Figure 3: Intermodel differences in CMIP6 climates and simulated AIS. Scatter plots show intermodel differences in modeled Antarctic climate and resulting states of the AIS forced by 36 CMIP6 climate models, represented by markers of different shapes and colors. (A to D) DJF near-surface (2-m) air temperature (T2m) (°C, vertical axes) averaged over ice shelves against Antarctic coastal ocean potential temperature at 400-m (°C, horizontal axes), (E to H) area of floating ice (10 × 106 km2, vertical axes) against area of grounded ice (106 km2, horizontal axes), and (I to L) contributions to GMSL change from the West AIS (WAIS) (m, vertical axes) against the East AIS (EAIS) (m, horizontal axes). (A) and (B) shows the raw (uncorrected) and bias-corrected preindustrial climates, respectively; (C) and (D) show the changes relative to the 1850–1869 period by year 2020 and 2100. Similarly, (E) and (F) and (I) and (J) show ISM results forced by the raw and bias-corrected climates, respectively; (G) and (H) and (K) and (L) show ice sheet changes from the initial preindustrial state at 2020 and 2100, respectively, forced by bias-corrected climates (Experiment CMIP6_BC_1850-2100). Gray squares show 16 to 84 percentile range of intermodel spread.
These ISM control experiments highlight the room for improvement in CMIP6 models’ performance in the Antarctic region. The simulations also corroborate the established wisdom that the WAIS is especially sensitive to ocean temperatures: For example, the climate model NESM3 has a mean circum-Antarctic warm bias of 1.5°C in θ400m (Fig. 3A), but this is sufficient to drive a partial collapse of the WAIS in the ISM on long time scales (Fig. 3I).
Despite that unrealistic AIS geometries were simulated by under many CMIP6-modeled climates, these experiments are not designed for evaluating CMIP6 climate models’ performance over Antarctica. Here, we have regarded reanalysis datasets as the “observational truth,” serving as a reference climate for calibrating the ISM model parameters, including the ocean melt rate coefficient and the basal sliding coefficients (BSCs). Because of the scarcity of observations available for Antarctica, reanalysis datasets may have substantial departures from the true climate state in some regions. These control experiments are run for 10,000 years, allowing the AIS to reach a quasi-equilibrium, but it is not clear how close the AIS was to such a state before the dawn of the Industrial Revolution, when anthropogenic climate forcing started to emerge. Furthermore, Earth’s orbital parameters drift substantially over 10,000 years, and the AIS is expected to respond accordingly. The availability of CMIP6 historical simulations, dating back to only 1850, makes the quasi-equilibrium assumption necessary for conducting an intercomparison of the AIS forced by different climate models, but the intrinsic uncertainty in the AIS’s natural variability cautions against judging these climate models based on their respective ISM simulations.
Near-equilibrium AIS under bias-corrected CMIP6 climates
The diverse polar climates simulated by CMIP6 models render the above approach unsuitable for assessing the uncertainty in the AIS’s future trajectory. An alternative strategy is to bias-correct CMIP6 climates against present-day observations. Spatially varying biases in CMIP6 monthly climate fields are calculated and subtracted from the raw model output (Methods). In this approach, we essentially remove CMIP6 models’ biases in present-day climates and focus on their changes from the reference period. However, because of CMIP6 models’ differing sensitivities to anthropogenic forcings, bias-corrected preindustrial climates for Antarctica still display significant intermodel variations, showing a large intermodel spread in preindustrial T2m and θ400m. Mean DJF T2m over ice shelves is up to 4.5 K lower than the present-day reference period. Simulated preindustrial annual mean θ400m averaged along the Antarctic coast is up to 1 K lower than present-day (Fig. 3B). Note that warming proceeds at a faster pace in the atmosphere than the subsurface ocean, underscoring complex processes at play in the Southern Ocean, where vigorous convection and upwelling around Antarctica may suppress the pace of warming (23).
In the experiment set CMIP6_BC_PI_CTL, the ISM is initiated from the present-day AIS and runs for 15,000 years until it reaches a quasi-equilibrium but forced with CMIP6 bias-corrected preindustrial climates. Compared with the initial state, the modeled preindustrial AIS in quasi-equilibrium generally shows thinning of the EAIS, consistent with reduced snowfall in a colder preindustrial climate. Under most CMIP6 models, ice shelves around the AIS expand, which is also consistent with lower preindustrial ocean temperatures. Intermodel differences in ice volume of the EAIS and the WAIS are 0.6- and 1.2-m sea level equivalent (SLE), respectively (Fig. 3I).
Projected changes in Antarctic climate and the AIS
Under the SSP5-8.5 scenario, all CMIP6 models included in this study show substantial warming relative to preindustrial in both T2m and θ400m over this century (Figs. 3D and 4). DJF T2m averaged over all Antarctic ice shelf surfaces increases by 0.3 to 2.6 K in 2020 and by 1 to 10 K in 2100; θ400m averaged along the Antarctic coast increases by −0.1 to 0.5 K in 2020 and up to 1.6 K in 2100 (Fig. 3, C and D). The amplitude of warming in climate models reveals dependence on the state of simulated reference climate. For instance, CAMS-CSM1-0 and MIROC6 are among the models with the greatest warm bias in T2m (Figs. 1A and 3A), but they also show the least warming (<2 K) by 2100. One of the contributing factors might be that, in preindustrial climates, these models are mostly free of austral summer sea ice, reducing the strength of sea ice-albedo feedback in future warming scenarios.
Figure 4: Simulated changes in ice thickness since 1850. (A) Changes in ice thickness since 1850 by year 2020 in simulations transiently forced by bias-corrected historical + SSP5-8.5 climates from 36 CMIP6 models (Experiment CMIP6_BC_1850–2100). (B) Same as (A) but for year 2100.
Experiment set CMIP6_BC_1850-2100 are 250-year ISM runs under transient bias-corrected CMIP6 climates in combined historical (1850–2014) and SSP5-8.5 (2015–2100) scenarios, with the ice sheet initiated from the respective 15,000-year control simulation under the bias-corrected preindustrial climate described previously (Experiment CMIP6_BC_PI_CTL). Climate fields are bias-corrected and drive the ISM year by year, so that an evolution of the AIS is obtained for each CMIP6 model. In this approach, we essentially remove each CMIP6 model’s bias in simulated present-day climate and focus on the course of simulated climate change and associated impact on the AIS, especially on the uncertainty in the AIS’s future projections.
Projected changes in the Antarctic climate from all CMIP6 models drive a reduction in both AIS volume and the extent of ice shelves (Figs. 3 and 5). The magnitude of ice loss, however, shows a large intermodel spread. CIESM shows the largest warming in atmospheric and oceanic temperatures and drives the most intense Antarctic ice loss. CESM2, CESM2-WACCM, and CNRM-CM6-1 are among the models with the largest warming in T2m by 2100 (Fig. 3C); they also drive some of the largest reductions in ice volume. Counterintuitively, the four variants of EC-Earth3 show greater oceanic warming, but they produce much less 21st century ice loss (Fig. 3, D and H). In the previous three models, ice surface melting and the loss of ice shelves overshadow sub-ice melting due to oceanic warming, which has been the focus of most recent studies on the sensitivity of the AIS, especially its marine-based WAIS portion (24). Climate models with the strongest atmospheric warming also produce the largest WAIS retreat, raising the GMSL by >0.25 m by 2100 (Fig. 3L). A contributing factor for this emerging correlation may be that the ISM used in this study resolves hydrofracturing and ice cliff failure processes, which make the ice shelves prone to collapse triggered by surface melting and thus increase the ISM’s sensitivity to atmospheric warming.


Experiment set CMIP6_BC_1850-2100 are 250-year ISM runs under transient bias-corrected CMIP6 climates in combined historical (1850–2014) and SSP5-8.5 (2015–2100) scenarios, with the ice sheet initiated from the respective 15,000-year control simulation under the bias-corrected preindustrial climate described previously (Experiment CMIP6_BC_PI_CTL). Climate fields are bias-corrected and drive the ISM year by year, so that an evolution of the AIS is obtained for each CMIP6 model. In this approach, we essentially remove each CMIP6 model’s bias in simulated present-day climate and focus on the course of simulated climate change and associated impact on the AIS, especially on the uncertainty in the AIS’s future projections.
Projected changes in the Antarctic climate from all CMIP6 models drive a reduction in both AIS volume and the extent of ice shelves (Figs. 3 and 5). The magnitude of ice loss, however, shows a large intermodel spread. CIESM shows the largest warming in atmospheric and oceanic temperatures and drives the most intense Antarctic ice loss. CESM2, CESM2-WACCM, and CNRM-CM6-1 are among the models with the largest warming in T2m by 2100 (Fig. 3C); they also drive some of the largest reductions in ice volume. Counterintuitively, the four variants of EC-Earth3 show greater oceanic warming, but they produce much less 21st century ice loss (Fig. 3, D and H). In the previous three models, ice surface melting and the loss of ice shelves overshadow sub-ice melting due to oceanic warming, which has been the focus of most recent studies on the sensitivity of the AIS, especially its marine-based WAIS portion (24). Climate models with the strongest atmospheric warming also produce the largest WAIS retreat, raising the GMSL by >0.25 m by 2100 (Fig. 3L). A contributing factor for this emerging correlation may be that the ISM used in this study resolves hydrofracturing and ice cliff failure processes, which make the ice shelves prone to collapse triggered by surface melting and thus increase the ISM’s sensitivity to atmospheric warming.
Figure 5: Simulated changes in the AIS’s area and sea level contribution. Top panels show changes in ice area relative to the preindustrial, where black, blue, and red lines represent all, grounded, and floating (shelf) ice, respectively. Bottom panels show changes in the AIS’s contribution to GMSL rise, where black, blue, and red lines are for the whole AIS, the EAIS, and the WAIS, respectively. Results from experiments with marine ice cliff instability (MICI) processes and forced with bias-corrected CMIP6 model climate (Experiment CMIP6_BC_1850-2100) are shown in the left column. Middle column shows results from experiments with MICI processes but forced with raw CMIP6 model climate, while the ISM is tuned separately for each CMIP6 model (Experiment CMIP6_RAW_1850-2100) (see Methods and figs. S13 to S16). Right column is for experiments forced with bias-corrected CMIP6 model climate, while MICI-related processes are turned off (Experiment CMIP6_BC_1850-2100_NO_MICI). In each panel, the full spread (0 to 100th percentile) in 36 simulations is shaded in light gray, and 16th to 84th percentile are in darker gray. The full spread and 16th to 84th percentile of respective variables for grounded ice/EAIS and floating ice/WAIS at 2100 are shown as blue and red boxplots, respectively, to the right of each panel.
