The OHC change due all three convergences of temperature in (8), Δh, is
Δℎ=Δ𝑇𝑐𝑝0𝜌0Δ𝑧, (9)
where ∆T, is the difference of the model’s temperature field (T) between the final decades of FAF-heat and FAF-passiveheat (9). In FAF-heat, the heat flux changes the transport processes (Φ′ ≠ 0) and the temperature (𝑇′ ≠ 0) and, thus there is a change in heat content due to all three types of temperature convergence.
The OHC change due to passive uptake of additional heat, Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)] is
Δℎ[Φ⎯⎯⎯⎯⎯(𝑇′)]=𝑇⎯⎯⎯⎯𝑎𝑐𝑝0𝜌0Δ𝑧, (10)
where the notation Δℎ[…] symbolically represents the change in OHC due to the convergence of temperature enclosed by the square brackets. Since passive temperature is initially 0, its decadal mean change by the end of simulation is simply 𝑇−𝑎, the time mean Ta from FAF-passiveheat for the years 61–70.
The OHC change due to the redistribution of unperturbed temperature, Δℎ[Φ′(𝑇⎯⎯⎯⎯)] is
Δℎ[Φ′(𝑇⎯⎯⎯⎯)]=Δ𝑇𝑟𝑐𝑝0𝜌0Δ𝑧, (11)
where ∆Tr is the difference between FAF-heat redistributed temperature, Tr, and FAF-passiveheat T, averaged over the final decade.
The OHC change due to the perturbation in the transport redistributing the added heat, Δℎ[Φ′(𝑇′)] is
Δℎ[Φ′(𝑇′)]=Δ𝑇𝑎𝑐𝑝0𝜌0Δ𝑧, (12)
where Δ𝑇𝑎 is the difference of Ta between FAF-heat and FAF-passiveheat (12).
Models analysed
Different suites of models are analysed in different parts of this work, subject to the availability of output fields. The first analysis required sea-surface height above geoid, ζ, ocean temperature, and seawater salinity, available from 13 FAFMIP AOGCMs (Table 1), although less than the full set of output for all experiments was available for CESM2, GISS-E2-R-CC and MIROC6. The ocean heat budget decomposition in Sect. 3.5 required 3-D fields of redistributed and added temperature, available for ten FAFMIP models (the exceptions being CESM2, GISS-E2-R-CC and MIROC6). A comparison of the sea-level response to 1pctCO2 forcing was also performed for a suite of 19 CMIP5 models and 16 CMIP6 models listed in Table 2. The ‘zos’ fields of MIROC5, CAMS-CSM1-0 and GISS-E2-1-G required correction for the inverse barometer effect due to sea ice loading, following (Griffies et al. 2016).
Table 2: List of models from CMIP5 and CMIP6 that appear in Fig. 4
From the 13 models that have performed FAFMIP experiments, five are from the CMIP5 era, seven from CMIP6, and one (HadCM3) is pre-CMIP5. All ocean model components of models feature similar horizontal resolution (roughly 1-by-1 degree of latitude), and so unresolved features such as mesoscale eddies are parameterized. Even the finest of these ocean grids (MPI-ESM1-2-HR, about 0.4-by-0.4 degrees of latitude) is ‘eddy-permitting’ and not ‘eddy-resolving’, as it can resolve some large ocean eddies, but it still employs an eddy flux parameterization to represent unresolved mesoscale and sub-mesoscale processes. While horizontal resolution is broadly similar across models, details such as the vertical grids or refined resolution near the equator are model-specific.
Results
FAF-all versus 1pctCO2
This section explores the diversity in Δζ in FAF-all versus 1pctCO2, to demonstrate the extent to which patterns of Δζ are generated by ocean processes rather than by the patterns and magnitude of all fluxes.
The spatial pattern of the sea-level response to all flux perturbations applied simultaneously (FAF-all, Fig. 3a) is similar to the pattern that results from 1pctCO2 forcing (Fig. 3c). The agreement between responses to 1pctCO2 and FAF-all forcing is an intended feature of the experimental design and shows that the mean pattern of CO2-forced sea-level change can be reproduced when the models are forced instead with perturbations to their surface fluxes. The spatial standard deviation of ∆ζ is a useful scalar that summarizes the magnitude (or heterogeneity) of the spatial pattern of dynamic sea-level change. The spatial standard deviation of ∆ζ is 0.082 m for FAF-all; larger than 0.059 m for 1pctCO2, indicating a stronger spatial pattern in FAF-all.
Fig. 3: Ocean dynamic sea-level response Δζ to greenhouse gas forcing in 1pctCO2 runs (above) and FAF-all runs (below) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Mean across models (above) and standard deviation across models (below)
The three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive Δζ north of 55° S and negative Δζ at higher latitudes, (2) the meridional dipole of positive Δζ in the northern North Atlantic against weakly negative Δζ in the southern North Atlantic, and (3) positive Δζ in the Arctic.
The large positive Δζ in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the “North Atlantic redistribution feedback”, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore “sees” a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.


The three prominent features of regional sea-level change identified in previous work (Church et al. 2013; Slangen et al. 2014; Gregory et al. 2016) are apparent here: (1) the Southern Ocean meridional gradient with positive Δζ north of 55° S and negative Δζ at higher latitudes, (2) the meridional dipole of positive Δζ in the northern North Atlantic against weakly negative Δζ in the southern North Atlantic, and (3) positive Δζ in the Arctic.
The large positive Δζ in the North Atlantic is greater in magnitude in FAF-all than 1pctCO2. This is due to the “North Atlantic redistribution feedback”, wherein the heat flux perturbation (which is strongly positive in the North Atlantic) causes the AMOC to decline (Winton et al. 2013; Gregory et al. 2016). The weakening of the AMOC reduces the northward heat transport, thus redistributing the OHC, leading to cooler SST at high latitudes, and reinforcing ocean heat uptake there (by reducing the heat loss from the ocean to the atmosphere). This occurs because the atmosphere is coupled to the redistributed temperature, Tr, and therefore “sees” a cooling in the North Atlantic due to redistribution, but does not respond to the added heat, which it cannot see. Because of this feedback, the heat input into the North Atlantic is about double what it would be in a 1pctCO2 simulation. By comparing FAF-heat experiments with two corresponding pairs of an AOGCM and an OGCM, Todd et al. (2020) find, however, that the AMOC weakening is greater by only about 10% in the AOGCM case due to the feedback. Their finding is consistent with our results, where the total OHC change in FAF-heat is about 10% greater (due to the redistribution feedback) than the time- and area-integral of the imposed perturbation. The feedback is a complicating feature of the simulation design, but does not diminish the utility of the experiments, because the imposed heat flux perturbation is the same for all models. The degree of AMOC weakening (and ocean heat transport change) shown by each model reflects the sensitivity of each model to common forcing, regardless of whether it resulted directly from the forcing or through the redistribution feedback.
When the different AOGCMs are forced with identical surface flux perturbations in FAF-all, the spread in sea-level response (Fig. 3d) is similar to the spread that results from 1pctCO2 forcing (Fig. 3b). The largest spread of sea-level change among the 11 models (measured as the standard deviation across models) is focused on the same three regions in FAF-all as in 1pctCO2—the Arctic, the Southern Ocean, and the North Atlantic—and is of similar magnitude. The area mean of inter-model standard deviation is 0.045 m in 1pctCO2, and 0.046 m in FAF-all. This evidence indicates that much of the spread in projections of the dynamic sea-level response to climate forcing arises due to differences in ocean model formulation, rather than in the surface flux forcing from the diverse atmosphere models. This conclusion is different from that of Huber and Zanna (2017), who found that the parametric uncertainty of a given model is too small to explain the spread of ocean responses to climate change. The dynamic sea-level responses of the individual AOGCMs to FAF-all forcing are included in the “Appendix” (Fig. 13 in “Appendix”).
