al., 2016; [PERSON] et al., 2015; [PERSON] et al., 2018) since it can introduce large uncertainties in ET estimates, especially in the tropics.
In the Amazon, the spatial and temporal drivers of ET are not fully understood, and these uncertainties are reflected in how RS models estimates ET ([PERSON] et al., 2021; [PERSON] et al., 2017; [PERSON] & [PERSON], 2018). ET measurements have provided valuable information about seasonality and dynamics at local scales ([PERSON] et al., 2009). Some national initiatives, as the Brazilian National Water Resource Information System (SINGREH) and the Meteorological Database for Research from the Brazilian National Water and Sanitation Agency (ANA) and the National Institute of Meteorology (INMET), respectively, and international research projects, as the Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA; [PERSON] & [PERSON], 2004), provided standardized hydrometeorological and surface flux measurements to understand energy, water, and carbon exchanges across different tropical ecosystems ([PERSON] et al., 2013; [PERSON] et al., 2013). However, due to the high cost of eddy covariance measurements and maintenance difficulties, there are only a few towers located across the basin, and these do not cover the whole Amazon climate-veg-etation complexity. Hence, through the calibration and validation of RS-based ET models, it has been possible to extend the spatial coverage of the ET, improving our knowledge about seasonality and patterns in data-scarce areas, covering long-term assessments.
RS models have shown that ET spatial pattern (Figure 4a), seasonality (Figure 4b), and main ET drivers vary across the basin, with monthly average rates ranging from 80 mm in the southern part (including Madeira and Tapajos basin) up to 160 mm in the northern part of the basin (Negro basin). Most models, as MOD16, usually show an increase in \(ET\) and forest greenness as the dry season progresses in the northeastern and central Amazon, where equatorial wet areas prevail, and spatial and temporal ET seasonality is mainly driven by incident radiation and LAI ([PERSON] et al., 2017), corroborating with eddy covariance measurements ([PERSON] et al., 2014), despite not all models agree with this pattern (Figure 4c). For instance, while MOD16 ET seasonality is consistent with eddy covariance measurements (at K34 and K83), with higher
rates during the dry season, seasonality of the GLEAM model (at K34), peaks during the wet season in wet regions in Amazon, since this model has a dependence on water availability, following the rainfall seasonality([PERSON] et al., 2016). Furthermore, in the south and southeastern parts of the Amazon basin (at Madeira and Tapajos basin), most of the RS-based models consistently indicate a decrease ET during the dry season, following water availability ([PERSON] et al., 2017; [PERSON] et al., 2019). However, when RS-based models estimate are compared to eddy covariance measurements (at local scale) or water balance estimates (at large scale), the representation of the ET seasonality is still uncertain, since most of the models are unable to consistently reproduce the seasonal cycles in tropical areas, considering that multiple drivers operate simultaneously across the Amazon. Overall, in the tropics, ET seasonality is mainly regulated by water and energy availability and how vegetation assimilates both ([PERSON] et al., 2014; [PERSON] et al., 2013). Alternatively, in large data scarce areas, estimating ET using multi-model ensembles and a dense observational network across the Amazon, RS-based models can be improved through calibration and validation, helping assess model uncertainties and to understand the land surface interactions in the tropics ([PERSON] et al., 2013; [PERSON] et al., 2019).
Figure 4.— Spatial and temporal patterns of evapotranspiration (ET) are differently represented by RS models. (a) Spatial variability of ET annual average (2003–2017) for Global Land-Surface Evaporation Amsterdam Model, SSEBop, MOD16, and PML models; the numbers on the lower left corner of each subplot represent the annual average ET. (b) ET seasonality for major Amazon sub-basins. (c) Monthly average comparison between estimates and eddy covariance measurements from the LBA project, using data from [PERSON] et al. (2013). The dry season is highlighted in gray as monthly precipitation rates <100 mm month\({}^{-1}\).
While flux tower measurements have shown, at local scales, that land cover changes can impact water and energy fluxes ([PERSON] et al., 2004), large scale assessment with satellites based on both energy balance and physical-based equations driven by vegetation phenology and meteorological reanalysis have reinforced these findings ([PERSON] and [PERSON], 2019; [PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2019). All these studies demonstrated significantly lower ET rates under pasture, agricultural, and deforested areas than in primary and secondary forests ([PERSON] et al., 2020). These results indicate that less water returns to the atmosphere, thus affecting the precipitation recycling and contributing to changes in the dry-to-wet season, possibly making the dry season longer ([PERSON] and [PERSON], 2010), while more of the precipitated water goes to runoff ([PERSON] et al., 2015). In addition, RS-based assessments demonstrated that drought events tend to affect anthropogenic systems as pasture and agriculture areas more than primary and secondary forests, leading to an increase in air temperature, and a decrease in LAI and ET ([PERSON] and [PERSON], 2019; [PERSON] et al., 2019). Results from MOD16 ET may assist in monitoring deforested areas in the Brazilian Amazon ([PERSON] et al., 2019). However, global remotely sensed ET, such as GLEAM, better reflect changes in vegetation greening and in air temperature increase than to deforestation, may due the lack of deforestation account in these models ([PERSON] et al., 2020). Influence of land use changes on the water cycle will be discussed further in Section 6.4.
Our understanding about energy partitioning in the Amazon biome has improved through RS models ([PERSON] et al., 2019; [PERSON] et al., 2020). For example, high resolution ET estimates using SEBAL in the south-western Amazon demonstrated significant differences among energy and water fluxes in forests and non-forest areas, such as pasture and cropland. In these anthropogenic areas, soil and sensible heat fluxes were from two to four times higher than in forested areas ([PERSON] et al., 2019). In a transitional region between Amazon and Cerrado biomes, converted areas can substantially change the energy and water fluxes, where latent heat flux is the major component in forested areas, while in deforested areas an increase in sensible heat flux is observed ([PERSON] et al., 2020). These studies showed that change in land use and land cover, can significantly affect ET rates, and observed ET rates was almost two times lower in pasture than in tropical forest ([PERSON] et al., 2020), and up to three times lower in non-forested areas ([PERSON] et al., 2019).
[PERSON] et al. (2017) summarized in 10 scientific questions the main outstanding knowledge gaps for the ET-based science. To address these questions, ET estimations need to be improved, aiming for high accuracy, high spatial and temporal scales, covering large spatial and long-term monitoring. Recent research demonstrated that RS models can estimate ET with reasonable accuracy and consistent agreement ([PERSON] et al., 2019; [PERSON] et al., 2017; [PERSON] et al., 2016; [PERSON] et al., 2019). However, for the individual ET components (soil evaporation, transpiration, and interception), they diverge considerably ([PERSON] et al., 2016; [PERSON] et al., 2018). For example, [PERSON] et al. (2016) showed that in tropical forests, soil evaporation is almost non-existent in GLEAM and JPL models, whereas with MOD16 this component may exceed transpiration. In the Amazon, canopy interception from JPL and MOD16 is nearly two times higher than in GLEAM model. Beyond the uncertainties related to canopy transpiration and soil evaporation, open water evaporation and ETestimation over Amazon wetlands is also a major knowledge gap. Wetland ET can be a complex process as it involves fluxes at different vegetation conditions for transpiration, evaporation from water intercepted in the canopy and from open and vegetated surface water. Changes in latent heat patterns over water bodies (rivers, wetlands, lakes and artificial reservoirs) affect the local climate circulation patterns through a breeze effect ([PERSON] et al., 2004), and have the potential to affect regional climate through precipitation suppression over the wetlands and convection initiation over wetland borders ([PERSON] et al., 2018). Wetland-upland differences in ET are still poorly understood over the Amazon, and only a few in situ monitoring gauges are available on floodable environments ([PERSON] et al., 2009) that could be used for model validation. Improvements of accuracy of ET components estimates lead us to better understand ET processes, and how these components are impacted by changes in temperature, green-house gases concentration, and in the hydrologic cycle ([PERSON] et al., 2017; [PERSON] et al., 2018).
Another challenge to RS-based ETIs to minimize the use of land cover parameterization to improve input model accuracy. While the performance of Penman-Monteith models can be influenced by surface conductance parameterizations to scale stomatal conductance to canopy level, Priestley-Taylor models estimates have dependence on the \(\alpha\) coefficient. Since ET models depend on meteorological inputs, errors can also be related in both approaches by forcing data and algorithm's structure ([PERSON] et al., 2015; [PERSON] et al., 2019). Moreover, measurements are still a significant limitation. In the Amazon biome, there are only eight public flux towers with data available, from the LBA project ([PERSON] et al., 2013), and they do not cover all vegetation and climate complexity in the Amazon basin. In addition, for surface energy balance models the main challenge, especially in the Amazon, is the requirement of clear sky conditions. However recent efforts to integrate microwave data to energy balance models are promising ([PERSON] et al., 2018), since microwaves are less affected by cloud cover than the thermal infrared wavelength.
RS is now supported by a range of sensors and satellites which provide thermal infrared images, and meteorological and surface observations, essential to estimate ET. In 2018 the Ecosystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) mission was launched by National Aeronautics and Space Administration (NASA) and will provide information about how vegetation responds to stress and how it uses water, focusing on vegetation temperature measurement, allowing understanding of ET dynamics and processes at a good temporal and spatial resolution ([PERSON] et al., 2017; [PERSON] et al., 2018). Other missions will improve ET estimates and will provide valuable information to validate current models. For example, the Joint Polar Satellite System (JPSS), a mission from National Oceanic and Atmospheric Administration (NOAA) and NASA, includes a range of sensors, such as the Visible Infrared Imaging Radiometer Suite (VIIRS), that collect visible and infrared imagery, providing useful global information to monitor vegetation, and as input to retrieval hydrological variables ([PERSON] et al., 2017; [PERSON] et al., 2018; [PERSON] et al., 2016). The Water Cycle Observation Mission (WCOM) from China aims to acquire consistent measurements of the water cycle components ([PERSON] and [PERSON], 2019; [PERSON] et al., 2016). The FLuminescence Explorer (FLEX) mission by European Space Agency, that will map vegetation fluorescence, providing information about photosynthetic activity and vegetation stress and health, also helping to improve constraints on transpiration ([PERSON] et al., 2017; [PERSON] et al., 2017). Beyond continuity of Landsat ([PERSON] et al., 2018) mission, will map long-term ET at high spatial scale, and the Gravity Recovery and Climate Experiment (GRACE) Follow-on that will bring significant opportunity to estimate ET with the water balance approach ([PERSON] et al., 2020).
RS has been crucial to improve our understanding of surface-atmosphere interactions through ET, despite the challenges that still exist, and these future missions are an excellent opportunity to address important scientific questions from ET-based science, allowing us to improve techniques, approaches and our knowledge about ET processes and how the impact of activities can affect the water cycle throughout the Earth, including the Amazon.
## 4 Surface Water
### Surface Water Elevation
Surface water is a key resource for all the communities living along the Amazon River. Yet monitoring surface water elevation (SWE) and discharge in the Amazon basin is a challenge. While the basin is facing pressure on its water cycle due to human activities, the number of gauges decreased globally in the last decades ([PERSON] et al., 2000). This threatens our capacity to understand natural and human-driven impacts of climate change on Amazonian rivers. Although, to this date, no satellite mission have been designed specifically for retrieving inland water elevations, remotely-sensed observations of SWE from radar altimetry are complementary to the historical gauge network ([PERSON] et al., 2012) and improve monitoring of Amazonian rivers ([PERSON] and [PERSON], 2006; [PERSON] et al., 2014).
Amazon basin has become an ideal laboratory for pioneering studies that have demonstrated the capacity of retrieving accurate SWE at particular locations from radar echoes and adapted retracking procedures. The first studies over the Amazon used observations from Seasat (Sea Satellite from NASA), launched in 1978, to derive the low water gradient of the Amazon main stem ([PERSON] et al., 1990).
The configuration of the satellite altimeter orbit defines the intersections between the satellite ground tracks and the river reaches, the so-called virtual stations (VSs), where SWE can be estimated. At a given VS, the SWE is retrieved through the inversion of the signal round-trip propagation time that provides the range. Several uncertainty corrections (due to delay in the propagation caused by the atmosphere, dynamics of Earth's surface, etc.) must be applied to this range to retrieve the SWE. [PERSON] and [PERSON] (2017)provide an extensive discussion on SWE estimation from satellite altimetry and the associated errors. Since the first satellites, the accuracy of the orbit, which depends on the density of the atmosphere and on the resolution of the gravitational field, has improved, and is now around one centimeter (against 60 centimeters for Seasat). Yet calculating the correct range remains challenging, as it is necessary to track (on board) or retrack (on the ground) the altimetric waveform ([PERSON] et al., 2006; [PERSON] et al., 2010), using algorithms to best fit the highly variable distribution of the echo energy bounced back by the different types of surfaces in the satellite field of view ([PERSON] et al., 2016).
Since the first studies using Seasat data, we now have more than 30 years of monitoring of inland waters by satellite altimetry. After Seasat came GEodetic and Oceanographic SATellite (GEOSAT), that was used by [PERSON] et al. (1993) to retrieve SWE time series over the Amazon, with uncertainties ranging from 0.19 to 1.09 m compared to in situ data. The European Remote Sensing satellite (ERS-1; launched in 1991) initiated a long family of satellites that followed the same 35-day repeat orbit (ERS-1, ERS-2, ENVISAT -Environmental Satellite, and SARAL -Satellite with ARgos and ALtika), which covered the 1991-2016 period. A major advance was made by the Observations des Surfaces Continentales par Altimetrie Radar (OSCAR) project, that evaluated the ICE-2 specific retracking of radar echoes for ice caps ([PERSON] et al., 2005) -a re-tracker based on fitting the leading edge and the trailing edge slope of radar waveforms to a Brown function-for ERS-1, ERS-2 and ENVISAT, and promoted its delivery in the Geophysical Data Records (data files containing along-track altimeter measurements and the corrections that are needed to be applied to the range in order to retrieve WSE).
The retracking of radar echoes was analyzed by [PERSON] et al. (2006, 2016) and [PERSON] et al. (2010) over 70 ERS-2 and ENVISAT VSs and a large range of river widths (from tens of meters to kilometers). They reported that the proper selection of the data considered as representative of the water body is as important as the choice of the retracking algorithm. The data from the 10-day repeat orbit of Topex/Poseidon (T/P) and Jason-2/3 have also been assessed in the Amazon basin. [PERSON] et al. (2013) highlighted the gain of Jason-2 (ranging from 2008 to 2016 on its nominal orbit) in comparison to T/P (from late 1992 to 2005), with an uncertainty around 0.35 m, possibly due to the sensor's better capacity to discriminate the surrounding floodplain from the river.
All these missions operated in low resolution mode, i.e., the footprint on ground is large (some kilometers, depending on radar operating band) and the echoes returning to the antenna are influenced by the surroundings. The SAR mode, active on Sentinel-3 satellites, allows a reduction of the surrounding contributions by slicing the disc illuminated by the echo at a given time ([PERSON], 1998). This reduction provides a much better along track resolution, however it does not resolve some issues such as cross-track sloping measurements ([PERSON] et al., 2013). The addition of a second antenna, as on Cryosat-2, allows the SAR Interferometric mode to correct these cross-track measurements, hence allowing an improvement in the accuracy of SWE time series. However, Croysat-2 is not popular for SWE monitoring over rivers since its orbit shifts around 30 km westward every 28.9 days, 7 km eastward every 89 days and comes back to the same place every 369 days. Indeed, most of the studies on the use of satellite altimetry in the Amazon basin have focused on repetitive orbits, even though some studies have explored the use of missions in drifting or long-term repetitive ones and found good accuracy for SWE monitoring (e.g., [PERSON] et al., 2018). As of today, main applications of drifting or long-term repetitive missions consist in constraining or calibrating hydrodynamic models, however no study has yet focused on the Amazon basin. Such missions, instead of providing a SWE observation on a 10-day or almost monthly basis with a large intertrack distance at the equator (between 60 and 100 km), provide a much denser spatial span but with observations separated from another in time. The use of ICESat (Ice, Cloud, and land Elevation Satellite) laser altimetry data was investigated by [PERSON] et al. (2012). They concluded that this mission can be a valuable source of data for monitoring rivers from the Amazon, with accuracies of some tens of centimeters when compared to gauges. The ICESat mission was continued by ICESat-2, launched in 2018. Studies by [PERSON] et al. (2013) and [PERSON] et al. (2017) concluded that the SAR mission Cryosat-2 offers new opportunities to monitor narrow rivers in the Amazon basin, and should help linking the present and future altimetry missions.
The differential interferometry technique with SAR data allows obtaining information about changes in surface displacements, such as topographic changes. Centimeter-scale measurements of water level changes throughout inundated floodplain vegetation using interferometric SAR were obtained over the Amazon floodplains for the first time ([PERSON], [PERSON], et al., 2001; [PERSON], [PERSON], & [PERSON], 2001; [PERSON] et al., 2000). This estimation is possible due to the radar pulse interactions with the water surface and the trunks of flooded vegetation causing a double-bounce path ([PERSON] et al., 2000; [PERSON] et al., 1995). [PERSON] et al., 2020 and [PERSON] et al. (2018) reviewed the methods and limitations of the technique for applications in wetlands.
To date, SWE information is available as raw data and as processed data. Some groups or institutions provide processed SWE time series (see Table 3). Each data set provides SWE on selected water bodies, all over the world or in specific regions, and have different objectives in terms of operability. Processing and filtering procedures vary between each group, and time series of the same VSs can vary from one group to another.
Figure 5 provides the location of all virtual stations in the Amazon basin from the Hydroweb website. Figure 5a is a representation of the median amplitude of SWE at each VS. Amplitude of SWE measured by the satellites is lower in the headwaters (0-3 m) and medium size rivers (3-6 m) compared to Solimoes-Amazonas main stem and its tributaries (9-12 m). Largest values are found for the Purus River (\(>\)15 m), a right bank tributary. Figures 5b and 5c provide the mean month for high and low flows, respectively, indicating the influence of rainfall partition in the northern and southern parts of the basin and the gradual shift due to the flood travel time along the rivers and floodplains (\(\sim\)1-3 months). Figures 5d and 5e provide multi-mission SWE time series ranging from 2002 to now with ENVISAT and Sentinel3-B and from 2008 to 2020 with Jason-2 and Jason-3, respectively. It shows the strong seasonal signal of the gradual flood of the Amazon rivers, and interannual variability of maximum and minimum stages.
Figure 5.— (a) Location of the virtual stations freely available on Theia-hydroweb ([[http://hydroweb.theia-land.fr/](http://hydroweb.theia-land.fr/)]([http://hydroweb.theia-land.fr/](http://hydroweb.theia-land.fr/))) and median amplitude of the time series. Dots are operational VSs (from currently flying missions and updated in near real time) and squares are research VSs (identified as reanalysis in table 5). VSs rounded in black are drawn in (d and e; b) month of maximum surface water elevation (SWE) for the mean monthly time series at each VS; (c) Month of the minimum SWE for the mean monthly time series; (d) Composite time series of the VSs close one to each other on the lower Negro River, VSs NEGRO_XMI444, NEGRO_XMI420 and NEGRO_XMI404, (e) Time series on the Amazon middle reach and Amazon lower reach composed of Jason-2 and Jason-3 observation at VS AMAZONAS_KMI534 and AMAZONAS_KMO397, respectively.
A straightforward application of these profiles is to derive the spatiotemporal variations of the water surface slope. While former studies focused on the spatial variations of the surface water gradient, a first try to estimate the temporal variations of the Amazon main stem slope was performed in [PERSON] et al. (2002) using VSs from the T/P mission. They revealed changes in the sign of the rate of slope variation that were explained by the river not reaching equilibrium. Although the slopes from [PERSON] et al. (2002) compared well with slopes from the Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) - a snapshot of profiles and slopes in February 2000 ([PERSON] & [PERSON], 2005)--and with gauge data ([PERSON] et al., 2013), these breaks in slope variation rate were not found in profiles extracted from more recent and complet. altimetric databases ([PERSON] et al., 2016). [PERSON] et al. (2016) estimated two different time series of slopes from satellite altimetry in the lower Negro River: the first was calculated using a daily interpolation of upstream and downstream SWE time series, providing a daily slope time series, and the second was calculated using the mean climatology of upstream and downstream VSs. Although the stage to discharge relationship was improved when considering the variation of slope with time estimated through both methods, it is the monthly means that provided the best improvement. This illustrates the difficulty in inferring slopes from non-daily uncertain observations.
By coupling satellite altimetry and a hydrologic and hydraulic model through stage to discharge rating curves, [PERSON] et al. (2016) provided a map of estimated bottom of river in the entire Amazon basin using data from ENVISAT and Jason-2 missions. This map was then used by [PERSON] et al. (2017) on a reach of the Xingu River to parameterize a hydraulic model. Such cases where the satellite ground-track crosscuts several times the same river reach allow a more refined analysis of water surface slope. This occurs ininuous rivers flowing from north to south (or the contrary) like the Xingu River, a right margin tributary of the Amazon River (Figure 2). Given these conditions, the authors verified that the presence of an obstacle in the river bed produces temporal changes in water surface slope observed by satellite altimetry. [PERSON] et al. (2019) proposed a benchmark of methods of altimetric data assimilation, ranging from direct insertion to a hydraulically based Kalman filter, to improve bathymetry estimates of the Madeira River. They concluded that satellite altimetry can be used for better constraining SWE and flood inundation simulations. An analysis of SWE from the ENVISAT mission revealed water passing from the Negro River to the Solimoes River through their interconnected floodplains at high stages ([PERSON] et al., 2012).
The capacity to observe channel-floodplain connectivity through altimetry was investigated by [PERSON] (2020). By observing seasonal changes in SWE in rivers and surrounding floodplains, they separated the role of channelized flows and of overbanks flows, which contributes to surface water storage and smooths the channelized-induced topography. The floodplain located between the Madre-de-Dios, the Beni, the Guapore and the Mamore rivers in the upper Madreia basin was characterized using ENVISAT and SARAL data ([PERSON] et al., 2018). Water level differences between the frequently flooded regions, with no direct connection to the Andes, and the regions subject to sporadic though large flood events were distinguished. Recently, [PERSON] et al. (2020) produced SWE time series in the complex Negro River interluvial wetlands from Sentinel3-A data. For the first time, they reported \(<\)1 m water level variations in these complex areas. Their results show that satellite altimetry can help understanding the hydraulic behavior of complex unaged areas and help validate hydrologic and hydraulics models.
[PERSON] et al. (2000, 2005, 2007) applied for the first time interferometric SAR (InSAR) in the central Amazon floodplains and showed that the water flows in the floodplains are dynamic in space and time, changing the direction with the flood wave of the river. Before the flood, the flows are controlled by the local topography and the surface water elevation in the floodplain is not equivalent to the river level ([PERSON] et al., 2007). By assuming that the water surface in the floodplain is equivalent to those in the main channel, estimates of water storage derived from flood routing can be overestimated, as shown by [PERSON] (2003). [PERSON] et al. (2010) compared temporal changes in floodplain water in the Amazon and Congo basins. While the Amazon River is connected by many channels to the floodplains and has complex flow patterns, the Congo Rivers (and especially the Cuvette Centrale) have sparse connections with interluvial areas and flow patterns that are not well defined and have diffuse boundaries. The patterns of water surface variations in the floodplains located on the Tapajos and Solimoes rivers were examined by [PERSON] et al. (2011) and [PERSON] et al. (2018), respectively. The most recent SAR missions allowed monitoring of smaller water bodies.
Through direct assessment or combination with other RS products, satellite altimetry can be used to derive non-measured hydrological variables. [PERSON] et al. (2014) were able to infer the varying exchanges between surface water and the groundwater base-level from 491 ENVISAT VSs located all over the basin. Estimates of deviations from groundwater base-level reached up to 5 m. [PERSON] et al. (2012) made a joint use of satellite altimetry and inundation extent to derive variations of surface continental water storage (see Section 5). These two variables were used in [PERSON] et al. (2019) to estimate the spatiotemporal variability of groundwater storage in the Amazon basin. [PERSON] et al. (2001) and [PERSON] et al. (2019) found signatures of global climatic events such as ENSO and sea surface temperature variations in the T/P and Jason-2 SWE time series, respectively. Since the SWE estimates are now delivered in near real time, rating curves that relate SWE with discharge and depth, have been the focus of several studies (see details in Section 6.2). These rating curves were either computed using local gauges ([PERSON] et al., 2006) or model outputs ([PERSON] et al., 2012; [PERSON] et al., 2006). By constraining the rating curve parameters into Manning-realistic bounds, [PERSON] et al. (2016) showed that discharges predicted from satellite altimetry are comparable to those measured in situ. The original SWE time series or their conversion into discharge offer an independent tool to validate hydrological models ([PERSON] et al., 2016) and their rainfall inputs, and in situ data ([PERSON] et al., 2014).
With its disruptive technology based on swath altimetry, almost-global coverage and joint observation of SWE, river width and slope, the SWOT mission, to be launched in 2022, will permit an unprecedented observation of SWE all along the river network and on major lakes and floodplains. As highlighted by [PERSON] et al. (2016), SWOT observation of SWE will permit a better monitoring of transboundary waters and wetlands in the Amazon. Dedicated to sample all rivers wider than 100 m and lakes larger than 250 x 250 m, the mission will permit a consequent reduction of global and regional models, noteworthy through data assimilation ([PERSON] et al., 2020; [PERSON] et al., 2020). The estimate of discharge from altimetry will benefit from SWOT data, both thanks to the global coverage and the observation of slopes, allowing a better constraining of uncertain hydraulics ([PERSON] et al., 2015).
Thanks to more than 20 years of studies, EO data sets, especially satellite altimetry, have been revealed as an unprecedented tool to monitor continental watersheds and their droughs and floods ([PERSON] et al., 2020). The current satellite altimetry missions opened the era of operational monitoring from space at large scale, and this will be of critical importance in the coming decades in the large tropical transboundary watershed that is the Amazon basin. With almost two thousand VSs distributed all over the basin and available for free on websites, and potentially hundreds more, satellite altimetry can favorably complement the traditional in situ network, whose location usually depends on the proximity to a city or town. However, to operationally monitor non-open waters such as permanently or seasonally flooded vegetated floodplains remains challenging. In fact, few lakes and reservoirs are monitored by altimetry routinely in the basin though more could be ([PERSON] et al., 2011; [PERSON] & [PERSON], 2006). The forthcoming missions will benefit from past research to improve the accuracy of SWE time series and promote its use for monitoring more local phenomena, such as floodplain-channel exchanges. Although limited due to availability of appropriate data, InSAR data sets help characterize floodplains/rivers connectivity and dynamics. The global coverage of the forthcoming SWOT mission will increase greatly our understanding on the global water cycle and should allow a better quantification of past and current inter-mission biases, helping turn satellite altimetry archives into a unique climatic data set and understanding the impacts of climate change and human activities on the basin. Such a task will benefit of the ongoing Validation of Altimetric Satellites for HYdrology in Brazil project (VASHYB, [[https://swot.jpl.nasa.gov/documents/1054/](https://swot.jpl.nasa.gov/documents/1054/)]([https://swot.jpl.nasa.gov/documents/1054/](https://swot.jpl.nasa.gov/documents/1054/))), which aims to validate SAR and InSAR observations. The SWOT mission will dramatically increase our capacity to model the Amazon basin and the variations of its water cycle, thanks to the new capacity to monitor hydrological variables (height, width, slope, and associated discharge) of hundreds of rivers 100 m wide ([PERSON] et al., 2016). The centimetric accuracy in SWE and slope ([PERSON], 2018) should provide new insights on water fluxes in the Amazon. Since the main limitation for a broader use of satellite altimetry remains its relatively low temporal sampling, future missions such as the SMall Attimetry Satellites for Hydrology mission (SMASH, [PERSON] et al., 2019), broadcasted together with the current constellation, should help tackle this issue.
### Surface Water Extent
Characterizing the extent and variation of surface water bodies and aquatic ecosystems, which include rivers, streams, lakes, wetlands, as well as seasonally inundated floodplains, forests and savannas, is of primary importance to the study of the water, energy and biogeochemical cycles of the Amazon River basin ([PERSON], 1997; [PERSON] et al., 2009). Indeed, covering about 20% of basin's surface area, with large temporal variability, the surface waters of the Amazon play a key role in the climate and in the maintenance of biodiversity. Amazon surface waters are a major source and sink of carbon dioxide ([PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON] et al., 2013) and the largest natural geographic source of methane in the tropics ([PERSON] et al., 2013; [PERSON] et al., 2004; [PERSON] et al., 2017; [PERSON] et al., 2013). In this context, understanding the dynamics of surface water extent is of primary importance to Amazon hydrology, biogeochemically processes and their link with climate, for effective management of water and fisheries resources (see Section 6.3) and for a disaster management for cities which are under flood risk (e.g., Iquitos, Porto Velho, Rio Branco, Cruzeiro do Sul). This is particularly true in the context of current global changes that impact the Amazon (see Section 6.4), with intense drought and flood events that recently affected large areas of this region ([PERSON] et al., 2012; [PERSON] et al., 2013; [PERSON] et al., 2008, 2011). In addition, monitoring the variations of surface water hydrological conditions is key to support the development of models of the Amazon water cycle and its surface hydrology (see Section 6.2).
Characterizing the distribution and quantifying seasonal and interannual variations in the extent of surface waters at the scale of the Amazon basin is a challenge given their large variety and variability, and the presence of cloud cover and forest vegetation. Early estimates of the distribution of surface water for large areas were based on static databases from aeronautical charts and aerial photographs, which often reflected the maximum open water extent ([PERSON], 2013; [PERSON], 1987) and did not provide information on their temporal and spatial variations. The Global Lakes and Wetlands Database ([PERSON], 2004) estimates the extent of floodplains and wetlands in the Amazon of \(\sim\)300-350 \(\times\) 10\({}^{3}\) km\({}^{2}\), but with large uncertainties ([PERSON] et al., 2018). The advent of satellite observations now allow monitoring the large-scale dynamic of surface waters, including those in the Amazon basin ([PERSON] et al., 2007; [PERSON] et al., 2007) enabling progress on understanding of the associated physical, biogeochemical, environmental and ecological processes.
Different RS-based techniques, using observations made in a wide range of the electromagnetic spectrum (visible, infrared, and microwave; [PERSON] et al., 2004; [PERSON] et al., 2016), have been developed, with varying degrees of success, to derive quantitative estimates of the extent and dynamics of surface waters and aquatic systems in the Amazon (Table 4). They encompass a wide range of spatial and temporal resolutions, often based on a trade-off between temporal and spatial coverages. Observations with low spatial resolution (e.g., \(\sim\)10-50 km from passive microwave sensors) are generally limited to the detection of relatively large inundated areas, or regions where the cumulative area of small areas represents a fairly large portion of the satellite footprint. They have the advantage of frequent temporal coverage, sometimes daily. High-resolution observations (e.g., \(<\)100 m from SAR for instance) provide information at a fine spatial scale but have low temporal frequency, often limiting observations over large areas to a few times per season. Optical and infrared observations offer good spatial and temporal resolution but have limited capabilities in the tropical Amazon region as they are unable to penetrate clouds and dense vegetation.
Passive microwave observations have demonstrated their usefulness for observing surface water and flood extent and provided some of the first estimates of Amazon surface water extent from satellite ([PERSON] & [PERSON], 1989) as reviewed in [PERSON] et al. (2018). Emissivities (and brightness temperatures) are sensitive to the presence of surface water ([PERSON], 1991; [PERSON] et al., 1994) with a decrease in emissivity in both linear polarizations (horizontal and vertical) and an increase for the difference in polarization, especially at low frequencies, due to the different dielectric properties between water, soil and vegetation. Surface water and inundation patterns in the large floodplains of the central Amazon ([PERSON] et al., 1998) and South America ([PERSON] et al., 2002) were derived by analysis of the 37-GHz polarization difference observed by the Scanning Multichannel Microwave Radiometer (SMMR; Nimbus-7 satellite, 1979-1987). By developing a relationship between the total flooded area along the Amazon River main stem and the monthly means of river stage at Manaus, they provided the first 94-year reconstruction of flooded area from the river stage in situ record, estimating the long-term mean of the flooded area along the Amazon River
\begin{table}
\begin{tabular}{l c c c c c} \hline & & Sensors/Satellite & & Spatial/temporal & \\ RS approaches & References & (Product name) & Original area of study & resolution & Time span \\ \hline Passive Microwaves & [PERSON] and & SIMR on Nimbus 7 & 4 major river basins & \(\sim\)25 km/Monthly & 1979–1985 \\ & [PERSON] (1989) & & of SA & & \\ & [PERSON] et al. (1994) & SIMR on Nimbus 7 & Central Amazon and & \(\sim\)25 km/Monthly & 1979–1985 \\ & & floodplains & & & \\ & [PERSON] et al. (1998) & SIMR on Nimbus 7 & Amazon River and & \(\sim\)25 km/Monthly & 1979-1985 (and 1902– \\ & & tributaries & & & 1995 reconstruction) \\ & [PERSON] et al. (2002) & SIMR on Nimbus 7 & 6 major floodplains & \(\sim\)25 km/Monthly & 1979–1987 \\ & & over SA. & & & \\ & [PERSON] et al. (2007) & AMSR/E on Aqua & Global & \(\sim\)25 km/daily & 2002–2011 \\ & [PERSON] et al. (2017) & SMOS (SWAF) & Amazon basin & \(\sim\)25–50 km/3-day & 2009–present \\ Active Microwaves & [PERSON] et al. (2003) & SAR on JERS-1 & Central Amazon & 100 m/Sep–Oct 95 and & Sep–Oct 95 and May– \\ & & & May–Jun 96 & Jun 96 \\ & [PERSON] et al. (2009) & SAR on ERS-2/ & Bolivian Amazon & 2 RADARSAT (50 m)/3 & 1996–1998 \\ & RADARSAT & & ERS (15 m) images & & \\ [PERSON] et al. (2013) & ScanSAR mode on & Lower Amazon River & 100 m/12 ScanSAR & 2007–2010 \\ & ALOS/PALSAR & floodplain & images & & \\ Ferreira-Ferreira & SAR on ALOS/PALSAR & Central Amazon & 12.5 m/13 ScanSAR fine & 2007–2010 \\ & et al. (2015) & floodplain & bream images & & \\ ([PERSON] et al., 2015) & SAR on JERS-1 & Amazon basin & 100 m/Sept–Oct 1995 & Sep–Oct 1995 and \\ & & & and May–Jun 1996 & May–Jun 1996 \\ [PERSON] et al. (2015) & ScanSAR mode on & Amazon basin & 100 m/323 ScanSAR & 2007–2010 \\ & ALOS/PALSAR & & images & & \\ Ovando & ScanSAR mode on & Bolivian Amazon & 100 m/45 ScanSAR and & 2007–2009 and \\ & & ALOS/PALSAR and & wetlands & 500 m/8-day MODIS & 2001–2014 \\ & MODIS reflectance & & images & \\ Park and & SAR on ALOS/PALSAR & Amazon floodplain & 12–350 m/19 images & 2006–2008 \\ & Latrubesse (2017) & & (Mixtuba) & & \\ [PERSON] et al. (2019) & SAR on ALOS/PALSAR & Amazon/Solimones & 30 m/23 images & 2007–2011 \\ & & River (Janauca) & & \\ [PERSON] et al. (2019) & SAR on ALOS/PALSAR & Central Amazon & 25 m/56 images & 2006–2011 \\ & [PERSON] et al. (2020) & ScanSAR on ALOS-2 & Amazon basin & 50 m/Yearly minimum & 2014–2017 \\ & PALSAR-2 & & and maximum & \\ Optical and infrared & [PERSON] et al. (2015) & Landsat (G3 WBM) & Global & 90 m/4 scenes of & 1990–2010 \\ & & & surface body free, at & \\ & & & & 5-year interval & \\ & [PERSON] et al. (2016) & Landsat (GSW) & Global & 30 m/Surface water & 1984–2015 \\ & & & occurence & \\ & Allen and & Landsat (GRWL) & Global & 30 m/static widths and & – \\ & [PERSON] (2018) & & areas & \\ & [PERSON] et al. (2019) & Landsat & Amazon basin & 30 m/Surface water & 1985–2017 \\ & & & changes & \\ Multi-satellite & Prigent & SSMI/AVHR/ERS & Global & \(\sim\)25 km/monthly & 1992–2015 \\ techniques (passive & et al. (2007, 2020) & (GIEMS) & & \\ microwaves in & combination & & & \\ & with other RS & & & \\ observations) & & & & \\ \hline \end{tabular}
\end{table}
Table 4: RS-Based Approaches Developed to Monitor the Extent of Surface Water in the Amazon (Non-Exhaustive List)main stem to be \(\sim\)47,000 km\({}^{2}\). Those studies have been followed by passive microwave-derived products of surface water extent over the Amazon, using Special Sensor Microwave/Imager (SSM/I), Advanced Microwave Scanning Radiometer (AMSR-E; [PERSON] et al., 2007) and most recently Soil Moisture Ocean Salinity (SMOS) observations ([PERSON] et al., 2017). [PERSON] et al. (2017) used the microwave L-band (1.4 GHz) observations from 2010 to 2017 to map the temporal evolution of the Amazon water bodies at coarse spatial resolution (\(\sim\)50 km) and weekly temporal resolution (product named SWAF) with the ability, thanks to the L-Band frequency, to better retrieve water under dense canopy. Passive microwave observations have inherent limitations because of their ground footprints in the typical order of 25-50 km, and their relatively low spatial resolution is often insufficient to observe small water bodies.
Multi-satellite methodologies that combine the complementary strengths of different types of satellite observations to retrieve surface water extent and their dynamics expand the information provided by passive microwave radiometers (Table 4). Though designed originally for global scale applications, these approaches have been evaluated in the Amazon basin. The Global Inundation Extent from Multi-Satellite (GIEMS, [PERSON] et al., 2010; [PERSON] et al., 2007, 2016, 2020) or the Surface WAter Microwave Product Series (SWAMPS) Inundated Area Fraction ([PERSON] et al., 2015) detect and quantify multi-decadal variability of surface water extent over tropical environments ([PERSON] et al., 2008; [PERSON] et al., 2008, 2013). The current version of GIEMS is available at \(\sim\)25 km spatial resolution on a monthly basis from 1992 to 2015 (GIEMS-2, [PERSON] et al., 2020, Figure 6a), while SWAMPS offers current and near-real-time information ([PERSON] et al., 2018). The use of these passive microwave-derived data sets helped reveal the sources and characteristics of the flood pulse and annual flood wave along the Amazon River and major tributaries. They contributed to show at basin scale the water extent seasonality, with a high flood season in May-June and low flood season in November in the central Amazon floodplain. At basin-scale, Amazon surface water extent (Figure 6b) varies from \(\sim\)100,000 km\({}^{2}\) (low season) to almost \(\sim\)400,000 km\({}^{2}\) (high season), but with large interannual variability, mainly driven by droughs (1998, 2005, and 2010) or floods (1997, 2014) extreme events ([PERSON] et al., 2010; [PERSON] et al., 2020). However, the maximum surface water extent from GIEMS and SWAMPS are lower than those from SAR estimates (Figure 6b).
[PERSON] et al. (2007) showed that seasonal flooding differed between the north and south parts of the basin due to seasonal differences in precipitation. [PERSON] et al. (2008) reported a phase lag in precipitation, flood extent, and peak flows at the basin scale, suggesting as in [PERSON] et al. (1989), that floodplains in large basins such as the Amazon can store a large volume of water and alter the water transport. [PERSON] et al. (1989) applied a simple water routing scheme and estimated that up to 30% of the discharge of the Amazon River is routed through the floodplains. However, studies such as [PERSON] et al. (2012), based on the large-scale hydrological model that used GIEMS to evaluate their floodplains simulations, suggested instead that the
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline & & Sensors/Satellite & & Spatial/temporal & \\ RS approaches & References & (Product name) & Original area of study & resolution & Time span \\ \hline & [PERSON] et al. (2015) & SSM/I, SSMIS, ERS, QuikSCAT, ASCAT & & \\ & & (SWAMPS) & & & \\ [PERSON] et al. (2013) & GIEMS/JERS-1 SAR & Central Amazon & 500 m/monthly & 1993–2007 \\ Fluet-Chouinard & GIEMS downscaled & Global & 500 m/max,/min./ & 1993–2007 \\ et al. (2015) & (named & & average & \\ & GIEMS-D15) & & & \\ [PERSON] et al. (2017) & GIEMS downscaled & Global & 90 m/monthly & 1993–2007 \\ & & (named & & \\ & GIEMS-D15) & & & \\ [PERSON] et al. (2019) & SMOS downscaled & Amazon basin & 1 km/3-day & 2010–2016 \\ & & (named SWAF-HR) & & \\ \hline \hline \end{tabular} Note. References, sensor/satellite name, product name (when available), original area of study, spatial/temporal resolution and time span of data availability are shown.
\end{table}
Table 4: Continuedactual value might be more than 5%. Furthermore, [PERSON] et al. (2020) reported that the ratio between river-foodplain discharge and basin discharge ranged between 5% and 40%, which is comparable to the range estimated from observations by [PERSON] et al. (1989) and [PERSON] et al. (2010) who used gravimetric and imaging satellite methods to estimate the amounts of water seasonally filling and draining from the mainstream Amazon floodplain. Hence, there is a need to better understand the processes that control Amazon inundations in order to quantify the various fluxes across floodplain environments, as is evident in applications of regional-scale flooding models ([PERSON] et al., 2014).
Synthetic aperture radars are active radar instruments that measure the backscatter of the observed surface at an angle of incidence (off-nadir), regardless of cloud cover, and allow delineation of open surface waters
Figure 6.— Surface water extent of the Amazon basin. (a) Map of maximum wetland and surface water extent (high water season) from JERS-1 SAR ([PERSON] et al., 2015) and map of annual maximum surface water extent (fraction in km\({}^{2}\) for each 773 km\({}^{2}\) pixel) averaged over 1992–2015 from GIEMS2 ([PERSON] et al., 2020) (D Basin-scale monthly mean surface water extent variability for 1992–2015 from GIEMS2 (solid black line) along with estimates of JERS-1 SAR-derived wetland and flooded area for high-water (dashed blue line) and low-water (solid blue line) seasons. Also shown are the Global Surface Water (GSW, [PERSON] et al., 2016) permanent surface water extent (green line, GSW permanent) and the total (permanent plus transitory) surface water extent at maximum (red line, GSW Total). (c) Map of maximum surface water extent at regional scale (boxes in panel (a) indicate the locations) from GIEMS-D15 ([PERSON] et al., 2015) and SWAF-HR ([PERSON] et al., 2019).
and inundated area with vegetation with a typical spatial resolution of 10-100 m ([PERSON] et al., 2017; [PERSON] et al., 1990; [PERSON] et al., 1997) The Spaceborne Imaging Radar-C (SIR-C) experiment provided high quality, multi-band and multi-polarization data for the Amazon that led to the development of new approaches using SAR. [PERSON] et al. (2000) demonstrated the ability of interferometric analyses to detect centimeter-scale variations in slope across the Amazon rivers and floodplains (see Section 4.1). [PERSON] et al. (1995) developed algorithms to detect inundation and vegetation within Amazon wetlands that benefitted from modeling of interactions between vegetation and radar, including the double-bounce effect, also done as part of SIR-C ([PERSON] et al., 1995). Understanding derived from this led to the use of data provided by the Japan Earth Resources Satellite-1 (JERS-1) to produce the first high-resolution wetland map for the central Amazon region under low-water and high-water conditions at 100-m resolution ([PERSON] et al., 2003). These results were validated with airborne, high-resolution, videography transects throughout the imaged area ([PERSON] et al., 2003). [PERSON] et al., (2003) found that 17% of the 1.77 million km\({}^{2}\) study area is occupied by wetlands, of which 96% are inundated at high water and 26% at low water. Flooded forests accounted for nearly 70% of the overall wetland area, but proportions of the wetland habitats showed large regional variations related to floodplain geomorphology. Those new estimates of the large inundated area were of major importance to understand the outgassing of methane and carbon dioxide from Amazon flooded areas (see Section 6.3).
The JERS-1 SAR estimates were extended to the entire wetlands of the lowland Amazon basin (region \(<\)500 m asl) (Figure 6a; [PERSON] et al., 2015), currently one of the standards for comparison with other satellite-derived products. It estimates the flooded extent (Figure 6b) to be \(\sim\)2.85 \(\times\) 10\({}^{5}\) km\({}^{2}\) for the low water season (October-November 1995) and of \(\sim\)6.34 \(\times\) 10\({}^{6}\) km\({}^{2}\) for the high water season (May-July 1996). An interesting comparison is one made for the central corridor of the Amazon ([PERSON] et al., 2007) between GIEMS and the 100 m resolution L-band JERS-1 SAR mosaic of [PERSON] et al. (2003) for low water (September-October 1995) and high water (May-June 1996). For both seasons, the spatial structures are similar but estimates of the surface water extent observed by SAR (118,000 km\({}^{2}\) for the low water season, 243,000 km\({}^{2}\) for the high water season) are larger than the area estimated by GIEMS (105,000 km\({}^{2}\) for the low water season, 171,000 km\({}^{2}\) for the high water season). Thanks to its better spatial resolution, the SAR estimates are capable to discriminate smaller water bodies than GIEMS (typically water bodies smaller than 80 km\({}^{2}\) that is, 10% of a GIEMS pixel), especially for the low water season. For the entire Amazon basin, the basin-wide estimates from GIEMS do not match the basin-wide SAR (Figures 6a and 6b) as reported in [PERSON] et al. (2015) which suggested that global data sets derived from lower-resolution sensors or optical sensors capture less than 25% of the wetland area mapped by the SAR.
The use of multi-temporal SAR coverage, such as the ScanSAR mode of ALOS/PALSAR, provide variations of flood extent at the scale of floodplain units, for example, Curuai floodplain along the lower Amazon River ([PERSON] et al., 2013), Mamirau floodplain ([PERSON] et al., 2015) or inundation patterns in central Amazon ([PERSON] et al., 2019; [PERSON] et al., 2019). [PERSON] et al. (2020) generated annual maximum and minimum inundation extent maps over the Amazon using ALOS-2/PALSAR-2 ScanSAR, in line with previous inundation maps by L-band JERS-1 and ALOS/PALSAR radar classifications of the inundation ([PERSON] et al., 2015). At the regional scale, [PERSON] et al. (2009) mapped the floods in the Bolivian Amazon from SAR C-Band microwave data of RADARSAT and ERS-2. Over the same region, the surface water dynamics of the Bolivian Amazon wetlands ([PERSON] et al., 2018), as well as the characterization of extreme flood events ([PERSON] et al., 2016) were investigated by combining ALOS/PALSAR SAR observations with MODIS multi-temporal flood maps and altimetry-derived water level variations (ENVISAT & SARAL). Other SAR satellite missions, such as the Copernicus Sentinel-1 SAR (launched in 2014), which offer a global revisit of 6-12 days, have not been yet fully exploited in the Amazon but offers new opportunities for mapping the spatial and temporal variations of surface waters at a fine scale in tropical environments. The near-future launch of SAR satellites, such as NISAR and SWOT ([PERSON] et al., 2016), will offer new opportunities to monitor Amazon surface water with dedicated sensors.
Optical and infrared imagery observations (e.g., Landsat, SPOT, QuickBird, Ikonos, AVHRR, MODIS, and Sentinel 2A/B) offer high spatial and temporal resolutions (\(\sim\)1-500 m, sub-daily to weekly) but in tropical environments, they are generally limited by the inability to penetrate clouds and dense vegetation. Therefore, assembling cloud-free coverage during the rising flood season of the central Amazon remains challenging ([PERSON], 2001; [PERSON] et al., 2015; [PERSON] et al., 2015). Nevertheless, classification of optical imagery using water indexes and related methods, as reviewed by [PERSON] et al. (2018), enables to estimate flood frequency based on temporal maps of surface water cover, and despite the limitations from vegetation canopy and cloud cover, this type of data can be of value to monitor open surface water. Several studies (Table 4) based on Landsat observations created global databases of the area of rivers (Global River Widths from Landsat -GRWL; [PERSON], 2018) and surface water ([PERSON] et al., 2014; [PERSON] et al., 2015) which can be used at the basin scale. Based on the decadal-scale monitoring of Landsat missions, the Global Surface Water data set (GSW, [PERSON] et al., 2016) uses 3 million images over 32 years (from 1984 to 2015) at a 30 m spatial resolution to derive a monthly record of water presence in classifying each Landsat pixel as open water, land, or non-valid observation using an expert system. In the Amazon basin, GSW estimates of surface water extent (permanent and total as the sum of permanent and transitory water bodies) are lower than the estimates from other RS-based techniques such as SAR or GIEMS (Figure 6b) and comparison of GSW with GIEMS-D3 (see further below) found seasonal water bodies in savannas and forest floodplains were not detected properly ([PERSON] et al., 2018). [PERSON] et al. (2019) developed another Landsat classification to estimate long-term changes in Amazon surface waters revealing the recent increase in areas associated with hydropower lakes. Recent satellite missions such as Sentinel 2A/B (since 2015, with 10 m spatial resolution at 5-10-day intervals, [PERSON] et al., 2020) or programs such as the RapidEye (since 2008, 5 m spatial resolution and a temporal resolution of 1-5.5 days, [PERSON] et al., 2019) or the PlanetScope (CubeSats, since 2014, with 3-5 m spatial resolution and daily revisit time; [PERSON] et al., 2019) constellations might bring new opportunities to study fine scale surface water extent of the Amazon.
In order to take advantage of the complementary strengths of various observations, for instance, the low resolution but long-term estimates of passive microwave versus the high resolution but limited in time observations from SAR, a downscaling methodology combining both estimates have been developed to retrieve monthly central Amazon at \(\sim\)500 m spatial for the 1993-2007 period ([PERSON] et al., 2013). Several other studies based on downscaling approaches using a floodability index provide high resolution maps of surface water extent over the Amazon, such as GIEMS-D15 ([PERSON] et al., 2015; \(\sim\)500 m spatial resolution and its 1-km adaptation as in [PERSON] et al., 2019) and GIEMS-D3 ([PERSON] et al., 2017, 90 m). Similarly, [PERSON] et al. (2019) proposed a downscaling methodology based on multi-source RS data (SMOS SWAF; combined with a global DEM and GSW data set) to map Amazon inland water under vegetation at \(\sim\)1 km spatial resolution every 3 days for 2010-2016 (named SWAF-HR). Figure 6 shows maps of maximum surface water extent from GIEMS-D15 and SWAF-HR for three regions, including interfluidic wetlands. Such observations are valuable to wetland conservation decisions, as the timing and duration of inundation often determine ecological characteristics and the provision of ecosystem services. For instance, [PERSON] et al. (2019) classified Amazon wetlands according to the timing and duration (months per year) of inundation detected with GIEMS-D15, and their link to precipitation regimes. It revealed that permanently inundated wetlands account for the largest area and are mainly floodplains located in the lowlands of the catchment. Seasonally inundated wetlands varied in the duration of inundation reflecting different rainfall and hydrological regimes. These regional differences in in inundation characteristics are important to conservation planning and wetland management especially in the context of anthropogenic interventions such as dams and waterway construction.
Finally, new RS techniques and methodologies are continuing to be developed and can help monitor the surface water extent of the Amazon basin. The potential for Global Navigation Satellite System-Reflectometry (GNSS-R) has been explored ([PERSON], 2020; [PERSON] et al., 2018; [PERSON] et al., 2019) using Cyclone GNSS (CYGNSS) constellation of GNSS-R satellites and a simple forward model that demonstrates how surface reflectivity measured by CYGNSS can capture flooding dynamic over the region.
In Section 5.1 \"Methods for Measuring Area\" of [PERSON] et al. (2007), the authors suggested that _\"Perhaps the best opportunity in the next few years for routine measurements of inundated area will result from the Japan Aerospace Exploration Agency's ALOS mission\"_. More than a decade later, it is worth noting that the extent and variability of surface water of the Amazon are still one of the most studied variables of the hydrological cycle, but that studies using ALOS observations remain recent and limited. Further studies and new observations are required to fully characterize Amazon surface water extent and the processes that drive the patterns and dynamics. In particular, polarimetric and interferometric L-band SAR data from the forthcoming NASA/ISRO SAR mission and the Ka-band Radar Interferometer (KaRIn) swath observations from the forthcoming SWOT mission will be capable of enhanced monitoring and comprehensive survey of large-scale surface water extent and dynamics of the Amazon.
### Floodplain and River Channels Topography
Along the Amazon River, the floodplain has many lakes and channels that vary in extent, depth, and connectivity ([PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2012). This complex topography affects the water flow through river-floodplain water exchanges, which in turn, are important for carbon, nutrients, and sediment fluxes ([PERSON] et al., 2009; [PERSON] et al., 2021). Accurate topographic information is essential for the characterization of the surface water in the floodplain, particularly for hydraulic numerical modeling ([PERSON] et al., 2013; [PERSON], [PERSON], et al., 2013; [PERSON] et al., 2014). Furthermore, topographic mapping is required for understanding the morphology and morphodynamics of the river channels and lakes. The SRTM DEM is a global topographic data set with 30-90 m of spatial resolution and accuracy of 8 m ([PERSON] et al., 2006) generated from C-band interferometry ([PERSON] et al., 2007) and has been widely used in hydraulic simulations and geometric characterization of the Amazon floodplains (Figure 7a). However, the data are affected by vegetation cover and have errors such as absolute bias, speckle noise (granular aspect in the image due to the random presence of pixels with extreme values), and stripe noise ([PERSON] et al., 2006). It is also not capable of describing bathymetry of inland water bodies as it observed surface water elevation only once.