These 250-year AIS simulations using bias-corrected climates from 36 CMIP6 models reveal both accelerating retreat of the AIS and increasing uncertainty in its future trajectory. Relative to its preindustrial state, the multimodel median rate of ice loss increases by almost an order of magnitude from 2020 to 2100 (Fig. 3, G and H). EAIS and WAIS display contrasting changes over the early stage of warming before 2020: The WAIS loses mass and contributes to a SLR under all CMIP6 models’ bias-corrected climate trajectories, while, under most CMIP6 models (27 of 36), the EAIS gains mass and draws down GMSL (Fig. 3K). Between 1850 and 2020, the EAIS produces a small negative (~−0.01 m) multimodel median contribution to GMSL rise, while reduction in the WAIS is more consistent across models. As the 21st century warming proceeds, the EAIS is expected to reverse its trend later and begin to lose mass (Fig. 5C). By 2100, the multimodel median reduction in ice area increases to 6 × 105 km2, and the multimodel median sea level contribution of the AIS approaches 0.3 m (Fig. 5), with the highest modeled SLR exceeding 1 m. The full range of the AIS’s sea level contribution by 2100 greatly exceeds its multimodel median value as a result of the strong nonlinearity in the ice sheet’s response to temperature change. While the CMIP multimodel mean/median has been shown to produce an accurate representation of modern climate state, and multimodel median sea level projections remain more policy relevant than end-members, we should beware of the existence of low-probability, high-consequence scenarios in future SLR.
Discussion
Effect of MICI on projected ice loss
The projected MMM rise in GMSL contributed by the AIS and associated uncertainty in these CMIP6-driven ISM simulations is noticeably greater than those assessed by ISMIP6 (15) and IPCC-AR6 (9). A possible factor might be the “marine ice cliff instability” (MICI) mechanism, which is accounted for in our ISM but has not been widely implemented in other ISMs. The ISM used in this study includes optional hydrofracturing and ice cliff failure mechanisms (25), which may give rise to MICI (5, 26, 27) under strong future warming scenarios but not in preindustrial and present-day climate conditions. MICI is a newly proposed mechanism, and there have been ongoing discussions concerning its validity. Self-sustaining ice loss triggered by MICI has been proposed to be necessary for explaining the Antarctic contribution to sea level high stands during the LIG and the Pliocene (5, 28) as well as the ice berg keel marks formed in deep water during the last deglaciation in the Amundsen Sea Embayment (29). On the other hand, some suggest that MICI is not well constrained and is not required to explain past sea level high stands (30), it may be mitigated by slow removal of ice shelves (31), and the progress of instability may be slowed by ice-mélange buttressing. Recent advances in modeling ice cliff failure reveal that MICI remains a feasible mechanism, but glacier models have shown a higher degree of complexity (32, 33) compared to the parameterization scheme originally implemented in our ISM.
Although key parameters for hydrofracturing and cliff failure have been updated and constrained by sea level proxy data and observational records (5), considering their associated uncertainty, we also carried out alternative experiments without MICI processes (Exp. CMIP6_BC_1850-2100_NO_MICI). Without MICI, the ISM runs show smaller sea level contributions from the AIS by 2100, ranging from −0.05 to 0.2 m, with a median of 0.02 m, more in line with the findings of a recent study using statistical emulators of ISMs (10). In the absence of hydrofracturing and ice cliff failure, the warming in near-surface air temperature increases surface melt but does not trigger widespread collapse of ice shelves, and any tall ice cliffs that do emerge where ice shelves are lost remain intact in the model. Ignoring hydrofracturing and ice cliff failure processes puts our model in the lower range among ISMs in terms of its sensitivity to climate warming, so in these simulations without MICI, the resulting uncertainty in future sea level change reflects the combination of widely differing CMIP6 climate fields and a low-sensitivity ISM. However, even without MICI-related processes, the full range of climate-driven sea level uncertainty contributed by the AIS still amounts to 0.25 m by 2100, exceeding uncertainties from other major contributors, including sea water thermal expansion, mountain glaciers, and the Greenland Ice Sheet (7).
Implications on observed ice sheet changes in recent decades


Although key parameters for hydrofracturing and cliff failure have been updated and constrained by sea level proxy data and observational records (5), considering their associated uncertainty, we also carried out alternative experiments without MICI processes (Exp. CMIP6_BC_1850-2100_NO_MICI). Without MICI, the ISM runs show smaller sea level contributions from the AIS by 2100, ranging from −0.05 to 0.2 m, with a median of 0.02 m, more in line with the findings of a recent study using statistical emulators of ISMs (10). In the absence of hydrofracturing and ice cliff failure, the warming in near-surface air temperature increases surface melt but does not trigger widespread collapse of ice shelves, and any tall ice cliffs that do emerge where ice shelves are lost remain intact in the model. Ignoring hydrofracturing and ice cliff failure processes puts our model in the lower range among ISMs in terms of its sensitivity to climate warming, so in these simulations without MICI, the resulting uncertainty in future sea level change reflects the combination of widely differing CMIP6 climate fields and a low-sensitivity ISM. However, even without MICI-related processes, the full range of climate-driven sea level uncertainty contributed by the AIS still amounts to 0.25 m by 2100, exceeding uncertainties from other major contributors, including sea water thermal expansion, mountain glaciers, and the Greenland Ice Sheet (7).
Implications on observed ice sheet changes in recent decades
Centennial and millennial trends in the AIS are dictated by long-term climate change, natural or anthropogenic, but internal variabilities of the climate system may still be important for multidecadal ice sheet changes, e.g., changes in polar ice sheets observed during the satellite era. Few of the ISM simulations driven by bias-corrected CMIP6 climates (Exp. CMIP6_BC_1850-2100) show an Antarctic contribution to GMSL over 1992–2017 consistent with that estimated by the Ice Sheet Mass Balance Intercomparison Exercise (IMBIE) team (34, 35). Forced by the multimodel mean outputs from 36 CMIP6 models, net contribution by the AIS during the IMBIE period 1992–2017 is minimal (Fig. 6A).
Figure 6: Simulated rates of GMSL change. (A) Contributions to the mean rate of change in GMSL during the IMBIE period (1992–2017) by the AIS in simulations forced by bias-corrected CMIP6 model climates, where the likely ranges estimated by IMBIE are marked by horizontal blue bars. (B) Same as (A) but for the WAIS. (C) Same as (A) but for the EAIS. (D) Same as (A) but for the late-century period 2081–2100 under the SSP5-8.5 scenario. Results from each model are shown in gray bars, and the horizontal dashed lines represent the multimodel mean. Gray bars labeled as “CMIP6” represent an ice sheet simulation forced by the multimodel mean climate fields of 36 models, while hollow blue bars are for a similar simulation but with forcings during 1980–2019 replaced by observed fields from ERA5 and WOA18.
In another simulation with the same climate forcing, but its 1980–2019 segment replaced by observational data (Exp. CMIP6_BC_MMM+OBS), Antarctica’s contribution to GMSL rise is more consistent with the IMBIE assessment, as a result of faster retreat of the WAIS and slower growth of the EAIS. A multidecadal warming trend since the 1970s in the circumpolar deep water (CDW) (fig. S12) (36), a relatively warm water mass circulating around Antarctica, may have enhanced basal melting of West Antarctic ice shelves. The ISM presents rates of ice loss comparable to IMBIE estimates when driven by the observed transient climate (fig. S12). Multimodel mean climate fields are essentially devoid of internal climate variabilities—provided that the number of models is large enough—due to cancellation of random phases from models. The observed multidecadal CDW warming trend, which may be partially caused by internal climate variability, cannot—and should not—be expected to be robustly reproduced in CMIP6 historical simulations, and its absence could be a factor for the generally small 1992–2017 trends from ISM simulations forced by CMIP6 models.
ISM intercomparison projects
A number of modeling studies concerning the uncertainty in future SLR contributed by the AIS have been carried out. The ISMIP6-Antarctica project (15) used ISMs from 13 modeling groups and six CMIP5 climate models. A smaller subset of CMIP6 models, all with an equilibrium climate sensitivity (ECS) near the upper end of climate models, has been used in similar ways to assess the future GMSL contributions by ice sheets under different emission scenarios (16). The work presented here complements the scope of existing ISM intercomparison projects. We have included 36 climate models from the CMIP6 ensemble, which encompass a wider range of ECS and more fully represent the contemporary understanding of the climate system and its future changes. CMIP6 models are known to have an overall higher ECS compared with CMIP5 models, primarily as a result of stronger positive cloud feedbacks from refined cloud schemes (37). Although only one ISM is used in this study, we have provided contrasting simulations with and without MICI processes, differing substantially in the sensitivity to atmospheric warming.
Under the Representative Concentration Pathway (RCP) 8.5 scenario, a radiative forcing scenario similar to its CMIP6 successor SSP5-8.5, ISMIP6 simulations with 13 different ISMs give an Antarctic contribution to GMSL during the period 2015–2100 between −7.8 and 30 cm (15). In those simulations, WAIS retreat shows great variance among projections, up to 18-cm SLE, while the EAIS mass change varies between −6.1- and 8.3-cm SLE. These ISMIP6 projections present less ice loss and associated uncertainty compared with those in our simulations with the MICI mechanism, which is not considered in ISMIP6. Another contributing factor is the higher ECS of CMIP6 models used here, which generally warm more rapidly under SSP5-8.5 compared with CMIP5 models under RCP8.5.
Effects of ISM calibration per climate model
Results discussed so far are all from ISM runs in a “single-ISM” framework, where the ISM is calibrated on the basis of observational data, with its parameters fixed for all CMIP6 climate models. Nonetheless, calibrating an ISM’s parameters so that, under a prescribed climate, it could simulate that a target ice sheet state is a common practice in the ice sheet modeling community, in which ISM parameters may absorb part of the spread in climate boundary conditions. Ice sheet intercomparison projects, e.g., ISMIP6, were carried out in similar ways, in which ISMs from decentralized development were calibrated separately with their own targets. To assess the effect of ISM tuning on projected Antarctic ice loss, we carried out a series of experiments to tune key ISM parameters for the preindustrial climate simulated by each CMIP6 model (Methods). This essentially results in multiple ISMs, each tailored for the respective CMIP6 model. We then run future projections of the AIS with the raw climate output from CMIP6 models, rather than bias-corrected climate as we did previously.
With this “multi-ISM” approach, the spread in simulated AIS forced by raw CMIP6 1850–2100 climate is smaller than that in single-ISM runs (Fig. 5). In comparison with ISMIP6 results, however, the dispersion of simulated Antarctic ice loss by 2100 in multi-ISM runs is still larger than that documented by ISMIP6-Antarctica. This may well be contributed to the more comprehensive set of climate models used in our study and CMIP6 models generally showing a higher climate sensitivity to elevated greenhouse gas levels, despite that the SSP5-8.5 scenario (8) used by CMIP6 models has slightly lower rates of greenhouse gas emissions than RCP8.5—its CMIP5 counterpart used by ISMIP6.