Sea-level response to 1% per year CO2 forcing in CMIP5 and CMIP6
There is strong similarity between the sea-level responses to 1pctCO2 forcing from the much larger CMIP5/6 ensembles (Fig. 4a, c) and the sea-level responses to our smaller suite of FAFMIP models (Fig. 3), especially in the North Atlantic, Arctic, and Southern oceans. This similarity indicates that the FAFMIP-participant models form a representative subset of the wider CMIP5 and CMIP6 ensembles. It also suggests that the findings of FAFMIP are likely to be applicable to a wider range of models than the 13 FAFMIP models analysed here.
Fig. 4: Multi model mean projections of ∆ζ (left) from 1pctCO2 forcing experiments averaged over years 91–100 for 19 CMIP5 models (a), 16 CMIP6 models (c). Standard deviation of the model spread (right). Models used are described in Table 2
The 1pctCO2 response in the two different CMIP eras is similar (Fig. 4a, c), in agreement with recent findings (Lyu et al. 2020). The similarity of responses of models from the different eras indicates that models from across the eras may be analysed together as one ensemble, rather than separately. The current generation of AOGCMs show diverse sea-level responses in the Arctic, Southern Ocean, North Atlantic and North Pacific (Fig. 4d), much like the previous generation (Fig. 4b), indicating a continuing need to focus on these regions.
The CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1°-by-1° of latitude, with a refinement to 1/3° at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.
Ocean response to perturbations in individual fluxes


The CMIP5 ensemble uses ten different ocean components (ignoring version differences) among its 19 members (Table 2). In the 16 different CMIP6 AOGCMs shown, there are eight different ocean model components. In the CMIP6 ensemble, six models use a version of NEMO (Nucleus for European Modelling of the Ocean), three use POP (Parallel Ocean Program), two use MOM (Modular Ocean Model), and the remaining five use an ocean component unique to the ensemble. Hence, there is a greater diversity of ocean components in terms of the number of unique ocean models in CMIP5. For all the CMIP6 models that use NEMO, the horizontal ocean resolution of the ORCA1 grid used is the same (roughly 1°-by-1° of latitude, with a refinement to 1/3° at equator), although different AOGCMs use different numbers of ocean vertical levels, which has effects on Southern Ocean OHU (Stewart and Hogg 2019). One might argue that there is a decrease in the diversity of representations of ocean processes in this ensemble of CMIP6 models, but the increasing use of common ocean components has apparently not reduced the spread of sea-level projections in response to 1pctCO2 forcing in the CMIP6 era versus CMIP5 (Fig. 4b, d). Sea-level projections from the CMIP6 ensemble were checked for similarities among models sharing a similar ocean component, but no clear correlation exists (not shown). One might therefore expect that diversity in air-sea fluxes (rather than in ocean models) causes the spread (e.g., Huber and Zanna 2017). However, the increased use of common ocean components does not necessarily mean that water properties and ocean transport processes are represented in the same way across models. NEMO and other ocean components support a potentially enormous variety of configurations through customisable combinations of different parameterisations and schemes, and spin-up procedures. Parameter choices of, for example, coefficients of vertical diffusivity and eddy mixing are important for setting OHU in the Pacific and Southern Oceans (Huber and Zanna 2017). The convergence of structure in ocean components does not directly translate into convergent representations of ocean heat uptake.
Ocean response to perturbations in individual fluxes
Comparison of the multi model mean ∆ζ from FAF-all with the sea-level response to individual perturbations allows us to determine which features result from changes to each flux. The spatial pattern of sea-level change from the heat flux forcing (Fig. 5c) most closely matches the response to all perturbations simultaneously applied (Fig. 3c). For FAF-heat, the spatial standard deviation is 0.080 m, which is close to that of FAF-all (0.082 m). The spatial standard deviation is 0.021 m for FAF-stress and 0.018 m for FAF-water. This indicates that the heat flux contributes the most to the sea-level change in FAF-all and 1pctCO2, in agreement with previous work (Bouttes and Gregory 2014; Gregory et al. 2016). The wind stress perturbation causes part of the pattern of ∆ζ, but its influence is mostly confined to the Southern Ocean (Fig. 5a). There, strengthened and poleward-shifted westerlies steepen the meridional sea-level gradient across the ACC (Frankcombe et al. 2013). The freshwater perturbation contributes the least sea-level change of the three perturbations, but it sets part of the spatial pattern of ∆ζ in the Southern and Arctic Oceans (Fig. 5e). Recall that the three key locations for which models show diverse predictions of ∆ζ in 1pctCO2 and FAF-all were the Arctic, the eastern subpolar North Atlantic and the Southern Ocean south of Australia and New Zealand (Fig. 3c, d). There is coincident diversity in the FAF-heat responses (Fig. 5d), which suggests that spread in FAF-all is due primarily to the heat flux perturbation. The dynamic sea-level responses of each AOGCM to each individually applied flux perturbation are shown in the “Appendix” (Fig. 13–16).
Fig. 5: Maps of multi model ensemble mean ocean dynamic sea-level response to individually-applied flux perturbations (left) and standard deviation across 13 AOGCMs (right) for the wind stress (FAF-stress, top), heat flux (FAF-heat, middle), and water flux (FAF-water, bottom) experiments. AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0
Wind stress
The wind stress perturbation creates a gradient of ∆ζ across the Southern Ocean (Fig. 5a). The intensified Southern Ocean westerlies drive a northward positive meridional ∆ζ gradient with a zonal mean of 0.05–0.025 m from 75° to 35° S. South of 60° S, ∆ζ diverges depending on the model (Fig. 5b). The models disagree on whether the wind stress perturbation causes negative or weakly positive depth integrated OHC change south of 60° S (Fig. 6g), which is not yet well understood but merits further investigation. The wind stress perturbation tends to weakly warm the surface ocean, cool the shallow subsurface and warm the deeper ocean (Fig. 6d, j). Part of the discrepancy between models occurs because although this area-integrated picture is qualitatively common to models, the depth at which each OHC change inflection occurs is model-specific. In agreement with Gregory et al. (2016), while the local OHC change due to the wind stress perturbation can be large (Fig. 6a, g, j) its global integral is small; two orders of magnitude smaller than the heat flux perturbation (not shown). Other work finds that the Southern Ocean OHC response to wind stress change is sensitive to the location of the zero wind stress curl, which may be a source of some of the spread reported here (Stewart and Hogg 2019).
Fig. 6: Multi model ensemble mean integrated ocean heat content (OHC) change for FAF-stress (left), FAF-heat (middle), FAF-water (right) for 12 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2 (FAF-stress and FAF-water only), GFDL-ESM2M, GISS-E2-R-CC (FAF-stress and FAF-water only), HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Depth integrated OHC change (a–c), area integrated OHC change (d–f), zonally and depth integrated OHC change (g–i), zonally integrated OHC change (j–l). Dashed lines in d–i indicate ± 2 standard deviations of ensemble spread. 1 GJ = 109 J, 1 ZJ = 1021 J, 1 EJ = 1018 J
The maps of ∆ζT, ∆ζS and ∆ζN show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55° and 30° S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced ∆ζT change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative ∆ζ (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).