The application of topographic data, such as SRTM DEM, together with radar (e.g., RADAM, JERS-1) and optical (e.g., Landsat) images allowed the geomorphological characterization of floodplains and river channels of the Amazon basin. [PERSON] et al. (1992) described lakes of different shapes based on RADAM maps along different sections of the main stem Solimoes/Amazonas rivers and their major tributaries. [PERSON] and [PERSON] (2002) and [PERSON] et al. (1996), described geomorphologically distinct regions along the upper and middle reach of the Amazon River. Scroll-bar topography, which forms long and narrow lakes, and oxbow lakes, located in abandoned river meanders, are dominant in the upstream reaches ([PERSON] et al., 1996; Figure 7). Downstream reaches are characterized by large, shallow lakes formed by the overbank deposition of fine sediments in a very flat floodplain topography ([PERSON] & [PERSON], 2002; [PERSON] et al., 1996; Figure 7). Active deposition of sediments across the floodplains was also identified and described by [PERSON] et al. (2017), [PERSON] and [PERSON] (2019), and [PERSON] et al. (2018) using RS data. [PERSON] et al. (2019), [PERSON] et al. (2014), [PERSON] et al. (2009), [PERSON] et al. (2012), and [PERSON] et al. (2019) characterized the channel's migration of rivers and floodplains. Sediment supplies play an important role in the evolution of Amazonian rivers, as the rivers with high sediment loads experience faster meander migration and higher cutoff rates than rivers with lower sediment loads ([PERSON] et al., 2014). Large and rapid geomorphological changes can also arise due to anthropogenic pressures such as livestock and channel irrigation. These may be the causes of the progressive erosion of a channel along the lower Amazon River that captured almost all discharge from the lower Araguari River, which previously had flowed directly to the Atlantic Ocean ([PERSON] et al., 2018; described in more details in Section 6.4).
In order to improve the applicability of SRTM data to hydraulic modeling of the Amazon, various techniques were developed such as the removal of the vegetation height ([PERSON] et al., 2013; [PERSON] et al., 2016; [PERSON], [PERSON], et al., 2013; [PERSON], [PERSON], & [PERSON], 2011; [PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2017), the interferometric bias ([PERSON] et al., 2015; [PERSON] et al., 2014), as well as smoothing and pit removal ([PERSON], [PERSON], et al., 2012). Despite the better topographic representation achieved by these methods, topographic information below the water surface cannot be recovered from SRTM. Also, the SRTM data set relies on one only overpass in February 2000. Therefore, some processes, such as infilling and drainage of the floodplain, may not be well represented in the numerical models. River bathymetry is also key information that is not systematically resolved. Recently [PERSON] et al. (2019) demonstrated the potential of assimilating satellite altimetry data into hydraulic models for its estimation. To estimate the topography in seasonally flooded areas, [PERSON] et al. (2008) combined SWE with flood extents derived from JERS-1 images to estimate a bathymetric DEM of the Curuai floodplain. [PERSON] et al. (2020) related water depth and a flood frequency map, derived from surface water mapping, to infer the Curuai bathymetry. [PERSON], [PERSON], [PERSON], et al. (2020) developed and applied a systematic method to estimate floodplain topography using a combination of flood frequency maps derived from optical RS and ancillary in situ water level data archives (Figure 7d). This was the first systematic and extensive mapping of a seasonally flooded area in a wetland, showing floodplain depths less than 5 m (15 m) in low (high) water, and that active storage volume in the open-water floodplain varies 104.3 km\({}^{3}\) on average each year. This data set was complemented over permanently flooded regions by a compilation of digitized nautical charts from the Brazilian Navy. Recently, [PERSON] et al. (2021) applied this methodology to the Amazon estuary showing the morphology of the intertidal floodplain.
The bathymetric information in permanently flooded areas relies on in situ field surveys. Among the studies cited here, only a few obtained in situ bathymetric information in floodplains ([PERSON] et al., 2008; [PERSON] et al., 2019; [PERSON] et al., 2015) and rivers ([PERSON] et al., 2007). Additional studies with detailed bathymetry include [PERSON] and [PERSON] (1995), [PERSON] et al. (2006), [PERSON] et al. (1995), and [PERSON] et al. (2012). As
Figure 7.— (a) Shuttle radar topography mission digital elevation model in central Amazon. (b) Oxbow lakes in Juruña River (Sentinel-2, October of 2020). (c) Channel width in the floodplain (adapted from [PERSON] et al., 2012). (d) Topography elevation of the floodplain channels and lakes (adapted from [PERSON], [PERSON], [PERSON], et al., 2020).
part of the first hydrological budget of an Amazon floodplain lake, [PERSON] and [PERSON] (1995) surveyed the lake's bathymetry, which was subsequently used in the hydrological model of [PERSON] et al. (2019). [PERSON] et al. (1995) conducted a bathymetric survey of Lake Batata, located near the confluence of the Trombetas River and the Amazon River. This lake received tailings from bauxite processing and the estimate was used for conservation and recovery studies. [PERSON] et al. (2006) conducted an extensive bathymmetric survey of the Lake Grande do Curai floodplain, in the eastern Amazon basin. The bathymetry was used to estimate volume, in hydraulic simulation ([PERSON] et al., 2014) and topographic assessment ([PERSON], [PERSON], & [PERSON], 2020). [PERSON] et al. (2012) illustrated the first systematic characterization of floodplain channels in central Amazon based on Landsat imagery and field survey (Figure 7c). Floodplain channel widths vary considerably (10-1,000 m), and channel depths are related to the local amplitude of the Amazon River flood wave (\(\sim\)10 m), and deeper when subject to local runoff.
Many advances have been made to characterize the topography of rivers and floodplains using RS techniques, among the promising prospects for new DEMs (e.g., The L-band reduces the systematic positive bias of vegetation due to its ability of penetrating the canopy. Images from the NISAR mission, a bi-band SAR satellite to be launched in 2022 with global coverage and revisiting periods of 12 days will improve the availability of L-band radar data. The SWOT mission will simultaneously measure the SWE and water extent, opening up new opportunities to create and improve new techniques to estimate river and floodplain topography. New unexplored data from ICESat-2 satellite (launched in 2018) could be useful for topography estimation and validation.
### Water Quality: Sediments, Chlorophyll, and Colored Dissolved Organic Matter
According to their physical and chemical water characteristics, rivers of the Amazon basin are classified into three types: white, black, and clear-waters rivers ([PERSON] et al., 2011; [PERSON], 1956). Nutrient-rich white-water rivers, such as Madeira and Solimoes rivers, which account for 98% of Amazon River's sediment discharge to the Atlantic Ocean are dominated by inorganic sediments mainly originated from the Andes ([PERSON] et al., 2015; [PERSON], 1994). Blackwater rivers (e.g., Negro River; Figure 8a) are rich in dissolved organic matter derived from podzolic soils ([PERSON] et al., 2011; [PERSON] et al., 2020). Clear-water rivers (e.g., Tapajos River; Figure 8b) are characterized by nutrient-poor, low sediment, and dissolved organic matter concentration ([PERSON] et al., 2015). The water-type diversity and the pathways throughout the Amazon floodplain have significant implications for floodplain lakes and contribute to their high biodiversity ([PERSON] et al., 2011; [PERSON] et al., 2020).
A feasible way to monitor the aquatic system's biogeochemical properties and water paths between the rivers and floodplain lakes is through satellite RS. The interaction between electromagnetic radiation and water bodies, described by radiative transfer theory ([PERSON], 1994), allows the development and calibration of algorithms for estimating optically active constituents (OACs: Total Suspended Sediments - TSS; Phytoplankton pigments such as Chlorophyll-a (Chl-\(a\)) and Phyoccupanin; and Colored Dissolved Organic Matter [CDOM]) in the water bodies. These OACs influence the underwater light field and, therefore, the inherent (e.g., absorption and backscattering coefficient) and apparent optical properties (e.g., Remote Sensing Reflectance-\(R_{n}\)) of the water bodies.
There are significant challenges applying RS to the monitoring of Amazon basin aquatic ecosystems: (a) frequent cloud cover makes it difficult to acquire images, (b)) the optical complexity of the waters that flow throughout the basin, characterized by high variability in the concentration of the OACs, (c) the lack of sensors with high radiometric, spectral, spatial resolution, and signal-to-noise ratio to detect the small changes in upwelling radiance from the water column, and (d) the difficulty of using RS in narrow rivers and small lakes. These challenges have existed since the beginning of RS applications to study Amazonian aquatic ecosystems in the early 1980s when the studies were focused on calibration/validation of algorithms based on in situ data. These methods were based mostly on empirical approaches ([PERSON], 1978; [PERSON], 1980; [PERSON] et al., 1993), with acceptable accuracy limited in time and space to the data set for which the algorithm was developed ([PERSON], 2011; [PERSON] et al., 2012). In the last decade, efforts have been made to adapt ocean color protocols ([PERSON] et al., 2003) to acquire inherent optical properties (IOPs) of the Amazonian waters ([PERSON] et al., 2015; [PERSON] et al., 2013; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2017;[PERSON] et al., 2018), allowing for the development of semi-analytical algorithms (SAA). As the apparent optical properties (AOPs) are proportional to the IOPs, SAA uses an inversion process based on radiative transfer theory to obtain IOPs from the AOPs. Once the IOPs are known, they are used to retrieve the OAC concentrations. Therefore, SAA algorithms better identify each constituent contribution, providing more comprehensive temporal and spatial coverage ([PERSON], 1993; [PERSON] et al., 2017).
The flourishing of satellite RS in the second decade of the 21 st century is due to two crucial technological advances. First, a new generation of sensors was better designed to study complex aquatic environments, with improved spectral and radiometric resolution (Landsat-8, Sentinel-2, and CBERS-04A). Second, the unprecedented increase in computing performance and data storage has improved image processing capability. However, the low radiometric resolution provided by sensors onboard earlier Landsat (Landsat-5
Figure 8: (a) Examples of white and black, and (b) Clear waters. (c) Examples of spectra of three water types (Source: Labissa; [[http://www.dpi.inpe.br/labissa/](http://www.dpi.inpe.br/labissa/)]([http://www.dpi.inpe.br/labissa/](http://www.dpi.inpe.br/labissa/))): white water - Amazon River (TSS of 288.5 mg L\({}^{-1}\); Chl-\(\alpha\) of 2.0 \(\mu\)g L\({}^{-1}\); aCDOM in 440 nm of 1.3 m\({}^{-1}\)); clear water—Tapajós River (TSS 5.7 mg L\({}^{-1}\); Chl-\(\alpha\) of 10.8 \(\mu\)g L\({}^{-1}\); aCDOM in 440 nm of 1.2 m\({}^{-1}\)); black water - Bua-Bua Lake (TSS 7.4 mg L\({}^{-1}\); Chl-\(\alpha\) of 3.6 \(\mu\)g L\({}^{-1}\); aCDOM in 440 nm of 2.9 m\({}^{-1}\)). (d) Spatial variability of suspended sediments in the central Amazon (adapted from [PERSON] & Paiva, 2019). (e) Suspended sediment time-series in situ (observed) and satellite-based Moderate Resolution Imaging Spectroradiometer (estimated) obtained from the HYBAM monitoring system ([[http://hidrostat.ana.gov.br](http://hidrostat.ana.gov.br)]([http://hidrostat.ana.gov.br](http://hidrostat.ana.gov.br))).
and Landsat-7) satellites has not prevented the development of studies taking advantage of the substantial temporal database available (1972 to now) as reported in [PERSON] et al. (2015) and [PERSON] et al. (2018).
In preparation for new sensors, spectral behavior studies of Amazon water types among a wide range of OAC concentrations have been done ([PERSON], 2005; [PERSON], 2002; [PERSON], 2006). Those spectra were organized into a spectral library linked to OACs data to create reference spectra for water types classification ([PERSON] et al., 2012). The spectral library was used as input to a Spectral Angle Mapper algorithm for deriving water type maps from Hyperion and Medium Resolution Imaging Spectrometer (MERIS) images acquired simultaneously with field campaigns, with reasonable accuracies (48% and 67% for Hyperion and MERIS respectively). This updated library was applied to classify Brazilian water types ([PERSON] et al., 2020). In proof of concept studies, MODIS images from AQUA and TERRA satellites were successfully used for estimating Chl-a ([PERSON] et al., 2006) and TSS ([PERSON] et al., 2018; [PERSON] and [PERSON], 2019; [PERSON] et al., 2018; [PERSON] et al., 2009) in Amazonian water bodies with a size compatible with the spatial resolution of the sensors.
Chl-\(a\) estimation, a proxy for phytoplankton abundance, remains challenging in the Amazon floodplain lakes due to high TSS masking chl-\(a\) spectral features ([PERSON] et al., 2016) at some times ([PERSON] et al., 2009, 2015; [PERSON] et al., 2007; [PERSON] et al., 2013; [PERSON] et al., 2019). A spectral mixture algorithm was applied to overcome this problem in Curuai lake floodplain ([PERSON] et al., 2006; [PERSON] et al., 2006), and higher chlorophyll concentrations were observed in low water periods (November and December), as a result of lakes enriched by dissolved nutrients in less turbid waters ([PERSON] et al., 2006). However, the empirical nature of those algorithms prevents their wide application. Therefore, new approaches have been investigated, including the use of semi-analytical algorithms ([PERSON], 2019). CDOM retrieval based on satellite imagery is scarce in Amazon lakes since the isolation of CDOM signature from the water leaving signal is complex in turbid waters ([PERSON] et al., 2021; [PERSON] et al., 2016). [PERSON] et al. (2019) proposed an empirical algorithm for estimating CDOM absorption at 440 nm from Sentinel-2/MSI images. Table 5 presents a summary of these studies.
There are many studies on sediment retrieval from satellite data. These studies are mainly focused on TSS estimates for rivers ([PERSON] et al., 2019; [PERSON] et al., 2018; [PERSON] and [PERSON], 2011; [PERSON] et al., 2015; [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2019; [PERSON] et al., 2014; [PERSON] and [PERSON], 2014; [PERSON] et al., 2013; [PERSON] et al., 2018) rather than for Amazon floodplain lakes ([PERSON] et al., 2009; [PERSON] and [PERSON], 2019; [PERSON] et al., 2019; [PERSON] et al., 2006, 2007). However, most of them are based on empirical algorithms, and only recently, some semi-analytical algorithms became available (Table 5). The HYSAM observatory provides an example of systematically derived TSS concentration using empirical algorithms from MODIS at 16 stations (TSS time-series; [[http://hidrosat.ana.gov.br](http://hidrosat.ana.gov.br)]([http://hidrosat.ana.gov.br](http://hidrosat.ana.gov.br))) in the main sediment-contributing rivers, including Amazon-Andean rivers in Peru and Bolivia ([PERSON] et al., 2012, 2018; [PERSON] et al., 2009; [PERSON] et al., 2013). Figure 8e is an example of a suspended sediment time-series obtained from the HYSAM monitoring system in Amazon River between 1999 and 2017 and illustrates substantial variability of TSS concentration, ranging from 25 up to 250 mg L\({}^{-1}\).
[PERSON] et al. (2014) mapped TSS in five Amazonian rivers using multiple regression and observed that regional-calibrated algorithms performed better than global algorithms due to changes in the optical properties of rivers. [PERSON] and [PERSON] (2014) also observed that calibrating a separate empirical algorithm for low and high-water seasons provided better results for the Amazonian river waters. [PERSON] et al. (2021) calibrated an empirical algorithm using Sentinel \(-2/\)MSI red reflectance for retrieving sediment concentration in the Negro River (\(<\)10 mg-L\({}^{-1}\)), characterized by high colored dissolved organic matter absorption (\(\alpha\)CDOM \(>\)7 m\({}^{-1}\) at 440 nm) and very low \(R_{n}\) signals. [PERSON] et al. (2020) also showed that the backwater effect of the Solimores River on the Negro River is the main factor contributing to the retention of 55% of the sediment load in the Anawilahmas Archipelago due to the low water slope and reduced flow velocity.
High variability in the OACs in floodplain lakes makes algorithm parametrizations difficult. For example, in the Curuai floodplain (lower reach of the Amazon River), TSS concentrations can vary from \(\sim\)5 mg L\({}^{-1}\) in the high-water season up to 1,000 mg L\({}^{-1}\) in the low water season due to sediment resuspension by winds ([PERSON] et al., 2007). Despite those issues, recent work provides successful TSS estimates in the floodplains of the lower Amazon River ([PERSON], [PERSON], et al., 2020; [PERSON] et al., 2019).
\end{table}
Table 5: OACs Algorithms for the Amazon BasinTSS trends have been documented in the Amazon River ([PERSON] et al., 2009; [PERSON] et al., 2018) and the Madeira River ([PERSON] et al., 2017; [PERSON] et al., 2020) that might be related to dam construction (see Section 6.4 for details). The seasonal and inter-annual dynamics of suspended sediment at the Amazon River estuary were studied using 8-day composite time series (2000-2013) of MODIS Aqua and Terra satellite continental products ([PERSON] et al., 2016). TSS concentrations were estimated using a near-infrared band algorithm previously developed for turbid water ([PERSON] et al., 2009). The results provided a better understanding of mud bank formation, migration, and coast geomorphology indicating the key role of satellite data combined with in situ measurements. RS data in Amazon were also used to evaluate silitation impacts caused by artisanal gold mining in the Tapajos River basin ([PERSON] et al., 2015, 2016; see Section 6.4 for details). Furthermore, [PERSON] and [PERSON] (2019) mapped for the first time the spatial-temporal pattern of sediment in clear, white, and the black water of the Amazon rivers (Figure 8d). Despite errors in the empirical model, temporally filtered reflectance in red and infrared revealed sediment variations in rivers and lakes. Therefore, it was possible to characterize hydrological processes, such as backwater effects, overbank flow, and sediment resuspension in lakes. It was observed that depression lakes of the middle reach receive sediments-rich water by overbank flow during the flood, and resuspension of sediments occurs in the low water period, as previously documented ([PERSON] et al., 2007). In ria lakes, the main water source comes from the local basin (surface runoff and local rainfall) with river inflows adding sediment during the low water period.
One of the main challenges regarding watercolor RS is identifying and separating each constituent contribution from the water column emerging signal. The high sediment concentrations, which can mask the contributions of Chl-\(a\) and CDOM, make this challenge especially significant in Amazonian waters ([PERSON] et al., 2021). The semi-analytical approach, which has performed well in other complex waters ([PERSON] et al., 2016; [PERSON] et al., 2018; [PERSON] and [PERSON], 2017), is an alternative to overcome this challenge. However, it depends on sensors with spectral, radiometric, and spatial characteristics suitable for inland waters for calibrating high-performance algorithms. Initial applications of this approach in Amazonian waters, using Landsat-8/OLI, Sentinel-2/MSI, and Sentinel-3/OLCI data, have shown promising results ([PERSON] et al., 2019; [PERSON] et al., 2015; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2020). Furthermore, hyperspectral sensors missions such as NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE; [PERSON] et al., 2019) and recently launched ones such as PRISMA ([PERSON] et al., 2020; [PERSON] et al., 2020) may help to overcome this challenge. Due to the extensive temporal variability in the constituent concentration, a promising approach is to integrate hybrid and semi-analytical algorithms to obtain adequate accuracy in a wide range of OACs. To cope with the frequent cloud coverage and obtain data compatible with aquatic dynamics, the concomitant use of inter-calibrated sensors data (Landsat-8/OLI, Sentinel-2/MSI, Sentinel-3/OLCI, and CBERS-4A/MUX), called the virtual constellation, can be a solution. In this sense, two ongoing initiatives are the Brazil Data Cube project ([[http://brazildtacube.dpi.inpe.br/portal/explore](http://brazildtacube.dpi.inpe.br/portal/explore)]([http://brazildtacube.dpi.inpe.br/portal/explore](http://brazildtacube.dpi.inpe.br/portal/explore))) and the Harmonized Landsat Sentinel ([PERSON] et al., 2018), which propose to provide intercalibrated data from different sensors. Moreover, to investigate dynamic processes in aquatic ecosystems, high spatiotemporal resolution nanosatellites represent a promising tool for understanding the short-term responses of floodplain lakes' biota to hydrological changes ([PERSON], [PERSON], et al., 2020; [PERSON] et al., 2020).
All the improvements in RS technologies in the last decades have supported more accurate algorithms for suspended sediment retrieval in the Amazon. However, as demonstrated in Table 5, Chl-\(a\) and CDOM estimates are still a challenge in those optically complex waters. Furthermore, the accurate retrieval of Chl-\(a\) and CDOM is dependent on precise RS data, which demands the inversion of those OACs. In this sense, new sensors with the high radiometric and spectral resolution are imperative. Finally, more robust techniques, such as semi-analytical algorithms, machine learning approaches, and cloud computing platforms (e.g., Google Earth Engine), can improve water quality RS studies in the Amazon basin.
## 5 Total Water Storage and Groundwater Storage
Water mass redistribution is a key parameter needed to understand the climate system and its temporal variations at monthly to multi-decadal time-scales. Over land, it corresponds to the continuous exchange of water masses between surface (i.e., rivers, lakes, wetlands, snow cover, and mountain glaciers) and sub-surface (soil moisture and groundwater) storages, and with the atmosphere and the ocean through rainfall,evapotranspiration, and runoff. Total water storage is the sum of the water contained in the different hydrological reservoirs. The importance of surface water in the Amazon basin was presented in Section 4. Groundwater storage also plays a major role in the hydrology of the Amazon and exerts a large influence on climate variability and rainforest ecosystems ([PERSON] et al., 2013). Strong memory effects of the Amazon groundwater system propagate climate anomalies over the region for several years ([PERSON] et al., 2019; [PERSON] & [PERSON], 2012; [PERSON] et al., 2014).
The GRACE mission, in operation from March 2002 to June 2017, and the GRACE Follow-On mission (GRACE FO), in orbit since May 2018, enable the monitoring of the spatio-temporal changes of Terrestrial Water Storage (TWS; [PERSON] et al., 2004). Its temporal anomaly is derived from GRACE observations which measure the very small variations in the Earth's gravity field ([PERSON] et al., 2004). GRACE-derived TWS Anomaly (TWSA) observations, in spite of their coarse spatial resolution of \(\sim\)200-300 km, have been widely used to analyze the impact of climate variability and global changes on the water masses redistribution over land ([PERSON] et al., 2019), and groundwater storages in combination with external observations ([PERSON] & [PERSON], 2018).
Over the whole Amazon basin, GRACE-derived TWS annual amplitude was found to range from 300 to 450 mm (Figure 9; [PERSON] et al., 2009; [PERSON] et al., 2008; [PERSON], [PERSON], & [PERSON], 2013; [PERSON] et al., 2010). This range corresponds to twice the annual amplitude of surface water storage of the whole basin ([PERSON] et al., 2012; [PERSON] & [PERSON], 2020), meaning that the annual amplitude of the subsurface storage variations (soil moisture and groundwater) also represents half of the TWS annual amplitude. Large variations of this value were observed among the major Amazon sub-basins depending on the extent of floodplains ([PERSON] et al., 2011, 2019; [PERSON] et al., 2013). Rainfall and GRACE-based TWSA were found to be highly correlated in the Amazon and its major sub-basins (over 2003-2010), even at interannual time-scales with Pearson's correlation coefficients generally higher than 0.7 (except in the basins located in the Andes) with a time-lag varying from 0 to 3 months ([PERSON], [PERSON], & [PERSON], 2013; [PERSON] & [PERSON], 2020). Similar results were obtained between TWSA and river discharges over the same time spans ([PERSON], [PERSON], & [PERSON], 2013). Good agreement was also observed between TWS and satellite-derived surface water extent (from GIEMS), rainfall, and discharge over various time-span ([PERSON] et al., 2008; [PERSON] et al., 2007, 2012; [PERSON] et al., 2018). These studies revealed the complexity of water transport among the different sub-basins of the Amazon with the presence of hysteresis in the relationship between surface water extent and TWSA.
The analysis of the spatio-temporal patterns of TWS changes provided new information on the impact of the extreme climate events (exceptional droughts and floods which occurred in 2005, 2010, 2012-2015, and 2009, 2012, respectively) on land water storage in the whole Amazon basin or in its major sub-basins ([PERSON] et al., 2009, 2010; [PERSON] et al., 2013; [PERSON] et al., 2018; [PERSON], [PERSON], & [PERSON], 2013). Examples of maps of difference in TWSA between a given month and its climatological mean are presented in Figures 9a and 9b for May 2009, and October 2010, respectively. These months were chosen as they correspond to the extremum of these climate events (droughts of 2005, 2010, and 2015, flood of 2009). This information has been revealed to be complementary to what can be obtained using spatialized rainfall and in situ water levels and discharges. For instance, the patterns of minimum TWSA during the droughts of 2005 and 2010 were found to be in good coincidence across the basin with the areas with large fire activity ([PERSON] et al., 2008; [PERSON] et al., 2008) and of considerable tree mortality ([PERSON] et al., 2009) as reported in Frappart, Ramillien, and Ronchail (2013). TWSA also helped, jointly with hydrological modeling, to characterize the recent extreme droughts which occurred in the Amazon, highlighting the importance of the interactions between subsurface and surface water storages to mitigate the deficit in surface reservoirs ([PERSON] et al., 2019).
A direct approach to estimate GW storage anomalies is to remove the contribution of the different hydrological compartments from GRACE-based TWSA as follows:
\[\Delta\text{GW}=\Delta\text{TWS}-\Delta\text{SW}-\Delta\text{SM}-\Delta \text{CW}-\Delta\text{SWE} \tag{1}\]
where \(\Delta\) represents the anomaly of water storage in the different hydrological compartments, SW is the surface water storage, SM is the soil moisture or water contained in the root zone, CW is the water contained in the canopy, and SWE is the snow water equivalent. This latter term was neglected in the studies performedin the Amazon basin as no reliable information on this water storage was available. In most cases, water from the other compartments (SW and SM) is provided by model outputs and/or in situ measurements. For Amazon, it is necessary to accurately take into account the SW component as it represents around half of the TWSA ([PERSON] et al., 2012, 2019). Using external information from hydrological models for SW, SM, and CW, groundwater storage anomalies were estimated over 2003-2015, revealing a strong link between the water and the water.
Figure 9.— Maps of TWSA during two extreme events (a) The flood in May 2009, and (b) The drought in October 2010. Mean annual changes in groundwater storage anomaly - (c) GWSA and (d) associated standard deviation over 2003–2010 (adapted from [PERSON] et al., 2019). (e) Time series of GRACE-based TWSA (km\({}^{3}\)) over the Amazon basin between 2003 and 2016. The vertical lines show the months of maximum (May 2009) and minimum (October 2010) values.
between geological properties and GW storage: the largest groundwater storage capacity in Brazil was found in regions with the highest permeability of the rock layers (e.g., the Guarani and Alter do Chao aquifers; [PERSON] et al., 2017). But in these cases, SW storage was limited to river storage, neglecting the storage in the extensive floodplains of the Amazon basin. In order to adequately take into account the contribution of SW components, methodologies were developed to estimate SW storage variations from RS observations ([PERSON] et al., 2008, 2012; [PERSON] and [PERSON], 2020). SW storage anomalies were obtained by combining surface water extent (generally from GIEMs, see Section 4.2) and altimetry-based time series of water levels (see Section 4.1) over rivers and floodplains. [PERSON] et al. (2012) estimated the monthly variations of SW storage at the basin scale during the 2005 drought and found that the amount of water stored in the river and floodplains of Amazon during this extreme event was 130 km\({}^{3}\)(70%) below its 2003-2007 average, representing almost a half of the anomaly of minimum TWS as estimated by GRACE.
Using this newly external information on SW storage variations, along with SM storage estimates from hydrological models, GW storage anomalies were first estimated over 2003-2004 in the Negro River Basin, one of the largest tributaries to the Amazon basin ([PERSON] et al., 2011). The spatial pattern of the annual amplitude of GW anomalies agrees well with the regional hydrogeological maps and the amplitude are consistent with observations of water level at local wells and altimetry-based time series of water levels in two adjacent wetlands where the groundwater table reaches the surface during the whole hydrological cycle ([PERSON] et al., 2011).
This approach was then extended to the whole Amazon basin over 2003-2010, using about 1000 ENVISAT RA-2 altimetry VSs of surface water elevation ([PERSON] et al., 2019). SW storage over the entire basin had an annual amplitude ranging between 900 and 1,300 km\({}^{3}\)([PERSON] et al., 2012). GW estimates had good agreement with scarce in situ groundwater observations and low-water maps of the GW table ([PERSON] et al., 2008). At basin-scale, the results have realistic spatial patterns when compared to hydrogeological maps of Brazil (e.g., porosity maps, aquifer boundaries, GW recharge). The seasonal amplitude of GW was estimated to contribute between 20% and 35% of the GRACE-derived TWS amplitude in the Amazon basin(-[PERSON] et al., 2019). The impact of the 2005 extreme drought on GW storage was also observed and lasted several years ([PERSON] et al., 2019).
Radar altimetry was used to estimate low-water maps of the GW table in the central part of the Amazon basin ([PERSON] et al., 2008). Owing to the connection between surface and groundwater during the low water period in the alluvial plains of the central Amazon (54\({}^{\circ}\)-70\({}^{\circ}\)W, 0\({}^{\circ}\)-5\({}^{\circ}\)S), annual lower water levels of 593 altimetry VSs were interpolated to generate yearly maps of groundwater base level (GWBL) between 2003 and 2009. The results show that GWBL is governed by the surface topography and that several years were needed for GWBL to recover from the extreme drought of 2005 ([PERSON] et al., 2014).
The recent launch of the GRACE Follow-On (GRACE-FO) offers an opportunity to extend the monitoring of TWS and GWS changes after 2018. Despite a lack of data between October 2017 (end of GRACE operation) and May 2018 (launch of GRACE-FO), two decades of TWSA will be soon available, allowing analysis of the impact of multi-year climatic events such as ENSO on land and ground water storages. The major drawbacks of these data are their low spatial (\(\sim\)200 km) and temporal (1 month) resolutions which are not sufficient to study the dynamics of fast hydrological events. To overcome these drawbacks, the GRACE-FO payload contains advanced versions of the sensors present on-board GRACE and a novel laser ranging interferometer (LRI), measuring the satellite-to-satellite distance in parallel with the K-band radar instrument. The LRI is expected to be 26-times more accurate than the K-band radar instrumentation on-board GRACE ([PERSON] et al., 2019). This better-expected accuracy is likely to improve the quality and the spatial resolution of the retrieved TWSA. New approaches based on the use of Kalman filter were developed to increase the TWSA temporal resolution to quasi-daily without degrading the spatial resolution ([PERSON] et al., 2015, 2020).
## 6 Integrative and Interdisciplinary Studies
RS data have provided breakthrough advances in the understanding of the Amazon's hydrology and associated aquatic environments. In Sections 2-5, we have presented and discussed scientific advances for individual components. In this Section, we introduce research agendas that have benefited from the integration of observations from multiple components of the Amazon water cycle. These include the computation of the water budget (Section 6.1), application of hydrological models (Section 6.2), understanding of aquatic ecosystems (Section 6.3), and past and ongoing environmental changes over the Amazon basin (Section 6.4).
### Water Budget
In order to better understand the complex hydrological processes in the Amazon basin, it is necessary to monitor each component of the water cycle and to understand how these components link and interact. Thus, studying the Amazon basin water budget (WB) requires the use of a large variety of observations, especially because the basin includes complex local environments (e.g., floodplains) and processes (e.g., soil moisture and canopy transpiration) that are difficult to characterize by satellite observations.
Among the WB literature, the Amazon basin has been one major region among global analyses of the water cycle ([PERSON] & [PERSON], 2018; [PERSON] et al., 2012; [PERSON] et al., 2011; [PERSON] et al., 2018) or the main focus of the analysis ([PERSON] et al., 2011; [PERSON] & [PERSON], 2018; [PERSON] et al., 2019; [PERSON] et al., 2014). Most WB studies used only one satellite product for each water component ([PERSON] et al., 2011; [PERSON] & [PERSON], 2018; [PERSON] et al., 2015; [PERSON] et al., 2019; [PERSON] et al., 2014; [PERSON] et al., 2011). The use of a multiplicity of the satellite products for each water component can reduce uncertainties, through an approach that is based on observations only ([PERSON], 2014) or integrating model simulations and re-analyses ([PERSON] et al., 2012; [PERSON] et al., 2018).
Continuous quality improvement and increased use of satellite products, associated with more sophisticated integration techniques, have allowed better characterization of the water cycle. WB analyses have been used to (a) directly estimate a missing water component such as ET ([PERSON] et al., 2017; [PERSON] et al., 2011), \(R\)([PERSON] et al., 2011; [PERSON] et al., 2014), and terrestrial water storage change \(dS\)([PERSON] et al., 2019), (b) diagnose the hydrological coherence of a combination of RS-based estimates and investigating discrepancies ([PERSON] & [PERSON], 2018; [PERSON] et al., 2019; [PERSON] et al., 2014), and (c) to optimize RS-based estimates to obtain a hydrologically coherent water cycle ([PERSON] & [PERSON], 2018; [PERSON] et al., 2012; [PERSON] & [PERSON], 2006; [PERSON] et al., 2021; [PERSON] et al., 2011). The three main uses of WB closure are detailed in the following paragraphs.
When estimating missing water components, the objective can be to investigate seasonal patterns ([PERSON] et al., 2011; [PERSON] et al., 2019) and more complex features such as trends and impacts due to land use and land cover changes ([PERSON] et al., 2014). The studies provide uncertainties for their estimates based on the relative uncertainties of the other components ([PERSON] et al., 2011). When focusing on ET, the literature stresses that ET is controlled by both \(P\) and radiation without being limited by one of these two ([PERSON] et al., 2017); but the seasonality remains unclear due to large uncertainty \(P\). Nevertheless, the indirect estimation ET has been used by [PERSON] et al. (2011) to evaluate model ET outputs over the Tocantins basin and the authors concluded that much effort is still required on the ET modeling.
Diagnosing WB coherency by combining RS products is a useful tool to assess the quality of the RS products. For instance, [PERSON] et al. (2019) demonstrated that the MSWEP and GLEAM data sets reduce the WB imbalance. [PERSON] et al. (2014) showed that recent versions of the TMPA also improve WB closure compared to older versions. [PERSON] and [PERSON] (2018) have jointly evaluated the surface and atmospheric water balances over the Amazon, and their diagnostic of the discrepancy between various ET estimates showed that RS-based ET products balance better the WB than the model and reanalysis outputs. As reported in [PERSON] and [PERSON] (2018) and [PERSON] et al. (2019), the WB imbalance relates at sub-basain to the drainage area and the climatic conditions (i.e., tropical or mountainous) which impact the signal-to-noise ratio of each water component.
Several studies have used the WB closure as a constraint for the optimization of satellite estimates, jointly for each water component. [PERSON] and [PERSON] (2006) developed an optimization of the satellite products using an assimilation scheme within a land surface model at the basin scale. This method has then been applied to the Amazon basin ([PERSON] et al., 2012; [PERSON] et al., 2011). [PERSON] et al. (2018) extended this scheme to the pixel scale by considering only simulated R. Similarly, [PERSON] (2014) described several approaches to integrate satellite observation (simple weighting, optimal interpolation, post-filtering, and neural networks) with the WB closure constraint but without the use of surface or hydrological models to obtain an observational database. [PERSON] and [PERSON] (2018) investigated Amazon hydrology using this framework, and [PERSON] et al. (2021) added inter-basins constraints on the budget closure using river discharges over several stations in the basin. This technical framework allows for the optimization of the satellite data sets and can be used to develop new tools in hydrology such as the assimilation of GRACE data ([PERSON] et al., 2018). For instance, in [PERSON] et al. (2021), the spatial patterns of \(P\), ET and \(dS\) were used to estimate the river discharge along the river network.
The estimation of the uncertainty of each water component is one of the main objectives of a WB analysis. Such characterizations are generally component- and site-specific. For instance, [PERSON] et al. (2019) extensively evaluated the satellite estimate uncertainty of \(P\) and ET using in situ data (i.e., 300 precipitation gauges and fourteen eddy-covariance monitoring sites), however, this approach is limited due to the sparsity of the observation network. [PERSON] et al. (2011) used the distance to non-satellite estimate while [PERSON] et al. (2018) and [PERSON] et al. (2021) used the spread of the satellite as a proxy for uncertainty. [PERSON] et al. (2011) or [PERSON] and [PERSON] (2018) used a literature review based on RS expertize to quantify the uncertainties of the satellite products. Studies generally assume a value of 5%-10% of error for \(R\) while \(dS\) errors from GRACE are often computed following the specifications for leakage and measurement covariance errors ([PERSON] et al., 2004). All the studies agree on the relatively high contribution of the \(P\) estimate in the total WB imbalance (\(\sim\)40%). [PERSON] et al. (2019) and [PERSON] et al. (2014) found a positive bias \(P\) when comparing them to in situ data, but all the integration approaches ([PERSON] et al., 2012; [PERSON] et al., 2021; [PERSON] et al., 2011) result in an increased \(P\) estimate. Furthermore, [PERSON] et al. (2019) considered that \(dS\) is the second contributor to the WB imbalance (\(\sim\)25%) while [PERSON] et al. (2011) and [PERSON] et al. (2021) found a higher contribution from ET (\(\sim\)30%). All the optimization strategies have shown that the WB can be balanced within the range of the RS-based uncertainties.
Figure 10a represents the climatology of the four water components in three basins and using several data sets for each water component. The three basins are: northern Negro catchment upstream of the Serrinha station, the central basin upstream of the Manacapuru station (including the drainage area upstream of the
Figure 10.— (a) Seasonal climatology of all the water components: precipitation (\(P\)), evapotranspiration (ET), water storage change (\(dS\)), and discharge measured at in situ gauges (\(R\)) described by one or multiple data sets. (b) Probability Density Function (PDF) of the resulting WB imbalances are shown at the sub-basin scale (right). PDF provides the bias and variance of the imbalance.
Tabatinga station), and the southern basin upstream of the Fazenda (Fz) Vista Alegre station (including the drainage area upstream of Porto-Velho station). The climatological season (i.e., annual cycle) of all the water components is represented in mm/month. All satellite products have bias and uncertainties, but this multi-component analysis can isolate the spatial patterns over the Amazon basin. For instance, the annual cycles of the WB differ on the northern and southern basins. As reported in the literature ([PERSON], [PERSON], et al., 2019; [PERSON], 2005), over southern basin, \(P\) is driven by the monsoon with a peak in January and has larger seasonal variations (e.g., min-max range) and lower annual average than on the northern basin, where \(P\) peaks in May. The \(P\) seasonality drives \(R\) over all basins (north and south) with a time-lag of 1-2 months. Over the central-western basin, \(R\) can be higher than \(P\) for a particular month, and the \(P\)-\(R\) peak is about 4 months related to the runoff and river discharge travel times inside the basin ([PERSON] et al., 2020). \(dS\) is in phase with \(P\) in the southern basin, but shows a particular season over the Negro and Branco basins: \(dS\) is equal to zero during the dry season and a linear transition exists between maximum and minimum. Over these basins, \(dS\) become negative while \(R\) was increasing, and reached its maximum 2 months later. This illustrates the effect of water storage in floodplain before releasing it into the river. ET seasonal variation is weaker but the ET peak seems to be in phase with \(P\) over the southern basin arguing for a water-limited bed behavior while the ET peak follows the \(P\) minimum month in the northern basin of an energy-limited system ([PERSON] et al., 2017). In [PERSON] et al. (2021), the correction ET based on the closure of the water cycle enhances the water limitation regime over the central Amazon basin and the energy limitation over the northern Amazon. In the south, during dry months (JIA), ET is higher than \(P\), and water that evaporates is provided by the soil storage which continues to lose water until November. For this season, the role of ET on the water cycle is relatively more important in the dry season than in the rainy season ([PERSON], 2005).
To investigate the overall WB imbalance related to the bias and uncertainty of all the water components, Figure 10b shows the Probability Density Function (PDF) of these imbalances at sub-basins scale. Spatially, there is a gradient in the mean of the PDF between the western and southern sub-basins. Western sub-basins have a lack of water (negative bias in the PDF), while southern sub-basins have an excess of water (positive bias). This gradient was reported by [PERSON] and [PERSON] (2018). Furthermore, the variance of the WB imbalance increases from south to north with the annual mean of P suggesting that a large part of the imbalance is due to \(P\)([PERSON] et al., 2019; [PERSON] et al., 2021). The optimization strategy based on the closure of the WB leads to a bigger correction of the water component over western and central sub-basins ([PERSON] et al., 2021).
The remaining precipitation uncertainties of the globally calibrated satellite products are mainly due to the increase of the precipitation measurement errors by satellite products during the rainy season, and the lack of in situ gauges used in calibration ([PERSON] et al., 2019). The Amazon hydrology could benefit from the use of a dedicated network of precipitation gauges such as HYBAM Observatory Precipitation ([PERSON], [PERSON], et al., 2009; [PERSON] et al., 2012) to obtain a regionally-calibrated satellite product for precipitation. Its gauges density over the Amazon basin is higher than the global gridded rainfall data set generally used to calibrate satellite products ([PERSON] et al., 2012).
Estimating ET in the Amazon basin remains a challenge (see Section 3). In Figure 10, the use of different ET data sets can lead to a difference of 30-50 mm/month which represents up to 50% of the ET value. Following [PERSON] et al. (2019), the establishment of generic methods for estimating uncertainties is of importance for improving our understanding of the terrestrial water cycle. As for \(P\), one source of the improvement will be the extensive use and increase of an eddy covariance network to better understand the uncertainties in ET models.
One technical improvement in the WB-based optimization approach might come with the spatial resolution of the analysis. WB analysis has been mostly done at the basin scale over the basin ([PERSON] & [PERSON], 2018; [PERSON] et al., 2011) even if several studies have been conducted in sub-basins defined by river discharge stations ([PERSON] et al., 2011; [PERSON] et al., 2021). Using topography information, it should be possible to consider the runoff over land and downscale the satellite products while closing the WB at a pixel level. The satellite data sets could even be downscaled temporally to obtain a better time resolution.
As discussed in Section 5, attempts have been made to decompose the TWS from GRACE into its surface ([PERSON] et al., 2012; [PERSON] et al., 2013) and groundwater ([PERSON] et al., 2019) components. Suchdecomposition could also be attempted within a full terrestrial WB analysis, especially when reliable soil moisture satellite estimates over the Amazon will become available. As mentioned in Section 4, long-term surface water data sets would also be necessary ([PERSON] et al., 2017; [PERSON] et al., 2019; [PERSON] et al., 2020).
The GRACE-FO mission launched in 2018, the extension of the TRMM data record with the GPM mission, and the launch of the SWOT mission will provide a comprehensive set of new observations. The continuity of these satellite missions monitoring the water components is mandatory to improve our understanding of spatial hydrology patterns through more precise WB analyses and assess potential long-term trends.
### Modeling the Amazon Water Cycle and Its Wetlands
Hydrologic and hydraulic models represent the water cycle storages and fluxes through a set of mathematical equations. Such process-based models are suitable tools to understand Amazon hydrological processes such as river-floodplain water exchange and groundwater-surface water interactions ([PERSON] & [PERSON], 2012; [PERSON], [PERSON], et al., 2013) and past floods and droughs ([PERSON] et al., 2017), to estimate variables in ungauged regions (e.g., distributed river discharge for the last century; [PERSON] et al., 2019), and to perform scenarios of hydrological alteration due to deforestation, flow regulation by reservoirs, and climate change ([PERSON] et al., 2020; [PERSON] et al., 2017; [PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2015; [PERSON] et al., 2014; [PERSON] et al., 2019; [PERSON] et al., 2016; [PERSON] et al., 2016).
During the last decades, many models have been applied in the Amazon at different scales, from reach (i.e., more detailed studies addressing a few kilometers long river-floodplain area) to the whole basin scale. Because of the basin's remoteness and vast dimensions, RS data sets are usually adopted as either forcing (e.g., precipitation), a priori information to estimate parameter values (e.g., topographic data), validation, or calibration/assimilation data (e.g., discharge, river water levels). A major distinction can be made between (a) hydrological models that simulate vertical processes as evapotranspiration, soil water infiltration, and runoff generation mechanisms and (b) hydraulic models of surface waters, which represent flow propagation along rivers and floodplains with physically-based equations and allow the computation of variables such as surface water elevation and slope, river discharge, and surface water extent and storage sizes the differences between the two approaches.
The first generation of models in the Amazon involved the development of large-scale hydrological models, starting with the studies by [PERSON] et al. (1989), [PERSON] and [PERSON] (1997), and [PERSON] et al. (2002). With the advent of RS data sets and higher computational capacity, several models have been developed, improving the physical representation of hydrological processes, increasing the model spatial resolution, and moving from monthly to daily estimates ([PERSON] et al., 2009; [PERSON] et al., 2008; [PERSON] et al., 2017; [PERSON] & [PERSON], 2012; [PERSON], [PERSON], et al., 2013). These models usually adopt the following RS-based input data: precipitation with the TMPA product ([PERSON] et al., 2008; [PERSON] et al., 2012; [PERSON] et al., 2015), and more recently GPM-IMERG ([PERSON] et al., 2017) and MSWEP ([PERSON], [PERSON], et al., 2017); landscape properties including terrain lengths and slopes, based on DEMs (most studies using SRTM DEM); and land use and vegetation maps (global maps as FAO, or regional ones as the Brazilian RadamBrasil soil maps). The most common validation data sets from RS are water level from satellite altimetry (Section 4.1), surface water extent (Section 4.2), and total water storage (Section 5).
These model applications deepened our comprehension of the water partition between soil, surface water, and groundwater, and acted as laboratories to improve global hydrological models, which in turn are fundamental elements of Earth System models. The assessment of land surface and global hydrological and hydrodynamic models in the Amazon has been a standard procedure in geoscientific model development and in model intercomparison projects ([PERSON] et al., 2010; [PERSON] et al., 2008; [PERSON] et al., 2012, 2014; [PERSON], [PERSON], et al., 2017; [PERSON] et al., 2014, 2017; [PERSON] et al., 2015; [PERSON] et al., 2019; [PERSON], [PERSON], et al., 2012; [PERSON] et al., 2011; [PERSON] et al., 2013). At the basin scale, the fraction of the total water storage corresponding to surface waters was estimated as 56%, 41%, and 27% by [PERSON], [PERSON], et al. (2013), [PERSON], [PERSON], et al. (2017); [PERSON], [PERSON], et al. (2017) and [PERSON] et al. (2013), respectively. These values have been compared to RS-based estimates ([PERSON] et al., 2012, 2019; [PERSON] et al., 2013). Furthermore, basin-scale average ET estimated as 2.39-3.26 mm/day by an ensemble of land surface models ([PERSON] et al., 2014), and as 2.72 mm/day by [PERSON], [PERSON], et al. (2013), were slightly lower than values by basin-scale RS ([PERSON] et al., 2019) and an in situ eddy-covariance networks ([PERSON] et al., 2010), which estimated values of 3.11-3.58 mm/day across a gradient from southern dry to equatorial wet Amazon forests. The role of soil water storage to sustain dry season ET in the Amazon was shown by modeling experiments at local ([PERSON] et al., 2017) and basin scale ([PERSON] et al., 2014). Some studies addressed the role of groundwater and soil storage on the water balance, and the importance of its representation into hydrological models. Applications at headwater basins showed the predominance of groundwater on headwater water storage ([PERSON] et al., 2012; [PERSON] et al., 2017), in agreement with in situ monitoring studies ([PERSON] et al., 1997). [PERSON] and [PERSON] (2012) suggested the same pattern at the whole basin scale. Their model also indicated important two-way feedback between floodwater and groundwater, and the existence of large areas not subject to surface flooding across the basin, but where a high water table level would be responsible for keeping high soil water content year-round. The simulation of multiple soil layers in the ORCHIDEE land surface model, in contrast to a simple 2-layer \"bucket\" model, was also shown to improve the representation of the soil water dynamics and the total water storage in the Amazon, especially for the drier regions in the southern sub-basins ([PERSON] et al., 2014).
Among hydraulic models of surface waters, a pioneer study by [PERSON] et al. (2007) is one of the first hydraulic modeling experiments performed over large domains, which later prompted the development of many global hydrodynamic model applications ([PERSON] et al., 2018). The authors applied the LIFLOOD-FP model to a 260 km reach of the Solimoes River and estimated the river-floodplain water exchange as at least 40% of the river volume in that reach. For a relatively different reach in the Central Amazon (from Sao Paulo de Olivenea to Oibidos), [PERSON] et al. (1989) estimated this ratio as 30% based on a simpler routing method, while [PERSON] et al. (2020) estimated a value of 40% for the Amazon system, based on large scale hydraulic modeling (see below). The authors also found the model accuracy to be higher for the high water period, as has been also reported by recent studies ([PERSON] et al., 2019; [PERSON] et al., 2014), likely due to misrepresentation of the terrain heterogeneities and small disconnected lakes during the dry season. Furthermore, since the river-floodplain water exchange often occurs through floodplain channels and breached levees that hinder its conceptualization as a simple overbanking flow ([PERSON] et al., 2012), hydraulic models have the challenge to estimate effective channel parameters that represent these complex processes ([PERSON] et al., 2018; [PERSON] et al., 2009). Recent efforts have been addressing this topic, considering for instance the incorporation into models of different cross section shapes ([PERSON] et al., 2015) as well as assimilation of satellite altimetry to infer bathymetry ([PERSON] et al., 2019; [PERSON] et al., 2020; [PERSON] et al., 2020). Other applications at reach or floodplain lake scale were developed by [PERSON] et al. (2008, 2017), [PERSON] et al. (2019), [PERSON] et al. (2009), and [PERSON] et al. (2007), and addressed the relative role of local runoff and river inflow as the main water input, ranging from local runoff-dominated systems in the Lago Calado ([PERSON] et al., 2019; [PERSON] & [PERSON], 1995) to river-dominated ones in the Curuai (Figure 11d) and Janauac systems ([PERSON] et al., 2008, 2017; [PERSON] et al., 2019; [PERSON] et al., 2014, 2014b), through either channelized or diffuse flow patterns. In the case of Curuai and Janauac, the Amazon or Solimoes river was responsible for 82% and 93% of the floodplain annual influxes, respectively ([PERSON] et al., 2017; [PERSON] et al., 2014).
The first basin-scale inundation model was introduced by [PERSON] et al. (2002), and numerous hydrologic models were developed and coupled to inundation schemes afterward ([PERSON] et al., 2008; [PERSON] et al., 2012; [PERSON], [PERSON] et al., 2017; [PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] & [PERSON], 2012; [PERSON], [PERSON], et al., 2013; [PERSON], [PERSON], et al., 2012; [PERSON] et al., 2011). The models featured varying degrees of physics representation, with the simulation of floodplains moving from simple storage components to dynamic hydraulic schemes, which can represent relevant processes such as backward effects. For hydraulic models, additional RS-based information required as input data includes river channel geometry as width, and floodplain topography from DEMs (mainly SRTM and its derivatives with vegetation removal to represent the bare terrain; see [PERSON] et al. (2013), [PERSON] et al. (2016), [PERSON] et al. (2019) and [PERSON], [PERSON], [PERSON], et al. (2020). For local scale hydraulic models, additional parameterization usually involves the definition of floodplain roughness based on land cover maps ([PERSON] et al., 2019; [PERSON] et al., 2014). RS validation data sets are typically surface water elevation and surface water extent ([PERSON] et al., 2011; [PERSON] et al., 2009).
These hydraulic model applications revealed the combination of backwater effects and floodplain storage to drive the flood wave behavior along Amazon rivers ([PERSON], [PERSON], et al., 2013), causing strong attenuation Figure 11. Recent applications of hydrologic and hydraulic models in the Amazon basin have added insights into the role of river floodplains on (a) Hydrogen shape ([PERSON] et al., 2016) and (c) In-stream travel times ([PERSON] et al., 2020), and provided the estimation of (b) Long-term discharge climatology ([PERSON], [PERSON], et al., 2013), (c) Long-term water level time series (example for the location of Manaus; [PERSON] et al., 2019), and (d) Floodplain water depths (example for the Curuai Lake, 2014 high and low water seasons; [PERSON] et al., 2014).
and delay up to 2.5 months. Floodplain storage is also responsible for the general negative hydrograph skewness in the main Amazon rivers, with a slower rising and a faster falling limb ([PERSON] et al., 2016, Figure 11a). [PERSON] et al. (2020) used particle tracking methods to estimate surface water travel times along the Amazon basin as 45 days (median), with 20% of Amazon River waters flowing through floodplains (Figure 11c). While basin-scale applications have employed 1D models (longitudinal direction along rivers), the necessity of representing the 2D diffuse flow in floodplains, especially during receding waters, was highlighted by [PERSON] et al. (2005), who combined interferometry data with a simple continuity-based model to show that floodplain storage changes decrease with distance from the main channel. Generally, the water level in the river-floodplain system is not horizontal, and the river-floodplain is not homogeneously mixed ([PERSON] et al., 2007), as assumed by several 1D models. While a proper characterization of the complex river-floodplain interactions with hydraulic models has been done at local scales ([PERSON] et al., 2019; [PERSON] et al., 2014), it is still to be developed for the regional scale--for instance, to be able to infer hyperresolution (e.g., 30 m spatial resolution) flooding patterns for the whole central Amazon at weekly to monthly resolution. Finally, the full coupling between hydrologic and hydraulic models has been suggested to improve the representation of the floodplain-upland interactions, for instance through a more proper representation of open water evaporation in flooded areas ([PERSON], [PERSON], et al., 2017). However, recent studies have suggested that this process has a relatively low impact on the total ET estimates because of the general energy-limited (and not water-limited) ET in the Amazon ([PERSON] et al., 2020; [PERSON], [PERSON], et al., 2013). A different conclusion is expected for semi-arid wetlands ([PERSON] et al., 2018).
Regional scale validation of inundation models has been done with surface water extent ([PERSON] et al., 2012; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2013; [PERSON] et al., 2007; [PERSON] et al., 2011) based on the products by [PERSON] et al. (2003), GIEMs from [PERSON] et al. (2007), and more recently with the SWAF database ([PERSON] et al., 2017) (see Section 4.2 for a description of these products). Although the flooding seasonal cycle is usually well captured by most models, estimates usually diverge in terms of magnitude ([PERSON] et al., 2020), and the fusion between different techniques is likely the optimal solution. However, more detailed validation experiments, for instance with maps based on SAR data, are needed, although many SAR data classifications were already developed for individual Amazon wetlands (Section 4.2). A recent application used ALOS/PALSAR imagery for a local scale model validation in the Janauacao floodplain system ([PERSON] et al., 2019).