Effects of ISM calibration per climate model
Results discussed so far are all from ISM runs in a “single-ISM” framework, where the ISM is calibrated on the basis of observational data, with its parameters fixed for all CMIP6 climate models. Nonetheless, calibrating an ISM’s parameters so that, under a prescribed climate, it could simulate that a target ice sheet state is a common practice in the ice sheet modeling community, in which ISM parameters may absorb part of the spread in climate boundary conditions. Ice sheet intercomparison projects, e.g., ISMIP6, were carried out in similar ways, in which ISMs from decentralized development were calibrated separately with their own targets. To assess the effect of ISM tuning on projected Antarctic ice loss, we carried out a series of experiments to tune key ISM parameters for the preindustrial climate simulated by each CMIP6 model (Methods). This essentially results in multiple ISMs, each tailored for the respective CMIP6 model. We then run future projections of the AIS with the raw climate output from CMIP6 models, rather than bias-corrected climate as we did previously.
With this “multi-ISM” approach, the spread in simulated AIS forced by raw CMIP6 1850–2100 climate is smaller than that in single-ISM runs (Fig. 5). In comparison with ISMIP6 results, however, the dispersion of simulated Antarctic ice loss by 2100 in multi-ISM runs is still larger than that documented by ISMIP6-Antarctica. This may well be contributed to the more comprehensive set of climate models used in our study and CMIP6 models generally showing a higher climate sensitivity to elevated greenhouse gas levels, despite that the SSP5-8.5 scenario (8) used by CMIP6 models has slightly lower rates of greenhouse gas emissions than RCP8.5—its CMIP5 counterpart used by ISMIP6.
Some CMIP6 models with a high climate sensitivity happen to display a warm bias in simulated present-day Antarctic climate. For instance, CESM2-WACCM drives one of the largest Antarctic ice loss by 2100 (∼1.05 m) in the single-ISM run, but the number reduces to only ∼0.25-m SLE in the multi-ISM run. Examining the tuned ocean melt factor (OMF) (fig. S13), we can see that, to compensate the warm bias in CESM-WACCM’s 400-m ocean temperature, the OMF has to be reduced to 0.72, much smaller than the OMF (5.0) used in single-ISM runs, which was calibrated on the basis of present-day observations. This, of course, greatly reduces the ISM’s sensitivity to oceanic warming. In the case of MIROC6, which has an exceptionally large warm bias in the surface air temperature, the temperature offset in the ISM’s positive-degree-day scheme (TPD) has to be increased to 4.64 K so that the modeled rate of surface meltwater production is around 100 Gt year−1. In other words, for the ISM tuned for MIROC6, ice and snow only melt at temperatures higher than 4.64 K. This is clearly unphysical but not an unexpected outcome of the tuning process. As warm bias in simulated modern polar climate is more prevalent than cold bias among CMIP6 models (Fig. 1A), tuning specifically for each CMIP6 model would generally reduce the ISM’s sensitivity to climatic warming and narrow the spread in projected ice loss.
Then, we come to the question whether this multi-ISM approach, in comparison with the single-ISM way, is more appropriate in assessing the uncertainty in projected Antarctic ice loss associated with climate models. The multi-ISM way hides climate models’ biases under tailored ISM parameter settings but may resort to parameters that are unphysical or contradicting to observational evidence.
Implications for Earth system model development
The large spread in modeled polar climate in the current generation CMIP6 models would make it highly challenging to conduct intercomparisons of “Earth system models” with embedded, active ice sheets. It is not uncommon for climate models from different modeling centers to share components, and the same ISM or its close variants may be incorporated in several Earth system models. For instance, the Parallel Ice Sheet Model (PISM) is used in NASA GISS and MPI-ESM models, and the Grenoble ice sheet and land ice (GRISLI) model is used in CNRM-CM and IPSL-CM6 (11). Our ISM simulations forced by raw CMIP6 climates have demonstrated that, even with the same ISM, structural differences between atmosphere-ocean models can result in widely varying equilibrium states of the AIS. It has been recognized that simulated paleo–ice sheet volume, such as that during the mid-Pliocene, is highly dependent on climate model–based forcings (17).
Results from our study highlight that biases in simulated polar climate from state-of-the-art climate models are large enough to drive the AIS to equilibrium states distinctly different from the present day, although the ISM simulates a realistic AIS with observational climate data. This poses a serious challenge to the practice of using paleo sea level to constrain the parameters of ice sheet processes, irrespective of the accuracy of ice volume and sea level reconstructions (38).
Since the advent of numerical general circulation models in the 1960s, climate models have followed an evolutionary path of increasing complexity with ever more components added for explicit simulation (39). Spanning a hierarchy of models (40), climate modeling has now entered the Earth system model phase, where the most sophisticated models have added biogeochemical cycles and land ice sheets to the atmosphere-land-ocean system. Integrated ice sheet components embedded within Earth system models allow consistent simulations of crucial processes for polar climate change, e.g., the ice-albedo feedback, ice-elevation feedbacks associated with an evolving ice sheet topography, and the climate feedbacks associated with ice sheet meltwater (41–43). Results from our study, however, warn of substantial ongoing uncertainty among Earth system models with interactive ice sheets for the evaluation of future SLR. While progress has been made in ice sheet modeling, the uncertainty in future changes of the AIS and associated impacts on GMSL have not been reduced to a level needed for straightforward decision-making, and more work is required. Current greenhouse gas emissions put the climate on track of a >3°C warming by 2100, and the time window is shrinking for reducing carbon emissions to avoid rapid and unstoppable SLR (5). For more robust sea level projections, improved understanding of processes important for polar climate, including cloud radiative forcing and deep ocean circulations and mixing, is urgently needed.
Methods
Ice sheet model
In this study, we use PSUICE3D (18), a numerical ISM with a hybrid approach to the dynamical equations governing ice sheet and ice shelf flow, which are described by the shallow ice and shallow shelf approximations, respectively, and are combined heuristically by an imposed mass flux condition across the grounding line (44). These hybrid ice dynamics capture the migration of grounding lines and essential mechanisms of ice sheet–ice shelf dynamics, e.g., the marine ice sheet instability (MISI) for an inward-deepening ice sheet bed, while allowing the model to be run on coarse grids (20 km in this study) so that a large ensemble of simulations can be carried out economically on centennial and millennial time scales and on continental spatial scales. Bedrock deformation under the weight of the ice sheet is represented by a local relaxation toward isostatic equilibrium and elastic lithospheric flexure. No explicit basal hydrology is implemented in the model other than allowing basal sliding where the basal temperature reaches the melt point. BSCs of the bed are obtained using an inverse method, in which the model is driven by present-day observational climate and the sliding coefficient at each grid point is tuned iteratively until the local ice thickness equilibrates toward the present-day observed value (21).
Ice sheet SMB is calculated as snowfall minus surface melt, while sublimation at the ice surface is ignored. The fraction of precipitation falling as snow is determined by a parameterized formulation based on the corresponding monthly surface air temperature Ta (45). Ice surface melt is calculated from Ta using a standard positive-degree-day (PDD) scheme with a coefficient of 0.005 m per degree-day, but the temperature baseline for zero melt (parameter TPD) is set at −1°C in single-ISM runs so that, under present-day climate, the total surface melt rate of Antarctic ice shelves is within the observational range (46).
Heavily parameterized in the current generation ISMs, ocean-induced ice shelf basal melt is recognized as a major source of uncertainty in the AIS’s response to climate change (11, 13, 15). Basal melt of Antarctic ice shelves is strongly influenced by the incursion of warm CDW, which occurs at ∼10-km spatial scales and daily to subdaily time scales (47) and cannot be faithfully simulated in a coarse resolution (∼100-km) ocean model typical of CMIP6 models. Recognizing these limitations, in this study, we use a simple parameterization scheme for basal melt rates, which assumes a quadratic dependence on the 400-m ocean temperature above the pressure melting point of ice (T_o − T_f)


Little et al. (2019)
Title:
The Relationship Between U.S. East Coast Sea Level and the Atlantic Meridional Overturning Circulation: A Review
Key Points:
The relationship between the AMOC and coastal sea level is important to flood risk projections and ocean circulation reconstructions
The amplitude and pattern of sea level variability associated with AMOC variations is location, forcing, timescale, and model dependent
Future research should address the complex spatiotemporal structure of AMOC and the role of near.coast ageostrophic processes
Corresponding author:
Little
Citation:
Little, C. M., Hu, A., Hughes, C. W., McCarthy, G. D., Piecuch, C. G., Ponte, R. M., & Thomas, M. D. (2019). The Relationship between U.S. East Coast sea level and the Atlantic Meridional Overturning Circulation: A review. Journal of Geophysical Research: Oceans, 124, 6435Ð6458. doi:10.1029/2019JC015152
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2019JC015152
Abstract
Scientific and societal interest in the relationship between the Atlantic Meridional Overturning Circulation (AMOC) and U.S. East Coast sea level has intensified over the past decade, largely due to (1) projected, and potentially ongoing, enhancement of sea level rise associated with AMOC weakening and (2) the potential for observations of U.S. East Coast sea level to inform reconstructions of North Atlantic circulation and climate. These implications have inspired a wealth of model- and observation-based analyses. Here, we review this research, finding consistent support in numerical models for an antiphase relationship between AMOC strength and dynamic sea level. However, simulations exhibit substantial along-coast and intermodel differences in the amplitude of AMOC-associated dynamic sea level variability. Observational analyses focusing on shorter (generally less than decadal) timescales show robust relationships between some components of the North Atlantic large-scale circulation and coastal sea level variability, but the causal relationships between different observational metrics, AMOC, and sea level are often unclear. We highlight the importance of existing and future research seeking to understand relationships between AMOC and its component currents, the role of ageostrophic processes near the coast, and the interplay of local and remote forcing. Such research will help reconcile the results of different numerical simulations with each other and with observations, inform the physical origins of covariability, and reveal the sensitivity of scaling relationships to forcing, timescale, and model representation. This information will, in turn, provide a more complete characterization of uncertainty in relevant relationships, leading to more robust reconstructions and projections.
Plain Language Summary
Sea level along the U.S. East Coast is influenced by changes in the density and currents of the North Atlantic Ocean. Indeed, there are simple theoretical considerations that relate indices of basin-scale flow to coastal sea level. Such a relationship could be leveraged to predict future sea level changes and coastal flooding given an expected change in climate and ocean circulation. Alternatively, it could be used to reconstruct ocean circulation from sea level measurements. This paper reviews the nature of this relationship and whether, and when, it is evident in climate models and observations. Although the current generation of large-scale climate and ocean models generally show an antiphase relationship between basin-scale ocean current strength and coastal sea level, the spatial pattern of sea level change differs from theory and between models. Supported by existing and emerging research, the authors hypothesize that these deviations result from important physical processes occurring on the continental shelf and slope, and the complexities of the 3-dimensional ocean circulation. A quantitative assessment of the importance of these processes is critical for understanding past and future climate and sea level changes in this heavily populated and vulnerable region.
