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Hallberg et al. (2013)
Title:
Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation
Corresponding author:
Robert Hallberg
Keywords:
Sea level, Climate change, Ocean models
Citation:
Hallberg, R., Adcroft, A., Dunne, J. P., Krasting, J. P., & Stouffer, R. J. (2013). Sensitivity of Twenty-First-Century Global-Mean Steric Sea Level Rise to Ocean Model Formulation. Journal of Climate, 26(9), 2947Ð2956. doi: 10.1175/jcli-d-12-00506.1
URL:
https://journals.ametsoc.org/view/journals/clim/26/9/jcli-d-12-00506.1.xml
Abstract
Two comprehensive Earth system models (ESMs), identical apart from their oceanic components, are used to estimate the uncertainty in projections of twenty-first-century sea level rise due to representational choices in ocean physical formulation. Most prominent among the formulation differences is that one (ESM2M) uses a traditional z-coordinate ocean model, while the other (ESM2G) uses an isopycnal-coordinate ocean. As evidence of model fidelity, differences in twentieth-century global-mean steric sea level rise are not statistically significant between either model and observed trends. However, differences between the two models’ twenty-first-century projections are systematic and both statistically and climatically significant. By 2100, ESM2M exhibits 18% higher global steric sea level rise than ESM2G for all four radiative forcing scenarios (28-49 mm higher), despite having similar changes between the models in the near-surface ocean for several scenarios. These differences arise primarily from the vertical extent over which heat is taken up and the total heat uptake by the models (9% more in ESM2M than ESM2G). The fact that the spun-up control state of ESM2M is warmer than ESM2G also contributes by giving thermal expansion coefficient that are about 7% larger in ESM2M than ESM2G. The differences between these models provide a direct estimate of the sensitivity of twenty-first-century sea level rise to ocean model formulation, and, given the span of these models across the observed volume of the ventilated thermocline, may also approximate the sensitivities expected from uncertainties in the characterization of interior ocean physical processes.
Introduction
Global-mean sea level has been rising throughout the twentieth century, with increased rates in recent decades (Church et al. 2011). The leading contributors have been documented as the melting of land ice (snow, mountain glaciers, and ice sheets) and the steric rise in sea level due to a warming and expanding ocean (Church et al. 2011), with smaller contributions from climatic and anthropogenic changes in land-water storage (Milly et al. 2003). Projecting twenty-first-century sea level rise (SLR) is of great societal importance but is subject to uncertainties in our understanding of the underlying physical processes. The dynamic response of marine-terminated ice sheets to warming oceans is poorly understood and has the potential to contribute to SLR at rates with a plausible order of magnitude of 10 mm yr^{-1} (Holland et al. 2008; Pfeffer et al. 2008). Because the response of clouds under changing climate is a leading order uncertainty in the earth’s changing radiative budget, and because of the close connection between this budget, ocean heat uptake, and SLR, the cloud response is another substantial cause of uncertainty in SLR. Similarly, uncertainties in the radiative forcing due to aerosols and the overall sensitivity of the feedbacks in the coupled system generally can also contribute to un.certainty in projections of SLR.
The ocean contribution to SLR is closely related to its net uptake of heat, although the properties of the water taking up that heat are of leading order importance to SLR. Additionally, interior ocean mixing of heat and salinity generally cause seawater to contract because of nonlinearities of the equation of state, even though they do not alter the net heat content of the ocean (Griffies and Greatbatch 2012). Changes in ocean circulation play a leading order role in determining where the temperature will increase because of the ocean circulation response to climate change, and hence in detecting steric sea level rise (e.g., Gnanadesikan et al. 2007a; Winton et al. 2013). Interior ocean diapycnal mixing and ocean mixed layer processes play a major role in regulating the ocean’s long-term uptake of heat (e.g., Dalan et al. 2005), but the explicit specification of diapycnal mixing in climate models remains largely empirical. Ocean models can also exhibit numerical artifacts, such as spurious diapycnal mixing (Griffies et al. 2000) or excessive entrainment in overflows (Legg et al. 2006), that can complicate their ability to project SLR for the real world. There is also evidence that representation of the rectified effects of ocean mesoscale eddies are an important source of uncertainty in the ocean circulation response to climate change (Hallberg and Gnanadesikan 2006; Farneti et al. 2010), and hence potentially for heat uptake and SLR. With such a broad range of processes contributing, it is worthwhile to estimate the overall magnitude of the contributions of oceanic uncertainties to uncertainties in projections of steric sea level rise.
This study examines global-mean steric sea level rise (GSSLR) from four climate change scenarios from two Earth system models (ESMs) that are identical apart from their ocean components. We utilize this framework to identify and quantify the uncertainties in GSSLR attributable to limitations in our understanding of the physics of the ocean and the numerical portrayal of the ocean’s dynamics. This approach is thus different than the typical ensemble survey of coupled model inter-comparison for uncertainty estimation, as it allows us to roughly distinguish ocean-derived GSSLR differences from atmospherically forced GSSLR differences, be.cause it avoids convolving issues relating to drift in sea level and overweighting z-coordinate ocean models (with very similar lineages and algorithmic choices) in the ensemble. This study finds systematic 18% differences in GSSLR between the two models. While these differences are large enough to warrant a more thorough study, they do not fundamentally alter previous estimates of sea level rise that can be expected to occur in the twenty-fist century.
The earth system models
This study uses two comprehensive earth system models with identical atmospheric, land surface, sea ice, and ocean ecosystem components, differing only in their physical ocean components (Dunne et al. 2012). The ESM2M uses a 50-level z*-coordinate ocean model, built with the Modular Ocean Model, version 4.1 (MOM4p1) code (Griffies 2009). The ESM2G uses a 63-layer isopycnal-coordinate version of the Generalized Ocean Layer Dynamics (GOLD) ocean model (Hallberg and Adcroft 2009). Both use nominal horizontal resolutions of 1˚ with a tripolar fold over the Arctic. Both have comprehensive sets of physical parameterizations representative of the state-of-the-art z-coordinate and isopycnal-coordinate ocean climate models, as described in Dunne et al. (2012). Both ocean models conserve heat, salt, and mass to numerical round off, and both use proper freshwater mass flux surface boundary conditions, instead of artificially converting them into virtual salt fluxes. Neither model’s atmosphere was changed or retuned from the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model, version 2.1 (CM2.1) (Anderson et al. 2004). The runs presented here use the temporally evolving concentrations of well-mixed radiatively active gases and aerosols (Lamarque et al. 2010) prescribed by phase 5 of the Coupled Model Intercomparison Project (CMIP5) for the historical period up to 2005, and the four standardized Representative Concentration Pathways (RCPs) (Moss et al. 2010; Taylor et al. 2012). The RCP scenarios are labeled with the approximate global-mean radiative forcing anomalies due to well-mixed gases at the end of the twenty-first century (e.g., RCP8.5 has about an 8.5 W m 22 radiative heating anomaly relative to the preindustrial control in 1850). The various RCP scenarios are based on plausible choices for anthropogenic emissions. The atmospheric concentrations of CO2 differ, particularly in the latter half of the twenty-first century. While the radiative forcing for RCP8.5 increases strongly throughout the twenty-first century, the radiative forcing in RCP2.6 peaks in midcentury before declining. RCP4.5 and RCP6.0 have radiative forcing in the twenty-first century between RCP8.5 and RCP2.6.


Both models have been spun up with 1860 radiative forcing for over 1000 years (2560 years for ESM2M and 1160 years for ESM2G), until their global-mean heat budgets were well balanced before starting their respective control runs. The ESM2M control runs exhibit a slight warming averaged over the volume of the ocean (dT/dt = -0.038˚C century^{-1} averaged over a 500-yr-long control run), while ESM2G has an even smaller cooling (dT/dt = -0.010˚C century^{-1}). The ocean heat (and steric sea level) budgets for the control runs of these models are thus much closer to balance than in most coupled climate models of this resolution (Sen Gupta et al. 2012). The 500-yr-long 1860 control run of ESM2G has an average steric sea level drop of 0.023 mm yr^{-1}, while ESM2M’s has an average steric sea level rise of 0.074 mm yr^{-1}. In these runs, the standard deviation of the detrended annual-mean global-mean steric sea level anomaly is 2.3 mm for ESM2G and 1.8 mm for ESM2M, and they are used as uncertainty estimates in the figures presented later.