Regarding surface water elevation, hydraulic models are typically capable of representing anomalies satisfactorily. Estimates of absolute values, however, are usually less accurate ([PERSON] et al., 2019), al
\begin{table}
\begin{tabular}{l c c} \hline & Hydrological models & Hydraulic models of surface waters \\ \hline Main simulated process & Vertical processes (e.g., evapotranspiration, soil water & River-floodplain interaction (e.g., floodplain storage, \\ & infiltration, and runoff generation mechanisms) and & backwater effects) \\ & groundwater dynamics & \\ Main forcing (boundary conditions) & Precipitation & River discharge, river water level, and precipitation \\ Main output variables & Water balance, evapotranspiration, soil water, and groundwater storage, river discharges & Inundation maps, river-floodplain water depths, \\ Typical scientific outcomes & Quantification of water balance components, water & longitudinal water levels along rivers, river discharges \\ & storage partition between surface and subsurface & Floodplain water storage and residence time, water travel times across river-floodplain systems, rating curves (water level-discharge relationships) for operational \\ & human alteration on water balance components (e.g., & use, impacts of human alteration on flood dynamics \\ Examples of studies & [PERSON] et al. (2009); [PERSON] et al. (2002); [PERSON] and [PERSON] (1997); [PERSON] et al. (2012); [PERSON] and [PERSON] (2012); [PERSON], [PERSON], et al. (2013); [PERSON] et al. (1989) & [PERSON] et al. (2020); [PERSON] et al. (2017); [PERSON] et al. (2012); [PERSON] and [PERSON] (2012); [PERSON], [PERSON], et al. (2013); [PERSON] et al. (2016); [PERSON] et al. (2019); [PERSON] et al. (2014); [PERSON] et al. (2020); [PERSON] et al. (2009); [PERSON] et al. (2007); [PERSON], [PERSON], et al. (2012) \\ \hline \end{tabular} Note. Some examples are provided in both categories since they refer to hydrologic-hydraulic models.
\end{table}
Table 6: Summary of Main Differences Between Hydrologic and Hydraulic Models of Surface Waters, With Examples of Model Applications in the Amazon Basinthough good results have been achieved ([PERSON] et al., 2007). The hundreds of virtual stations available (see Section 4.1) have provided breakthrough improvements of modeling systems, especially in terms of distributed model validation with dozens of virtual stations ([PERSON] et al., 2020; [PERSON], [PERSON], et al., 2017; [PERSON], [PERSON], et al., 2013) and recent model calibration and assimilation ([PERSON] et al., 2019; [PERSON] et al., 2021). Validation exercises yielded Nash-Sutcliffe coefficients higher than 0.6 for 60% of the 212 ENVISAT virtual stations assessed by [PERSON], [PERSON], et al. (2013), and amplitude errors lower than 0.8 m and absolute bias lower than 2.3 m for most of the stations analyzed by [PERSON], [PERSON], et al. (2012). The combination of satellite altimetry with a hydraulic model for an ungauged reach of the Xingu River led [PERSON] et al. (2017) to propose the concept of hydraulic visibility through RS data sets, that is, the capability of current and future satellite altimetry data to properly estimate river hydraulic variables. Altimetry data were shown to be relevant for the understanding of the hydraulic functioning of ungauged braided reaches in Amazonian rivers, especially along stretches with heterogeneous bed morphology and strong downstream control, which have major effects on surface water elevation and slope ([PERSON] et al., 2002).
The main output variables that have been addressed by hydrologic-hydraulic models are ET, soil water storage, river discharge, surface water elevation, and surface water extent. However, other variables are also important for an effective understanding of the water cycle and need to be better constrained within modeling systems. For instance, only a few studies have addressed simulated water velocity ([PERSON] et al., 2011; [PERSON], 2020; [PERSON] et al., 2019) and flood storage ([PERSON] et al., 2020; [PERSON], [PERSON], et al., 2017; [PERSON], [PERSON], et al., 2013) in the Amazon wetlands, which are fundamental variables to understand flood dynamics, even though the latter (flood storage) was already estimated by different RS methods (see Section 5).
As there are still uncertainties in both models and RS estimates, model calibration, and data assimilation (DA) techniques have been developed to improve model predictability, based on the optimal combination/ analysis of these two. Model calibration was performed with satellite altimetry by [PERSON] et al. (2013) and [PERSON] et al. (2021), showing the benefits of using such data sets toward model general improvement in terms of discharge estimation. In turn, the evaluation of DA techniques (mainly the Kalman Filter-based methods) within the Amazon involved many experiments with RS data (e.g., satellite altimetry), from reach to regional scale ([PERSON] et al., 2019; [PERSON] et al., 2018; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2013). These studies showed the applicability of such methods to improve model estimates and representation of the water cycle in general. The usefulness of DA schemes for better estimating discharges was demonstrated for forecasting ([PERSON], [PERSON], et al., 2013), comprehension of past extreme events ([PERSON] et al., 2019), and near-real-time discharge estimation ([PERSON] et al., 2016). The study by [PERSON] et al. (2019) was the first to show discharge estimation in a spatially distributed way for the last 100 years (Figure 11e), estimating extreme drought and flood events in unrecorded locations. They follow a general pattern of the significant trend of increasing drought events in the south and flood events in the western and northwestern regions of the Amazon ([PERSON] et al., 2004; [PERSON] et al., 2017; [PERSON], [PERSON], et al., 2009; [PERSON] et al., 2016; [PERSON] et al., 2017). RS data other than discharge and water levels can also be used through DA and could be applied in the Amazon, e.g., soil moisture ([PERSON], 2017; [PERSON] et al., 2008; [PERSON] et al., 2015); terrestrial water storage change ([PERSON] et al., 2018, 2019) and flooded water extent. Additionally, the forthcoming SWOT mission will provide breakthrough information for the hydraulic modeling of the Amazon rivers. Many studies have been discussing the utility of the mission to better estimate hydraulic variables in the Amazon, from reach (lower Madeira River; [PERSON] et al., 2019) to the basin scale ([PERSON] et al., 2020; [PERSON] et al., 2020). New frameworks for the incorporation of satellite altimetry water levels will set up the development of the next generation of hydraulic models for the Amazon, aiming at better representing local processes as water surface heterogeneities that occur due to hydraulic controls as channel width reductions ([PERSON] et al., 2017; [PERSON] et al., 2019; [PERSON] et al., 2020).
Most model applications in Amazon wetlands focused either on parts of the central Amazon floodplains or the whole Amazon basin. The simulation of river floodplains still has some limitations to be accurately performed over complex, dynamic river systems as in the Andes foothills, which are associated with multiple alluvial fans, wetlands disconnected from the main river in terms of surface waters but connected through groundwater (e.g., the groundwater-fed backswamp forests; [PERSON] et al., 2007), and relatively quick hydrographs, which in turn hamper RS-based monitoring of variables as inundation extent and water levels. More advances on the estimation of topography along forested wetlands and adjacent channels are necessary, as well as coupled surface-groundwater model techniques. In addition to river floodplains, other types of wetlands exist in the Amazon basin, which is often named interluvial wetlands ([PERSON] et al., 2011). They combine endogenous and exogenous flooding processes to different degrees ([PERSON] et al., 2009), and are more subject to local rainfall and less connected to adjacent rivers ([PERSON] et al., 2019). They are associated with varying vegetation and ecosystem types (e.g., savanna, forest, grasslands). While 1D hydraulic models have proven satisfactory to simulate flooding along river floodplains ([PERSON] et al., 2009), interluvial wetlands require a 2D simulation to properly capture the wetland diffuse flow. [PERSON] et al. (2020) provided a first model assessment focusing on the Negro interluvial wetlands, which are associated with neeotectonic events and savanna environment within the Amazon rainforest ([PERSON] et al., 2017), and thus largely differ from the central Amazon in terms of flooding, vegetation and soil characteristics. [PERSON] et al. (2011) used a time series of Radarsat images and in situ measurements of water level and local rainfall to estimate changes in inundation in an interluvial wetland in the Negro basin. 1D models were shown to be unrealistic for simulating surface water elevation in these areas. Future studies should further address the hydrology of these complex wetland systems, including the Llanos de Moos ([PERSON] et al., 2004; [PERSON] et al., 2018), Roraima ([PERSON] et al., 2002), and Peruvian ([PERSON], 2001) interluvial wetlands, aiming at better understanding the hydrological differences between floodplains and interluvial wetlands, which in turn will improve our understanding of the various particular Amazon ecosystems relying on them, and the differences in terms of river-wetland connectivity.
The downstream part of the Amazon basin remains relatively unexplored in terms of hydraulic modeling and RS. This can be explained by the intricate dynamics of the estuary, which has energetic behavior over a broad range of timescales from the intra-daily tides propagating upstream from the Atlantic Ocean through the Amazon delta to the seasonal-to-interannual timescales driven by the hydrology of the basin. Moreover, tidal effects remain sensible up to about 900 km upstream of the river mouth ([PERSON] et al., 2009). One of the challenges in the hydraulic continuum of the lower Amazon is the understanding of the relative roles of the upstream forcing and of the oceanic influence in shaping the spatial and temporal patterns of variability of water level, flow velocity, and flooding extent along the course of the estuary. Promising initiatives have been made to model this complex estuary, mostly relying on coastal ocean circulation models, either in two-dimensional configurations ([PERSON] et al., 2005; [PERSON] and [PERSON], 2005), or more recently through full-blown tri-dimensional modeling ([PERSON] et al., 2020). These studies in particular shed light on the distinct behavior of the tidal waves during their upstream propagation in the Amazon estuary. However, to date, a comprehensive, high-resolution hydraulic modeling framework embracing the complex geometry of the whole hydraulic continuum of the lower Amazon, and accounting for the full range of interactions between oceanic and riverine forcing factors, is lacking. This can be explained, at least partly, by the fact that the monitoring of water level variability is instrumental in the success of hydraulic modeling of the lower Amazon for calibration/validation purposes; however, spaceborne altimetry has been hardly used in the Amazon estuary.
Finally, new EO data as SWOT-derived water levels ([PERSON] et al., 2016), channel water widths ([PERSON] and [PERSON], 2018; [PERSON] et al., 2014), floodplain topography ([PERSON], [PERSON], [PERSON], et al., 2020), and soil moisture estimates (SMOS, SMAP), as well as new precipitation data sets (e.g., rainfall estimation using soil moisture data as the SM2 RAIN [PERSON] et al., 2013, 2014), gravimetry missions (GRACE-FO), and techniques to retrieve groundwater storages (e.g., [PERSON] et al., 2019), open great opportunities for the next decade of hydrological and hydraulic modeling development in the Amazon basin. A major goal of the Amazon modeling community should be to move toward hyperresolution models, capable of providing locally relevant estimates everywhere ([PERSON] et al., 2015; [PERSON] et al., 2019; [PERSON] et al., 2011), as well as better representing all processes within the water cycle, including groundwater dynamics which has been misrepresented in most surface water-oriented hydrological models ([PERSON] and [PERSON], 2012; [PERSON] et al., 2018). The move to hyper-resolution models has been promoted at a global scale due to the development of new numerical techniques, equation sets, and software engineering, as well as increased computing power ([PERSON] et al., 2018). Such modeling systems could then be coupled to models of other processes, as recently done by researchers aiming at understanding flooding impacts on photosynthesis and biosphere in general ([PERSON] et al., 2018), feedbacks between surface waters and atmosphere ([PERSON] et al., 2019), sediment exports and floodplain trapping ([PERSON] et al., 2021; [PERSON] et al., 2018), carbon storage and emissions through wetlands and uplands ([PERSON] et al., 2019; [PERSON] et al., 2020), and dynamics of biogeochemistry cycles at the basin scale or over wetlands ([PERSON] et al., 2020). All these efforts will require additional RS data and will move forward our predictability of the effects of ongoing environmental changes in the Amazon basin.
### Aquatic Ecosystems
Floodplains are the largest aquatic system in the Amazon basin, support a diverse biota, and are important to the biogeochemistry and economy ([PERSON] et al., 2015; [PERSON], 1997; [PERSON] et al., 2011; [PERSON] et al., 2009). Amazon floodplains contain thousands of lakes, thousands of km\({}^{2}\) of vegetated wetlands and are characterized by large seasonal and inter-annual variations in depth and extent of inundation. Hydrological conditions are central to the ecological structure and function of these aquatic ecosystems, and floodplain hydrology is complex because it combines local inputs and regional-scale fluxes with large spatial variability. Applications of innovations in RS and hydrological measurements and modeling to the investigation of Amazon floodplains have led to advances in the understanding of the ecology of floodplains, in general.
Key aspects of hydrology relevant to floodplain ecosystems in the Amazon and elsewhere are the amplitude, duration, frequency, and predictability of variations in discharge and inundation ([PERSON] & [PERSON], 2021). Two conceptual frameworks of general relevance to river systems were motivated by studies in the Amazon. [PERSON] et al. (1989) emphasized the flood pulse and defined floodplains in terms of river stage, associated physical and chemical conditions, and adaptions of organisms to these conditions; [PERSON] (1997) elaborated these concepts for the central Amazon. [PERSON] (1997) examined hydrologic aspects of inundation of floodplain systems with RS and simple models and introduced the concept of the perrible zone, the mixing zone of water from the river and local catchment. Both these conceptual developments are supported by hydrological measurements of Amazon floodplain lakes, the first by [PERSON] and [PERSON] (1995), subsequently modeled by [PERSON] et al. (2019) and [PERSON] et al. (2008, 2017). Floodplains play an important role in the carbon balance and nitrogen biogeochemistry of the Amazon basin and are sites of large fluxes of methane and carbon dioxide to the troposphere and high rates of aquatic plant production. Studies designed to estimate the magnitude and variability of gas fluxes and productivity in the Amazon have combined RS with field data in innovative ways applicable to aquatic ecosystems in general. [PERSON] et al. (2004) used habitat-specific methane fluxes in combination with seasonal changes in the surface water extent of the aquatic habitats derived from active and passive microwave RS to estimate regional methane fluxes. On the mainstream Solim0 es-Amazons rivers and their fringing floodplains, annual methane emissions were estimated to vary between approximately 0.7 and 2.4 TgC year\({}^{-1}\)([PERSON] et al., 2004). Furthermore, methane fluxes per m\({}^{2}\) were higher during lower water levels than during high water in an Amazon floodplain lake, and fluxes in proximity to vegetation were higher than those from habitats in open water ([PERSON] et al., 2020). [PERSON] et al. (2002) and [PERSON] (2016) also used estimates of surface water extent to calculate carbon dioxide fluxes. [PERSON] et al. (2020) estimated N\({}_{2}\)O emissions from denitrification in Amazonian wetlands by adapting a simple denitrification model forced by open water surface extent from the Soil Moisture and Ocean Salinity (SMOS) satellite and reported a pattern in denitrification linked to inundation.
Seminal approaches with RS data were used to delineate inundated area and extent of flooded forests, open water, and herbaceous plants (e.g., [PERSON] et al., 2002; [PERSON] et al., 1995, 2003, 2015; Section 4.2) and used to improve estimates of seasonal and interannual variations in methane fluxes. As described in Section 4.2, new satellite-borne sensors and remote-sensing products can now be used to update such approaches (e.g., [PERSON] et al., 2019; [PERSON] et al., 2020). These data can be combined with remotely sensed changes in aquatic habitats, recent field measurements (e.g., [PERSON] et al., 2020; [PERSON] et al., 2020), and modeling (e.g., [PERSON] et al., 2014) to significantly improve estimates of emissions. More generally, the vegetative-hydrologic classification scheme used in these analyses meets the criteria for a \"functional parameterization\" of wetlands ([PERSON] & [PERSON], 1998), with classes suitable for biogeochemical and biodiversity applications
The primary productivity of aquatic plants is often high but challenging to measure, especially for herbaceous plants with large seasonal and spatial variations. On Amazon floodplains, the productivity of her baceous aquatic plants is strongly influenced by hydrological variations ([PERSON] et al., 2008; [PERSON], 1997). For instance, the growth of herbaceous aquatic plants in floodplain lakes follows water level variation. Extending field measurements of plant productivity to a regional scale was first done by [PERSON] (2005) using SAR estimates of plant biomass. Lower values were found in regions where plants developed only in the beginning of the flood season, and higher values in areas closer to the Amazon River, where the availability and influence of nutrient-rich water is greater. Further work by [PERSON] et al. (2010, 2013) used C-band SAR combined and optical data to investigate responses of horizontal expansion and vertical growth of herbaceous plants to variations in the flooded area and water level in two large floodplains along the Amazon
Figure 12. Major vegetation types and estimated mean flood duration maps in the Mamirauá Sustainable Development Reserve, Central Amazon, Brazil (adapted from [PERSON] et al., 2015). The maps were based on a time series of ALOS/PALSAR-1 image data comprising nine dates between 2007 and 2010 chosen to provide the largest and most uniform range of water level conditions within the available imagery for the area. The water bodies were derived from the flood class of 365 days per year on average, that is, permanent water bodies. More details on [PERSON] et al. (2015).
River. Over the period from 1970 to 2011 vertical growth varied by a factor of 2 and maximum annual cover varied by a factor 1.5. Years with exceptionally large changes in water level resulted in the highest productivity because horizontal expansion and vertical growth were both enhanced.
The productivity of Amazon aquatic ecosystems is also related to nutrient supply and optical conditions within the water ([PERSON], 2001). Applications of satellite-borne imaging spectrometers to the optically complex waters of the Amazon have revealed chlorophyll and suspended sediment levels (e.g., [PERSON] et al., 2009; [PERSON] et al., 2006; Section 4.4), which are related to planktonic productivity. Other studies employing data from optical sensors have been used to describe aquatic vegetation (e.g., [PERSON] et al., 2007; [PERSON] & [PERSON], 1997; [PERSON] et al., 2002), and indicate fluvial dynamics ([PERSON] et al., 2014; [PERSON] et al., 1995), both important aspects of aquatic ecosystems. However, observations with optical RS are frequently impeded by cloud cover or smoke, and forest canopies are often too dense to allow detection of flooding. Alternatively, time series of SAR data are available for several subregions within the Amazon basin and can be used to generate high-resolution maps of vegetation and inundation. For example, [PERSON] et al. (2015) used a hydrologically-based time series of ALOS/PALSAR-1 SAR data to distinguish between land cover classes and map water extent and mean flood duration (Figure 12). The authors depicted the uneven distribution of flooded areas at different water levels, that is, some water level stages result in large expansions of the inundated areas while other stages have less effect.
Complex flow patterns, revealed by interferometric SAR analyses ([PERSON] et al., 2007), and differences in sources of water, evident in hydrological models ([PERSON] et al., 2017; [PERSON] et al., 2019), account, in part, for the variations in nutrients, suspended sediments, and productivity ([PERSON] et al., 2017). A further example of how advances in hydrological modeling contributed to the understanding of Amazon flood-plains is provided by [PERSON] et al. (2014, 2014b). They added a simple model of hydrological balance to the LISFLOOD-FP hydraulic flooding model and applied it over 15 years. This work also emphasized the importance of detailed topography which they derived from a combination of data from the SRTM with extensive echo-sounding. The model simulated well changes in water level, flooding extent, and river-floodplain flows. [PERSON] et al. (2018) combined these results with measurements of suspended sediments to demonstrate variations in sediments supply and loss from the floodplain.
Variations in the distribution and inundation of floodplain habitats play a key role in the ecology and production of many commercially important fish in Amazonia. [PERSON] et al. (2015) demonstrated that number of fish species and their abundance were directly related to the presence of flooded forests and inversely related to distance from the river. [PERSON] et al. (2018) used both Landsat and SAR data to characterize aquatic habitats and found that spatial patterns of fish biodiversity on Amazon floodplains were associated with forest cover and landscape gradients. Additional examples of connections between fisheries and fish ecology are provided in [PERSON] et al. (2009) and [PERSON] et al. (2021).
Tree phenology on both fertile, eutrophic floodplains (vazrea) and nutrient-poor, oligotrophic floodplains (igapo) follow variations in inundation ([PERSON] et al., 2010). Seasonal inundation also provides connectivity that is critical for gamma diversity ([PERSON] et al., 2007; [PERSON] et al., 2002). Avian diversity varies among the aquatic habitats ([PERSON], 2015; [PERSON] et al., 2021). At the community level on large river floodplains, birds and fishes have more stable communities in environments with rhythmic annual floods ([PERSON] et al., 2015; [PERSON] et al., 2009). In a floodplain lake near the confluence of Amazon and Negro rivers, for instance, [PERSON] et al. (2017) detected an abrupt and persistent change in fish assemblage structure that lasted for more than a decade after the extreme drought of 2005.
Disturbances of the natural variations of the flooded area, hydrological connectivity, or land cover are disruptive for wetland systems. [PERSON] et al. (2019) used SAR RS to assess the impacts of the Balbina dam on the downstream igapo forests in the Uatuma River. The authors showed that 12% of the floodplain forests died because of the altered flood pulse and another 29% of the remaining living forest stands may be undergoing mortality. [PERSON] et al. (2021) provide further evidence for changes in floodplain forests below the Balbina dam over 35 years [PERSON] et al. (2018) combined fisheries data and habitat coverage derived from SAR analyses to determine the effects of land cover change on fishery yields. They showed that the removal of flooded forests can reduce fish yields and that other floodplain habitat cannot replace forest removal to improve fish yields.
Several challenges and knowledge gaps remain in the linkage of hydrology to the functioning of aquatic ecosystems in the Amazon basin and elsewhere. Wet soil without standing can have high rates of biogeochemical processes such as methane release. While difficult to detect with RS, models offer promise if operating at the correct scales. Streams and small rivers, as well as ponds, can release disproportionally high amounts of carbon dioxide, but their surface areas are seldom known; high spatial resolution RS products will help alleviate this problem. Interfluid and savanna wetlands, often unmutated by rain rather than rivers, are not well represented by basin-scale hydrological models and will require fine-scale topographic data combined with multi-temporal RS of immunodation. Within the Amazon basin, particularly large data gaps exist in the Llanos de Moxos (Bolivia), peatlands in the Pastaza-Marafon foreland basin (Peru), and coastal freshwater wetlands.
### Environmental Changes
In the last decades, Amazon has been subject to large environmental changes. Extensive rainforest areas have been deforested, being converted to pasturelands, croplands, or mining. These land cover changes alter the partitioning of precipitation into evapotranspiration, surface runoff and deep drainage, transport of sediments, river discharge, and river color, and influence the processes of formation of rainfall in Amazonia. At the same time, forest areas have been flooded by artificial dams to produce hydropower, affecting flood pulses downstream of the dam, while the forests' ecohydrology has adapted to the flood patterns. RS has been an important tool to detect and map these environmental changes and their impacts on the hydrological cycle.
The role of deforestation on the Amazon hydrological cycle could only be understood after large-scale mapping of land use and land cover (LULC) in Amazonia. The first of these maps were produced by [PERSON] et al. (2002). They merged RS imagery from AVHRR with agricultural census data to produce a spatially explicit LULC map for the Amazon and Tocantins basins for 1995. Based on this data set and agricultural census data for 1960, [PERSON] et al. (2003) evaluated how land use increases in the upper Toantins basin affected its discharge from 1949-1969 to 1979-1999. Although precipitation did not change significantly from the former to the latter period, the annual mean discharge increased by 24% (\(P<0.02\)), while the rainy season discharge increased by 28% (\(P<0.01\)), and seasonal peaks occurred about one month earlier. Such variations could be credited both to reduced ET and reduced infiltration during the rainy season. The reduction in evapotranspiration is a consequence of three factors: the increased albedo reduces the net radiation at the surface; the reduced roughness length decreases atmospheric turbulence, weakening vertical motions; and the reduced root depth leaves less soil moisture available to plants. Additional factors that can also influence local evapotranspiration include compaction of the soil surface or sub-surface and reduction of leaf area index through grazing ([PERSON], 2005).
Other LULC maps were produced for the Brazilian Amazon using similar techniques ([PERSON] et al., 2011 for 1940-1995; [PERSON] et al., 2016 for 1940-2012, Figures (a)a and (b)b). Purely RS products are available for more recent periods, like the MODIS MOD44 tree cover product (2002-recent), Landsat-based PRODES (1988-recent, [[http://www.otlinep.br/prodes/](http://www.otlinep.br/prodes/)]([http://www.otlinep.br/prodes/](http://www.otlinep.br/prodes/))) and TerraClass (2004-2014, [[https://www.terraclass.gov.br/](https://www.terraclass.gov.br/)]([https://www.terraclass.gov.br/](https://www.terraclass.gov.br/))) official government products for the Brazilian Amazon, and MapBIMas for the Pan-Amazonia (1985-recent, [[https://mapbimas.org/](https://mapbimas.org/)]([https://mapbimas.org/](https://mapbimas.org/)) --Figures (c)c and (d)d). Several authors have used these data sets to study the effects of LULC changes on the hydrological regime of several of the Amazon tributaries and the Amazon-Cerrado arc-of-deforestation as a whole ([PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2011; [PERSON] et al., 2018; [PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 2016), generally finding increased mean and low-flow discharge and decreased basin-wide evapotranspiration with deforestation.
In addition to river discharge, LULC changes may also affect the precipitation, particularly during the beginning and end of the rainy season. The first evidence of this was provided by [PERSON] et al. (2011). They compared four Landsat-based land cover maps from 1975 to 2005 against the rainy season onset dates calculated from daily rain gauge data, concluding that, for stations that lie inside the major deforested area, the rainy season's onset has significantly shifted to, on average, 11 days (and up to 18 days) later in the year over the last three decades. However, for stations that lie in areas that have not been heavily deforested, the onset has not shifted significantly. Recent studies confirmed these results. Repeating the same analysis for southern Amazonia from 1974 to 2012, and after removing regional trends and interannual variability, [PERSON] al. (2019) confirmed a delay in the onset of 1.2-1.7 days per each 10% increase in deforestation. In addition, the probability of occurrence of dry spells in the early and late rainy seasons is higher in areas with greater deforestation.
Figure 13:
Moreover, using daily rainfall data from the Tropical Rainfall Measurement Mission 3B42 product and the [PERSON] et al. (2016) 1-km land-use data set, [PERSON] et al. (2020) evaluated the quantitative effects of deforestation on the onset, demise, and length of the rainy season in southern Amazon for 1998-2012. After removing the effects of geographical position and year, they verified a relationship between onset, demise, and length of the rainy season and deforestation. Onset delays \(\sim\)0.4 \(\pm\) 0.12 days, demise advances \(\sim\)1.0 \(\pm\) 0.22 days, and length decreases \(\sim\)0.9 \(\pm\) 0.34 days per each 10% deforestation increase relative to the existing forested area (\(p<10^{-5}\) in all three trends).
Another breakthrough owned to RS was identifying the \"deforestation breeze\" effect, which affects rainfall distribution. [PERSON] et al. (2017) used remotely-sensed land-use, precipitation, and cloudiness data combined with a regional climate model, finding that small-scale deforestation patches trigger thermally-driven atmospheric circulation cells in Rondonia. This circulation creates a precipitation anomaly dipole over the deforested area, with enhanced precipitation downwind and suppressed precipitation upwind in the thermal cell's descending branch. The observed dipole in Rondonia is substantial, with the precipitation change in the two regions being \(\pm\)25% of the deforested area mean.
These regional circulation phenomena make the relationship between deforestation and rainfall totals dependent on the scale of analysis. Combining TRMM 3B42 rainfall and PRODES land use data, [PERSON] et al., (2021) found that this relationship is nonlinear at smaller scales but always leads to a decrease in southern Amazon total annual rainfall at larger scales. At the mesoscale (a 28-km TRMM grid cell), small deforested fractions (up to a 57% deforestation threshold) lead to a slight increase in rainfall (2.2 mm year\({}^{-1}\) per percent of the cell deforested, \(p<10^{-5}\)). However, for deforested fractions above this threshold, rainfall declines at about twice this rate, 5 mm year\({}^{-1}\) per additional percent of the cell deforested (\(p<10^{-5}\)). Aggregating both deforestation and rainfall to larger grid cells (56-km, 112-km) gradually reduces the nonlinear threshold for increase/decrease rainfall impacts. Upon reaching the sub-synoptic scale (224-km grid cell, or 64 TRMM 3B42 pixels), deforestation consistently leads to a linear reduction in rainfall of 4.1 mm year\({}^{-1}\) per additional percent of the cell deforested (\(p<10^{-5}\)) even for small deforestation fractions.
Although several techniques to infer surface water and channel properties from RS have been developed in recent years (as described in Section 4), relatively few studies apply these techniques to assess how anthropic and natural environmental changes affect these properties in the Amazon basin. [PERSON] et al. (2017) used tree cover data from [PERSON] et al. (2013), Landsat images, and RS estimates of TSS of [PERSON] and [PERSON] (2014) to investigate the current and potential impacts of dams in the basin. They found that the Santo Antonia and Iiran dams caused a 20% reduction in mean surface suspended sediment concentration in the Madeira River, despite unusually high flood discharges in the years analyzed after their start-of-operation. They also used Landsat images to calculate channel migration rates for each sub-basin, finding an average migration rate of 0.02 \(\pm\) 20% channel widths per year.
Satellite retrieval of TSS has also been used to document trends in the Amazon River's main stem, although there is no apparent consensus on the causes of the observed trends. Such techniques allow for expansion and extrapolation of field data sets, being especially useful in the Amazon since runoff and TSS are poorly correlated at the Amazon River's lowest reaches due to asynchronism of the peak water discharges of the Solmoes, Madeira, and Negro rivers ([PERSON] & [PERSON], 2009). [PERSON] et al. (2009) used 18 TSS sampling campaigns from 1995 to 2003 and MODIS images to obtain a 12-year (1995-2007) continuous series of TSS at the Oblidos station, the last gauge station in the Amazon River before it reaches the Atlantic Ocean. They find a 20% increase in sediment discharge in the period with no discernible trends in water discharge and cite changes in land use and rainfall patterns as likely explanations. Recently, [PERSON] et al. (2020) used similar
Figure 13.— Examples of environmental changes in the Amazon are documented by remote sensing. Panels (a–d) show two different satellite-based land use data sets for the Amazon and Toacantiras-Araquia basins. On top, the Brazilian Historical Land Use data set (BHALU, [PERSON] et al., 2016), which combines satellite and census data to estimate the fraction of each 1 \(\times\) 1 km pixel occupied by different land uses from 1950 (a) to 2012 (b) in Brazil. The BHALU data set includes areas of natural vegetation, pastures, and croplas. Only total agricultural land use (pastures + crops) is shown. In the middle, the Mapbiomas Amazonia data set (MapBiomas Amazonia Project, 2021; [[https://mapbiomas.org/](https://mapbiomas.org/)]([https://mapbiomas.org/](https://mapbiomas.org/))), a detailed classification of land-use of the combined Pan-Amazonia rainforest area and the Amazon and Toacantiras-Araquia basins from 1985 (c) to 2018 (d). The data set distinguishes 15 land use classes, which were combined in four here for simplicity. The bottom four panels show a major recent hydro-morphological event in the Amazon, the capture of almost all of the water flow from the Araguari River by the Amazon River. The Araguari River used to flow directly to the Atlantic Ocean (e), (f). Starting with a major flood event in 2011, the Urcuurtiuba channel grew until the Araguari River was connected to the Amazon mouth around 2015 (g), (h). Panels (e–h) were drawn using data from the Global Surface Water Explorer ([[https://global-surface-water.appspot.com](https://global-surface-water.appspot.com)]([https://global-surface-water.appspot.com](https://global-surface-water.appspot.com)), [PERSON] et al., 2016). See text for more details.
techniques to obtain an updated (1996-2018) time series of TSS and find that sediment loading increased until 2007 but decreased afterward. They infer that this reversal is due to decreased sediment contribution from the Madeira river after the construction of the Santo Antonio and Jirau dams in the late 2000s, in agreement with [PERSON] et al. (2017).
[PERSON] et al. (2018) used similar techniques to generate an extended 32-year (1984-2016) time series of suspended sediment transport (SST, the product of TSS by river discharge). They argued that there is a recurrent pattern of SST rising and falling in cycles likely associated with climate fluctuations and that trends such as those observed by [PERSON] et al. (2009) are a consequence of short time series. However, SST depends on river discharge variability, and [PERSON] et al. (2009) and [PERSON] et al. (2020) found no trends in river discharge in their shorter time series.
Some studies also investigated the impact of mining on suspended solids in sub-basins of the Amazon. Artisanal and small-scale mining, especially gold, is common in some regions, such as the Tapajos River basin. These small mining operations often use low-end techniques such as water jets and dredges that can cause proportionally high land degradation levels and water contamination ([PERSON] et al., 2018). They are also often illegal and unregistered, making RS an important tool for identifying and mapping these activities. The only publicly available data set (to our knowledge) on mining areas in the Amazon basin is the TerraClass project, which is based on visual interpretation of Landsat images and is available only for a few years between 2004 and 2014. [PERSON] et al. (2018) combined multiple data sets to develop an automated classification method that can distinguish between industrial and small-scale mining and ore types based on Sentinel-2. They found that in 2017 64% of the total mining area in the several key mining regions in the basin comprised small-scale gold and tin mining.
[PERSON] et al. (2015) estimated total suspended solids (TSS) in the Tapajos River basin based on Landsat images. They found that increases in TSS are strongly associated with reported increases in mining activity at seasonal and decadal timescales. [PERSON] et al. (2016) updated the Landsat-based identification of mining areas as from the TerraClass project. They described the evolution of mining areas in the same basin, identifying different eras of mining impacts on TSS related to the introduction of different technologies and variations in the gold price. Comparing sub-basins with different kinds of land alteration, they also indicated that mining activities have a much higher effect on TSS than deforestation for agricultural purposes.
Landsat images have also been used to document and understand a major hydro-morphological event in the Amazon: the recent capture of almost all of the water flow from the Araguari River by the Amazon River ([PERSON] et al., 2018). The Araguari is a large river, with an average annual discharge >1,000 m\({}^{3}\) s\({}^{-1}\), which used to flow directly to the Atlantic Ocean until the rapid formation of the Urucurituba channel connecting it to the Amazon River in the early 2010s. The initial headwater migration of the proto-Urcuturituba was likely associated with deforestation for buffalo farming around 2007. The first connection to the Araguari was attributed to a high flow event in 2011. The rapid growth of the channel, which increased in width by about 5 m per month until 2015, is likely a consequence of complex hydro-morphodynamic processes related to tidal currents and estuarine deposition that ultimately led to the blockage of the Araguari River mouth. This channel's formation caused large changes in the hydraulic pattern, sediment dynamics, and ecosystems in the Araguari estuary, being the first known observation of estuarine distributary network development by headwater erosion.
RS techniques contributed input, calibration, and validation data to many models that provided important insights on the consequences of environmental changes in the Amazon basin (see Section 6.2). These models can integrate hydrological, hydraulic, climate, and land-use processes and are important tools in many studies investigating the impacts of past and future changes in the environment. One of the main applications of these models is to analyze future scenarios (e.g., climate change, deforestation). Another application is attributing the effects of different processes in the variability of the observed data.
[PERSON] et al. (2016) examined climate change projections on discharge and inundation extent in the Amazon basin using the regional hydrological model MGB with 1-dimensional river hydraulic and water storage simulation in floodplains forced by five GCMs IPCC's Fifth Assessment Report CMIP5. The model was validated against a mix of in situ and RS data. Results indicate an increased mean and maximum river discharge
\begin{table}
\begin{tabular}{l c c c} \hline \hline & \multicolumn{3}{c}{Breakthrough lessons about} \\ & \multicolumn{1}{c}{Seminal developments in RS} & Amazon/General hydrology learned from RS & Knowledge gaps and new opportunities for the Amazon \\ Variable & \multicolumn{1}{c}{performed in Amazon} & \multicolumn{1}{c}{from RS} & \\ \hline Precipitation & 1) Spatial distribution of rainfall & 1) Spatial distribution of & 1) Improved algorithms for \\ & at regional scale ([PERSON] & “hot-spot” regions (Chavez &ographic rains ([PERSON] \\ & et al., 2009). & \& [PERSON], 2017; [PERSON] & et al., 2011; [PERSON] et al., 2015). \\ & 2) Rain trend over the last few decades ([PERSON] et al., 2020). & 2) Reduced rainfall over main & 2) Strategic network of rain gauges. \\ & & rivers (Pavia, Collischon, \& [PERSON], 2011; [PERSON], [PERSON], \\ & et al., 2011). & 3) Rainforest inducted early wet \\ & & season onset ([PERSON] et al., 2017). \\ Evapotranspiration & 1) Water flux estimates in the tropics at large scales ([PERSON] & 1) Understanding of \\ & & environmental drivers and _ET_ & \\ & & seasonality basin-wide, with & (\(<\)30 m) ET estimates on long \\ & 2) Observational data for model calibration and validation & more energy limitation and & time series (\(>\)40 years). \\ & and multi-model assessments & small seasonally in the wettest & 2) Combining surface energy \\ & ([PERSON] et al., 2013; [PERSON] & \\ & & & \\ & & & \\ & & & \\ & & & \\ & & & \\ & & & \\ \end{tabular}
\end{table}
Table 7: Synthesis of Scientific Advances in Understanding the Amazon Hydrology With Remote Sensingfor large rivers draining the Andes in the northwest contributes to increased mean and maximum discharge and inundation extent over Peruvian wetlands (e.g., Pacaya-Samiria region) and Solimoes River in western Amazon. In contrast, decreased river discharges (mostly dry season) are projected for eastern and southern basins and decreased inundation at low water in the central Amazon.
With the renewed interest in the last decades in constructing hydroelectric dams in the Amazon basin ([PERSON] & [PERSON], 2016), many modeling studies attempted to quantify the environmental impacts of new and existing dam projects. [PERSON] et al. (2017) used several models to evaluate the impacts of six planned dams in the Andean region of the Amazon. Since a sizable portion of sediment production in the basin occurs in this region, these dams are predicted to reduce the basin-wide supply of sediments, phosphorus, and nitrogen by 64%, 51%, and 23%, respectively. Along with changes in nutrient and sediment supply, mercury dynamics and flood pulse attenuation are projected by the authors to cause major impacts on downstream aquatic and floodplain fertility and channel geomorphology. Indeed, [PERSON] et al. (2019) found massive tree mortality in floodplain forests (igapo) downstream of the Balbina reservoir using SAR images, with about 40% of the igapo 49 km downstream of the reservoir either dead or undergoing mortality.
Expected environmental changes in the basin, such as deforestation and climate change, can also significantly impact hydropower production itself, often leading to generation well below the dam's expected capacity. Most recent dam designs follow a run-of-the-river concept, avoiding the large environmental impacts of enormous reservoirs from older designs but making power generation more dependent on river discharge variations ([PERSON], 2020). [PERSON] et al. (2020) combine a land-use and a hydrological model to assess the direct impacts of climate change and deforestation on hydropower production of existing and planned dams in the Tapajos basin. Although decreasing evapotranspiration from deforestation tends to increase annual mean discharge, reduced water retention increases surface runoff and flash flows during the rainy season and reduces discharge during the dry season. Since turbines are normally working at maximum capacity in the rainy season, this excess flow is wasted, and generation in the dry season is reduced. [PERSON] et al. (2020) find that projected climate change and deforestation combined can delay peak energy generation by a month (worsening the mismatch between peak production and consumption), reduce dry season generation by 4%-7% and increase interannual variability of power production by 50%-69%.
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline & & Breakthrough lessons about & \\ & & Seminal developments in RS & Amazon/General hydrology learned from RS & Knowledge gaps and new opportunities for the Amazon \\ Variable & performed in Amazon & & & \\ \hline Water quality: Sediments, chlorophyll and colored dissolved organic matter & 1) Estimates of sediment concentration in rivers (Bayley & 1) Spatiotemporal dynamics maps of the underwater light field & 1) Evaluation of phytoplankton community dynamics using RS as \\ & & & [PERSON], 1978; [PERSON] and et al., 1993), chlorophyll & ([PERSON] \& Paiva, 2019; \\ & in floodplain lakes ([PERSON] et al., 2006), and colored gas dissolved organic material in lakes ([PERSON] et al., 2019). & [PERSON], [PERSON], et al., 2020; [PERSON] et al., 2006). & 2) Robust algorithms for CDOM and Chlorophyll-a retrieval in optically complex inland waters. \\ & & 2) Extended time-series of 2) Semi-analytical algorithms for water quality estimates & suspended sediments in the Amazon Region ([PERSON] et al., 2020; \\ & & & [PERSON] et al., 2009; [PERSON] et al., 2015; [PERSON], [PERSON], et al., 2018). & \\ Total water storage (TWS) and groundwater storage (GWS) & 1) Large scale estimates of the TWS using GRACE data ([PERSON] et al., 2004). & 1) Spatial signatures of droughs and floods in TWS ([PERSON] et al., 2004). & 1) More accurate estimates of surface water storage from SWOT will improve the determination of GWs anomalies. \\ & 2) Determination of GWs changes using RS products and model outputs ([PERSON] et al., 2011). & 2) Spatio-temporal signatures of droughs on surface water storage ([PERSON] et al., 2012; [PERSON] et al., 2013). & 2) Long-term monitoring of \\ & & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Continued
Deforestation has the indirect effect of reducing precipitation and delaying the onset of the rainy season, which further illustrates the dependency of hydropower generation on forests. [PERSON] et al. (2013) combine land-use, hydrological, and climate models to assess the direct and indirect effects of deforestation alone on hydropower generation of the Belo Monte energy complex in the Xingu River basin. They find that when considering only the direct effects of deforestation on river flow, a 20%-40% deforestation of the basin would lead to a 4%-12% increase in mean discharge with similar increases in power generation. However, when the climate effects of deforestation of the Amazon region were considered, rainfall inhibition in the basin counterbalanced the direct effects and led to a 6%-36% reduction in discharge. Under the business-as-usual deforestation scenario for 2050 (40% of the Amazon forest removed), they simulated that power generation was reduced to 25% of maximum plant output.
\begin{table}
\begin{tabular}{l l} \hline \hline & Breakthrough lessons about Amazon/General & Knowledge gaps and new opportunities for the \\ & hydrology learned & Amazon \\ \hline Water budget & 1) Sub-basain scale water cycle analysis & 1) Finer spatio-temporal resolution of the \\ & ([PERSON] et al., 2011). & water budget analysis using river map \\ & 2) Water budget closure enforcement (Pan & information. \\ & 2) Sensitivity of the closure to the water \\ & 3) Continuous river discharge estimate based & component bias, in particular, ET estimate. \\ & on water cycle closure with satellite estimate. & 3) Groundwater exchange estimate might be \\ & obtained at fine-scale in constraining the water \\ & & cycle at the surface. \\ \hline Modeling the Amazon water cycle and its wetlands & 1) River-floodplain hydrodynamic interactions at local and large scales ([PERSON], [PERSON], 2013; [PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON] et al., 2007). & 1) Heter spatio-temporal resolution of \\ & & flood dynamics, considering sedimentation \\ & & processes, in diverse wetland types (floodplains \\ & & and interfluvial). \\ & 2) Groundwater dynamics across scales & 2) Better parameterization of groundwater \\ & and climates, and floodplain-groundwater & processes across the Amazon basin. \\ & interaction ([PERSON] \& [PERSON], 2012). & 3) Lack of convergence among water storage \\ & 3) TVS components (surface, subsurface) & partitions (e.g., divergent estimates of surface \\ & at basin scale ([PERSON], [PERSON], 2013; [PERSON] et al., 2013). & water fraction). \\ Aquatic ecosystems & 1) Integration of temporal and spatial & 1) Extent of saturated soils under forests and in \\ & variations of inundation and associated aquatic & riparian corridors. \\ & habitats into the estimation of carbon dioxide & 2) Modelling of inundation variations in \\ & and methane fluxes to the atmosphere ([PERSON] et al., 2004; [PERSON] et al., 2002). & interfluvial wetlands and savanna wetlands. \\ & 2) Areal estimation of major aquatic habitats & 3) Areal extent of streams and small rivers, \\ & in Amazon and seasonal and interannual & especially in the Andean region. \\ & variations in the areas ([PERSON] et al., 2015; & 4) High-resolution topographic data on \\ & [PERSON] \& [PERSON], 2010). & floodplains. \\ & 3) Biomass and growth of aquatic plants on \\ & floodplains ([PERSON], 2005; [PERSON] et al., 2013). & 1) Effects of changes in land use on the river \\ Environmental changes & 1) Effective changes in land use on the river \\ & discharge ([PERSON] et al., 2003). & between local changes in land use and large- \\ & 2) Influence on changes in land use on onset & scale climate mechanisms on the water cycle of \\ & of the rainy season ([PERSON] et al., 2011; [PERSON] et al., 2019), duration of the rainy season & the Amazon basin. \\ & [PERSON] et al., 2019), and total rainfall & 2) Initiate monitoring of forest degradation in \\ & ([PERSON] et al., 2020), and total rainfall & its different forms, so that the long-term effects \\ & ([PERSON] et al., 2021). & on forest hydrology can be studied. \\ & 3) Apply existing techniques to assess changes & \\ & in water and floodplain properties caused by \\ & anthropic changes (land use change, damming, \\ & mining). \\ \hline \hline \end{tabular}
\end{table}
Table 8: Synthesis of Scientific Advances in Multidisciplinary and Integrative Efforts in the Understanding of the Amazon Basin Hydrology and Ecosystems
## 7 Synthesis of Scientific Advances, Future Challenges, and Priorities
The various achievements of more than three decades of scientific advances on the hydrology of the Amazon basin with satellite data, along with the development of new RS techniques, and some selected research opportunities, are summarized in Table 7 and Table 8. Section 7.1 presents the main findings obtained in the Amazon, which has been a RS natural laboratory for hydrology advancement. Section 7.2 highlights how these experiences can be used to foster the understanding of the water cycle in other large river basins worldwide. Section 7.3 discusses the knowledge gaps and research opportunities on Amazon waters, thanks to an unprecedented and continued monitoring of the Amazon basin with upcoming and future satellite missions. Finally, Section 7.4 discusses how to move forward from scientific advances toward more sustainable water resources and risk management, and Section 7.5 highlights recommendations for future studies on Amazon waters from space.
### The Amazon Basin as a Remote Sensing Laboratory for Hydrology
As the largest river basin in the world, characterized by strong hydrological signals in precipitation, evapotranspiration, water storage change, and discharge, the Amazon basin has been an ideal natural laboratory for the seminal development of RS techniques and their applications to foster our understanding of hydrological processes. Table 7 summarizes for various hydrological variables key seminal developments made in the RS field over basin along with breakthrough lessons learned regarding Amazon hydrological functioning. Additionally, Figure 14 illustrates the major characteristics of Amazon hydrological storages and
Figure 14: Schematic illustration of the integrated hydrological processes of the water cycle in the Amazon basin. The main sensors on board orbiting satellites that have helped measure these processes are indicated. The annual estimates of each component averaged over the entire basin are shown. The references (*) related to these estimates are provided along with the text in Section 7.1.
fluxes as characterized by RS observations and analyses. Over the past decades, the need to understand the ongoing environmental changes in the Amazon basin, that could impact the global water, energy, and carbon cycles, has motivated a series of multidisciplinary and integrative efforts that foster scientific advances in our understanding of Amazon hydrology and ecosystems (Table 8).
Advances in precipitation estimates from RS have allowed the characterization of the spatial and temporal distributions of rainfall at local to regional scales over the Amazon basin and provide records long enough to assess rainfall trends over the last few decades (Tables 2 and 7 for developed precipitation products). The average rainfall in the basin was estimated as 2,200 mm year\({}^{-1}\) (Figure 3), and the heaviest rainfall occurs in hot-spot regions in the Andes mountain ranges initiated by convection processes altered by the topography, where rainfall can reach values higher than 6,000 mm year\({}^{-1}\) ([PERSON] & [PERSON], 2017; [PERSON] et al., 2015; Figure 3). Large-scale analysis of RS-derived precipitation revealed the effect of winds over large water bodies that causes reduced rainfall over these areas ([PERSON], [PERSON], et al., 2011; [PERSON], [PERSON], & [PERSON], 2011).
RS observations were key to providing the first large-scale evapotranspiration estimates in tropical regions, especially over Amazon. Also, they provided unprecedented observational data for the evaluation, calibration, and validation of models (Table 2). Furthermore, RS allowed the characterization of ET temporal and spatial variability over the Amazon basin (Figure 4) and the understanding of its environmental drivers, revealing contrasting regimes between the more energy-limited ones in the equatorial part of the basin and more water-limited regimes in the southern areas ([PERSON] et al., 2017). Amazon basin annual average evapotranspiration is estimated as 1,100-1,500 mm year\({}^{-1}\) (based on SSEOP, MOD16, PML, and GLEAM global models--Figure 4, and water balance by [PERSON] and [PERSON] (2018), with higher rates in the northern portions, as in the Negro River basin, decreasing toward the southern parts ([PERSON] et al., 2021; [PERSON] et al., 2017). Various RS-based approaches result in significant divergences in estimating evapotranspiration over the basin (Figures 4 and 10). For instance, RS-based ET annual rates at the basin scale were 15%-37% higher than those obtained from water balances ([PERSON] et al., 2021).
The characterization of continental water surfaces, including their elevation and extent, was possible thanks to adaptations of satellite techniques not primarily designed for hydrology or inland water monitoring applications. A striking example is that of altimetry satellite missions, initially designed to observe the ocean, but with promising applications to the large rivers of the Amazon ([PERSON] et al., 1990) and with the potential to derive SWE of rivers and lakes. Since then, various altimetry databases for the global monitoring of lakes and rivers have been developed (Table 3). The SAR differential interferometry technique, originally developed in geophysics, was also tested and applied for the first time in central Amazon floodplains to characterize SWE changes ([PERSON] et al., 2000). Both altimetry and SAR techniques were important to characterize SWE variations in Amazon rivers and their connectivity with the floodplains ([PERSON], 2020). The water surface gradient of the Amazon River varies both spatially and temporally, with values ranging from 1.5 cm km\({}^{-1}\) (800-1,020 km upstream) to 4.0 cm km\({}^{-1}\) (2,900-4,000 km upstream; [PERSON] et al., 2002). The monomodal flood pulse of the main Amazon River is well captured with radar altimetry (\(\sim\)4-12 m amplitude; Figure 5). This pulse controls the SWE variations in the central Amazon floodplains. During the annual flood, the SWE variations in rivers and adjacent floodplains, as seen from SAR or altimetry, are similar ([PERSON] et al., 2007), but connectivity is reduced during the low-water period ([PERSON], 2020) as the flows are controlled by the local topography ([PERSON] et al., 2007) and SWE in both environments is not always equivalent ([PERSON], 2003).
The first large-scale surface water extent mapping from RS was also carried out for the Amazon basin ([PERSON] et al., 1994) using passive microwave observations. Using several sensors, many estimates and databases have been developed at different spatial and temporal scales (Table 4). These include innovative high-resolution mapping of wetlands and flooded vegetation using L-band SAR ([PERSON] et al., 2003), which provided the first estimates of flood extent in the entire Amazon wetlands, ranging between \(285\times 10^{3}\) and \(635\times 10^{3}\) km\({}^{2}\) in periods of low (Oct-Dec) and high waters (Apr-Jun), respectively ([PERSON] et al., 2015; Figure 6). Significant differences among various RS-based estimates of surface water extent exist over basin (Figure 6), with in general lower maximum flooded area found by coarse-scale products than SAR-derived maps. Seminal approaches with RS data were used to delineate Amazon large-scale surface water area and extent of flooded forests, open water, and herbaceous plants, revealing their complex seasonal and interannual patternsinfluenced by local and regional-scale variability ([PERSON] et al., 2017; [PERSON] et al., 2004; [PERSON] et al., 2015; [PERSON] & [PERSON], 2010). While the width of the Amazon River floodplain is similar throughout the central Amazon, the area of flooded forest decreases from upstream to downstream, where both the number and size of open water lakes increases ([PERSON] et al., 2015; [PERSON] et al., 1996).
In combination with field data, mapping surface water extent in the Amazon basin enabled pioneering regional estimates of methane emissions (Table 7), with an estimate of methane emissions of \(\sim\)22 Tg C year\({}^{-1}\) for the lowland basin ([PERSON] et al., 2004). The spatial configuration of the Amazon floodplain habitats in relation to vegetation types is related to flooding patterns (Figure 14; [PERSON] et al., 2015). Herbaceous aquatic plants on central Amazon floodplains have a growth related to water level variation and the flood extent ([PERSON], 2005; [PERSON] et al., 2013). Furthermore, the increasing effect of dams in the Amazon basin has been assessed through analyses of flood extent dynamics ([PERSON] et al., 2020; [PERSON] et al., 2019) and impacts on tree mortality ([PERSON] et al., 2019).
The first morphometric characterization in the Amazon basin using RS data showed that 11% of the floodplain along the Amazon River and lower reaches of major tributaries is covered with lakes ([PERSON] et al., 1992). In fact, the floodplain topography along the Amazon River is complex, with several channels and lakes connected to the river ([PERSON], 2012; [PERSON] et al., 1996). Floodplain channel widths vary largely (10-1,000 m), and channel depths are tied closely to the local amplitude of the Amazon River flood pulse (8-12 m, [PERSON] et al., 2012; Figure 7). The recent capture of almost all of the water flow from the Araguari River by the Amazon River, the first known observation of estuarine distributary network development by headwater erosion, was also documented with RS techniques ([PERSON] et al., 2018). The need for accurate topographic data for hydrological applications was emphasized in several studies in the central Amazon ([PERSON] et al., 2013; [PERSON] et al., 2007; [PERSON], [PERSON], et al., 2012), in which key improvements such as vegetation removal were made. Global DEMs still do not accurately represent the floodplain topography, but surface water extent data combined with WSE allowed the first topographic mapping in seasonally flooded areas in the central Amazon with an accuracy of 0.89 m ([PERSON], [PERSON], [PERSON], et al., 2020). In these areas, 75% of the open-water areas have a depth of less than 2 m (8 m) in the low (high) water period ([PERSON], [PERSON], [PERSON], et al., 2020).
The Amazon River exports the largest sedimentary supply to the world's ocean (\(1.1\times 10^{9}\) tons per year ([PERSON] et al., 2020; Figure 14). Several seminal studies and algorithm developments using RS to characterize the water composition of rivers and lakes were primarily conducted in Amazon (see Table 5), such as the pioneering estimates of sediment concentration in rivers ([PERSON], 1978; [PERSON] et al., 1993), chlorophyll in floodplain lakes ([PERSON] et al., 2006) and colored dissolved organic material ([PERSON] et al., 2019). The spatio-temporal pattern of these components is related to SWE variations and mixing processes from different sources. The shallow depths during the low water period and the large area of floodplain lakes favor conditions for sediment resuspension ([PERSON] et al., 2007; [PERSON] & [PERSON], 2019; Figure 8). The chlorophyll mapping in floodplain lakes showed higher pigment concentrations during the low water season ([PERSON] et al., 2006). Increasing trends in sediment concentration in rivers were linked to changes in land use ([PERSON] et al., 2009; Amazon River) and the impact of mining ([PERSON] et al., 2015, 2016; Tapajos River). Conversely, the construction of the Santo Antonio and Jirau dams seems to have contributed to a reduction of sediment concentration in the Madeira River ([PERSON] et al., 2017; [PERSON] et al., 2020).