Sea Level Variability Along the United States East Coast and Its Societal Importance
The densely populated U.S. East Coast is especially vulnerable to the impacts of sea level change, with ~2.4 million people and ~1.4 million housing units between Maine and Florida less than 1 m above local mean high water (Strauss et al., 2012). Here, sea level rise is already having adverse environmental, societal, and economic consequences, including increases in the severity and frequency of coastal flooding (e.g., Ezer & Atkinson, 2014; Moftakhari et al., 2015; Ray & Foster, 2016; Sweet et al., 2018; Wdowinski et al., 2016). Regional rates of sea level rise, and their associated consequences, are projected to increase substantially over the coming century (Figure 1a; Brown et al., 2018; Dahl et al., 2017; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, Yip, 2015; Ray & Foster, 2016; Vitousek et al., 2017).
Figure 1: (a) Monthly mean tide gauge sea level (in millimeters relative to year 2000) at the Battery (New York City; blue line). Projections of relative sea level (RSL) change, relative to year 2000, for RCP 2.6 (blue) and RCP 8.5 emission scenarios (red; Kopp et al., 2014). Shading after the year 2000 indicates 17th to 83rd percentile range of RSL projections. (b) Annual mean RSL (in millimeters, with arbitrary offset) measured at 15 U.S. East Coast tide gauges (Holgate et al., 2013) with long and relatively complete records. (c) Linear trend in RSL along the U.S. East Coast from 1900Ð2017, in millimeters per year, from a Bayesian reconstruction (panel taken from Piecuch, Huybers, et al., 2018).
Understanding the drivers of future change in relative sea level (RSL, i.e., that observed by tide gauges and relevant to coastal locations; see Gregory et al., 2019), and the ability of numerical models to represent such drivers, is critical. However, this is a complex task, given the many contributing processes that operate over different temporal and spatial scales, including, for example: freshwater input from land and the cryosphere, thermal expansion of sea water, glacial isostatic adjustment, and oceanic mass and volume redistribution (see Kopp et al., 2015; Milne et al., 2009; Stammer et al., 2013, for more thorough reviews of these processes).
The relative contributions of these processes to U.S. East Coast RSL vary across space and through time. For example, vertical land motion (due primarily to glacial isostatic adjustment) accounts for the majority of the large-scale spatial variation in recent centennial trends and underlies the high rates of RSL rise in the Mid-Atlantic (Figure 1c; Karegar et al., 2017; Piecuch, Huybers, et al., 2018). However, ongoing climate-related processes - associated with net freshwater input, atmosphere-ocean momentum and buoyancy fluxes, and ocean mass and volume redistributionÑdominate the interannual to multidecadal, spatially variable, U.S. east coast RSL signals during the twentieth century (Figure 1b; Andres et al., 2013; Bingham & Hughes, 2009; Davis & Vinogradova, 2017; Ezer, 2013; Ezer et al., 2013; Frederikse et al., 2017; Goddard et al., 2015; Park & Sweet, 2015; Piecuch et al., 2016; Piecuch, Bittermann, et al., 2018; Piecuch & Ponte, 2015; Thompson & Mitchum, 2014; Woodworth et al., 2014; Yin & Goddard, 2013).


Understanding the drivers of future change in relative sea level (RSL, i.e., that observed by tide gauges and relevant to coastal locations; see Gregory et al., 2019), and the ability of numerical models to represent such drivers, is critical. However, this is a complex task, given the many contributing processes that operate over different temporal and spatial scales, including, for example: freshwater input from land and the cryosphere, thermal expansion of sea water, glacial isostatic adjustment, and oceanic mass and volume redistribution (see Kopp et al., 2015; Milne et al., 2009; Stammer et al., 2013, for more thorough reviews of these processes).
The relative contributions of these processes to U.S. East Coast RSL vary across space and through time. For example, vertical land motion (due primarily to glacial isostatic adjustment) accounts for the majority of the large-scale spatial variation in recent centennial trends and underlies the high rates of RSL rise in the Mid-Atlantic (Figure 1c; Karegar et al., 2017; Piecuch, Huybers, et al., 2018). However, ongoing climate-related processes - associated with net freshwater input, atmosphere-ocean momentum and buoyancy fluxes, and ocean mass and volume redistributionÑdominate the interannual to multidecadal, spatially variable, U.S. east coast RSL signals during the twentieth century (Figure 1b; Andres et al., 2013; Bingham & Hughes, 2009; Davis & Vinogradova, 2017; Ezer, 2013; Ezer et al., 2013; Frederikse et al., 2017; Goddard et al., 2015; Park & Sweet, 2015; Piecuch et al., 2016; Piecuch, Bittermann, et al., 2018; Piecuch & Ponte, 2015; Thompson & Mitchum, 2014; Woodworth et al., 2014; Yin & Goddard, 2013).
Of interest in this review paper is RSL variability related to changes in ocean circulation and density that may be causally coupled, or simply correlated, with the Atlantic Meridional Overturning Circulation (AMOC; see section 2). We thus focus on variability in “dynamic sea level” (DSL), that is, the height of the sea surface above the geoid, with the inverse barometer correction applied (Gregory et al., 2019). Secular DSL changes are evident in 21st century climate model simulations and are projected to be a principal driver of acceleration in 21st century sea level and its spatial variation along the east coast (Bilbao et al., 2015; Bouttes et al., 2014; Carson et al., 2016; Chen et al., 2018; Church et al., 2013; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, Vecchi, et al., 2015; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Perrette et al., 2013; Slangen et al., 2014; Yin et al., 2009; Yin, 2012; Yin & Goddard, 2013). Various studies have shown these large-scale regional DSL anomalies to be correlated with a decline in AMOC strength (section 4). However, current-generation climate models also show a wide range in future projections of regional DSL rise. They may also exhibit systematic biases due to poorly resolved processes that influence near-coast DSL (section 6).
An improved theoretical and observational basis for AMOC-DSL relationships would enable assessments of the reliability of individual model projections, and climate models more generally, allowing improved estimates of the magnitude, spatial pattern, and time of emergence of expected sea level rise. In addition, a robust “signature” of AMOC (or some other feature of the large-scale circulation) in coastal RSL could be leveraged to infer preinstrumental changes in AMOC and/or climate. Recent improvements to analysis of the tide gauge record, including approaches to cope with data gaps and account for vertical land motion and glacial isostatic adjustment (Kopp, 2013; Piecuch, Huybers, et al., 2017), have intensified the interest in exploiting this relationship to inform reconstructions of ocean variability (e.g., Butler et al., 2015; Kienert & Rahmstorf, 2012; McCarthy et al., 2015). Proxies that predate the tide gauge record offer the opportunity to extend these reconstructions over centennial to millennial timescales (e.g., Kemp et al., 2017, 2018).
Here, motivated by these considerations, we review evidence for the covariation of AMOC and U.S. East Coast sea level. In section 2, we define AMOC and its relationship to the large-scale circulation of the North Atlantic Ocean. Section 3 presents a simple diagnostic scaling argument between AMOC strength and DSL. Section 4 surveys AMOC-DSL linkages in numerical simulations (where long-period relationships are able to be assessed) and includes a new analysis of the AMOC-DSL scaling coefficient in Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations. Section 5 examines observational linkages between AMOC components and coastal sea level, clarifying the specific components of AMOC (e.g., Gulf Stream) invoked, the regional fingerprint of such linkages, and the timescales over which the relationship has been documented. In section 6, we suggest potential origins of along-coast variations, intersimulation differences in scaling relationships, and discrepancies between models and observations; section 7 highlights new research directions that can help assess these discrepancies more extensively and quantitatively.
AMOC and the North Atlantic Ocean Circulation
The U.S. East Coast borders the western boundary of the North Atlantic Ocean, which is characterized by a spatially and temporally complex system of surface and deep currents (Figure 2).
Figure 2: Schematic of key AMOC.related components of the North Atlantic Ocean (modfied from Garcia-Ibanez et al., 2018). Abbreviations are as follows: NRG = Northern Recirculation Gyre; LC = Labrador Current; DWBC = Deep Western Boundary Current; IC = Irminger Current; EGIC = East Greenland.Irminger Current. Three source waters for North Atlantic Deep Water are noted: LSW = Labrador Sea Water; ISOW = Iceland-Scotland Overflow Water; DSOW = Denmark Straits Overßow Water. Box indicates the U.S. East Coast region.
At U.S. East Coast latitudes, the large-scale ocean circulation is dominated by two opposing gyres. At subtropical latitudes, southward wind-driven transport in the interior of the gyre is closed by a western boundary current, composed of the Gulf Stream to the north and the Florida and Antilles currents further south. At subpolar latitudes, the North Atlantic Current (NAC) splits into various branches that flow northwards along the eastern side of the subpolar gyre (Rhein et al., 2011). These currents flow cyclonically around the subpolar gyre, contributing to the upper parts of the western boundary currents comprising the East and West Greenland Currents and the Labrador Current. Part of the NAC also flows into the Nordic Seas (e.g., Dickson & Brown, 1994; Sarafanov et al., 2012). Along these high-latitude branches, warm and salty surface waters originating from the tropical and subtropical Atlantic increase in density and transform into North Atlantic Deep Water through a variety of processes, including cooling, mixing, and convection (Marotzke & Scott, 1999; Spall & Pickart, 2001; Thomas et al., 2015).
In addition to these large-scale flows, there are important currents along the U.S. East Coast continental shelf, shelf break, and slope: flowing northward over the continental shelf south of Cape Hatteras (the South Atlantic Bight) and southward along the shelf between Cape Hatteras and Nova Scotia (Figure 2). These currents are driven by a combination of local wind and buoyancy forcing as well as interactions with the larger-scale flow field (see section 6). In the South Atlantic Bight, interactions between the shelf current and the Gulf Stream are clearly important, but there is evidence of locally wind driven variability closer to the shore (Lee et al., 1991; Stegmann & Yoder, 1996; Yuan et al., 2017). To the north of Cape Hatteras, the Slope Current has its origins in the Labrador Current and the East Greenland Current (Chapman & Beardsley, 1989; Rossby et al., 2014). Its strength is therefore linked to the AMOC, through the strength of the Labrador Current, as well as through interactions with the Northern Recirculation Gyre (Andres et al., 2013; Zhang, 2008), the Deep Western Boundary Current (e.g. Zhang & Vallis, 2007), and the Gulf Stream (Ezer, 2015).