There are some pertinent differences in the spun-up ocean control states of the two models, both in the ocean interior and at the surface. As shown in Figure 1, the main thermocline extends too deeply in ESM2M and is too shallow in ESM2G relative to observations (see also Dunne et al. 2012). While the models use explicit diapycnal diffusivities of similar magnitudes in the main thermocline, ESM2M includes both parameterizations that indirectly enhance diapycnal mixing (e.g., Gnanadesikan et al. 2007b) and numerically induced diapycnal mixing (Ilicak et al. 2012; Griffies et al. 2000). The overly sharp thermocline in ESM2G may indicate that it is underrepresenting mixing processes in the thermocline. Below the thermocline, ESM2G uses an enhanced diapycnal diffusivity relative to ESM2M, following the prescription of Gargett (1984), while both models use similar abyssal tidal mixing parameterizations following Simmons et al. (2004). Under historical climate forcing, ESM2M is an average of 1˚C warmer relative to the observed climatology for 1980-2000, while ESM2G is 0.25˚C cooler than the climatology (Figure 1, middle). The root-mean-square (RMS) temperature errors relative to climatology for ESM2G are substantially smaller than for ESM2M below 500 m, while ESM2M has smaller RMS errors above 500 m, converging to similar RMS errors at the surface (Figure 1, right). Differences in the parameterizations of other processes, such as eddy mixing, could also contribute substantially to differences in both the oceans’ mean states and to GSSLR. The annual-mean near-surface temperatures in 1980-2000 of the historical simulations average 0.4˚C colder in ESM2G than ESM2M, with smaller differences in midlatitudes and zonal-mean differences exceeding 1.5˚C between 50˚ and 75˚N. The northern sea ice is more extensive than observed, especially in ESM2G, and the southern sea ice is less extensive than observed, especially in ESM2M (Dunne et al. 2012). These differences between the spun-up mean states of the two models figure prominently in their differing projections of GSSLR.
Figure 1: (left) Horizontal-mean potential temperatures from ESM2M (red) and ESM2G (blue) averaged over years 1981-2000 of the historical runs, along with the observed horizontal-mean temperature from the World Ocean Atlas, 2001 (WOA2001) (dashed) (Conkright et al. 2002). (middle) As in (left), but for horizontal-mean temperature bias from ESM2M and ESM2G relative to observed. (right) As in (left), but for horizontal RMS temperature errors for ESM2M and ESM2G. The WOA2001 dataset was chosen as a reference because most of the observations are from the 1980s and 1990s, giving a consistent comparison with this time average from the models.
Projected global steric sea level rise
The GSSLR for the historical and twenty-first-century projections under the four RCP scenarios are shown in Figure 2. This figure includes both thermosteric and halosteric contributions, although the focus here is on exploring the thermosteric differences, since the global-mean differences in the halosteric sea level rise are relatively small. The two models are statistically similar through.out the twentieth century, including responses of similar magnitudes to major volcanic eruptions such as Krakatoa (1883), Agung (1963), and Pinatubo (1991). The mean rate of GSSLR in the latter twentieth century in both models (1.16 mm yr^{-1} for ESM2M and 1.10 mm yr^{-1} for ESM2G) is slightly higher than observational estimates of sea level rise from thermal expansion of 0.8 ± 0.15 mm yr^{-1} for 1972Ð2008 (Church et al. 2011), while observed global-mean halosteric sea level rise is much smaller, just 0.04 ± 0.02 mm yr^{-1} averaged from 1955 to 2003 (Ishii et al. 2006), and not as well constrained observationally.
Figure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 ± 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.
In the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.


Figure 2: Global-mean steric sea level from concentration-forced simulations with ESM2M (red) and ESM2G (blue), relative to the mean for 1861-1900, for ensembles of historical runs with four members for ESM2M and seven members for ESM2G (up to 2005) and for the four CMIP5 standardized RCPs (starting in 2005). The marks to the right of the plot are projected to 2100 from linear fits over the last 40 years, with errors estimated from the variance during that same period. Long-term mean steric sea level drifts from the control runs of +0.076 mm y^{-1} and -0.025 mm yr^{-1} have been subtracted from ESM2M and ESM2G, respectively. The three black lines show the observationally based estimate of thermosteric SLR from 1972 to 2008 of 0.80 ± 0.15 mm yr^{-1} Church et al. (2011); the vertical offset for these black lines is arbitrary.
In the twenty-first-century scenarios, there are systematic and statistically significant differences between the two models. By the middle of the twenty-first century, ESM2M exhibits a significantly larger GSSLR than ESM2G, and by the end of the twenty-first century (2081-2100), the 20-yr-averaged GSSLR relative to 1881-1900 is about 18% higher in ESM2M than in ESM2G for each of the four RCP scenarios (Fig. 2). Put differently, the values of GSSLR attained by ESM2G by the end of the twenty-first century are reached 28, 21, 16, and 11 years earlier by ESM2M for scenarios RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. Figure 2 also shows that the ocean formulation is responsible, both directly and indirectly via differences in the spun-up mean ocean state, for an uncertainty in projections of GSSLR that is of comparable magnitude to the differences between successive RCP forcing scenarios.
The first reason for the higher GSSLR in ESM2M than in ESM2G is simply because it takes up more heat. This is readily evident in Fig. 3 (bottom), where ESM2M warms substantially more than comparable ESM2G simulations, with volume-mean temperature increasing about 9% more in ESM2M than in ESM2G. These differences in heat uptake are primarily found over the broad depth range from 200 to 2000 m (Fig. 4, left). The warming itself is much more strongly surface intensified in both models than are the differences between the models, and it is quite similar at the surface (apart from RCP2.6, where near-surface temperatures start diverging around 2050, as seen in Fig. 3); this point is discussed further below. To leading order, the heat is being taken up primarily in the thermocline of both models, but the main thermocline is deeper in ESM2M than in ESM2G, giving a greater volume of water to warm. As shown in Fig. 4 (middle left), the density changes contributing to the differences in GSSLR between the models are broadly distributed over the top 2500 m of the models, with roughly equal contributions coming from the depth ranges of 0–600 m, 600–1200 m, and 1200–2500 m. By contrast, well over half the total GSSLR comes from the topmost 600 m in all the cases. Differences in salinity changes compensate or augment the GSSLR differences because of differences in thermal changes at varying depths (Fig. 4, right), but when vertically integrated, the differences in salinity changes between the models contribute less than 0.2 mm to the difference in GSSLR. The larger heat uptake in ESM2M than ESM2G accounts for about half the difference in GSSLR between the models.
Figure 3: (top) Time series of global-mean SST, relative to the mean for 1880–1920, from ESM2M (red) and ESM2G (blue) for ensembles of historical runs and the four CMIP5 radiative scenarios. The values on the right are projections to 2100 from linear fits over the last 40 years, with error bars indicating the variance from these trends over the same 40-yr period. (bottom) Time series of globally integrated heat content anomalies, expressed as volume-mean ocean temperature anomalies in degrees Celsius.
Figure 4: (left) Vertical profiles of the horizontal-mean temperature change for ESM2M (red) and ESM2G (blue) averaged over a 40-yr period relative to 1861–1900. The historical intervals are a century apart (1961–2000), while for RCP2.6 and RCP8.5, the intervals are two centuries apart (2061–2100). (middle left) Vertical profiles of the horizontal-mean contributions to GSSLR (spatially integrated density anomalies divided by the ocean’s surface area and a mean density) from the same runs. (middle right) Profiles of the difference in contribution to GSSLR, ESM2M minus ESM2G. (right) Vertical profiles of the dominant terms in the differences between ESM2M and ESM2G in GSSLR contributions for RCP8.5. The average of the models’ temperature changes acting on the difference between the models’ thermal expansion coefficient differences (blue) and the differences in water-mass property changes acting on the mean thermal expansion and haline contraction coefficients of the two models (solid black) explain almost the entire signal shown in the third panel. The dashed and dotted lines show the separate profiles of GSSLR contributions from the temperature and salinity change differences, respectively, acting on the mean of the models’ thermal expansion and haline contraction coefficients.
