Figure 4: Ocean dynamic SLC northwest of Europe, as simulated by (a) the CMIP5 GCM HadGEM2-ES and (b) dynamically downscaled using regional ocean model NEMO-AMM7, and by (c) the CMIP5 GCM MPI-ESM-LR and (d) dynamically downscaled, for the scenario RCP8.5 (2074–2099 minus 1980–2005). Figure adapted from Hermans et al. (Reference Hermans, Tinker, Palmer, Katsman, Vermeersen and Slangen2020).
Vertical land motion
In addition to the ocean and ice contributions, relative SLC is affected by VLM (Table 1), which may amplify or even dominate the SLC experienced at coastal locations. AR5 and SROCC used GIA models to estimate the VLM contribution to SLC, whereas AR6 based its VLM estimate on the geological background rate at tide gauge stations, derived using the Gaussian Process Model from (Kopp et al., Reference Kopp, Horton, Little, Mitrovica, Oppenheimer, Rasmussen, Strauss and Tebaldi2014; Table 1). Neither method provides a satisfactory answer, given that the former excludes non-GIA VLM contributions, and the latter requires assumptions regarding the spatio-temporal extrapolation of the tide-gauge derived background rates to areas without tide gauge information by using a GIA model as a prior. AR6, therefore, stated that ‘there is low to medium confidence in the GIA and VLM projections employed in this Report. In many regions, higher-fidelity projections would require more detailed regional analysis’.
Work published after the IPCC AR6 literature deadline has provided new observation-based estimates of VLM for 99 coastal cities based on InSAR observations (Wu et al., Reference Wu, Wei and D’Hondt2022) and along the world’s coastlines using GNSS data (Oelsmann et al., Reference Oelsmann, Passaro, Dettmering, Schwatke, Sánchez and Seitz2021). However, even with better observational estimates, significant assumptions are required when extrapolating these into the future. Both AR5 and AR6 assume VLM rates remain constant over time, an assumption that is wrong in regions that are tectonically active (where VLM will be nonlinear and stochastic) or where VLM occurs in response to groundwater and gas extractions (which is strongly dependent on societal choices). A potential solution is to use expanded geological reconstructions of paleo sea level on millennial time scales to constrain long-term average trends (Horton et al., Reference Horton, Shennan, Bradley, Cahill, Kirwan, Kopp and Shaw2018b).
Conclusions and future perspectives
In this overview, we have discussed several aspects of sea-level projections: recent developments in the projections, how they compare against observations, and potential future research directions: ‘how we got here’ (section ‘Key advances in sea-level projections up to IPCC AR6’), ‘where we are’ (section ‘Comparison of the AR5 model simulations with observations’) and ‘where we’re going’ (section ‘Moving towards local information’).
Key differences between AR5, SROCC and AR6 include the use of new climate model information (CMIP6) and the use of emulators to constrain the projections to the AR6 assessment of Equilibrium Climate Sensitivity (section ‘Updated climate model information and the use of emulators’), new information for the different projected contributions to sea-level change (section ‘Differences in the projected contributions to SLC’), and the treatment of projections outside the likely range (section ‘Sea-level projections outside the likely range’).
The likely range projections of GMSL and regional SLC at 2100 show relatively modest changes from AR5 to SROCC and AR6, given approximately equivalent climate change scenarios (sections ‘Updated climate model information and the use of emulators’ and ‘Differences in the projected contributions to SLC’): under RCP2.6/SSP1–2.6 from 0.25–0.58 m (AR5) to 0.33–0.62 m (AR6); under RCP8.5/SSP5–8.5 from 0.49–0.95 m (AR5) to 0.63–1.01 m (AR6). Substantial reductions in the uncertainty of the Greenland and glacier contributions to GMSL at 2100 under SSP5–8.5 for AR6 are counterbalanced by an increase in the Antarctic uncertainty, which leads to relatively small changes in overall uncertainty at 2100 between AR5 and AR6.
In AR6, the explicit inclusion of low confidence projections highlighted the deep uncertainty associated with the dynamical ice sheet contribution (section ‘Sea-level projections outside the likely range’), which was communicated through the use of ‘low-likelihood high-impact’ storylines (IPCC, Reference Masson-Delmotte, Zhai, Pirani, Connors, Péan, Berger, Caud, Chen, Goldfarb, Gomis, Huang, Leitzell, Lonnoy, JBR, Maycock, Waterfield, Yelekçi, Yu and Zhou2021; Fox-Kemper et al., Reference Fox-Kemper, Hewitt, Xiao, Aðalgeirsdóttir, Drijfhout, Edwards, Golledge, Hemer, Kopp, Krinner, Mix, Notz, Nowicki, Nurhati, Ruiz, Sallée, Slangen, Yu, Masson-Delmotte, Zhai, Pirani and Zhou2021a). Regional SLC projections based on the low confidence projections were also provided by AR6, but we highlight that more work is needed on understanding and physical modelling of the ice sheet contributions, and on the potential for different regional estimates associated with the partitioning of Greenland and Antarctic ice mass loss.
Our comparison of AR5 projections with observations for the period 2007–2018 shows that the rates of change agree within uncertainties for GMSL and for individual contributions (section ‘Comparison of the AR5 model simulations with observations’), which is in line with previous studies focusing on total sea-level change (Wang et al., Reference Wang, Church, Zhang and Chen2021a) and the ocean heat uptake contribution (Lyu et al., Reference Lyu, Zhang and Church2021). Monitoring the projections against observed changes is important as it can help to constrain future projections.
In terms of future developments of sea-level projections (section ‘Moving towards local information’), we highlight the need for dynamical ocean downscaling to represent processes missing in GCMs, such as tidal effects and local currents in shelf sea regions, to better estimate future ocean dynamic SLC. This would also improve simulations of key small-scale processes at the ocean-ice interface that affect the climatic drivers of ice sheets and therefore projections of their future evolution. It would also lead to a better quantification of the effects on mean SLC on, for example, tidal characteristics and wave propagations to understand the potential compounding effects on future coastal flood hazards. A second aspect that is relevant to relative sea-level projections, in particular in low-lying delta regions, is the need for improved VLM observational estimates and projections. This will particularly impact coastal SLC projections, as flood risks depend on (and in some parts of the world are dominated by) the movement of the land in addition to the changes in water level.
In this paper, we have focused on sea-level projections up to 2100. However, it is important to note that sea-level change does not stop in 2100. Currently, projections beyond 2100 are typically based on different methods compared with the projections up to 2100, due to a lack of model simulations and literature. For instance, in AR6 the time series were extended to 2150 assuming constant ice sheet rates post 2100 and the Gaussian process emulators were substituted with parametric fits. Unfortunately, the use of different methods tends to lead to discontinuities in the time series. To fill this gap, we need better understanding and process modelling of the different components, such that consistent methods can be used to generate long-term projections for the next IPCC assessment report and beyond. This will allow investigations of for instance the sea-level response to surface warming overshoot scenarios, or the inclusion of tipping points in sea-level projections (e.g., Lenton et al., Reference Lenton, Rockström, Gaffney, Rahmstorf, Richardson, Steffen and Schellnhuber2019). These are only some of the many potential research avenues associated with long-term sea-level projections, all of which are important to investigate given the long-lasting commitment and widespread consequences of future sea-level rise.


Li et al. (2022)
Title:
The Impact of Horizontal Resolution on Projected Sea-Level Rise Along US East Continental Shelf With the Community Earth System Model
Key Points:
The high resolution (HR) Community Earth System Model reduces biases in dynamic sea level (DSL) and circulation on US east continental shelf
Compared to the low resolution model, the HR projects enhanced (reduced) trends of DSL rise along the US south (north) east continental shelf
Different DSL rise patterns are related to different Gulf Stream reductions under a weakening Atlantic Meridional Overturning Circulation
Corresponding author:
Dapeng Li
Citation:
Li, D., Chang, P., Yeager, S. G., Danabasoglu, G., Castruccio, F. S., Small, J., et al. (2022). The Impact of Horizontal Resolution on Projected Sea‐Level Rise Along US East Continental Shelf With the Community Earth System Model. Journal of Advances in Modeling Earth Systems, 14(5), e2021MS002868. doi:10.1029/2021ms002868
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021MS002868
Abstract
The Intergovernmental Panel on Climate Change Fifth Assessment Report lists sea-level rise as one of the major future climate challenges. Based on pre-industrial and historical-and-future climate simulations with the Community Earth System Model, we analyze the projected sea-level rise in the Northwest Atlantic Ocean with two sets of simulations at different horizontal resolutions. Compared with observations, the low resolution (LR) model simulated Gulf Stream does not separate from the shore but flows northward along the entire coast, causing large biases in regional dynamic sea level (DSL). The high resolution (HR) model improves the Gulf Stream representation and reduces biases in regional DSL. Under the RCP8.5 future climate scenario, LR projects a DSL trend of 1.5–2 mm/yr along the northeast continental shelf (north of 40° N), which is 2–3 times the trend projected by HR. Along the southeast shelf (south of 35° N), HR projects a DSL trend of 0.5–1 mm/yr while the DSL trend in LR is statistically insignificant. The different spatial patterns of DSL changes are attributable to the different Gulf Stream reductions in response to a weakening Atlantic Meridional Overturning Circulation. Due to its poor representation of the Gulf Stream, LR projects larger (smaller) current decreases along the north (south) east continental slope compared to HR. This leads to larger (smaller) trends of DSL rise along the north (south) east shelf in LR than in HR. The results of this study suggest that the better resolved ocean circulations in HR can have significant impacts on regional DSL simulations and projections.