Due to large spatial and temporal changes of freshwater stored in surface, soil root zone, and aquifers, the Amazon basin is the ideal laboratory to explore measurements of gravity field variations from the GRACE satellite mission and derive TWS variations, linked to the redistribution of water mass over the continental surfaces (Figure 9). The first GRACE-derived estimates of TWS variations ([PERSON] et al., 2004) and groundwater storage changes ([PERSON] et al., 2011) were presented for the Amazon basin. TWS change in the Amazon is estimated as \(\sim\)1,800-2,700 km\({}^{3}\) year\({}^{-1}\) (Figure 14) with different contributions from surface water storage (\(\sim\)49%), root zone soil moisture (\(\sim\)27%), and groundwater (\(\sim\)24%) ([PERSON] et al., 2019). The residence time of the water stored in the Amazon basin, that is, the average time that the water remains in the basin before leaving by runoff or evapotranspiration was estimated at two months ([PERSON] et al., 2018). GRACE data helped to monitor periods of extreme droughts (e.g., 2009) and floods (e.g., 2005, 2010; [PERSON] et al., 2009), quantify water deficit during such events ([PERSON] et al., 2012), understand groundwaterdynamics across different scales and climates, and the interaction between floodplains and groundwater ([PERSON] & [PERSON], 2012).
RS has proven to be a great complement to in situ observations that have traditionally been used to calibrate/ assimilate and validate hydrologic and hydrodynamic models (Table 6 and Figure 11). In the case of the Amazon basin, the pioneering development or application of models have provided a major understanding of basin-wide river-floodplain systems ([PERSON] et al., 2002; [PERSON], [PERSON], et al., 2013; [PERSON] et al., 2014; [PERSON] et al., 2020; [PERSON] et al., 2009; [PERSON] et al., 2007; [PERSON] et al., 2011), the role of groundwater in hydrological buffering and headwater basin dynamics ([PERSON] et al., 2012), and partitioning of total water storage ([PERSON], [PERSON], et al., 2013; [PERSON] et al., 2013). While [PERSON] et al. (2007) developed one of the first large scale hydraulic models, the large-scale hydrologic-hydrodynamic model of the entire basin by [PERSON], [PERSON], et al. (2013) allowed the representation of physical processes such as the backwater effects in the main river and the attenuation of the flood wave due to water storage in the floodplains. These large-scale applications set the way for global hydrodynamic model applications are used today to understand flood risk from continental to Earth scale ([PERSON] et al., 2018, 2021). Applications of two-dimensional models in a reach of the Amazon River showed that the floodplain receives large amounts of water from the river, and small increases in peak discharge promote large changes in this flow ([PERSON] et al., 2014). Recently, [PERSON] et al. (2020) estimated, using an innovative hydrological tracking model, surface water travel times along the Amazon basin as 45 days (median), with 20% of Amazon River waters flowing through floodplains. Furthermore, with the integration of RS data and hydrological modeling, the assessment of past floods and droughts was possible ([PERSON] et al., 2012; [PERSON] et al., 2019).
RS techniques were also important for understanding how the hydrological cycle responds to environmental changes. Long-term changes in discharge could be attributed to changes in land cover via changes in evapotranspiration, as first shown for the Tooments River ([PERSON] et al., 2003). The average annual discharge increased by 24% between 1949-1986 and 1979-1998, associated with increased agricultural land use in the basin (from 30% to 49%). The presence of the forest was established as important for determining precipitation patterns both in and outside the region. The deep roots, low albedo, and high ET rates of the rainforest induce the wet season onset to be several weeks before what it would be without it, in a mechanism dubbed'shallow convection moisture pump'([PERSON] et al., 2017). The changes in land-surface fluxes caused by deforestation were found to cause reductions in precipitation totals, delays on the rainy season onset, and longer dry spells during the wet season, with negative consequences for hydropower generation, regional agriculture, and the resilience of the forest itself ([PERSON] et al., 2020; [PERSON] et al., 2011; [PERSON], 2020; [PERSON] et al., 2020; [PERSON] et al., 2014; [PERSON] et al., 2013).
The Benefits of the Lessons Learned in the Amazon to Understand the Hydrology of Other Large Tropical River Basins
Amazon basin can be seen as a RS laboratory for fostering the understanding of the water cycle and hydrology in general. While these advances have prompted the scientific understanding of Amazon hydrology, they have also set up new developments, techniques, and analyses that contribute to a better understanding of other large basins' hydrological cycles and at the global scale. Without being exhaustive, here we discuss some key studies that benefit from such advances and how they have contributed to hydrological progress in other regions. In particular, as the second-largest river basin in the world, with similar environmental characteristics as the Amazon basin, such as extensive floodplains and dense forests, the Congo River Basin is the new frontier of tropical hydrological research ([PERSON] et al., 2016), gaining more scientific attention in recent years and benefiting from the lessons learned from Amazon hydrology. The \"Hydrologic Research in the Congo Basin\" conference in Washington, D.C (USA) in 2018 delineated new research opportunities for the basin. This effort to gather African and international communities around a joint objective of a better understanding of the Congo basin response to climate change led to an extensive monograph ([PERSON] et al., 2021) that indicates the usefulness of RS and model methodologies built for the Amazon basin.
The first development of satellite altimetry data sets (Section 4.1) in the Amazon basin was turned into free-ly available global data sets providing long-term WSE at thousands of virtual stations (Table 3), enabling the characterization of the surface hydrology variability from altimetry in the Congo basin ([PERSON] et al., 2020), Indian inland waters ([PERSON] et al., 2017) and the Niger River basin ([PERSON] et al., 2018). The integration of satellite altimetry and hydrological modeling had seminal advances in the Amazon, including model validation and development of rating curves for near real-time monitoring of discharges from the space (Section 6.2), that was further performed in other tropical basins as the Congo ([PERSON] et al., 2019, 2021; [PERSON] et al., 2020), Tsiribihina in Madagascar ([PERSON] et al., 2020), Niger ([PERSON] et al., 2018), and Ogooue ([PERSON] et al., 2020).
Studies based on initial RS developments in the Amazon further performed comparative hydrology approaches, for instance, by studying jointly the floodplain dynamics in the central Amazon, the Congo, and the Brahmaputra wetlands with SAR ([PERSON] et al., 2010) and GRACE ([PERSON] et al., 2011), highlighting the unique features of each of these river systems. Amazon basin, with its extensive river floodplains, largely contrasts with Congo Cuvette Centrale, mainly dominated by interfluvial wetlands, with less river-weteland interaction ([PERSON] et al., 2010). Following studies using SAR observations to map flood and wetlands extent and distinguish vegetation types in Amazon (Section 4.2), seasonal flooding dynamics, water level variations, water storage, and vegetation types over the Congo basin were derived from JERS-1 ([PERSON], 2002), ALOS-PALSAR SAR and Envisat altimetry data ([PERSON] et al., 2017; [PERSON] et al., 2015; [PERSON] et al., 2015) or GRACE ([PERSON] et al., 2017)
The development of large-scale, multi-satellite RS techniques to monitor surface water storage variability, with initial techniques and analysis developed and assessed for the Amazon basin (Sections 4.1 and 5) were further applied to the Orinoco River in South America ([PERSON] et al., 2015), to study droughs in the Ganges-Brahmaputra River ([PERSON] et al., 2015) and to quantify the relative contribution of surface and groundwater variations in the Mekong ([PERSON] et al., 2019), the Chad ([PERSON] et al., 2020) and the Congo ([PERSON] et al., 2018; [PERSON] et al., 2017) basins.
Given the global relevance in terms of climate and ecosystems, the presence of large floodplains and dimensions in accordance with the resolution of coarse-scale models, many advances and developments of land surface and hydrological models were first assessed over the Amazon basin (Section 6.2), and later prompted the development of global-scale models ([PERSON] et al., 2018; [PERSON] et al., 2011). Examples include the introduction of basin-scale inundation schemes that were later introduced to other river basins ([PERSON] et al., 2020; [PERSON] et al., 2020), at continental scale ([PERSON] et al., 2018) and at the global-scale ([PERSON] et al., 2010; [PERSON] et al., 2012; [PERSON] et al., 2011). Recent advances in large-scale sediment transport using RS observations and modeling followed a similar path, with pioneering works in Amazon (Section 4.4) being followed by progress for all of South America ([PERSON] et al., 2021).
### Tackling the Current Knowledge Gaps With Future Satellite Missions
This review shows the tremendous achievements made during more than three decades of scientific advance on the hydrology and the water cycle of the Amazon basin with the help of RS. It also helped to identify the various knowledge gaps remaining to promote a comprehensive understanding of the Amazon hydrology. Here, we summarize these knowledge gaps (Tables 7 and 8) and present the new research opportunities with future satellite missions.
Regarding RS-based precipitation, current algorithm challenges involve the definition of dynamic thresholds of temperature brightness in IR sensors and processing of MW data to avoid confusing the summit of the Andes snow peaks with cold clouds ([PERSON] et al., 2011; [PERSON] et al., 2015). Better algorithms for detecting solid precipitation are necessary for improved understanding of local processes in Amazon basin headwaters in the Andes Mountains ([PERSON] et al., 2015; [PERSON] et al., 2011; [PERSON] et al., 2014). In situ observations are fundamental for the calibration of remote sensors. Therefore a strategic network of traditional stations and ground-based radars in key points of the Amazon must necessarily be part of a future agenda. Finally, new low-cost technologies such as nanosatellites have proven viable while maintaining scientific requirements, which should continue to be encouraged for future missions ([PERSON] et al., 2019).
RS models can reasonably estimate average ET rates in the Amazon basin, but correctly representing ET seasonality is still challenging, and understanding differences among individual ET components as soil evaporation, transpiration, and an interception. More studies are needed to disentangle the controls ET across the basin (water and energy limitation, and vegetation phenology) since multiple drivers operate simultaneously ([PERSON] et al., 2017). Besides, a major knowledge gap is a difference between ET Amazon uplands and wetlands, and the effect of open water evaporation on the regional climate. Current satellite-based models need to minimize the use of parameterization (or better constrain it), while the accuracy of input data must be improved. A major limitation of SEB models is their requirement of clear sky conditions, which may be improved by the use of microwave data ([PERSON] et al., 2018) and the combination with other types of ET models as those based on vegetation index models. In situ measurements are fundamental to achieve this goal, yet today there are only eight flux towers with publicly available data in the Amazon basin. For vegetation index-based models (e.g., MOD16, GLEAM), improving the understanding of soil water deficit controls ET across the basin is also necessary, given the high dependence of these products on soil moisture content. Some breakthrough ongoing and future missions will provide a new understanding of ET dynamics in the Amazon basin. The ECOSTRESS is addressing the response of vegetation to water deficit with unprecedented details, while the VIIRS collects visible and infrared imagery, extending the time series from its predecessor MODIS and improving its estimates, and the FLEX mission will map vegetation fluorescence, a proxy of photosynthetic activity and vegetation stress and health. The continuity of the Landsat missions will ensure the development of long-term ET at a high spatial scale, while the GRACE-FO mission will provide new data for water balance approaches to estimate ET. This will ultimately allow us to model ET at high spatial resolution (<30 m) and for long time periods (>40 years).
The surface water bodies and aquatic ecosystems of Amazon are still challenging the current available RS observations. Despite the substantial progress in the last decades, there are still limitations. Currently, there is a trade-off over the Amazon basin between spatial and temporal resolutions in satellite observations, with generally high temporal sampling associated with lower spatial resolution and vice-versa. Therefore, there is a need for a finer spatio-temporal resolution to adequately monitor water extent, level, and slope of the surface water and floodplain inundation. There is also a need to improve the accuracy of these estimates to understand more local phenomena, such as floodplain-river exchanges and dynamics or the complex flooding processes of extensive interfluvial areas. Similarly, only a few lakes and reservoirs in Amazon are monitored routinely from space, using altimetry. With dense vegetation and cloud cover, the context of the Amazon basin makes it still challenging to monitor surface waters such as permanently or seasonally flooded forests and floating herbaceous plants.
The forthcoming NASA/ISRO L-band SAR mission, with its combination of radar wavelengths and polarizations and 12-day orbit passes, will help to precisely measure small changes of surface water extent in the Amazon basin, including areas with standing vegetation. Furthermore, with its technology based on swath altimetry from the KaRIn, quasi-global coverage, and joint observation of surface water elevation, extent, river width, and slope, the SWOT mission, to be launched in 2022, will permit unprecedented monitoring of Amazon surface water and rivers at 100 m resolution in two horizontal dimensions. The centimetric accuracy in SWE and slope ([PERSON], 2018) will help to better characterize freshwater fluxes in the Amazon basin. The current satellite altimetry missions, especially the Copernicus program, are now setting the era of operational monitoring from space at large-scale for the coming decades, with clear benefits for large tropical transboundary watersheds such as the Amazon basin. With nearly two thousand virtual stations distributed over the basin, potentially hundreds more, freely available on multiple websites, conventional satellite altimetry can favorably complement the traditional and necessary in situ network. Since the main limitation for broader use of current satellite altimetry remains its relatively low temporal sampling, future missions in development, such as SMASH ([PERSON] et al., 2019), broadcasted together with the current constellation, should help to tackle this issue. Further developments in satellite observations are nevertheless required to fully characterize Amazon surface water extent and elevation. They should combine, in the future, the benefits of SWOT swath global measurements with a high temporal sampling of SMASH-like constellation into a SWOT-like satellite constellation providing global and daily observations.
Besides the concept of new satellite missions, it is worth noticing that the upcoming unprecedented availability of information regarding Amazon surface extent and elevations will challenge the current analysis capabilities. New development of analysis tools or fusion techniques with artificial intelligence to combine various RS observations (visible, IR, MW, and GNSS-R) is needed. Similarly, new techniques for fusion with local to regional modeling, data assimilation, and better constraining of uncertain hydraulics should also dramatically increase our capacity to model the Amazon basin and the variations of its water cycle.
Fiodolplain and river channel topography and bathymetry have not yet been fully characterized in the Amazon basin, despite recent efforts with local and regional estimates, preventing a better understanding of habitats related to flood pulse and limiting the accuracy of hydraulic models. In addition, the association between sediment concentration in rivers and channel migration is still poorly understood ([PERSON] et al., 2014). The development of new techniques and RS data for topography mapping is needed. The main challenge is vegetation removal, as many bands and sensors cannot penetrate vegetation. LiDAR and altimetric data, such as ICESat-2 (launched in 2018), which allow bare earth mapping, have still been little exploited in the Amazon basin for this task.
Interferometry and altimetry data have been used in the Congo basin to derive the floodplain bare earth DEM ([PERSON] et al., 2019), despite not being able to provide continuous topography. Furthermore, NISAR and SWOT satellites will open opportunities with more accurate estimates of the surface water extent and distributed SWE over water bodies. Thus, new methodologies for topographic mappings, such as the waterline method ([PERSON] et al., 2019) and Flood2 Topo ([PERSON], [PERSON], & [PERSON], 2020), can be further developed. Nevertheless, observing river and floodplains bathymetry from space will remain a continuing challenge since adequate solutions for its direct measurement are still lacking, even if future altimetric observations seem to open a new way forward.
White, black, and clear water rivers of the Amazon basin have particular characteristics with large variations of COA (sediment, chlorophyll, and CDOM). Despite the development of many algorithms for estimating these components, little has been explored to implement those algorithms to address scientific questions, as [PERSON] et al. (2020) reported worldwide. In addition, the characterization of natural processes, such as the spatio-temporal variation of phytoplankton in lakes, has not been widely explored. Sediment concentration estimates could be better exploited to assess the effects of dams, mining, and land use changes in the Amazon basin. On the other hand, there are still technical challenges for these estimates using RS data, such as the high cloud cover in the basin. The main challenge is discretizing the COA spectra, which can be partially overcome with new sensors with high radiometric and spectral resolution.
The recent launch of the GRACE-FO mission offers an opportunity to extend the monitoring of TWS and GWS changes over more than two decades, allowing us to start analyzing the impact of multi-year climatic events such as ENSO on land and groundwater storage throughout the Amazon basin. The major drawbacks of these data remain their low spatial and temporal (\(\sim\)200 km and 1 month) resolutions which are not sufficient to study the dynamics of more local and rapid hydrological events. To overcome these drawbacks, the GRACE-FO payload contains advanced versions of the sensors used on GRACE, allowing a better-expected accuracy to improve the quality and the spatial resolution of the retrieved TWSA. Combined with new methodological approaches based on a Kalman filter, it should increase the TWSA temporal resolution to quasi-daily without degrading the spatial resolution ([PERSON] et al., 2015, 2020). With the upcoming availability of SWOT observations, unprecedented and finer estimates of surface water storage over large areas will improve the determination of GWS anomalies. They will allow us to understand better the interactions between flood dynamics and aquifer recharge in the Amazon basin. Groundwater exchange in the basin, which remains poorly characterized with satellites, should also benefit from integrating these new observations and could be further estimated in better constraining the water budget at the surface. A comprehensive set of observations dedicated to hydrology, with the continuity of the current satellite missions, is mandatory to improve our understanding of hydrology patterns through more precise water budget analyses and to assess long-term trends.
Given the uncertainties in both hydrological models and RS estimates, model calibration and data assimilation techniques have been recently developed by incorporating mainly water level (satellite altimetry) data and, to a lesser extent, GRACE TWS. Other variables to be better assimilated are flood extent and storage, soil moisture, and evapotranspiration. While most hydrologic and hydraulic model applications have been used to estimate variables such as evapotranspiration, soil water storage, river discharge, surface water elevation, and extent, new studies must investigate other variables such as water flow velocity and flood storage. There is also a lack of convergence among water storage partitions (e.g., divergent estimates of surface water fraction), which must be addressed by better constraining models with EO observations and by performing model intercomparison projects. On the other hand, while the Amazon wetlands were mainly studied for the central Amazon floodplains, other types of wetlands do exist, as the interfluvial ones in large areas of the Llanos de Moxos, Pacaya-Samira, and Negro. They deserve more efforts from the hydrological community, especially considering their particular flood dynamics, more dependent on local rainfall.
Furthermore, high-resolution 2D modeling of the full Amazon mainstem mapping velocity fields and the complex river-floodplain interactions still are not explored. The downstream part of the Amazon basin remains relatively unexplored in terms of hydrodynamic modeling and RS, for example, the relative roles of the upstream forcing and the oceanic influence on the dynamics of the river-estuary-ocean continuum. In addition to a better representation of hydrological processes, for example, groundwater dynamics that are poorly represented in surface hydrology-oriented models, hydrologic-hydrodynamic models' future depends on the growing availability of new EO data. These include SWOT-derived water levels and discharges, channel water widths, floodplain topography, soil moisture (e.g., SMOS, SMAP), precipitation (e.g., SM2 RAIN), gravimetry (GRACE-FO), and techniques to retrieve groundwater storages (e.g., [PERSON] et al., 2019). These data will promote the basis for modeling estimates at the high temporal and spatial resolution, aiming ultimately at providing locally relevant hydrological estimates everywhere ([PERSON] et al., 2015; [PERSON] et al., 2011).
While most major components of the water cycle have been relatively well addressed in the literature, as shown in this review, soil moisture stands out as the less reliable component. This low reliability relates to the difficulty of retrieving this variable under densely vegetated areas ([PERSON] et al., 2005). The relatively poor performance of current soil moisture data sets (e.g., SMAP, AMSR-E, and SMOS) in these environments is well known, even when products are combined ([PERSON] et al., 2011) or merged ([PERSON] et al., 2005; [PERSON] et al., 2016). Most soil moisture-oriented studies were performed with hydrological models and in situ data in a few headwater locations. Moreover, there is an inherent ambiguity in passive microwave observations between water-saturated soils and surface waters. Consequently, the large surface water fraction in the Amazon basin affects the soil moisture retrievals by this type of observation. This ambiguity in the satellite observations has triggered the development of a product such as a SMOS-based surface water product ([PERSON] et al., 2017). There is an urgent need to better monitor soil moisture at different spatial-temporal resolutions in the Amazon basin, especially considering its major role in controlling the Amazon forest dynamics and phenology, evapotranspiration, and the water cycle in general. This observation supports the development of SMOS-HR, the High-Resolution follow-on mission of SMOS, which is currently undergoing feasibility study by the French space agency and which goal is to ensure continuity of L-band measurements while increasing the spatial resolution to \(\sim\)10 km without degrading the radiometric sensitivity and keeping the revisit time of 3 days unchanged.
Similarly, river discharge, historically one of the first hydrological variables that have been observed in situ, is still not properly measured from space. This review stresses a need to accurately estimate river discharge using RS in Amazon with fine spatial and temporal resolution. River discharge has already been estimated indirectly by RS data (e.g., [PERSON] et al., 2007; [PERSON], 2005; [PERSON] et al., 2013; [PERSON] et al., 2006), but still poorly complements the current in situ network of the Amazon basin. Upcoming missions, such as SWOT, in combination with current satellite missions, will soon help us move toward more comprehensive monitoring of river discharge in the Amazon basin.
The ongoing and future environmental alterations in the Amazon basin urge the understanding of the basin hydrology under the perspective of a changing system. The long-term effects of multiple human impacts (land use change, climate change, damming, mining, and fires) on the Amazon must be better understood. Changes in land-atmosphere feedback due to deforestation will affect the Amazon water cycle, but the magnitude of this change is still under debate. There is relatively little understanding of how they interact, especially in terms of how the impact of land-use changes in local climate can be different under large scale meteorological conditions that are changing with the global climate (e.g., [PERSON] et al., 2020) and how these would affect the land and water ecosystems in the basin. Furthermore, techniques to map forest degradation and discern primary and secondary vegetation are still relatively new. The impacts of those subtler but pervasive land-use changes on Amazon hydrology are yet to be understood. Finally, although the influence of the Amazon forest on the hydroclimate outside the Amazon has been increasingly documented, the consequences of its deforestation and degradation outside the basin are yet to be understood.
Furthermore, the proliferation of dams in tropical basins as the Amazon, Congo, and the Mekong require basin-scale planning and analysis tools to foster mutual benefits in understanding these changes (e.g., [PERSON] et al., 2021; [PERSON] et al., 2017; [PERSON] et al., 2019; [PERSON] et al., 2016), and RS data stand out as powerful tool to monitor large scale impacts of existing man-made reservoirs (e.g., [PERSON] et al., 2019), and infer their characteristics, such as water level and stage-area-volume relationships (e.g., [PERSON], [PERSON], & [PERSON], 2020; [PERSON] et al., 2012; [PERSON] et al., 2019). Better data and knowledge of these impacts are also the base for better hydro-geomorphological models that could quantify the expected impacts of planned reservoirs and, therefore, aid in creating designs that minimize environmental impacts.
### How to Use RS-Based Scientific Advances to Foster Water Resources Management in the Amazon Basin?
While the Amazon basin served as an important natural laboratory for RS development that produced significant scientific advances related to its hydrological processes in the last decades (Tables 7 and 8), the Amazon is currently undergoing extensive anthropogenic pressure (Section 6.4) and urgently calls for better basin-scale water resources planning and new environmental monitoring tools. RS has the potential to democratize essential information for decision-makers, for instance, to monitor \"politically unguaged\" regions where information is not publicly available ([PERSON] & [PERSON], 2020). Although RS is now a reality and documented knowledge on the Amazon basin is much better than decades ago, there is still an open road to move all these advances toward effective applications in decision making and water resources management.
Deforestation and fire monitoring may be the most advanced and promising examples in the context of Amazon environmental management. Since 1988, satellite-based monitoring systems using MODIS, Landsat and CBERS imagery as the DETER ([PERSON] et al., 2015, [[http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/deter/](http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/deter/)]([http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/deter/](http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/deter/))), PRODES ([[http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/prodes](http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/prodes)]([http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/prodes](http://www.obt.inpe.br/OBT/assuntos/programs/amazonia/prodes))), Imazon ([[https://imazon.org.br/categories/boeltim-do-desmatamento/](https://imazon.org.br/categories/boeltim-do-desmatamento/)]([https://imazon.org.br/categories/boeltim-do-desmatamento/](https://imazon.org.br/categories/boeltim-do-desmatamento/))) and Queimadas ([[http://queimadas.dgi.inpe.br/queimadas/portal](http://queimadas.dgi.inpe.br/queimadas/portal)]([http://queimadas.dgi.inpe.br/queimadas/portal](http://queimadas.dgi.inpe.br/queimadas/portal))) have been systematically supporting local governments and NGOs on the monitoring and control of deforestation and fires. Technical advances made it possible to monitor deforestation in near real-time, on the scale of days, weeks, or months. However, institution building and related civil-society engagement are still needed to facilitate effective actions within complex government frameworks and bridge the gap between technology and policy toward deforestation reduction ([PERSON] et al., 2018).
Amazon neighborhood countries have mature Water Resources Agencies, Geology and Hydrometeorological Services as the ANA, the Peruvian and Bolivian National Meteorology and Hydrology Services (SENAM-HIs), and the Brazilian Geological Survey (CPRM). These institutions have dedicated efforts to the challenging task of systematically monitoring Amazon's vast territory and rivers and promoting open hydrological data sets. In this sense, RS is starting to be incorporated into operational monitoring (e.g., SIPAM [[http://hidro.sipam.gov.br/](http://hidro.sipam.gov.br/)]([http://hidro.sipam.gov.br/](http://hidro.sipam.gov.br/)), Hidrosat, [PERSON] et al., 2015; near real-time flood simulations at sub-daily scale, [PERSON] et al., 2021). In particular, precipitation has been widely monitored through RS data by multiple meteorological agencies, while other water cycle variables have received less attention. These organizations have been developing technical reports about the national situation and water resources planning, including the Amazon basin (e.g., Water Resources Situation Report, Agencia Nacional de Aguas, 2019a; National Water Security Plan, Agencia Nacional de Aguas, 2019b; flow forecasts at the national level and at hourly and daily scale by SENAMHI Peru available at: [[https://www.senamhifi.gob.pe/?&p=pronosto-caudales](https://www.senamhifi.gob.pe/?&p=pronosto-caudales)]([https://www.senamhifi.gob.pe/?&p=pronosto-caudales](https://www.senamhifi.gob.pe/?&p=pronosto-caudales))). Currently, they are mostly supported by the national hydrometeorological networks that are still scarce and could be greatly enhanced with the data and knowledge produced by RS. Some of these countries also have advanced Water Resources Laws and regulations, such as the Brazilian National Water Resources Management System created by Law 9433, 1997 (Brasil, 1997), but most of the efforts on the development and implementation of such regulation are devoted to river basins in more densely populated regions and not in the context of the complexity of the international/transboundary and larger river basin of the world. Also, even though the Amazon basin is in the epicenter of international scientific discussion, it appears not to be the main focus of technical and scientific developments on the water resources field in the Amazon countries, as revealed by the recent synthesis of advances from Brazilian hydrology community ([PERSON], 2020).
Most flooding studies in the Amazon aimed to understand ecosystem services and the natural system (Sections 4.2 and 6.2). Still, many Amazon urban centers are at flood risk (e.g., Amazon River at Iquilots, Ma deira River at Porto Velho, Acre River at Rio Branco, Jurua river at Cruzeiro do Sul), and suffer annually from overbanking flow ([PERSON] et al., 2020). While this paper was being drafted, the Brazilian Acre state was recovering from a humanitarian crisis caused by floods at Acre River at Rio Branco, Jurua River at Cruzeiro do Sul, and Negro River at Manaus, enhanced by the COVID-19 pandemic. Thus, the several flood monitoring tools developed could be translated into effective flood risk mapping and real-time monitoring for disaster management. International initiatives such as the Copernicus Emergency Management Service ([[https://emergency.copernicus.eu/](https://emergency.copernicus.eu/)]([https://emergency.copernicus.eu/](https://emergency.copernicus.eu/))) and the International Charter \"Space and Major Disasters\" ([[https://disasterscharter.org/](https://disasterscharter.org/)]([https://disasterscharter.org/](https://disasterscharter.org/))) have the potential to provide important EO data for real-time disaster management. Furthermore, the transboundary character of many Amazon sub-basins (e.g., Madeira River, with floods at Porto Velho in Brazil being partially generated in upstream Bolivian reaches) makes RS data a fundamental tool to fulfill the disparity in data availability among countries. On the other hand, in many areas of the Amazon, droughts have a larger societal impact than floods, given the adaptation of livelihoods to the annual flooding regime and the interruption of the provision of goods and general transport through rivers during extremely dry periods ([PERSON] et al., 2008). Recent technical efforts include evaluation of hydrological forecasts from physically based hydrological models supported by RS (Section 6.2), development of site-specific statistical forecasting and real-time monitoring systems (e.g., SACE system from [[http://www.cprn.gov.br/sace/](http://www.cprn.gov.br/sace/)]([http://www.cprn.gov.br/sace/](http://www.cprn.gov.br/sace/)); systems available for the Madeira, Acre, Xingu, Branco and some reaches of the Amazon manisteny), prototypes of hydrological model-based monitoring systems (e.g., South America River Discharge Monitor - SARDIM [[https://sardim.herokuapp.com/](https://sardim.herokuapp.com/)]([https://sardim.herokuapp.com/](https://sardim.herokuapp.com/)); [PERSON] et al., 2020), global flood forecast systems (e.g., GLOFAS, [PERSON] et al., 2013) and efforts on monitoring and alerts of natural hazards by centers as CEMADEN from Brazil (Centro Nacional de Alerta e Monitoramento de Desastres Naturais). Drought monitor systems based on in situ and RS-based observations and local community interpretation (e.g., ANA Drought Monitor [[http://monitordesecas.ana.gov.br/](http://monitordesecas.ana.gov.br/)]([http://monitordesecas.ana.gov.br/](http://monitordesecas.ana.gov.br/))) are evolving, and there are no operational hydrological forecasting systems at the Amazon basin, national or continental scales ([PERSON] et al., 2016).
Impacts from human activities may propagate through the Amazon River network and neighbor countries since the ongoing developments of hydropower projects, and agricultural expansion alters the hydrological, sediments, and ecosystem dynamics ([PERSON] et al., 2018; [PERSON] et al., 2017). Recent research has explored integrated planning looking for the best hydropower development solutions ([PERSON] et al., 2020; [PERSON] et al., 2016), while organizations, like the Amazon Cooperation Treaty Organization, aim to promote sustainable development at the Amazon basin with the participation of its neighboring countries. However, current national-scale policies and regulations do not promote fully integrated water resources planning, as new projects are usually accessed individually. RS can encourage a common and transparent understanding of Amazon water-related issues.
The RS scientific community now has the challenge to promote knowledge, data sets, and applications on water-environmental changes, aiming at enhanced water resources management and planning. Potential pathways include: (a) training decision-makers and multiple stakeholders on the language of RS (e.g., Applied Remote Sensing Training Program - ARSET [[https://appliedsciences.nasa.gov/what-we-do/capacity-building/arset](https://appliedsciences.nasa.gov/what-we-do/capacity-building/arset)]([https://appliedsciences.nasa.gov/what-we-do/capacity-building/arset](https://appliedsciences.nasa.gov/what-we-do/capacity-building/arset))), (b) encouraging local engagement by bridging the gap between RS based science and in situ and traditional knowledge ([PERSON] et al., 2020), (c) initiatives of science communication and citizen science ([PERSON] et al., 2014; e.g., www.amazoniacenciaicuidadana.org/, [[https://www.ufrgs.br/conexoseamazonicas/](https://www.ufrgs.br/conexoseamazonicas/)]([https://www.ufrgs.br/conexoseamazonicas/](https://www.ufrgs.br/conexoseamazonicas/)), [[https://ipam.org.br/biblioceca-artigos-cientificos](https://ipam.org.br/biblioceca-artigos-cientificos)]([https://ipam.org.br/biblioceca-artigos-cientificos](https://ipam.org.br/biblioceca-artigos-cientificos)), [[https://imazon.org.br/categories/](https://imazon.org.br/categories/)]([https://imazon.org.br/categories/](https://imazon.org.br/categories/)), [[https://infoamazonia.org/](https://infoamazonia.org/)]([https://infoamazonia.org/](https://infoamazonia.org/))), (d) development of open access data sets focused on specific applications (e.g., aquatic ecosystem conservation; [PERSON] et al., 2016); (e) developing monitoring systems focused on environmental changes and water-related disasters, (f) developing open hydrological repositories (e.g., HYSAM, [[https://hybam.obs-mip.fr/](https://hybam.obs-mip.fr/)]([https://hybam.obs-mip.fr/](https://hybam.obs-mip.fr/)), SERVIR-Amazonia, [[https://servir.ciat.cgiar.org/](https://servir.ciat.cgiar.org/)]([https://servir.ciat.cgiar.org/](https://servir.ciat.cgiar.org/))), and (g) developing a basin-scale research agenda focused on directly supporting water resources decision making (e.g., scenarios of hydropower development; [PERSON] et al., 2020).
### Recommendations
Based on the knowledge gaps and the perspectives presented in the previous sections, we provide the following recommendations for future studies on Amazon waters from space.
#### 7.5.1 Recommendation 1: Observations
Current limitations of satellite data for the Amazon basin are often related to the space-time resolution (e.g., SWE and slope, surface water extent, ET), time span (e.g., surface water extent, TWS, GWS, ET, topography), and accuracy (e.g., surface water extent, GWS anomalies). The largest limitations in monitoring the Amazon hydrology from space refer to soil moisture and river discharge, which have been poorly addressed due to vegetation interference in sensors or by the nature of the variable, respectively, which hampers its estimation from the space. Similarly, river and floodplain channel bathymetry provides great challenges, that may be solved with the assimilation of altimetry data into models. The increasing availability of long-term archives of RS data sets should be ensured by national space and water agencies in complement to existing in situ monitoring networks, which are fundamental to properly calibrate and validate RS estimates. The latency time of RS data distribution (e.g., precipitation and SWE) should be reduced to a few hours to be used by water/risk management. Ensuring satellite observation to be archived into climatic data sets can foster the understanding of the impacts of climate change and human activities on the basin.
#### 7.5.2 Recommendation 2: Models, Algorithms, and Integration
Technical limitations are related to the development of algorithms (e.g., orographic rains, CDOM and chlorophyll retrieval, water budget closure, and hydrodynamic models), and data fusion (e.g., ET, SWE, and surface water extent). The recognition of uncertainties in multiple RS data and trade-offs between temporal and spatial resolution point to the need for more integrative approaches, for example, for mapping long-term flooding and evapotranspiration patterns at high spatio-temporal resolutions, and artificial intelligence will play a major role in this. The better coupling of EO data sets with hydrological-hydraulic models and land surface models (e.g., data assimilation, spatiotemporal interpolation) is also a necessary step forward in Earth System modeling by considering the dynamic aspect of Amazon hydrology.
#### 7.5.3 Recommendation 3: Characterization of Hydrological Processes in a Changing Amazon
The development of long-term data sets is fundamental to understand Amazon hydrological processes across multiple decades. While RS data currently focus on a set of a few hydrological variables, many others require more attention from the hydrologic community, such as river discharge and water velocity, surface and groundwater storage, soil moisture, CDOM, and Chlorophyll-a. Most studies in the Amazon basin also focus on a few areas (e.g., the varizen environment in the central Amazon floodplains), and many other complex river-wetland systems or streams and small rivers, especially in the Andean region, also require attention. Upcoming and future satellite observations will bring new opportunities for the Amazon basin regarding the characterization of natural processes, including phytoplankton in waters, floodplain topography, aquatic ecosystems, groundwater dynamics, and the monitoring of anthropogenic environmental changes.
#### 7.5.4 Recommendation 4: Toward the Use of RS to Support Sustainable Science in the Amazon Basin
The Amazon basin harbors an incredibly large and still poorly known biodiversity, which provides massive ecosystem services for the globe and some of the most complex and intriguing river-wetland systems in the world. While EO through satellites has provided breakthrough scientific advances on the comprehension of the Amazon water cycle in the last decades, the forthcoming years with the new hydrology-oriented missions will provide a new milestone on monitoring Amazon waters from space. Advance knowledge from RS should be translated into valuable information and indicators to support the Amazon basin's environmental governance and sustainable science. RS has the potential to democratize essential information for decision-makers, moving toward a more sustainable future for the largest basin in the world.
## Data Availability Statement
This is a review study for which no new data was generated. Data supporting the figures are available via the cited references.
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wiley/fab7de79_5c76_4f0f_bf96_328a30147a2a.md | # Gr Biogeosciences
Hot or Not? An Evaluation of Methods for Identifying Hot Moments of Nitrous Oxide Emissions From Soils [PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON], 1,2,3
1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana IL, USA, 1
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1 Institute for Sustainability, Energy, and Environment, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 1
[PERSON]
## 6 Journal of Geophysical Research: Biogeosciences
### 6.1 Resources: [PERSON], [PERSON], [PERSON]. [PERSON], [PERSON]
**Switzer:** [PERSON],
[PERSON]
**Supervision:** [PERSON], [PERSON], [PERSON]
**Validation:** [PERSON]
**Viswalidate:** [PERSON]
**Viswalidate:** [PERSON]
**Writing - original draft:** [PERSON], [PERSON], [PERSON]
**Writing - review & editing:** [PERSON]
**Wetting - review & editing:** [PERSON], [PERSON], [PERSON]. [PERSON], [PERSON]**
**Journal of Geophysical Research: Biogeosciences**
**10.1029/2024 JG008138**
relatively infrequent manual chamber-based emissions measurements that may miss many of the hot moments ([PERSON] et al., 2020; [PERSON] & [PERSON], 2015). Understanding N2O hot moments from high temporal resolution data sets derived from autochamber and micrometeorological measurements can help guide improved manual chamber measurement sampling to better capture hot moments ([PERSON] & [PERSON], 2021; [PERSON] et al., 2021; [PERSON] et al., 2019), and help parameterize models to more accurately predict N2O budgets on regional to global scales ([PERSON] et al., 2022). Despite these data sets becoming more common ([PERSON] et al., 2020; [PERSON] et al., 2020), there currently is no standard approach for hot moment identification, and the implications of different approaches on hot moment identification and quantification have not previously been evaluated.
The concept of biogeochemical hot moments was popularized by [PERSON] et al. (2003) over two decades ago and has inspired many studies investigating the importance and cause of N2O hot moments ([PERSON] et al., 2017). Yet there is no consensus on N2O hot moment identification because hot moments lack a quantitative definition. Based on the conceptual definition that hot moments are \"short periods that exhibit disproportionately high reaction rates relative to longer intervening time periods\" ([PERSON] et al., 2003), most conservatively, N2O hot moments should represent less than 50% of data points in a time series of N2O emission measurements and emissions greater than the average of the time series. Thus, a common interpretation of N2O hot moments is that they occur relatively rarely, only when triggered by events, such as rainfall, fertilization, or freeze-thaw ([PERSON] et al., 2009; [PERSON] et al., 2012; [PERSON] et al., 2017, 2020), and these events create conditions more favorable for N2O production than baseline conditions. As such, N2O hot moments should account for far less than 50% of the data points in N2O emission time series, though how much less depends on the frequency of hot moment triggers in a given system. Similarly, a common interpretation of \"disproportionately high reaction rates\" suggests that N2O hot moments represent emissions far greater than the average emission, though how much greater depends on the outlier detection methods used to identify N2O hot moments as well as the magnitude and frequency distribution of the emission data sets. Given these qualitative criteria for defining N2O hot moments in terms of the proportion of a time series attributed to hot moments and the magnitude of the emissions, it is still possible to evaluate how well quantitative hot moment identification approaches meet these dual criteria.
There are many outlier detection methods that could be used for identifying N2O hot moments ([PERSON], 2020), wherein emission values above a threshold are considered part of an N2O hot moment. Since N2O hot moments can be obvious in time series of net N2O flux data, thresholds are sometimes arbitrarily determined when visualizing the data set ([PERSON] et al., 2021; [PERSON] et al., 2024). As a more rigorous approach, statistical methods can be used to identify data points as outliers based on their deviation from a standard distribution, with standard deviation (SD) and interquartile range (IQR) methods most commonly used for N2O hot moment identification (e.g., [PERSON] et al., 2023; [PERSON] & [PERSON], 2021; [PERSON] & [PERSON], 2024; [PERSON] et al., 2015; [PERSON] et al., 2012; [PERSON] et al., 2014; [PERSON] et al., 2022). The SD method identifies outliers as values exceeding a number of SDs above the mean, whereas the IQR method is typically applied by identifying outliers 1.5 times the IQR above the third quartile or below the first quartile. These two methods are distribution-based approaches that assume a normal distribution to the data set. However, this assumption belies the very behavior of N2O hot moments (episodic and large emission pulses), which typically leads to right-skewed N2O flux data sets. Logarithmic transformation of data sets may not be sufficient to achieve normal distributions for highly skewed data sets and cannot be applied to data sets with negative (e.g., N2O consumption) values. The SD method is sensitive to the frequency distribution of the data set because both the standard deviation and mean are inflated in right-skewed distributions. In contrast, the IQR method is more robust against non-normal distributions. Alternatively, distribution-free methods, such as isolation forest (IF) classification, could be more appropriate for standardized hot moment identification across data sets that vary in flux magnitude and frequency distribution ([PERSON] et al., 2022). Isolation forest (IF) classification is a distance-based, machine learning method that uses binary trees to identify anomalous data points based on short path-lengths in the trees that indicate that the data points are few and different from the rest of the data set. These outlier detection methods have not been compared across N2O flux data sets that vary in flux magnitude and distribution, leaving uncertain how much the methods can differ in hot moment identification and the estimated fraction of annual N2O emissions attributed to hot moments.
In addition to considering the sensitivity of the outlier detection method to the frequency distribution of flux data, the stringency with which each of these methods is applied determines the percentage of flux measurements identified as hot moments. The stringency of the IF method can be tuned by adjusting a contamination factor, butit does not inherently lead to the identification of a certain percentage of data points as outliers in the same way as the statistical methods. For example, assuming a data set is normally distributed, using 1.5x the interquartile range (1.5x IQR; e.g., [PERSON] et al., 2012) of the measured net N\({}_{2}\)O fluxes, flux values higher than 99.3% of the distribution are considered part of N\({}_{2}\)O hot moments. Using four standard deviations (4 SD) above the mean (e.g., [PERSON] and [PERSON], 2021), only flux values in the top 0.1% of the distribution are identified as hot moments. While the IQR method is typically only applied at the 1.5x IQR stringency, there is no standard stringency with which the SD method is applied. The performance of the SD method at varying stringencies therefore warrants comparison to separate this from how the SD method compares against other outlier detection methods.
Seasonal variation in N\({}_{2}\)O flux magnitude and distribution could lead to bias in hot moment identification and quantification when considering whole year data sets compared to seasonally subdivided data sets. In agro-ecosystems, N\({}_{2}\)O hot moments are largely governed by seasonally distinct triggers ([PERSON] et al., 2013). In the early growing season fertilization with ammonium (NH\({}_{4}\)+) or nitrate (NO\({}_{3}\)-) drives hot moments ([PERSON] et al., 2012; [PERSON] et al., 2014). Throughout the growing season, irrigation or rainfall drives hot moments ([PERSON] et al., 2017; [PERSON] et al., 2022). During the winter and spring, freeze-thaw and thaw drive hot moments, respectively ([PERSON] et al., 2013; [PERSON] et al., 2017). The flux magnitudes of these hot moments vary, with fertilization-driven hot moments typically yielding larger-magnitude N\({}_{2}\)O fluxes than rainfall-driven hot moments ([PERSON] et al., 2019). Thaw-related hot moments can be even larger than fertilization or rainfall-driven hot moments but vary in magnitude depending on the strength of a freeze event prior to thaw ([PERSON] et al., 2002; [PERSON] et al., 2009). Mitigating both larger and smaller N\({}_{2}\)O hot moments can potentially be important to reducing annual N\({}_{2}\)O emissions, with mitigation strategies targeting the different mechanisms responsible for N\({}_{2}\)O hot moments in different seasons. However, studies to date have conducted hot moment identification on whole year data sets such that the larger fertilization and thaw-driven N\({}_{2}\)O emission pulses elevate the thresholds used to identify N\({}_{2}\)O hot moments, causing the smaller, more frequent hot moments from other seasons to be missed. Because seasonally subdivided hot moment identification has not been previously conducted, it is not known how much these smaller N\({}_{2}\)O hot moments contribute to annual N\({}_{2}\)O emissions.
Here, we evaluated different outlier detection methods on whole year and seasonally subdivided net N\({}_{2}\)O flux data sets to determine which approach best captured N\({}_{2}\)O hot moments across data sets varying in N\({}_{2}\)O flux magnitude and distribution. We chose to evaluate both commonly cited methods in the hot moment literature and a distribution-free method, as these are representative of approaches with varying inherent sensitivity to N\({}_{2}\)O flux magnitude and distribution. We took advantage of a unique study in which one year of hourly measurements of net N\({}_{2}\)O flux were collected from 16 autochambers located in a \(\sim\)5 ha area of a conventionally tilted maize field in central Illinois, USA. The autochambers were placed to capture variation in N\({}_{2}\)O dynamics, including consistent N\({}_{2}\)O cold spots and episodic N\({}_{2}\)O hot spots ([PERSON] et al., 2024). The variation in N\({}_{2}\)O flux magnitude and distribution among the 16 autochamber data sets provided the opportunity to robustly assess how hot moment identification using (a) the 2 SD or 4 SD, 1.5x IQR, and IF methods, and (b) whole year data sets versus seasonally subdivided data sets (early growing season, late growing season, and non-growing season) affected hot moment threshold values and quantification of N\({}_{2}\)O hot moment fluxes. Based on our findings, we provide recommendations to standardize hot moment identification approaches.
## 2 Methods
### Net N\({}_{2}\)O Flux Data Collection
Net N\({}_{2}\)O fluxes were measured in a commercial field located near Villa Grove, IL that was cultivated in maize-soy rotations with conventional tillage and planted with maize (Z _mays_) during the 2022 growing season. Deep chissel tillage was performed in November 2021. Pre-planting fertilizers were applied at the rate of 19.7 kg N\(\,\)ha\({}^{-1}\),93.1 kg P ha\({}^{-1}\), and 53.8 kg K h\({}^{-1}\) in April 2022. Prior to planting, 134.5 kg N\(\,\)ha\({}^{-1}\) of anhydrous ammonia was injected into the soil on 7 May 2022. Maize was planted on 10 May 2022. Finally, 32% urea-ammonium-nitrate (UAN) was Y-dropped as side-dressing (i.e., UAN liquid was injected on one side of each crop row) at 90.2 kg N\(\,\)ha\({}^{-1}\) with ammonium thiosulfate at 13.2 kg N\(\,\)ha\({}^{-1}\) on 11 June 2022. Z _mays_ was harvested on 28 October 2022. The soil in the field is roughly 70% Drummer silty clay loam and 30% Millbrook silt loam (Soil Survey Team; USDA-NRCS, 2023). In this region, the mean annual air temperature is 10\({}^{\circ}\)C, with a maximum monthly mean temperature of 24.4\({}^{\circ}\)C in July and a minimum of \(-\)5.5\({}^{\circ}\)C in January (MidwesternRegional Climate Center). The mean annual precipitation is 1,008 mm, of which most rainfalls occur during the period of May to July (Illinois-Climate-Network, 2017).
To capture spatial and temporal variability in soil N\({}_{2}\)O emissions at the field scale, net soil-atmosphere fluxes of N\({}_{2}\)O were measured hourly using automated chambers at 16 locations in the maize field. The chambers were distributed among four sampling nodes (named Node 1-4) within a \(\sim\)5 ha area of the field, with nodes 50-100 m distance apart. The node locations were selected to represent variation in temporal patterns in emissions measured manually in the 2021 growing season ([PERSON] et al., 2024). Moreover, soil organic matter (SOM), pH, and topographic position varied among the four nodes, as measured in 2021 (Table S1 in Supporting Information S1). At each node, four automated chambers (LI-8200-104, LI-COR Biosciences, Lincoln, NE, USA) were radially installed at 12 m distance from a N\({}_{2}\)O gas analyzer (LI-7820, LI-COR Biosciences, Lincoln, NE, USA) that sequentially measured hourly net soil-atmosphere N\({}_{2}\)O fluxes from each chamber continuously with an automated gas sampling multiplexer (LI-8250, LI-COR Biosciences, Lincoln, NE, USA). Chambers were numbered Chamber 1-4 based on their clockwise position around the node's center. When referencing a chamber at a specific node we use to following shorthand: Chamber 4 at Node 2 = N2C4, and so forth. Chamber collars (20 cm diameter) were permanently installed directly adjacent from the crop row, allowing the chambers to be oriented such that the chamber top did not shade the crops or the collar footprint when the chambers were fully open between measurements. There was no vegetation between the crop rows and therefore no vegetation in the chamber footprint. Measurements continued from May 2022 until April 2023, excluding a \(\sim\)3-week period in October-November 2022 during crop harvest and shorter outages for instrument maintenance or repair. The data sets were not gap-filled for this study. Using SoilFluxPro version 5.2.0 (LI-COR Biosciences, Lincoln, NE, USA), N\({}_{2}\)O fluxes were calculated from an exponential fit applied to the change in N\({}_{2}\)O concentration in the headspace from 30 to 490 s of the measurement period (total period 520 s). If the modeled exponential fit for a given flux measurement had an R\({}^{2}\) of <0.6, then data were visually inspected for evidence of bad chamber closure (e.g., non-monotonic fluctuations in the N2O concentration over time), which warranted exclusion of the flux measurement from the data set. Excluded flux data represented <0.03% of the total data set.
### Comparison of Hot Moment Identification Approaches
We compared three outlier detection methods (2 SD or 4 SD, 1.5x IQR, and IF) on whole year data sets and seasonally subdivided data sets to determine how the hot moment identification approaches affected the hot moment threshold values, the percentage of hot moment contributions to annual or seasonal N\({}_{2}\)O emissions, and the percentage of time in the year or season attributed to hot moments. The year was divided into three seasons: the early growing season (May 13-July 7, 2022) when hot moments were driven by fertilizer inputs, the late growing season (July 8-October 30, 2022) when hot moments were driven by rain events, and the non-growing season when hot moments were driven by freeze-thaw events (November 1, 2022-April 9, 2023). The breakpoints between the seasons were visually determined from plotting the whole year data sets for the 16 autochambers together (Figure S1 in Supporting Information S1).
We ran each of the outlier detection methods for the whole year and by individual season for each of the 16 autochambers. For the SD method, we calculated the mean and SD of the data set and then determined the hot moment threshold value as either two SD or four SD above the mean. For the 1.5x IQR method, the IQR is calculated as the difference between the 75 th percentile (Q3) and the 25 th percentile (Q1) of the data set. To identify the hot moment threshold, we calculated the upper threshold, which is Q3 plus 1.5 times the IQR. The IF method isolates anomalies instead of profiling normal data points. The algorithm utilizes 'isolation trees' to partition the data space, where anomalies are identified based on shorter path lengths in these trees, indicating easier isolation compared to normal points. For IF, we employed the IsolationForest function from sklearn. ensemble module in Python (version 3.10), setting the contamination parameter to 'auto'. This configuration allows the algorithm to automatically estimate the proportion of outliers in the data set. This approach classifies data points with an anomaly score below 0 as anomalies. The threshold for identifying significant hot moments in N\({}_{2}\)O flux was determined by the lowest net N\({}_{2}\)O flux value that corresponded to an anomaly score below this threshold.
Although all 16 autochamber data sets were right-skewed (Figure S2 in Supporting Information S1), for several reasons we chose not to transform the data sets to achieve normal distributions. First, about 4% of the net N\({}_{2}\)O flux measurements across all data sets were negative fluxes that would have to be excluded to proceed with log transformation. Second, log transformation would diminish the data points on the high end of the frequency distributions such that the hot moment identification methods would not capture these extreme values as \"hot moments.\" Third, IF is an unsupervised learning algorithm that does not assume a specific distribution, negating the need for transformation.
Using the determined threshold values above which a data point was considered part of a hot moment, we calculated the cumulative hot moment N\({}_{2}\)O emissions and the number of hot moment data points. We calculated the percentage of hot moment contributions to cumulative N\({}_{2}\)O emissions from the cumulative hot moment N\({}_{2}\)O emissions divided by cumulative N\({}_{2}\)O emissions. We also calculated the percentage of time in hot moments from the number of hot moment data points divided by the total number of N\({}_{2}\)O flux data points. These calculations were performed separately for each of the 16 autochambers across the whole year and by individual season.
### Statistical Analyses
We used one-way ANOVAs and Tukey pairwise comparisons to determine the effect of outlier detection method on threshold values, percentage of hot moment contributions to the cumulative N\({}_{2}\)O emissions, and the percentage of time in hot moments in the whole year and in individual seasons. We also conducted similar analyses within each outlier detection method to determine the effect of season. Additionally, we calculated Pearson's coefficient of skew using the median for each autochamber's N\({}_{2}\)O flux measurements. The 16 autochambers were considered independent replicates for this analysis because of the high variation among autochamber data sets, even within sampling nodes. This analysis was performed separately for the whole year data sets and for each of the three individual season data sets. These statistical analyses were performed in RStudio (version 4.2.2 (2022-10-31) --\"Innocent and Trusting\" 2022 The R Foundation for Statistical Computing; Team, R 2019). Statistical significance was determined as \(P<0.05\).
## 3 Results
### Comparison of Hot Moment Threshold Values
On average across all 16 autochamber data sets, the SD method yielded 1-2 orders of magnitude higher threshold values compared to the 1.5x IQR and IF methods, which had comparably lower threshold values (Table 1). The 4 SD method threshold values were significantly higher than the other two methods when considering the whole year and individual seasons (Table 1). This difference was detectable despite high variation in threshold values among autochambers: for the whole year analysis, thresholds ranged from 0.39-2.2, 0.0002-2.2, and 3.7-36 nmol N\({}_{2}\)O m\({}^{-2}\) s\({}^{-1}\) for 1.5x IQR, IF, and 4 SD methods, respectively (Figure S3 in Supporting Information S1). When the SD method was applied using 2 SD, the threshold values were still higher than for the 1.5x IQR and IF methods but due to large variance, these differences were statistically significant only for the comparison with the IF method for the whole year and late growing season (Table 1).