A second factor in the differing GSSLR between these two models is the difference in the thermal expansion coefficients where the heating occurs; the thermal expansion coefficient is a strongly increasing function of temperature and pressure, so the two models could be taking up similar amounts of heat, but in different locations, leading to differing amounts of GSSLR (see, e.g., Griffies and Greatbatch 2012). This effect is evident in Fig. 4 (left and middle-left panels), where the contributions to GSSLR are relatively concentrated in the warmer near-surface waters compared with the heat uptake, and it is explicitly diagnosed for RCP8.5 in Fig. 4 (right). ESM2G has a sharper thermocline than ESM2M, and is, on average, about 1.25°C colder than ESM2M at the same depths below the topmost few hundred meters (Fig. 1, middle), with differences in thermal expansion coefficients based on the horizontal-mean temperatures peaking at about 750-m depth, where it is 14% larger in the ESM2M historical run than in ESM2G (and 8% larger than for observed temperatures; in ESM2G it is 6% smaller than observed). The thermal expansion coefficients have smaller relative differences above 750 m because the water is warmer, on average, and they have smaller relative differences below 1000 m because of the effects of pressure. Averaged over the whole volume of the ocean, the simulated thermal expansion coefficient averaged from 1981 to 2000 is 1.1% smaller than observed in ESM2G and 6.6% larger than observed in ESM2M. For RCP8.5, between 1870 and 2090 the volume-mean thermal expansion coefficient increases by about 2.8% in both cases. When weighted by the models’ temperature changes, the mean thermal expansion coefficients are 4% smaller than observed for ESM2G and 3.1% larger than observed for ESM2M for 1981–2000 and increase in the simulations by 10.4% and 11.0% between 1870 and 2090 for RCP8.5. The fact that the warming of the top 2000 m occurs, on average, some 40 m deeper in ESM2M than ESM2G (Fig. 4) also tends to give larger GSSLR in ESM2M than ESM2G, but only by about 0.5%, and it is a minor contributor to the GSSLR differences between the models. The simple fact that the thermal expansion coefficient is a strong function of temperature, and that the control state of ESM2M is warmer than ESM2G, accounts for a roughly 7% larger GSSLR in ESM2M than ESM2G.


Nonoceanic factors that might affect GSSLR, such as atmospheric feedbacks and differences in sea ice that have confounded previous attribution efforts (see Bindoff et al. 2007), do not contribute directly in this study, since those components are identical. However, surface differences in the spun-up mean state of the coupled models can lead to different responses in the atmosphere or sea ice. For instance, the global-mean SSTs in the ESM2G RCP2.6 simulation cool substantially in the latter half of the twenty-first century (Fig. 3, top), tracking the decline in the radiative forcing of RCP2.6, as high-latitude haloclines form in both the Northern and Southern Hemispheres and the sea ice expands. These ice-covered haloclines locally limit the otherwise large ocean heat loss, and the ocean’s warming (Fig. 3, bottom) is not greatly slowed by this global-mean near-surface cooling, even as the lower-latitude surface cooling slows the uptake of heat by warmer waters and sea level rise slows (Fig. 2). Other scenarios exhibit somewhat similar behavior, although they figure less prominently in the differences between the two models’ projections of GSSLR than in RCP2.6.
The RCP8.5 simulations are particularly intriguing, in that the sea surface temperature anomalies exhibit strikingly similar histories throughout the twenty-first century (Fig. 3, top), and by the end of the twenty-first century, summertime sea ice is too limited to do much in either model, but there are still 9% differences in integrated heat uptake (Fig. 3) and 18% differences in GSSLR (Fig. 2). In the near-surface waters (an average from 0 to 400 m is shown in Figs. 5a,b), which dominate the GSSLR signals, both models exhibit temperature changes that are remarkably similar both in magnitude (ESM2M warms just 4% more than ESM2G) and in their spatial patterns. These near-surface temperature changes include both contributions that are directly forced by the uptake of heat from the atmosphere and internal redistributions of heat tied to circulation changes, such as the spinup of the Antarctic Circumpolar Current and the weakening of the Gulf Stream. Some of the heating differences between the models may reflect a deeper rapidly ventilated thermocline in ESM2M than in ESM2G. The volume of water between 50°N and 50°S that is ventilated within 50 years (as measured by a passive “ideal age” tracer) is roughly 20% larger in ESM2M than ESM2G (172-m versus 141-m average thicknesses in 1981–2000). If the surface warming signal is partly acting as a Dirichlet boundary condition for the ocean’s interior temperature, this greater volume of rapidly ventilated water would lead to a larger heat uptake and GSSLR. These relative differences in the volumes of ventilated water are similar to the differences in the volumes of water warmer that some temperatures appropriate to the thermocline (e.g., 12°C). Whether the differences in ventilation drive the differences in near-surface stratification (see Fig. 1) or whether it is the reverse is beyond the scope of this paper; certainly, there is a connection between them and with the amount of heat that the upper ocean can take up on time scales of decades. However, these near-surface heating differences are not the dominant driver of GSSLR differences in the RCP8.5 simulations.
Figure 5: Temperature change for RCP8.5 averaged over the years 2081–2100, relative to 1861–1900 and corrected for long-term mean drifts, for (left) ESM2G and (right) ESM2M and averaged over the depth ranges of (a),(b) 0–400 m and (c),(d) 800–1200 m. The horizontal-mean temperature changes are 1.59°, 1.66°, 0.56°, and 0.73°C in (a)–(d), respectively. Between 0 and 400 m, the average warming is 4% larger in ESM2M than ESM2G, but between 800 and 1200 m, the average warming is 29% larger in ESM2M than ESM2G.
At a depth of 800–1200 m in the RCP8.5 scenario (Figs. 5c,d), the heat uptake is of profoundly different magnitude between the models (the temperature increase is 29% larger in ESM2M than ESM2G), but still with very similar patterns. This depth is chosen for greater scrutiny because there is a peak in the difference in SLR contributions from water-mass changes between the models at about 1000 m (Fig. 4, right). Both exhibit warming (and an increase in salinity) in the western Atlantic because of a slowdown of the Atlantic meridional overturning circulation with a somewhat stronger warming signal in ESM2M than ESM2G. The Pacific is comparable to the Atlantic in the integrated heat change difference between the models in the 800–1200-m depth range and actually dominates the horizontally averaged steric sea level rise difference because there is no compensating salinity signal. The North Pacific signal is too deep for any of the water involved to have been directly influenced by the surface heat flux anomalies; instead, it is due to circulation changes. The broad warming of the eastern Pacific in both models is consistent with a broad downward displacement of the isopycnals of approximately 100 m in both models. The cooling signals on the western side of the Pacific basin are consistent with a vertical contraction of the subtropical gyres as the overlying waters become more strongly stratified. The temperature signal at about 1000 m in the Pacific is much larger in ESM2M than ESM2G, primarily because the vertical temperature gradients at this depth are much larger in ESM2M than ESM2G (Fig. 1). These deep temperature signals, which make up a large portion of the overall GSSLR difference, illustrate the importance of the ocean’s initial state in determining the details of its forced GSSLR signal.
Discussion and summary
This study examines the differences between the GSSLR projected by two earth system models, which differ only in their ocean components, in order to estimate the uncertainties in twenty-first-century GSSLR projections arising solely from uncertainties in the numerical representation of ocean dynamics and parameterizations of physical processes in the ocean. The interior ocean–mean states of these two models have water-mass biases that broadly straddle the observed properties of the ocean, and their ocean components might be considered cutting-edge geopotential- and isopycnal-coordinate ocean climate models. ESM2G exhibits twenty-first-century GSSLR that is consistently 18% smaller than in ESM2M for all four radiative forcing scenarios. Differences in the amount of heat taken up by the two models would account for a 9% difference in GSSLR, while differences in the thermal expansion coefficient due to different control states would account for a 7% difference. While these differences are highly statistically significant, they are also small enough to suggest that uncertainties in the ocean do not qualitatively alter the expected magnitude of twenty-first-century GSSLR.
There are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., Böning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models’ very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models’ dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models’ identical pre-spin-up initial conditions.
The regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean’s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.