The maps of ∆ζT, ∆ζS and ∆ζN show that the wind forced sea-level change in the Southern Ocean is almost entirely thermosteric (Fig. 7c), as suggested by Gregory et al. (2016). The perturbation causes heat to accumulate between 55° and 30° S while higher latitudes cool (Fig. 6a, g). This is consistent with a wind driven enhancement of the residual meridional overturning documented elsewhere (Liu et al. 2018). The halosteric change in the Southern Ocean is much smaller and opposes the thermosteric change (Fig. 7e). The wind-forced ∆ζT change is largest in the Atlantic and Indian sectors of the Southern Ocean, and the models generally agree on the pattern and magnitude of this feature, although the details of the magnitude near the South American coast are model dependent, (Fig. 7d). The non-steric component dominates the sea-level change in the Antarctic shallow shelf seas (Fig. 7g). Elsewhere, in the Pacific sector and Weddell Sea, the AOGCMs predict different magnitudes of negative ∆ζ (Fig. 7a, b) and this spread is thermosteric (Fig. 7d).
Fig. 7: Multi model ensemble mean dynamic sea-level response to momentum flux forcing (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM-GC31-LL, MIROC6, MPI-ESM1-2-HR, MPI-ESM-LR and MRI-ESM2-0. Multi model mean momentum flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
In some models, but not all, the wind stress perturbation drives sea-level change in the Arctic East Siberian Sea and northwestern Atlantic (Fig. 5b). GISS-E2-R-CC predicts widespread, large positive ∆ζ in the Arctic, while CanESM5, MPI-ESM1-2-HR and HadCM3 predict a gradient of ∆ζ that is negative at the pole and increases southwards (Fig. 14). HadGEM3-GC31-LL shows positive ∆ζ at the pole. The other models predict near zero ∆ζ in the Arctic. The spread in the North Atlantic is due to the responses of HadGEM2-ES, MPI-ESM-LR, MPI-ESM1-2-HR and GFDL-ESM2M, which predict weakly positive ∆ζT and ∆ζS here, while the other models show ∆ζ ≈ 0 (Fig. 14).
Heat flux
The heat flux perturbation drives the most change in sea level, both in terms of magnitude and area of effect (Fig. 5c). The perturbation causes positive OHC change over most of the ocean area (Fig. 6b) in the upper 1000 m (Fig. 6e, k). Note that even though the heat flux perturbation adds large amounts of heat to the global ocean, it is possible for the net OHC change in some locations to be weakly negative; either because of negative values of the perturbation flux or via the redistribution of heat by changing ocean transport. The models agree that the largest OHC change occurs in south of 30° S, and the changes elsewhere are more model dependent (Fig. 6h). In the upper 300 m, the ensemble spread of the area integrated OHC change is on the order of half the mean change (Fig. 6e). This spread indicates that the strength of the mechanisms by which heat is transported away from the surface is different among models. The largest values of ∆ζ are in the North Atlantic. The most intense perturbation to the heat flux per unit area is directed here. As described earlier in Sect. 3.1, the North Atlantic redistribution feedback means that the magnitude of North Atlantic sea-level response is greater in FAF-heat and FAF-all than in 1pctCO2 experiments.
In general, the pattern of ∆ζ is similar across most models, and the magnitude of the change varies between models (Fig. 5). The fact that the hotspots of inter-model spread (Fig. 5d) are coincident with most of the strongest ∆ζ features reflects this. The multi-model mean map of ∆ζ (Fig. 5c) therefore reflects a pattern that is very similar to each individual model’s response, rather than the mean of several very different patterns. Most models show the maximum ∆ζ between 45° and 65° N in the western North Atlantic (Fig. 15). All models predict the Atlantic dipole of positive ∆ζ north of 45° N and weakly negative ∆ζ near Cape Hatteras in the western basin around 35° N. The weak dynamic sea-level drop occurs at the center of the subtropical gyre, consistent with the decline of the dynamic sea-level gradient across the Gulf Stream. In the eastern basin off the west Saharan-African coast most models predict a “tropical arm” of positive ∆ζ that diminishes westward (Fig. 5c), which is weak in HadGEM2-ES and absent in GFDL-ESM2M (which shows near zero ∆ζ, Fig. 15e, h). Most models predict a small region of negative ∆ζ north of Iceland. MPI-ESM-LR and MRI-ESM2-0 instead predict positive ∆ζ north of Iceland and negative/neutral ∆ζ to the south of Iceland (Fig. 15k, m). HadGEM2-ES and MPI-ESM1-2-HR exhibit regions of negative/neutral ∆ζ both south and north of Iceland (Fig. 15h, l).
The steric sea-level rise in the Atlantic subpolar gyre, north of 45° N, is due predominantly to positive ∆ζS (i.e. freshening), opposed by weaker negative ∆ζT (Fig. 8c). North of 45° N, there is positive ∆ζS and weaker negative ∆ζT,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of ∆ζ, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).
Fig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)


The steric sea-level rise in the Atlantic subpolar gyre, north of 45° N, is due predominantly to positive ∆ζS (i.e. freshening), opposed by weaker negative ∆ζT (Fig. 8c). North of 45° N, there is positive ∆ζS and weaker negative ∆ζT,, in agreement with previous work (Bouttes et al. 2014; Saenko et al. 2015). This is consistent with a reduced northward flux of heat and salt as a result of a weakened AMOC. The models disagree on the magnitude of ∆ζ, particularly to the south of Iceland (Fig. 8b) and most of this spread is due to diversity in predictions of thermosteric change, but the halosteric response is also uncertain across models (Fig. 8d, f). The sea-level change on the shelves of the subpolar North Atlantic has a strong non-steric component (Fig. 8g), consistent with an increase of on-shelf ocean mass (Yin et al. 2010).
Fig. 8: Multi model ensemble mean dynamic sea-level response to heat flux forcing (a) and the standard deviation across models (b) for 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0. Multi model mean heat flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
The thermosteric and halosteric effects change sign south of 45° N and the thermal effect dominates, but they compensate more closely, and so ∆ζ is smaller than further north. The 45° N latitude line coincides with the divide between the North Atlantic subpolar and subtropical gyres formed by the northern boundary of the North Atlantic Current. The opposing changes either side of the divide are consistent with a change in the inter-gyre exchange of heat and salt: a warmer and saltier subtropical gyre and a cooler and fresher subpolar gyre. Further south, most models predict positive ∆ζ in the eastern basin off the West African coast (Fig. 8a). There is also considerable inter-model spread in the thermosteric and halosteric contributions (Fig. 8d, f). Interestingly, five models predict a mixture of thermo- and halosteric contributions (ACCESS-CM2, CanESM2, CanESM5, HadGEM3-GC31-LL, MPI-ESM1-2-HR), four models predict the tropical arm as being purely halosteric (HadCM3, MIROC6, MPI-ESM-LR and MRI-ESM2-0), one model predicts a purely thermosteric effect (HadGEM2-ES), and one model shows no positive ∆ζ feature here at all (GFDL-ESM2M) (not shown).
In the North Pacific, all models respond to the heat flux perturbation with a North–South dipole in ∆ζ that changes sign around 35° N (Fig. 8c). This meridional dipole has the opposite sign to that of the North Atlantic. In the western basin, the pattern is essentially the same across models, and its extent eastward is model dependent (Fig. 15). The dipole is mostly thermosteric (Fig. 8c), owing to a stronger accumulation of heat per unit area north of 35° N in the region east of Newfoundland than further south (Fig. 6b). This is sea-level change is consistent with a steepening of the across-current sea-level slope, and an intensification of the Kuroshio western boundary current (Chen et al. 2019).