When subdividing the data sets into the early, late, and non-growing seasons, the threshold values determined by a given outlier detection method differed significantly among seasons (Table 1, Figure S3 in Supporting Information S1). All three methods yielded higher threshold values in the early growing season compared to the other two seasons, although for the IF method this was not statistically significant for the early versus non-growing season comparison (Table 1, Figures S4 and S5 in Supporting Information S1). Seasonally subdividing the data sets led to significantly increased and borderline significantly increased early growing season hot moment thresholds compared to whole year thresholds for the 1.5x IQR method and the SD methods, respectively, whereas it did not significantly decrease the late- and non-growing season thresholds relative to the whole year thresholds for these methods. In contrast, seasonally subdividing the data sets led to significantly and borderline significantly decreased late- and non-growing season thresholds, respectively, compared to whole year thresholds for the IF method, and it did not change the early season threshold relative to the whole year threshold (Table 1).
### Comparison of Hot Moment Contributions to Cumulative N\({}_{2}\)O Emissions
For the whole year and each season, the percentage of cumulative N\({}_{2}\)O emissions from each chamber that was attributed to hot moments was, on average, lowest for the SD method applied as 2 SD or 4 SD compared to the other two outlier detection methods (Table S2, Figure S6 in Supporting Information S1). However, this pattern did not necessarily hold when comparing the three methods for a given chamber within an individual season (Figure 1). In the early growing season, the three methods were sometimes indistinguishable. For example, regardless of the outlier detection method, 99%-100% of the cumulative seasonal N\({}_{2}\)O emissions was attributed to hot moments for the five autochambers with the highest cumulative early season N\({}_{2}\)O emissions (N1C3, N1C4, N4C1, N4C2, and N4C3; Figure 1). For one chamber (N3C2), the IF method attributed 100% of cumulative seasonal N\({}_{2}\)O emissions to hot moments in all three seasons, which was far higher than the other two methods.
For all outlier detection methods, the mean percentage of cumulative seasonal N\({}_{2}\)O emissions attributed to hot moments was greater in the early growing season compared to the late and non-growing seasons (Figure 2, Table S2 in Supporting Information S1). However, this pattern did not necessarily hold across all chambers (Figure 1). For example, in Node 2, for Chambers 1 and 3, most of the cumulative annual flux was attributed to the non-growing season, but for Chambers 2 and 4 the cumulative N\({}_{2}\)O flux was more evenly distributed among the seasons (Figure 1).
The percentage of time attributed to hot moments was higher for whole year data sets compared to the sum of seasonally subdivided data sets for the 1.5x IQR and SD methods but was the opposite for the IF method (Figure 2, Table S2 in Supporting Information S1). The hot moment contributions for 1.5x IQR, IF, 2 SD, and 4
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{4}{c}{Outlier detection method} & Compare by method \\ \cline{2-5} & 1.5x IQR & Isolation forest & 2 SD & 4 SD & ANOVA main effects \\ \hline
**Time interval** & & & & & \\ Whole year & 1.5 \(\pm\) 0.24 (**ab, A**) & 0.89 \(\pm\) 0.14 (**b, B**) & 5.3 \(\pm\) 4.4 (**n, AB**) & 9.9 \(\pm\) 2.0 (**c, AB**) & \(P\) \(<\) 0.001, \(F\) = 12 *** \\ Early growing season & 5.0 \(\pm\) 0.90 (**a, B**) & 0.92 \(\pm\) 0.36 (**a, B**) & 10 \(\pm\) 10 (**ab, A**) & 19 \(\pm\) 4.6 (**b, B**) & \(P\) \(<\) 0.001, \(F\) = 8.2 *** \\ Late growing season & 1.3 \(\pm\) 0.44 (**ab, A**) & 0.07 \(\pm\) 0.03 (**a, A**) & 2.2 \(\pm\) 1.9 (**bc, B**) & 3.9 \(\pm\) 0.83 (**c, A**) & \(P\) \(<\) 0.001, \(F\) = 9.1 *** \\ Non-growing season & 0.91 \(\pm\) 0.28 (**a, A**) & 0.34 \(\pm\) 0.07 (**a, AB**) & 1.5 \(\pm\) 1.5 (**ab, B**) & 2.7 \(\pm\) 0.66 (**b, A**) & \(P\) = 0.0013, \(F\) = 5.9** \\
**Compare by time interval** & & & & \\ ANOVA main effects & \(P\) \(<\) 0.001, \(F\) = 13 *** & \(P\) = 0.01, \(F\) = 4.6 * & \(P\) \(<\) 0.001, \(F\) = 8.4 *** & \(P\) \(<\) 0.001, \(F\) = 8.1 *** \\ \hline \hline \end{tabular} _Note._ Different lowercase letters indicate statistically significant Tukey pairwise differences among the outlier detection methods within a time interval (e.g., compare means across each time interval row). Different uppercase letters indicate statistically significant Tukey pairwise differences among the time intervals for each outlier detection method (e.g., compare means down each threshold method column). The column of ANOVA main effects corresponds to the differences among outlier detection methods, and the row of ANOVA main effects corresponds to the differences among seasons for a given method. For all one-way ANOVA, df = 2. For \(P\) \(<\) 0.001, ***; \(P\) \(<\) 0.01 **; \(P\) \(<\) 0.05, *. To see all threshold values and summary boxplots for each autochamber by method and season, see Figures S3 and S4 in Supporting Information S1
\end{table}
Table 1: _Mean \(\pm\) SE Net N\({}_{2}\)O Flux Threshold Values (mmol N\({}_{2}\)O \(m^{-2}\) s\({}^{-1}\)) for the Four Hot Moment Outlier Detection Methods Applied to Whole Year Data Sets and Seasonally subdivided Data Sets (N = 16 in All Cases)_
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{4}{c}{Outlier detection method} & Compare by method \\ \cline{2-5} & 1.5x IQR & Isolation forest & 2 SD & 4 SD & ANOVA main effects \\ \hline
**Time interval** & & & & \\ Early growing season & 9.3 \(\pm\) 1.0 (**a, A**) & 65 \(\pm\) 9.7 (**b, B**) & 4.2 \(\pm\) 1.9 (**a, A**) & 0.81 \(\pm\) 0.11 (**a, A**) & \(P\) \(<\) 0.001, \(F\) = 39 *** \\ Late growing season & 7.7 \(\pm\) 1.2 (**a, A**) & 89 \(\pm\) 7.2 (**b, B**) & 3.9 \(\pm\) 1.2 (**a, A**) & 0.85 \(\pm\) 0.15 (**a, A**) & \(P\) \(<\) 0.001, \(F\) = 136 *** \\ Non-growing season & 8.8 \(\pm\) 0.58 (**a, A**) & 23 \(\pm\) 5.3 (**b, A**) & 3.8 \(\pm\) 1.1 (**a, A**) & 1.2 \(\pm\) 0.07 (**a, A**) & \(P\) \(<\) 0.001, \(F\) = 13 *** \\
**Compare by time interval** & & & & \\ ANOVA main effects & \(P\) = 0.51, \(F\) = 0.70 & \(P\) \(<\) 0.001, \(F\) = 19 *** & \(P\) = 0.79, \(F\) = 0.23 & \(P\) = 0.08, \(F\) = 2.7 \\ \hline \hline \end{tabular} _Note._ Different lowercase letters indicate statistically significant Tukey pairwise differences among the outlier detection methods within a time interval (e.g., compare means across each time interval row). Different uppercase letters indicate statistically significant Tukey pairwise differences among the time intervals for each outlier detection method (e.g., compare means down each threshold method column). The column of ANOVA main effects corresponds to the differences among outlier detection methods, and the row of ANOVA main effects corresponds to the differences among seasons for a given method. For all one-way ANOVA, df = 2. For \(P\) \(<\) 0.001, ***; \(P\) \(<\) 0.01 **; \(P\) \(<\) 0.05, *. To see all threshold values and summary boxplots for each autochamber by method and season, see Figures S3 and S4 in Supporting Information S1
\end{table}
Table 2: _Mean Percentage (%) of Time for Each Season That was Identified as a Hot Moment Using the Different Outlier Detection Methods, Averaged Across All Chambers (n = 16 in All Cases); \(\pm\) Corresponds to 1 SE From the Mean, and Letters Correspond to Tukey Pairwise Differences_Figure 1: Hot moment contributions to the cumulative N\({}_{2}\)O flux for each automated chamber over the whole sampling period (May 2022–April 2023). For each automated chamber (each panel in the figure), the three bars correspond to three outlier detection methods, the different color portions within each bar correspond to a different season, and the shaded fraction of each colored portion corresponds to the N\({}_{2}\)O flux values that were included in hot moments. Flux values greater than or equal to the threshold value were considered part of a hot moment. The percentage values written inside each colored bar portion corresponds to the percentage of the N\({}_{2}\)O flux for each season that was attributed to hot moments of N\({}_{2}\)O.
SD differed by 19%, 9%, 8%, and 12%, respectively, for the summed seasonal contributions versus the whole year contributions (Figure 2, Table S2 in Supporting Information S1). Chamber by chamber, there was some more notable variation between the two approaches, but not across all chambers. Chambers that varied by 20% or more between the seasonally summed versus whole year hot moment contributions included: all Node 1 chambers, N3C1 and N4C3 for 1.5x IQR, N2C2, N2C4, and N4C4 for IF, and N4C1 and N4C2 for 4 SD (Figure S6 in Supporting Information S1).
### Comparison of the Amount of Time Attributed to Hot Moments
The percentage of time within each season attributed to hot moments was significantly lower for the SD and 1.5x IQR methods compared to the IF outlier detection method (Table 2, Figure S7 in Supporting Information S1). Within each season, roughly 1%, 4%, and 9% of data points were categorized as hot moments by the 4 SD, 2 SD, and 1.5x IQR methods, respectively. Among seasons, the 1.5x IQR and SD methods attributed similar percentages of time to hot moments. In contrast, on average across all 16 autochambers, the IF method led to a highly variable percentage of time attributed to hot moments, ranging from 23% in the non-growing season to 89% in the late growing season. In addition, IF attributed higher percentages of time to hot moments during the early and late growing seasons, but a much lower percentage of time to hot moments during the non-growing season (Table 2, Figure S7 in Supporting Information S1).
## 4 Discussion
To better measure and mitigate N2O emissions, we must first be able to identify and quantify hot moments of N2O since they contribute disproportionately to annual N2O budgets. Currently, there is no standard approach for hot moment identification, which challenges synthesis of knowledge about N2O hot moments across studies. The work we present here is the first assessment of different approaches for hot moment identification and their implications for hot moment quantification.
Our analysis of 16 hourly net N2O flux data sets that vary in N2O flux magnitude and distribution revealed that the SD method yielded hot moment threshold values too high, and the IF method yielded threshold values too low (Table 1). This led to missed N2O hot moments or low net N2O fluxes mischaracterized as hot moments, respectively (Figures S3 and S4 in Supporting Information S1, Figure 1). Reducing the stringency of the SD
Figure 2: Mean \(\pm\) SE hot moment contribution percentages (%) for the four hot moment outlier detection methods applied to the seasonal, whole year, and sum of seasons’ hot moment contribution percentages data sets (\(n=16\) in all cases). One-way ANOVAs and Tukey pairwise comparisons were conducted among the time intervals for each outlier detection method (e.g., compare means within each panel), and among the outlier detection methods within a time interval (e.g., compare same color bars across panels). Details of all statistical analyses are included in Table S2 in Supporting Information S1.
method from 4 SD to 2 SD roughly halved the hot moment threshold values, but this still led to significantly lower hot moment contribution to cumulative N\({}_{2}\)O emissions compared to both the 1.5x IQR and IF methods (Table S2 in Supporting Information S1). Hot moment identification by the 1.5x IQR method was most consistent with the qualitative definition of N\({}_{2}\)O hot moments, yielding an estimate that on average 9% of the net hourly N\({}_{2}\)O fluxes measured over the year were hot moments that contributed 66% of the cumulative N\({}_{2}\)O emissions (Table 2, Table S2 in Supporting Information S1).
Seasonally subdividing the annual data sets facilitated identification of smaller hot moments in the late and non-growing seasons when N\({}_{2}\)O hot moments were generally smaller (Table S2, Figures S4 and S5 in Supporting Information S1, Figure 1). However, it also increased the SD and 1.5x IQR hot moment threshold values in the early growing season when N\({}_{2}\)O hot moments were larger, leading to lower estimates of hot moment contributions to annual N\({}_{2}\)O emissions (Table 1, Figure S6 in Supporting Information S1). In the case of chambers N4C1 and N4C2, for 4 SD the seasonally summed hot moment contributions were substantially lower than for the whole year analysis because of particularly extreme early season hot moments that carried extra weight within early season analysis compared to whole season analysis. This led to both increased standard deviation and mean to elevate the threshold for hot moment identification in the early season analysis, excluding moderately high N\({}_{2}\)O emissions from the estimates of hot moment contributions. In the case of specific chambers for 1.5x IQR and IF that also had substantial difference between seasonally summed versus whole year hot moment contributions, the distinguishing features of the magnitude and frequency distribution that led to this were unclear. In the interest of identifying the N\({}_{2}\)O hot moments that are most important to measure and mitigate, we recommend whole year analyses as opposed to seasonally subdivided analyses.
### Evaluation of Hot Moment Outlier Detection Methods
Our analysis suggests that the 4 SD method was too stringent for hot moment identification; the method misses what would reasonably be considered hot moments in visual evaluations of the 16 autochamber data sets (Figure S8 in Supporting Information S1). By definition, this method should only identify the top 0.1% of the net N\({}_{2}\)O flux data as hot moments in data sets exhibiting normal distributions. When we applied the 4 SD method to untransformed right-skewed data sets, approximately 1% of the net N\({}_{2}\)O flux data were identified as hot moments (Table 2, Figure S7 in Supporting Information S1). On average across the 16 autochamber data sets, the 4 SD method yielded 10 times higher hot moment threshold values which led to three times lower estimates of hot moment contributions to annual N\({}_{2}\)O emissions compared to the 1.5x IQR and IF methods (Table 1 and Figure 1). The high threshold values estimated by the 4 SD method not only caused smaller hot moments to be missed but also caused net N\({}_{2}\)O fluxes on the rising and falling limbs of large hot moment pulses to be missed (Figure S8 in Supporting Information S1). An exception to this stark difference between methods was the autochamber data sets that included extremely high N\({}_{2}\)O fluxes following fertilization, which led to comparably high early growing season hot moment contributions (99%-100%) estimated by all four methods (Figures 1 and 2, Table S2 in Supporting Information S1). Relaxing the stringency of the SD method from 4 SD to 2 SD led to a \(\sim\)50% reduction in the hot moment threshold values but these were still higher than values estimated from the 1.5x IQR and IF methods. Our analysis suggests that the SD method would not capture the importance of the smaller-magnitude hot moments to cumulative annual N\({}_{2}\)O budgets because the threshold value is highly sensitive to the magnitude of the outlier flux values. We conclude that the SD method is appropriate only when used on flux data sets with normal distributions, regardless of the stringency with which it is applied.
The 1.5x IQR and IF methods yielded similar estimates of hot moment contributions to annual or seasonal N\({}_{2}\)O emissions (Figure 1, Figure S6 in Supporting Information S1), but the IF method often attributed considerably more net N\({}_{2}\)O flux data to hot moments (Figure S7 in Supporting Information S1, Table 2). This was due to lower hot moment threshold values estimated by the IF method which led to more N\({}_{2}\)O flux data points attributed to hot moments (Table 1, Figures S3 and S4 in Supporting Information S1). However, these smaller \"N\({}_{2}\)O hot moments\" contributed little to cumulative N\({}_{2}\)O emissions over the year or the individual season (Figures S3, S4 and S5 in Supporting Information S1, Figure 1). This was most exaggerated in the late growing season, which was marked by few and small hot moments across most autochambers. On average across the 16 autochamber data sets, the late growing season threshold value estimated by the IF method was so low (10 times lower than that estimated by the 1.5x IQR method), that 89% of late growing season net N\({}_{2}\)O flux data points were attributed to hot moments (Figures S4, S5 in Supporting Information S1, Figure 2, Table S2 in Supporting Information S1). Even in the early growing season when large hot moments occurred, the IF method on average attributed 65% of net N\({}_{2}\)O flux data points to hot moments (Figure 2, Table S2 in Supporting Information S1). The IF method, therefore, appears too permissive in identifying N\({}_{2}\)O hot moments, which should represent short periods of high net N\({}_{2}\)O fluxes that disproportionately contribute to cumulative N\({}_{2}\)O emissions ([PERSON] et al., 2020). We used the IF method with the contamination factor set on \"auto,\" which allows the machine-learning algorithm to determine the percentage of net N\({}_{2}\)O fluxes that are anomalous as opposed to setting the contamination factor to a fixed value that would determine this percentage. In contrast, the percentage of net N\({}_{2}\)O fluxes attributed to hot moments by the 1.5x IQR method was constrained to \(\sim\)9%, which is more in line with the qualitative definition of hot moments that suggests that hot moments should account for far less than 50% of the measured net N\({}_{2}\)O fluxes (Table 2, Figure S7 in Supporting Information S1; [PERSON] et al., 2020). As the flux distribution becomes more right-skewed, this percentage of N\({}_{2}\)O fluxes identified as hot moments will become greater even though the calculation of the hot moment threshold value is robust against non-normal distributions. We conclude that, of the three outlier detection methods we evaluated, the 1.5x IQR method strikes the best balance in identifying hot moments based on the qualitative criteria regarding the proportion of a time series attributed to hot moments and the magnitude of the emissions. Moreover, the 1.5x IQR method is the least sensitive to flux magnitude and distribution out of the three outlier detection methods that we evaluated, suggesting that it could be applied in a standardized manner across data sets.
### Evaluation of Whole Year Versus Seasonally Subdivided Analyses
Because different mechanisms trigger different magnitude N\({}_{2}\)O hot moments in the different seasons, we evaluated seasonally subdivided N\({}_{2}\)O flux data sets to ensure that hot moments were appropriately identified in all seasons. Although most of the 16 autochamber data sets exhibited large N\({}_{2}\)O hot moments in the early growing season and smaller N\({}_{2}\)O hot moments in the late- and non-growing seasons (Figure 1, Figure S8 in Supporting Information S1), the threshold values estimated from the analysis of whole year data sets did not exclude the smaller N\({}_{2}\)O hot moments (Table 1). As such, seasonally subdividing the data sets was not necessary to improve hot moment identification. On the contrary, it detrimentally affected hot moment identification in the early growing season by raising the hot moment threshold value estimated by the SD and 1.5x IQR methods (Table 1). This resulted in a decrease in estimated hot moment contributions to annual N\({}_{2}\)O emissions (Figures 1 and 2, Table S2 in Supporting Information S1). For the IF method, the low threshold values estimated for the late- and non-growing seasons led to more than half of those seasons being inappropriately identified as hot moments, thereby increasing the estimated hot moment contribution to annual N\({}_{2}\)O emissions relative to whole year analysis (Figure 1). We conclude that seasonal subdivision of N\({}_{2}\)O flux data sets can be counterproductive to N\({}_{2}\)O hot moment identification and quantification regardless of the outlier detection method.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
All code and data necessary to reproduce our results are available in our online GitHub repository ([[https://github.com/jiacheng-x/N2O-analysis](https://github.com/jiacheng-x/N2O-analysis)]([https://github.com/jiacheng-x/N2O-analysis](https://github.com/jiacheng-x/N2O-analysis))) and permanently archived at the Illinois Data Bank ([[https://doi.org/10.13012/B2](https://doi.org/10.13012/B2) IDB-8414089_V1]([https://doi.org/10.13012/B2](https://doi.org/10.13012/B2) IDB-8414089_V1), [PERSON] et al., 2024).
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* [PERSON] et al. (2019) [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2019). N2O flux measurements over an irrigated maize crop: A comparison over three methods. _Articultural and Forest Meteorology_, _264_, 56-72. [[https://doi.org/10.1016/j.aepfcom.2018.09.017](https://doi.org/10.1016/j.aepfcom.2018.09.017)]([https://doi.org/10.1016/j.aepfcom.2018.09.017](https://doi.org/10.1016/j.aepfcom.2018.09.017))
* Team (2019) [PERSON] (2019). _A language and environment of statistical computing_. R Foundation for Statistical Computing. Retrieved from [[https://github.com/jscahcai-h3/N2O-analysis](https://github.com/jscahcai-h3/N2O-analysis)]([https://github.com/jscahcai-h3/N2O-analysis](https://github.com/jscahcai-h3/N2O-analysis)).
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* [PERSON] et al. (2020) [PERSON], [PERSON], [PERSON], & [PERSON] (2020). Mitigation of nitrous oxide emissions in the context of nitrogen loss reduction from ge | wiley | Hot or Not? An Evaluation of Methods for Identifying Hot Moments of Nitrous Oxide Emissions From Soils | Emily R. Stuchiner, Jiacheng Xu, William C. Eddy, Evan H. DeLucia, Wendy H. Yang | https://doi.org/10.1029/2024jg008138 | 2,025 | CC-BY |
wiley/fa9caaee_6a3b_4e45_8746_9bfb686a3778.md | # IGR Earth Surface
Research Article
A Case Study on Drivers of the Isotopic Composition of Water Vapor at the Coast of East Antarctica
[PERSON]
1 School of Architecture, Civil and Environmental Engineering, CRYOS, EPFL, Lausanne, Switzerland, \"WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland, \"Now at Geophysical Institute and Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway
[PERSON]
1 School of Architecture, Civil and Environmental Engineering, CRYOS, EPFL, Lausanne, Switzerland, \"WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland, \"Now at Geophysical Institute and Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway
[PERSON]
2 School of Architecture, Civil and Environmental Engineering, CRYOS, EPFL, Lausanne, Switzerland, \"WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland, \"Now at Geophysical Institute and Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway
[PERSON]
1 School of Architecture, Civil and Environmental Engineering, CRYOS, EPFL, Lausanne, Switzerland, \"WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland, \"Now at Geophysical Institute and Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway
###### Abstract
Stable water isotopes (SWIs) contain valuable information on the past climate and phase changes in the hydrologic cycle. Recently, vapor measurements in the polar regions have provided new insights into the effects of snow-related and atmospheric processes on SWIs. The purpose of this study is to elucidate the drivers of the particularly depleted vapor isotopic composition measured on a ship close to the East Antarctic coast during the Antarctic Circumnavigation Expedition in 2017. Reanalysis data and backward trajectories are used to model the isotopic composition of air parcels arriving in the atmospheric boundary layer (ABL) above the ship. A simple model is developed to account for moisture exchanges with the snow surface. The model generally reproduces the observed trend with strongly depleted vapor \(\delta^{\text{it}}\)O values in the middle of the 6-day study period. This depletion is caused by direct air mass advection from the ice sheet where the vapor is more depleted in heavy SWIs due to distillation during cloud formation. The time spent by the air masses in the marine ABL shortly before arrival at the ship is crucial as ocean evaporation typically leads to an abrupt change in the isotopic signature. Snow sublimation is another important driver when the isotopic composition of the sublimation flux differs substantially from that of the advected air mass, for example, marine air arriving at the coast or free-tropospheric air descending from high altitudes. Despite strong simplifications, our model is a useful and computationally efficient method for understanding SWI dynamics at polar sites.
[PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2023). A case study on a driver's of the isotopic composition of water vapor at the south of East Antarctica. _Journal of Geophysical Research: Earth Surface, 128_, e0223 JF007062. [[https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062]([https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062)
6
A Case Study on Drivers of the Isotopic Composition of Water Vapor at the Coast of East Antarctica
1
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2023). A case study on a driver's of the isotopic composition of water vapor at the south of East Antarctica. _Journal of Geophysical Research: Earth Surface, 128_, e0223 JF007062. [[https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062]([https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062)
6
A Case Study on Drivers of the Isotopic Composition of Water Vapor at the Coast of East Antarctica
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2023). A case study on a driver's of the isotopic composition of water vapor at the south of East Antarctica. _Journal of Geophysical Research: Earth Surface, 128_, e0223 JF007062. [[https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062]([https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062)
6
A Case Study on Drivers of the Isotopic Composition of Water Vapor at the Coast of East Antarctica
[PERSON], [PERSON], [PERSON], [PERSON], [PERSON], & [PERSON] (2023). A case study on a driver's of the isotopic composition of water vapor at the south of East Antarctica. _Journal of Geophysical Research: Earth Surface, 128_, e0223 JF007062. [[https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062]([https://doi.org/10.1029/2023](https://doi.org/10.1029/2023) JF007062)
6
## Plain Language Summary
Stable water isotopes are useful to reconstruct historical temperature conditions from ice cores. This method is possible because phase changes of water alter the isotopic composition. For example, if an air mass cools down, forms clouds, and produces rain or snowfall, the water vapor preferentially loses heavy water molecules. This study aims to explain a remarkable vapor isotopic signal measured on a ship close to the East Antarctic coast during 6 days in 2017. We model the isotopic composition of air parcels along their pathways to the ship and develop a novel approach to represent moisture exchange with the snow surface. The modeled vapor isotopic composition at the ship reaches a distinct minimum, similar to the measurements, when the air parcels move directly from the ice sheet to the ship. As expected, the vapor isotopic composition is lower over the ice sheet than over the ocean, largely due to cloud formation. However, moisture uptake from the snow surface and from the ocean shortly before arrival at the ship can strongly and abruptly influence the isotopic signature of the air masses. Although our model is not perfect, it helps to improve the interpretation of isotope measurements at polar sites.
## 1 Introduction
Stable water isotopes (SWIs) are widely used as both tracers in the global hydrologic cycle ([PERSON], 2014; [PERSON] et al., 2010) and as climate proxies in ice cores (EPICA community members, 2004; [PERSON] et al., 1994; [PERSON] et al., 1979). The isotopic composition (\(\delta^{\text{1S}}\)O or \(\delta\)D) describes the abundance of a heavy water isotopologue ( \(\text{H}_{2}{}^{\text{1S}}\)O or HD\({}^{\text{1S}}\)O) in a water sample, in relation to a standard as defined in Text S1 of Supporting Information S1. The heavy isotopologues contain stronger molecular bonds than the light isotopologue, \(\text{H}_{2}{}^{\text{1S}}\)O, which leads to slight differences in the saturation vapor pressure of the isotopologues (e.g., [PERSON] et al., 1970; [PERSON] and [PERSON], 1969). Therefore, the solid phase is generally more enriched in SWIs than the liquid phase and, to a stronger degree, than the vapor phase. This effect is known as equilibrium fractionation. Phase changes in natural conditions such as ocean evaporation can additionally be associated with kinetic fractionation, resulting from the fact that the heavy isotopologues have lower molecular diffusivities in air than the light isotopologue (e.g., [PERSON] and [PERSON], 1984). Kinetic fractionation will play a relevant role if the phase change occurs at a fast rate. This willbe the case if a strong vertical humidity gradient enhances ocean evaporation, which is typical in the cold sector of extratropical cyclones ([PERSON] et al., 2021).
The isotopic compositions of water vapor and snow are affected by several processes, starting from ocean evaporation in the moisture source region ([PERSON] & [PERSON], 1965; [PERSON] & [PERSON], 1979), transport processes in the atmosphere ([PERSON] et al., 2006), cloud formation and precipitation ([PERSON] & [PERSON], 1994; [PERSON] & [PERSON], 1984), and postdepositional processes at and below the snow surface ([PERSON], 1998; [PERSON] et al., 2005, 2007; [PERSON] et al., 2001; [PERSON] et al., 2003; [PERSON] & [PERSON], 2003). When an air mass experiences more and more cloud formation, the fractionation effects give rise to isotopic distillation of atmospheric vapor. As a result, snowfall and surface snow on the Antarctic Ice Sheet generally become more depleted in heavy SWIs with increasing distance from the coast and elevation ([PERSON] et al., 2008).
Isotopic fractionation also plays an important role in phase changes at the Earth's surface. These phase changes influence air masses transported in the atmospheric boundary layer (ABL) as this layer is typically well mixed by turbulence and thus affected by surface-atmosphere interactions. While the fractionation effects are well understood in the case of ocean evaporation, they are subject of current research in the case of snow sublimation. Traditionally, it was assumed that sublimation occurs layer by layer without fractionation ([PERSON] et al., 1991; [PERSON], 2004; [PERSON] et al., 2008). More precisely, it was argued that self-diffusion in ice is slow enough such that the snow layer affected by sublimation would transform completely into vapor before being mixed with the snow layer underneath. Consequently, the average isotopic composition of the sublimation flux would equal the initial isotopic composition of the sublimating snow layer. However, recent experimental studies found evidence of fractionation during sublimation. For example, [PERSON] et al. (2021) sampled near-surface vapor and snow in northeast Greenland with a high temporal resolution on clear-sky summer days and compared the isotope dynamics with sublimation measurements. These observations demonstrated that alternating periods of sublimation and vapor deposition can lead to clear diurnal cycles in the vapor isotopic composition, which are consistent with changes in the snow isotopic composition. Similar diurnal cycles in the vapor isotopic composition were reported for Dome C on the Antarctic plateau and explained by local sublimation and vapor deposition ([PERSON] et al., 2016). These findings are supported by controlled experiments in cold laboratories, showing that snow-vapor exchange at the surface and in the pore space alters the isotopic compositions of snow and vapor (e.g., [PERSON] et al., 2017; [PERSON], 2009). Equilibrium fractionation explains a large part of these SWI dynamics although the measurements indicate some influence of kinetic fractionation ([PERSON] et al., 2016; [PERSON] et al., 2021; [PERSON] et al., 2021).
The influence of kinetic fractionation is often assessed using deuterium excess, also called d-excess and defined as \(\delta\)D \(-\) 8 \(\delta^{1}\)O ([PERSON], 1964). This definition is motivated by the fact that most precipitation samples from across the world lie, on average, on a line with a slope of 8 in the \(\delta\)D-\(\delta^{1}\)O diagram, which agrees approximately with the classic Rayleigh distillation model for an air mass cooling from 20 to \(-\)20\({}^{\circ}\)C with an initial vapor isotopic composition in equilibrium with ocean water. This model describes condensation assuming equilibrium fractionation and an immediate removal of the liquid or solid water phase. While kinetic fractionation changes the d-excess value, equilibrium fractionation is generally expected to have a negligible effect on this value. However, [PERSON] (1964) notes that the \(\delta\)D-\(\delta^{1}\)O relationship for a specific precipitation event depends on several parameters, including the initial vapor isotopic composition, initial temperature, and condensation temperature. These dependencies imply that equilibrium fractionation can influence d-excess in certain conditions. For example, the classic Rayleigh distillation model predicts the d-excess of snowfall to increase significantly when reaching very low temperatures and very depleted isotopic compositions, which are typical for the Antarctic plateau (e.g., [PERSON] et al., 2017; [PERSON] et al., 2016).
The isotopic composition of atmospheric vapor observed at a specific polar site is influenced by weather changes on different time scales. At Thule Air Base, coastal northwest Greenland, [PERSON] et al. (2020) observed a strong seasonal cycle in vapor isotopic composition controlled by shifts in sea-ice extent, which define the distance to marine moisture sources. Synoptic weather events led to variations over multiple days, superimposed on the seasonal cycle. At Syowa station, coastal East Antarctica, [PERSON] et al. (2016) also found a strong influence of synoptic weather systems, causing advection of marine or glacial air masses with distinct isotopic signatures. At other coastal polar sites, shifts between these air masses manifest themselves in pronounced diurnal cycles in the vapor isotopic composition, at least in summertime high-pressure periods. An example is Dumont d'Urville, coastal East Antarctica, where strong katabatic winds advect dry air with strongly depleted \(\delta^{1}\)O values from the interior of the ice sheet during the coldest hours of the day ([PERSON] et al., 2019). Similar diurnal cycles can be observed at Kangerlussuaq, southwest Greenland, where an ice-free strip of land alternatingly experiences katabatic winds and a see breeze ([PERSON] et al., 2014).
Apart from measurements, models are an important tool for understanding the dynamics of SWIs in the atmosphere and the driving processes. There are two modeling approaches: (a) Lagrangian models which simulate moist processes and isotopic fractionation along air parcel trajectories ([PERSON] et al., 2017; [PERSON], 1994; [PERSON] et al., 2006; [PERSON], 1984; [PERSON] et al., 2011); and (b) Eulerian models, such as general circulation models (GCMs), which consider the temporal change on a fixed three-dimensional grid (e.g., [PERSON] et al., 1984; [PERSON] et al., 2012). Eulerian models provide a more accurate representation of the spatial variability of the isotopic composition of water vapor across the hydrologic cycle by accounting for the mixing of air masses of different origins and the highly variable pathways water vapor may take between evaporation and condensation. For example, GCMs are able to satisfactorily reproduce the global and seasonal variations in the isotopic composition of precipitation ([PERSON] et al., 2000; [PERSON] & [PERSON], 2010). However, it is more difficult to discern the effect of individual processes on isotopic variability using Eulerian models as these processes can be isolated less easily, compared to the computationally more efficient Lagrangian models ([PERSON] et al., 2018). [PERSON] et al. (2021) used a combination of both approaches to better understand vapor isotopic measurements along the ship route of the Antarctic Circumnavigation Expedition (ACE). The output of the Eulerian model COSMO\({}_{\text{iso}}\) was analyzed along backward trajectories starting at the position of the ship. This method demonstrated that the cold and warm sectors of extratropical cyclones, associated with evaporation and dew formation, respectively, were important drivers of the vapor isotopic composition over the open ocean.
The ACE campaign also provided insights into meridional SWI variations in the ABL of the Atlantic and the Southern Ocean ([PERSON], [PERSON], et al., 2020). From November 2016 to April 2017, continuous SWI time series were recorded on the ship as it traveled from Germany via South Africa to Antarctica and back. The vapor was generally more depleted in heavy SWIs with distance from the tropics, reflecting average patterns in temperature and specific humidity and their influence on the fractionation processes.
In the present study, we develop a Lagrangian model to explain the vapor isotopic signal of a specific event during the ACE campaign. We investigate in detail a 6-day period in January 2017, in which the ship stayed close to the Mertz glacier, East Antarctica, and the values of vapor \(\delta^{\text{iso}}\)O reached a pronounced minimum. The objectives are to (a) reproduce the \(\delta^{\text{ISO}}\) values of water vapor observed at the Mertz glacier using a Lagrangian model with simple isotope dynamics and (b) better understand the influences of air mass origin and isotopic fractionation during moisture exchange with the Earth's surface and during cloud formation. Our model accounts for equilibrium fractionation but neglects kinetic effects during all phase changes apart from ocean evaporation. As some other models still neglect isotopic fractionation during snow sublimation, we analyze how sensitive the modeled vapor \(\delta^{\text{iso}}\)O is with respect to the assumptions that snow sublimation is or is not associated with equilibrium fractionation. Although our model represents some processes less accurately than the COSMO\({}_{\text{iso}}\)-based modeling framework of [PERSON] et al. (2021), we are able to directly distinguish the effects of individual processes with a lower computational effort. The main novelty of our isotope model is the fact that the isotopic composition of sublimating surface snow is computed by accounting for the history of snowfall and surface-atmosphere exchange. This computation represents the first modeling step, which is performed in an Eulerian frame of reference, considering a multi-layer snowpack. The last aspect is an advantage over the COSMO\({}_{\text{iso}}\) model, which treats the snowpack as a single homogeneous layer. As sublimation and vapor deposition affect primarily the uppermost few centimeters of the snowpack and sustained sublimation may uncover deeper snow layers, a realistic description of the isotopic composition of snow may require the approach of a multi-layer snowpack.
## 2 Data and Methods
### Water Vapor Measurements at the Mertz Glacier
The ACE expedition involved many research projects in multiple disciplines such as atmospheric chemistry and physics (e.g., [PERSON] et al., 2019) and oceanography (e.g., [PERSON] et al., 2019). The vapor isotopic measurements were performed on the ship at heights of approximately 8 and 13.5 m a.s.l. using PICARRO cavity ring-down laser spectrometers with a high temporal resolution of 1 s ([PERSON], [PERSON], et al., 2020). Most of the time, the isotopic composition was slightly more depleted at the upper height, compared with the lower height, and a strong correlation was found between both heights. We follow the aforementioned authors and focus on the measurements at the upper height, which are less influenced by sea spray. More details and an overview of the measured time series can be found in the aforementioned article.
The ship track around Antarctica can be divided into three legs (Figure 1). Here, we focus on a small section of leg 2 in the proximity of the outlet of the Mertz glacier, East Antarctica, corresponding to the 6-day period from 27 January to 1 February 2017. This period includes two consecutive days with exceptionally depleted values of \(\delta^{18}\)O and \(\delta\)D, compared with the remaining time series. The event coincided with low values of specific humidity and high values of d-excess (Figure 5 in [PERSON], [PERSON], et al. (2020)), typical of continental Antarctic interior air masses (e.g., [PERSON] et al., 2019).
### Modeling Approach
We developed a model, which considers the most common three SWIs ( \(\mathrm{H_{2}}^{16}\mathrm{O}\), \(\mathrm{H_{2}}^{18}\mathrm{O}\), \(\mathrm{HD}^{18}\mathrm{O}\)). The model consists of two parts: (a) _Model Sublimation_ uses an Eulerian frame of reference to compute the isotopic composition of surface snow, which determines that of the sublimation flux; (b) _Model Air Pareel_ uses a Lagrangian frame of reference to quantify the vapor isotopic composition along air parcel trajectories, considering vapor exchange with the snow or ocean surface and vapor removal due to cloud formation (Figure 2).
First, Model Sublimation is run with a spin-up period of approximately 6 months to allow for the development of realistic snow isotopic compositions. Subsequently, the output of Model Sublimation is used in Model Air Pareel when the air parcel takes up water vapor from the snow surface, that is, when the parcel is located in the ABL and the snow is sublimating. For the phase changes of sublimation, vapor deposition, and condensation, we only consider equilibrium fractionation as a first-order approximation and use temperature-dependent formulas for the fractionation factors from Merlivat and Nief (1967), Majoube (1970), and Majoube (1971). To evaluate the importance of fractionation during sublimation, we compare two simulations, which assume that snow sublimation is associated with equilibrium fractionation (Run E) or not associated with any fractionation (Run N). In both simulations, kinetic fractionation is only taken into account in the process of ocean evaporation by applying the widely used Craig-Gordon formula in its original form ([PERSON], 1965; [PERSON] et al., 2008).
Figure 1: Map showing the three legs of the ship track (solid lines) of the Antarctic Circumumumagen Expedition, average sea-ice cover (blue colors) in the period from 17 January 2017 to 1 February 2017, initial locations of the modeled air parcels (dots), and location of Dome C (yellow cross). The red rectangle highlights the ship track in the study period (close to the Mertz glacier).
Figure 2: Schematic illustration of the modeling approach. The net accumulation of snow mass in one time step (\(\Delta\)_t_), denoted by \(\Delta\)_m_, may be positive or negative.
The next sections explain the input data and main characteristics of the two model parts while further methodological details and equations can be found in Texts S1-S3 of Supporting Information S1. Important model constants and parameters are listed in Table S1 of Supporting Information S1. For brevity, we refer to the surface water vapor flux as the surface flux from here on. All time information in this paper is given in UTC time while local time at the outlet of the Mertz glacier corresponds to UTC + 10 hr.
#### 2.2.1 Input Data
The model uses ERA5 reanalysis data produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) with spatial and temporal resolutions of 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\) and 1 hr, respectively ([PERSON] et al., 2018). The following variables were retrieved: land-sea mask, mean evaporation rate, air temperature and dew point temperature at 2 m height, surface temperature, atmospheric pressure, snowfall rate, and sea-ice cover. The mean evaporation rate characterizes both ocean evaporation and snow sublimation and is based on the common Monin-Obukhov bulk parameterization, assuming constant roughness lengths on the ice sheet (\(z_{\text{on}}\) = 0.0013 m, \(z_{\text{tr}}\) = \(z_{\text{to}}\) = 0.00013 m) and dynamic roughness lengths for the ocean depending on a wave model (ECMWF, 2016). In addition to the snow surface, drifting and blowing snow particles contribute to the sublimation flux ([PERSON] et al., 2022) and consequently they may change their isotopic composition. However, drifting and blowing snow is not represented in the ERA5 reanalysis and there is little knowledge about isotopic effects of this process. In the main analysis, we use data for latitudes south of 30\({}^{\circ}\)S from July 2016 to February 2017. The first six months serve as a spin-up period to reduce uncertainties arising from the initialization of the snow isotopic composition. For purposes of validation, we compare results of Model Sublimation with isotope measurements at Dome C, East Antarctica, published by [PERSON] et al. (2016, 2018). To this end, ERA5 data for the grid cell including Dome C (75\({}^{\circ}\)S, 123.25\({}^{\circ}\)E) and the period from January 2013 to January 2016 are used.
Model Air parcel additionally assimilates 10-day backward air parcel trajectories taken from Thurnherr, Wernli, and Aemisegger (2020). These trajectories were calculated with the Lagrangian analysis tool LAGRANTO ([PERSON], 2015; [PERSON], 1997) using the 3D-wind fields from the ECMWF operational analyses. Every hour, a set of trajectories was launched from up to 56 vertical levels between 0 and 500 hPa above sea level along the ACE cruise track. For each trajectory, the time step was 3 hr. In this study, the following variables were extracted for trajectories arriving in the ABL above the ship in the period from 27 January to 1 February 2017: air pressure at heights of the air parcel and the ABL, specific humidity, and air temperature.
#### 2.2.2 Model Sublimation
The isotopic composition of the sublimation flux depends on that of the surface snow (e.g., [PERSON] et al., 2021). The latter is initialized with typical values for snowfall depending on the temperature and then computed prognostically. The effects of snowfall, sublimation, and vapor deposition on the snow isotopic composition are simulated with time in each grid cell, which is considered as snow-covered land (land fraction >50% and latitude south of 60\({}^{\circ}\)S). Model Sublimation uses a time step of 1 hr and simulates the period from 1 July 2016 to 1 February 2017 in the main analysis.
The snowfall \(\delta^{\text{iso}}\)O is parameterized as a linear function of the daily running mean air temperature because in the literature, this relationship is derived from daily mean values. We apply the same linear function to snowfall over the whole Antarctic continent although different \(\delta^{\text{iso}}\)O-temperature slopes have been measured at different sites. In our baseline simulation, the function for snowfall \(\delta^{\text{iso}}\)O is taken from [PERSON] et al. (2016) and characterized by an intermediate slope of 0.45% K\({}^{-1}\). Sensitivity tests are performed using functions from [PERSON] et al. (2012) and [PERSON] and [PERSON] (2006) with low and high slopes of 0.35% K\({}^{-1}\) and 0.78% K\({}^{-1}\), respectively (Texts S2, S4, and S5 in Supporting Information S1). The \(\delta\)D value of snowfall is always derived using the \(\delta\)D-\(\delta^{\text{iso}}\)O relationship of [PERSON] et al. (2008) based on mean isotopic compositions of snow, firn, or ice at many Antarctic sites (Equation 10 in Supporting Information S1).
The snowpack is modeled as a series of 100 layers, each with the same thickness and a constant density of 350 kg m\({}^{-3}\). This density does not account for the natural spatiotemporal variability but represents a typical average value for the uppermost tens of centimeters of the snowpack (e.g., [PERSON] et al., 2022). For the location of Dome C, we tested three values for the snow layer thickness (0.1, 1, and 2 cm) and compared the surface snow \(\delta^{\text{iso}}\)O with measurements of [PERSON] et al. (2018). A thickness of 1 cm led to a good agreement and was therefore selected for the remaining analysis (Text S4 and Figure S1 in Supporting Information S1). We assume that the snowpack always exists on the Antarctic Ice Sheet, that is, in grid cells south of 60\({}^{\circ}\)S with a land fraction greater than 50%. If the snowfall and surface fluxes add or remove snow mass at the surface, a simple mixing mechanism will guarantee that the thickness and mass of the snow layers remain constant. More precisely, a part of each layer is mixed with an adjacent layer to compensate for the mass gain or loss at the surface (Figure 2). We neglect changes in snow density and assume that snow added by snowfall or vapor deposition has the same density as the snowpack. The mixing mechanism is a vastly simplified version of a realistic vapor transport mechanism ([PERSON] et al., 2020). In reality, the interplay between ventilation, isotope diffusion within the snowpack, and recrystallization can cause a continuous replacement of the interstitial water vapor in the surface snow layer. However, it is still an open question how the combination of these processes can quantitatively change the isotopic compositions of snow and water vapor in the ABL. Therefore, our model is based on the following assumptions: (a) no isotope diffusion within the snow layers; (b) no impact of snow metamorphism on the isotopic profile; (c) fractionation only at the uppermost snow layer because of its direct contact with the atmosphere; and (d) no ventilation within the snow layer.
The deposition flux forms surface hoar with an isotopic composition that depends on the isotopic composition of the atmospheric vapor. Model Sublimation estimates the isotopic composition of the atmospheric vapor as the mean of two hypothetical values, describing two idealized situations. In the first situation, the vapor is formed by local snow sublimation and thus characterized by the isotopic composition of the sublimation flux, which differs between Runs E and N. In the second situation, the vapor originates from a non-local source region and has undergone isotopic distillation. This effect is expressed by assuming the vapor to be in isotopic equilibrium with snowfall. We apply this parametrization regardless of whether snowfall occurs at the location and time of interest or not. The snowfall isotopic composition is estimated as a simple function of the daily running mean air temperature, as described above.
The highly parametrized estimate of the vapor isotopic composition is only used to compute the effect of a limited amount of vapor deposition in Model Sublimation and to initialize some air parcels in Model Air Parcel. In reality, however, the relative importance of local and non-local vapor origins is expected to vary depending on the weather conditions. Locally sourced vapor is typically abundant in clear-sky conditions in austral summer because solar radiation enhances sublimation by heating the snow surface. On the contrary, surface cooling in austral winter or in the coldest hours of the day can cause vapor deposition although the intensity of this flux is generally lower than that of the sublimation flux. Additionally, marine air intrusions in coastal areas can lead to events of vapor deposition as warm and moist air is cooled by the snow surface. Nevertheless, vapor deposition at the snow surface plays a limited role in our main analysis because the total mass removed from all modeled air parcels due to vapor deposition is 46 times lower than the total mass taken up by all parcels due to snow sublimation. On the contrary, vapor deposition is relevant in a validation and sensitivity study with Model Sublimation at Dome C (Text S4 in Supporting Information S1). This site is located in the interior of the Antarctic Ice Sheet where the particularly cold atmosphere can only take up a small amount of water vapor, limiting sublimation and increasing the relative importance of vapor deposition. The ERA5 data suggests that vapor deposition outweighs sublimation at Dome C with a net surface flux of 2.7 kg m\({}^{-2}\) yr\({}^{-1}\) in the years of 2013-2015. Figure S2b in Supporting Information S1 shows that, if using Run E, the highly parametrized estimate for vapor \(\delta^{\rm 19}\)O reproduces the mean value measured by [PERSON] et al. (2016) at Dome C in a 24-day period in austral summer 2014/2015 (mean bias error of \(-0.2\%\)e) although the temporal variability is strongly underestimated. This comparison suggests that Run E uses a reasonable first-order approximation of the vapor isotopic composition with uncertainties of a few \(\%\)e for \(\delta^{\rm 19}\)O. On the contrary, Run N leads to vapor \(\delta^{\rm 19}\)O values, which are clearly more enriched than the measurements (mean bias error of 10.8\(\%\)e).
#### 2.2.3 Model Air Parcel
We consider air parcels with a constant volume of \(1\times 1\times 1\) m\({}^{3}\), traveling along the trajectories that are located in the ABL when reaching the position of the ship. This criterion is met if the air pressure is higher at the location of the trajectory than at the top of the boundary layer. The pressure at the top of the ABL is taken from the trajectory data set and based on ECMWF operational forecasts. As a result, we select 6 to 24 trajectories per arrival time (13 trajectories on average). The surface of each grid cell is represented by one of four surface types: (a) ice-free ocean if the land fraction is \(\leq\)50% and the sea-ice cover is \(\leq\)90%, (b) snow-covered sea ice if the land fraction is \(\leq\)50% and the sea-ice cover is higher than 90%, (c) snow-covered land if the land fraction is higher than 50% and the latitude is south of 60\"S, and (d) snow-free land if the land fraction is higher than 50% and the latitude is north of 60\"S.
The somewhat arbitrary threshold for sea ice is rather high (90%) because the ocean water is typically warmer and contributes more strongly to the surface flux, compared to a snow surface of the same area. On the contrary, the threshold for the land-sea boundary is set to 50% to be consistent with the modeling approach of the ERA5 data set. A more sophisticated treatment of sea ice could theoretically be implemented by dividing the evaporation flux into contributions from the ice-free ocean and snow-covered sea ice. Yet, the relative contributions do not correspond to the fractions of surface area. As any assumption on the relationship between the flux contribution and area fraction would be arbitrary, we choose the simple threshold approach to account for areas with the strongest impact of sea ice.
The air parcels are not always initialized 10 days before arriving at the ship. Instead, the time of initialization equals the first time at which the trajectory is located in the ABL and the following two restrictions are respected: (a) Over the ice-free ocean, evaporation must occur at the time and location of initialization; (b) the air parcels are not allowed to travel through the ABL over snow-free land because there, the isotopic composition of the surface flux is not known. If these restrictions prevent the initialization, the model will select the next possible time, meeting the criteria. Restriction (a) allows us to estimate the initial isotopic composition of the parcel using the Craig-Gordon formula simplified with the global closure assumption (e.g., [PERSON] et al., 2020). Under this assumption, the isotopic composition of atmospheric vapor over the ocean equals that of the evaporation flux.
If the initialization occurs over snow-covered land or sea ice, the isotopic composition of the parcel will be initialized as a function of the isotopic compositions of surface snow and snowfall (same assumption as used in Model Sublimation for atmospheric vapor). It is challenging to model the isotopic composition of snow on top of sea ice, especially because it can be influenced by sea spray ([PERSON] et al., 2019). Apart from that, Model Sublimation is not applicable to snow-covered sea ice because a spin-up period of several months will not make sense if the sea-ice area changes with time. As a first-order approximation, Model Air parcel assumes that the isotopic composition of surface snow above sea ice equals that of the nearest grid cell with snow-covered land at any time of the simulation. An overview of the locations of initialization and the position of the ship is given in Figure 1. On average, the air parcels are initialized 5.3 days before arriving at the ship. The specific humidity of the parcel is initially taken from the trajectory data set and then modeled prognostically.
Along the trajectory, the specific humidity and isotopic composition of the parcel can increase or decrease due to the surface flux and decrease due to cloud formation. If the air parcel moves above the ABL, only cloud formation may influence the isotopic composition of the parcel (Figure 2). As soon as the parcel enters the ABL again, the model considers both cloud formation and the surface flux. Assuming a well-mixed ABL with a height-constant vapor density, the moisture flux into or out of the parcel (\(J_{\mathrm{a}}\)) due to the surface flux (\(J\)) is computed as
\[J_{\mathrm{a}}=J\,\frac{d_{\mathrm{a}}}{d_{\mathrm{ABL}}}, \tag{1}\]
where \(d_{\mathrm{a}}\) = 1 m and \(d_{\mathrm{ABL}}\) are the depths of the air parcel and ABL, respectively. The specific humidity in Model Air Parcel agrees approximately with that in the trajectory data set (Figure S3 in Supporting Information S1). Considering all data points from the initialization of the air parcels to the arrival at the ship, the specific humidity in Model Air Parcel is characterized by a RMSE of 0.6 g kg\({}^{-1}\) and a correlation coefficient of \(\rho\) = 0.94 when compared with the trajectory data set. Comparing only the values at the final position of the air parcels (i.e., at the ship) with the trajectory data set, specific humidity tends to be underestimated with RMSE = 0.9 g kg\({}^{-1}\) and \(\rho\) = 0.45.
The isotopic composition of the sublimation flux is taken from Model Sublimation whereas the isotopic composition of the deposition flux is assumed to be in isotopic equilibrium with the air parcel. Consequently, the isotopic composition of the deposition flux can differ between Model Air Parcel and Model Sublimation as the latter uses a simpler estimate based on idealized vapor origins. In the case of vapor deposition, condensation, or ocean evaporation, the isotopic composition of the vapor exchanged between the surface and the air parcel depends and feeds back on the air parcel's isotopic composition (Text S3 in Supporting Information S1). To guarantee an accurate feedback, the time step needs to be small enough, especially if the vapor mass taken up or removed from the air parcel is in the same order of magnitude as the vapor mass contained in the parcel. Therefore, the effects of ocean evaporation, condensation, or vapor deposition are computed stepwise by dividing each 3-hr time step into 32 subintervals of equal length. This value was justified using an example situation, for which the number of subintervals was continuously increased by a factor of two until the isotopic composition of the parcel at the end of the 3-hr step changed by less than 1%. An uncertainty in the order of 1% due to the temporal discretization is acceptable, considering that other model assumptions, for example, about the snowfall isotopic composition in Model Sublimation, lead to higher uncertainties.
Cloud formation occurs as soon as the specific humidity of the air parcel exceeds its saturation value. Isotopic fractionation during cloud formation is calculated using the classic Rayleigh distillation model with equilibrium fractionation ([PERSON] & [PERSON], 1984; [PERSON] et al., 2011). In this model, the cloud water precipitates immediately. In reality, the air is supersaturated in mixed-phase clouds and therefore, kinetic fractionation is expected to occur. Although this kinetic effect may be relevant for reproducing measurements of d-excess ([PERSON] & [PERSON], 1984), we neglect this effect because the supersaturation ratio is a poorly constrained parameter and our analysis focuses on the less sensitive \(\delta^{\rm{1s}}\)O values. The equilibrium fractionation factors used in the Rayleigh model are computed as in [PERSON] et al. (2011), accounting for mixed-phase clouds with a gradual, linear shift from the vapor-liquid to the vapor-ice transition as the air temperature decreases from 0 to \(-20^{\rm{o}}\)C. Changes in air density along the trajectory influence the vapor mass contained in the parcel as they imply exchange of air with the surrounding atmosphere. The model assumes that this exchange of air does not have a direct effect on the isotopic composition of the parcel.