There are two significant caveats to the findings reported here. The first is that since neither of these models explicitly resolves ocean eddies, the role of ocean eddies in rectifying distributions of ocean heat uptake (e.g., Böning et al. 2008), and thus modulating GSSLR, is a source of uncertainty that cannot be addressed here. The second caveat is that these results only apply to the time scales out to 2100. For longer-term projections, the abyssal and deep-ocean responses are much more important. Given the very large differences in the abyssal circulation between the models, which can be detected in the models’ very different ideal age distributions (see Fig. 13 of Dunne et al. 2012) and lead to the models’ dramatically different abyssal temperatures (Fig. 1, left), the two models studied here can be expected to have quite different magnitudes of GSSLR for time scales of multiple centuries to millennia. For instance, the differences in the spun-up temperature profiles between the models (Fig. 1), which accumulated over the course of spin-up runs of over a thousand years, would cause steric sea level differences between the models of approximately 0.6 m, relative to the models’ identical pre-spin-up initial conditions.
The regions where the GSSLR differences appear are also regions where models have profoundly different interior ocean biases. This observation suggests that accurately capturing the ocean’s mean state, especially the stratification (which regulates how circulation changes translate into density changes), the thermocline depth (which appears to partially control the volume of water over which heat is taken up in the twenty-first century), and the mean temperatures (which substantially impact the thermal expansion coefficient) are useful steps toward reducing uncertainties in projections of twenty-first-century sea level rise. To the extent that the uncertainties in projected rise and biases in the spun-up state of the ocean have striking similarities and may have similar causes, or that the biases in the spun-up state directly affect projections of GSSLR, the utility of coupled climate models to accurately predict GSSLR might be appraised by evaluating simulated interior ocean temperature and stratification biases.
The fact that it is the lower thermocline that dominates the GSSLR differences between the models, and not the upper main thermocline that dominates GSSLR itself, suggests that differences in the processes that set and alter the interior ocean water-mass properties in these density ranges may largely explain the differences between these two models. Formation of mode waters and intermediate waters are problematic for many of the coupled models that are included in CMIP5 (e.g., Downes et al. 2011) and are a focus of ongoing development. The two models also represent very differently the overflows (e.g., Legg et al. 2006) that are an integral part of the ocean’s overturning circulation and the formation of water masses that are found at this depth. Increasing diapycnal diffusion is well known to broaden the lower thermocline. Ilicak et al. (2012) diagnose that ESM2M has spurious (numerically induced) diapycnal mixing that is about a third of the size of the explicitly parameterized intended mixing, while that in ESM2G is only about an eighth as large. While this global diagnostic cannot say where this spurious mixing is occurring, it could help explain both the greater breadth of the main thermocline and the deeper penetration of heat in ESM2M compared to ESM2G. Greater scrutiny of the models’ representation of the processes that control the water-mass structure and location of the lower main thermocline might be of particular value for further reducing the oceanic uncertainty in projections of GSSLR.
The biggest uncertainties in projecting twenty-first-century sea level rise are in how much mass the Antarctic and Greenland ice sheets will lose dynamically. Twenty-first-century SLR due to ice sheet dynamics is unknown to within about 1 m of sea level rise (e.g., Pfeffer et al. 2008); while recent rates of observed ice sheet mass loss would only contribute approximately 130 ± 40 mm in the twenty-first century, this increases to between 450 and 700 mm if observed accelerations in ice sheet mass loss continue (Rignot et al. 2011). A second major source of uncertainty is what radiative forcing scenario humans will collectively choose for our planet, here differing between the highest and lowest CMIP5 scenarios by about 125 mm of GSSLR by 2100. Uncetainties in the representation of the dynamics of the ocean and atmosphere and of key physical processes, such as clouds or small-scale ocean mixing, also map significantly onto uncertainties in projected GSSLR. The various coupled climate models used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report give 5% and 95% estimates of twenty-first-century GSSLR that differ by ±42% from the mean for a given forcing scenario (Meehl et al. 2007), or a range of about 190 mm. Since these IPCC models are largely independent, this value is likely to be dominated by atmospheric differences, especially in changing cloud distributions, although ocean differences will also contribute. The comparison presented here suggests that the uncertainty in twenty-first-century steric sea level rise due only to the ocean model formulation and physical processes in the ocean is approximately 28–49 mm (depending on the forcing scenario).
To put these results into the long-term perspective, it is important to recognize that the uncertainties in twenty-first-century GSSLR arising from the ocean (of order 0.05 m) are small compared with the potential sea level rise stemming from interactions between the oceans and ice sheets (of order 1 m). While additional work to improve our ability to capture the physics and dynamics of the ocean in numerical models will be useful, and the role of ocean eddies in modulating GSSLR is largely unexplored, by far the most prominent open questions regarding the ocean’s role in sea level rise center on the interactions between the oceans and ice sheets and how they will evolve in coming centuries.


Dangendorf et al. (2021)
Title:
Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level
Key Points:
Regional coastal sea levels are largely dominated by sterodynamic sea-level variations
Steric sea level signals originate from open ocean regions often thousands of kilometers away
Better understanding of sterodynamic sea-level variations is key for robust near-term coastal sea-level estimates
Keywords:
steric dynamic sea level, coastal sea level, tide gauge, Empirical Orthogonal Functions
Corresponding author:
Dangendorf
Citation:
Dangendorf, S., Frederikse, T., Chafik, L., Klinck, J. M., Ezer, T., & Hamlington, B. D. (2021). Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level. Nature Climate Change, 11(6), 514–520. doi:10.1038/s41558-021-01046-1
URL:
https://www.nature.com/articles/s41558-021-01046-1
Abstract
Understanding historical and projected coastal sea-level change is limited because the impact of large-scale ocean dynamics is not well constrained. Here, we use a global set of tide-gauge records over nine regions to analyse the relationship between coastal sea-level variability and open-ocean steric height, related to density fluctuations. Interannual-to-decadal sea-level variability follows open-ocean steric height variations along many coastlines. We extract their common modes of variability and reconstruct coastal sterodynamic sea level, which is due to ocean density and circulation changes, based on steric height observations. Our reconstruction, tested in Earth system models, explains up to 91% of coastal sea-level variability. Combined with barystatic components related to ocean mass change and vertical land motion, the reconstruction also permits closure of the coastal sea-level budget since 1960. We find ocean circulation has dominated coastal sea-level budgets over the past six decades, reinforcing its importance in near-term predictions and coastal planning.
Introduction
The ability to predict and estimate future coastal sea-level changes depends on a thorough understanding of the observational record. Recent studies provide evidence that the global sea-level budget — the comparison of observed sea-level rise with the sum of individual contributions — can be reasonably closed with independent observations from remote sensing techniques and Argo floats since 2005 (refs. 1,2,3) but also with a combination of observations and reanalysis estimates since 1900 (ref. 4). This points to notable progress since the 2013 fifth assessment report of the Intergovernmental Panel on Climate Change [5]. The budget has also been closed regionally for larger areas off the coast since 2005 (refs. 6,7) and at basin scales since the 1950s [4,8]. However, at the coast, where information is most needed, budget assessments have higher uncertainty due to the number of additional processes that cancel out in the global mean. These include: changes in the sterodynamic component [9], due to ocean circulation change and steric (density-driven) expansion; gravitational, rotational and deformational effects accompanying global barystatic (ocean mass-driven) sea-level changes; and vertical land motion induced by glacial isostatic adjustment, tectonics or local subsidence.
For barystatic sea level and vertical land motion, a number of observations and model estimates now provide constraints at decadal [10] to century scales11. Specifically, the barystatic estimates due to ice-mass loss, terrestrial water storage and glacier melting and their representation at individual locations have considerably improved [4,8].