In addition to these large-scale flows, there are important currents along the U.S. East Coast continental shelf, shelf break, and slope: flowing northward over the continental shelf south of Cape Hatteras (the South Atlantic Bight) and southward along the shelf between Cape Hatteras and Nova Scotia (Figure 2). These currents are driven by a combination of local wind and buoyancy forcing as well as interactions with the larger-scale flow field (see section 6). In the South Atlantic Bight, interactions between the shelf current and the Gulf Stream are clearly important, but there is evidence of locally wind driven variability closer to the shore (Lee et al., 1991; Stegmann & Yoder, 1996; Yuan et al., 2017). To the north of Cape Hatteras, the Slope Current has its origins in the Labrador Current and the East Greenland Current (Chapman & Beardsley, 1989; Rossby et al., 2014). Its strength is therefore linked to the AMOC, through the strength of the Labrador Current, as well as through interactions with the Northern Recirculation Gyre (Andres et al., 2013; Zhang, 2008), the Deep Western Boundary Current (e.g. Zhang & Vallis, 2007), and the Gulf Stream (Ezer, 2015).
In aggregate, these horizontal and vertical flows result in an “overturning” circulation that transports over 1 PW of heat poleward (Trenberth & Fasullo, 2017). In this paper, this AMOC is defined as the stream function of the zonally and cumulatively vertically integrated meridional velocity of the Atlantic Ocean north of 35°S (Buckley & Marshall, 2016; Zhang, 2010). In models and observations, the AMOC reveals upper and lower interhemispheric overturning cells of water that are sourced by high-latitude sites of deep water formation in the northern and southern hemispheres respectively (Figure 3).
Figure 3: The AMOC, averaged over the 1959–2012 period, from a 1/12° resolution model simulation as described in Hughes et al. (2018). The flow is clockwise around positive values, and the stream function is calculated by integrating the southward velocity both zonally and upwards from the bottom. The black contour is at zero.
The upper overturning cell reflects northward transport in the upper ocean currents, including those mentioned earlier in this section, compensated by southward flowing North Atlantic Deep Water at intermediate depths. In models, the maximum of the AMOC stream function is typically located around the latitude of the Gulf Stream separation and at approximately 1,000-m depth. Below this upper cell is a lower cell of Antarctic Bottom Water that originates from sources at high southern latitudes (Buckley & Marshall, 2016; Kuhlbrodt et al., 2007). See Buckley and Marshall (2016) and other reviews in this special issue, particularly Bower et al. (2019), for a more comprehensive description of AMOC structure and variability.
A Simple Theoretical Basis for AMOC-DSL Covariability
A diagnostic relationship between the AMOC and DSL can be derived from the zonal momentum equation:
frac{rho}{r cos{phi}} frac{D}{Dt} left(u r cos{phi}right) - rho f v + rho f w cot{phi} = -frac{1}{r cos{phi}} frac{partial p}{partial lambda} + F_x, (1)
where r is the Earth’s radius, u is the zonal velocity, v is the meridional velocity, w is the vertical velocity, f is the Coriolis frequency, phi is latitude, lambda is longitude, p is pressure, rho is density, F_x is the eastward viscous force per unit volume, and D/Dt is the material rate of change. For a derivation and discussion of the equations of motion see, for example, Vallis (2006, Chapter 2) and Gill (1982, Chapter 4). If we (1) zonally integrate over the basin and (2) neglect the advection of relative angular momentum (the first term), the term involving w (usually neglected in the Primitive Equations), and the viscous term (assuming we are below the surface Ekman layer, and that any bottom Ekman layer occupies only a small fraction of the zonal integralÑthis assumes that we are at depths where it is meaningful to consider the ocean to have sidewalls), this reduces to an integrated geostrophic balance:
f T = p_E - p_W, (2)
where T is the northward mass transport across the section (the zonal integral of rho v). Equation (2) relates the northward mass transport to the difference between pressure at the eastern end (p_E) and the western end (p_W) of the section. These pressures are bottom pressures, which become equivalent to DSL (with a scaling of approximately 1 cm/mbar of pressure) as the depth tends to zero at the coast.
This zonally integrated geostrophic balance can be used to derive a simple scaling between the AMOC and DSL at the western boundary. First, we note that the eastern boundary pressure is very close to being a function of depth alone, independent of latitude, at least below a depth of around 100 m (Hughes et al., 2018; Hughes & de Cuevas, 2001). Subtracting off this reference function of depth in our definition of p (which now should be considered to be a pressure anomaly, referenced to the eastern boundary value), we find that p_E = 0. Then, integrating over depth from the surface (z = 0) to the depth of the maximum in the overturning streamfunction (z = -H), we find that the total northward mass transport above this depth is given by
Q = int_{-H}^0{T dz} - frac{1}{f} int_{-H}^0{p_W dz} = -frac{H}{f}overline{p_W}, (3)
where overline{p_W} is the western boundary pressure averaged over the depth range above the maximum overturning. The relationship to coastal sea level then follows from the assumption that the depth-averaged pressure in this zone is related to the boundary pressure near the surface, {p_W}_0, which is in turn related to inverse barometer-corrected boundary sea level h_W by rho_0 g h_W = {p_W}_0, where we use a reference density rho_0. Rewriting in terms of this near.surface western boundary pressure anomaly, we find
Q = -frac{H_e}{f} {p_W}_0 = - frac{H_e}{f} rho_0 g h_W, (4)
requiring the definition of an effective layer thickness
H_e = int_{-H}^0{frac{p_W}{{p_W}_0}dz},  (5)
which may be interpreted as the layer thickness used to multiply the near-surface boundary pressure anomaly (proportional to sea level), in order to get the correct depth-integrated pressure force on the sidewall. If the pressure anomaly (or equivalently the northward transport) is independent of depth above -H, H_e = H. If the zonally integrated flow (or pressure anomaly) is largest at the surface and decreases linearly to zero at the maximum of the overturning, H_e = 0.5 H. Rearranging (5), we find that the coastal sea level signal can be written as
h_W = -frac{Q}{rho_0}frac{f}{g H_e}, (6)
in which it is shown how the coastal sea level signal h_W is negatively related to the strength of the overturning Q/rho_0, and the size of the signal is larger if the effective layer thickness H_e is smaller.
Figure 3 reveals a fairly uniform (or slowly decreasing with increasing depth) northward zonally integrated flow above about 1,000-m depth, balanced by a deeper return flow (with more complicated flows in the top few hundred meters, representing the wind-driven flows superimposed on the large-scale MOC). Assuming f = 10^{-4} s^{-1} (true at a latitude of about 43¡N), equation (6) predicts a sea level change of 1 cm/Sv of meridional transport (less for latitudes closer to the equator, and slightly more for more poleward latitudes). If, rather than constant transport per unit depth above 1,000 m (as in a simple two-layer model), we assume a linear rise from zero at 1,000 m to a maximum at the surface, then pressure at the surface is twice the depth average, leading to a scaling of -2 cm/Sv. Realistic scalings are likely to be between these limits, subject to the assumption of geostrophic balance in equation (2), and the approximation that the vertical profile of the flow remains constant (temporal variations in H_e are proportionally smaller than those in Q). The dependence on f means that this scaling should also lead to smaller sea level signals closer to the equator, again assuming that proportional variations in H_e are smaller than those in f.
Evidence of an AMOC-DSL Relationship in Numerical Models


h_W = -frac{Q}{rho_0}frac{f}{g H_e}, (6)
in which it is shown how the coastal sea level signal h_W is negatively related to the strength of the overturning Q/rho_0, and the size of the signal is larger if the effective layer thickness H_e is smaller.
Figure 3 reveals a fairly uniform (or slowly decreasing with increasing depth) northward zonally integrated flow above about 1,000-m depth, balanced by a deeper return flow (with more complicated flows in the top few hundred meters, representing the wind-driven flows superimposed on the large-scale MOC). Assuming f = 10^{-4} s^{-1} (true at a latitude of about 43¡N), equation (6) predicts a sea level change of 1 cm/Sv of meridional transport (less for latitudes closer to the equator, and slightly more for more poleward latitudes). If, rather than constant transport per unit depth above 1,000 m (as in a simple two-layer model), we assume a linear rise from zero at 1,000 m to a maximum at the surface, then pressure at the surface is twice the depth average, leading to a scaling of -2 cm/Sv. Realistic scalings are likely to be between these limits, subject to the assumption of geostrophic balance in equation (2), and the approximation that the vertical profile of the flow remains constant (temporal variations in H_e are proportionally smaller than those in Q). The dependence on f means that this scaling should also lead to smaller sea level signals closer to the equator, again assuming that proportional variations in H_e are smaller than those in f.
Evidence of an AMOC-DSL Relationship in Numerical Models
Numerical simulations allow analysis of AMOC-DSL relationships that can be compared to the theoretical considerations of the previous section, while incorporating local and large-scale forcing, complex 3-D flows, and ageostrophic processes, to the extent permitted by their resolution. Most analysis of numerical simulations has focused on 21st century, centennial-timescale, AMOC-DSL relationships. In this section, we thus focus on longer timescales, although we contrast these results with selected studies that have examined covariability over shorter timescales, often with a focus on the historical record.
The connection between U.S. East Coast sea level rise and the AMOC in coupled climate models was first established by Levermann et al. (2005) through “hosing” simulations (in which extreme freshwater forcing is applied to the subpolar North Atlantic). They found that, in a climate model with a relatively coarse (3.75° horizontal resolution) ocean, a weakened AMOC is associated with DSL rise in most of the Atlantic basin, with a scaling coefficient of up to −5 cm/Sv. Most subsequent numerical simulations that have assessed this relationship show a more complex spatial pattern of DSL change (e.g., Kienert & Rahmstorf, 2012; Landerer et al., 2007; Lorbacher et al., 2010; Yin et al., 2010), and a smaller (less negative) scaling coefficient (e.g., Bingham & Hughes, 2009; Little et al., 2017; Schleussner et al., 2011). However, the correlation between DSL rise over portions of the U.S. East Coast and a decline in AMOC (and, often, a rise in steric height in the western North Atlantic intergyre region) has been repeatedly noted, in simulations forced by future greenhouse gas emission scenarios, freshwater input into the subpolar North Atlantic, or both (e.g., Hu et al., 2009; Hu et al., 2011; Hu & Bates, 2018; Hu & Deser, 2013; Kienert & Rahmstorf, 2012; Krasting et al., 2016; Landerer et al., 2007; Lorbacher et al., 2010; Pardaens et al., 2011; Yin et al., 2010; Yin & Goddard, 2013).
The AMOC weakens over the 21st century in most CMIP3 and CMIP5 simulations (Church et al., 2013), with a rate that varies widely across emissions scenarios and models (e.g., Figure 4a; Bakker et al., 2016; Cheng et al., 2013; Heuzé, 2017; Huber & Zanna, 2017; Schleussner et al., 2011; Weaver et al., 2012).