Plain Language Summary
Projecting future sea-level rise has great socioeconomic value. Based on long-term global high-resolution Community Earth System Model simulations, we analyze future sea-level rise in the Northwest Atlantic Ocean. Two identical sets of simulations were conducted with different horizontal resolutions. Comparisons between the two sets of simulations show different sea-level rise projections along the US east continental shelf between the low-resolution (LR) and high-resolution (HR) models. At the northeast shelf, HR projects a sea-level rise of 0.8 mm/yr, less than half of the trend (1.7 mm/yr) projected by LR. At the southeast shelf, HR projects a sea-level rise of 0.6 mm/yr, while the trend in LR is statistically insignificant at only 0.15 mm/yr. We attribute the different sea-level rise projections to the different ocean circulations simulated in LR and HR. Under global warming, LR projects a decrease in Gulf Stream flow along the entire east continental slope, while the decrease in Gulf Stream strength is confined to the southeast continental slope in HR. This study provides an explanation for the discrepancy in regional sea-level rise projections between low- and high-resolution climate models and thus improves our understanding of projected future sea-level rise.
Introduction
Sea-level rise has been listed as one of the major impacts of global warming by the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (Collins et al., 2013). Based on an analysis of an urban protection data set, Hallegatte et al. (2013) predicted an increase in the cost of global flooding from ∼$6 billion/year in 2005 to $60–63 billion/year in 2050 due to future sea-level rise and land subsidence. With ∼41% of global population residing in coastal areas (Martínez et al., 2007), understanding future coastal sea-level rise is of great socioeconomic importance.
The US east coast has been recognized as one of the hot spots for future sea-level rise (Little et al., 2019; Yin et al., 2009). Based on Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model (CM) global simulations at 1˚ horizontal resolution, Yin et al. (2009) reported ∼20 cm future dynamical sea level (DSL) rise off the US northeast coast. By decomposing the DSL rise into local steric height and mass transport components, they found: (a) negative and positive (referenced to global mean) local steric height increases in coastal and open ocean regions; (b) a large cancellation between the negative local steric height and the positive mass transport in coastal regions. Studies also indicate that DSL along the US east coast is related to the Atlantic Meridional Overturning Circulation (AMOC). Based on “hosing” experiments (in which freshwater forcing is artificially applied at the subpolar North Atlantic Ocean), Levermann et al. (2005) first showed DSL rises near the North America coasts under a weakening AMOC. They attribute the changes in DSL to changes in geostrophic circulation (Levermann et al., 2005). Near the US northeast coasts, the same DSL and AMOC relation has been repeatedly documented in subsequent climate simulations forced by future global warming scenarios (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009). By comparing 25 different models (at ∼1˚ horizontal resolution) participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5), Little et al. (2019) showed that most models exhibit DSL rises near the US northeast coast with decreasing AMOC. However, large uncertainty exists in projected future DSL rises given the spread across different models (Little et al., 2019).
Most climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1˚) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1˚) and high-resolution (0.1˚ ocean and sea ice; and 0.25˚ atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.


Most climate simulations submitted for CMIPs are based on standard resolution (a nominal horizontal resolution of 1˚) climate models (e.g., Flato et al., 2013). Recent advancements of computing power and storage capacity have enabled high resolution (HR) climate simulations. Based on comparisons of a pair of century long CESM simulations at the standard resolution (1˚) and high-resolution (0.1˚ ocean and sea ice; and 0.25˚ atmosphere and land), Small et al. (2014) showed that the HR CESM produces more realistic regional simulations than the standard resolution model. Using a longer and much more comprehensive set of CESM simulations than in Small et al. (2014), Chang et al. (2020) found that HR CESM significantly improves climate simulations in many aspects at both basin and regional scales. Chang et al. (2020) further showed that increasing model horizontal resolution can affect future climate projections, in line with previous studies (Roberts et al., 2020; van Westen et al., 2020). By analyzing GFDL CM simulations with different horizontal resolutions, Saba et al. (2016) showed that the warming rate projected by HR is almost double the rate projected by LR in the North Atlantic continental shelf. They suggested that the enhanced warming in HR was associated with improved ocean circulation.
The refinement in model horizontal resolution improves sea level simulations. Higginson et al. (2015) suggested that models with coarse resolution may produce erroneous coastal sea level due to inadequate model resolution. By comparing global ocean sea-ice simulations at four different horizontal resolutions (2˚, 1˚, 0.5˚, and 0.25˚), Penduff et al. (2010) showed that the 0.25˚ resolution model can capture sea-level variability more realistically than the others in ocean eddy active regions. Thus, the impacts of model horizontal resolution on future sea-level change deserve focused exploration (Little et al., 2019). In this study, we examine the benefits of HR climate simulations by analyzing the projected sea level change in the Northwest Atlantic Ocean. The novelty of this work lies in the fact that the pair of HR and LR CESM simulations analyzed in this work are much longer than those analyzed in previous studies. They consist of a 500-year preindustrial control (CTRL) simulation and a 250-year (1850–2100) historic and future transient (TNST) climate simulation branched from CTRL (Chang et al., 2020). These multi-century simulations completed by the International Laboratory for High-Resolution Earth System Prediction (iHESP) are much longer than the simulation period (1950–2050, 100 years) specified in the High Resolution Model Intercomparison Project (HighResMIP, Haarsma et al., 2016). The long integration time reduces model drift and thus potentially improves the fidelity of simulation results. The objectives of this work are to (a) compare LR and HR CESM with observations to validate model results, (b) estimate the long-term sea-level trends along the US east continental shelf in HR and LR, (c) explore how refinement in model resolution impacts ocean circulation and sea-level projections. The reason we focus on ocean circulation is because previous studies have shown DSL rises near the US east coast are associated with a weakening AMOC (Levermann et al., 2005; Little et al., 2017; Yin et al., 2009). However, previous sea-level projections near the US east coasts are all based on LR models. Here we revisit this issue and compare HR and LR projected sea-level rise. Although the resolution of HR is much higher than that of LR (see Table 1 for details), HR is still too coarse to fully resolve small scale dynamical processes near the coasts. Regional downscaling with higher resolution is needed to simulate the full range of coastal dynamics relevant to sea-level rise. The manuscript is structured in five sections. Sections 2 and 3 describe data and methods, respectively. Section 4 presents results and discussion, followed by a summary in Section 5.
Table 1: Four 250-Year CESM Simulations Analyzed in This Study
Resolution   |  TNST/CTRL   |   Nominal horizontal resolution for ocean and sea-ice (atmosphere and land)   |   Vertical layers for ocean (atmosphere)     |    Climate forcing
LR      TNST    1 (1)   60 (30) 1850–2005: Historic forcing, 2006–2100: RCP 8.5
LR      CTRL    1 (1)   60 (30) 251-500 model year: Climate forcing of 1850
HR      TNST    0.1 (0.25)      62 (30) 1850–2005: Historic forcing, 2006–2100: RCP 8.5
HR      CTRL    0.1 (0.25)      62 (30) 251-500 model year: Climate forcing of 1850
Note. LR and HR stand for low and high resolution, respectively. TNST and CTRL stand for historic/future-transient and pre-industrial control simulations, respectively. TNST simulations were branched from respective CTRL simulations at year 250.
Data
CESM CTRL and TNST Climate Simulations
A comprehensive overview of the CESM CTRL and TNST climate simulations completed as a part of the iHESP partnership is presented in Chang et al. (2020). Here, we present a brief summary of the CESM simulations (Table 1). The CESM CTRL and TNST simulations are designed following the CMIP5 protocol (Taylor et al., 2012). The CTRL experiment is a 500-year simulation forced with perpetual climate forcing for year 1850. The TNST simulation is branched from the CTRL simulation at year 250 and forced with historic climate forcing from 1850 to 2005 and RCP 8.5 emission scenario climate forcing from 2,006 to 2,100. The model code base is CESM1.3 and the component models include the Parallel Ocean Program version 2 (POP2; Danabasoglu et al., 2012; Smith et al., 2010) for the ocean, the spectral element dynamical core (SE-dycore) Community Atmosphere Model version 5 (CAM5; Neale et al., 2012) for the atmosphere, the Community Land Model version 4 (Lawrence et al., 2011) for the land, and the Community Ice Code version 4 (Hunke & Lipscomb, 2008) for the sea ice. For HR CESM, the nominal horizontal resolutions are 0.1˚ for the ocean and sea ice and 0.25˚ for the atmosphere and land, with 62 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. For LR CESM, the nominal horizontal resolution is 1° for all the component models with 60 vertical levels for the ocean and 30 hybrid sigma vertical levels for the atmosphere. Both POP2 and CAM5 utilize stretched vertical grids.
For global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field “x” as: ∆ x = (x(TNST)2 – x(TNST)1) – (x(CTRL)2 – x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.