However, the role of steric sea-level changes and their signature along shallow coastlines is still poorly understood [12,13]. The steric component, defined as the depth integral of density changes in the ocean, is the dominant driver of sea-level variability in the (deep) open ocean (Fig. 1a) with mostly minor contributions coming from ocean-bottom pressure14 (Fig. 1b). In contrast, at the coast where the ocean’s depth decreases to zero, the resulting steric contribution vanishes as well (Fig. 1a). Thus, changes in ocean density will necessarily lead to larger expansion and contraction of the water column in the deep ocean than at the shallow coast15, driving a sea-surface height gradient between the two. This gradient needs to be balanced and hence forces changes in ocean-bottom pressure, with the latter becoming the dominant contributor to sea-level variability at the coast (Fig. 1b). However, due to a wide variety of ocean dynamic processes, coastal sea-level variability cannot be directly derived from steric sea-level changes in the nearby open ocean12,16,17 (Fig. 1c). Due to the lack of this direct relation between the open-ocean steric effects and coastal sea level, both the geographical origin and the underlying processes of the resulting coastal sterodynamic sea-level variations (hereafter SDSL) are poorly understood, inhibiting their proper quantification6,18. Particularly challenging in many coastal regions is the presence of strong boundary currents and coastally trapped waves that mediate open-ocean steric effects to the coast and introduce, due to their coast-parallel flow and propagation, substantial alongshore coherence in sea level often extending over thousands of kilometres17. Indeed, sea-level signals at the continental coasts often originate from perturbations at remote locations13,16, hindering the simple across-shelf integration of steric height from the nearby deep ocean as previously described by ref. 12. While global ocean reanalyses should provide a physically consistent solution for simulating coastal SDSL, they currently face challenges such as drifts and biases due to air–sea fluxes and ocean mixing errors, coarse model resolution or the assimilation of observations that become sparse back in time19. As a consequence, they poorly reproduce observations at the coast20,21 (particularly spatial trends; Extended Data Fig. 1). These knowledge and modelling gaps about past SDSL changes are critical to resolve given that sea-level information is most needed at the coast. Together with the improved information about non-steric processes, these factors call for an alternative, and ideally data-driven, approach for estimating SDSL in the coastal zone.
Fig. 1: Relative roles of ocean-bottom pressure and steric components for coastal SDSL. a,b, Shown is the explained SDSL variance through steric height (a) and ocean-bottom pressure (b) in a historical ocean simulation with the CNRM-CM6-1-HR ESM. c, Schematic of the relationship between deep-ocean steric expansion and ocean-bottom pressure changes on the shallow shelf. The exchange is largely controlled by boundary currents and coastally trapped waves.
Here, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.
Identification of regions of common variability
We start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000 m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P ≤ 0.05) with the corresponding regional mean of SDSLTG.


Here, we reassess coastal sea-level changes in light of increasing data and knowledge of the non-steric contributions and by introducing a two-step statistical framework for estimating coastal SDSL changes. In the first step, we investigate the statistical link between coastal SDSL variability and open-ocean steric height to identify the source regions that communicate with the coast and discuss our current understanding of the physical processes that are involved. In a second step, we use this statistical link to reconstruct coastal SDSL solely on the basis of open-ocean steric height by applying a regression approach based on empirical orthogonal functions (EOFs). Finally, we use the reconstructed SDSL estimates to analyse the coastal sea-level budget for nine selected regions.
Identification of regions of common variability
We start by identifying the geographic source regions of coastal SDSL variability. We select 89 tide-gauge records spanning the period from 1960 to 2012 (the chosen period is constrained by the availability the different datasets; Methods), grouped into nine regions of coherent variability (North Sea, Northwest Atlantic north/south of Cape Hatteras, Northeast Pacific, Hawaii, Japan Sea, West Australia, New Zealand and Western Pacific) and shown in Fig. 2a and Extended Data Fig. 2. These records are first corrected for vertical land motion and barystatic sea-level components to isolate density-related SDSL signals (Methods). Then we follow the principal idea presented in refs. 22,23 for the North Sea and the Northwest Atlantic north of Cape Hatteras and correlate the tide-gauge residuals (hereafter SDSLTG) with steric height time series from improved (via mapping methods and correction schemes for instrumental biases) gridded temperature and salinity fields over the upper 2,000 m (ref. 24) in the adjacent open ocean. A comparison with other steric products can be found in Methods. As source regions, we define all locations showing a significant correlation (P ≤ 0.05) with the corresponding regional mean of SDSLTG.
Fig. 2: Origin and reconstruction of coastal SDSL changes. a, Spatial correlation patterns between the detrended SDSL residuals at tide gauges (SDSLTG, grey dots) and detrended steric height from the open ocean for nine coastal regions. Only significant correlations (P ≤ 0.05) are shown. Note that in some regions, correlation patterns of different regions may overlap. b, Illustration of the reconstruction of SDSLEOF in observations (top) and in validation experiments with ESMs (here illustrated by the CNRM-CM6-1-HR ESM, bottom) for the Northwest Atlantic south of Cape Hatteras. Shadings represent the 95% confidence intervals (CI) from all Monte-Carlo samples. c, Correlation and trend differences between reconstructed SDSLEOF and the a priori known SDSLTG in the validation experiments with 12 ESMs. Also shown is the correlation between SDSLEOF and SDSLTG in actual observations (orange dots). TG, tide gauge; NW, northwest; NE, northeast; NCH, north of Cape Hatteras; SCH, south of Cape Hatteras.
For all regions, significant correlations are widely spread over the oceans and often extend thousands of kilometres away from the tide-gauge sites (Fig. 2a globally and Extended Data Fig. 3 for expanded views into each region). Along eastern boundaries the correlation patterns range from the (sub)tropics to high latitudes with narrowing bands of high correlations along the continental slope moving poleward. In the Atlantic (Extended Data Fig. 3a), steric sea-level variations near the Strait of Gibraltar have recently been linked to both local wind forcing and Atlantic Meridional Overturning Circulation changes16,25, while further north along the Portuguese coastline, sea-level variability is tightly connected to longshore wind forcing13,26,27,28. The along-shelf coherence (Extended Data Fig. 3a) is consistent with the hypothesis that coastally trapped waves communicate SDSL variations from the eastern boundary into the North Sea16,17,28. A similar, but much more pronounced, correlation pattern can be found in the Northeast Pacific, where the largest correlations, r > 0.9, occur around the Equator and off the California coast (Extended Data Fig. 3d). This is consistent with ref. 29, who demonstrated that coastal sea levels along the Californian coastline vary in concert with fluctuations in equatorial trade winds and longshore winds generated around the Aleutian Low. Westerlies in the western and central Pacific generate equatorial Kelvin waves, which first propagate eastward along the Equator and then, after being reflected at the eastern boundary, travel northward as coastal Kelvin waves16,30.
For the western regions in the Atlantic and Pacific, correlations indicate a dynamic connection to the western boundary currents (Kuroshio and Gulf Stream), although with an interesting distinction in the Atlantic north and south of Cape Hatteras31 (Extended Data Fig. 3b,c). North of Cape Hatteras the correlation pattern follows the continental slope into the Labrador Sea and the Subpolar Gyre. This agrees with ref. 23, who provided evidence that Labrador Sea density anomalies (driven by both atmospheric processes in the upper layers and variations in the Deep Western Boundary Current at intermediate and deeper levels) propagate southward as coastally trapped waves32. South of Cape Hatteras, however, highest correlations are directly centred on the Gulf Stream pathway. This is consistent with the suggestion that coastal sea-level variability in this region is linked to a fast barotropic response of the coastal ocean to (overturning-related) large-scale heat divergence in the open ocean33,34 and/or subtle variations in the strength and position of the Gulf Stream35.
In the Indo-Pacific regions (West Australia and Western Pacific), coastal SDSL variations are highly coherent even between widely separated regions leading to overlapping correlation patterns extending from the Bay of Bengal into the Central Pacific (Extended Data Fig. 3g,i). These signals are linked to the El Niño/Southern Oscillation and primarily driven by equatorial trade winds36. These trade winds induce westward propagating equatorial Rossby waves, which first cross the Indonesian throughflow region and then travel poleward as coastally trapped waves along the west coast of Australia37,38. The coasts of New Zealand show coherence with the larger South Pacific Gyre region as well as the warm subtropical currents in the Tasman Sea extending onto the southwestern Australian continental shelves. Sasaki39 used an eddy-resolving ocean general circulation model to show that long baroclinic Rossby waves, forced by wind stress curl over the subtropical gyre, are an important driver of New Zealand’s decadal sea-level variability. For gauges at Hawaii, a typical example of an open-ocean site surrounded by steeply sloping topography, highest correlations are pronounced locally northeast of the islands, indicating a more local control of coastal sea-level variations.
In summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.
Reconstruction of SDSL at the coast
The large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.