The lower latitudes of the Arctic around the East Siberian and Beaufort Seas show positive ∆ζ in response to the heat flux perturbation, while ∆ζ is negative at higher latitudes. The only exception to this is HadCM3 (Fig. 15), which predicts strongly negative ∆ζ everywhere in the Arctic, contributing strongly to the large inter-model spread there (Fig. 8b). The Arctic shows a strong non-steric component of ∆ζ (Fig. 8g), corresponding to a shift of mass from the highest latitudes onto the shelves. The patterns of Arctic sea-level change in 1pctCO2 and FAF-all are very similar (Fig. 3), suggesting that the coupling of sea ice to redistributed temperature rather than regular temperature in FAFMIP experiments (Sect. 2.2) does not introduce unintended effects on ocean transport. Nevertheless, the diverse representations of sea ice in AOGCMs generally remains a key source of uncertainty in the projection of future polar climate change (Meredith et al. 2019).
The Southern Ocean sea-level change in response to heat flux forcing is smallest at the highest latitudes (negative ∆ζ), changing sign to positive ∆ζ between 40° and 55° S (Fig. 8a). All models predict a maximum of ∆ζ off the South African coast that extends eastward. The spatial pattern of negative ∆ζ across much of the Southern Ocean is predicted by all models. CanESM2, HadGEM3-GC31-LL, MPI-ESM-LR and GFDL-ESM2M (and to a lesser extent, HadCM3 and ACCESS-CM2) show positive ∆ζ in the sector between 130° and 160° E, south of Australia and New Zealand (not shown). This inter-model variation is also identifiable in the spread of sea-level responses in FAF-all (Fig. 3d) and is thermosteric (Fig. 8d).
The Southern Ocean Δζ zonal gradient in FAF-heat is the result of both thermosteric and halosteric effects (Fig. 8a, c, e). Gregory et al. (2016) pointed out that the gradient of Δζ across the Southern Ocean arises primarily because more heat accumulates in the mid latitudes (around 45° S) than further south (Fig. 9a). However, if sea-level change were simply proportional to OHU, then Δζ would show a prominent maximum at 45° S and decline until 25° S. Instead, Δζ increases northward to about 45° S, with only a slight decline further North (Fig. 9b, solid black line). The waters further North are warmer and therefore have greater thermal expansivity, which, in addition to the convergence of heat between 30–45° S, creates a thermosteric maximum around 40° S (Fig. 9b, red dotted line). However, at the same latitude, the changing salinity causes a halosteric effect that opposes the thermosteric effect and the meridional gradient of Δζ plateaus, instead of peaking at 40° S and declining to the north (Fig. 9b, cyan dashed line). Note that the deviation between the steric sea-level change (Fig. 9b, cyan dashed line) and the dynamic change (Fig. 9b, solid black line) north of 40° N indicates a considerable barotropic component of the change due to the redistribution of ocean mass (Lowe and Gregory 2006; Yin et al. 2010; Bouttes and Gregory 2014 and Fig. 8g).
Fig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing Δζ (black solid line), the thermosteric component ΔζT (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0
Freshwater flux
Interestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).


Fig. 9: Comparison of the multi model ensemble mean zonally- and depth-integrated OHC change in response to heat flux forcing (a) and zonal mean dynamic sea-level change (b) for 11 AOGCMs, showing Δζ (black solid line), the thermosteric component ΔζT (red dotted line) and the sum of thermo- and halosteric components (cyan dashed line). AOGCMs used: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR, MRI-ESM2-0
Freshwater flux
Interestingly, the sea-level response to freshwater forcing is strongly thermosteric as well as halosteric (Fig. 10c, e). The North Atlantic is sensitive to opposing, nearly compensating thermal and haline effects. The sea-level change in the Arctic is mostly halosteric, whereas the Southern Ocean shows a mostly thermosteric response. The sea-level change on the Antarctic shelves is non-steric (Fig. 10g).
Fig. 10: Multi model ensemble mean dynamic sea-level response to freshwater flux perturbation (a) and the standard deviation across models (b) for 13 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, CESM2, GFDL-ESM2M, GISS-E2-R-CC, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0. Multi model mean freshwater flux-forced thermosteric (c), halosteric (e), and non-steric (g) contributions, and the standard deviation across models (d, f, h) where the area mean has been subtracted from (g)
The locations where the models disagree on the sea-level response to freshwater forcing are not always coincident with the locations of largest sea-level change (Fig. 10a, b), particularly in the North Atlantic and the Arctic. This indicates that different models predict different features (Fig. 16), rather than all models responding with similar patterns of different magnitude. The models predict diverse patterns of sea-level change in the subpolar North Atlantic (Fig. 10b) because they disagree on the eastward extent of the sea-level change (Fig. 16). Presumably, simulated North Atlantic currents have differing sensitivities to freshwater forcing.
The sea-level changes closest to the Antarctic coast are predicted with some agreement across models (Fig. 10b). The inter-model spread around 50°–60° S south of Australia arises due to different thermosteric responses to freshwater forcing (Fig. 10d). A poleward contraction of the ACC here would explain the positive Δζ (Fig. 10a) but the inter model spread suggests that not all models predict this (Figs. 10b, 16a, b, d, f, h, j).
In the Arctic, the freshwater forcing is widespread and positive, due to a mixture of increased river runoff and precipitation. This causes freshening, which in turn causes halosteric sea-level rise (Fig. 10e). However, the models disagree on the spatial extent of the halosteric sea-level rise (Fig. 10f).
Linearity of sea-level responses to flux perturbations
Here we explore how sea level responds to flux perturbations applied individually versus simultaneously. If the sea-level response to all perturbations is linear, then the sum of the responses when the perturbations are applied individually Δζsum,
Δ𝜁𝑠𝑢𝑚=Δ𝜁𝑤𝑖𝑛𝑑+Δ𝜁ℎ𝑒𝑎𝑡+Δ𝜁𝑤𝑎𝑡𝑒𝑟, (13)
should equal the response when the fluxes are applied together, Δζall. The differences between Δζsum and Δζall represent the nonlinear sea-level response to simultaneous flux forcing and is explored for 11 AOGCMs (Table 1, excluding CESM2 and GISS-E2-CC). The significance of nonlinear features is tested against the variability of the seven decades of FAF-passiveheat, calculated as the standard deviation of seven decadal averages, which we assume is representative of the internally generated variability in the other experiments as well. The quantity Δζsum − Δζall is calculated using four independent simulations (FAF-heat, -stress, -water, -all), each with its own unforced variability. The difference Δζsum − Δζall can therefore be affected by the unforced variability of four different simulations, so the standard deviation of the difference is twice the standard deviation of unforced decadal variability (from FAF-passiveheat). For a Δζsum − Δζall feature to be judged significant at the 5% level, it must be larger than four times the unforced standard deviation. Locations where Δζsum − Δζall is not significant are set to 0 for each model, before being averaged in Fig. 11 to reveal only significant differences. The features removed through this process are small in spatial extent and magnitude, and are particular to each model (not shown). The flux perturbations show significant nonlinear interaction in the Arctic and subpolar North Atlantic (Fig. 11a). Across the Arctic, Δζsum − Δζall is negative, meaning most models predict a stronger dynamic sea-level change in FAF-all than the individual flux perturbation experiments suggest.
Fig. 11: Multi model ensemble mean nonlinear sea-level response to flux perturbations (a) and standard deviation (b) across 11 AOGCMs: ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MIROC6, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0
For most of the global ocean, Δζsum − Δζall is small and therefore Δζsum approximates the patterns of Δζall. However, small values of multi-model mean Δζsum − Δζall are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, Δζwind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model’s results is necessary to explore this.
In the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the Δζsum − Δζall dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.
HadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.