Figure 4: (a) Change in maximum AMOC strength for a 28 Coupled Model Intercomparison Project Phase 5 model, RCP4.5-forced, ensemble, from 1976–2000 to 2076–2100, as calculated by Chen et al. (2018). (b) Ensemble mean dynamic sea level change (m) from 1976–2000 to 2076–2100.
The amplitude and spatial pattern of DSL changes associated with 21st century AMOC weakening has been noted in several studies (Schleussner et al., 2011; Yin et al., 2009). However, such studies have generally considered the ensemble mean DSL change (Figure 4b), or a small subset of available models, and have often focused on the Northeast United States only, limiting analysis of intermodel or regional differences.
An assessment of the robustness of the scaling of North Atlantic DSL to AMOC change across climate models is missing in the literature. To fill this gap, we perform a brief analysis using available datasets, including the results of Chen et al. (2018), who investigated the relationship between 21st century changes in DSL and the annual-mean maximum AMOC stream function below 500 m in a large (30-member) CMIP5 ensemble. Models included in this ensemble show an AMOC decline from 1976–2000 to 2076–2100 ranging from approximately zero to 8 Sv (Figure 4a).
In Figure 5, we calculate the AMOC-DSL scaling coefficient for 25 CMIP5 models over this century-long period, at a 1° horizontal resolution.
Figure 5: Map of the ratio of dynamic sea level change to AMOC change (m/Sv; 2076–2100 minus 1976–2000) for 25 RCP4.5-forced Coupled Model Intercomparison Project Phase 5 models with AMOC weakening larger than 2 Sv.
There are broad similarities in the spatial pattern of scaling coefficients and that of the ensemble mean DSL change (Figure 4b), with only a few models showing dramatic differences from the subtropical high/subpolar and coastal low relationship (e.g., MRI-CGCM and FGOALS-g2). However, the amplitude of the scaling coefficient near the U.S. East Coast ranges widely, both north and south of Cape Hatteras, across the ensemble, along with substantial meridional gradients along these coastal regions within individual models.
The diversity of model-specific scaling coefficients along the western boundary can also be shown with a regression of DSL change against AMOC change, that is,
∆DSL(x,y,m) = α(x,y) ∆AMOC(m) + ε(x,y,m) (7)
where x and y are longitude and latitude, m is the model index, α is a local scaling coefficient, and ε is a residual. (Although the RCP 4.5 scenario is shown, spatial patterns of DSL change, and DSL change associated with AMOC change, do not exhibit strong RCP-dependence; Chen et al., 2018; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009).
Local regression coefficients, shown in Figure 6b, indicate a meridional tripole in the North Atlantic; models with more AMOC weakening are associated with larger DSL rise in the subtropical gyre and larger DSL fall in most of the subpolar gyre and the tropics. This pattern bears some similarity to the dominant mode of sea surface height variability over the historical record (e.g., Hakkinen & Rhines, 2004; Yin & Goddard, 2013), the multimodel mean 21st century change observed in CMIP simulations (Figure 4b; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009, 2010), and a regression of DSL on AMOC strength in a model simulation of the historical period (Figure 6a). Coastal regression coefficients range from approximately −1.5 to 0 cm/Sv, with more negative values in U.S. East Coast regions north of Cape Hatteras.


There are broad similarities in the spatial pattern of scaling coefficients and that of the ensemble mean DSL change (Figure 4b), with only a few models showing dramatic differences from the subtropical high/subpolar and coastal low relationship (e.g., MRI-CGCM and FGOALS-g2). However, the amplitude of the scaling coefficient near the U.S. East Coast ranges widely, both north and south of Cape Hatteras, across the ensemble, along with substantial meridional gradients along these coastal regions within individual models.
The diversity of model-specific scaling coefficients along the western boundary can also be shown with a regression of DSL change against AMOC change, that is,
∆DSL(x,y,m) = α(x,y) ∆AMOC(m) + ε(x,y,m) (7)
where x and y are longitude and latitude, m is the model index, α is a local scaling coefficient, and ε is a residual. (Although the RCP 4.5 scenario is shown, spatial patterns of DSL change, and DSL change associated with AMOC change, do not exhibit strong RCP-dependence; Chen et al., 2018; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009).
Local regression coefficients, shown in Figure 6b, indicate a meridional tripole in the North Atlantic; models with more AMOC weakening are associated with larger DSL rise in the subtropical gyre and larger DSL fall in most of the subpolar gyre and the tropics. This pattern bears some similarity to the dominant mode of sea surface height variability over the historical record (e.g., Hakkinen & Rhines, 2004; Yin & Goddard, 2013), the multimodel mean 21st century change observed in CMIP simulations (Figure 4b; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Yin, 2012; Yin et al., 2009, 2010), and a regression of DSL on AMOC strength in a model simulation of the historical period (Figure 6a). Coastal regression coefficients range from approximately −1.5 to 0 cm/Sv, with more negative values in U.S. East Coast regions north of Cape Hatteras.
Figure 6: (a) From Woodworth et al. (2014). Regression coefficients of annual mean sea level and overturning transport (at the same latitude) for depths between 100 and 1,300 m using a 1° ocean model, for the period 1950–2009, without wind forcing. (b) Linear regression coefficient (α) of DSL change against the change in maximum AMOC strength for the models shown in Figure 5 (m/Sv). (c) Variance in DSL change explained by AMOC change (%). DSL = dynamic sea level; AMOC = Atlantic Meridional Overturning Circulation.
However, regression coefficients in Figure 6b diverge from those obtained through a regression of annual mean DSL on AMOC over the 1950–2009 period (Figure 6a) and those predicted by equation 6, particularly along the western boundary, where the CMIP5-derived pattern does not show a universal anticorrelation of sea level and the AMOC. (We note that the single-valued AMOC index used in Figure 6b is different than the meridionally varying index used in Figure 6a. However, we would not expect this to affect the sign of regression coefficients, if AMOC transport changes are meridionally coherent). Perhaps more important than the spatial pattern in Figure 6b is the fact that only a small fraction of intermodel DSL variance is explained by differences in AMOC strength change (Figure 6c). In coastal regions, and in the subpolar gyre, factors unrelated to AMOC strength are principally responsible for the wide spread in 21st century projections of U.S. East Coast DSL rise (Yin et al., 2009, 2010; Kopp et al., 2014; Little, Horton, Kopp, Oppenheimer, & Yip, 2015; Minobe, 2017).
It is possible that differences between Figures 6a and 6b originate in a timescale-dependent relationship. This was suggested by Yin and Goddard (2013, their Figure 3) based on (1) similarities between the DSL patterns of observed decadal trends and 21st century model trends; (2) similarities between observed and modeled Empirical Orthogonal Function (EOF) patterns (describing interannual variability); and (3) differences between DSL patterns associated with long-term trends and interannual variability. Similar conclusions were drawn by Lorbacher et al. (2010). Model-derived scaling coefficients for interannual AMOC-DSL relationships north of Cape Hatteras appear to be more consistent than those in Figure 5, and more consistent with the theoretical values in section 2. For example, Bingham and Hughes (2009) find a scaling of -1.7 cm Sv−1, Woodworth et al. (2014) find -1.5 cm Sv−1, and Little et al. (2017) obtain −1.8 cm/Sv. However, the wide spread in scaling coefficients across models under identical forcing (Figure 5) suggests that differences in model representation are critical over longer timescales. Although an analysis of these regional and inter-model differences is beyond the scope of this review, we highlight its importance and discuss possible explanations in sections 6 and 7.
Evidence of an AMOC-DSL Relationship in Observations
The first direct, continuous, basin-wide, observations of the AMOC began in 2004 with the RAPID project (Rapid Climate Change; Cunningham et al., 2007). This record is now complemented by two other basin-wide in situ programs: NOAC at 47°N (North Atlantic Changes; Mertens et al., 2014) and OSNAP, around 60°N (Overturning in the Sub-polar North Atlantic; Lozier et al., 2017). Although RAPID observations have revealed a wealth of information, they provide only a 13-year time series at 26°N at time of writing. This limited record hinders an observation-based assessment of AMOC-DSL relationships, especially over the decadal and longer timescales of primary interest here. Over shorter timescales, Ezer (2015) compared monthly RAPID observations to the Atlantic City-Bermuda tide gauge sea level difference, finding a correlation of 0.27. In the same analysis, Ezer noted substantial differences in correlations, and lag/lead relationships, between the sea level difference and the three individual components of AMOC observed by RAPID (Ekman, Florida Current, and Mid-Ocean transport). Piecuch et al. (2019) also note differing relationships between each of these AMOC components and New England coastal sea level, with only the Ekman component exhibiting strong coherence.
In addition to the RAPID record, longer observations of elements of the North Atlantic circulation are available: for example, the Florida Current time series since 1982 (Meinen et al., 2010), the Oleander time series of Gulf Stream transport since 1992 (Rossby et al., 2014), and the position of the Gulf Stream Extension since 1955 (Joyce & Zhang, 2010). Studies based on models (e.g. Saba et al., 2016; Sanchez-Franks & Zhang, 2015) and observations (e.g., Kopp, 2013; McCarthy et al., 2015; Park & Sweet, 2015) have shown strong statistical relationships between US east coast sea level and these metrics at up to multidecadal timescales. We consider evidence in this section for relationships between DSL and these and other elements of the North Atlantic circulation, while emphasizing that changes in the latter do not necessarily imply changes in AMOC, as defined in section 2. We briefly discuss the nature of potential linkages with AMOC in section 6.3.
Linkages Between DSL and AMOC Components
The relationship between coastal DSL and the Gulf Stream has been assessed using theory, observations, and models. Studies have considered the roles of Gulf Stream transport, velocity, and position, both upstream and downstream of the detachment at Cape Hatteras, as well as the strength of the Florida Current.
Early studies focused on the relationship between tide gauge observations and the Gulf Stream over seasonal timescales between Florida and Cape Hatteras. Two linkages between ocean circulation and DSL were considered: the cross-stream (shelf) sea level gradient, related to ocean circulation via geostrophy, and the downstream (along-coast) sea level gradient, related via the Bernoulli principle. Montgomery (1941) found little evidence for a relationship of the downstream sea level gradient to velocity (in the Gulf Stream).


In addition to the RAPID record, longer observations of elements of the North Atlantic circulation are available: for example, the Florida Current time series since 1982 (Meinen et al., 2010), the Oleander time series of Gulf Stream transport since 1992 (Rossby et al., 2014), and the position of the Gulf Stream Extension since 1955 (Joyce & Zhang, 2010). Studies based on models (e.g. Saba et al., 2016; Sanchez-Franks & Zhang, 2015) and observations (e.g., Kopp, 2013; McCarthy et al., 2015; Park & Sweet, 2015) have shown strong statistical relationships between US east coast sea level and these metrics at up to multidecadal timescales. We consider evidence in this section for relationships between DSL and these and other elements of the North Atlantic circulation, while emphasizing that changes in the latter do not necessarily imply changes in AMOC, as defined in section 2. We briefly discuss the nature of potential linkages with AMOC in section 6.3.