### Data From the COSMO\({}_{\rm{low}}\) Model
[PERSON], [PERSON], et al. (2020) published regional high-resolution simulations with the isotope-enabled GCM COSMO\({}_{\rm{low}}\) covering parts of the Southern Ocean and Antarctic Ice Sheet during the ACE expedition. We compare vapor isotopic data from one of these simulations with the results of Model Air Parcel. While methodological details of the COMOiso simulation are described by the aforementioned authors and [PERSON] et al. (2021), we summarize the features that are most important for our comparison. The horizontal grid spacing (0.125\({}^{\circ}\)) is half of that for the ERA5 data and the model includes 40 vertical levels. Isotopic fractionation during ocean evaporation is modeled using the Craig-Gordon formula with a simple parameterization of the kinetic fractionation factor according to [PERSON] and [PERSON] (2009). The snowpack is represented by a one-layer surface snow model. For snow sublimation, the COSMO\({}_{\rm{low}}\) model considers equilibrium fractionation.
From the COSMO\({}_{\rm{low}}\) simulation called leg2_run1, we extract specific humidity and the specific water vapor contents of H\({}_{2}\)\({}^{\rm{2N}}\)O and HD\({}^{\rm{1s}}\)O at the lowest model level in the grid cell containing the position of the ship. This model level corresponds approximately to the measurement height. The vapor isotopic compositions for the COSMO\({}_{\rm{low}}\) simulation are computed as
\[\delta_{\rm{i}}=\frac{\vartheta_{\rm{i}}}{q}-1 \tag{2}\]
and expressed in %e, where \(q\) is specific humidity and \(q_{\rm{i}}\) is the specific water vapor content of a heavy water isotopologue divided by the isotopic ratio of the Vienna Standard Mean Ocean Water.
## 3 Results and Discussion
As expected, the simulated dynamics of \(\delta^{\rm{1s}}\)O and \(\delta\)D are very similar. Therefore, we only present results for \(\delta^{\rm{1s}}\)O and briefly discuss d-excess.
### Comparison of Modeled and Measured Vapor Isotopic Compositions
Figure 3 compares the ensemble averaged vapor \(\delta^{\rm{1s}}\)O and d-excess of the air parcels with the measurements on the ship close to the Mertz glacier. We show the baseline simulations using the relationship of [PERSON] et al. (2016) to parameterize the snowfall isotopic composition in Model Sublimation. For comparison, the figure includes results from the Eulerian model COSMO\({}_{\rm{low}}\) published by [PERSON], [PERSON], et al. (2020).
Similar to the measurements, our model predicts vapor \(\delta^{\rm{1s}}\)O values at the ship of approximately \(-15\)%e in the beginning and at the end of the investigated 6-day period and a pronounced minimum in the middle of the period. In the simulation considering equilibrium fractionation (Run E), this minimum is more pronounced (\(\delta^{\rm{1s}}\)O = \(-40\)%e), compared to the simulation neglecting fractionation during snow sublimation (Run N, \(\delta^{\rm{1s}}\)O = \(-34\)%e). Differences between both model runs are mainly visible in the middle of the study period. Overall, both runs achieve a similar agreement with the measurements with root-mean-square errors (RMSE) of 4.4 and 4.2%e and Pearson correlation coefficients of 0.77 and 0.75 for Run E and Run N, respectively.
In a few short periods, we observe strong deviations of up to \(\pm\)15%e between the modeled and measured \(\delta^{\mathrm{it}}\)O values. Run E predicts clearly too depleted vapor isotopic compositions on 28 January around 03:00 and in the earliest and latest hours of 30 January. On the contrary, the modeled isotopic composition is clearly too enriched on 29 January around 12:00. As will be shown later, the cases with too depleted isotopic compositions occur at times when the air parcels have experienced a substantial influence of snow sublimation along their trajectories, which is also visible from the noticeable difference between Run E and Run N. Therefore, it is likely that the isotopic composition of the surface snow is biased, at least in certain areas. This problem can arise from uncertainties in the \(\delta\)-temperature relationship for snowfall, applied in Model Sublimation. Figure S4 and Text S5 in Supporting Information S1 show that the lowest \(\delta^{\mathrm{it}}\)S0 values at the ship are sensitive with respect to the \(\delta\)-temperature relationship. With the relationships of [PERSON] (2006) and [PERSON] et al. (2012), the lowest vapor \(\delta^{\mathrm{it}}\)O values are approximately 5%e higher and lower, respectively, compared to the baseline simulation. Therefore, the generalization of a site-specific, empirical \(\delta\)-temperature relationship for snowfall is a strong simplification in the model and contributes to deviations between the model and the measurements. All three \(\delta\)-temperature relationships tested in this study characterize high-elevation sites on the Antarctic plateau where the temperatures are low and the distillation effect drives the isotopic composition of the snowfall. In coastal areas, however, the snowfall isotopic composition is expected to depend additionally on the humidity conditions in the vapor source region ([PERSON] et al., 2016), which is neglected in Model Sublimation. Furthermore, the
Figure 3: Modeled and measured (a) \(\delta^{\mathrm{it}}\)O and (b) d-excess of atmospheric water vapor at the ship close to the Mertz glacier from 27 January to 1 February 2017. We show the modeled ensemble averages and standard deviations for multiple air parcels in the baseline simulations. The measurements represent 1-hr mean values and standard deviations. In the legend, root-mean-square errors (RMSE) and Pearson correlation coefficients (\(\rho\)) are specified for the model-measurement comparison. The yellow shading indicates times when the ship was located in a grid cell modeled as snow-covered land; at the other times, the ship was in a grid cell treated as ice-free ocean. The vertical gray dashed lines indicate times analyzed in Figure 5.
\(\delta\)-temperature relationships become more uncertain when applied to temperatures outside the range observed at the high-elevation sites.
Another important source of uncertainty is the simplified representation of sea ice. Air parcels taking up moisture from the surface of grid cells with a sea ice cover below the applied threshold of 90% only experience the effect of ocean evaporation in the model while in reality, a part of the moisture uptake is caused by sublimation of snow or ice with a depleted isotopic composition, compared to the liquid ocean water. Additionally, the isotopic composition of sublimating snow on top of sea ice may be influenced by sea spray, which is neglected in the model.
Moreover, the coarse spatial resolution may contribute substantially to the model-measurement deviations as the coastline is not accurately represented. The model may overestimate or underestimate the time spent by the air parcels in the marine ABL shortly before arriving at the ship, depending on whether the ship is located in a grid cell treated as ice-free ocean or snow surface (yellow shading in Figure 3). If an air parcel with a strongly depleted \(\delta^{\text{1H}}\)O value reaches the coast and takes up moisture from the ice-free ocean, the isotopic signature of the parcel can change abruptly as the evaporation flux is much more enriched in heavy SWIs than the air parcel. This effect is particularly strong due to kinetic fractionation, which is driven by the vertical gradients of the water isotopologues above the ocean surface. For an air mass with a very depleted \(\delta^{\text{1S}}\)O value, the abundance of the heavy isotopologue will decrease strongly with height above the ocean surface, which enhances the evaporation of the heavy isotopologue. In extreme cases, this kinetic effect can outweigh the effect of equilibrium fractionation such that the evaporation flux can be more enriched in SWIs than the ice-free ocean (Equation 13 in Supporting Information S1). As the air parcel spends more time in the ABL over the ice-free ocean, the parcel's isotopic composition becomes more similar to that of the ocean and the kinetic effect is generally less pronounced than before.
Further sources of uncertainty with probably minor impacts on the vapor \(\delta^{\text{1S}}\)O values may be (a) a bias in the initial isotopic composition of air parcels over the ocean due to the global closure assumption or a bias in the surface water \(\delta^{\text{1S}}\)O; (b) the neglect of kinetic fractionation during cloud formation; (c) the neglect of mixing of air masses with different isotopic compositions, for example, at weather fronts; (d) uncertainties of the ABL height provided with the trajectory data set, influencing the modeled time period and magnitude of moisture exchange between the air parcels and the surface; and (e) the simple assumption that the vapor mass exchanged between the atmosphere and the surface is homogeneously distributed between the surface and the ABL height (Equation 1). This last assumption neglects the fact that, even in a perfectly mixed ABL, an air parcel located close to the surface would take up slightly more mass of vapor from the evaporation or sublimation flux than a parcel at a greater height because the air density decreases with height. The assumption of a perfectly mixed ABL could be implemented more rigorously by considering the mass ratio instead of the thickness ratio for the air parcel and the ABL in Equation 1. Yet, this choice only has a minor effect on our analysis as the ABL height is generally small (780 m on average). Additionally, the air in the ABL is not always perfectly mixed, especially in a stable ABL.
Although there are some hours with a large model-measurement mismatch, Model Air parcel is able to reproduce the general trend and timing of the vapor depletion event on 29 and 30 January 2017. This depletion event is less visible in the \(\delta^{\text{1S}}\)O time series extracted from the COSMO\({}_{\text{iso}}\) simulation, which predicts a minimum \(\delta^{\text{1S}}\)O that is 10% more enriched, compared to the measurements (Figure 3a). This mismatch may be related to the fact that the snowpack is represented as a single layer with vertically homogeneous isotopic compositions in the COSMO\({}_{\text{iso}}\) model. As demonstrated with a sensitivity analysis for Model Sublimation (Text S4, Figure S1 in Supporting Information S1), the seasonal and shorter-term variability of the snow isotopic composition decreases significantly with increasing thickness of the considered snow layers.
The measured d-excess of water vapor at the ship is mostly close to zero in the first two and last two days of the study period and exhibits higher values of approximately 13% in the middle of the period when the most depleted isotopic compositions are reached (Figure 3b). Our model generally overestimates the measured d-excess values, especially for Run E in the middle of the study period (maximum d-excess: 37%e). Some disagreement between the modeled and measured d-excess is expected, given the poor representation of kinetic fractionation. Future work could improve the model by parameterizing kinetic fractionation during cloud formation using the semi-empirical approach of [PERSON] and [PERSON] (1984). Additionally, the d-excess of snowfall in Model Sublimation is uncertain because it is based on the \(\delta\)D-\(\delta^{\text{1S}}\)O relationship derived by [PERSON] et al. (2008) from a variety of samples including snowfall, snow pits, firn cores, and ice cores, which may partly be influenced by postdepositional processes such as sublimation. Compared to our model, the COSMO\({}_{\text{iso}}\) model performs better in reproducing the measured d-excess although the maximum d-excess is slightly underestimated by the COSMO\({}_{\text{iso}}\)simulation (Figure 2(b)). Due to the limitations of our model with respect to d-excess, the remaining analysis focuses on the \(\delta^{\text{1I}}\)O signal.
### Drivers of the Vapor Isotopic Composition
Previous studies at other coastal polar sites have found distinct isotopic signatures for air masses advected from the ocean and those advected from the ice sheet (e.g., [PERSON] et al., 2019; [PERSON] et al., 2014; [PERSON] et al., 2016, 2016). Therefore, it is a plausible hypothesis that shifts between such air masses largely explain the observed isotope dynamics close to the Mertz glacier. The more depleted isotopic composition and higher d-excess of vapor over the ice sheet is generally thought to result from the distillation effect of cloud formation with contributions from both equilibrium and kinetic fractionation ([PERSON] & [PERSON], 1984; [PERSON] et al., 2016; [PERSON] et al., 2008). However, the sublimation and deposition fluxes including isotopic fractionation also influence the variability of the vapor isotopic signal. As the ocean is often a strong vapor source, the distance between the ship and the ice sheet or sea ice may play an important role. In the marine boundary layer, a strong vertical humidity gradient, typically associated with cold air advection over a relatively warm ocean surface, leads to strong evaporation with enhanced kinetic fractionation. This effect can cause differences of several %e in the vapor \(\delta^{\text{1I}}\)O between cold and warm sectors of extratropical cyclones but it is unlikely to explain a large decrease of more than 10% ([PERSON] et al., 2021). We now investigate which of the aforementioned drivers play a dominant role in our case study.
On the first day and during most of the last 2 days of the study period, the ship moved towards and away from the ice sheet, respectively (Figure 1). Due to a longer distance to the ice sheet, it is likely that recent ocean evaporation caused the relatively enriched vapor \(\delta^{\text{1I}}\)O at this time. From 28 January 2017, 02:00, to 31 January 2017, 06:00, the ship stayed in close proximity to the ice sheet. In this phase, the \(\delta^{\text{1I}}\)O remained relatively enriched for one day and then dropped to very depleted values. The fact that only the most depleted \(\delta^{\text{1I}}\)O values and the highest d-excess values in the time series are sensitive with respect to assumptions in Model Sublimation (Figure 3 and Figure S4 in Supporting Information S1) is consistent with the hypothesis that processes over the ocean drove the vapor isotopic composition in the first and last two days of the period while processes over the Antarctic Ice Sheet influenced the isotopic signature in the middle of the period.
Moreover, the rather small differences between Runs E and N demonstrate that isotopic fractionation during snow sublimation can only explain a small part of the minimum in the \(\delta^{\text{1I}}\)O time series. Regarding d-excess, the difference between Runs E and N shows that equilibrium fractionation during sublimation influences the modeled d-excess. This influence is caused by the fact that the \(\delta\)D-\(\delta^{\text{1I}}\)O slope associated with equilibrium fractionation amounts to a value lower than 8 at very depleted isotopic compositions and low temperatures (e.g., [PERSON] et al., 2017; [PERSON] et al., 2016). For the same reason, the modeled d-excess is also influenced by other processes such as vapor deposition and cloud formation, which are represented assuming equilibrium fractionation. Consequently, the increased d-excess values in the middle of the study period do not necessarily reflect an influence of kinetic fractionation.
The initial isotopic composition of the air parcels can influence the model results, especially if the time between initialization and arrival at the ship is short. Air parcels initialized over the ocean start their trajectories with fairly uniform \(\delta^{\text{1I}}\)O values between approximately \(-17\%\)e and \(-11\%\)e (Figure 3(a)). These initial values are similar to the final isotopic composition modeled at the ship during the first two and last 2 days of the investigation period, suggesting that ocean evaporation is an important driver. As expected, air parcels initialized over snow have more variable and more depleted initial \(\delta^{\text{1I}}\)O values than those initialized over ocean. Interestingly, there are almost always some air parcels that are initialized over snow and the range of their initial \(\delta^{\text{1I}}\)O values remains similar throughout the period (approximately \(-70\%\)e to \(-40\%\)e in Run E). However, when the most depleted \(\delta^{\text{1I}}\)O values are observed at the ship, almost all air parcels are initialized over snow. This fact supports the hypothesis that the air masses originate from the interior of the ice sheet at this time.
To assess the importance of different moisture exchange processes along the trajectories, we show in Figure 3(b) the ensemble-averaged relative contribution of specific processes to the total absolute exchange of moisture mass between an air parcel and the surrounding. Moisture uptake from the ocean is relevant throughout the study period and often represents the process with the strongest contribution to the total moisture exchange. The contribution of moisture uptake from snow surfaces is variable in time and becomes highest when the modeled vapor isotopic composition at the ship is most depleted and sometimes significantly more depleted than the measured values (Figures 2(a) and 3(b)). In most of these cases, moisture uptake from the snow surface contributes more than any other process to the total moisture exchange. Moisture removal due to cloud formation is a relevant process for most of the time but plays a minor role in the middle of the study period when sublimation is the dominating process. Overall, the contribution of cloud formation to the total moisture exchange correlates strongly with the travel time of the air parcels, that is, the time between initialization and arrival at the ship (Figures 4b and 4c). This correlation reflects the fact that a longer travel time increases the probability for air mass lifting and cooling. Vapor removal due to the surface flux generally represents the smallest term in the moisture budget with a relative contribution of no more than 5%.
Although the parcels experience little cloud formation in the middle of the period, the distillation effect of cloud formation may still be responsible for the very depleted \(\delta^{\mathrm{it}}\)O values as this effect influences indirectly the initial isotopic composition of air parcels, which begin their trajectory over the interior of the ice sheet. More precisely, the initial isotopic composition of a parcel over snow depends on the snowfall isotopic composition, which decreases with lower air temperatures, reflecting more isotopic distillation due to a larger temperature difference between the ocean (typical vapor source) and the air parcel.
Figure 4: (a) Comparison between initial \(\delta^{\mathrm{it}}\)O of individual air parcels and ensemble-averaged final \(\delta^{\mathrm{it}}\)O at the ship; (b) Ensemble average of the relative exchange of moisture mass between an air parcel and the surrounding due to different processes between initialization and arrival at the ship; the sum of the displayed values is 100% at each time; (c) Average travel time of the air parcels and average times spent in the atmospheric boundary layer (ABL) over snow-covered land or sea ice and the ABL over the ice-free ocean. The vertical gray dashed lines indicate times analyzed in Figure 5.
In the middle of the study period, the air parcels spend very little time in the ABL over the ice-free ocean (at times only in the last time step) while they spend more time in the ABL over snow-covered land or sea ice (Figure 4c). Overall, Figures 3 and 4 show that the air masses with the most depleted \(\delta^{1\text{O}}\) values and the highest d-excess values originate from the ice sheet and their isotopic signature is influenced by snow sublimation. This isotopic signature seems to only reach the ship if the air masses spend little time in the ABL over the ice-free ocean shortly before their arrival such that ocean evaporation cannot overwrite the signature.
To better understand which drivers act in which sections of the air parcel trajectories, we illustrate the \(\delta^{1\text{O}}\) values along individual trajectories in space and time for three different arrival times in Figure 5. The arrival times include situations with relatively enriched and depleted \(\delta^{1\text{O}}\) values while the ship is close to the ice sheet, the ensemble averaged travel time of the air parcels is at least 4 days, and the modeled vapor \(\delta^{1\text{O}}\) only deviates
Figure 5.— Vapor \(\delta^{1\text{O}}\) along air parcel trajectories in the baseline simulation of Run E for three different times of arrival at the ship (gray dashed lines in Figures 3 and 4). (a, c, and e) Each of the three cases is illustrated with a map and (b, d, and f) \(\delta^{1\text{O}}\)-time diagram. The number of trajectories is denoted by n and areas treated as snow-covered sea ice are colored dark gray in the maps. The surface snow and sublimation flux are only shown in panels (b, d, and f) when sublimation affects the air parcel. Trajectories arriving at the ship at a lower height are plotted on top of others.
slightly from the measured one. Figures 4(a) and 4(b) show a situation leading to relatively enriched \(\delta^{\mathrm{1S}}\)O values at the ship. In this case, the air parcels travel some distance in the ABL over the ice-free ocean parallel to the Antarctic coast before moving in the ABL over a snow-covered area in the last 10 hr of their travel. Almost half of the air parcels are initialized over the ice sheet and exhibit strongly depleted \(\delta^{\mathrm{1S}}\)O values around \(-52\%\) until they enter the ABL over the ice-free ocean. Due to ocean evaporation, the \(\delta^{\mathrm{1S}}\)O of the air parcels quickly increases and reaches values comparable to those of parcels initialized over the ocean.
Figures 4(c) and 4(d) refer to a situation with one of the most depleted \(\delta^{\mathrm{1S}}\)O values measured at the ship. Four of seven air parcels are initialized over the ice sheet and take a direct and short route to the ship where they only take up moisture from the ice-free ocean in the last time step. Their final \(\delta^{\mathrm{1S}}\)O values are similar to those of the other three parcels that are initialized over the ocean and travel over the interior of the ice sheet before taking the same final route as the parcels initialized over snow. While the parcels are lifted over the ice sheet and above the ABL, their isotopic composition becomes increasingly depleted due to the distillation effect of cloud formation and reaches extreme \(\delta^{\mathrm{1S}}\)O values of approximately \(-60\%\) to \(-75\%\). After reaching these extreme values, the air parcels maintain their isotopic composition for approximately 4 days because cloud formation stops as soon as the parcels begin to descend and the surface flux does not affect the free troposphere above the ABL. Only towards the end of the trajectories as the parcels move over the escarpment zone of the ice sheet, they enter the ABL over snow. At this time, approximately 20 hr before the arrival at the ship, snow sublimation adds vapor with a relatively enriched \(\delta^{\mathrm{1S}}\)O value to the parcels (Figure 4(d)). The sublimation flux in the escarpment zone is relatively enriched in heavy SWIs compared to the air parcels because their isotopic composition was shaped at higher and colder levels over the interior of the ice sheet. Additionally, the parcel isotopic composition is particularly sensitive with respect to moisture uptake after most of the initial vapor mass was removed from the parcels due to cloud formation. As a consequence, the moisture uptake in the escarpment zone increases the isotopic composition of the parcels abruptly. This increase caused by sublimation is similarly strong as another increase in the last time step, when the parcels reach the ice-free ocean and take up moisture from the water surface.
The situation shown in Figures 4(e) and 4(f) leads to an intermediate \(\delta^{\mathrm{1S}}\)O at the ship. All air parcels start their trajectories over the ocean and finally travel over the coastal zone of the ice sheet. Already over the ocean, cloud formation and condensation at the surface begin to decrease the \(\delta^{\mathrm{1S}}\)O of the parcels. As soon as the parcels reach the ice sheet, their \(\delta^{\mathrm{1S}}\)O continues to decrease because snow sublimation adds vapor with a more depleted \(\delta^{\mathrm{1S}}\)O value to the air parcels. In this situation, the sublimation flux is more depleted in heavy SWIs compared to the parcels because the latter carry the isotopic signature of processes over the ocean.
## 4 Conclusions
We developed a Lagrangian isotope model with the aim to reproduce and explain the vapor \(\delta^{\mathrm{1S}}\)O time series measured on the ACE ship close to the Mertz glacier in a 6-day period in austral summer 2017. The vapor mass and isotopic composition of air parcels was modeled along trajectories between an initial location in the ABL and the final location in the ABL at the ship. While isotope effects of cloud formation and ocean evaporation were represented with common approaches (classic Rayleigh distillation model and Craig-Gordon formula, respectively), the effect of snow sublimation was estimated using a novel approach, considering changes of the isotopic composition in a multi-layer snowpack due to snowfall, sublimation, and vapor deposition.
Similar to the measured values, the modeled vapor \(\delta^{\mathrm{1S}}\)O at the ship reaches a pronounced minimum value of \(-40\%\)e in the middle of the study period. The RMSE of the baseline simulation amounts to \(4.4\%\)e, which is reasonable considering the model limitations such as the generalization of a site-specific \(\delta^{\mathrm{1S}}\)O-temperature relationship for snowfall and the strongly simplified representation of snow on top of sea ice. Our analysis confirms the hypothesis that the relatively enriched \(\delta^{\mathrm{1S}}\)O values are associated with air masses advected from the ocean whereas the strongly depleted \(\delta^{\mathrm{1S}}\)O values are caused by direct advection of air masses from the Antarctic Ice Sheet. This result is consistent with similar observations at other coastal polar sites in the literature. As expected, cloud formation leads to very depleted vapor isotopic compositions over the ice sheet. Snow sublimation can also significantly modify the isotopic composition of the air parcels depending on their origin. For example, air parcels originating from high levels over the interior of the ice sheet may carry a strongly depleted isotopic signature to the escarpment zone of the ice sheet and then experience an abrupt and strong enrichment in heavy SWIs due to a relatively enriched sublimation flux. The model run considering equilibrium fractionation during snow sublimation leads to a more pronounced minimum in the vapor isotopic composition at the ship, comparedwith the model run neglecting fractionation during sublimation. Although the latter model run agrees slightly better with the measured isotopic composition at the ship, snow sublimation may still be associated with fractionation as the model-measurement agreement is also influenced by the other model uncertainties. A critical factor for the vapor \(\delta^{18}\)O at the ship is the time that the air parcels spend in the marine ABL shortly before arriving at the ship because ocean evaporation can quickly overwrite their isotopic signature.
Our modeling approach could be adapted for a study similar to [PERSON] et al. (2006) to simulate the vertical isotope profile in snow pits using backward trajectories for events of snow accumulation at an Antarctic site and deriving the isotopic composition of local snowfall from that of the air parcels. In contrast to the model of [PERSON] et al. (2006), our model accounts for the postdepositional effects of snow sublimation and vapor deposition. However, further improvements in our model such as the parameterization of kinetic fractionation during cloud formation and snow-atmosphere exchange as well as a more sophisticated vapor transport mechanism in the snowpack may be important for this purpose. Moreover, the deposition of drifting and blowing snow can contribute to snow accumulation and influence the isotopic composition of surface snow. To understand the latter effect, fundamental research is needed as the isotopic composition of drifting and blowing snow particles may be altered by sublimation, which has not been studied so far.
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Model results were generated using Copernicus Climate Change Service information (2021) available at [[https://doi.org/10.24381/cds.adbb2d47](https://doi.org/10.24381/cds.adbb2d47)]([https://doi.org/10.24381/cds.adbb2d47](https://doi.org/10.24381/cds.adbb2d47)) ([PERSON] et al., 2018). The air parcel trajectories were downloaded from [[https://doi.org/10.5281/zenodo.4031705](https://doi.org/10.5281/zenodo.4031705)]([https://doi.org/10.5281/zenodo.4031705](https://doi.org/10.5281/zenodo.4031705)) ([PERSON], [PERSON], & [PERSON], 2020). The calibrated isotope measurements from the ACE campaign were downloaded from [[https://doi.org/10.5281/zenodo.3250790](https://doi.org/10.5281/zenodo.3250790)]([https://doi.org/10.5281/zenodo.3250790](https://doi.org/10.5281/zenodo.3250790)) ([PERSON] & [PERSON], 2020). Simulation data of the COSMO\({}_{\mathrm{uno}}\) model were downloaded from [[https://doi.org/10.3929/ethz-b-000445744](https://doi.org/10.3929/ethz-b-000445744)]([https://doi.org/10.3929/ethz-b-000445744](https://doi.org/10.3929/ethz-b-000445744)) under the CC BY 4.0 license available at [[https://creativecommons.org/licenses/by/4.0](https://creativecommons.org/licenses/by/4.0)]([https://creativecommons.org/licenses/by/4.0](https://creativecommons.org/licenses/by/4.0)) ([PERSON], [PERSON], et al., 2020). Validation data from the Dome C site containing \(\delta^{18}\)O of surface snow and atmospheric vapor were retrieved from [[https://doi.org/10.5194/tc-12-1745-2018-supplement](https://doi.org/10.5194/tc-12-1745-2018-supplement)]([https://doi.org/10.5194/tc-12-1745-2018-supplement](https://doi.org/10.5194/tc-12-1745-2018-supplement)) and [[https://doi.org/10.5194/acp-16-8521-2016-supplement](https://doi.org/10.5194/acp-16-8521-2016-supplement)]([https://doi.org/10.5194/acp-16-8521-2016-supplement](https://doi.org/10.5194/acp-16-8521-2016-supplement)), respectively ([PERSON] et al., 2016, 2018). The python programming code and the main model output including the data shown in the figures are available at [[https://doi.org/10.16904/envidat.417](https://doi.org/10.16904/envidat.417)]([https://doi.org/10.16904/envidat.417](https://doi.org/10.16904/envidat.417)) ([PERSON] et al., 2023). The figures were made with Matplotlib version 3.5.1, available under the Matplotlib license at [[https://matplotlib.org/](https://matplotlib.org/)]([https://matplotlib.org/](https://matplotlib.org/)).
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wiley/fa9b1e8f_1fc2_4095_803a_315d4a9eb968.md | Relative contributions of environmental factors on different time scales to tropical cyclogenesis over the eastern North Pacific
[PERSON]
1 Center for Monson System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
2 Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, China
3 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
4 School of Earth Sciences, Zhejiang University, Hangzhou, Zhejiang, China
5 Tongli Zhejiang College, Jiaxing, Zhejiang, China
6
###### Abstract
The present study investigates relative contributions of large-scale environmental factors on interannual, intraseasonal, and synoptic time scales to tropical cyclone (TC) genesis over the eastern North Pacific (ENP) during TC seasons of 1979-2013 from the perspective of TC genesis time and position. Conditional sorting displays that the synoptic component is more important in the contribution of lower-level vorticity and mid-level specific humidity to TC genesis compared to interannual and intraseasonal components. The convection contributes to TC genesis mainly through synoptic and intraseasonal components. Synoptic-scale tropical disturbances mainly obtain barotropic eddy energy from climatological mean flows. TCs appear most frequently when vertical wind shear anomalies are between 0 and 3 m s\({}^{-1}\), in which interannual and intraseasonal westerly wind anomalies make a positive contribution due to climatological easterly wind shear. When total SST exceeds 28\({}^{\circ}\)C, the interannual component of sea surface temperature (SST) is positive, and then it has a positive contribution to TC genesis. In addition, there are notable differences of relative contributions of different time scale components of large-scale factors among the ENP, northern Atlantic Ocean, and western North Pacific.
different time scales, environmental factors, TC genesis, the eastern North Pacific 2
to the phases of climate modes over the Pacific Ocean (e.g., [PERSON] and [PERSON], 2000a, 2000b, 2001; [PERSON] _et al._, 2007, 2009; [PERSON] _et al._, 2015). For example, studies have compared the TC genesis over the western North Pacific domain during El Nino and La Nina years (e.g., [PERSON] and [PERSON], 2002; [PERSON] _et al._, 2007; [PERSON] _et al._, 2014) and during the active and inactive phases of the Madden-Julian Oscillation ([PERSON], [PERSON] _et al._, 2009; [PERSON] _et al._, 2012). TC genesis, however, is a synoptic-scale event occurring in a local region. The conditions of TC genesis are determined by a combination of different time scale components of large-scale environmental factors. Therefore, it is necessary to focus on the instantaneous state and specific location of TC genesis to examine relative contributions of different time scale components of large-scale environmental factors. This perspective from TC genesis position and time was recently employed by [PERSON] _et al._ (2018, 2019), who has diagnosed large-scale conditions of TC genesis over the western North Pacific and northern Atlantic Ocean.
TC genesis is closely associated with regional dynamic and thermodynamic factors ([PERSON], 1968, 1979; [PERSON], 2004; [PERSON] _et al._, 2007; [PERSON] and [PERSON], 2011). In the interannual time scale, these large-scale environmental factors over the ENP are significantly modulated by the El Nino-Southern Oscillation (ENSO) (e.g., [PERSON] and [PERSON], 1999; [PERSON] _et al._, 2007; [PERSON] _et al._, 2011; [PERSON] _et al._, 2015; [PERSON] and [PERSON], 2015). For instance, [PERSON] _et al._ (2007) identified that vertical wind shear is the main contributor to the difference of genesis potential anomaly composites between El Nino and La Nina years and potential intensity plays a secondary role. [PERSON] _et al._ (2011) showed that during the central Pacific warming, the descending motion with dry air induces the suppression of TC activity over the ENP, whereas during the eastern Pacific warming, the reduction of vertical wind shear induces the enhancement of TC activity over the ENP, which is consistent with [PERSON] _et al._ (2007).
In the intraseasonal time scale, the large-scale environmental conditions of TC genesis over the ENP are significantly modulated by the MJO with a period of 30-60 days ([PERSON] _et al._, 1997, 2000; [PERSON] and [PERSON], 2000a, 2000b, 2001; [PERSON] and [PERSON], 2008; [PERSON] _et al._, 2009; [PERSON] _et al._, 2012; [PERSON] and [PERSON], 2014) and quasi-biweekly oscillation with a period of 10-20 days (e.g., [PERSON] _et al._, 2018). [PERSON] _et al._ (2012) and [PERSON] _et al._ (2018) found that mid-level relative humidity and lower-level relative vorticity are the two most important factors affecting the TC genesis frequency associated with the MJO and quasi-biweekly oscillation over the ENP. [PERSON] and [PERSON] (2001) suggested that the lower-level barotropic dynamics in terms of barotropic energy conversion help explain the modulation of TC activity by the MJO over the ENP. In the synoptic time scale, African easterly waves often create the necessary precursors for TC genesis, not only over the northern Atlantic Ocean ([PERSON], 1993; [PERSON] and [PERSON], 2001; [PERSON] _et al._, 2017), but also over the eastern Pacific Ocean ([PERSON], 1991; [PERSON], 2000; [PERSON] _et al._, 2013a, 2013b; [PERSON] _et al._, 2017; [PERSON] _et al._, 2019). For example, [PERSON] _et al._ (2013a) pointed out that there is a significant distinction between developing easterly waves and non-developing easterly waves, including infrared threshold coverage, lightning flash rates, and lower-level precipitation radar reflectivity. In addition, the waves are more likely to develop into TCs when they move through environments characterized by high sea surface temperature (SST), weak vertical wind shear, high moisture, and strong lower-level vorticity ([PERSON] _et al._, 2011; [PERSON] _et al._, 2013a, 2013b).
These previous results indicate that the contribution of various factors to ENP TC genesis may depend on the time scales. Thus, this work attempts to address two questions through a new composite method used in [PERSON] _et al._ (2018, 2019). First, we investigate relative contributions of various environmental factors to TC genesis over the ENP on three time scales. The three time scales comprise interannual, intraseasonal, and synoptic components. Second, we compare the contribution differences of three time scale variations of large-scale factors to TC genesis over the ENP with those over the northern Atlantic Ocean and western North Pacific.
The remainder of the paper is arranged as follows. Section 2 describes the data and methods. Section 3 examines the relative contributions of three time scale components of various large-scale environmental factors to TC genesis over the ENP. Contributions of different time scale components to TC genesis among the three basins are compared in Section 4. A summary is provided in Section 5 along with a short discussion.
## 2 Data and Methods
The TC genesis data over the ENP come from the U.S. best-track hurricane database (HURDAT1), archived in National Climate Data Center's International Best Track Archive for Climate Stewardship (IBTrACS) v03r10 ([PERSON] _et al._, 2010). The time of TC genesis is defined when the maximum wind speed exceeds 25 kts at the first time over the ENP. There are no non-developing tropical cloud clusters in this dataset ([PERSON] _et al._, 2013). The present analysis focuses on the period from 1979 to 2013. Note that we have performed a parallel analysis using the maximum wind speed of 34 kts as the criterion for TC genesis. The obtained results are almost the same (figures not shown).
The daily mean interpolated satellite Outgoing Long-wave Radiation (OLR) is obtained from the National Oceanic and Atmosphere Administration (NOAA) ([PERSON] and [PERSON], 1996). OLR is often used as a proxy for deep convection in the tropical and subtropical regions because cloud top temperature is an indicator of cloud height ([PERSON] and [PERSON], 1999; [PERSON] and [PERSON], 2002). Conventional dynamic and thermodynamic variables come from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA)-Interim dataset with a horizontal resolution of \(0.5^{\circ}\times 0.5^{\circ}\) in latitude and longitude ([PERSON] _et al._, 2011).
The monthly mean SST dataset is obtained from the Hadley Center, which has a horizontal resolution of \(1^{\circ}\times 1^{\circ}\) and is available from 1870 to the present ([PERSON], 2003). The daily mean SST is extracted from the NOAA Optimum Interpolation (OI) SST V2 data with a \(0.25^{\circ}\) horizontal resolution starting from September 1981 ([PERSON] _et al._, 2007). The original OI SST data of \(0.25^{\circ}\)horizontal resolution are converted to \(1^{\circ}\) horizontal resolution. Due to the length limitation of SST data, only the period 1982-2013 is chosen.
The interannual, intraseasonal, and synoptic components of various environmental factors are obtained using the same method as [PERSON] _et al._ (2017, 2018). The daily anomaly time series are obtained by subtracting climatological daily mean time series from the original daily mean time series for each environmental variable. The interannual component more than 90 days is obtained by applying a 91-day running mean to the daily anomaly time series and the intraseasonal component with a period of 10-90 days is obtained by subtracting a 91-day running mean from a 9-day running mean of the daily anomaly time series. The synoptic component with a period of 3-8 days is obtained in a similar manner.
In the present study, we use eddy kinetic energy as an indicator of synoptic disturbances and examine the relative contribution of barotropic energy conversion from climatological mean flows, interannual and intraseasonal wind flows to TC genesis. The basic flows are separated into climatological mean winds, interannual and intraseasonal wind flows in the formula of barotropic energy conversion. Eddy winds are similar to the above synoptic component of environmental factors.
The percent contributions of different time scale variations of large-scale environmental factors to TC genesis are calculated according to the procedure shown in Figure 1. First, we calculate total daily anomalies of environmental quantities and the components on the three time scales averaged in a \(7.5^{\circ}\times 7.5^{\circ}\) box centered at the TC genesis location except for SST for which the average is in a \(5^{\circ}\times 5^{\circ}\) box at the time of TC genesis. Then, the values of anomalies are separated into 10 bins based on the distribution of total anomalies of each quantity. Third, we average the total anomalies and the three components in each bin to get their averaged values in that bin. Last, we calculate the ratio of the averaged anomalies of the three components with respect to absolute value of the averaged total anomalies in each bin, which is the percent contribution of the three time-scale components in that bin. Formula to calculate the percent contributions in the fourth step is as follows:
\[\mathrm{P}_{int}=\overline{\frac{X_{int}}{|\overline{X}|}};\mathrm{P}_{iso}= \overline{\frac{X_{iso}}{|\overline{X}|}};\mathrm{P}_{syn}=\overline{\frac{X_{ syn}}{|\overline{X}|}},\]
where \(|\overline{X}|\) is absolute averaged total anomaly in each bin at the time of TC genesis, \(\overline{X_{int}}\) is averaged interannual anomaly in each bin, \(\overline{X_{iso}}\) is averaged intraseasonal anomaly in each bin, \(\overline{X_{syn}}\) is averaged synoptic anomaly in each bin. For a given variable, the total percent contribution in each bin is equal to 100% (such as vorticity) or \(-100\%\) (such as OLR). The percentage of TC genesis
Figure 1: Flow chart of procedure to calculate percent contributions of different time scale components of large-scale environmental factors to TC genesis
frequency number in each bin is also calculated in a similar manner.
## 3. Contributions of Different Time Scale Components to Tropical Cytogenesis
In this section, we examine the relative contributions of different time scale components of environmental factors to TC genesis over the ENP. Figure 2a shows the climatological monthly mean TC number forming over the ENP (0\({}^{\circ}\)-25\({}^{\circ}\)N and 180\({}^{\circ}\)-80\({}^{\circ}\)W). The maximum number of TC genesis is in August. There is no TC genesis in February and April. The most active TC genesis season is from July to October, which is the same as that over the northern Atlantic Ocean and western North Pacific ([PERSON] et al., 2018, 2019). Thus, we mainly focus on the season from July to October (JASO for brevity) for the following analysis. [PERSON] and [PERSON] (2015) show that the peak season extends from June to October since both June and October have the same frequency of TC occurrence. This discrepancy is because [PERSON] and [PERSON] (2015) used 17 m s\({}^{-1}\) threshold for TC genesis and their analysis covered a longer time period. The TC genesis over the ENP is mainly located in the region of 6\({}^{\circ}\)-22.5\({}^{\circ}\)N and 140\({}^{\circ}\)-85\({}^{\circ}\)W (Figure 2b). In this region, climatological mean winds are easterly in the lower level, which is the same as that over the northern Atlantic Ocean ([PERSON] et al., 2019). Additionally, most TCs are generated in the region with the SST value above 27.5\({}^{\circ}\)C. The number of TC genesis cases is 488 in this box region during JASO of 1979-2013. For JASO of 1982-2013, there are 457 TC cases in the ENP. We perform a conditional sorting analysis for these TC cases centered at the TC genesis location at times of TC genesis.
We analyze the relative contributions of different time scale components of six environmental factors to TC genesis over the ENP including OLR, 850-hPa relative vorticity, 850-hPa barotropic energy conversion, 700-hPa specific humidity, SST, and vertical zonal wind shear between 200 hPa and 850 hPa. Note that when relative vorticity, barotropic energy conversion, specific humidity, and SST anomalies are larger than zero or when OLR anomalies are smaller than zero, the contribution from these factors to TC genesis is positive. Conversely, the contribution is negative. Figure 3 displays the relative contributions in percent of OLR, relative vorticity, specific humidity anomalies due to interannual, intraseasonal, and synoptic time scales and the percentage of TC genesis frequency represented by the probability density function. Barotropic energy conversion due to climatological mean, interannual, and intraseasonal wind flows is also shown together in Figure 3.
For OLR, the relative contributions of the different time scales are variable, depending on the OLR range. Approximately 73% of TCs (358/488) form when the OLR anomalies are between \(-\)70 W m\({}^{-2}\) and \(-\) 10 W m\({}^{-2}\). In this range, the contributions from the synoptic and intraseasonal variations are comparable (Figure 3a). About 14% (69/488) of TCs form when the OLR anomalies are between \(-\)10 W m\({}^{-2}\) and 0 (Figure 3a). For this range of OLR anomalies, the synoptic variation has the greatest positive contribution, and the intraseasonal variation plays a secondary role. There are 60 TC genesis cases (12%) when the OLR anomalies are positive. Within this range, the most negative contribution is from the synoptic variability (Figure 3a).
Approximately 93% of TCs (485/488) appear when the relative vorticity anomalies are larger than 0 (Figure 3b). In this range, the synoptic component has the largest positive contribution, followed by the intraseasonalcomponent. In addition, there are 34 TC genesis cases (7%) when the relative vorticity anomalies are negative, in which the negative contribution is mainly from the intraseasonal component (Figure 3b).
High mid-level humidity is closely associated with the development of convection, which is a necessary condition for TC genesis ([PERSON], 1968; [PERSON], 2004). Approximately 55% of TCs (269/488) appear when the mid-level specific humidity anomalies are between 0 and 1 g kg\({}^{-1}\), with the major positive contribution from the synoptic component (Figure 3c). A few TCs (33%, 162/488) occur when the specific humidity anomalies are between 1 g kg\({}^{-1}\) and 3 g kg\({}^{-1}\). Within this range, the contribution from the intraseasonal component is comparable to that from the synoptic component (Figure 3c). There are 52 TC cases (10%) forming within negative mid-level specific humidity anomalies (Figure 3c). The interannual and intraseasonal components make the major negative contributions to TC genesis when the total mid-level specific humidity anomalies are below zero. [PERSON] _et al._ (2018) indicated that TC genesis may be more dependent on dynamical factors than thermodynamic factors over the western North Pacific because more TCs are generated when the mid-level specific humidity anomalies are unfavorable for TC genesis. However, over the ENP, the rates of TCs forming in the unfavorable vorticity and humidity conditions do not show a significant difference. Thus, it is inferred that TC genesis over the ENP may depend not only on dynamical factors but also on thermodynamic factors. This appears to agree with [PERSON] and [PERSON] (2015) who found that relative vorticity and relative humidity favored TC genesis during inactive years over the ENP basin.
Barotropic energy conversion is an important source for developing synoptic disturbances in the eastern Pacific basin, through which the synoptic-scale disturbances could obtain energy from the large-scale basic flows ([PERSON] _et al._, 1997). Approximately 82% of TCs (403/488) are generated over the ENP when the barotropic energy conversion is between 0 and 18 \(\times\) 10\({}^{-5}\) m\({}^{2}\) s\({}^{-3}\) (Figure 3d). The greatest contribution is related to climatological mean flows. When the barotropic energy conversion value is larger than 18 \(\times\) 10\({}^{-5}\) m\({}^{2}\) s\({}^{-3}\), the synoptic-scale disturbances mainly obtain energy from the climatological mean and intraseasonal flows. Approximately 15% of TCs (75/488) form when the barotropic eddy conversion is below zero (Figure 3d), which is smaller than that over the western North Pacific ([PERSON] _et al._, 2018). This indicates that barotropic energy conversion may play a greater role in TC genesis over the ENP.
Weak vertical wind shear is a necessary condition for TC genesis, which is useful for the accumulated condensational heating to remain in the center of a tropical disturbance and impel the tropical disturbance to develop into TC ([PERSON], 1996). The warm SST provides the moisture and heat energy to spawn TC genesis ([PERSON], 1979). With respect to vertical wind shear and SST distribution, we calculate the percent contribution of different time scale components, not only based on the total anomalies but also based on the total value. Climatological mean vertical wind shear is easterly wind shear with an absolute value smaller than 5 m s\({}^{-1}\) over the ENP (Figure 2). Thus, weak vertical westerly shear anomalies are expected to be the most favorable for TC genesis over the ENP (Figure 4a). The most frequent TCs appear when the vertical wind shear anomalies are between 0 and 3 m s\({}^{-1}\) (Figure 4a). Among the three components, the interannual and intraseasonal components make the largest positive contribution. When absolute vertical wind shear anomalies are gradually large, the intraseasonal component is the most unfavorable due to the greatest value.
TC genesis is directly associated with total vertical wind shear. Approximately 34% (168/488) of TCs over the ENP form in the range of easterly wind shear between \(-4\) m s\({}^{-1}\) and 0 (Figure 4b). The main positive contribution is from the interannual and intraseasonal components because interannual and intraseasonal westerly wind shear anomalies are against climatological easterly wind shear. This result is consistent with Figure 4a. Intra-seasonal wind shear is the largest component when the total shear is larger than 0 and smaller than \(-4\) m s\({}^{-1}\) (Figure 4b). Because there is no clear threshold value of vertical wind shear for TC genesis, it is only inferred that with the increase in the total absolute wind shear, the intraseasonal component makes the largest negative contribution due to the great value and the interannual and synoptic components have the least unfavorable contribution due to the small value (Figure 4b).
Approximately 39% (179/457) of TCs occur when the SST anomalies are positive. In this case, the interannual component has a robustly largest positive contribution to TC genesis, which is followed by intraseasonal component (Figure 4c). Approximately 61% of TCs appear within negative SST anomalies, and all three components make negative contributions to TC genesis (Figure 4c). This result is consistent with that over the western North Pacific and northern Atlantic Ocean ([PERSON] _et al._, 2018, 2019). When the climatological mean SST is included, almost all the TCs (only one exception) form when the total SST value is above 26\({}^{\circ}\)C (Figure 4d), which is thought to be a necessary condition for TC genesis ([PERSON], 1968, 1979). Approximately 25% (113/457) of TCs are generated when the SST value is between 28\({}^{\circ}\)C and 28.5\({}^{\circ}\)C (Figure 4d). In this range, the positive contribution is from the interannual component, and the synoptic and intraseasonal components make negative contributions to TC genesis. When the SST value is larger than 28.5\({}^{\circ}\)C, the interannual component still has the largest positive contribution (Figure 4d). When the SST value is smaller than 28\({}^{\circ}\)C, the three component anomalies are below zero with the largest negative contribution from the intraseasonal component.
## 4. The comparison among various basins
TC genesis over the different basins may be associated with various time scale components of environmental factors. Thus, it is necessary to compare the relative contribution discrepancy of different time scale componentsof environmental factors to TC genesis among the ENP, western North Pacific and northern Atlantic Ocean. Figure 5 shows the total averaged positive contribution of four factors over the three basins. There are palpable similarities and remarkable differences among these three basins. The contributions of vorticity and humidity to TC genesis are similar over the ENP and northern Atlantic Ocean, with the main positive contribution from the synoptic component (Figure 5b,c). On the other hand, the major contribution of barotropic energy conversion is similar over the ENP and western North Pacific (Figure 5d). In contrast, the positive contribution of convection from the synoptic and intraseasonal components is comparable over the ENP, which is different from the northern Atlantic Ocean and western North Pacific (Figure 5a).
To identify the reasons for the discrepancy in the relative contributions of these factors to TC genesis among three basins, the ratio of the standard deviations of OLR, vorticity, and humidity between the synoptic and
Figure 5: The positive contributions (%) from anomalies of (a) OLR, (b) relative vorticity, (c) specific humidity on interannual (red), intraseasonal (green), and synoptic (orange) time scales and (d) barotropic energy conversion from interannual (red), intraseasonal (green) variations, and climatological mean (yellow) flows over the ENP, northern tropical Atlantic Ocean (NTA) and western North Pacific (WNP)
Figure 6: The ratio of the standard deviations of variations of (a) OLR, (b) lower-level relative vorticity, and (c) mid-level specific humidity between the synoptic and intraseasonal time scales over the Pacific and Atlantic Ocean
intraseasonal components is shown in Figure 6. The standard deviations of OLR, vorticity, and humidity are larger on the synoptic time scale than on the intraseasonal time scale over the ENP and northern Atlantic Ocean, particularly for relative vorticity (Figure 6b). Over the western North Pacific, the standard deviations of specific humidity are larger on the intraseasonal time scale than on the synoptic time scale in most of the domain (Figure 6c). In addition, the standard deviations of OLR and vorticity are larger on the synoptic time scale than on the intraseasonal time scale over the western North Pacific but with smaller magnitude than that over the ENP and northern Atlantic Ocean. Thus, it is concluded that the contribution of OLR, relative vorticity and specific humidity to TC genesis over the ENP is closer to that over the Atlantic Ocean than that over the western North Pacific.
## 5 Summary and Discussion
This present study examines the contributions of six large-scale environmental factors to TC genesis over the ENP from a local and instantaneous perspective, which has been performed previously in the western North Pacific and Atlantic Ocean ([PERSON] _et al._, 2018, 2019). The total anomalies of each variable centered around the TC genesis location are separated into interannual, intra-seasonal, and synoptic time scale components. Then we analyze and compare the relative contributions of different time scale components to TC genesis. Furthermore, the contributions of the three time scale components over the ENP are compared with those over the northern Atlantic Ocean and western North Pacific.
On the one hand, the composite results based on the TC genesis time and position over the ENP show that the major positive contribution of relative vorticity and specific humidity to TC genesis are due to synoptic component. The contribution from the synoptic component of convection is nearly comparable to that from the intra-seasonal component. The synoptic scale tropical disturbances obtain eddy kinetic energy mainly from climatological mean flows. On the other hand, most TCs form when the total vertical zonal wind shear is between \(-4\) m s\({}^{-1}\) and \(0\) with the major positive contributions from intraseasonal and interannual components. In addition, the TC genesis over the ENP is, to a great extent, associated with climatological mean and interannual component of SST.
The main conclusions and comparisons among the three basins are summarized in Table 1. The synoptic components of relative vorticity and specific humidity are the most significant over the ENP and northern Atlantic Ocean, whereas the synoptic scale tropical disturbances obtain the barotropic eddy energy mainly from climatological mean flows over the ENP and western North Pacific. The contribution of different time scale components of OLR shows various characteristics among these three basins. Over the ENP, the positive contribution from the synoptic and intraseasonal components is comparable, while the contributions from the synoptic and intraseasonal components are the largest over the northern Atlantic Ocean and western North Pacific, respectively.
The present study indicates that the synoptic variations of vorticity and humidity are the highest over the ENP. The relationship between the magnitude of synoptic component and the interannual variation of TC genesis over the ENP will be examined in future work. This is currently being planned.
###### Acknowledgements.
We appreciate the comments of two anonymous reviewers. This study is supported by the 2019 Open Research Program of the Shanghai Typhoon Institute (Grant TFJJ201901), the Open Grants of the State Key Laboratory of Severe Weather (Grant 2020 LASW-B01) and the National Natural Science Foundation of China (Grant 41505048). The SST data were obtained from [[ftp://ftp.cdc.noaa.gov/Datasets/noaa.oisst.v2.highres](ftp://ftp.cdc.noaa.gov/Datasets/noaa.oisst.v2.highres)]([ftp://ftp.cdc.noaa.gov/Datasets/noaa.oisst.v2.highres](ftp://ftp.cdc.noaa.gov/Datasets/noaa.oisst.v2.highres)). The IBTrACS data were obtained from [[http://www.ncdc.noaa.gov/ibtracts/index.php](http://www.ncdc.noaa.gov/ibtracts/index.php)]([http://www.ncdc.noaa.gov/ibtracts/index.php](http://www.ncdc.noaa.gov/ibtracts/index.php)). The ERA-Interim data set was obtained from ECMWF ([[https://www.ecmwf.int/en/research/climate-reanalysis/era-interim](https://www.ecmwf.int/en/research/climate-reanalysis/era-interim)]([https://www.ecmwf.int/en/research/climate-reanalysis/era-interim](https://www.ecmwf.int/en/research/climate-reanalysis/era-interim))).
## 6 Orcid
_[PERSON]_[[https://orcid.org/0000-0002-2064-7018](https://orcid.org/0000-0002-2064-7018)]([https://orcid.org/0000-0002-2064-7018](https://orcid.org/0000-0002-2064-7018))
_[PERSON]_[[https://orcid.org/0000-0003-3934-2780](https://orcid.org/0000-0003-3934-2780)]([https://orcid.org/0000-0003-3934-2780](https://orcid.org/0000-0003-3934-2780))
_[PERSON]_[[https://orcid.org/0000-0002-4239-2853](https://orcid.org/0000-0002-4239-2853)]([https://orcid.org/0000-0002-4239-2853](https://orcid.org/0000-0002-4239-2853))
\begin{table}
\begin{tabular}{l l l l l} \hline & **OLR** & **Vorticity** & **Humidity** & **Barotropic energy conversion** \\ \hline Eastern North Pacific & Synoptic + intraseasonal & Synoptic & Synoptic & Climatological mean \\ Northern Tropical Atlantic & Synoptic & Synoptic & Synoptic & Climatological mean + intraseasonal \\ \hline Western North Pacific & Intraseasonal & Intraseasonal + synoptic & Intraseasonal & Climatological mean \\ \hline \end{tabular}
\end{table}
Table 1: The summary of the main contribution component of various factors to tropical cyclogenesis over the eastern North Pacific, western North Pacific, and northern tropical Atlantic Ocean
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**How to cite this article:** [PERSON], [PERSON], [PERSON],
[PERSON], [PERSON] Relative contributions of environmental factors on different time scales to tropical cyclogenesis over the eastern North Pacific. _Atmos Sci Lett._ 2021;22:e1037. [[https://doi.org/10.1002/asl.1037](https://doi.org/10.1002/asl.1037)]([https://doi.org/10.1002/asl.1037](https://doi.org/10.1002/asl.1037)) | wiley | Relative contributions of environmental factors on different time scales to tropical cyclogenesis over the eastern North Pacific | Xi Cao, Renguang Wu, Juan Feng, Xiping Zhang, Yifeng Dai | https://doi.org/10.1002/asl.1037 | 2,021 | CC-BY |
wiley/fa791829_7ba9_42d6_926c_e9942b96e518.md | # GeoHealth
Research Article
10.1029/2023 GH000888
###### Abstract
The Multi-Threat Medical Countermeasure (MTMC) technique is crucial for developing common biochemical signaling pathways, molecular mediators, and cellular processes. This study revealed that the Nod-like receptor 3 (NLPR9) inflammasome pathway may be a significant contributor to the cytotoxicity induced by various organophosphorus pesticides (OPPs). The study demonstrated that exposure to six different types of OPPs (paraoxon, dichlorovs, fenthion, diptrex, dibrom, and dimethoate) led to significant cytotoxicity in BV2 cells, which was accompanied by increased expression of NLRP9 inflammasome complexes (NLPR9, ASC, Caspase-1) and downstream inflammatory cytokines (IL-1B, IL-18), in which the order of cytotoxicity was dichlorovs \(>\) diptrex \(>\) dibrom \(>\) paraoxon \(>\) fenthion \(>\) dimethoate, based on the IC\({}_{50}\) values of 274, 410, 551, 585, 2,158, and 1,527,566 \(\upmu\)M, respectively. The findings suggest that targeting the NLRP9 inflammasome pathway could be a potential approach for developing broad-spectrum antitoxic drugs to combat multi-OPPs-induced toxicity. Moreover, inhibition of NLRP9 efficiently protected the cells against cytotoxicity induced by these six OPPs, and the expression of NLRP9, ASC, Caspase-1, IL-18, and IL-18 decreased accordingly. The order of NLRP9 affinity for OPPs was dimethoate \(>\) paraoxon \(>\) dilecthorovs \(>\) dibrom \(>\) (fenthion and diptrex) based on \(K_{D}\) values of 89.8, 325, 1.460, and 2,690 \(\upmu\)M, respectively. Furthermore, the common molecular mechanism of NLRP3-OPPs was clarified by the presence of toxicity effector groups (benzene ring, nitrogen/oxygen-containing functional group); =O, -O, or =S (active) groups; and combination residues (Gly271, Asp272). This finding provided valuable insights into exploring the common mechanisms of multiple threats and developing effective therapeutic strategies to prevent OPPs poisoning.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34
## 2 Material and Methods
### Chemicals
Six kinds of OPPs, including paraoxon, dichlorvos, fenthion, dipeterex, dibrom, and dimethoate, were purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. (Shanghai, China). The NLRP9 inflammasome inhibitor, MCC950, was purchased from Selleck Biotechnology Co., Ltd. (Houston, TX, USA). Cell Counting Kit-8 (CCK-8) and Cytotoxicity LDH Assay Kit-WST were obtained from Dojindo Laboratories (Kumamoto, Japan).