Decomposition of ocean heat uptake


For most of the global ocean, Δζsum − Δζall is small and therefore Δζsum approximates the patterns of Δζall. However, small values of multi-model mean Δζsum − Δζall are not necessarily indicative of agreement between models that the responses to perturbations sum linearly. In the western North Pacific and Southern Ocean south of Australia and New Zealand (Fig. 11b) some models show some nonlinear interactions between the flux perturbations. South of Australia and New Zealand, Δζwind is small, so the interaction is between the freshwater and heat fluxes. It could be that local details of the change in sea-ice cover in response to heat flux forcing are model specific, causing the momentum forcing to have different results in FAF-all versus FAF-stress where no heat perturbation is applied. More detailed investigation into each model’s results is necessary to explore this.
In the northwest Pacific, in the Kuroshio separation region, the AOGCMs show various sensitivities to the three individual forcings (not shown). For ACCESS-CM2, GFDL-ESM2M, MIROC6 and MPI-ESM-LR, the Δζsum − Δζall dipole is positive to the south and negative to the north, indicating that simultaneously applied flux perturbations do not produce the same degree of intensification of the across-current slope as when the perturbations are applied individually. For CanESM5, the dipole is reversed. For the other models there is no strong nonlinear sea-level response.
HadGEM2-ES, MPI-ESM1-2-HR, and GFDL-ESM2M show strong nonlinear interactions between forcings in the North Atlantic, as these models are sensitive to all three perturbations here (not shown). The spread in the North Atlantic indicates that the AMOC response to the flux perturbations (and also the nonlinear interactions between them) is model-specific.
Decomposition of ocean heat uptake
As shown above, ocean dynamic sea-level change is largely thermosteric, and reflects changes in OHC. Here, we decompose the OHC change (see Sect. 2.4 and “Appendix” for details) of ten AOGCMs (Table 1, excluding CESM2, GISS-E2-R-CC, MIROC6) into contributions from changes in ocean transports and the uptake of the imposed perturbation. Most of the heat added to the oceans in FAF-heat is stored in the Southern Ocean, between 30° S and 60°S (Figs. 6h, 12a), particularly in the Indo–Pacific sectors. The North Atlantic shows the highest rate of heat uptake per unit area, but the small total area of the basin means its contribution the global total OHU is smaller than that of the much larger Southern Ocean (Fig. 6h). The Arctic also shows moderate rates of heat storage per unit area (Fig. 12a), but this basin stores less heat than other latitudes because of its small total area (Fig. 6h).
Fig. 12: Decomposition of depth-integrated ocean heat uptake in ten AOGCMs (ACCESS-CM2, CanESM2, CanESM5, GFDL-ESM2M, HadCM3, HadGEM2-ES, HadGEM3-GC31-LL, MPI-ESM-LR, MPI-ESM1-2-HR and MRI-ESM2-0) in FAF-heat, left panels show the multi-model ensemble mean and right panels show the standard deviation across models for the total ocean heat uptake mean (a) and spread (b). Components of heat uptake (c, e, g) are shown as a percentage of the total (a). Passive uptake of added heat, Δh[Φ−(T′)], mean (c) and spread (d). Pure redistribution of unperturbed heat, Δh[Φ′(T−)] mean (e) and spread (f). Redistribution of added heat by the perturbed transport, Δh[Φ′(T′)], mean (g) and spread (h)
In the Southern Ocean, passive heat uptake in the Southern Ocean (Fig. 12c) is close to 100% of the total heat uptake (Fig. 12a). The OHC change due to the perturbed transport (Fig. 12e, g) is much smaller than the total passive uptake, but is locally important and strongly negative near the Ross and Weddell gyres. Further, there is relatively little spread of Δℎ[Φ−(𝑇′)] across models (Fig. 12d). This means that these AOGCMs agree that heat uptake by the Southern Ocean is mostly passive, in agreement with recent findings (Bronselaer and Zanna 2020). The perturbed transport has secondary influence on heat uptake in the Southern Ocean. Both Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇−)] are important components in the Indian sector (Fig. 12c, e), and the spread here is not due to passive uptake (Fig. 12d). South of Australia and New Zealand, where the total OHC change differs across models (Fig. 12b) the spread comes from Δℎ[Φ′(𝑇−)] (Fig. 12f), which could suggest a model-dependent reduction of upwelling.
OHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative Δℎ[Φ′(𝑇−)] and Δℎ[Φ′(𝑇′)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with Δℎ[Φ′(𝑇′)] and Δℎ[Φ−(𝑇′)] also playing smaller roles.
Moderate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇′)] are strongly positive while Δℎ[Φ′(𝑇−)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of Δℎ[Φ′(𝑇−)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive Δℎ[Φ′(𝑇′)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.


OHU in the North Atlantic is characterized by positive passive heat uptake that is partially opposed by the perturbed transport (Fig. 12c, e, g). Strong negative Δℎ[Φ′(𝑇−)] and Δℎ[Φ′(𝑇′)] mean that the effect of transport change here is large, cooling the basin. Furthermore, this transport change manifests differently in different models (Fig. 12f, h). Indeed, the large spread in total heat uptake south of Iceland (Fig. 12b) results mostly from the redistribution of unperturbed temperature (Fig. 12f), with Δℎ[Φ′(𝑇′)] and Δℎ[Φ−(𝑇′)] also playing smaller roles.
Moderate heat storage per unit area by the Arctic Ocean is commonly predicted across AOGCMs, but there are large differences between them (Fig. 12a, b). Here, the total OHC change has contributions from all three components: Δℎ[Φ−(𝑇′)] and Δℎ[Φ′(𝑇′)] are strongly positive while Δℎ[Φ′(𝑇−)] is negative. Similarly, the spread of OHU has roots in all three components (Fig. 12d, f, h), highlighting that the mechanisms of Arctic heat uptake are highly model dependent. Since the heat flux perturbation into the Arctic is quite weak, the OHC change results from the oceanic transport of heat. Some of the added heat is brought into the basin by the unperturbed transport, (Fig. 12c). The negative values of Δℎ[Φ′(𝑇−)] (Fig. 12e), indicate reduced poleward transport of unperturbed heat, possibly due to the weakened AMOC (although reduced heat transport through the Bering Strait cannot be ruled out). The widespread positive Δℎ[Φ′(𝑇′)] in the Arctic (Fig. 12g) could be explained by the following mechanism: the heat flux perturbation causes a weakened Atlantic overturning, which causes added heat to flow northwards into the Arctic from the North Atlantic and/or North Pacific instead of being subducted and transported equatorward. Further work should explore whether such a mechanism is at work.
The equatorial Atlantic shows moderate area-weighted OHU (Fig. 12a). The equatorial Atlantic OHU is mostly driven byΔℎ[Φ′(𝑇−)], (Fig. 12e) and passive heat storage is important in the west, (Fig. 12c). The local heat flux perturbation is near zero (Fig. 1a) and so the heat content change here is mostly a consequence of Φ′, rather than T′. These results echo previous work, which also identify an important role of active transport change in the low latitudes (e.g. Garuba and Klinger 2018). This is one of the few locations where the redistribution of unperturbed heat has a large positive depth integral. Elsewhere in the tropics, although Δℎ[Φ′(𝑇−)] is a large component, the total heat storage per area is smaller (Fig. 12a). In the western basin, Δℎ[Φ′(𝑇′)] is weakly negative, in contrast with the eastern. This could be consistent with a weakened poleward transport of heat causing an accumulation of unperturbed and added heat, and a coincident reduced westward equatorial transport of added heat. Reduced upwelling of unperturbed temperature as a part of the weakened poleward transport of unperturbed heat could explain the accumulation of Δℎ[Φ′(𝑇−)] here. Changes in the subtropical and subpolar gyre circulation (and the exchange of heat between them) as suggested by previous authors could also play a role that has not yet been explored. A complete explanation is currently lacking but warranted (Boeira Dias et al. 2020).