Observational Datasets


For global simulations, the deep ocean typically takes thousands of years to reach an equilibrium (Danabasoglu, 2004; Griffies et al., 2014). Due to the relatively short spin-up time (250 years), model drift exists in the CESM simulations (see Chang et al., 2020). The impacts of such drift, however, can be minimized by referencing TNST to CTRL simulations (Griffies et al., 2014; van Westen et al., 2020). In this work, we compute the projected change in field “x” as: ∆ x = (x(TNST)2 – x(TNST)1) – (x(CTRL)2 – x(CTRL)1), where x(TNST) and x(CTRL) stand for a variable x from TNST and CTRL simulations, respectively, and the subscripts 1 and 2 denote two different time windows. The CESM outputs monthly averaged fields. All the displayed results in Section 4 are yearly averages determined from monthly model outputs.
Observational Datasets
Five observational datasets are used to evaluate model results. The first is the sea surface height (SSH) above geoid obtained from satellite altimeters between 1993 and 2019 (Taburet et al., 2019). It includes data observed from all altimeter missions, and the temporal and spatial resolutions are daily and 0.25˚, respectively. The second is the climatological mean near-surface velocity from drifters (Laurindo et al., 2017). The time period for the climatological mean is 1979–2020 and the spatial resolution is 0.25˚. The third data set is the World Ocean Atlas (WOA) climatological mean temperature and salinity (Locarnini et al., 2018; Zweng et al., 2019). The time period for climatological mean is 2005–2017 and the spatial resolution is 0.25. The fourth data set is the ETOPO5 bathymetry with a spatial resolution of 5 min (NGDC, 1993). The four observational data sets above may not be fully representative at the coasts due to their resolutions and/or lack of measurements. Therefore, they can only be used to compare LR and HR simulation in the open ocean off the coast. The last data set is AMOC measured by the RAPID-MOC array at 26.5° N (McCarthy et al., 2015). The measurements started from April 2004 and are still in progress. All CESM simulations and observational data sets are publicly available and the access to the datasets is provided in the acknowledgment section.
Methods
SSH Decomposition
The methods to decompose SSH (η) are discussed in detail in Griffies et al. (2014) and Griffies and Greatbatch (2012). Here, we summarize the key equations in this section. More detailed information of the relevant equations and derivations is presented in the Supporting Information.
For a hydrostatic fluid, η tendency can be decomposed as:
urn:x-wiley:19422466:media:jame21583:jame21583-math-0024 (1)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0025 is the gravitational acceleration, urn:x-wiley:19422466:media:jame21583:jame21583-math-0026 is the surface density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0027 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0028 are the pressure at the surface and the bottom, urn:x-wiley:19422466:media:jame21583:jame21583-math-0029 is the water depth, urn:x-wiley:19422466:media:jame21583:jame21583-math-0030 is the in-situ density, urn:x-wiley:19422466:media:jame21583:jame21583-math-0031 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0032 are the vertical and time coordinates, respectively (Equation (13) in Griffies et al., 2014). The first term on the right-hand side of Eq (1) measures sea-level change associated with mass change and it’s related to barotropic mass transport and surface mass flux (see Equations (47–49) in Griffies et al. (2014) and the Supporting Information for details). The second term on the right-hand side of Equation (1) measures sea-level change associated with local density change. This decomposition was first used by Gill and Niller (1973) to analyze sea-level fluctuation. Landerer et al. (2007) and Yin et al. (2009) later used this decomposition to interpret climate models simulated sea-level patterns under global warming.
For the POP2 model, which uses the Boussinesq approximation and zero surface water flux, SSH explicitly computed by the model is the DSL (Griffies et al., 2014). DSL (urn:x-wiley:19422466:media:jame21583:jame21583-math-0033) is defined as the anomaly from the global mean sea level: urn:x-wiley:19422466:media:jame21583:jame21583-math-0034, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0035 is the globally averaged sea level (Griffies et al., 2014), and urn:x-wiley:19422466:media:jame21583:jame21583-math-0036 is zero at every time step in POP2. Thus, all terms in Equation (1) should be interpreted as anomalies from the global mean when decomposing the POP2 SSH field. Since the bottom pressure is not available from POP2 output, we estimate the mass transport term as the residual between SSH and local steric height.
Boussinesq Approximation and Sterodynamic Sea-Level
Many ocean models including POP2 employ the Boussinesq approximation which conserves the volume rather than the mass of a fluid parcel. Greatbatch (1994) showed that Boussinesq models do not account for sea-level changes associated with the net expansion (or contraction) of the global ocean. Further comparison between Boussinesq and non-Boussinesq models shows: (a) very similar large-scale sea level patterns (see Figure 3 in Griffies & Greatbatch, 2012); (b) corrections are needed in Boussinesq models to study the impact on earth rotation and geoid associated with water mass redistribution (Bryan, 1997; Kopp et al., 2010). For assessing future sea-level change with a Boussinesq model, the only correction required is to add a globally uniform, time-varying factor known as the global mean steric sea-level (Greatbatch, 1994; Griffies et al., 2014). Since this correction is globally uniform, it has no dynamical effects (Greatbatch, 1994).
The global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):
urn:x-wiley:19422466:media:jame21583:jame21583-math-0039
(2)
urn:x-wiley:19422466:media:jame21583:jame21583-math-0040
(3)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).


The global mean steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0037) is computed as the global average of local steric sea level (urn:x-wiley:19422466:media:jame21583:jame21583-math-0038):
urn:x-wiley:19422466:media:jame21583:jame21583-math-0039
(2)
urn:x-wiley:19422466:media:jame21583:jame21583-math-0040
(3)
where urn:x-wiley:19422466:media:jame21583:jame21583-math-0041 indicates a global average, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0042 kg/m3 is the reference density (van Westen & Dijkstra, 2021). Since density changes can result from temperature and salinity changes, local steric height (urn:x-wiley:19422466:media:jame21583:jame21583-math-0043) can be decomposed into thermosteric and halosteric components. Although local thermosteric and halosteric heights can be of the same order of magnitude, the global mean halosteric height is zero (Gregory et al., 2019). Thus, urn:x-wiley:19422466:media:jame21583:jame21583-math-0044 is essentially due to thermosteric component and is referred to as global mean thermosteric sea-level (Gregory et al., 2019). The sum of DSL and global mean thermosteric sea-level (correcting for the Boussinesq approximation) is referred to as the sterodynamic sea-level (Gregory et al., 2019).
The sterodynamic sea-level changes only account for changes in sea-level associated with ocean circulation and density changes (Gregory et al., 2019), while the actual sea-level can be influenced by other processes such as glacial melting, changes in land-water storage, and vertical land motion. The current version of CESM does not include these processes. Thus, sea-level changes associated with these processes are not considered in this study.
Externally Forced Sea-Level Changes
In this study, we are interested in the externally forced sea-level changes. By referencing TNST to CTRL simulations, sea-level changes in response to anthropogenic climate forcing can be extracted (a schematic is presented in Figure S1 in the Supporting Information S1). While internal variability can give rise to large decadal fluctuations in sea-level in the North Atlantic Ocean (Chafik et al., 2019; Griffies & Bryan, 1997; Yeager, 2020), externally forced sea-level changes are expected to manifest as robust long-term trends. Hence we use linear trend analysis with significance tests to identify externally forced sea-level changes. Given that externally forced sea-level changes may not necessarily be linear with time, we also examine sea-level differences between present and future time periods. The two analysis methods give very similar spatial patterns of sea-level response to the RCP8.5 CO2 emission scenario.
Results and Discussion
Evaluation of Model Simulations Against Observations
We first compare the model results with the existing observations before discussing future sea-level projections. Figure 1 shows DSL mean and variance from the satellite observations, HR, and LR simulations. For the mean DSL, HR shows two major improvements over LR: (a) HR reduces mean DSL bias along the entire US east continental shelf; and (b) HR produces more realistic mean DSL patterns along the Gulf Stream extension than LR (Figures 1a–1c). Along the northeast continental shelf (north of Cape Hatteras, marked as the blue star in Figures 1a–1c), HR reduces the negative DSL bias of ∼40 cm in LR. Along the southeast shelf (south of Cape Hatteras), HR reduces the positive DSL bias of ∼20 cm in LR (Figures 1a–1c). In addition, HR improves the Gulf Stream separation point over LR, although the overshooting issue still exists. The Gulf Stream separation point was determined from visual inspection. A non-biased method is to select a (fixed) DSL/SSH isoline and quantify the separation latitude, for example, as was done for the East Australian Current (Cetina-Heredia et al., 2014). Observations show that the Gulf Stream leaves the US east coast near Cape Hatteras at 35° N (Figure 1a). HR simulated Gulf Stream meanders past 35° N and separates from the coast close to 40° N, while LR simulated Gulf Stream does not show a clear separation from the coasts (Figures 1b-1c). The attachment of the Gulf Stream to the coast is a common issue in coarse resolution ocean model simulations (Chassignet & Marshall, 2008; Dengg et al., 1996; Saba et al., 2016; Schoonover et al., 2017). A realistic Gulf Stream separation has been found when model horizontal resolution increases up to 1/50urn:x-wiley:19422466:media:jame21583:jame21583-math-0048 (equivalent to 1.5 km in mid latitudes), and the effects of submesocale processes are explicitly represented (Chassignet & Xu, 2017). Despite this shortcoming, the simulated mean DSL along the Gulf Stream extension is much closer to observations in HR than in LR. For DSL variance, HR and the observations show similar spatial patterns along the continental shelf with large variance in the south and small variance in the north, even though the magnitudes in HR are larger than observations (Figures 1d-1e). In contrast, LR produces opposite spatial patterns with small (large) variance along the south (north) east shelf (Figure 1f). In the Gulf Stream extension region, the variance in HR is closer to observations than LR (Figures 1d–1f). This improvement is likely attributed to the better representation of oceanic mesoscale eddies in HR, which has been listed as one of the existing problems for coarse resolution climate model projections of future sea-level change (Fasullo & Nerem, 2018).