Enzyme-linked immunosorbent assay (ELISA) kits were purchased from Abcam (Cambridge, UK). PrimeScript RT reagent kit with gDNA Eraser and TB Green Premix Ex TaqMan II was purchased from Takara Bio, Inc. (Kusatsu, Japan). The hNLRP3 LRR recombinant protein was obtained from ImmunoClone Biosciences Co., Ltd. (Huntington Station, NY, USA).
### Cell Cultures and Treatment
BV2 microglial cells were supplied by the Cell Resource Center, Institute of Basic Medicine, Chinese Academy of Medical Sciences (Beijing, China), and cultured in Dulbecco's Modified Eagle Medium (DMEM) containing 10% fetal bovine serum. BV2 cells (5 \(\times\) 10\({}^{4}\) cells/mL) were seeded in 96-well (100 \(\mu\)L/well) and 6-well (2 mL/well) plates and incubated at 37\({}^{\circ}\)C with 5% CO\({}_{2}\) in a humidified incubator for 24 hr. BV2 cells were respectively treated with six different OPPs at gradient concentrations (0, 125, 250, 500, 1,000 \(\mu\)M) for 24 hr. For the intervention group, BV2 cells were pre-treated with MCC950 (10 \(\mu\)M) for 0.5 hr and then treated with OPPs for 24 hr.
### Cell Viability Assay
To conduct the cell viability assay, the growth medium was removed from the BV2 cells cultured in a 96-well plate. The CCK-8 reagent was mixed with complete medium (1:9 volume ratio), and 100 \(\mu\)L of the CCK-8 reagent mixture was added to each well. The plate was incubated for 4 hr, and absorbance was measured at 450 nm using a microplate reader (BNR05740; Molecular Devices, Sunnyvale, CA, USA). The average absorbance from each sextuplicate set of wells was calculated, and the background control value was subtracted from the absorbance value. The percentage of viable cells was determined using the following equation:
\[\text{Cell viability (\%) = [(As - Ab) / (Ac - Ab)]\times 100,}\]
where As is the absorbance of the experimental well (containing the medium, CCK-8 reagent, cells, and compound), Ac is the absorbance of the control well (containing the medium, CCK-8 reagent, and cells), and Ab is the absorbance of the blank well (containing the medium and CCK-8 reagent).
### LDH-Based Cytotoxicity Assay
To use the Cytotoxicity LDH Assay Kit, lysis buffer (10 \(\mu\)L) was added to the high control well of a 96-well plate containing BV2 cells, which was then incubated for 0.5 hr. The working solution was prepared by adding 5 mL of the assay buffer to the dye mixture vial, of which 100 \(\mu\)L was added to each well. The plate was protected from light and incubated at room temperature for 0.5 hr. Subsequently, 50 \(\mu\)L of stop solution was added to each well, and the absorbance was measured immediately at 490 nm using a microplate reader (BNR05740, Molecular Devices). The average absorbance was calculated from each sextuplicate set of wells, and the background control value was subtracted from the absorbance value. The percentage of cytotoxicity was determined using the following equation:
\[\text{Cytotoxicity (\%) = [(Aa - Ab1) / (Ab2 - Ab1)]\times 100,}\]
where Aa is the absorbance of the experimental well (containing medium, cells, and compound), Ab2 is the absorbance of the high control well (containing medium, cells, and lysis buffer), and Ab1 is the absorbance of the low control well (containing medium and cells).
### Real-Time Quantitative PCR (RT-qPCR)
TRIzol Reagent (1 mL) was directly added to BV2 cells in 6-well plates, and total RNA was extracted according to the manufacturer's instructions. Total RNA was used for cDNA reverse transcription, which was performed according to the PrimeScript RT protocol with the following reaction conditions: 42\({}^{\circ}\)C for 2 min, 4\({}^{\circ}\)C for \(\infty\) (removal of genomic DNA), 37\({}^{\circ}\)C for 15 min, 85\({}^{\circ}\)C for 5 s, and 4\({}^{\circ}\)C for \(\infty\) (reverse transcriptional reaction). The RT-qPCR was performed in accordance with the TB Green Premix Ex Taq II protocol. Primer sequences and product lengths were as follows: NLRP3 (83 bp) forward primer 5\({}^{\circ}\)-ATTACCGCGACGAAAGG-3\({}^{\circ}\), reverse primer 5\({}^{\circ}\)-CATGAGTGTGGTAGATCCAAG-3\({}^{\circ}\); ASC (90 bp) forward primer 5\({}^{\circ}\)-GTGAGAGTGCTGAT-3', reverse primer 5'-CTTGCTTTGCTGGGT-3', Caspase-1 (121 bp) forward primer 5'-GGACATCCTCTCATCCTCAGAAAAAC-3', reverse primer 5'-TTTCTTTCCAAAAACTTTCGGGCTTT-3'; IL-19 (76 bp) forward primer 5'-ACAGGCATCCCGAGATGAAAC-3', reverse primer 5'-CCATTAGGGTGAGAGAGCTTTC-3'; IL-18 (20 bp) forward primer 5'-GTGACCCCAGAGCCGAGCTG-3', reverse primer 5'-CCTGGAAACACGGTTTTCGAAAGA-3', and 8-actin (154 bp) forward primer 5'-GGCTGTATTCCCCCTC-CATCG-3', reverse primer 5'-CCAGTTGGTGTAACAAATGCCATG-3'. RT-qPCR was performed using the CFX96 Real-Time System (Bio-Rad Laboratories, Hercules, CA, USA) with the following reaction conditions: 95\({}^{\circ}\)C for 30 s, 40 cycles of 95\({}^{\circ}\)C for 5 s, 61\({}^{\circ}\)C for 30 s, and 72\({}^{\circ}\)C for 30 s, followed by a melting curve from 65 to 95\({}^{\circ}\)C in 0.5\({}^{\circ}\)C/5 s increments. Calculations were performed using the CFX Manager\({}^{\text{TM}}\) Version 1.0 software (Bio-Rad Laboratories Ltd., USA) and are represented as fold-change in expression [2\({}^{\text{a}\text{AC}\text{(}\text{(}\text{)}\text{)}}\) on a linear scale.
### Detection of Proinflammatory Cytokines
The ELISA kits (cat. ab197742 and ab216165) were used to quantify the IL-1B and IL-18 secreted into the culture supernatants of BV2 cells after incubation for 24 hr, following the manufacturer's instructions. BV2 cell culture supernatants were centrifuged and collected at 2,000 rpm for 10 min to remove the remaining cells. Next, 50 \(\mu\)L of the sample, standard, and antibody cocktails were added to each well. The plates were incubated for 1 hr at room temperature on a shaker at 400 rpm. Each well was washed with 350 \(\mu\)L wash buffer, and 100 \(\mu\)L of TMB solution was added to each well and incubated for 10 min in the dark on a shaker at 400 rpm. Then, 100 \(\mu\)L of stop solution was added to each well. The absorbance was recorded at 450 nm using a microplate reader (BNR05740, Molecular Devices). For IL-1B and IL-18 extracellular expression, standard curves were created from 1.56 to 100 pg/mL and 31.3 to 2,000 pg/mL, with sensitivities of 1 and 10.5 pg/mL, and concentrations were expressed as pg/mL, respectively.
### Two-Stage Mass Spectrometry (MS/MS) Analysis
NLRP3 recombinant proteins were separated by sodium dodecyl-sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and stained with Coomassiee Brilliant blue (CBB) R-250; NLRP3 protein bands were precisely excised on a clean glass plate using a sharp blade. Peptides (2 \(\mu\)L) were analyzed at high resolution using a NanoLC-Orbitrap Elite MS/MS system (Thermo Fisher Scientific, Co., Ltd. USA) with an automatic sampler for data acquisition. The system was operated in positive ion spray ionization mode, with an injection speed of 0.3 \(\mu\)L/min, capillary voltage of 2.2 kV, mass-to-charge ratio range of 300-1,800 m/z, and 35% collision energy. Data were processed using Proteome Discovery 2.4. Qualitative assessment of proteins and mass-to-charge ratios (m/z) of fragment peaks were performed by comparing the differences in the MS/MS spectra.
### Surface Plasmon Resonance (SPR) Analysis
The binding capacity of the hNLP3 LRR recombinant protein to OPPs was determined by SPR according to the Biacore 8 K system (Cytiva, USA) using the CM5 chip. After obtaining the baseline signal, the sample loop was flushed with phosphate-buffered saline (PBS), and 80 \(\mu\)g/mL of hNLP3 protein (diluted by acetate as pH 4.0) was added and contacted for 10 min at 10 \(\mu\)L/min and 25\({}^{\circ}\)C. The following analytes were used: paraoxon (15.625, 62.5, 125, 250, 500 \(\mu\)M), dichlorovs (31.25, 62.5, 125, 250, 500 \(\mu\)M), fenthion (62.5, 125, 250, 500, 1,000 \(\mu\)M), diptrexe (62.5, 125, 250, 500, 1,000 \(\mu\)M), and dimethoate (31.25, 125, 250, 500, 1,000 \(\mu\)M). The contact and dissociation times of the analytes and proteins were 120 and 300 s, respectively. An affinity model was used to determine the association (\(k_{\text{a}}\)), dissociation (\(k_{\text{d}}\)), and affinity constants (\(K_{D}\)).
### Molecular Docking
The macromolecular structure of the hNLP3 inflammasome used for molecular docking simulation was obtained from the Protein Data Bank (PDB ID 6 NPY, [[https://www.rcsb.org](https://www.rcsb.org)]([https://www.rcsb.org](https://www.rcsb.org))), and undesired structures were managed using the SEQ module of the Molecular Operating Environment (MOE) version 20.09 software ([PERSON] et al., 2019; [PERSON] et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2019). The structures of the OPPs (paraoxon, dichlorovs, fenthion, diptrexe, dibrom, and dimethoate) were derived from the PubChem database ([[https://pubchem.ncbi.nlm.nih.gov/](https://pubchem.ncbi.nlm.nih.gov/)]([https://pubchem.ncbi.nlm.nih.gov/](https://pubchem.ncbi.nlm.nih.gov/))) in SDF format. Small molecules were minimized and saved. Macromolecular docking pockets were determined using the Site Finder module. Molecular docking simulations were performed using the Docking Module, and all docking processes were completed under an Amber 10: EHT force field, using an R-field dominant solvent model with a pH of 7.0 and a temperature of 300 K. The generalized-Born volume integral/weighted surface area (GBVI/WSA) dG scoring function was used to score the 30 structures, with London dG scores for flexible docking ([PERSON] et al., 2021; [PERSON] et al., 2021; [PERSON] et al., 2019). Macromolecules and small molecules have been screened for improved interaction performance.
### Statistical Analysis
The experimental data are expressed as the standard error of the mean (SEM). GraphPad Prism version 6.0 software (GraphPad Software, La Jolla, CA, USA) was used for the data analysis. One-way analysis of variance for multiple comparisons was used to analyze differences between groups, and \(P\) < 0.05 was considered statistically significant.
## 3 Results
### OPPs-Induced Cytotoxicity in BV2 Cells
#### 3.1.1 OPPs Treatment Decreases the Cell Viability in BV2 Cells
To determine the cytotoxicity of six different OPPs compounds in BV2 cells, cell viability was evaluated using a CCK-8 kit after treatment with different kinds and concentrations of OPPs for 24 hr. Compared with treatment with 0 \(\upmu\)M OPPs, the cell viability of BV2 cells treated with paraoxon (125 \(\upmu\)M, \(P\) < 0.01; 250 \(\upmu\)M, \(P\) < 0.0001; 500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S1a in Supporting Information S1), dichlorvos (125 \(\upmu\)M, \(P\) < 0.001; 250 \(\upmu\)M, \(P\) < 0.0001; 500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S1b in Supporting Information S1), fethion (500 \(\upmu\)M, \(P\) < 0.001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S1c in Supporting Information S1), diptrex (125 \(\upmu\)M, \(P\) < 0.05; 250 \(\upmu\)M, \(P\) < 0.01; 500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S1d in Supporting Information S1), diptrex (250 \(\upmu\)M, \(P\) < 0.05; 500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S1e in Supporting Information S1), and dimethoate (125 \(\upmu\)M, \(P\) < 0.001; 250 \(\upmu\)M, \(P\) < 0.001; 500 \(\upmu\)M, \(P\) < 0.01; 1,000 \(\upmu\)M, \(P\) < 0.01) (Figure S1f in Supporting Information S1) significantly decreased.
#### 3.1.2 OPPs Increased the Cytotoxicity in BV2 Cells
The cytotoxic effects of OPPs in BV2 cells were further detected using the LDH assay after treatment with different kinds and concentrations of OPPs for 24 hr. Compared with treatment with 0 \(\upmu\)M OPPs, BV2 cells treated with paraoxon (125 \(\upmu\)M, \(P\) < 0.001; 250 \(\upmu\)M, \(P\) < 0.0001; 500 \(\upmu\)M, \(P\) < 0.0001) (Figure S2a in Supporting Information S1), dichlorvos (125 \(\upmu\)M, \(P\) < 0.001; 250 \(\upmu\)M, \(P\) < 0.001; 500 \(\upmu\)M, \(P\) < 0.0001) (Figure S2b in Supporting Information S1), fethion (250 \(\upmu\)M, \(P\) < 0.01; 500 \(\upmu\)M, \(P\) < 0.01; 1,000 \(\upmu\)M, \(P\) < 0.001) (Figure S2c in Supporting Information S1), diptrex (125 \(\upmu\)M, \(P\) < 0.01; 250 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure S2d in Supporting Information
fenthion, diperex, dibrom, and dimethoate were significantly increased, respectively (compared with that in 0 \(\upmu\)M OPPs-treated cells, \(P<0.0001\), Figures S3a-S3e in Supporting Information S1). Thus, the six OPPs significantly increased the expression of NLRP3 inflammasome complexes and downstream inflammatory cytokines in BV2 cells.
MCC950 Reverses the Expression of NLRP3 Inflammasome Complexes and Inflammatory Cytokines Induced by OPPs in BV2 Cells
Changes in OPPs-induced cytotoxicity were measured after blocking the NLRP3 inflammasome to determine whether it was a crucial target involved in OPPs poisoning. Compared with the OPPs treatment group (500 \(\upmu\)M), those pre-treated with MCC950 (10 \(\upmu\)M, NLRP3 inflammasome specific inhibitor) exhibited a significant decrease in NLRP3 mRNA expression in BV2 cells treated with paraoxoon (\(P<0.05\)), dichlorovos (\(P<0.0001\)), fenthion (\(P<0.0001\)), diperex (\(P<0.0001\)), dibrom (\(P<0.0001\)), and dimethoate (\(P<0.0001\)) (Figure 1a). ASC mRNA expression in BV2 cells treated with paraoxon (\(P<0.0001\)), dichlorovos (\(P<0.0001\)), fenthion (\(P<0.0001\)), diperex (\(P<0.01\)), dibrom (\(P<0.001\)), and dimethoate (\(P<0.0001\)) also decreased after MCC950 intervention (Figure 1b). Otherwise, Caspase-1 and IL-18 mRNA expressions in BV2
\begin{table}
\begin{tabular}{l c c} \hline \hline Toxicants & BV2 cells (\(\upmu\)M) & BV2 cells + MCC950 (10 \(\upmu\)M) (\(\upmu\)M) \\ \hline Paraoxon & 551 & 1,282 \\ Dichlorovos & 274 & 358 \\ Fenthion & 2,158 & 3,304 \\ Diperex & 410 & 492 \\ Dibrom & 585 & 762 \\ Dimethoate & 1,527,566 & 2,666,859 \\ \hline \end{tabular}
\end{table}
Table 1: _IC\({}_{50}\) Values of OPPs in BV2 Cells_
Figure 1: mRNA expression changes of the NLRP3 inflammasome and associated inflammatory cytokines in BV2 cells treated with OPPs and MCC950 intervention. (a) mRNA Expression of NLRP3, (b) mRNA Expression of ASC, (c) mRNA Expression of Caspase-1, (d) mRNA Expression of IL-1\(\beta\), and (e) mRNA Expression of IL-18.
cells treated with paraaxon, dichlorovs, fenthion, diperex, dibrom, and dimethoate were significantly decreased, respectively (Figures 1c and 1e, \(P\) < 0.0001), and IL-1\(\beta\) mRNA expression after treatment with paraaxon (\(P\) < 0.05), dichlorovs (\(P\) < 0.0001), fenthion (\(P\) < 0.0001), diperex (\(P\) < 0.010), dibrom (\(P\) < 0.0001), and dimethoate (\(P\) < 0.0001) (Figure 1d) was decreased by MCC950 intervention, respectively. These results indicated that MCC950 intervention reduced the activation of the NLRP3 inflammasome and associated inflammatory cytokine mRNA expression in multiple OPPs-treated BV2 cells.
### MCC950 Reduced the Cytotoxicity of BV2 Cells Induced by OPPs
#### 3.4.1 MCC950 Increased the Cell Viability of BV2 Cells Induced by OPPs
Compared with those following OPPs treatment (125, 250, 500, 1,000 \(\upmu\)M), BV2 cells pre-treated with inflammasome specific inhibitor MCC950 (10 \(\upmu\)M) significantly increased cell viability of BV2 cells treated with paraoxon (250 \(\upmu\)M, \(P\) < 0.001; 500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.0001) (Figure 2a), dichlorovs (125 \(\upmu\)M, \(P\) < 0.01; 250 \(\upmu\)M, \(P\) < 0.0001; 500 \(\upmu\)M, \(P\) < 0.05; 1,000 \(\upmu\)M, \(P\) < 0.05) (Figure 2b), fenthion (500 \(\upmu\)M, \(P\) < 0.05; 1,000 \(\upmu\)M, \(P\) < 0.001) (Figure 2c), diperex (500 \(\upmu\)M, \(P\) < 0.0001; 1,000 \(\upmu\)M, \(P\) < 0.01) (Figure 2d), dibrom (500 \(\upmu\)M, \(P\) < 0.05; 1,000 \(\upmu\)M, \(P\) < 0.001) (Figure 2e), and dimethoate (125 \(\upmu\)M, \(P\) < 0.05) (Figure 2f). These results indicated that NLRP3 may play a critical role in OPPs-induced cytotoxicity.
Figure 2: Cell viability of BV2 cells treated with OPPs and MCC950 intervention. BV2 cells treated with different concentrations of (a) paraoxon, (b) dichlorovs, (c) fenthion, (d) diperex, (e) dibrom, and (f) dimethoate.
#### 3.4.2 MCC950 Decreased the Cytotoxicityicity of BV2 Cells Induced by OPPs
Compared with OPPs treatment (125, 250, 500, 1,000 uM), BV2 cells pre-treated with MCC950 (10 uM) exhibited significantly decreased cytotoxicity when treated with paraoxon (125 uM, \(P<0.05\)) (Figure 3a), dichlorovos (250 uM, \(P<0.05\); 500 uM, \(P<0.05\)) (Figure 3b), fenton (250 uM, \(P<0.001\)) (Figure 3c), diprex (1,000 uM, \(P<0.01\)) (Figure 3d), dibrom (125 uM, \(P<0.05\)) (Figure 3e), and dimotheade (250 uM, \(P<0.05\); 500 uM, \(P<0.05\); 1,000 uM, \(P<0.05\)) (Figure 3f). Moreover, the LC950 values of BV2 cells treated with paraoxon, dichlorovos, fenthion, diprex, dibrom, and dimotheade after MCC950 (10 uM) intervention were 1,282, 358, 3,304, 492, 762, and 2,666,859 uM, respectively (Table 1), which indicated that MCC950 could markedly decrease cytotoxicity induced by OPPs.
MCC950 Decreased the IL-19 and IL-18 mRNA Expression in an Extracellular Medium of BV2 Cells Treated With OPPs
These results indicated that NLRP3 is a potential key target for OPPs-induced BV2 cell cytotoxicity. The NLRP3 inflammasome is a large molecular platform activated by various chemicals that trigger cellular cascade responses after activating inflammatory caspases and processing pro-IL-19 and pro-IL-18 ([PERSON] et al., 2019; [PERSON], 2015; [PERSON], 2019). IL-19 and IL-18 expression in the extracellular medium of BV2 microglia were determined by ELISA assay after treatment with OPPs (125, 250, 500 uM) for 24 hr. Compared with treatment with 0 uM OPPs, the expression of IL-19 and IL-18 in the extracellular medium of BV2 cells treated with paraoxon, dichlorovos, fenthion, diprex, dibrom, and dimotheade were all significantly increased
Figure 3.— Cytotoxicityicity of BV2 cells treated with OPPs were decreased by MCC950 intervention. (a) Paraxoon, (b) dichlorovos, (c) fenthion, (d) diperex, (e) dibrom, and (f) dimotheade.
Figure 4: IL-1\(\beta\) and IL-18 extracellular expressions in BV2 cells treated with OPPs were decreased by MCC950 intervention. (a) Paraxoxon, (b) dichlorovos, (c) fenthion, (d) Dipterex, (e) dityhorn, (f) dimethoate for IL-1\(\beta\) expression; (g) paraoxon, (h) dichlorovos, (i) fenthion, (j) dipterex, (k) dibrom, and (l) dimethoate for IL-18 expression.
(Figures 4a-4l, \(P<0.0001\)). Compared with OPPs treatment (125, 250, 500 \(\mu\)M), MCC950 (10 \(\mu\)M) intervention exhibited significantly reduced IL-1\(\beta\) and IL-18 expression in the extracellular medium of BV2 cells, respectively (Figures 4a-4l, \(P<0.0001\)). In summary, the expression of IL-1\(\beta\) and IL-18 in OPPs-induced BV2 cells was significantly decreased by MCC950 treatment. NLRP9 is an essential target that mediates downstream cytokine expression and contributes to OPPs toxicity in BV2 cells.
### Molecular Mechanism of the NLRP3-OPPs Interaction
#### 3.6.1 Tandem Mass Spectrometry (MS/MS) Results
The amino acid sequence of the hNLRP3 LRR protein was confirmed using MS/MS. The SDS-PAGE analysis indicated that the molecular weight of the hNLRP3 LRR was 41 kDa (Figure S4a in Supporting Information S1). The secondary structure was determined by collision-induced dissociation (CID), and m/z was determined by MS/MS after enzymology (Figures S4c-S4m and Table S1 in Supporting Information S1) and indicated that the molecular weight and amino acid sequence of the purchased hNLRP3 LRR were consistent with the corresponding sequences on the National Center for Biotechnology Information (NCBI) website (Figure S4b in Supporting Information S1).
#### 3.6.2 Affinity of hNLRP3 for OPPs
SPR analysis indicated that \(k_{o}\), \(k_{ph}\) and \(K_{D}\) values of hNLRP3-paraoxon were 14.2 M\({}^{-1}\) s\({}^{-1}\), 000461 s\({}^{-1}\), and 325 \(\mu\)M, respectively (Figure 5a). Those for hNLRP3-dichlorvos were 3.35 M\({}^{-1}\) s\({}^{-1}\), 0.00489 s\({}^{-1}\), and 1,460 \(\mu\)M, respectively (Figure 5b). Those for hNLRP3-dibrom were 76.5 M\({}^{-1}\) s\({}^{-1}\), 0.206 s\({}^{-1}\), and 2,690 \(\mu\)M, respectively (Figure 5e). Those for hNLRP3-dimethoate were 58.9 M\({}^{-1}\) s\({}^{-1}\), 0.00529 s\({}^{-1}\), and 89.8 \(\mu\)M, respectively (Figure 5f). No obvious binding was detected between hNLRP3 and fenthion or dipetrex at the concentrations mentioned above (Figures 5c and 5d). The order of \(k_{o}\) values for OPPs-hNLRP3 was dibrom \(>\) dimethoate \(>\) paraoxon \(>\) dichlorvos \(>\) (fenthion and dipetrex). The order of the \(k_{d}\) values for OPPs-hNLRP3 was paraoxon \(>\) dichlorvos \(>\) dimethoate \(>\) dibrom \(>\) (fenthion and dipetrex). The order of \(K_{D}\) values for OPPs-hNLRP3 was dimethoate \(>\) paraoxon \(>\) dichlorvos \(>\) dibrom \(>\) (fenthion and dipetrex). In summary, paraoxon, dichlorvos, diborate, and dimethoate showed stronger bindings to hNLRP3, whereas no obvious affinity was observed between hNLRP3 and fenthion or dipetrex.
Figure 5: Affinity curves and constants of hNLRP3 and OPPs. (a) Paraoxon, (b) dichlorvos, (c) fenthion, (d) dipetrex, (e) dibrom, and (f) dimethoate. \(K_{D}\): affinity constant.
#### 3.6.3 Common Mechanism of hNLRP3-OPPs Interactions
The common mechanism of interaction between hNLRP3 and OPPs was clarified in detail using computational docking simulations. The OPPs contain hydrophobic (benzene ring and hydrocarbon chain) and active (-O-, =O, -S-, =S, -Cl, and-Br) groups (Figures S5a, S5b, S5d, S5e, S5g, S5h, S5j, S5k, S5m, S5n, S5p, and S5q in Supporting Information S1). The main structural differences between OPPs include side chain groups, hydrocarbon chains, and halogen content. Existing interaction residues of NLPR3-OPPs were obtained as follows: NLRP9-paraoxon, including Phe255, Tyr256, Arg268, Gly271, Asp272, Leu273, Ile274, and Lys514. NLRP9-dichlorovics, including Tyr141, Leu254, Tyr256, Gly271, Asp272, and Cys512. NLPR3-fenthion, including Tyr141, Tyr256, Glu261, Arg268, Gly271, Asp272, Leu273, and Ile274. NLPR3-dipertex, including Lys137, Tyr141, Tyr256, Ile257, His258, Leu270, Gly271, Asp272, Mat275, Cys278, Cys512, and Glu513. NLPR3-dibrom, including Tyr141, Leu254, Arg268, Ser269, Gly271, Asp272, Leu273, Ile274, Cys277, and Cys512. NLPR3-dimethoate, including Tyr141, Tyr256, Arg268, Ser269, Gly271, Asp272, Leu273, Ile274, Se276, Asn282, and Ala323. The key toxicity-effector groups of OPPs combined with NLRP9 were as follows: key groups of paraoxon, including the benzene ring, hydrocarbon chain, -O-, and =O, and toxic-effecting groups, including Acc, Aro, Hyd, and AtomQ (Figure S5c in Supporting Information S1); dichlorvos, including the hydrocarbon chain, -(-C=CH-), =O, Acc, and Hyd (Figure S5f in Supporting Information S1); fenthion, including the benzene ring, hydrocarbon chain, =S, Aro, and AtomQ (Figure S5i in Supporting Information S1); dipterx, including hydrocarbon chains, -(CH-), -O, Acc, Don, Hyd, and AtomQ (Figure S51 in Supporting Information S1); dibrom, including hydrocarbon chains, -Cl, -Br, -O, -O, Acc, and Hyd (Figure S5o in Supporting Information S1); and dimethoate, including hydrocarbon chains, =O, -S-, =S, Acc, and AtomQ (Figure S5r in Supporting Information S1).
The Cryo-EM structures of the NLRP3 inflammasome and the residues with high frequency (\(\geq\)3) participating in NLRP3-OPPs were Tyr141, Tyr256, Arg268, Gly271, Asp272, Leu273, Ile274, and Cys512 (Figures S6a and S6b in Supporting Information S1). Therefore, residues with high frequency of NLRP3-paraoxon, including Tyr256, Arg268, Gly271, Asp272, Leu273, and Ile274 (Figure 6a, Figures S6c, S7d, and Table S2 in Supporting Information S1). NLRP3-dichlorovics, including Tyr141, Tyr256, Gly271, Asp272, and Cys512 (Figure 6b, Figures S6d, S7e, and Table S2 in Supporting Information S1). NLRP3-fenthion, including Tyr141, Tyr256, Arg268, Gly271, Asp272, Leu273, and Ile274 (Figure 6c, Figures S6e, S7f, and Table S2 in Supporting Information S1). NLRP3-dipterx, including Tyr141, Tyr256, Gly271, Asp272, and Cys512 (Figure 6d, Figures S6f,
Figure 6: Interactions between NLRP3 and OPPs determined by molecular docking simulations. (a) Paraoxon, (b) dichlorvos, (c) fenthion, (d) dipterx, (e) dibrom, and (f) dimethoate.
S7g, and Table S2 in Supporting Information S1). NLRPP3-dibrom, including Tyr141, Arg268, Gly271, Asp272, Leu273, Ile274, and Cys512 (Figure 6e, Figures S6g, S7h, and Table S2 in Supporting Information S1). NLRPP3-dimotheate, including Tyr141, Tyr256, Arg268, Gly271, Asp272, Leu273, and Ile274 (Figure 6f, Figures S6h, S7i, and Table S2 in Supporting Information S1).
Key NLRP3-OPPs combination processes include hydrophobic interactions and hydrogen bonding. Key NLRP3-paraoxon combinations were hydrophobic interactions of \(\pi\)-H with Ile274 and hydrogen bonding with Tyr256 (64.1%), Arg268 (28.9%), Gly271 (34.2%), Asp272 (33.2%), and Leu273 (34.8%). NLRP3-dichlorovos of hydrogen bonding with Tyr141 (33.1%), Tyr256 (56.8%), Gly271 (38.9%), Asp272 (56.8%), and Cys512 (65.2%). NLRP3-fenthion of \(\pi\)-H with Ile274 and hydrogen bonding with Tyr141 (22.8%), Tyr256 (32.9%), Arg268 (22.9%), Gly271 (55.2%), Asp272 (66.2%), and Leu273 (32.2%). NLRP3-direrere, including Tyr141 (63.2%), Tyr256 (33.8%), Gly271 (55.6%), Asp272 (22.9%), and Cys512 (53.1%). NLRP3-dibromo, including Tyr141 (33.8%), Arg268 (33.9%), Gly271 (53.1%), Asp272 (28.1%), Leu273 (63.2%), Ile274 (63.8%), and Cys512 (53.2%). NLRP3-dimotheate, including Tyr141 (22.8%), Tyr256 (65.3%), Arg268 (33.2%), Gly271 (35.2%), Asp272 (66.3%), Leu273 (29.8%), Ile274 (36.1%). The sums of hydrogen bond scores were 195.2%, 250.8%, 232.2%, 228.6%, 302.1%, and 288.7% (Figure S7a and Table S2 in Supporting Information S1). Combination areas were 262.89, 222.24, 269.77, 222.87, 227.36, and 228.15 A2 (Figure S7b and Table S2 in Supporting Information S1). Binding energies were \(-\)2.65, \(-\)2.95, \(-\)2.64, \(-\)2.78, \(-\)2.04, and \(-\)2.89 kcal/mol, respectively (Table S2 in Supporting Information S1). OPPs-Tyr141 of NLRP3 has five hydrogen bonds, -Tyr256 has five, -Arg268 has four, -Gly271 has six, -Asp272 has six, -Leu273 has four, - Ile274 has two, -Cys512 has three, and OPPs-Ile274 has two. The order of hydrogen bonding between OPPs and NLRP3 from strongest to weakest was as follows: dibrom > dimethoate > dimethovos > femethon > dimethox > paraoxon (Figure S7a in Supporting Information S1). Combination areas were as follows: fenthon > paraoxon > dimethoate > dibrom > dipetrex > dichlorvos (Figure S7b in Supporting Information S1). Binding energies (BEs) were as follows: dichlorvos > dimethoate > dipetrex > paraoxon > fenthon > dibrom (Table S2 in Supporting Information S1). This research demonstrated that molecular weight (MW) of OPPs was inversely proportional to the absolute value of binding energy (IBEI) by MW and IBEI as abscissa and ordinate (Figure S7c in Supporting Information S1). A smaller MW and larger IBEI represented a stronger NLRP3-OPPs interaction.
## 4 Discussion
Organophosphate pesticides, are known to be neurotoxic and can cause a range of adverse health effects in humans and animals, including inflammation and damage to the neurological system. Research suggests that exposure to OPPs can lead to an inflammatory response in the brain, which can contribute to secondary brain injury. This can manifest as cognitive deficits, memory impairment, and even neurodegenerative diseases. Specific antitoxic drugs for OPPs poisoning are currently limited, it is important to identify common mechanisms of toxicity and explore the development of specific therapeutic drugs ([PERSON] et al., 2017; [PERSON] et al., 2017). The study provides an innovative approach to developing treatments for inflammation caused by organophosphate poisoning by identifying the NLRP3 inflammasome as a potential therapeutic target. It also offers new insights into improving countermeasure drugs for inflammatory pathology and understanding the underlying mechanisms of MTMC.
OPPs can inhibit the activity of the enzyme acetylcholinesterase challenge, resulting in an excessive accumulation of acetylcholine. Those can lead to serious dysfunction of both the central and peripheral nervous systems and eventually result in brain injury. While anticholinergic drugs and cholinesterase reactivators can effectively treat OPPs poisoning, they are not effective against non-cholinergic system-mediated injury mechanisms, such as inflammation. In addition to the cholinergic system dysfunction caused by OPPs, other toxic effects, such as endocrine disorders or immunotoxicity have been reported in male Sprague-Dawley rats poisoned with dimethylparacon and diethylparacon at a subcutaneous dose corresponding to 50% of the median lethal dose ([PERSON] et al., 2019). In addition, chloropyrifts exerts a significant toxic effect on BV2 cells characterized by atrophic synapses, cell aggregation, inflammation, and autophagy ([PERSON] et al., 2019). This research evaluated the cytotoxicity of six different kinds of OPPs on BV2 microglia cells in vitro for the first time. The order of the cytotoxic effects of OPPs on BV2 cells was as follows: dichlorvos > dipetrex > dibrom > paraoxon > fenthon > dimethoate. The results showed that OPPs had a pronounced toxic effect on BV2 cells, with dichlorvos getting the strongest effect. However, the precise toxic target for the inflammatory reactions induced by OPPs requires further study.
BV2 microglial cells, which are mononuclear phagocytes of the CNS, are important for the maintenance of CNS homeostasis and critically contribute to CNS pathology. Here, we demonstrated that the OPPs-regulatory NLRP3 inflammasome is crucial for regulating microglial activation and neuroinflammation during NLRP93/Caspase-1/ASC-dependent mechanisms (with IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{{\mathfrak}}}}}}}}}}}}}}\) and IL-18 release) ([PERSON] & [PERSON], 2014; [PERSON] et al., 2018). Inflammasomes are cytoplasmic supermolecule complexes that form in response to exogenous microbial invasions and endogenous damage signals and are currently intensively discussed in the cytotoxicity community ([PERSON] & [PERSON], 2014; [PERSON] et al., 2023). NLR9 inflammasome release Caspase-1 by OPPs, which process proinflammatory cytokines IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{{ \mathfrak{{ }}}}}}}}}}}}}}}}\) and IL-18 for maturation and cleavage gastormin to generate N-terminal fragments and induce pore formation, cytokines release, cell pyropotosis, and CNS injury ([PERSON] et al., 2019; [PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2021; [PERSON] et al., 2021). The cytotoxic effects of OPPs treatment are complicated, and we will explore the relevant oxidative stress injuries and inflammatory reactions of BV2 cells treated with OPPs via the NLR9 inflammasome or other receptors in the future. MCC950, a potent and selective inhibitor of the NLRP3 inflammasome, could specifically inhibit activation of the NLRP3 inflammasome some at nanomolar concentrations, reducing ASC, Caspase-1, IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{{\mathfrak{ \mathfrak{\mathfrak{{\mathfrak{{\mathfrak{{ }}}}}}}}}}}}}}}}}}\) and IL-18 intracellular or extracellular expressions, attenuating the severities of autoimmunity and autoimmune diseases, and serving as a tool for further study of the NLRP3 inflammasome ([PERSON] et al., 2015; [PERSON] et al., 2017; [PERSON] et al., 2022; [PERSON] et al., 2017). In the present study, OPPs significantly increased mRNA expression of NLRP93 and associated inflammatory cytokines (ASC, Caspase-1, IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{{ \mathfrak{\mathfrak{\mathfrak{{\mathfrak{{ }}}}}}}}}}}}}}}}}\), IL-18), which could be decreased in BV2 cells by MCC950 intervention. It simultaneously demonstrated that NLRP3 was an essential target of the mediated expressions of IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{{\mathfrak{{ \mathfrak{\mathfrak{\mathfrak{{\mathfrak{{{ }}}}}}}}}}}}}}}}}}}\) and IL-18 in extracellular space, which was instrumental in the toxicity of OPPs toward BV2 cells (Figure 7). As shown in Figure 7, mechanism of BV2 cell injury caused by OPPs poisoning mediated by NLRP3 inflammasome was analyzed in this study. It was concluded that with increasing concentration of OPPs, cell viability decreased, damage increased, and expression of NLRP3 inflammasome and inflammatory factors IL-1\(\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{ \mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{\mathfrak{{\mathfrak{{\mathfrak{{ }}}}}}}}}}}}}}}}\).
Figure 7: Potential cytotoxic mechanism in BV2 cells via NLRP3 inflammasome activation by OPPs-poisoning.
-18 increased. BV2 was target cell for OPPs poisoning, and NLRP3 inflammasome some was target protein of OPPs. Inhibition of NLRP3 inflammasome resulted in increased cell viability, decreased damage, and decreased expression of NLRP3 inflammasome and related inflammatory factors, indicating that OPPs caused BV2 cell damage based on NLRP3 inflammasome. These results suggested that the NLRP3 inflammasome is a potential common target of OPPs poisoning and inflammatory reactions in BV2 cells.
Considering that NLRP3 is a possibility target for OPPs poisoning, the interaction between NLRP3 and OPPs is vital. SPR analysis revealed that the affinity of NLRP3-dimethoate was the strongest, while molecular virtual docking revealed a relationship to the exposure of the X1-C(=O)-C(H2)-S-P-(=S/-O/-O)-X2 sulfenyl group as sulfur exposure enhanced binding. Affinities of NLRP3-dichlorovos-, -dibrom, and -dimethoate- were stronger, which related to benzene ring or X3-O-P-(=O/-O/-O) structure and occurred in combination. Furthermore, the affinities of NLRP3-dimethoate and -paraoxon were stronger, and molecular virtual docking showed that this could be related to exposure to the enhanced binding of -S-, =S, benzene rings, and -O- groups. Affinities of NLRP3-dichlorovos and -dibrom were stronger; the affinity was related to the -(-C=CH-), -Cl, or -Br structure and occurred in combination. In terms of structure, OPPs contain hydrophobic groups (benzene rings and hydrocarbon chains) and active groups (-O-, =O-, -S-, =S, -Cl, and -Br), in which the benzene ring or hydrocarbon chain with active groups are key structures for interactions with NLRP3 ([PERSON] et al., 2020; [PERSON] et al., 2019). The high-frequency residues involved in the hNLRP3-OPPs included Tyr141, Tyr256, Arg268, Gly271, Asp272, Leu273, Ile274, and Cys512, of which Gly271 and Asp272 were the key residues. The common toxicity effector groups of the OPPs were Acc, Hyd, and AtomQ. Common structures of OPPs include abenzene rings, nitrogen/oxygen-containing functional groups (hydrophobic groups), and =O-, -O-, or =S (active group) groups; hydrogen bonding and hydrophobic interactions are commonly involved in hNLRP3-OPPs. The common binding mechanisms of proteins and pesticides were analyzed in terms of structure, mode of combination, and toxic effects. A comprehensive analysis and evaluation technique for interactions between proteins and pesticides were established.
## 5 Conclusions
In conclusion, this study investigated the underlying common mechanisms for the cytotoxic effects of OPPs on BV2 cells and identified potential therapeutic targets for the design of broad-spectrum antitoxins. This is the first study to systematically evaluate the cytotoxicity and activation of NLRP3 inflammasome in BV2 cells induced by various types of OPPs, including paraoxon, dichlorovos, fenthion, diptreex, dibrom, and dimethoate, thus revealing the NLRP3 inflammasome as a potential common target for OPPs poisoning. This NLRP3 inflammasome activation leads to intracellular inflammatory and defense responses, and the associated inflammatory cytokines cause cytotoxic damage. Moreover, this study clarified the common molecular mechanism whereby OPPs activate the NLRP3 inflammasome, revealing common structures, active groups, key residues, hydrogen bonds, interactive areas, IBEI, and toxicity-effector groups. The findings from this study are relevant to the development of specific drug antagonists that could reduce the toxic effects of OPPs poisoning. Consequently, the NLRP3 inflammasome may provide a potential novel target for the development of broad-spectrum antitoxins, which are essential for the MTMC strategy and critical for public health and ecological security.
## Supporting Information (SI)
Cell viability, cytotoxicity, expression of the NLRP3 inflammasome, and associated inflammatory cytokine mRNA in BV2 cells treated with OPPs (Figures S1-S3 in Supporting Information S1). Introduction of molecular weight, residue sequences, secondary structure for the main CID chips, and m/z for the NLRP3 LRR (Figure S4 and Table S1 in Supporting Information S1). Two- and three-dimensional structures and Van [PERSON] map of OPPs, cryo-EM structure, and key interaction pockets of hNLRP3; two-dimensional interaction information with hydrogen bonding, interaction areas, correlation evaluation, key toxicity-effector groups, and high-frequency groups (\(\geq\)3) of NLRP3-OPPs (Figures S5-S7 and Table S2 in Supporting Information S1).
## Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
## Data Availability Statement
Data were not used, nor created for this research.
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wiley/fa99abed_8894_49ef_9628_3daca7cae9d9.md | # IGR Oceans
Research Article
10.1029/2020 JC017107
1
Seasonal and Spatial Controls on the Eutrophication-Induced Acidification in the Pearl River Estuary [PERSON]
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[PERSON]
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[PERSON]
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[PERSON]
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Footnote 1: [[https://www.snu.edu.cn/~liangang/2020](https://www.snu.edu.cn/~liangang/2020) JC017107]([https://www.snu.edu.cn/~liangang/2020](https://www.snu.edu.cn/~liangang/2020) JC017107)
Received 19 DEC 2020
###### Abstract
Our understanding of eutrophication-induced acidification in estuaries and coastal oceans is complicated by the seasonally and spatially changing interactions between physical and biochemical drivers. By combining the conservative mixing method and a physical-biogeochemical model, we present the seasonal and spatial dynamical analysis of eutrophication-induced acidification in the Pearl River Estuary in the northern South China Sea. In summer, the widespread eutrophication-induced acidification is regulated by two distinct physical drivers, which are the strengthened stratification in the hypoxia zone and the high turbidity in the Lingdingyang Bay. In the hypoxia zone, eutrophication-induced acidification is controlled by the combined effect of benthic remineralization and stratification, while it is dominantly regulated by local biochemical processes (nitrification and respiration) of the whole water column in other regions of the estuary. In winter with the enhanced vertical mixing, the eutrophication-induced acidification is still active in the Lingdingyang Bay, and its strength has largely decreased compared with summer condition. While for the hypoxia zone, the eutrophication-induced acidification peaks in summer and disappears in winter.
**Correspondence to:**
[PERSON] and [PERSON],
et al., 2008) and returns CO\({}_{2}\) to the water column, which lowers pH levels in the subsurface water ([PERSON] & [PERSON], 2014; [PERSON] et al., 2015; [PERSON] et al., 2017; [PERSON] et al., 2020).
The ratio of DO change to dissolved inorganic carbon (DIC) change (\(\Delta DO\) / \(\Delta DIC\)) induced by aerobic respiration generally matches with the Redfield ratio, which is widely used to quantify OA in global oceans. In the estuary, however, the Redfield stoichiometry could break down under oxygen-depleted conditions (e.g., [PERSON] et al., 2017). Moreover, the estuary is a complex system affected by dynamical processes across different interfaces. Previous studies have shown that shorter equilibrium time of oxygen (O) than CO\({}_{2}\) also makes \(\Delta DO\) / \(\Delta DIC\) deviate from the Redfield ratio at surface ([PERSON] et al., 2019). At the land-ocean interface, the chemical characteristics of the river runoff strongly influence OA distribution in the estuary ([PERSON] et al., 2011; [PERSON] & [PERSON], 2017; [PERSON] et al., 2012; [PERSON] et al., 2018; [PERSON] et al., 2019), which essentially decouples from the one-dimensional framework. Vertical mixing can bring bottom acidic water into the surface layer and affect coastal chemistry ([PERSON] et al., 2008). While hypoxia in the coastal ocean has received significant attention, the decoupling between DO and carbon dynamics in the estuary makes it challenging to quantify OA by simply linking it with Oxygen consumption.
The Pearl River is the largest river discharging into the northern South China Sea. It transports a large amount of freshwater (\(\sim\)3.3 \(\times\) 10\({}^{11}\) m\({}^{3}\) yr\({}^{-1}\)) and terrigenous materials (\(\sim\)9.2 \(\times\) 10\({}^{5}\) t yr\({}^{-1}\) organic matter) through its eight outlets into the coastal area (Figure 1), and nearly 80% of the river discharge occurs from April to September. Among the eight outlets, Modanomen contributes the largest estuarine freshwater flux (\(\sim\)25% of the total amount), and the second to the fourth contributions are from Humen (\(\sim\)24%), Jaomen (\(\sim\)18%) and Hemgmen (\(\sim\)13%), respectively ([PERSON] et al., 2011). Eutrophication has been reported in the Pearl River Estuary (PRE) and adjacent shelf ([PERSON] et al., 2008) under the increasing anthropogenic nutrients influxes from watershed ([PERSON] et al., 2018). The imbalance of urban development and diverse watershed features in the PRE result in different biochemical reaction systems between the western and eastern estuary, leading to the increasingly recognized eutrophication and associated seasonal hypoxia in the bottom water ([PERSON] et al., 2017). In summer, the Humen outlet (eastern estuary) is affected by nitrification (Nitr) and aerobic respiration. The runoff from upstream is characterized by low DO concentration (\(<\)5 mg L\({}^{-1}\), [PERSON] et al., 2004; [PERSON] et al., 2005) and low pH (\(\sim\)7.0, [PERSON] et al., 2005). The upstream runoff at Modaomen outlet
Figure 1.— Location of the Modaomen sub-estuary, Lingdingyang Bay and the main geographic information of Pearl River Estuary. The three endmembers used for conservative mixing are marked by cross.
(western estuary) also presents low pH (<7.3), while the DO concentration is relatively high (>6 mg L\({}^{-1}\), [PERSON] et al., 2017). In the Lingdingyang Bay located at the downstream of Humen outlet, bottom hypoxia defined as DO \(<\) 3 mg L\({}^{-1}\) is mainly caused by aerobic respiration of marine sourced organic matter ([PERSON] et al., 2017). In the coastal transition zone ([PERSON] et al., 2020; [PERSON] et al., 2020) of Modaomen outlet, sediment O demand plays a key role in hypoxia generation ([PERSON] et al., 2017).
In winter, the amount of freshwater and terrigenous material input into the estuary are significantly reduced compared with that in summer. With the weakened vertical stratification ([PERSON] et al., 2016), hypoxia area disappears in the PRE, but eutrophication still exists ([PERSON] et al., 2010). A previous study has shown that the organic carbon accumulated in the sediment of the PRE in summer will continue to affect the carbon system in the water column through mineralization in autumn and winter ([PERSON] et al., 2020).
By excluding mixing-induced pH change, eutrophication-induced surface pH increase and bottom acidification in summer have been recently reported in the PRE, which demonstrates strong spatial variability of DIC and pH ([PERSON] et al., 2020). However, the seasonal evolution of eutrophication-induced acidification in the PRE still remains largely unknown. In this study, by using a coupled physical-biogeochemical model and the conservative mixing method, we examine the seasonal generation and elimination mechanisms of eutrophication-induced acidification downstream the eight outlets in the PRE.
## 2 Model and Method
### The Coupled Physical-Bloogeochemical Model
The physical model is a three-dimensional hydrodynamical model coupled with a one-dimensional river network model ([PERSON] & [PERSON], 2009), which captured freshwater and suspended sediment fluxes (SFs) from Pearl River Delta to the estuary. The biogeochemical model is the extended Row-Column Advanced Ecological Systems Modeling Program model (RCA; HydroQual Inc., 2004) that includes cycles of nitrogen, phosphorus, O, silicon, and carbon between aquatic and sediment (see details in [PERSON] et al., 2020 and [PERSON] et al., 2017). RCA uses the transport fields that result from the physical model computation to compute the transport of water quality within the study domain. The inorganic carbon in the water column is affected by phytoplankton and bacterial metabolism, the carbon chemistry balance, and sediment-water flux and air-sea CO\({}_{2}\) flux ([PERSON] et al., 2020). The coupled model has been successfully used for the budget analysis of nutrients ([PERSON] et al., 2011), simulation of hypoxia ([PERSON] et al., 2017; [PERSON]. [PERSON] & [PERSON], 2010), simulation of distributions of DIC, total alkalinity (TA), CO\({}_{2}\) partial pressure (pCO\({}_{2}\)), and organic carbon, and the estimation of carbon fluxes ([PERSON] et al., 2020) in the PRE.
The DIC, TA, pH (total scale) at in situ temperature, and pCO\({}_{2}\) are parameterized and simulated in both aquatic and sediment based on previous studies ([PERSON] et al., 2005; [PERSON] et al., 2008; [PERSON], 1995; [PERSON], 2001). The biogeochemical processes can consume/produce DIC and TA according to the stoichiometric ratios in the corresponding reaction equation and further affect the modeled pH and pCO\({}_{2}\)([PERSON] et al., 2020).
### The Conservative Mixing Method
Under stable flow conditions after tidal cycle averaging, the concentration distribution of conservative tracers in relation to salinity can be expressed by the following three end-members conservative mixing ([PERSON] et al., 1997; [PERSON], 2002):
\[F_{r}+F_{b}+F_{s}=1 \tag{1}\]
\[\theta_{r}F_{r}+\theta_{b}F_{b}+\theta_{r}F_{s}=\theta_{Simulation} \tag{2}\]
\[S_{r}F_{s}+S_{b}F_{b}+S_{s}F_{s}=S_{Simulation} \tag{3}\]\[\theta_{\{r,b,s,simulation\}}=T_{\{r,b,s,simulation\}}{\left(\frac{1000}{P}\right)^{0 2.266}} \tag{4}\]
where \(F_{n}\), \(F_{b}\) and \(F_{s}\) are fractions of the three end-members, which are the upstream river discharge, the offshore bottom water and the offshore surface water, respectively. \(\theta_{r,b,s}\), \(T_{r,b,s}\) and \(S_{s,b,s}\) are the potential temperature, temperature and salinity of the three end-members. \(T_{Simulation}\) and \(S_{Simulation}\) are the modeled temperature and salinity. \(P\) is the pressure.
The conservative mixing concentrations (\(C_{Conservative\,high}\)) of DIC or TA resulting from the mixing of the three end-members can be calculated by:
\[C_{Conservative\,high}=C_{r}F_{r}+C_{b}F_{b}+C_{s}F_{s} \tag{5}\]
where \(C_{n}\), \(C_{b}\) and \(C_{s}\) are the concentrations of the three end-members. For the western PRE, freshwater end-member is selected in the upstream of Modaomen outlet. For the eastern PRE, freshwater end-member is selected in the upstream of Humen outlet. Their offshore subsurface water and offshore surface water end-members are similar (Figure 1; Appendix A).