Discussion
Diversity of sea-level response to common air-sea flux perturbation
The largest and most widespread features of dynamic sea-level change in response to 1pctCO2 forcing have been shown to result mostly from the change in air-sea heat flux. Further, the inter-model uncertainty of the pattern of Δζ results from model-specific ocean transport responses to standardized air-sea flux changes, rather than diversity in the flux changes themselves. For the most part, the spread in response to heat flux perturbation relates to different models responding with a similar pattern of sea-level change, whose magnitude differs across models. The North Atlantic hosts a large diversity of Δζ across models, but although the geographic pattern is different across models, the sea-level changes have similar dynamical origins. We find that the North Atlantic inter-model variance is mostly due to the redistribution of preindustrial heat being different in each model, probably in turn due to the spread in predicted weakening of the AMOC. The spread of Δζ also has smaller contributions from uptake of added heat by both the perturbed and unperturbed transport. Part of the spread of North Atlantic sea-level change arises because added heat penetrates into the deep ocean in deep convection sites that are geographically different among models (Bouttes et al. 2014), but this reason is found to be secondary in our analysis. Other authors pointed out that ocean heat uptake is sensitive to model-specific factors such as SST biases (He and Soden 2016), mesoscale eddy transfer (Exarchou et al. 2015; Saenko et al. 2018), stratification (Huber and Zanna 2017) and the isopycnal diffusion scheme (Exarchou et al. 2015). These factors may explain why the models that we have examined show similar horizontal patterns of heat uptake with differing magnitudes even though these models are forced with identical heat inputs.
Previous work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system’s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component’s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.
Role of individual and simultaneous flux perturbations causing key regional sea-level changes


Previous work has highlighted that individual models when forced with different surface fluxes can produce diverse ocean responses in terms of sea level (Bouttes and Gregory 2014) and ocean heat uptake (Huber and Zanna 2017). Indeed, the uncertainty in surface fluxes is key challenge for climate modelling. By forcing different AOGCMs with common flux perturbations the spread of sea-level projections can be more directly attributed to the diversity of ocean model formulation than in prior studies. Huber and Zanna (2017) tested the parametric uncertainty of a single a model (i.e. the sensitivity of ocean heat uptake to the choice of parameter values), finding it to be small. Parametric uncertainty is only a subset of the total uncertainty due to the different representation of ocean processes in models (Zanna et al. 2018). Therefore, while previous work shows that accurate representation of surface fluxes is essential in climate simulations, our findings add that the use of ocean models with differing structures is also a key uncertainty. Nevertheless, there is clearly still more to learn about the link between the diversity caused by differences in surface fluxes versus differing ocean models. For instance, differences in ocean model design may lead to differences in steady state properties (e.g. stratification strength, mean temperature, overturning strength etc.), which in turn affect the steady state air-sea fluxes as well as the system’s sensitivity to change. On the other hand, one could argue that changes in air-sea fluxes that result from the ocean response to common flux forcing are the result of each ocean component’s unique sensitivity to forcing. While previous studies and the present study have separated the spread due to ocean models and the spread due to air-sea flux change in different ways, clearly they affect each other and this connection is not yet fully understood.
Role of individual and simultaneous flux perturbations causing key regional sea-level changes
One of the key features of the sea-level response to heat flux forcing was the contrast in meridional dipoles in the North Pacific and North Atlantic (Gregory et al. 2016). In the North Atlantic, the meridional dipole is positive to the north, while in the North Pacific, it is positive to the south. The opposite dipoles are consistent with recent work investigating why the Kuroshio current is predicted to strengthen in AOGCM simulations of climate change, whereas the Gulf Stream weakens (Chen et al. 2019). Those authors described how the air-sea heat flux that results from a warming climate causes stronger warming to the east of the Kuroshio than to the west, steepening the across-current density slope. In the North Atlantic, the heat flux change causes a reduction of northward salinity transport that freshens the high latitudes, reducing the across-current slope and weakening the current. This is consistent with the dynamic sea-level changes that result from FAF-heat. The thermosteric change tends to steepen the across-current slope of the Gulf Stream, but this is counteracted by the larger opposing effect of haline contraction. Our results show that the intensity and pattern of Kuroshio strengthening is similar across models, but the change in the North Atlantic is more uncertain across models (Fig. 12f). The Gulf Stream dipole, unlike the Kuroshio dipole, is likely to be affected by the AMOC weakening, and so will be different for each model. Further, Bouttes and Gregory (2014) reported that the sea-level change in the western North Pacific was caused by both the wind stress and heat flux perturbations. In our ensemble, not every model’s Kuroshio and extension regions were sensitive to wind forcing.
The water flux perturbation shows the smallest changes of all three perturbations when applied alone, but it nevertheless has important local effects in parts of the Southern Ocean, Arctic and subpolar North Atlantic. However, the importance of the water flux change may be underestimated by considering experiments in which only one flux is varied because of nonlinear interactions between flux perturbations. Other work has described how the sea-level responses to individually applied flux perturbations combine approximately linearly (Bouttes and Gregory 2014), which we also find is true to first order. However, we have identified that the nonlinear interaction between the three forcings is model dependent, which cannot be understood from a multi-model mean perspective. Models such as GFDL-ESM2M and MRI-ESM2-0 show strong nonlinear amplification of the sea-level response in the North Atlantic when all fluxes are perturbed simultaneously. Further, other work has shown that perturbing freshwater fluxes increases the uptake of heat by the subpolar Atlantic (Garuba and Klinger 2018).
The Southern and Arctic Oceans host many local features of dynamic sea-level change that are model specific. Coupled models (including the ones analysed here) show markedly different sea-ice extents and sensitivities to forcing (Turner et al. 2013). It seems likely that at least some of the model spread in projections of ∆ζ stems from the fact that sea-ice thermodynamics are model specific. The Weddell Gyre and its heat budget are thought to be sensitive to regional wind forcing (Jullion et al. 2010; Saenko et al. 2015). The spread of ∆ζ and ∆ζT in response to FAF-stress in the western Weddell Gyre indicates that some models show a significant thermosteric response to intensified westerlies. Inter-model differences in Arctic dynamic sea-level change and heat uptake have very different mechanisms for each model. The diversity of Arctic climate responses forcing is not necessarily limited to the representation of the oceans, but perhaps also poor representation of ice albedo and cloud feedbacks (Karlsson and Svensson 2013), biases in the unperturbed state (Franzke et al. 2017) or other factors that have not been explored.
The east Atlantic “tropical arm” of positive ∆ζ in response to heat flux forcing is halosteric, but is not predicted by all models. The analysis of ocean heat content therefore yields little information about the cause of the feature. The feature bears strong resemblance to the tropical arm SST anomalies characteristic of the Atlantic Multidecadal Variability (Yuan et al. 2016), however, our ∆ζ feature is the result of 70 years of integration of step forcing rather than variability, and is a vertical integral signal rather than purely SST. Nevertheless, the similarity between that pattern of variability and the forced response we present suggests common driving mechanisms may be responsible. In the context of the AMV, the tropical arm is thought to arise in response to midlatitude warm SST anomalies that weaken the tropical trade winds, which reduce low cloud and dust loading, thereby warming tropical SST (Yuan et al. 2016). Observations and some models show that the tropical SST arm coincides with freshening in the upper 50 m (Kavvada et al. 2013), which is consistent with the positive ∆ζS response to FAF-heat. The origin of the freshening in our simulations is not known, and the roles of input from the subpolar Atlantic, the Mediterranean or elsewhere are not ruled out. Whether this is driven by the atmospheric response to forcing, the thermohaline circulation or a mixture of effects is not clear, but merits further investigation.
Caveats, unmodeled processes and further outlook
FAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.