Figure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)–(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993–2019. The blue star in (a)–(c) denotes Cape Hatteras.
DSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a–2c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40–60 cm/s, less than half of the observed values of 120–140 cm/s. In contrast, HR simulated current speed is ∼120 cm/s or greater (Figure 2b), much closer to the observations. At ∼40° N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d–2f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10–20 cm/s, much less than the current speed of ∼50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.


Figure 1: Left column: mean dynamic sea level (DSL) from Altimeter observation (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: Variance of daily DSL from Altimeter observation (d), HR (e) and LR (f). For the variance of observed sea level, we first compute anomalies from the global mean and then compute variance. For (e)–(f), we directly compute variance of model sea surface height output. The time period for climatological mean and variance is 1993–2019. The blue star in (a)–(c) denotes Cape Hatteras.
DSL and surface currents are related through the geostrophic relationship for large-scale ocean circulations such as the Gulf Stream. Thus, the reduced DSL bias in HR is associated with improved Gulf Stream circulation. Compared with drifter observations, LR simulates a too weak Gulf Stream current both along the US southeast continental slope (south of Cape Hatteras) and in the extension region (Figures 2a–2c). Specifically, along the southeast continental slope, the near surface current speed in LR is only 40–60 cm/s, less than half of the observed values of 120–140 cm/s. In contrast, HR simulated current speed is ∼120 cm/s or greater (Figure 2b), much closer to the observations. At ∼40° N, HR and observations show southwestward shelf currents, which are absent in LR (Figures 2d–2f). The improved ocean circulations due to refined model resolution has also been reported in other models (Chassignet et al., 2020; Saba et al., 2016). In the Gulf Stream extension region, the current speed in LR is 10–20 cm/s, much less than the current speed of ∼50 cm/s in both HR and observations. However, the aforementioned overshooting problem is evident in both LR and HR (Figures 2b-2c). Although HR clearly shows an improved representation of the Gulf Stream and its extension compared to those of LR, it does not completely eliminate all the biases, particularly the overshooting bias.
Figure 2: Left column: mean near surface velocity from drifter observations (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: mean near surface velocity from drifter observations (d), HR (e) and LR (f) zoomed into the US northeast continental shelf and slope. The velocity is sampled at 15-m depth. The time period for the climatological mean is 1979–2020. Red star in (d) indicates Boston, Massachusetts. For clarity, vectors are plotted at every four grid points in (a), every 10 grid points in (b), and every grid point in (c) to approximate a spatial resolution of 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0050 (the resolutions of drifter, HR and LR are 0.25urn:x-wiley:19422466:media:jame21583:jame21583-math-0051, 0.1urn:x-wiley:19422466:media:jame21583:jame21583-math-0052 and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0053, respectively). To highlight small-scale circulations, vectors are plotted on every 2 grid points in (d), every 5 grid points in (e), and every grid point in (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0054 for both observations (d) and HR (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0055 for LR (f).
In addition to improved DSL and ocean circulations, HR reduces biases in near surface temperature and salinity along the northeast continental shelf (Figure 3). Compared to the WOA climatology, HR reduces the warm temperature and high salinity biases of LR in the Gulf of Maine (Figure 3). These bias reductions may be attributed to the improved ocean circulation in HR (Figures 2d–2f). In LR, the overshooting Gulf Stream brings warm and saline water to the Gulf of Maine, causing ∼4° C bias in near surface temperature and ∼3 g/kg bias in near surface salinity (Figure 3). In HR, the southwestward shelf current transports cold and fresh water from the Gulf of St. Lawrence and the Labrador Sea to the Gulf of Maine, reducing the temperature and salinity biases (Figure 3). Although HR improves surface salinity in the Gulf of Maine, it shows a negative salinity bias (∼−1 g/kg) in the Gulf of St. Lawrence (Figures 3d–3f). The low salinity water there may explain the negative salinity bias in the Gulf of Maine as southwestward shelf currents move from the Gulf of St. Lawrence to the Gulf of Maine.
Figure 3: Left column: mean temperature at 15-m depth from World Ocean Atlas (WOA), (a), high resolution (HR) (b), and low resolution (LR) (c). Right column: mean salinity at 15-m depth from WOA (d), HR (e) and LR (f). Arrows are the mean velocities at 15-m depth from drifter observations (a), (d), HR (b), (e), and LR (c), (f). The averaging time period for temperature and salinity is 2005–2017. Red star indicates Boston, Massachusetts. Vectors are plotted on every two grid points in (a), (d), every 5 grid points in (b), (e), and every grid point in (c), (f). This yields an approximate spatial resolution of 0.5urn:x-wiley:19422466:media:jame21583:jame21583-math-0057 for both drifter (a), (d) and HR (b), (e), and 1urn:x-wiley:19422466:media:jame21583:jame21583-math-0058 for LR (c), (f).
Projected Future Sea-Level Rise
Under the future RCP 8.5 emission scenario, both LR and HR project increasing DSL trends along the US east continental shelf but with different amplitudes (Figures 4a and 4d). Along the northeast shelf (north of 40° N), LR projects a DSL trend of 1.5–2 mm/yr, more than double the DSL trend of 0.5–1 mm/yr projected by HR. Along the southeast shelf (south of 35° N), HR shows a DSL trend of 0.5–1 mm/yr, while LR shows a statistically insignificant trend of less than 0.5 mm/yr. Although LR and HR project different DSL trends along the US east shelf, the global mean thermosteric sea-level rise is in close agreement between the two models (Figure 5). This is consistent with the finding by Van Westen et al. (2020) and may be attributed to the fact that the global mean thermosteric sea-level rise is related to ocean heat uptake, which is largely determined by the RCP8.5 emission scenario specified in LR and HR. Between 2,001 and 2,100, LR and HR project a similar average trend of ∼3 mm/yr for global mean thermosteric sea-level rise (Figure 5).
Figure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.
Figure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.


Figure 4: Trends of dynamic sea level (DSL) (a), (d), local steric height component (b), (e), and mass transport component (c), (f) from the low resolution (LR) (left column) and high resolution (HR) (right column). Trends are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where trends are statistically insignificant (p > 0.1). Global mean thermosteric sea-level rise is removed in (b), (e). Red, blue, and black stars mark Boston, Cape Hatteras, and Jacksonville, respectively. The difference of DSL, local steric height, and mass transport components between two time periods shows similar spatial patterns as Figure 4. We present that plot in Figure S2 in the Supporting Information S1.
Figure 5: Global mean thermosteric sea-level relative to 1,850. Shaded areas are from 2,001 to 2,100, when global mean thermosteric sea-level starts to increase due to global warming.
Figures 4b–4e, 4f show the trends of local steric height and mass transport components (both are relative to global mean, see Section 3) in the Northwest Atlantic Ocean. For both LR and HR, negative and positive local steric height trends mostly occur in continental shelf and open ocean regions, respectively. This indicates that the local steric height increase is lower than the global mean in continental shelf and greater than the global mean in the open ocean. This is because the local steric height is a depth integral (Equation (3)), so that the steric response increases with water depth. The negative local steric height trends in continental shelf are compensated by positive mass transport trends (Figures 4c and 4f). These are consistent with the model simulation results reported by Yin et al. (2009). Different contributions of local steric height and mass transport to DSL are noted between LR and HR (Figure 4). Here we choose two regions (marked as the 3° × 3° black boxes in Figures 4a and 4d) to analyze the difference between LR and HR. At the northeast shelf near Boston, Massachusetts (highlighted as the red star in Figure 4), the larger increases in mass transport and the smaller decreases in local steric height lead to larger increases in DSL in LR (Figure 4, Table 2). We further quantify the relative contributions of mass transport and local steric height to the difference in DSL trends between LR and HR. At the northeast shelf box region, LR and HR project DSL rises of 1.66 and 0.8 mm/yr, respectively (Table 2, Figure 6a). The difference in projected DSL rise (0.86 mm/yr) results from the difference in local steric height and mass transport (Figures 6b and 6c). Between LR and HR, the difference in local steric height is 0.55 mm/yr (see the fourth row in Table 2), accounting for 64% of the DSL difference (0.86 mm/yr). The difference in mass transport accounts for the remaining 36% of the DSL difference. The same analysis performed for the southeast shelf box region reveals the difference in mass transport (0.32 mm/yr) accounts for 65% of the DSL trend difference (0.49 mm/yr), and the difference in local steric height accounts for the remaining (Table 2, Figures 6d–6f). Because the mass transport is estimated as the residual between DSL and local steric height (see Section 3), we next focus on comparing the differences in local steric height between LR and HR.