In summary, for all nine regions the identified correlation patterns are consistent with known processes induced by ocean dynamics (like wave guides and propagation characteristics) that have also been identified in basic ocean simulation experiments16. This underpins the physical nature of the statistical relationship and suggests that coastal SDSL changes are primarily remotely forced by perturbations in the open ocean and transferred to the coast (Fig. 1c) through the action of (coastally trapped) Kelvin and Rossby waves.
Reconstruction of SDSL at the coast
The large-scale coherence between coastal and open-ocean steric sea level indicates that a purely data-driven reconstruction of SDSL signals along the coast might be possible. Here, we apply an EOF regression approach40 to compute the covariance relationship between coastal SDSLTG and steric height from each source region over 1960 to 2012. This relationship is then used to analyse SDSLTG solely on the basis of steric height in the open ocean (hereafter, SDSLEOF; Methods). The EOF effectively filters the common signal and removes noise from both datasets. The regression character further allows for a scaling of the steric height, which becomes necessary if signals are either amplified (for example, due to resonance processes generated by winds) or damped (for example, due to bottom friction) when travelling towards the coast. We note, however, that the EOF does not consider any time lags, which might play a role if baroclinic Rossby waves with long travel times are involved in the transfer.
To test the robustness of the reconstruction against overfitting and to assess uncertainties, we use ocean simulations from 12 Earth system models (ESM) over the period 1850–2012 with historical forcing (Supplementary Table 2). In the ESMs coastal SDSL, open-ocean steric height and ocean-bottom pressure variations are a priori known and therefore form an ideal testbed for the EOF approach (using source regions similarly determined in each ESM as for the observational record; Methods). We extract in total 12,000 realizations of 53-yr periods to calibrate the reconstruction (with randomly varied model parameters; Methods) and use an independent, random 53-yr period (from the remaining model years) for validation. The resulting time series are displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. In all model runs, the EOF reconstruction mimics coastal SDSL variations reasonably well, which is reflected in significant correlation coefficients over all models and subsamples providing only subtle differences between calibration and validation periods (Fig. 2c). EOF reconstructions in tropical and subtropical coastal regions with known links to the El Niño/Southern Oscillation show slightly larger correlations (median r ≥ 0.86, P ≤ 0.05) than those at higher latitudes (for example, the Northwest Atlantic north of Cape Hatteras) or in large continental shelf seas (for example, the North Sea) (median r = 0.64–0.77, P ≤ 0.05). This is probably related to increased and atmospherically forced barotropic variability in these records, which might mask the remotely forced and density induced SDSL variations28,41,42. Similarly well reconstructed are linear trends in the ESMs (Fig. 2d). These usually agree with the model internal true coastal SDSL signal within a range ±0.7 mm yr–1 in all subsamples and regions and show little evidence for systematic trend biases (median trend differences are of the order of ±0.06 mm yr–1 over both calibration and validation periods) (Fig. 2d). Overall, this demonstrates the skill of the EOF approach in reconstructing coastal SDSL from open-ocean steric height and motivates its application to observations.
The SDSLEOF reconstructions based on open-ocean steric height observations from the source regions are again displayed, as an example, for the Northwest Atlantic south of Cape Hatteras in Fig. 2b and for all regions in Extended Data Fig. 4. We generated an ensemble of 5,000 SDSLEOF reconstructions at each site, which is based on varying barystatic sea-level corrections at tide-gauge records (Methods) and randomly varied parameter choices in the EOF approach (Methods). In agreement with the ESM experiments, the ensemble SDSLEOF reconstructions show significant median correlations to SDSLTG that range from r = 0.62 (P ≤ 0.05) in the Northwest Atlantic south of Cape Hatteras to r = 0.95 (P ≤ 0.05) in the Western Pacific (Fig. 2c). In the three regions that are directly influenced by western boundary currents (Northwest Atlantic south of Cape Hatteras, Japan Sea and New Zealand), SDSLEOF displays slightly lower (but still good) agreement with coastal residual sea level than in the other regions. This is probably related to the more complex dynamics involving mesoscale eddy activity and slowly propagating Rossby waves39,43,44 that are hard to capture in the EOF approach without any consideration of time lags. Such time lags seem to play a minor role in regions dominated by coastally trapped waves, which typically have travel times below a month from the source regions to the coasts26,30. Overall, the EOF reconstructions display an encouraging performance in transferring open-ocean steric height signals toward the coast that exceeds those from standard reanalysis products (Extended Data Fig. 1) and even holds for longer timescales as further discussed in the budget assessment below.
Implications for the coastal sea-level budget
Taking advantage of the improved representation of SDSL variability at the coast, we finally reassess the total coastal sea-level budget for each region by adding the barystatic component back to the reconstructed SDSL component and comparing it to the vertical land motion corrected coastal sea level in each region. This budget is displayed in Fig. 3 for linear (Fig. 3a,b and Table 1) and nonlinear trends (Fig. 3c) during 1960 to 2012. In all regions the trend budget can be closed within the respective uncertainties (Fig. 3b and Table 1) that are, particularly in Northern Europe and North America, dominated by vertical land motion (Fig. 3b). Median differences to observations are everywhere within a range ±0.2 mm yr–1. The only exception is Hawaii, where the median trend is overestimated by 0.4 mm yr–1. We note, however, that there are also substantial uncertainties in the underlying steric products (Extended Data Fig. 5 and Methods) that may account for these differences. At all locations, except Hawaii and the Japan Sea, SDSL components explain the major fraction of the total trend budget (Fig. 3a).
Fig. 3: Coastal sea-level budget over 1950 to 2012. a, Shown are (as pie diagrams for each region) the fractions of the coastal trend budget that are explained by SDSLEOF and barystatic components. b, The linear trend budget of coastal sea level for nine regions after correcting each tide gauge for glacial isostatic adjustment and residual vertical land motion. Blue bars represent regional averages, while the stacked blue/orange bars represent the budget estimated with SDSLEOF and barystatic sea level. c, The rates derived from a nonlinear trend for each component and region. All shadings and error bars represent 95% CI derived from the 5,000-member ensemble.
Table 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.
Region
Observations
(mm yr–1)
Budget
(mm yr–1)
SDSLMEFOF
(mm yr–1)
Barystatic GRD
(mm yr–1)
North Sea
2.01 (1.30;2.76)
2.09 (1.58;2.52)
1.73 (1.28;2.09)
0.36 (0.17;0.56)
NW Atlantic
NCH
1.43 (0.78;2.40)
1.42 (1.02;1.87)
0.76 (0.50;1.14)
0.65 (0.39;0.87)
NW Atlantic
SCH
1.40 (0.52;2.32)
1.48 (1.12;1.80)
0.76 (0.56;0.98)
0.72 (0.42;0.97)
NE Pacific
1.23 (0.20;2.26)
1.40 (0.97;1.80)
1.02 (0.89;1.20)


Table 1 Linear trend budget. Linear trends for coastal sea level (corrected for vertical land motion), the total budget and each contributor over the period 1960 to 2012. All trends are given as a median of the 5,000-member ensemble with the 95% CIs provided in brackets. GRD, gravity, rotation and deformation. NW Atlantic NCH/SCH, Northwest Atlantic north/south of Cape Hatteras; NE Pacific, Northeast Pacific.