Caveats, unmodeled processes and further outlook
FAFMIP experiments were designed to provide insight into the causes of model spread in greenhouse gas-forced climate change experiments, particularly the 1pctCO2 experiment. The design aimed to mimic the magnitude of 100 years of 1pctCO2 forcing, but the North Atlantic redistribution feedback (wherein the perturbation weakens the AMOC, causing an advection-driven cooling and increasing the air-sea heat flux into the North Atlantic, see Sects. 2.2 and 3.1) causes the total heat input into the North Atlantic to be larger than the just the imposed perturbation (Gregory et al. 2016). Todd et al. (2020) investigated the strength of this unwanted feedback by forcing ocean-only models (which have no redistribution feedback) with the same heat flux perturbation as this study, and compared the ocean heat transport response with the response of coupled AOGCMs (which do have the feedback). Those authors find that the feedback causes an additional 10% AMOC weakening versus the change that occurs in fully coupled AOGCMs. The feedback affects the North Atlantic heat uptake and transport, but has limited impact elsewhere and its effect on global ocean heat uptake is smaller than the perturbation of interest. In the AOGCMs we examine, global total heat uptake is about 10% greater than the area- and time-integral of the imposed perturbation. Therefore, the forced changes in the North Atlantic presented in this work are larger than one would expect from 100 years of 1pctCO2 forcing. Nevertheless, the fact that the imposed perturbation is common to all models matters more than the precise magnitude, when investigating the sensitivity of ocean model responses to common forcing.
Previous work investigating ‘pattern scaling’ has shown that the spatial structure of sea-level change remains similar across a range of magnitudes of forcing (Hawkes 2013; Perrette et al. 2013; Slangen et al. 2014; Bilbao et al. 2015). The spatial patterns of change and the underlying drivers presented here are therefore likely to be qualitatively applicable to greenhouse gas-forced experiments. Nevertheless, the sensitivity of the ocean response to different heat inputs into the North Atlantic is an open area of research, and will be further investigated in future work. Additional FAFMIP experiments, which apply heat inputs like those presented here, except with differing magnitudes in the North Atlantic, are already underway, and will be presented in future work.
FAFMIP experiments do not account for the input of freshwater by the melting of the Greenland and Antarctic ice sheets. Over the North Atlantic area (50°–70° N, 70° W–30° E), the freshwater perturbation integrates to a freshwater input of 0.007 Sv (1 Sv = 106 m3 s−1). This is comparable in magnitude to the input of 0.006 Sv (0.00065 m year−1 or 0.01625 m of global mean sea-level rise) of meltwater from the Greenland Ice Sheet (GIS) over 1993–2018 (Frederikse et al. 2020), albeit applied for a much longer duration. Recent projections (Oppenheimer et al. 2019) of the GIS contribution to global mean sea-level rise by the year 2100 relative to 2000 across the full range of emissions scenarios are 0.063 to 0.119 m (0.00063–0.00119 m year−1), which corresponds to a freshwater input of about 0.007–0.013 Sv. This rough comparison suggests that the rate of addition of meltwater from the GIS alone is 1–1.8 times stronger than the local water flux perturbation in the North Atlantic. The water flux perturbation in the Southern Ocean (south of 45° S) integrates to 0.115 Sv. The Antarctic Ice Sheet (AIS) loss contribution to recent historical global mean sea-level rise is smaller than that of the GIS, at 0.00032 m year−1 or 0.008 m over 1993–2018, approximately 0.003 Sv (Frederikse et al. 2020). The AIS, unlike the GIS, is dominated by marine melting (Paolo et al. 2015; Wouters et al. 2015), a coupled atmosphere-ice sheet-ocean process that cannot yet be fully interactively represented in climate models (Oppenheimer et al. 2019). As such, projections of the AIS contribution to future global mean sea level remain highly uncertain, although recent estimates of the AIS have an across-scenario range of 0.040–0.120 m by the year 2100 relative to 2000 (Oppenheimer et al. 2019), equivalent to 0.0004–0.0012 m year−2 or 0.004–0.013 Sv. The AIS contributions are therefore on the order of 0.03–0.1 times the perturbation imposed over the Southern Ocean. The water flux perturbation studied here was sufficient to produce features of regional sea-level change 0.05–0.1 m greater than the global mean in the Northwestern Atlantic and the coastal Southern Ocean. The missing GIS and AIS meltwater contributions (which are locally of a similar order to the freshwater perturbation that we imposed) could plausibly enhance the local freshwater-forced sea-level changes by an amount the order of 0.01–0.1 m, especially in the northwestern Atlantic. Note that this rough estimate of unmodeled meltwater contributions is not intended as a quantitative account, but instead serves to highlight a need for experiments that include these effects (Nowicki et al. 2016).
Gravitational, rotational and deformational (GRD) processes associated with ice mass loss to the oceans, which typically impose a negative feedback on sea-level rise by elevating retreating glaciers away from marine heat, are also not accounted for in this study. However, the magnitude of these effects is too small to reduce the rate of AIS melting over the twenty-first century sea-level rise, and become more important after the year 2250 (Larour et al. 2019; Oppenheimer et al. 2019). More generally though, GRD processes are vital in the determination of local relative sea-level change through the 21st Century and beyond (Mitrovica et al. 2011; Oppenheimer et al. 2019). The complex interaction between atmosphere–ocean-ice sheet-GRD processes makes it difficult to speculate about the net effects of all processes, and highlights a need to interactively simulate all such elements of the system.
Echoing findings from the previous generation of coupled atmosphere–ocean climate models, the regions showing the largest dynamic sea-level changes at the end of the twenty-first century also show the largest inter-model uncertainty (Church et al. 2013, Figs., 3, 4). Regions with both large projected changes and large uncertainty are the northwestern Atlantic, the Arctic, parts of the Southern Ocean and the northwest Pacific. This uncertainty highlights an ongoing need to better understand the reasons for diverse predictions of ocean transport change in these regions. This inter-model spread cannot presently be readily reduced by excluding models, since it is not trivial to determine the relative robustness of each AOGCM projection. Accordingly, the upper and lower limits of future sea-level scenarios should be constructed with the consideration that the dynamic sea level in these regions could be larger or smaller than the multi-model ensemble mean suggests. There is an increasing understanding that the diversity of cloud feedbacks is an important cause of the variations of climate sensitivity across different AOGCMs (Zelinka et al. 2020). Establishing realistic representations of cloud feedbacks in AOGCMs is therefore a key step to reduce the spread future climate and sea-level projections. Regarding ocean components, Lyu et al. (2020) have recently attributed the spread of sea-level projections to biases in model mean states, and so the reduction of such biases remains an important goal for climate projection.
Conclusions
This work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:
Most of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.
The increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.
The main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.
The sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.
The Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.


Conclusions
This work documents how FAFMIP experiments are useful tools to derive a new understanding of the drivers of dynamic sea-level change in idealized greenhouse gas forcing experiments. Notably, these latest FAFMIP results show that:
Most of the spread of predictions of dynamic sea-level change in response to idealised greenhouse gas forcing by AOGCMs can be reproduced by forcing models with common air-sea flux perturbations. These findings show that the diverse representation of the ocean component in climate models is a key uncertainty in sea-level projection under greenhouse gas forcing.
The increased air-sea heat flux associated with greenhouse gas forced climate change sets the broad spatial pattern of dynamic sea-level change. The dynamic sea-level changes that result from the changing freshwater flux and wind stress have important effects locally but are smaller contributors to the global change.
The main effect of the wind-stress change is to rearrange the distribution of heat in the Southern Ocean, which steepens the meridional sea-level gradient.
The sea-level response to the change in surface freshwater flux is mostly confined to the Arctic and the Southern Ocean south of Australia and New Zealand, although models disagree on whether North Atlantic is affected significantly.