Table 2: Contributions of Local Steric Height and Mass Transport to Dynamic Sea Level (DSL) Trends on the Northeast Shelf Near Boston, Massachusetts and on the Southeast Shelf Near Jacksonville, Florida
Boston, Massachusetts   DSL     Local steric height     Mass transport
LR      1.66 urn:x-wiley:19422466:media:jame21583:jame21583-math-0064 0.19      −2.55 urn:x-wiley:19422466:media:jame21583:jame21583-math-0065 0.11     4.22 urn:x-wiley:19422466:media:jame21583:jame21583-math-0066 0.20
HR      0.80 urn:x-wiley:19422466:media:jame21583:jame21583-math-0067 0.26      −3.10 urn:x-wiley:19422466:media:jame21583:jame21583-math-0068 0.23     3.91 urn:x-wiley:19422466:media:jame21583:jame21583-math-0069 0.16
LR–HR   0.86    0.55    0.31
Jacksonville, Florida   DSL     Local steric height     Mass transport
LR      0.15 urn:x-wiley:19422466:media:jame21583:jame21583-math-0070 0.20      −2.74 urn:x-wiley:19422466:media:jame21583:jame21583-math-0071 0.14     2.89 urn:x-wiley:19422466:media:jame21583:jame21583-math-0072 0.14
HR      0.64 urn:x-wiley:19422466:media:jame21583:jame21583-math-0073 0.29      −2.57 urn:x-wiley:19422466:media:jame21583:jame21583-math-0074 0.14     3.21 urn:x-wiley:19422466:media:jame21583:jame21583-math-0075 0.21
HR–LR   0.49    0.17    0.32
Note. The trends and 95% confidence intervals are computed with the time series in Figure 6 from 2,001 to 2,100. The unit is mm/yr.
Figure 6: Time series of dynamic sea level, local steric height and mass transports on the northeast shelf near Boston, Massachusetts (a–c) and on the southeast shelf near Jacksonville, Florida (d–f). The values are spatially averaged within the boxes highlighted in Figures 4a and 4d. Thin and thick lines are yearly mean and 10-year running mean, respectively. Shaded areas in (a–f) are from 2,001 to 2,100, when Atlantic Meridional Overturning Circulation strength starts to decrease (see Figure 9d).
Two factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a–7c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.
Figure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.
Figure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001–2,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.


Two factors contribute to the local steric height differences between LR and HR: bathymetry and in-situ density. Along the US southeast continental shelf, bathymetry in LR is deeper than that in HR and ETOPO5 (Figures 7a–7c). In addition, the land-sea mask in LR does not accurately represent the coastline due to the coarse horizontal resolution (Figures 7c and 7f). In the Gulf of Maine, HR resolves small scale bathymetry features such as the Northeast channel, Jordan Basin, Wilkinson Basin, and Georges Basin (Figure 7d). These features are completely missing in LR. Given that the local steric height is a depth integral, the misrepresented bathymetry in LR causes biases in local steric height. Within the Gulf of Maine (highlighted as the black box in Figure 7d), the maximum depth in HR is 330 m, 50% deeper than the maximum depth of 220 m in LR (Figures 7e-7f, Figure 8). In addition to bathymetry difference, LR and HR project different density changes in the future (Figure 8a). Since both density and bathymetry affect local steric height, we next explore the impacts of the two factors on local steric height in the Gulf of Maine box region.
Figure 7: Left column: bathymetry contours along the US east continental shelf from ETOPO5 (a), high resolution (HR) (b) and low resolution (LR) (c). Right column: bathymetry in the Gulf of Maine from ETOPO5 (d), HR (e) and LR (f). In (d), JB, WB, GB, and NC stand for the Jordan basin, Wilkinson basin, Georges basin, and Northeast channel, respectively. The black box in (d) indicates the region for spatially averaged profiles shown in Figure 8.
Figure 8: Depth profiles of in-situ density change (a), temperature change (b), and salinity change (c) averaged in the Gulf of Maine. The region for spatial averaging is highlighted in Figure 7 (d). The change is calculated as the difference of the mean values between 2,081-2,100 and 2,001–2,020 in the TNST simulations and corrected with the CTRL simulations to account for potential model drift.
To study the impact of bathymetry on local steric height, we integrate HR projected density changes (urn:x-wiley:19422466:media:jame21583:jame21583-math-0076) from the surface to the depths used in LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0077) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0078), respectively (so the only difference is bathymetry between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0079 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0080 has a shallow bias and urn:x-wiley:19422466:media:jame21583:jame21583-math-0081 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0082 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0083 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0084 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0085 = 8.4 cm. Thus, if LR projects same density change as HR and the only difference is bathymetry, then the bias in LR bathymetry can lead up to 50% difference in local steric height changes in that region. To study the impact of density on local steric height, we integrate the projected density changes of LR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0086) and HR (urn:x-wiley:19422466:media:jame21583:jame21583-math-0087) from the surface to urn:x-wiley:19422466:media:jame21583:jame21583-math-0088 (so the only difference is density between LR and HR. The reason why we do not use urn:x-wiley:19422466:media:jame21583:jame21583-math-0089 is because urn:x-wiley:19422466:media:jame21583:jame21583-math-0090 has no values between urn:x-wiley:19422466:media:jame21583:jame21583-math-0091 and urn:x-wiley:19422466:media:jame21583:jame21583-math-0092 (see Figure 8a). The two calculations yield urn:x-wiley:19422466:media:jame21583:jame21583-math-0093 = 4.2 cm, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0094 = 8.3 cm. Thus, if HR uses the same bathymetry as LR and the only difference is density changes, then the difference in density projections can cause ∼50% difference in local steric height changes in that region.
Both temperature and salinity changes contribute to density changes. In the Gulf of Maine box region, HR projects a 5° C increase in surface temperature from 2001 to 2100, ∼40% larger than the temperature increase (3.6° C) projected by LR (Figure 8b). The enhanced warming projected by HR is consistent with Saba et al. (2016), who showed larger warming rates along the Northwest Atlantic shelf in climate models with higher horizontal resolutions. In addition to enhanced warming, HR also projects larger salinity increases in the entire water column than LR (Figure 8c). The large salinity increases partially compensate the density decreases due to high temperature, leading to reduced density decreases (even density increases at 70 m depth) in HR than that in LR (Figure 8). Note that the density increases near 70 m in HR (Figure 8a) contribute negatively to the local steric height changes.
Associations With AMOC
Previous studies have related DSL changes in the North Atlantic Ocean to AMOC (Chafik et al., 2019; Little et al., 2017; Yin et al., 2009). We start by comparing AMOC overturning streamfunctions between LR and HR. For the mean states (the mean states were computed as the averages over the last 100 years (400–500) of the control simulations, Figures 9a and 9b), differences are noted (a) below 3,000-m depth in the Atlantic basin, and (b) in mid latitudes (∼40°N) between 800 and 1,400 m depth. The former difference may be related to the Nordic Seas overflow parameterization (Danabasoglu et al., 2010), which is used in LR and disabled in HR. At ∼40°N and between 800 and 1,400 m depth, the mean AMOC transport in LR (20–22 Sv, 1 Sv = 106 m3/s) is stronger than that (mostly 16–20 Sv) in HR. One factor that may explain such difference is the mixed layer depth (MLD) bias in the north Atlantic deep water formation regions. By comparing LR, HR and observed MLD, Chang et al. (2020) showed LR contains large positive bias in the north Atlantic deep water formation regions such as Labrador Sea (see their Figure 15). MLD bias there may affect deep water formation and AMOC variability (Yeager et al., 2021). Exploring the impacts of MLD and deep water formation on AMOC is beyond the scope of this work. A study assessing the contributions of the Labrador Sea water formation to AMOC can be found in Yeager et al. (2021).
Figure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401–500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5°N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5°N and 1000-m depth.


Figure 9: Atlantic Meridional Overturning Circulation (AMOC) overturning streamfunction climatological mean for low resolution (LR) (a) and high resolution (HR) (b). AMOC overturning streamfunctions are averaged during the last 100 years (year 401–500) of the CTRL simulations to minimize model drift. (c) Comparison of AMOC overturning streamfunctions from LR, HR and RAPID observations at 26.5°N. The observed AMOC overturning streamfunction is averaged from April 2004 to March 2020. LR and HR AMOC overturning streamfunctions are averaged from 1986 to 2005. This time period is chosen to avoid the impact of the RCP8.5 CO2 forcing (starts from 2006) on AMOC simulations. (d) AMOC strength from the TNST simulations and corrected by the CTRL simulations. AMOC strength is calculated as the AMOC overturning streamfunction at 26.5°N and 1000-m depth.
Figure 9c presents the climatological mean (1986–2005) AMOC overturning streamfunctions at 26.5°N. Compared to the RAPID observations (Smeed et al., 2014, 2018), LR and HR show realistic vertical structures in the upper 2,000 m, with the maximum values at 1,000-m depth. Below 3,000-m depth, model biases are evident and LR is in closer agreement with observations than HR. The large differences between HR and observations maybe related to the aforementioned overflow parameterization (Chang et al., 2020; Danabasoglu et al., 2010). By comparing AMOC simulations from multiple global models, Danabasoglu et al. (2014) showed that large biases between models and RAPID observations at depth are common if the overflows are not parameterized. Under the RCP8.5 emission scenario, LR and HR project similar reductions of AMOC strength (∼8 Sv) from 2,001 to 2,100 (Figure 9d, AMOC strength is defined as the AMOC overturning streamfunction at 26.5°N and 1,000-m depth).