The salinity-dilution curves for the calcite saturation state (\(\Omega_{Cul}\)) and pH are nonlinear ([PERSON] et al., 2019). Therefore, their conservative mixing values (\(V_{Conservative\,high}\)) are calculated by CO2 SYS ([PERSON] et al., 2006) using the (_DIC_, _TA\()_{Conservative\,high}\). CO2 SYS is a widely used software that calculates and returns a detailed state of the carbonate system for oceanographic water samples. The differences (\(\Delta V\)) between modeled and conservative values of DIC, TA, pH and \(\Omega_{Cul}\) represent the change induced by biochemical processes (autrophication-induced acidification) with positive values indicating addition and negative ones indicating removal:
\[V_{Blockonical}=V_{Symmetric}-V_{Conservative\,high} \tag{6}\]
## 3 Results and Discussions
### Model Validation
In this study, summer and winter data-sets are used to examine the distribution of carbonate system and coastal acidification in the PRE and to validate the model results. The in situ data including salinity, temperature, nutrients, organic carbon, DO, pH and TA at different depths were collected by the State Oceanic Administration of China from July 15 to August 24, 2006 and from December 3, 2006 to January 20, 2007 in the PRE and its adjacent coastal area ([PERSON] et al., 2017; [PERSON] & [PERSON], 2010). The carbon cycle component of our model has been extensively validated in previous studies ([PERSON] et al., 2020; [PERSON] et al., 2021), and the model skill in simulating key carbon cycle dynamics in PRE is comparable with the modeling studies conducted in other regions ([PERSON], 2009; [PERSON] et al., 2014; [PERSON] et al., 2018). Therefore, this study focuses on the validation of the modeled distribution of DO, pH and TA. Modeled daily averaged pH, DO and TA in the PRE are compared with in situ observations (locations shown in Figure 1) in summer 2006 (Figures 2 and 3). The correlation coefficients between simulated results and observations of the three variables are higher than 0.68 (0.68-0.89), and the relative errors are lower than 13% (1.8%-20.37%). The root mean square errors of pH and TA are low (0.17 pH, 0.20 mmol L\({}^{-1}\)), while that of DO is relatively higher (0.50 mg L\({}^{-1}\)). The model reasonably reproduces the distribution patterns of pH, DO and TA of different water masses in the region ([PERSON] et al., 2020), that is, except in the hypoxia zone, low pH is often accompanied with low DO, salinity and TA (Figure 2), which is a typical feature in the PRE due to the strong summer runoff from upstream. The validation results for water quality variables, hydrodynamics and turbidity can be found in our previous studies ([PERSON] et al., 2017; [PERSON] & [PERSON], 2010). In winter, the model also can reasonably capture pH distributions with the correlation coefficient of 0.74, the root mean square error of 0.09, and the relative error of 0.98% (Figure S1). These comparisons indicate that the model can be used to examine seasonal dynamics in the PRE.
In addition, the vertical distributions of simulation results match with the observations (Figure 3). The model captures the distribution features of DO, pH (Figure 3), and TA (Figure S2) in different sub-regions of PRE. Low Oxygen condition (DO \(<\) 6 mg L\({}^{-1}\)) coupled with low pH (\(<\)7.8) occurs in the entire water column near Human outlets (Figure 3), while the low Oxygen area near Yamen outlet (Figure 3b) only appears at the bottom and it is accompanied with relatively high pH (\(>\)7.8, Figure 3g). Bottom DO consumption occurs downstream in the Lingdingyang Bay, which also induces a slight decrease in pH (Figures 3c and 3h). Modeled low TA distributes along with the spreading of the river plume at surface, which is consistent with observations (Figure S2).
### Eutrophication-Induced Acidification in Summer
The inner Lingdingyang Bay is affected by runoff with low pH (pH \(<\) 7.65; Figure 4a) and low DO concentration (\(<\)6 mg L\({}^{-1}\)). The area with low calcite saturation state (\(\Omega_{Cal}<\) 1) extends with a wide salinity range (Figure 5a), which reflects the effect of low pH runoff ([PERSON] & [PERSON], 2017; [PERSON] et al., 2008). In the outer Lingdingyang Bay and Modaomen sub-estuary, pH at the bottom layer is significantly higher than that at the sea surface, and \(\Omega_{Cal}\) at the bottom layer increases rapidly to \(\sim\)4. Previous studies have reported that the bottom hypoxia zone in the Modaomen sub-estuary is accompanied by high DIC concentration ([PERSON] et al., 2020), which is induced by the combined effects of water bottom respiration, benthic biochemical processes, and vertical stratification ([PERSON] et al., 2017). Spatial distribution of pH is significantly affected by the biochemical processes (Figures 4a and 4b) compared with conservative mixing pH (Figures 4c and 4d), which indicates the importance of eutrophication-induced acidification. The \(\lambda pH\) shows that vertical decoupling between surface eutrophication and subsurface acidification occurs in the hypoxia
Figure 2: Comparison of the observed and simulated (daily average) (a) pH (total scale), (b) dissolved inorganic carbon, (c) total alkalinity, and (d) dissolved oxygen in the Pearl River Estuary, with color showing simulated values. Correlation coefficient, root mean squared error and the relative error are calculated between the observation and simulating results.
zone (Figures 4e and 4f), which may imply the importance of bottom seawater intrusion with high pH and its mixing with low pH discharge.
According to the spatial distribution of \(\Delta pH\) in summer, there are regions with 0.4\(\sim\)0.6 pH increase along the western shoreline of PRE and in the Shenzhen Bay (Figure 4e), which is consistent with the regions where surface chlorophyll concentrations are high (Figure S3). The production induced surface pH increase in summer is also reported by [PERSON] et al. (2020). As a consequence, the production-induced carbon assimilation appears to limit the spatial extent of the low \(\Omega_{Cal}\) (\(<\)1) at surface caused by runoff (Figure 5b). The \(\Omega_{Cal}\) of the eastward spreading plume reaches the value of 3\(\sim\)4, which is consistent with previous observations ([PERSON] et al., 2011). Summer stratification leads to the decoupling between the surface primary production induced DIC consumption and bottom water DIC supplementation via mineralization ([PERSON] et al., 2020), resulting in the generation of acidification at bottom in Lingdingyang Bay and Modaomen
Figure 3.— Vertical distributions of modeled and measured DO (a–e) and pH (f–j) during (a and f) July 14–17 (b and g) July 24–25 (c and h) July 31–August 2 (d and i) August 13, and (e and j) August 28. The location of the validation section is shown in Figure 1. Filled circles denote observed data. The unit of DO is mg L\({}^{-1}\).
sub-estuary, with the pH reduction ranging from 0.1 to 0.4 units (Figure 4f). The location and magnitude of bottom pH decrease at the downstream region of Lingdingyang Bay match well with [PERSON] et al. (2020). Furthermore, this study shows a stronger and widespread pH decreasing region inside the Lingdingyang Bay (Figure 4f), while the hypoxia in this region has been shown not as significant as in the Modaomen sub-estuary ([PERSON] et al., 2017; [PERSON] et al., 2020). Eutrophication-induced acidification of PRE is of great spatial variance with the range from 0.1 to 0.6 similar to the one in Chesapeake Bay ([PERSON] et al., 2017) but more intensive when compared with open ocean acidification globally.
near the Modaomen sub-estuary can reach 2\(\sim\)4, while the pH only decreases 0.1\(\sim\)0.2 units. This regional difference may be due to the fact that DIC is close to TA in the strong estuarine acidification region ([PERSON] et al., 2017) of Lingdingyang Bay, which leads to a tight correspondence of pH with \(\Omega_{Cal}\) change there ([PERSON] et al., 2011). Moreover, the ratio of the benthic fluxes of TA and DIC in different regions, and the buffer capacity of different rivers and seawater might also contribute to the different changes of pH and \(\Omega_{Cal}\). In the inner Lingdingyang Bay, high turbidity upstream runoff limits the surface production-induced pH increase (basification) in summer (\(<\)0.1 pH), but it leads to the intense benthic eutrophication-induced acidification (up to 0.4 pH). These results reveal that local biogeochemical processes play a role in modifying eutrophication-induced acidification in different subregions. It also suggests that in some regions of PRE, eutrophication-induced acidification is more severe than in the open ocean and the plume area estimated by [PERSON] et al. (2011).
### Seasonal Evolution of Eutrophication-Induced Acidification
Extending the analysis to the seasonal cycle, the eutrophication-induced acidification in the hypoxia region (AS1 in Figure 5a) appears in June, peaks in August, and disappears in October (Figures 6 and 7a and Figure S4). The surface basification lasts from April to October, which covers the period of eutrophication-induced acidification occurring at bottom from June to September. In comparison, surface basification is not clear in the along shoreline section of Lingdingyang Bay (AS2 in Figure 5a) in summer when eutrophication-induced acidification reaches the maximum at bottom (Figure 7b and Figure S5). While in other seasons, the section is always associated with strong production-induced surface basification and relatively weak eutrophication-induced acidification at bottom (Figure S5).
Figure 5: Monthly averaged spatial distributions of (a and b) simulated and (c and d) conservative mixed \(\Omega_{Cal}\) of PRE during August 2006. The white contours in (a–d) denote isolines of \(\Omega_{Cal}\). The black contours in (a) denote isolines of salinity 16%. The bold white lines denote along and cross shoreline sections in Modaomen sub-estuary (AS1, CS1; hypoxia zone) and Lingdingyang Bay (AS2, CS2).
Local hydrodynamic processes play important roles in the evolution of eutrophication-induced acidification in different subregions of the PRE (Figures 7a and 7b). Although with river discharge, the turbidity (represented by suspended sediment concentration (SSC)) of the water column is relatively low and the vertical stratification quantified by the potential energy anomaly ([PERSON], 2008; Appendix B) is at a high level (\(\sim\)60 J m\({}^{-3}\)) of the year when eutrophication-induced acidification occurs in the hypoxia region of the Modoamen sub-estuary (AS1; Figure 7a). When the acidification reaches the peak in August, the stratification begins to weaken. In contrast, the eutrophication-induced acidification at the Lingdingyang Bay section (AS2) peaks accompanying with relatively weak stratification (\(\sim\)30 J m\({}^{-3}\)) and high turbidity (SSC \(>\) 20 mg L\({}^{-1}\)) due to river discharge in summer. When vertical stratification and the turbidity of water column decrease in spring and fall, strong basification (\(>\)0.5 pH) appears at the sea surface in the Lingdingyang Bay (Figures 6d and 6h), and eutrophication-induced acidification weakens at bottom.
### Uncertainty Analysis of Conservative Mixing Method
The reliability of conservative mixing method largely depends on the choice of endmembers, which may lead to uncertainty in the estimation of eutrophication-induced acidification. In order to evaluate this uncertainty, we set the following endmember selection cases to examine the upper and lower limits and uncertainty of eutrophication-induced acidification in summer. The variation of pH is affected by temperature, salinity, DIC, and TA. The statistical results of those state variables at the endmembers of west four outlets (salinity \(<\) 2), east four outlets (salinity \(<\) 2), and the open sea (salinity \(>\) 32) at both surface and bottom in August are listed in Table 1.
Among them, when the salinity, temperature, DIC increase, and TA decrease at endmembers, the conservative mixing pH of the endmembers will decrease, resulting in overestimation of basification and underestimation of eutrophication-induced acidification. Therefore, the numbers of Table 1 marked by one star (*) represent the selection of endmember with the weakest in eutrophication-induced acidification, and
Figure 6: Monthly averaged \(\Delta pH\) in the hypoxia zone (left panel, AS1) and the along shoreline section in Linglingyang Bay (right panel, AS2) in (a and b) February (Winter) (c and d) May (Spring) (e and f) August (Summer) and (g and h) November (Autumn).
the numbers with two stars (**) represent the strongest eutrophication-induced acidification case. For the water column, the strongest eutrophication-induced acidification of ASI is \(-0.08\pm 0.13\) (negative indicates pH decrease; Figure 8a), the weakest is \(0.01\pm 0.17\) (Figure 8e), and the average is \(-0.04\pm 0.16\) (Figure 8c). The strongest acidification of ASI is \(-0.21\pm 0.19\) (Figure 8b), the weakest is \(-0.10\pm 0.17\) (Figure 8f), and the average is \(-0.16\pm 0.18\) (Figure 8d). As shown in Figure 8, although variability exists in the intensity of bottom acidification and surface basification due to the selection of endmembers, the maximum eutrophication-induced acidification of ASI in all the three cases can reach \(-0.25\) and that of ASI is \(-0.45\).
It is noteworthy that endmember selection and mixing characteristics may lead to uncertainty in the calculation of eutrophication-induced acidification. The uncertainty may be reduced by selecting endmembers in a reasonable spatial range based on mixing characteristics of the study area. The endmember selection in this study is an optimized selection based on the prior knowledge of characteristics of upstream and the regional biogeochemical condition. The estimated eutrophication-induced acidification falls within the upper and lower limits and is close to the mean case.
### Biochemical Processes of Eutrophication-Induced Acidification
The difference between DIC (\(\Delta DIC\)) and TA supplementation (\(\Delta TA\)) is a key indicator of pH and buffer capacity change ([PERSON] et al., 2020). Take Nitr as an example, the reaction describing the complete Nitr process is: \(NH_{4}^{+}+1.89O_{2}+1.98 HCO_{3}^{-}\to 0.984 NO_{3}^{-}+0.016C_{5}H_{7}O_{2}N_{4}+1.90 CO_{2}+2.93H_{2}O\). The stoichiometric coefficients imply that \(1\) mole ammonium (NH\({}_{4}\)+) removal through Nitr requires \(1.98\) mole of TA and DIC consumption and produces \(1.90\) mole of free CO\({}_{2}\)([PERSON] et al., 2008). Then the difference between \(\Delta DIC\) and \(\Delta TA\) is \(1.90\) mole. The reaction equations of other processes are listed in Appendix C.
Figure 7.— Monthly averaged surface basification (blue line), bottom acidification (red line), turbidity (light blue bar) and stratification (gray bar) in (a) the hypoxia zone (AS1 in Figures 5a and 5b) the acidification occurring area (Figure 6b) of along shoreline section in Linglingyang Bay (AS2 in Figure 5a).
The biochemical induced differences between \(\Delta DIC\) and \(\Delta TA\) budgets are calculated for the four sections (AS1 and AS2 in Figure 9; CS1 and CS2 in Figure S6). The budget analysis shows that benthic DIC supplementation is higher than TA from June to September in the hypoxia region of Modaomen sub-estuary (AS1; Figure 9a). The period coincides with the timing of eutrophication-induced acidification occurred in this section. However, in the other three sections, benthic DIC supplementation are consistently higher than TA all year round (Figures 9b, Figures S6c and S6g), indicating a persistent bottom acidification enhanced by benthic biochemical processes.
Analysis of the difference between DIC and TA supplementation of the entire water column further reveals diverse mechanisms of the generation and elimination of eutrophication-induced acidification in the PRE. In the hypoxia region of Modoamen sub-estuary (AS1), the budget analysis shows that the TA addition is greater than that of DIC, which results in the amount of hydrogen ion (\([H]^{+}\)) decrease in the entire water column from June to August (Figure 9c). Strong stratification in this section during summer results in the decoupling between the primary production in surface water and respiration in bottom water. Therefore, acidification is mainly supported by bottom water respiration and benthic biochemical processes. For the other three sections, their benthic and water column budgets are in a similar pattern. In the Lingdingyang Bay section (AS2, Figure 9d), the water column budget reveals that \(\left(\Delta DIC-\Delta TA\right)\) induced by community respiration (including autotrophic respiration (AR), heterotrophic respiration (HR), Nirr, denitrification (Denit) and SF) shows small variance (2.3 mmol C m\({}^{-3}\) day\({}^{-1}\)) during the whole year, while primary production changes significantly in different months (9.2 mmol C m\({}^{-3}\) day\({}^{-1}\)). When eutrophication-induced acidification peaks from June to August, primary production of the entire water column is weakest during the year, turbidity is highest, and stratification is at a relatively weak level than the Modoamen sub-estuary (Figure 9d). In other months, low water turbidity benefits for the increase of primary production, and with relatively stable and weak stratification, the eutrophication-induced acidification is sharply decreased in the Lingdingyang Bay.
In addition, significant differences in biochemical contributions to the eutrophication-induced acidification are found in different regions of the PRE. In the hypoxia region of Modoamen sub-estuary (AS1), the eutrophication-induced acidification is mainly driven by AR, HR, sediment release, and Nirr (Figure 9a). The existence of strong water stratification highlights the importance of the sediment release process to eutrophication-induced acidification in this region. While for the sections in Lingdingyang Bay, Nirr, AR and HR (Figures 9b and 9d and Figure S6) are shown to be the driving factors for eutrophication-induced acidification. Moreover, the temporal evolution of eutrophication-induced acidification of AS1 is different from AS2, because the bottom water respiration and benthic remineralization play key roles at AS1 while water column biochemical processes dominate the eutrophication-induced acidification at AS2.
### Conceptual Model of the Eutrophication-Induced Acidification in Pearl River Estuary
In the coastal area influenced by river plume, [PERSON] et al. (2011) revealed the surface eutrophication and subsurface acidification and suggested that the subsurface acidification is induced by aerobic respiration. The PRE receives a large amount of terrestrial material input seasonally at eight outlets, which leads to the evolution of eutrophication-induced acidification largely different from the coastal plume area and the open ocean. The benthic respiration and remineralization are active during the whole year. The local physical dynamics result in two distinct types of eutrophication-induced acidification in the estuary (Figure 10).
In wet season (summer), river discharge strongly affects the entire estuary. The particulate matter carried by the discharge settles down to the
Figure 9.— Budget differences (\(\Delta DIC-\Delta TA\)) for the benthic layer (a and b) and the entire water column (c and d) along AS1 (a and c) and AS2 (b and d) sections. The biochemical processes include sediment flux, nitrification, denitrification, ammonium related production (PP NH4), NO\({}_{0}\), “related production (PP NO3), autotrophic respiration and heterotrophic respiration. The red line with blue circles denotes the summation of all the terms.
sediment at the inner side of the salinity front, forming a high turbidity area near the outlet (Figure 10) and leading to the benthic carbon accumulation in the sediment ([PERSON] et al., 2020). The remineralization of settled organic matter causes the occurrence of eutrophication-induced acidification at bottom in the high turbidity area (Type I, turbidity enhanced). This process is clear in the alongshore section of Lingdingyang Bay (AS2). While the plume water with low salinity spreads away from the outlet and interacts with the open sea, stratification and light availability increase, which stimulates the algae bloom and results in the pH increase in the upper layer. When organic matters sink down from the salinity front, they will be remineralized and release DIC into bottom water, which will induce the acidification at bottom when strong stratification exists (Type II, stratification enhanced). This process occurs in the hypoxia region of Modaomen sub-estuary (AS1).
In dry season (winter), eutrophication-induced subsurface acidification reduced (Figure 10). The organic matter accumulated in the sediments from late spring to autumn are gradually remineralized. The released NH\({}_{4}\)+ from sediment affects the primary production of PRE in winter ([PERSON] et al., 2014). Due to the reduction of river discharge, the high turbidity zone and the salinity front shrink to the upstream region. The turbidity of the estuary water is low and vertical stratification is weakened, which benefits the vertical exchange. Therefore, for Type I (turbidity enhanced), although the benthic DIC supplementation via biochemical processes in winter is still higher than TA (Figure 9b), the strengthen of eutrophication-induced acidification is sharply decreased relative to summer. While for Type II (stratification enhanced), the physical environment can no longer support the decoupling between primary production and respiration, which leads to the disappearance of eutrophication-induced acidification in the hypoxia zone.
### Comparison With Other Coastal Area
The stratification enhanced type of eutrophication-induced acidification in the PRE in summer is consistent with the formation mechanism proposed by previous studies in the north Gulf of Mexico ([PERSON] et al., 2011; [PERSON] et al., 2017). That is, stratification weakens water mixing, resulting in the decoupling between the surface basfication and subsurface acidification. Moreover, the PRE shows its characteristics in the elimination of eutrophication-induced acidification. Due to the shallow water depth (\(<\)15 m) and the strong influence of river discharge, vertical salinity gradient can dominate the stratification in the PRE. The decay of salinity stratification in autumn and winter benefits the CO\({}_{2}\) mixing/evasion from the bottom water, which weakens the acidification of water column. In other marginal seas ([PERSON], 2018), temperature stratification occurs in summer and autumn, which results in the CO\({}_{2}\) generated by mineralization of organic matter accumulated in the bottom water, and the continuation of acidification in autumn. Therefore, the formation and evolution of seasonal stratification, as well as the effect of physical factors such as water residence time, may lead to significant differences in the intensity, range, and duration of ocean acidification in different coastal systems.
The existence of turbidity-enhanced type of eutrophication-induced acidification in the PRE indicates that processes inducing the decoupling of primary production and respiration in space and time will lead to the occurrence of acidification ([PERSON] et al., 2011; [PERSON] et al., 2017). The high turbidity weakens the light availability and limits the primary production. In this case, the acidification cannot be balanced by local primary production. Moreover, eutrophication-induced acidification in the PRE is spatially varied. It exists in the Lingdingyang Bay almost all year round, while it is a seasonal phenomenon in the hypoxia zone. The year-round continuous positive (\(\Delta DIC-\Delta TA\)) supplementation induces eutrophication-induced acidification in the Lingdingyang Bay and leads to an important environmental risk. When eutrophication exacerbates in the plume area and coastal area, the eutrophication-induced acidification reported in summer ([PERSON] et al., 2017) may extend to other seasons and affect the coastal carbon cycle system (i.e., air-sea CO\({}_{2}\) flux). The spatial variability of eutrophication-induced acidification in the PRE suggests that the combination of buffering capacity of the carbonate system from different water masses and the biochemical processes (e.g., primary productivity, Denit, precipitation/dissolution of CaCO\({}_{3}\)) will result in diverse coastal acidification mechanisms ([PERSON], 2019). For example, [PERSON] et al. (2017) found that the benthic DIC efflux and small detritus remineralization are the main factors driving local acidification in the north Gulf of Mexico, while the respiration and Nitr in water and sediment are the main factors in the PRE, and the oxidation of reduced chemicals (i.e., H\({}_{3}\)S, NH\({}_{4}\)+, Mn\({}^{2+}\), Fe\({}^{+}\)) is responsible for the pH minimum in the low O\({}_{2}\) zone in the Chesapeake Bay ([PERSON] et al., 2017).
## 4 Conclusions
In this study, we present the seasonal and spatial analysis of eutrophication-induced acidification in the PRE. The eutrophication-induced acidification in PRE is a dynamical evolution process throughout the year, which is connected with localized changes in primary production, remineralization of organic matters and physical processes. The different chemical characteristics of discharge water at the eight river outlets also affect the acidification and basification caused by local biochemical reactions in the PRE. The estuary receives continuous nutrient influxes from terrestrial and sediment throughout the year, resulting in the persistent risk of the eutrophication-induced acidification in the subtropical estuary such as the PRE. The mixing of runoff and open sea water in the estuary results in a sharp and variable seaward gradient of carbonate system in the estuary. Our results show that, stratification and turbidity are important local physical factors affecting the generation and elimination of eutrophication-induced acidification with significant spatial and temporal variabilities. In the hypoxia zone, eutrophication-induced acidification is primarily controlled by the remineralization occurs in the water bottom and sediment, and enhanced by stratifica
Figure 10: A conceptual model for generation and elimination of the eutrophication-induced acidification in Pearl River Estuary.
tion in summer. It results in the coexistence of surface basification and bottom acidification in summer, which are absent in other seasons. In other regions, the evolution of eutrophication-induced acidification is dominantly regulated by local biochemical processes (Nitr and respiration) of the whole water column due to the existence of high turbidity.
Appendix A Endmember Values of DIC, TA, Salinity, Potential Temperature and Temperature in Each Month of 2006
\begin{tabular}{l c c c c c c c c c c} \hline \hline & \multicolumn{6}{c}{West four outlets} & \multicolumn{6}{c}{East four outlets} \\ \cline{2-13} & DIC & TA & \(S\) & \(\emptyset\) & \(T\) & DIC & TA & \(S\) & \(\emptyset\) & \(T\) \\ \cline{2-13} Unit & mmol/L & mmol/L & \%e & \({}^{\text{\tiny{a}}}\)C & \({}^{\text{\tiny{a}}}\)C & mmol/L & mmol/L & \%e & \({}^{\text{\tiny{a}}}\)C & \({}^{\text{\tiny{a}}}\)C \\ \hline Jan & 2.09 & 2.07 & 3.12 & 17.65 & 17.67 & 2.11 & 2.12 & 4.79 & 17.51 & 17.52 \\ Feb & 1.99 & 1.94 & 3.80 & 17.59 & 17.61 & 2.01 & 2.01 & 6.13 & 18.27 & 18.29 \\ Mar & 1.89 & 1.80 & 1.01 & 18.53 & 18.56 & 1.89 & 1.82 & 1.92 & 19.28 & 19.29 \\ Apr & 1.79 & 1.67 & 0.23 & 21.51 & 21.53 & 1.77 & 1.65 & 0.65 & 22.23 & 22.24 \\ May & 1.70 & 1.58 & 0.11 & 25.77 & 25.80 & 1.57 & 1.45 & 0.18 & 25.46 & 25.47 \\ Jun & 1.59 & 1.49 & 0.10 & 28.50 & 28.54 & 1.36 & 1.27 & 0.10 & 27.92 & 27.94 \\ Jul & 1.48 & 1.40 & 0.10 & 29.50 & 29.54 & 1.14 & 1.10 & 0.10 & 29.43 & 29.45 \\ Aug & 1.57 & 1.47 & 0.10 & 29.97 & 30.01 & 1.26 & 1.17 & 0.10 & 30.45 & 30.47 \\ Sep & 1.66 & 1.56 & 0.13 & 29.84 & 29.88 & 1.37 & 1.27 & 0.19 & 30.66 & 30.68 \\ Oct & 1.76 & 1.64 & 0.54 & 27.38 & 27.42 & 1.51 & 1.37 & 0.86 & 28.38 & 28.39 \\ Nov & 1.83 & 1.72 & 1.08 & 22.66 & 22.69 & 1.54 & 1.46 & 1.00 & 23.27 & 23.28 \\ Dec & 1.92 & 1.89 & 1.68 & 19.23 & 19.25 & 1.78 & 1.80 & 1.44 & 19.03 & 19.04 \\ \hline \hline \end{tabular}
\begin{tabular}{l c c c c c c c c c c} \hline \hline & \multicolumn{6}{c}{Sea Surface} & \multicolumn{6}{c}{Sea Bottom} \\ \cline{2-13} & DIC & TA & \(S\) & \(\emptyset\) & \(T\) & DIC & TA & \(S\) & \(\emptyset\) & \(T\) \\ \cline{2-13} Unit & mmol/L & mmol/L & \%e & \({}^{\text{\tiny{a}}}\)C & \({}^{\text{\tiny{a}}}\)C & mmol/L & mmol/L & \%e & \({}^{\text{\tiny{a}}}\)C &
## Appendix B Potential Energy Anomaly Calculation
As a convenient measure, the potential energy anomaly \(\phi\) has been defined by [PERSON] (1981) as the amount of mechanical energy (per m\({}^{3}\)) required to instantaneously homogenize the water column with a given density stratification:
\[\phi=\frac{1}{D}\int\limits_{-H}^{\eta}gz(\overline{\rho}-\rho)dz=\frac{1}{D} \int\limits_{-H}^{\eta}gz\bar{\rho}dz \tag{31}\]
with the depth-mean density
\[\overline{\rho}=\frac{1}{D}\int\limits_{-H}^{\eta}gz\rho dz \tag{32}\]
the deviation from the depth-mean density, \(\bar{\rho}=\overline{\rho}-\rho\), the mean water depth \(H\), the sea surface elevation \(\eta\), the actual water depth \(D=\eta+H\) and the gravitational acceleration \(g\).
## Appendix C Biochemical Reactions in Water Column and Sediment Pore Water
### Biochemical reactions in water column
Photosynthesis with ammonium:
\[106\;CO_{2}+16 NH_{4}^{+}+H_{2}PO_{4}^{-}+106H_{2}O\;\rightarrow\;Protoplasm+106O_{2}+15H^{+}\]
Photosynthesis with nitrate:
\[106 CO_{2}+16 NO_{3}^{-}+H_{2}PO_{4}^{-}+122H_{2}O+17H^{+}\;\rightarrow\;Protoplasm+138O_{2}\]
Nitrification:
\[NH_{4}^{+}+1.89O_{2}+1.98 HCO_{3}^{-}\;\rightarrow\;0.016C_{5}H_{7}O_{2}N+0.984 NO_{3}^{-}+1.03H_{2}O+1.90H_{2}CO_{3}\]
Dentrrification:
\[5 CH_{2}O+4 NO_{3}^{-}\;\rightarrow\;3H_{2}O+SCO_{2}+2N_{2}+4 OH^{-}\]
Biochemical reactions in sediment pore water
Aerobic layer
Oxidation of hydrogen sulfide:
\[H_{2}S+2O_{2}\;\rightarrow\;SO_{4}^{2-}+2H^{+}\]
Oxidation of methane:
\[CH_{4}+2O_{2}\;\rightarrow\;CO_{2}+2H_{2}O\]
Anaerobic layer
Sulphate reduction:
\[2H^{+}+2 CH_{2}O+SO_{4}^{2-}\;\rightarrow\;2 CO_{2}+H_{2}S+2H_{2}O\]
### Data Availability Statement
Data were not used, nor created for this research. The measurements at PRE and the model outputs in this study are available at [[http://doi.org/10.5281/zenodo.4300997](http://doi.org/10.5281/zenodo.4300997)]([http://doi.org/10.5281/zenodo.4300997](http://doi.org/10.5281/zenodo.4300997)).
## Appendix A Journal of Geophysical Research: Oceans
### Acknowledgments
This study is supported by the National Key Research and Development Program of China (2015 FFC1016084), the National Natural Science Foundation of China (2015 FFC1016084), the National Natural Science Foundation of China (2018 FFC116084), the China (2018 FFC116084), the National Natural Science Foundation of China (2018
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wiley/fa644ddc_5c00_4af1_bc2e_dbed4a4fcf87.md | # Earth and Space Science
Method
Near Real-Time Earthquake Monitoring in Texas Using the Highly Precise Deep Learning Phase Picker
[PERSON]\({}^{1}\)
[PERSON]\({}^{1}\)
\({}^{2}\)Bureau of Economic Geology, The University of Texas at Austin, Austin, TX, USA, \({}^{2}\)Previous: National Research Institute of Astronomy and Geophysics (NRIAG), NRIAG, Helwan, Egypt, \({}^{3}\)Now at: Division of Physical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
[PERSON]\({}^{1}\)
\({}^{1}\)Bureau of Economic Geology, The University of Texas at Austin, Austin, TX, USA, \({}^{2}\)Previous: National Research Institute of Astronomy and Geophysics (NRIAG), NRIAG, Helwan, Egypt, \({}^{3}\)Now at: Division of Physical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
[PERSON]\({}^{1}\)
\({}^{1}\)Bureau of Economic Geology, The University of Texas at Austin, Austin, TX, USA, \({}^{2}\)Previous: National Research Institute of Astronomy and Geophysics (NRIAG), NRIAG, Helwan, Egypt, \({}^{3}\)Now at: Division of Physical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
[PERSON]\({}^{2,3}\)
\({}^{1}\)Bureau of Economic Geology, The University of Texas at Austin, Austin, TX, USA, \({}^{2}\)Previous: National Research Institute of Astronomy and Geophysics (NRIAG), NRIAG, Helwan, Egypt, \({}^{3}\)Now at: Division of Physical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
###### Abstract
Artificial intelligence (AI) seismology has witnessed enormous success in a variety of fields, especially in earthquake detection and \(P\) and \(S\)-wave arrival picking. It has become widely accepted that DL techniques greatly help routine seismic monitoring by enabling more accurate picking than traditional pickers like STA/LTA. However, a completely automatic AI-driven earthquake monitoring framework has not been reported due to the concerns of potential false positives using DL pickers. Here, we propose a novel AI-faciliated near real-time monitoring framework using a recently developed deep learning (DL) picker (EQCCT) that has been deployed in the Texas seismological network (TexNet). For the West Texas area, TexNet's seismic monitoring relies on the EQCCT picker to report earthquake events. For earthquakes with a magnitude above two, the picks are further validated by analysts to output the final TexNet catalog. Due to the fast-increasing seismicity caused by continuing oikgas production in West Texas, this AI-facilitated framework significantly relieves the workload of TexNet analysts. We show the mean absolute error (MAE) of automatic magnitude estimation for the magnitude-above-two earthquakes is smaller than 0.15 in West Texas and MAEs of hypocenter locations within 2.6 km in both distance and depth estimates. This research provides more evidence that DL pickers can play a fundamental role in daily earthquake monitoring.
Key Words.: **Axi**: 10.1029/2024 EA003890
earthquakes and a huge number of moderate-size events. In the meantime, despite the high recall rate in large earthquake events, the \(P\) and \(S\) wave arrival times cannot be picked with high accuracy due to the complex waveform features and high noise labels in the field. As a result, after large earthquakes (M >3.5), significant intervention by TexNet analysts is required to adjust the arrival times to outsource a high-quality hypocenter location and estimate the magnitude of the earthquake. In addition to the moderate-size earthquakes, there are a large number of false alarms within the catalog using the traditional STA/LTA picker.
Considering the fast-increasing seismicity in all magnitude ranges due to continuing oil&gas production, manual adjustment of the arrival pickers becomes prohibitively labor-intensive and should better be minimized. Deep learning phase pickers have been widely studied in the past decade and have undergone many case verifications from around the world ([PERSON] et al., 2023; [PERSON] et al., 2022). Many studies have shown that deep learning phase pickers can be far more accurate than traditional STA/LTA pickers ([PERSON] et al., 2012; [PERSON], 2009) or more advanced template matching-based pickers ([PERSON] et al., 2017; [PERSON] et al., 2015). Notably, [PERSON] et al. (2023) developed a cloud-based automatic earthquake detection and location workflow using PhaseNet. However, there is a common issue in most of the deep learning pickers, that is, despite the high detection recall, there might still be high picking errors (e.g., early or delayed picks) within the picked \(P\) and _S_-wave phases. As for the rapid response to large-magnitude events, analysts' adjustments are still required to ensure high location accuracy. For small and moderate-size events, a sophisticated workflow that includes both location and relocation steps is used for correcting inaccurate arrival picks. Here, we demonstrate the high picking accuracy of a newly developed deep learning picker, EQCCT ([PERSON] et al., 2023), in two scenarios, that is, moderate-to-large events (M >2) (hereafter referred to as M2 events) and other smaller events. For the moderate-to-large events, we demonstrate that location and magnitude estimation arising from deep learning pickers are sufficiently accurate for rapid response purposes. For the smaller events, we demonstrate that through an integrated workflow, we can output a highly complete catalog in near real time.
## 2 Method
### EQCCT - The Latest Deep Learning Phase Picker
The transformer is a powerful tool for extracting important information from input data. EQCCT, based on a compact Convolutional Transformer (CCT), can identify the locations of \(P\) and _S_-wave arrival times within the input data. EQCCT uses a sample-based picking approach, assigning an output label to each input sample. It employs a triangle function centered around \(P\) and _S_wave arrival times as the target label. EQCCT is a newly developed phase picker first published in [PERSON] et al. (2023). It is based on the latest deep learning architecture, that is, compact convolutional transformer (CCT), which combines the benefits of the first-generation convolutional network as used in PhaseNet and the second-generation transformer network as used in EQTransformer and overcomes their individual drawbacks. For example, EQCCT can be more effective in extracting the time-series feature than PhaseNet and can be faster than EQTransformer. In ([PERSON] et al., 2023), many detailed benchmark comparisons with PhaseNet [PERSON] et al. (2023), and EQTransformer ([PERSON] et al., 2020) in terms of picking
Figure 1: Workflow for creating a high-resolution catalog using the deep learning picker. In the framework, there is one intermediate catalog, which is directly from the SeiSComP software and isap91 velocity model. The NonLinLoc with a regional 1D velocity model (DBID) is used to refine the catalog to correct the depth errors. Here, we only consider the generation of the hypocenter locations of detected earthquake events, while the magnitude estimation is skipped from this workflow and is based on the method developed in [PERSON] et al. (2020).
accuracy on different testing datasets have been conducted. Here, we will focus on its application in near real-time monitoring at TexNet.
EQCCT consists of two independent models, one for _P_-wave picking and the other for _S_-wave. Both models are trained independently using the same dataset. Training involves an augmented version of the STEAD dataset ([PERSON] et al., 2019), with EQCCT taking 60 s three-component seismograms as input. Augmentation techniques include shifting, adding a second earthquake in the same 60 s window, adding noise, and corrupting seismograms by dropping one or two components. This augmentation improves the generalization ability of the EQCCT when applied to different datasets.
Convolutional layers extract feature maps from the input data, followed by a patching layer that divides the features into non-overlapping windows. EQCCT also includes transformer blocks to enhance the extracted features. The core layer is the Multi-Head Attention (MHA) network, which assigns higher attention to the important information, particularly the location of arrival times. MHA comprises four self-attention heads, and the output is the combination of these heads. Dropout layers, like Stochastic Depth Dropout (SDD) layers ([PERSON] and [PERSON], 2016), are integrated to prevent overfitting.
As a result, EQCCT demonstrates strong picking performance with a small output threshold (e.g., 0.1) and remains reliable when applied to various datasets ([PERSON] et al., 2023). The overlap ratio between neighboring 60 s windows in default is set to 0.3.
### General Workflow for Near Real-Time Monitoring
Following single-station-based earthquake detection, \(P\) and _S_-wave arrival picking, we design an integrated workflow shown in Figure 1 to locate and relocate the earthquake events. The complete open-source earthquake monitoring framework can be found at [[https://github.com/chenyk1990/sc3](https://github.com/chenyk1990/sc3) flow]([https://github.com/chenyk1990/sc3](https://github.com/chenyk1990/sc3) flow). After the \(P\) and _S_-wave picks are obtained using the EQCCT method, we apply the state-of-the-art SeisComP software with the LOCSAT locator and the isap91 velocity model ([PERSON] et al., 1995) to associate the \(P\) and _S_-wave picks and obtain the initial hypocenter locations. The proposed AI detection module is connected to the SeisComp messaging system. It does not listen to seedlink directly in real time, instead it reads from the archive through FDSNWS with a short
Figure 2: Map of the Texas stations and event distributions. The green frame box indicates the area of interest of the Coulson monitoring example. The red frame box indicates the area of interest of the Culberson monitoring example. The inset shows the event and station distribution of the whole state of Texas. The cyan frame box highlights the area of West Texas studied in this paper.
processing latency (currently of 10 min). The tests shown in this paper are all based on SeisComp3, which is no longer used by TexNet but is completely compatible with SeisComp6. The SeisComp6 version of this AI detection workflow has been run by TexNet recently. Based on the examples shown later, we found that the recall values for \(M>2\) earthquakes are almost 100%, indicating significantly reduced arrival picking errors compared with state-of-the-art automatic methods.
The association and location procedures are iterated until the optimal association and hypocenter location are obtained when the \(P\) and \(S\)-wave traveltime residuals are minimized. To correct the depth errors and refine the hypocenter locations, we further apply the NonLinLoc method ([PERSON] et al., 2009) with a regional 1D velocity (DB1D) to apply a secondary location on the associated picks from the last step using LOCSAT. To facilitate a fair comparison with the TexNet catalog, we use exactly the same location workflow as the routine TexNet monitoring, including association, location, and refined location, except for different \(P\) and \(S\)-wave picks, and the same parameters for all individual tasks through the workflow. In previous TexNet daily monitoring, we used an enhanced STA/LTA picker while in the new TexNet daily monitoring, we use the EQCCT as the picker. For moderate-to-large (M >2) earthquakes, the earthquake catalog after the NonLinLoc step is output for manual quality control before being put online in the public TexNet catalog. For small (M <2) earthquakes, the high-resolution catalog after the relocation step is output as the final product. The whole workflow detailed in Figure 1 is completely automatic.
## 3 Examples
We conduct tests in two regions, Coalson and Culberson. The studied areas are indicated in Figure 2 as the green and red frame boxes. Figure 2 also plots all the TexNet recorded events and station distributions. In the state of
Figure 3: Monitoring test in Coalson area. (a) Magnitude error distribution. (b) Scatter plot of EQCCT magnitude V.S. preferred magnitude. Preferred magnitude denotes the most accurate magnitude decided at TexNet using the most reliable picks, velocity models, and location workflows.
Texas, there are several seismically active basins, here, we only study the Delaware basin region in West Texas, indicated by the cyan frame box in the inset of Figure 2.
The two monitoring examples are shown in Figure 3 for Coalson and 4 for Culberson. We chose the period between 2022/11/28 and 2022/12/31 to study the near-real-time monitoring performance. Here, we mainly study the magnitude estimation accuracy ([PERSON] et al., 2020) because the magnitude is the primary factor that we consider regarding whether manual picking is performed on an automatically detected event in the Coalson area (depicted by the green frame box in Figure 2) and the given period, we detect 1,471 events, with a minimum magnitude around \(-1\) Ml and a maximum above 3 MI. Here, we compare the EQCCT magnitude with the preferred magnitude. The preferred magnitude means the best magnitude estimation for a certain event, either from Texnet analysts' manual picking or from a rigorous location procedure. The magnitude from EQCCT denotes the magnitude output directly from the automatic EQCCT workflow. The magnitude difference distribution is plotted in Figure 3a, where it is clear that the magnitude difference is mostly around the zero coordinate. The mean absolute error of magnitude estimation is 0.03 and the standard deviation is 0.23. The red dashed line indicates the mean magnitude difference (0.03). Figure 3b shows the scatter plots between EQCCT magnitude and preferred magnitude in three cases, that is, reported, preliminary, and final. Reported events are events that are directly output from the EQCCT-based workflow without going through the manual picking process. Preliminary events mean that the events have been manually reviewed by Texnet analysts but have not been finalized. The final events mean the events that have gone through several analysts' checks and have been considered as the best solutions. We can see that both preliminary and final events have very small errors using EQCCT, meaning that only a few changes were made during the manual picking process. Note that \(M=1.9\) is the threshold for manually checking the EQCCT-triggered events. Above magnitude 1.9, events will go through a manual check by TexNet analysts. In this Coalson example, 43 M2 events were observed after manual checks. There is only one M \(<\)1.9
Figure 4: Monitoring test in Culberson area. (a) Magnitude error distribution. (b) Scatter plot of EQCCT magnitude V.S. preferred magnitude. Preferred magnitude denotes the most accurate magnitude decided at TexNet using the most reliable picks, velocity models, and location workflows.
event from EQCCT (\(M_{EQCCT}=1.88\)) with a final magnitude above 2 (\(M_{manual}=2.01\)), meaning that the recall of M2 events is 97.7%. It is worth noting that there is a human factor in the quality control process as manual picks are conducted by multiple analysts, so the manual results are not strictly the ground truth but are relatively robust.
Then, we test the near real-time monitoring performance in Culberson County. With the same monitoring period and the geographic area of interest depicted by the red frame box in Figure 2, we detect 3,350 events, with a minimum magnitude below \(-1\) MI and a maximum above 3.5 MI. The magnitude difference distribution is plotted in Figure 4a. The mean absolute error of magnitude estimation is 0.04, and the standard deviation is 0.33. The red dashed line indicates the mean magnitude difference (0.04). Figure 4b shows the scatter plots between EQCCT magnitude and preferred magnitude in two cases, that is, reported and final. In this example, preliminary events have all been marked as final events. Similarly, we can see that all final events have very small errors using EQCCT, meaning that EQCCT picks are highly accurate. Specifically, in this Culberson example, there are 45 M2 events after a manual check. There are no M <1.9 events from EQCCT with a final magnitude above 2, meaning that the recall of M2 events is 100%.
We then compare the near real-time picking results using EQCCT on earthquakes in two scenarios: large earthquakes and small earthquakes. Figure 5 shows the comparison of picking and location results between TexNet analysts (manual) and EQCCT. Figure 5a shows the 90 s waveforms from 17 stations for the M3.5 event (texnet2022 vod) on the TexNet public catalog. We plot the manual (dashed lines) and EQCCT (solid lines) picks on top of the waveforms as the vertical lines. In general, the manual and EQCCT picks (P and S) almost overlap each other. For a better and more detailed view, we zoom the waveforms, highlighted by the red rectangles, in Figure 5b, where we can see more clearly the overlapping or mismatch between manual and EQCCT picks. Most picks have very small picking errors (e.g., <0.05 s), while only a few have relatively larger and more observable errors. The largest picking errors appear on the TX.PB40 station (third last from bottom to top), possibly because
Figure 5.— Waveform comparison for a large earthquake (\(M=3.5\)). (a) Waveforms in different stations corresponding to the TexNet event texnet2022 vod with picks from EQCCT and manual picks on top of the waveforms (vertical lines). (b) Zoomed comparison (the first 20 s). (c) Station distribution and event location comparison on the map view. (d) Station distribution and event location comparison on the depth slice. The near real-time EQCCT monitoring result is almost the same as the manually picked result in terms of magnitude (error <0.05), origin times (error <0.02 s), hypocenters (error <0.5 km for longitude, latitude, and depth).
of its relatively higher noise level. For the most part, EQCCT picks are highly accurate compared with manual picks, which makes the hypocenter locations of the two scenarios very close (<0.1 km in latitude, longitude, and depth). The location comparisons and station distributions are shown in Figures 5c and 5d. The magnitude error is only 0.04, and the origin time error is only 0.02 s. This example demonstrates that EQCCT is sufficiently accurate in near real-time monitoring for large earthquake events (e.g., M >3.5 events, which requires event characterization almost immediately after the occurrence).
We then show another small magnitude (M <1.0) event (texnet2022 vvro) in Figure 6. This event is detected by TexNet traditional automatic picker, which is an optimized STA/LA method ([PERSON] et al., 2012), and is labeled as a reported event. Because it has a very small magnitude, TexNet analysts do not manually pick the events. Here, we only compare the EQCCT picks with the reported picks (from the traditional picker) and the EQCCT location with the reported location (from the automatic association and location workflow based on the traditional picker). Similarly, Figure 6a plots the 90 s waveforms and the EQCCT (solid vertical lines) and reported picks (dashed vertical lines). Figure 6b shows the zoomed comparison between the picks. Notably, the traditional picker only detects the event from three stations, while EQCCT detects the event from eight stations. More importantly, EQCCT almost picks P and S arrivals from all the stations. From observation, it is obvious that EQCCT picks are more accurate than the picks from the traditional picker. The stations that are not triggered by the traditional picker are highlighted by the cyan labels on the right or left part of each waveform in (a) or (b). The corresponding stations are also plotted in 6(c) and 6(d) as the cyan inverted triangles. The blue inverted triangles show the three stations that are triggered by the traditional picker. As a result, the reported location much deviates from the EQCCT location. From a comprehensive viewpoint, the EQCCT automatic location for this small earthquake
Figure 6.— Waveform comparison for a small earthquake (M <1). (a) Waveforms in different stations corresponding to the TexNet event texnet2022 vvro with picks from EQCCT and reported picks on top of the waveforms (vertical lines). (b) Zoomed comparison (the first 20 s). (c) Station distribution and event location comparison on the map view. (d) Station distribution and event location comparison on the depth slice. The reported picks here indicate using a traditional, well-optimized picker ([PERSON] et al., 2012). In this case, the traditional picker only detects the event in three stations highlighted by blue while the EQCCT detects in eight stations. The arrivals are obviously more accurate using EQCCT.
event is more reliable than the reported location. This example indicates that even for small-magnitude events, EQCCT is also more precise when used in near real-time monitoring.
To further demonstrate the evolution of the catalog through the near real-time detection workflow shown in Figure 1, we show a comparison of different catalogs between reported events and EQCCT detected events in Figure 7. Figures 7a and 7b show the initial catalog directly from the traditional picker and EQCCT picker using the iasp91 velocity model and the LOCSAT method ([PERSON] et al., 1995). On top of the maps are two focal mechanisms that correspond to the 2020 M4.9 Mentone earthquake and the 2022 M5.4 Coalson earthquake. Figures 7c and 7d show the refined catalog using the regional velocity model in the Delaware basin and the NonLinLoc method. The refined location process removes a few events that do not meet the location quality and makes the refined locations a little more focused compared with the initial catalog. Figures 7e and 7f show the relocated catalog after applying the Growclust method ([PERSON], 2017). It is worth noting that GrowClust is not run in real-time. It is run separately as soon as a catalog has been constructed within a certain period of time. Ideally, the GrowClust calculation can be run on an hourly basis by including newly detected events in the past hour. The event locations become more focused and well delineate the large-scale fault system in West Texas. All the catalogs presented in Figure 7 are generated automatically, which shows the significant
Figure 7: Comparison between the reported and EQCCT detected events along the near real-time monitoring workflow. (a) 1,998 reported events using the iasp91 velocity model detected by the traditional picker at Teenet. (b) 10,746 EQCCT detected events using the iasp91 velocity model. (c) (d) Refined locations of the reported events and EQCCT detected events using the regional velocity in the Delaware basin and the NonLinLoc method. (e) (f) Related locations of the reported events and EQCCT detected events using the Growclust method. All the catalogs shown here are generated automatically.
advantage of the EQCCT picker in creating a highly complete catalog that facilitates regional seismotectonic analysis. Figure 8 shows event distribution in different scenarios. Figure 8a shows the frequency magnitude plot. Figure 8b shows the daily earthquake number distribution. Figure 8c shows the daily magnitude distribution, where we can clearly see that EQCCT significantly boosts the detectability of low-magnitude earthquakes.
## 4 Discussion
### Influence of Station Density
Figure 9 shows how the station density will affect the number of detected earthquakes. Figure 9a shows the 11,563 detected events using 21 stations between 2022/10/01-2022/11/01 in the West Texas area. The station locations are plotted as inverted triangles, colored by their deployment time. As we decrease the number of stations according to their deployment time, we find that the detectability of the proposed EQCCT workflow decreases correspondingly. However, even when we decrease the number of stations to 60% of the existing stations, we still detect a huge number of events (7,533). When we further decrease the number of stations to 8 stations, the detected number of events further decreases to 4,866 events. This test also indicates that the proposed workflow is robust even in a moderately dense regional network.
### Uncertainty Analysis
The uncertainty of picking models is crucial for estimating the location and relocation uncertainty. To evaluate the uncertainty of the EQCCT picks, we apply a Monte Carlo dropout Gal and Ghahramani (2016) strategy, where the model predicts the output probabilities of the arrival times several times and calculates the average. We use the
Figure 8: Event distribution for different catalogs. (a) Frequency-magnitude distribution. (b) Distribution of daily earthquakes. (c) Daily earthquake magnitude distribution. It is clear that EQCCT significantly boosts the detectability of small earthquakes daily.
Monte Carlo dropout layers in the Conv and MLP blocks. We ran the EQCCT 10 times to predict the STEAD test set. Then, we obtain the standard deviation (uncertainty) of the three predictions for each test waveform. The \(P\) and \(S\)-wave uncertainty of the STEAD set is shown in Figure 10. Most of the \(P\) and \(S\)-wave picks have small uncertainty, which indicates the robustness of the EQCCT's picking performance. For the STEAD set, the average of the \(P\)-wave uncertainty and \(S\)-wave uncertainty is 0.01 and 0.03 s, respectively.
Figure 10: The uncertainty of the EQCCT for (a) \(P\)-wave and (b) \(S\)-wave picks.
Figure 9: Station effect on the EQCCT catalog. The stations are colored according to their installation time. (a) Detected events assuming the up-to-date station distribution. (b) Event magnitude distribution corresponding to (a). (c) Detected events assuming only 12 stations exist. (d) Event magnitude distribution corresponding to (c). (e) Detected events assuming only 8 stations exist. (f) Event magnitude distribution corresponding to (e).
### Location Outliers
Despite the fairly accurate magnitude estimation, the near real-time location using EQCCT is not 100% accurate. There are several inevitable outlier hypocenters using the current EQCCT picking model. Figure 11 shows a comparison between the automatically generated hypocenter location using EQCCT and the manually analyzed location for the aforementioned Coalson and Culberson monitoring examples. Here we only analyze the M2 events because we only manually pick the events for magnitude-above-two events. The left column (a,c, e) shows the location comparisons in longitude-latitude, longitude-depth, and latitude-depth slices for the Coalson area. Red circles denote the EQCCT location; gray circles denote the manual location, and green lines connecting each pair of locations denote the location error. The right column (b,d,f) shows the same location
Figure 11: Comparison between EQCCT and manual locations for M2 events. Left column: Coalson area; Right column: Culberson area. The location performance is generally robust except for only several outliers in a 1-month period. (a, c, and e) Show different spatial slices for comparing EQCCT and manual locations for the Coalson area. (b, d, and f) Show different spatial slices for comparing EQCCT and manual locations for the Culberson area.
### Efficiency in Earthquake Analysis
Analysts' workloads have been dramatically relieved due to the proposed AI-assisted automatic detection and location workflow. On the one hand, the average speed to analyze and adjust the picks that are initially from the automatic pickers has been increased to at least three times. Traditional STA/LTA-based workflow requires analysts to adjust almost every pick on each waveform, while the new EQCCT picker makes most picks good enough, with less need to adjust the pick positions. This makes analysts' life easier on a daily basis. On the other hand, to help analysts better understand the patterns of certain earthquake swarms or aftershocks, the proposed workflow significantly increases the overall efficiency. For example, traditionally, the TexNet crew, including around 5-8 analysts, are able to analyze around 200 M2 earthquakes per month. However, due to the newly developed workflow, in half a day, we are able to analyze more than 50 times more earthquakes with the same length of data (e.g., 1 month).
## 5 Conclusion
Real-time monitoring requires the accurate detection, rapid location, and magnitude estimation of moderate-to-large earthquakes. The deep-learning-based EQCCT picker has been demonstrated to be robust in the West Texas monitoring areas, including the Coalson and Culberson regions. The successful applications in these areas are
Figure 12: Comparison between EQCCT and manual locations for Midland events. The EQCCT pickers are applied to catalog events from the Midland basin. The outliers are caused by picking errors. (a-c) How different spatial slices for comparing EQCCT and manual locations for the Midland area.
attributed to the relatively higher station density. The Midland basin, however, does not enjoy the same robustness as the EQCCT picker. We have analyzed the detection, location, and magnitude estimation accuracies using the EQCCT picker for thousands of M2 earthquakes, as compared to the TexNet catalog that is from manual quality control. Most importantly, the detection recall of M2 events using EQCCT is almost 100%, making it reliable to use AI for near real-time monitoring. The tiny difference in the location and magnitude estimation errors comes from the slight picking errors in several stations where the signal-to-noise ratio is low. The robust near real-time monitoring performance enabled by the EQCCT picker suggests that we can rely on AI techniques to heavily relieve the workload of analysts, thereby enabling the analysis of smaller earthquakes.
## Data Availability Statement
The data and source codes of this paper are fully open-access. The data can be downloaded via the IRS DMG. The EQCCT picker can be accessed through [PERSON] (2024) [[https://figshare.com/articles/code/Models/21865440](https://figshare.com/articles/code/Models/21865440)]([https://figshare.com/articles/code/Models/21865440](https://figshare.com/articles/code/Models/21865440)). The near real-time automatic earthquake monitoring code can be found at [PERSON] (2024) [[https://github.com/che-nyk1990/sc3](https://github.com/che-nyk1990/sc3) flow]([https://github.com/che-nyk1990/sc3](https://github.com/che-nyk1990/sc3) flow).
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