Linkages Between DSL and AMOC Components
The relationship between coastal DSL and the Gulf Stream has been assessed using theory, observations, and models. Studies have considered the roles of Gulf Stream transport, velocity, and position, both upstream and downstream of the detachment at Cape Hatteras, as well as the strength of the Florida Current.
Early studies focused on the relationship between tide gauge observations and the Gulf Stream over seasonal timescales between Florida and Cape Hatteras. Two linkages between ocean circulation and DSL were considered: the cross-stream (shelf) sea level gradient, related to ocean circulation via geostrophy, and the downstream (along-coast) sea level gradient, related via the Bernoulli principle. Montgomery (1941) found little evidence for a relationship of the downstream sea level gradient to velocity (in the Gulf Stream).
Attempts to relate the cross-stream gradient to Gulf Stream fluctuations were more successful. By examining tide gauges along the Florida coastline, and between Charleston and Bermuda, Montgomery (1938) concluded that fluctuations in Gulf Stream strength could be seen in cross-stream sea level measurements. The study of Iselin (1940) supported the utility of tide gauges south of Cape Hatteras (Key West to Charleston) for estimating the Gulf Stream strength. Both studies were based on comparison with shipboard hydrography and related a summer-to-fall increase in sea level to a drop in Gulf Stream transport. Hela (1951) revisited the two earlier studies to relate the annual cycle of sea level difference from Miami to Cat Cay, Bahamas to transport estimates of the Gulf Stream from ship drift (Fuglister, 1948), finding a high correlation (r = 0.95) between the zonal sea level gradient and meridional transport in the Gulf Stream. Blaha (1984) removed local effects of the inverse barometer, seasonal steric effects, river runoff, and local wind stress, to demonstrate that the residual sea level variability had a robust correlation with Gulf Stream transport on seasonal timescales. More recently, Park and Sweet (2015) found an interannual- to decadal-timescale relationship between Florida Current transport and tide gauge observations at three locations in Florida using empirical mode decomposition, with a scaling coefficient determined to be consistent with geostrophic balance.
Similar techniques have been used to examine links between Gulf Stream transport variability and sea level in the Mid-Atlantic Bight. Ezer (2013) found a longer-period relationship between Mid-Atlantic Bight DSL and the sea surface gradient across the detached Gulf Stream. The offshore DSL gradient was found to be correlated with sea level at individual tide gauge locations over decadal timescales, as suggested by Yin and Goddard (2013). However, the robustness of these longer period relationships, found using statistical techniques including empirical mode decomposition, has been questioned (Chambers, 2015). Model-based support for observed Florida Current and Gulf Stream correlations is stronger on short timescales: for example, while idealized modeling studies show that an oscillatory transport of Gulf Stream is associated with coherent coastal sea level variations along the southeast U.S. coast (Ezer, 2016), Woodworth et al. (2017) do not see evidence of Florida Current transport variations in annual mean sea level, either averaged south of Cape Hatteras or in the difference of sea level averaged over the coastline north and south of Cape Hatteras.
Coastal sea level has also been related to the position of the Gulf Stream on leaving the coast at Cape Hatteras, known as the Gulf Stream North Wall (GSNW; Fuglister, 1955). Indices of the GSNW based on sea surface temperature exist since 1966 (Taylor & Stephens, 1980) and based on temperature at 200 m since 1955 (Joyce & Zhang, 2010). The GSNW has been shown to exhibit quasi-decadal fluctuations that are similar to those in sea level data along the U.S. East Coast (McCarthy et al., 2019; Nigam et al., 2018). Kopp (2013) found a significant antiphase relationship between the GSNW index and DSL north of Cape Hatteras and a likely in-phase relationship between GSNW and DSL south of Cape Hatteras. McCarthy et al. (2015) noted the difference of sea level south and north of Cape Hatteras projected onto the surface velocity of the GSNW. Whether these sea level variations reflect AMOC strength changes relies upon an understanding of the interaction of different AMOC components: Early explanations associated an AMOC strengthening with a northward shift in the GSNW (e.g., Eden & Jung, 2001). However, recent literature indicates the inverse; AMOC strengthening drives a southward shift in the GSNW due to coupling between the Gulf Stream, Deep Western Boundary Current, and topography (Joyce & Zhang, 2010; Sanchez-Franks & Zhang, 2015; Yeager, 2015; Zhang & Vallis, 2007).
AMOC variability may also be related to heat content and density variations in the subtropical and subpolar gyres (Williams et al., 2014). Such changes in gyre properties have been found to be correlated with U.S. East Coast sea level changes (Thompson & Mitchum, 2014). Frederikse et al. (2017) find that, after being adjusted for local atmospheric (wind and pressure) effects and smoothed on decadal timescales, sea level changes from tide gauges north of Cape Hatteras over 1965–2014 are correlated with upper-ocean steric height changes in the Labrador Sea and the deep midlatitude North Atlantic intergyre region. This is consistent with the strong relationship between U.S. coastal sea level and Labrador Sea level in the CMIP5 ensemble (Minobe et al., 2017).
Other studies have considered property differences between gyres, in particular the meridional density gradient, as an indicator of AMOC strength (Butler et al., 2015; De Boer et al., 2010; Kienert & Rahmstorf, 2012; Rahmstorf, 1996; Rahmstorf et al., 2015; Sijp et al., 2012; Thorpe et al., 2001). The meridional density gradient can be related to the gyre-scale sea level gradient, which has been shown to be related to the strength of the AMOC over sufficiently long timescales (multidecadal and longer; Butler et al., 2015). This relationship was investigated by McCarthy et al. (2015), who used differences in DSL north and south of Cape Hatteras as an estimate of the meridional density gradient between the subtropical and subpolar gyres. The meridional gradient projected strongly onto the circulation in the intergyre region and changes in the subpolar heat content on interannual to decadal timescales. Output from a NEMO 0.25° simulation related the differences in DSL north and south of the modeled Gulf Stream separation to the meridional heat transport at 40°N, indicating a relationship to AMOC.
Possible Sources of Regional, Intermodel, and Model-Observational Discrepancies
The diagnostic geostrophic relationship between AMOC transport and U.S. East Coast sea level derived in section 3 implies a scaling coefficient of order −1 to −2 cm/Sv with little alongshore variation. Although some numerical simulations find coefficients within this range over portions of the U.S. East Coast, a uniform along-coast scaling of AMOC strength and DSL is not evident (section 4). These deviations from theory likely result from neglect of terms in the more complete zonal momentum balance (e.g., friction, nonlinearities, time dependence), or a breakdown in the assumption that U.S. East Coast sea level is related to the depth-averaged boundary pressure via a constant effective layer thickness (He in equation 6). Similarly, intermodel differences under identical forcing must originate in the relative magnitude of neglected dynamical terms, and their treatment in models. Observations of other components of the North Atlantic circulation offer general support for antiphase relationships between large-scale meridional transport and DSL along portions of the U.S. east coast but are constrained by their limited record length and indirect relationship with AMOC (section 5).


Possible Sources of Regional, Intermodel, and Model-Observational Discrepancies
The diagnostic geostrophic relationship between AMOC transport and U.S. East Coast sea level derived in section 3 implies a scaling coefficient of order −1 to −2 cm/Sv with little alongshore variation. Although some numerical simulations find coefficients within this range over portions of the U.S. East Coast, a uniform along-coast scaling of AMOC strength and DSL is not evident (section 4). These deviations from theory likely result from neglect of terms in the more complete zonal momentum balance (e.g., friction, nonlinearities, time dependence), or a breakdown in the assumption that U.S. East Coast sea level is related to the depth-averaged boundary pressure via a constant effective layer thickness (He in equation 6). Similarly, intermodel differences under identical forcing must originate in the relative magnitude of neglected dynamical terms, and their treatment in models. Observations of other components of the North Atlantic circulation offer general support for antiphase relationships between large-scale meridional transport and DSL along portions of the U.S. east coast but are constrained by their limited record length and indirect relationship with AMOC (section 5).
In this section, we highlight findings from three areas of research that can at least partially account for these regional, intermodel, and model-observational discrepancies via: (1) friction and bathymetry at the coast, (2) local forcing, and (3) temporal and spatial incoherence of AMOC and its components. In section 7, we suggest opportunities to better integrate these findings into the sea level literature.
Friction and Topographic Influence on Coastal Sea Level
Most analyses noted in sections 4 and 5 interpret AMOC-DSL relationships based on geostrophy. To understand offshore influences on coastal sea level, however, requires addressing ageostrophic flows and forcing on the slope and shelf, where water column thickness goes to zero and friction is important.
Recently, Minobe et al. (2017) have addressed coastal DSL onshore of a western boundary current using a reduced gravity, vertical sidewall model. Such a framework bears similarity to that used in other studies of remotely forced coastal sea level variability in western boundary regions (e.g., Hong et al., 2000; Thompson & Mitchum, 2014). In this model, interior DSL gradients are moderated by friction within a coastal boundary layer. Their main result can be written as
frac{h_W}{f} = (frac{h_W}{f})_0 + int_y^{y_0} frac{beta h_I}{f^2} dy’
where h_W and h_I are sea level as a function of latitude (y) at the western boundary and in the ocean interior respectively (h_I is taken near the boundary, but to the east of any western boundary current.) The integral is from the y value of interest to a reference point y_0 further north, where frac{h_W}{f} = (frac{h_W}{f})_0. The western boundary sea level is determined from a combination of the interior ocean sea level and the sea level from higher latitudes; coastal sea level anomalies are smaller than those in the interior and shifted toward the equator for reasons which become clearer if the vertical sidewall case is seen as a limiting case of a sloping continental shelf and slope.
The southward shift and weakening of the “interior” sea level signal as it approaches the coast is reminiscent of the linear, barotropic case with a sloping sidewall as explored by Becker and Salmon (1997) following the ideas of Welander (1968). Instead of being controlled by contours of constant f, as in the flat-bottom case, the flow is controlled by contours of constant f/H, where H is the ocean depth. With varying bathymetry, the subpolar gyre intrudes between the coast and the extension of the subtropical gyre, resulting in a reversing pattern of currents along the continental slope, rather than a simple single-signed western boundary current. Similar behavior is found in highly nonlinear and baroclinic cases with a sloping sidewall (e.g., Jackson et al., 2006, their Figure 1). Sea level signals from the interior therefore appear further equatorward at the coast.