As the AMOC strength decreases, LR and HR project weakened Gulf Stream currents but with different amplitudes (Figure 10). LR projects a decrease in near surface current speed along the entire US east continental slope with the largest decrease occurring at 40° N. For HR, the current speed decreases are mainly confined along the southeast continental slope. The spatial patterns of current speed trends are related to the mean ocean circulation (Figure 2). LR simulated Gulf Stream does not have a clear separation point from the shore, and it moves northward along the entire continental slope (Figures 2c and 2f). As a result, the weakening Gulf Stream currents affect the entire east continental slope. HR simulated Gulf Stream leaves US east continental slope at ∼40° N (Figure 2b), so the effects of weakening Gulf Stream are mainly confined along the southeast slope. For 1 Sv of AMOC reduction, HR projects a larger decrease in Gulf Stream currents at the southeast continental slope compared to LR (Figure 10, Figures 11a, 11b). In addition to the large Gulf Stream reductions, HR shows narrow bands of enhanced current speed on the landside of the Gulf Stream. The increases in current speed are associated with the shift of Gulf Stream path. At 31.5° N, the mean Gulf Stream currents (indicated by the 80 and 120 cm/s velocity contours in Figure 11d) slightly shift toward the continental slope as the Gulf Stream weakens. LR also shows enhanced current speed on the landside of Gulf Stream but the enhancements are only noticed in a few grid points. At 31.5° N, the continental slope and shift in Gulf Stream path are completely absent in LR (Figure 11c).
Figure 10: Regressions of velocity speed at 15-m depth on Atlantic Meridional Overturning Circulation strength from low resolution (a) and high resolution (b). Regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). Green lines in (a) denote the cross sections for Figure 11.
Figure 11: Top panel: Regressions of velocity speed on Atlantic Meridional Overturning Circulation strength across 31.5° N from low resolution (LR) (a) and high resolution (HR) (b). Bottom panel: velocity speed averaged during historical time (2,001–2,020, solid contours) and future time (2,081–2,100, dashed contours) across 31.5° N from LR (c) and HR (d). The cross-section is highlighted as the green line in Figure 10a. In (a)–(b), regressions are computed from the TNST simulations from 2,001 to 2,100 and corrected by the CTRL simulations to account for potential model drift (see Section 2.1). Black dots indicate the regions where regressions are statistically insignificant (p > 0.1). In (c)–(d), contours with same color have the same velocity speed and the unit of contour labels is cm/s.
Based on geostrophic balance (e.g., urn:x-wiley:19422466:media:jame21583:jame21583-math-0103, where urn:x-wiley:19422466:media:jame21583:jame21583-math-0104 is the meridional geostrophic velocity, and urn:x-wiley:19422466:media:jame21583:jame21583-math-0105 is the Coriolis parameter), large DSL gradient exists across the Gulf Stream. As the AMOC strength decreases, the weakened Gulf Stream currents reduce the DSL gradient across the Gulf Stream. This can lead to DSL rises on the landside of the Gulf Stream and DSL decreases in the open ocean. Compared to HR, LR projects larger current speed decreases along the northeast continental slope, and smaller current speed decreases along the southeast continental slope (Figure 10). This will lead to larger DSL rises along the northeast shelf and smaller DSL rises along the southeast shelf, in line with the projected DSL trends shown in Figures 4a and 4d. In addition to the different Gulf Stream reductions between LR and HR, the landward shift in the Gulf Stream path projected by HR can also affect regional DSL patterns in the future. These suggest that the better resolved Gulf Stream in HR can have significant impacts on regional DSL projections.
Here we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.
Summary and Conclusions
In this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.
HR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region
Both LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)
Compared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40° N), and larger trends of DSL rise along the southeast shelf (south of 35° N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC


Here we examine the difference in DSL patterns between LR and HR with geostrophic balance. The geostrophic balance is typically valid in the open ocean and the mid shelf (Fewings & Lentz, 2010). At the inner shelf and coastal zone, geostrophic balance does not hold because of the significance of friction, wave and wind stress (Fewings & Lentz, 2010; Little et al., 2019; Thorpe, 2007). Although HR shows significant improvement on ocean circulation compared to LR, HR is still too coarse to fully resolve coastal dynamics. A regional downscaling with higher resolution is needed to further explore how coastal sea-level responds to a weakening Gulf Stream and AMOC.
Summary and Conclusions
In this study, we analyze DSL rise along the US east continental shelf in a pair of HR and LR CESM simulations. This study is motivated by Little et al. (2019), who pointed out the need for exploring sea-level rise near the US east coast when HR climate simulations are available. Three major findings from the analysis are listed below.
HR reduces biases in DSL and ocean circulation along the US east continental shelf and the Gulf Stream extension region
Both LR and HR models project DSL rise along the US east shelf under the RCP8.5 emission scenario, consistent with previous projections based on LR climate models (Landerer et al., 2007; Little et al., 2017; Yin et al., 2009)
Compared to LR, HR projects smaller trends of DSL rise along the northeast shelf (north of 40° N), and larger trends of DSL rise along the southeast shelf (south of 35° N). The different DSL patterns are attributable to the difference in Gulf Stream changes in response to a weakening AMOC
The improved ocean circulation associated with refined horizontal resolution has been reported in numerous studies (Chassignet et al., 2020; Saba et al., 2016; van Westen et al., 2020). Here we show that the HR CESM simulates realistic Gulf Stream currents along the southeast continental slope and southwestward shelf currents along the northeast shelf. The southwestward shelf currents carry cold and fresh water from the Labrador Sea to Gulf of Maine, reducing warm temperature and high salinity bias. These results are consistent with Saba et al. (2016), who showed improved regional circulations and reduced temperature and salinity bias in the HR GFDL CM simulations. In addition to reduced biases in ocean circulation, HR better resolves small scale features of bathymetry and coastline. These make HR more suitable for regional sea-level study than LR. Jean-Michel et al. (2021) reported a global reanalysis product with a horizontal resolution of 1/12urn:x-wiley:19422466:media:jame21583:jame21583-math-0108 called GLORYS12. Such HR data products provide valuable information for regional studies.
In response to a weakening AMOC under global warming, both LR and HR models project decreasing Gulf Stream currents but at different spatial locations. The weakening Gulf Stream currents occur along the entire east continental slope in LR, while they are confined along the southeast continental slope in HR. The difference in Gulf Stream changes is related to the mean ocean circulation patterns. Compared with observations, LR simulated Gulf Stream does not show a clear separation from the shore. Thus, the weakening Gulf Stream currents affect the entire east continental slope. In contrast, HR simulated Gulf Stream leaves the shore at ∼40° N (HR still contains bias given the observed separation point at ∼35° N), so the effects of weakening Gulf Stream are confined along the southeast continental slope. The decreasing Gulf Stream currents can lead to DSL rise on the landside of the Gulf Stream through geostrophic balance. In this study, we focus on the contribution of ocean circulation to DSL. In addition to ocean circulation, sea-level can be influenced by many other processes such as coastal trapped waves (Hughes et al., 2019) and atmospheric forcing (Chafik et al., 2019; Llovel et al., 2018). Based on observational and reanalysis data, Chafik et al. (2019) demonstrated a high correlation between along-shelf winds and sea level along the European coast. Yin et al. (2020) analyzed GFDL simulations and showed the Gulf of Mexico coasts, particularly New Orleans, are most vulnerable to storm related extreme sea-level under global warming. Here we do not consider atmospheric forcing because the role of atmospheric variability on low frequency sea-level changes is still in debate. Woodworth et al. (2014) argued winds can generate low frequency sea-level changes near the coasts, while Little et al. (2019) suggested atmospheric forcing dominates high frequency sea-level variability. The low frequency sea-level variability is mainly associated with AMOC reductions (Little et al., 2017; Yin et al., 2009). Future work is encouraged to explore how atmospheric variability impacts future sea-level changes. Due to the volume conservation constraint in the ocean model used here, the simulated DSL changes do not account for global mean sea-level changes due to volume expansion or contraction. The global mean sea-level change can be estimated with the globally averaged steric height (Greatbatch, 1994; Yin et al., 2010). Under the future RCP 8.5 emission scenario, LR and HR models project similar global mean thermosteric sea-level rise of ∼3 mm/yr from 2,001 to 2,100. Including the global mean thermosteric sea-level rise, HR projects a sterodynamic sea-level rise of 3.5–4 mm/yr along the east shelf. In contrast, LR projects a smaller trend (3–3.5 mm/yr) along the southeast shelf, and a larger trend (4.5–5 mm/yr) along the northeast shelf. These trends do not account for sea-level rise due to glacial melting. Thus, future work may focus on exploring the contributions of glacial melting to sea-level rise. Recent studies have consistently shown that HR climate models produce overall more realistic simulations than LR models (Chang et al., 2020; Griffies et al., 2015; Saba et al., 2016; Small et al., 2014; van Westen et al., 2020). Higher horizontal resolutions enable to resolve more baroclinic modes. These baroclinic modes contains vertical structures and therefore high vertical resolutions become important. Stewart et al. (2017) showed increasing vertical resolutions can lead to ∼ 30% increases in SSH variance south of 40° S. The benefits of HR models can not only be used to learn physical mechanisms but also to diagnose parametrization schemes (Bachman et al., 2020). However, due to high computing costs, HR model ensembles and future projections are still scarce. As of now, only 7 models have completed and published their HR simulation results following CMIP6 HighResMIP protocol (Haarsma et al., 2016). We encourage future efforts to focus on creating more ensembles and simulating different future climate scenarios to improve the robustness of future projections. Another option to reach this goal would be to reduce LR models biases with accurate subgrid parameterizations. Recent advancement of machine learning may help solve this problem (Guillaumin & Zanna, 2021).