Region
Observations
(mm yr–1)
Budget
(mm yr–1)
SDSLMEFOF
(mm yr–1)
Barystatic GRD
(mm yr–1)
North Sea
2.01 (1.30;2.76)
2.09 (1.58;2.52)
1.73 (1.28;2.09)
0.36 (0.17;0.56)
NW Atlantic
NCH
1.43 (0.78;2.40)
1.42 (1.02;1.87)
0.76 (0.50;1.14)
0.65 (0.39;0.87)
NW Atlantic
SCH
1.40 (0.52;2.32)
1.48 (1.12;1.80)
0.76 (0.56;0.98)
0.72 (0.42;0.97)
NE Pacific
1.23 (0.20;2.26)
1.40 (0.97;1.80)
1.02 (0.89;1.20)
0.38 (–0.02;0.71)
Hawaii
1.55 (1.24;1.89)
1.18 (0.71;1.58)
0.47 (0.27;0.67)
0.71 (0.31;1.05)
Japan Sea
1.29 (0.89;1.75)
1.13 (0.64;1.60)
0.48 (0.12;0.81)
0.65 (0.35;0.96)
West Australia
1.48 (1.11;1.85)
1.60 (1.10;2.04)
0.89 (0.61;1.19)
0.71 (0.34;1.03)
New Zealand
1.74 (1.16;2.35)
1.66 (1.12;2.11)
0.99 (0.64;1.25)
0.66 (0.32;0.99)
The budget terms also explain the observed interannual variability, which is expressed by an explained variance ranging from 38% at sites in the Northwest Atlantic south of Cape Hatteras to 91% along the Californian coast in the Northeast Pacific (Fig. 2c and Extended Data Fig. 4). The temporal variability is largely dominated by the SDSL component at all sites (Fig. 3c), although barystatic sea level through ice-mass loss and natural and anthropogenic terrestrial water storage variations (Methods) adds an accelerating signal to the rates. Largest accelerations in barystatic sea level are found around the Hawaiian Islands, where rates have been increasing from close to 0 to >2 mm yr–1 since the late 1990s. However, in the total budget, this acceleration has been reversed by strong negative anomalies in the SDSL components since the early 2000s (Fig. 3c). In contrast, Northern European coastlines only exhibit a small barystatic sea-level signal with an average rate of 0.4 (0.2; 0.6) mm yr–1 over 1960 to 2012 but this is (despite the large uncertainties in different steric products) counterbalanced by the largest average SDSL rates of all sites (Fig. 3b). In the Northeast Pacific, SDSL shows the well-known sea-level suppression since the 1970s45, while at gauges in the Western Pacific and West Australia, SDSL is characterized by a sustained acceleration from close-to-zero rates before the 1980s to >14 mm yr–1 in the 2010s (in an opposite direction to the negative SDSL rates at Hawaii); a value that is six times larger than the simultaneous barystatic sea-level rise. This acceleration has previously been attributed to anthropogenic forcing46 and represents the most pronounced SDSL sea-level change signal of all sites. Further accelerations in the SDSL terms can be seen in the Japan Sea and New Zealand since the early 1980s and along the coasts of Northeast America north of Cape Hatteras since the 1990s but their magnitudes are far smaller than those seen in the tropical Indo-Pacific regions and an attribution to natural and anthropogenic forcing has not yet been achieved.
The large site-specific rates also suggest substantial regional SDSL deviations from the simultaneous global mean (Fig. 4b) that are considerably larger than the spatial variations that have been contributed by barystatic sea level. Such deviations are important for coastal planning purposes, particularly at engineering-relevant timescales of a few decades. To generalize the potential of coastal SDSL variations to deviate from the global mean at varying timescales, we calculate moving trends for window sizes between 10 and 53 yr for both coastal SDSL and global mean steric sea level and assess their respective ratio (Fig. 4). At decadal timescales (~10 yr), local variations can be several hundred times larger or smaller than the global mean in any region considered here. This number decreases with increasing timescale but regional deviations can still be as large as ten, six and three times the simultaneous global mean for periods of 20, 30 and 50 yr, respectively. Given the dominance of SDSL variations at these timescales (Fig. 3c), this indicates that the key to more robust near-term coastal sea-level estimates for the coming decades clearly lies in a better understanding of SDSL variations and their geographical origin.
Fig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53 yr. Three periods at 20, 30 and 50 yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10 yr, are shown in b.
Our results represent a notable advance in estimating drivers of regional coastal sea level over the past 53 yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.
Methods
Tide-gauge data and corrections


Fig. 4: Scaling of local and global SDSL. a, The maximum ratio between coastal SDSLEOF and global mean steric sea level observed for different periods and each of the nine regions between 1960 and 2012. The ratios have been derived from moving trends calculated for window sizes ranging from 10 to 53 yr. Three periods at 20, 30 and 50 yr have been highlighted, demonstrating that SDSL can differ by up to ten, six and three times from the global mean. The tick black line highlights the factor 1 indicating variations of magnitude equal to the global mean. The corresponding SDSL time series, smoothed with a singular spectrum analysis using an embedding dimension of 10 yr, are shown in b.
Our results represent a notable advance in estimating drivers of regional coastal sea level over the past 53 yr. Regardless of the accelerating barystatic sea-level terms around the globe, coastal sea-level variations are still largely dominated by the SDSL terms. This highlights the urgent need for a better understanding of the underlying physics to provide robust, near-term sea-level predictions. Our analysis represents a step in this direction as it demonstrates that for all analysed regions, coastal SDSL signals originate from the open ocean that are often thousands of kilometres away from individual sites. This reinforces the key role of large-scale ocean circulation in transferring the steric signal to the coast. The transfer can accurately be approximated using the EOF technique introduced here and allows for, together with the other components, improved closure of the coastal sea-level budget. Further modelling studies, such as those recently undertaken for the Northern European Shelf28,47, are required to clarify the involved oceanographic processes and to develop dynamical downscaling procedures that allow for more robust projections along the coast48.
Methods
Tide-gauge data and corrections
We make use of a set of 89 annual tide-gauge records from nine coastal regions taken from the online portal of the Permanent Service for Mean Sea Level in Liverpool49 and listed in Supplementary Table 1. The nine coastal regions have been selected on the basis of previous studies demonstrating that their tide-gauge records show similar dynamic sea-level variability4,21,25,29,36,39,43. In each region, individual records have been chosen on the basis of criteria such as data availability (>75%, except of a few exceptions primarily in the Indo-Pacific) and homogeneity (visual inspections and data flags). The individual records, together with their corresponding virtual stations and a cross-correlation matrix, are shown in Extended Data Fig. 2. Nine clusters of pronounced positive correlations appear, thus underpinning the coherence within each region. Existing data gaps have been filled with the local realizations from the hybrid sea-level reconstruction from ref. 50. The local realizations from the hybrid reconstruction include a local residual process from the Kalman Smoother that accounts for local effects such as vertical land motion (but does not contribute to the sea-level fields in the ocean and the corresponding global mean sea level) and therefore almost perfectly mimics their long-term trends50,51. They are also highly correlated with the real tide gauges (Supplementary Table 1). The gap-filling is a requirement for the EOF approach outlined below and avoids issues with benchmark differences when being merged to regional means52. We note, however, that the median percentage of data gaps is only 6% over all sites (Supplementary Table 1) and thus has a negligible influence on our results. Our major aim here is to investigate the SDSL variability in each of these regions. A challenge in this regard stems from the fact that tide-gauge records are affected by numerous different additional processes (vertical land motion and barystatic sea level) that may mask the actual SDSL signals. To isolate the SDSL variability at each site, we therefore initially remove vertical land motion and barystatic components. Each of these corrections comes with notable uncertainties. These uncertainties are considered here and build the basis for a probabilistic ensemble assessment with 5,000 members.
The first correction corresponds to vertical land motion, which primarily affects coastal sea level at lowest frequencies and induces spatially varying trends between individual locations. To correct for vertical land motion, we fit a linear trend to the differences between each tide-gauge record (before the gap-filling) and the nearest-neighbour time series from the hybrid reconstruction (that does not include the residual component and is corrected for its median glacial isostatic adjustment field) from ref. 50, which combines a process-based Kalman Smoother51 with ordinary EOF reconstructions53. As the Kalman Smoother aligns a series of predescribed processes (barystatic fingerprints, dynamic sea-level changes from climate models and 161 glacial isostatic adjustment models but excluding non-climatic local vertical land motion; ref. 51) to a global set of tide gauges, the difference between the hybrid reconstruction and tide gauges should, next to model errors, predominantly be driven by local vertical land motion51. The basic idea is similar to the Gaussian process approach used in ref. 54 for future projections and estimates based on the difference between tide-gauge records and satellite altimetry10 but it has the advantage of providing much longer residual series covering the entire length of tide-gauge records back to 1900 (that is, the period over which the hybrid reconstruction is available). As a preliminary cross-validation, we compare our estimates to the vertical land motion dataset from ref. 4. Their dataset is based on Global Navigation Satellite System observations and differences between tide gauges and nearby satellite altimetry but corrected for the nonlinear crustal components of present-day barystatic sea-level change and, therefore, is directly comparable to ours. The corrections are only available at 65 out of our 89 tide-gauge sites. Both datasets are significantly correlated (r = 0.78, P ≤ 0.05) with a root mean square difference of 0.8 mm yr–1 (which is substantially smaller than that from satellite altimetry minus tide gauge (1.22 mm yr–1); ref. 55) but vertical land motion estimates from the hybrid reconstruction show a higher correlation to linear trends from tide-gauge observations (r = 0.91, P ≤ 0.05) than those from ref. 4 (r = 0.67, P ≤ 0.05) (Extended Data Fig. 6). For this reason, as well as the fact that the hybrid reconstruction provides vertical land motion estimates at more stations than the ref. 4 dataset, we proceed with the hybrid reconstruction-based vertical land motion estimates. The largest uncertainty in the hybrid reconstruction-based vertical land motion estimates stems from the 161 glacial isostatic adjustment models used in the Kalman Smoother from ref. 53 that consider different solid-Earth parameters (lithosphere thickness and mantle viscosity) and varying global deglaciation histories over the past 20,000 yr. The second uncertainty in the vertical land motion estimates is related to fitting of the linear trend to noisy data. This uncertainty has been modelled considering that the residuals are normally distributed but temporally correlated. To consider both uncertainties in the budget assessment, we perturb the vertical land motion estimates with random noise from the fitting uncertainty as well as the uncertainty from the 161 glacial isostatic adjustment models (considering their spatial correlation). This results in a 5,000-member ensemble of plausible vertical land motion corrections at each site.