Wise et al. (2018) assess the influence of continental shelf bathymetry, using linear dynamics and ocean bottom pressure as the central variable (equivalent to sea level in a single layer case). In this formalism, sea level is “advected” along contours of gH/f (such contours can be thought of as representing the stream function of a fictitious flow carrying the sea level signal toward the coast at a speed which becomes the long Rossby wave speed over a flat bottom). The “advection” is toward the west and then toward the equator along the slope, in competition with a “diffusion” by bottom friction (Figure 7).
Figure 7: From Wise et al. (2018). Sea level contours (nondimensional; dashed negative) for a given idealized coastal bathymetry along the western boundary of an ocean basin, where x and y are the nondimensional across-shore and alongshore coordinates, respectively. Vertical dotted lines indicate the continental shelf break at x = S and continental slope floor at x = 1. Panels show sea level patterns for different Péclet numbers: (a) Pa = 0.1, (b) Pa = 0.1, (c) Pa = 10, and (d) Pa = 200. Panels (b)–(d) show only the coastal region.
As the coast is approached, the geostrophic shoreward flow becomes balanced by an offshore flow in the bottom Ekman layer, as in Csanady (1978). Friction is required for alongshore sea level gradients to exist without a flow through the coast, as a purely geostrophic balance would imply.
When shelf bathymetry is included, coastal sea level is still determined by the combination of a poleward reference value, and a weighted integral of interior sea level between that poleward latitude and the latitude of interest. However, the coastal sea level anomaly can be smaller than that predicted in the Minobe et al. (2017) configuration: the western pressure signal can all be on the continental slope, with shallower currents causing it to be cancelled out at the coast. Wise et al. (2018) find that coastal DSL depends crucially on the strength of the bottom friction and the shelf bathymetry. The major dependence is on a nondimensional number, the analogue Péclet number Pa = βHL/r, where H is the offshore layer thickness, L is the width of the topography, and r is a linear bottom friction coefficient (Figure 7). As friction weakens, the coastal signal shifts further south and becomes weaker compared to the interior sea level.
Equation 8 is a limiting case for a vertical sidewall, in which the solution becomes independent of the strength or form of the friction. In this linear case, the vertical sidewall limit is found to produce the largest coastal signal, for a given upper layer thickness. The mechanism here can be considered to be a breakdown of the assumption that there exists a meaningful effective layer thickness He. Counterpropagating currents over topography mean the boundary pressure pW can change sign over the upper continental slope, so equation 5 shows that He can become larger than H. Thus, the coastal sea level can be smaller than that implied by the depth-averaged pressure divided by a meaningful effective layer depth. This reduction of the coastal signal can be interpreted as the result of the influence of coastal trapped waves, which carry the interior signal equatorward along the western boundary, as seen for periods of a few days in the model simulations of Ezer (2016). See Hughes et al. (2019) for more detail on the smoothing and “advective” effect of coastal trapped waves on boundary sea level.
We should note, though, that although friction plays a crucial role in communicating sea level changes to the coast, it does so in a manner which does not affect the zonal momentum balance (equation 1), which remains geostrophic.
Locally (Shelf-) Forced Sea Level Variability
The presence of locally forced sea level variability along the shelf may interfere with the simple AMOC-DSL scaling. Similar to section 6.1, ageostrophic dynamics are relevant, although in this case they may also upset the zonal momentum balance.
Local meteorological and terrestrial forcing mechanisms, namely, winds, barometric pressure, and river runoff, have long been shown to drive U.S. East Coast sea level variability. Part of this variability can be static in nature, as with the case of inverted barometer effects related to atmospheric pressure, which are found to contribute sizably to variability at many tide gauges (Piecuch & Ponte, 2015; Ponte, 2006). By definition, static signals are not directly related to circulation changes. As such, their separate treatment, and removal if possible, is useful when assessing the relation between tide gauge and AMOC variability.


Equation 8 is a limiting case for a vertical sidewall, in which the solution becomes independent of the strength or form of the friction. In this linear case, the vertical sidewall limit is found to produce the largest coastal signal, for a given upper layer thickness. The mechanism here can be considered to be a breakdown of the assumption that there exists a meaningful effective layer thickness He. Counterpropagating currents over topography mean the boundary pressure pW can change sign over the upper continental slope, so equation 5 shows that He can become larger than H. Thus, the coastal sea level can be smaller than that implied by the depth-averaged pressure divided by a meaningful effective layer depth. This reduction of the coastal signal can be interpreted as the result of the influence of coastal trapped waves, which carry the interior signal equatorward along the western boundary, as seen for periods of a few days in the model simulations of Ezer (2016). See Hughes et al. (2019) for more detail on the smoothing and “advective” effect of coastal trapped waves on boundary sea level.
We should note, though, that although friction plays a crucial role in communicating sea level changes to the coast, it does so in a manner which does not affect the zonal momentum balance (equation 1), which remains geostrophic.
Locally (Shelf-) Forced Sea Level Variability
The presence of locally forced sea level variability along the shelf may interfere with the simple AMOC-DSL scaling. Similar to section 6.1, ageostrophic dynamics are relevant, although in this case they may also upset the zonal momentum balance.
Local meteorological and terrestrial forcing mechanisms, namely, winds, barometric pressure, and river runoff, have long been shown to drive U.S. East Coast sea level variability. Part of this variability can be static in nature, as with the case of inverted barometer effects related to atmospheric pressure, which are found to contribute sizably to variability at many tide gauges (Piecuch & Ponte, 2015; Ponte, 2006). By definition, static signals are not directly related to circulation changes. As such, their separate treatment, and removal if possible, is useful when assessing the relation between tide gauge and AMOC variability.
Effects of local winds have been extensively examined in the observational studies of Blaha (1984), Andres et al. (2013), Domingues et al. (2018), and others. Simple regression analyses suggest an important contribution of local winds, particularly the alongshore component, to observed tide gauge variability at interannual to decadal timescales. Setup from onshore winds can also contribute to static variability at the coast (e.g., Thompson, 1986), but separate estimation of these effects has not been examined in detail. Recent studies (Domingues et al., 2018; Li et al., 2014; Little et al., 2017; Piecuch et al., 2016; Woodworth et al., 2014) reinforce the importance of near-coastal winds and barotropic dynamics to explain US east coast tide gauge records over interannual to decadal timescales.
Much less studied has been the effect of river runoff. Meade and Emery (1971) found that about 20–29% of variations in detrended annual mean sea level in U.S. East Coast tide gauges could be accounted for by changes in riverine input. Their results are consistent with the analysis by Piecuch, Bittermann, et al. (2018), who relate sea level signals to the buoyancy-driven geostrophic coastal currents associated with the runoff. Other studies focusing on different river systems and utilizing different data sets have concluded that riverine input is negligible. For example, Hong et al. (2000) found contributions from runoff to be unimportant relative to winds for tide gauges south of 38°N (see also Blaha, 1984). Calafat et al. (2018) did not find a relationship between river runoff and decadal modulations in the amplitude of the sea level annual cycle along the South Atlantic Bight. However, beyond the few studies noted here, most US east coast sea level studies have ignored riverine effects.
Regardless of its origin, the presence of local forcing can lead to large sea level variations that mask the open ocean influence, and thus the emergence of AMOC-associated sea level variability relative to locally forced variability. For example, correlations of DSL and AMOC are weaker in simulations that include wind forcing, particularly close to the coast and along the Northeast U.S. shelf (Figure 8).
Figure 8: From Woodworth et al. (2014). (a) Correlations of detrended values of annual mean sea level and overturning transport at the same latitude for depths between 100 and 1,300 m using the simulations shown in Figure 6a (without wind forcing). (b) As in Figure 8a, with winds.
The fact that atmospheric variability has an almost white spectrum means that locally forced variability will tend to be the dominant influence at higher frequencies, with emergence of the open ocean influence at lower frequencies. Little et al. (2017) conclude, using a climate model ensemble, that coherence with AMOC emerges along the northeast U.S. coast at periods of around 20 years. This conclusion echoes Woodworth et al. (2014), who find that local winds dominate nearshore sea level variability on interannual timescales.
We note, however, that local forcing may evolve over longer timescales and may be responsible for some of the model spread seen in Figure 5. For example, Woodworth et al. (2017) suggest that changes in the 20th century wind field may underlie long-period changes in coastal sea level. Furthermore, atmospheric forcing is spatially coherent over very large scales; changes in local forcing may be associated with large-scale patterns of change that also influence AMOC and/or remote regions of the ocean.
Spatiotemporal Complexity of AMOC, Hydrography, and Current Changes
The fact that AMOC is the residual of a spatially and temporally complex system of surface and deep currents (Figure 2; see other reviews in this volume) underscores the relevance of the previous two sections for interpretations of observations: any current used as a proxy for AMOC (e.g., the Florida Current) may be characterized by an ageostrophic momentum balance (e.g., due to inertial terms in western boundary currents, or frictional effects in coastal currents). In fact, it is likely that ageostrophic terms become more important at these smaller scales.
An additional important consideration is that currents may be zonally or meridionally compensated, either over shorter timescales, or in the steady state. Observations and modeling studies reveal that changes in AMOC can arise from changes in any of its components, including the interior subtropical gyre (Duchez et al., 2014; Smeed et al., 2018; Zhao & Johns, 2014) and subpolar gyre (Kwon & Frankignoul, 2014; Yeager, 2015), western boundary currents (Beadling et al., 2018; Thomas et al., 2012), and the formation of deep water at high latitude (Medhaug et al., 2011). Additional changes and variability also arise through near-surface Ekman transports (Kanzow et al., 2007), their barotropic compensation (Jayne & Marotzke, 2001), and eddy transports (e.g., Thomas & Zhai, 2013). All of these exhibit varying degrees of zonal and meridional coherence, reflecting a multitude of forcings occurring over different timescales (Wunsch & Heimbach, 2013).
For example, the Gulf Stream, by which we refer to the full western boundary current near southern Florida, has two branches: the Florida Current and the Antilles Current, which flows offshore of the Bahama Banks (Figure 2). While the Florida Current carries a larger mean transport (about 32 Sv compared with about 5 Sv in the Antilles Current), both exhibit comparable variability (Lee et al., 1996). Thus, the total western boundary current flow could be constant, but its effect on coastal DSL would vary depending upon the respective contributions of the Florida and Antilles currents. In addition, assessing trends in the volume transport of complex, evolving, western boundary currents is challenging. This difficulty underlies the debate surrounding Ezer et al.’s (2013) conclusion that a Gulf Stream decline was responsible for accelerated sea level rise in the mid-Atlantic Bight (Ezer, 2015; Rossby et al., 2014). The deviation in Gulf Stream transport calculations found across studies is perhaps not surprising, given longitudinally varying changes in the Gulf Stream velocity, width, and position (Dong et al., 2019), and the presence of Gulf Stream meanders, eddies, and recirculation gyres.