Bamber et al. (2019)
Title:
Ice sheet contributions to future sea-level rise from structured expert judgment
Key Points:
Potential contributions of ice sheets to future sea-level rise (SLR) remain the largest source of uncertainty in SLR projections
For a +2 °C temperature scenario, consistent with the Paris Agreement, the study estimates a median SLR contribution of 26 cm by 2100, with a 95th percentile value of 81 cm. For a +5 °C temperature scenario, more consistent with unchecked emissions growth, the corresponding values are 51 cm and 178 cm, respectively.
Beyond 2100, uncertainty and projected SLR increase rapidly. For the +5 °C scenario, the 95th percentile ice sheet contribution by 2200 is 7.5 m due to instabilities in both West and East Antarctica.
Scenarios of 21st century global total SLR exceeding 2 m should be used for planning purposes.
Keywords:
sea-level rise, climate predictions, ice sheets, Greenland, Antarctica
Corresponding author:
Jonathan L. Bamber
Citation:
Bamber, J. L., Oppenheimer, M., Kopp, R. E., Aspinall, W. P., & Cooke, R. M. (2019). Ice sheet contributions to future sea-level rise from structured expert judgment. Proceedings of the National Academy of Sciences, 116(23), 11195–11200. doi:10.1073/pnas.1817205116
URL:
https://www.pnas.org/doi/full/10.1073/pnas.1817205116
Significance
Future sea level rise (SLR) poses serious threats to the viability of coastal communities, but continues to be challenging to project using deterministic modeling approaches. Nonetheless, adaptation strategies urgently require quantification of future SLR uncertainties, particularly upper-end estimates. Structured expert judgement (SEJ) has proved a valuable approach for similar problems. Our findings, using SEJ, produce probability distributions with long upper tails that are influenced by interdependencies between processes and ice sheets. We find that a global total SLR exceeding 2 m by 2100 lies within the 90% uncertainty bounds for a high emission scenario. This is more than twice the upper value put forward by the Intergovernmental Panel on Climate Change in the Fifth Assessment Report.
Abstract
Despite considerable advances in process understanding, numerical modeling, and the observational record of ice sheet contributions to global mean sea-level rise (SLR) since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change, severe limitations remain in the predictive capability of ice sheet models. As a consequence, the potential contributions of ice sheets remain the largest source of uncertainty in projecting future SLR. Here, we report the findings of a structured expert judgement study, using unique techniques for modeling correlations between inter- and intra-ice sheet processes and their tail dependences. We find that since the AR5, expert uncertainty has grown, in particular because of uncertain ice dynamic effects. For a +2 °C temperature scenario consistent with the Paris Agreement, we obtain a median estimate of a 26 cm SLR contribution by 2100, with a 95th percentile value of 81 cm. For a +5 °C temperature scenario more consistent with unchecked emissions growth, the corresponding values are 51 and 178 cm, respectively. Inclusion of thermal expansion and glacier contributions results in a global total SLR estimate that exceeds 2 m at the 95th percentile. Our findings support the use of scenarios of 21st century global total SLR exceeding 2 m for planning purposes. Beyond 2100, uncertainty and projected SLR increase rapidly. The 95th percentile ice sheet contribution by 2200, for the +5 °C scenario, is 7.5 m as a result of instabilities coming into play in both West and East Antarctica. Introducing process correlations and tail dependences increases estimates by roughly 15%.
Introduction
Global mean sea-level rise (SLR), which during the last quarter century has occurred at an accelerating rate (1), averaging about +3 mm⋅y−1, threatens coastal communities and ecosystems worldwide. Adaptation measures accounting for the changing hazard, including building or raising permanent or movable structures such as surge barriers and sea walls, enhancing nature-based defenses such as wetlands, and selective retreat of populations and facilities from areas threatened by episodic flooding or permanent inundation, are being planned or implemented in several countries. Risk assessment for such adaptation efforts requires projections of future SLR, including careful characterization and evaluation of uncertainties (2) and regional projections that account for ocean dynamics, gravitational and rotational effects, and vertical land motion (3). During the nearly 40 y since the first modern, scientific assessments of SLR, understanding of the various causes of this rise has advanced substantially. Improvements during the past decade include closing the historic sea-level budget, attributing global mean SLR to human activities, confirming acceleration of SLR since the nineteenth century and during the satellite altimetry era, and developing analytical frameworks for estimating regional and local mean sea level and extreme water level changes. Nonetheless, long-term SLR projections remain acutely uncertain, in large part because of inadequate understanding of the potential future behaviors of the Greenland and Antarctic ice sheets and their responses to future global climate change. This limitation is especially troubling, given that the ice sheet influence on SLR has been increasing since the 1990s (4) and has overtaken mountain glaciers to become the largest barystatic (mass) contribution to SLR (5). In addition, for any given future climate scenario, the ice sheets constitute the component with the largest uncertainties by a substantial margin, especially beyond 2050 (6).
Advances since the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (7) include improved process understanding and representation in deterministic ice sheet models (8, 9), probabilistic projections calibrated against these models and the observational record (10), and new semiempirical models, based on the historical relationship between temperature and sea-level changes. Each of these approaches has limitations that stem from factors including poorly understood processes, poorly constrained boundary conditions, and a short (∼25 y) satellite observation record of ice sheets that does not capture the time scales of internal variability in the ice sheet climate system. As a consequence, it is unclear to what extent recent observed ice sheet changes (11) are a result of internal variability (ice sheet weather) or external forcing (ice sheet climate).
Where other methods are intractable for scientific or practical reasons, structured expert judgement (SEJ), using calibrated expert responses, provides a formal approach for estimating uncertain quantities according to current scientific understanding. It has been used in a wide range of applications, including natural and anthropogenic hazards such as earthquakes, volcanic eruptions, vector-borne disease spread, and nuclear waste security (12). That said, it should not be regarded as a substitute for fundamental research into driving processes, but instead as a source of complementary insights into the current state of knowledge and, in particular, the extent of the uncertainties (12). An SEJ study conducted in advance of the AR5 (13) (hereafter BA13) provided valuable insights into the uncertainties around ice sheet projections, as assessed at that time.
Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14–16), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.
Here, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts’ uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts’ judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).


Since then, regional- and continental-scale, process-based modeling of ice sheets has advanced substantially (8, 9, 14–16), with the inclusion of new positive feedbacks that could potentially accelerate mass loss, and negative feedbacks that could potentially slow it. These include solid Earth and gravitational processes (17, 18), Antarctic marine ice cliff instability (19), and the influences of organic and inorganic impurities on the albedo of the Greenland Ice Sheet (20). The importance of these feedbacks is an area of continuing research. Therefore, alternative approaches must be exploited to assess future SLR and, critically, its associated uncertainties (21), to serve the more immediate needs of the science and policy communities.
Here, we report the findings of an SEJ exercise undertaken in 2018 via separate, 2-d workshops held in the United States and United Kingdom, involving 22 experts (hereafter SEJ2018). Details of how experts were selected are provided in SI Appendix, Note 1. The questions and format of the workshops were identical, so that the findings could be combined using an impartial weighting approach (Methods). SEJ (as opposed to other types of expert elicitation) weights each expert using objective estimates of their statistical accuracy and informativeness (22), determined using experts’ uncertainty evaluations over a set of seed questions from their field with ascertainable values (Methods). The approach is analogous to weighting climate models based on their skill in capturing a relevant property, such as the regional 20th century surface air temperature record (23). In SEJ, the synthetic expert (i.e., the performance weighted [PW] combination of all of the experts’ judgments) in general outperforms an equal weights (EW) combination in terms of statistical accuracy and informativeness, as illustrated in SI Appendix, Fig. S3. The approach is particularly effective at identifying those experts who are able to quantify their uncertainties with high statistical accuracy for specified problems rather than, for example, experts with restricted domains of knowledge or even high scientific reputation (12).
The participating experts quantified their uncertainties for three physical processes relevant to ice sheet mass balance: accumulation, discharge, and surface runoff. They did this for each of the Greenland, West Antarctic, and East Antarctic ice sheets (GrIS, WAIS, and EAIS, respectively), and for two schematic temperature change scenarios. The first temperature trajectory (denoted L) stabilized in 2100 at +2 °C above preindustrial global mean surface air temperature (defined as the average for 1850–1900), and the second (denoted H) stabilized at +5 °C (SI Appendix, Fig. S1). The experts generated values for four dates: 2050, 2100, 2200, and 2300. Experts also quantified the dependence between accumulation, runoff, and discharge within each of the three ice sheets, and between each ice sheet for discharge only, for the H scenario in 2100. We used temperature trajectories rather than emissions scenarios to isolate the experts’ judgements about the relationship between global mean surface air temperature change and ice sheet changes from judgements about climate sensitivity.