The next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.


The next components that we remove from the tide-gauge records are the barystatic terms due to contemporary mass redistribution. Here, we make use of a 5,000-member ensemble by ref. 4 that combines sea-level contributions from ice-sheet56,57,58,59,60, glacier11,61 and terrestrial water storage62,63,64,65 observations and reanalysis estimates and accounts for observational and model uncertainties. The barystatic effects have little effect on interannual variability of sea level but they are highly nonlinear and produce large spatial variability between individual locations (Fig. 3b). Removing the two 5,000-member ensembles of vertical land motion and barystatic sea level results in an ensemble of SDSLTG residuals including the uncertainties resulting from the initial corrections.
In addition to vertical land motion and barystatic effects, tide-gauge records are also affected by the barotropic response of the ocean to atmospheric forcing. This consists of barotropic wind forcing and the inverted barometer response to sea-level pressure fluctuations over the oceans and represents a dominant fraction of the sea-level spectrum from intra-annual to decadal scales42. While the barotropic wind forcing term is usually considered as an inherent process of SDSL, it may introduce large variability of opposite sign at different locations27,28 and mask the actual SDSL variability seen by a tide gauge41. The latter may particularly be the case, when SDSL signals have, for instance, been initiated by wind forcing in remote regions affected by different atmospheric circulation systems than those responsible for the local barotropic signals. For this reason, we initially remove these wind and pressure effects from each tide-gauge record for the correlation and EOF analyses. Note, however, that we later add this component back to SDSL for the overall validation and the budget assessment. Thus, the SDSLEOF components shown in Figs. 1–3 in fact represent SDSL plus atmospheric pressure effects. As an estimate of these effects, we use the outputs from barotropic simulations with the MIT global circulation model forced with atmospheric reanalysis winds and sea-level pressure from the twentieth century reanalysis66 over the period 1871–2012. Further details on the model configuration and detailed validations can be found in refs. 21,42. The wind and pressure components are most important at higher latitudes, where stratification is weak, and they introduce both spatially varying temporal trends as well as pronounced intra-annual to decadal variability [42].
Steric height data
We estimate steric changes from a gridded temperature24 and salinity reconstruction67 on the basis of hydrographic profiles covering the upper 2,000 m of the ocean over the 1960 to 2012 period using the TEOS-10 GSW software for MATLAB68. This temperature and salinity reconstruction is based on an optimal interpolation approach, which uses the CMIP5 multimodel ensemble to derive correlation scales and to set the initial field. We note that there are many other gridded temperature and salinity datasets available that use different mapping methods than ref. 24. Three of these datasets have additionally been analysed here: ref. 69 and EN4 (EN4.2.1.)70 with two different mechanical bathythermograph (MBT) and expendable bathythermograph (XBT) bias corrections schemes following refs. 71,72. There are notable differences in linear trends calculated from each of the steric height datasets over 1960 to 2012 (Extended Data Fig. 5a–d) that are particularly pronounced in areas of major ocean circulation systems (>2 mm yr–1)73. These large differences between individual products may be partly related to the distinct mesoscale eddy activity that is not resolved by hydrographic observations as well as the different mapping approaches in each reconstruction24. They also feed in the SDSLEOF reconstruction (that essentially covers information from these circulation systems) when applied to each dataset individually (Extended Data Fig. 5e,f). However, the SDSLEOF reconstruction based on the ref. 24 dataset has the smallest trend differences to the SDSLTG in most regions (Extended Data Fig. 5) and also provides the best representation of variability (Extended Data Fig. 5f). It is interesting to note that regions with the largest interproduct trend spread also show the largest spread in correlations to SDSLTG with ref. 24 data providing far better agreement than all other products. For this reason, and since the dataset from ref. 24 has been shown to represent a methodological improvement over former reconstructions, we limit our analysis in the main paper to this particular dataset.
EOF reconstruction
The EOF approach assumes that two or more sets of variables share a certain degree of similar variability, which can be expressed by distinct spatial patterns (EOF modes) for each individual variable (here, steric height from the open ocean and SDSLTG at the coast) and a common principal component (PC) corresponding to each spatial pattern. In the literature, similar approaches (but using canonical correlation analysis74 or cyclostationary EOFs40) have been used to reconstruct sparse/short climatic data (for example, precipitation) on the basis of covariates covering much longer periods than the variable of interest (for example, sea-level pressure or sea-surface temperature). Here, we use this approach to transfer steric height estimates from the source regions (identified with the correlation patterns in Fig. 2a) to the coast represented by the tide-gauge residuals after removing vertical land motion, barystatic sea level and (barotropic) wind and pressure effects (SDSLTG). This is done in three steps:
We calculate EOFs over the 1960–2012 period between detrended and smoothed (using a randomly chosen smoothing window between 3 and 5 yr) steric height and SDSLTG. This produces several different modes with variable-specific spatial patterns and common PCs. In our reconstruction, we only use a subsample of these modes that share a certain degree of variance in each region. We randomly varied the corresponding threshold, such that only those modes are considered that cumulatively explain between 92 and 98% of the variance of the entire coupled field. On average, this resulted in the consideration of five (West Pacific) to nine (North Sea) modes in the different regions.
The spatial pattern of the steric height from the EOF analysis is then projected back onto the entire (1960–2012) non-detrended and non-smoothed steric height fields from the source region to produce a series of each PC.
Finally, the PCs from step 2, now solely based on steric height from the open ocean, are projected onto the spatial patterns from tide-gauge residuals (SDSLTG), which produces an EOF-based SDSL reconstruction (SDSLEOF) over the entire 1960–2012 period at each site.
The SDSLEOF reconstructions are then evaluated as spatial averages over all sites in each region. By using varying barystatic corrections and by considering randomly varied parameter choices, we produce 5,000 ensemble members that are used to assess uncertainties of the EOF reconstruction. The EOF approach has two major advantages compared to simple field averages over the source region as formerly used in refs. 22,23 While a simple area average assumes that the steric signal from the open ocean is one on one transferred toward the coast, there are factors at play that may dampen or amplify the signal while propagating from the open ocean toward the coast. The regression character of the EOF approach explicitly takes this into account and scales the signal to match the variability seen at tide gauges. Furthermore, EOF analysis decomposes a field into common modes. As typical for many other atmospheric or oceanographic time series, most of the variance of the entire field is contained in the first few modes, while local effects move as noise into lower EOFs. Thus, the EOF approach is robust against local outliers. To test the stability of the EOF reconstruction against increasing data uncertainties in the steric products before the 1980s, we also calculated a second 5,000-member ensemble on the basis of PCs calculated since solely 1980 (Extended Data Fig. 7). We do not find any significant differences in the reconstructions based on PCs calculated over the entire period or only since 1980. Correlations are, in all cases, >0.98 with the only exception being the three western boundary currents where the correlation coefficients are between 0.92 and 0.94. The trends are also not significantly different between the two ensembles (Extended Data Fig. 7b).
Earth system models