An important and unique element of SEJ2018 was the elicitation of intra- and inter-ice sheet dependencies (SI Appendix, Note 1.5). Two features of dependence were elicited: a central dependence and an upper tail dependence. The former captures the probability that one variable exceeds its median given that the other variable exceeds its median, whereas the latter captures the probability that one variable exceeds its 95th percentile given that the other exceeds its 95th percentile. It is well known that these two types of dependence are, in general, markedly different, a property that is not captured by the usual Gaussian dependence model. The latter always imposes tail independence, regardless of the degree of central dependence, and can produce large errors when applied inappropriately (24). For example, if GrIS discharge exceeds its 95th percentile, what is the probability that runoff will also exceed its 95th percentile? This probability may be substantially higher than the independent probability of 5%, and ignoring tail dependence may lead to underestimating the probability of high SLR contributions. On the basis of each expert’s responses, a joint distribution was constructed to capture the dependencies among runoff, accumulation, and discharge for GrIS, WAIS, and EAIS, with dependence structures chosen, per expert, to capture central and tail dependences (Methods and SI Appendix, Note 1.5). In BA13, heuristic dependency values were applied on the basis of simple assumptions about the response of processes to a common forcing.
To help interpret the findings, experts were also asked to provide qualitative and rank-order information on what they regard to be the leading processes that could influence ice dynamics and surface mass balance (snowfall minus ablation); henceforth, this is termed the descriptive rationale. Further details can be found in the SI Appendix. The combined sea-level contribution from all processes and ice sheets was determined assuming either independence or dependence. Here, we focus on the findings with dependence; we examine the effect of the elicited dependencies and the approach taken in SI Appendix, Note 1.5.
The ice sheet contributions were expressed as anomalies from the 2000–2010 mean states, which were predefined (SI Appendix, Table S7). The baseline sea-level contribution for this period was prescribed as 0.76 mm⋅y−1 (0.56, 0.20, and 0.00 mm⋅y−1 for GrIS, WAIS, and EAIS, respectively) and has been added to the elicited values discussed here. This is close to an observationally derived value of 0.79 mm⋅y−1 for the same period, which was published subsequently to the SEJ workshops (4).
Results and Discussion
Fig. 1 shows the probability density functions (PDFs) for both temperature trajectory scenarios for the combined ice sheet contributions, assuming some dependencies exist between ice sheet processes, as elicited from the expert group (SI Appendix, Note 1.5). The associated numerical values are detailed in Table 1, and plots for all four epochs are provided in SI Appendix, Fig. S2. They display similar characteristics to Fig. 1. The PDFs were generated using Monte Carlo sampling from the intrinsic range obtained from the expert responses (22). All PDFs are non-Gaussian and exhibit an extended upper tail, especially for the H temperature scenario. We believe this reflects the experts’ joint view that large amplitude, nonlinear instabilities could be triggered at this higher temperature, even by 2050. For example, for 2050, the median [and likely range, defined as the 17–83% probability range, as in the AR5 (25)] of the ice sheet contributions are 10 cm (5–18 cm) for the L scenario and 12 cm (6–24 cm) for the H scenario. The tail behavior is discussed further in SI Appendix, Note 1.1. By 2100, the differences between the scenarios grow larger, with projected contributions of 26 cm (12–53 cm) and 51 cm (22–113 cm; Fig. 2 and Table 1).
Fig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm⋅a−1 is included. Note that there is more than a factor five change in the x axis scales.
Table 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000–2010 of 0.76 mm y−1. The AR5-defined likely range (17–83%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.
Year and ice sheet      Low     High
Mean ± SD       50%     5–95%   17–83%  Mean ± SD       50%     5–95%   17–83%
2050
 PW01 SLR       11 ± 8  10      1–27    5–18    15 ± 12 12      1–38    6–24
 GrIS   7 ± 5   5       2–18    3–11    9 ± 7   6       2–27    4–14
 WAIS   7 ± 8   5       0–23    1–7     5 ± 6   4       0–18    1–10


Fig. 1: PDFs for the L (blue) and H (red) temperature scenarios for the combined ice sheet SLR contributions at (A) 2100 and (B) 2300. All four time intervals are shown in SI Appendix, Fig. S2. The horizontal bars show the fifth, 17th, 50th (median), 83rd, and 95th percentile values. The baseline rate of 0.76 mm⋅a−1 is included. Note that there is more than a factor five change in the x axis scales.
Table 1: Projected sea-level rise contributions from each ice sheet and combined. Individual ice sheet and total sea-level contributions for both temperature scenarios and for the four periods considered: 2050, 2100, 2200, and 2300. All values assume the dependencies elicited for the 2100 H case. Because the PDFs are not Gaussian, the mean and median values differ; the latter is a better measure of central tendency. All values are cumulative from 2000 and include the baseline imbalance for 2000–2010 of 0.76 mm y−1. The AR5-defined likely range (17–83%) is provided alongside the 90% credible interval. PW01 denotes the performance weighted combination of experts based on their calibration score.
Year and ice sheet      Low     High
Mean ± SD       50%     5–95%   17–83%  Mean ± SD       50%     5–95%   17–83%
2050
 PW01 SLR       11 ± 8  10      1–27    5–18    15 ± 12 12      1–38    6–24
 GrIS   7 ± 5   5       2–18    3–11    9 ± 7   6       2–27    4–14
 WAIS   7 ± 8   5       0–23    1–7     5 ± 6   4       0–18    1–10
 EAIS   0 ± 2   0       −4–4    −2–1    0 ± 4   0       −6–7    −3–2
2100
 PW01 SLR       32 ± 25 26      3–81    12–53   67 ± 56 51      7–178   22–112
 GrIS   19 ± 16 13      2–57    7–31    33 ± 30 23      2–99    10–60
 WAIS   13 ± 16 8       −3–44   2–23    27 ± 33 18      −5–93   3–46
 EAIS   3 ± 6   0       −8–12   −3–4    6 ± 17  2       −11–46  −4–11
2200
 PW01 SLR       89 ± 72 72      5–231   30–149  204 ± 260       130     5–750   40–251
 GrIS   49 ± 47 34      5–149   19–79   77 ± 69 55      3–216   23–122
 WAIS   37 ± 45 26      −24–128 1–76    80 ± 113        51      −25–324 −3–138
 EAIS   4 ± 15  2       −15–34  −6–10   48 ± 158        6       −29–398 −10–19
2300
 PW01 SLR       155 ± 137       120     0–426   47–259  310 ± 322       225     14–988  87–466
 GrIS   78 ± 75 55      7–237   30–145  130 ± 117       98      7–349   39–225
 WAIS   67 ± 88 44      −47–248 6–131   117 ± 136       83      −36–384 7–228
 EAIS   10 ± 41 3       −29–96  −8–24   63 ± 195        10      −53–498 −14–51
Fig. 2: Median and likely range (17th–83rd percentile as used in the AR5) estimates of the ice sheet SLR contributions for different temperature scenarios and different studies. AR5 RCP ice sheet contributions are shown for RCP 2.6 and RCP 8.5 by combining contributions from the different sources (gray bars). BA13 is shown for the elicited temperature increase of 3.5 °C by 2100 (orange bar). This study (SEJ2018, in blue) is shown for the L and H temperature scenarios using solid lines. Dashed lines are interpolated from the L and H findings, using stochastic resampling of the distributions assuming a linear relationship between pairs of L and H samples.
The relative contribution of each ice sheet to total SLR (used here to refer to the sum of the three ice sheet contributions) depends on the temperature scenario. To demonstrate this, we compare the mean projections for the three ice sheets for the overall 2100 H distribution, for the same distribution conditional on the total contribution being above the median total projection (>51 cm), and the same distribution conditional on the total being above the 90th percentile (>141 cm). In the unconditional distribution, GrIS dominates the mean projection, contributing 33 cm (49%) of the 67-cm total, compared with 27 cm for WAIS and 6 cm for EAIS: proportions that approximately mirror the present-day contributions (4). The GrIS share declines for larger total contributions. For the mean of the upper half of total SLR projections, GrIS contributes 49 cm (46%) of 106 cm total compared with 44 cm for WAIS and 13 cm for EAIS; for the mean of the top decile, GrIS contributes 60 cm (30%) of the 194-cm total compared with 95 cm for WAIS and 39 cm for EAIS.
Statistically, the declining GrIS share and declining GrIS/AIS ratio reflect a higher mean estimate but slightly less skewed distribution for GrIS than for WAIS, and a long tail for EAIS (Fig. 3), as well as the assessed dependence structure between different terms. Physically, this is likely a result of the role of highly nonlinear dynamic processes coming into play for marine sectors of the AIS that are needed to achieve the higher values of total SLR, whereas at lower total SLR values, more linear processes dominate. It is also noteworthy that the fifth percentiles for both temperature scenarios and for all epochs are less than their current values, suggesting a scenario in which increased snowfall, primarily over the AIS (Table 1), plausibly compensates for any changes in ice dynamics and enhanced melting over the GrIS.
Fig. 3: Individual ice sheet contributions to SLR for 2100 L (A) and H (B) temperature scenarios, assuming dependences between the ice sheets in terms of the processes of accumulation, runoff, and discharge. PDFs were generated from 50,000 realizations of the relevant SEJ distributions. Horizontal bars indicate the fifth, 50th, and 95th percentile values (i.e., the 90% credible range). Also shown are the likely range (17th–83rd percentile) as defined in the AR5 and the total AIS contribution (WAIS plus EAIS assuming the inter ice sheet dependencies elicited). Note that this is not simply the sum of WAIS and EAIS contributions because of inter-ice sheet dependencies. The AIS values are compared with a recent emulator approach (30) in SI Appendix, Fig. S11.