The Southern Ocean absorbs a large portion of the added heat perturbation, where models agree that most of this heat is taken up like a passive tracer, without strongly affecting the local transport.
The flux perturbations create nonlinear dynamic sea-level responses when applied simultaneously, especially in the Arctic and the North Atlantic, but the details are different across models.
FAFMIP simulations provide new avenues to probe the sea-level response to greenhouse gas forcing, and ocean heat-content change generally. The results presented here represent a step highlighting where AOGCMs give diverse predictions of sea-level change because of their different ocean models. Many details of local processes that cause the sea-level changes described here remain to be fully explored. We have highlighted that a key source of spread of AOGCM predictions of sea-level change in the North Atlantic is because the change of local transport is highly model dependent; subsequent work should uncover what characteristics of ocean models cause this. AOGCMs give diverse predictions about Arctic heat uptake, owing to the interaction between passive and active heat uptake processes that call for more detailed examination. Further process-based analysis of FAFMIP simulations will shed new light on the key areas of uncertainty highlighted here.


Kopp et al. (2014)
Title:
Probabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites
Key Points:
Rates of local sea-level rise differs from rate of global sea-level rise
Differences arise from land motion, ocean dynamics, and Antarctic mass balance
Local sea-level rise can dramatically increase flood probabilities
Corresponding author:
Robert E. Kopp
Citation:
Kopp, R. E., R. M. Horton, C. M. Little, J. X. Mitrovica, M. Oppenheimer, D. J. Rasmussen, B. H. Strauss, and C. Tebaldi (2014), Probabilistic 21st and 22nd century sea-level projections at a global network of tide-gauge sites, Earth’s Future, 2, 383 – 406, doi:10.1002/2014EF000239.
URL:
https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2014EF000239
Abstract
Sea-level rise due to both climate change and non-climatic factors threatens coastal settlements, infrastructure, and ecosystems. Projections of mean global sea-level (GSL) rise provide insufficient information to plan adaptive responses; local decisions require local projections that accommodate different risk tolerances and time frames and that can be linked to storm surge projections. Here we present a global set of local sea-level (LSL) projections to inform decisions on timescales ranging from the coming decades through the 22nd century. We provide complete probability distributions, informed by a combination of expert community assessment, expert elicitation, and process modeling. Between the years 2000 and 2100, we project a very likely (90% probability) GSL rise of 0.5 to 1.2 m under representative concentration pathway (RCP) 8.5, 0.4 to 0.9 m under RCP 4.5, and 0.3 to 0.8 m under RCP 2.6. Site-to-site differences in LSL projections are due to varying non-climatic background uplift or subsidence, oceanographic effects, and spatially variable responses of the geoid and the lithosphere to shrinking land ice. The Antarctic ice sheet (AIS) constitutes a growing share of variance in GSL and LSL projections. In the global average and at many locations, it is the dominant source of variance in late 21st century projections, though at some sites oceanographic processes contribute the largest share throughout the century. LSL rise dramatically reshapes flood risk, greatly increasing the expected number of “1-in-10” and “1-in-100” year events.
Introduction
Sea-level rise figures prominently among the consequences of climate change. It impacts settlements and ecosystems both through permanent inundation of the lowest-lying areas and by increasing the frequency and/or severity of storm surge over a much larger region. In Miami-Dade County, Florida, for example, a uniform 90-cm sea-level rise would permanently inundate the residences of about 5% of the county’s population, about the same fraction currently threatened by the storm tide of a 1-in-100 year flood event [Tebaldi et al., 2012]. A 1-in-100 year flood on top of such a sea-level rise would, assuming geographically uniform flooding, expose an additional 35% of the population (Climate Central, Surging Seas, 2013, retrieved from SurgingSeas.org, updated November 2013).
The future rate of mean global sea-level (GSL) rise will be controlled primarily by the thermal expansion of ocean water and by mass loss from glaciers, ice caps, and ice sheets [Church et al., 2013]. Changes in land water storage, through groundwater depletion and reservoir impoundment, may have influenced twentieth-century sea-level change [Gregory et al., 2013] but are expected to be relatively minor contributors compared to other factors in the current century [Church et al., 2013].
Local sea-level (LSL) change can differ significantly from GSL rise [Milne et al., 2009; Stammer et al., 2013], so for adaptation planning and risk management, localized assessments are critical. The spatial variability of LSL change arises from: (1) non-uniform changes in ocean dynamics, heat content, and salinity [Levermann et al., 2005; Yin et al., 2009], (2) perturbations in the Earth’s gravitational ﬁeld and crustal height (together known as static-equilibrium effects) associated with the redistribution of mass between the cryosphere and the ocean [Kopp et al., 2010; Mitrovica et al., 2011], (3) glacial isostatic adjustment (GIA) [Farrell and Clark, 1976], and (4) vertical land motion due to tectonics, local groundwater, and hydrocarbon withdrawal, and natural sediment compaction and transport [e.g., Miller et al., 2013].
Most past assessments of LSL change have focused on specific regions, such as the Netherlands [Katsman et al., 2011], the U.S. Paciﬁc coast [National Research Council, 2012], New York City [Horton et al., 2011; New York City Panel on Climate Change, 2013], and New Jersey [Miller et al., 2013]. Slangen et al. [2012], Slangen et al. [2014], Perrette et al. [2013], and Church et al. [2013] [AR5] have produced global projections of LSL using Coupled Model Intercomparsion Project (CMIP) projections [Taylor et al., 2012] for thermal expansion and ocean dynamics, along with estimates of net land ice changes, their associated static-equilibrium eﬀects and GIA.
Here we expand upon past efforts to project LSL globally. First, we present a complete probability distribution. This is critical for planning purposes; the likely (67% probability) ranges presented in AR5 and many other previous efforts provide no information about the highest 17% of outcomes, which may well be key to risk management. Second, we indicatively extend our projections to 2200, in order to inform both decision-making regarding long-term infrastructure investment decisions and their longer term land use consequences, and also greenhouse gas mitigation decisions in the context of long-term sea-level rise commitments [Levermann et al., 2013]. Finally, using a Gaussian process model [Kopp, 2013] of historical tide-gauge data [Holgate et al., 2013], we include probabilistic estimates of local non-climatic factors.
We first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.
Methods
LSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.
Figure 1: Logical ﬂow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.


We first present our framework and projections for selected locations (projections for all tide-gauge locations are included in the Supporting Information), then assess the effects of sea-level rise on coastal flooding risk at these locations. Throughout, we seek to employ transparent assumptions and an easily replicable methodology that is useful for risk assessment and can be readily updated with new information.
Methods
LSL projections require the projection and aggregation of the individual components of sea-level change [e.g., Milne et al., 2009] at each site of interest. Here, we project three ice sheet components (the Greenland Ice Sheet, GIS; the West Antarctic ice sheet, WAIS; and the East Antarctic ice sheet, EAIS); glacier and ice cap (GIC) surface mass balance (SMB); global mean thermal expansion and regional ocean steric and ocean dynamic effects (which we collectively call oceanographic processes); land water storage; and long-term, local, non-climatic sea-level change due to factors such as GIA, sediment compaction, and tectonics. In our base case, we allow correlations, derived from the SMB model, between different mountain glaciers but otherwise assume that, conditional upon a global radiative forcing pathway, the components are independent of one another. To calculate GSL and LSL probability distributions, we employ 10,000 Latin hypercube samples from time-dependent probability distributions of cumulative sea-level rise contributions for each of the individual components. The sources of information used to develop these distributions are described below and summarized in Figure 1.
Figure 1: Logical ﬂow of sources of information used in local sea-level projections. GCMs, global climate models; GIC, glaciers and ice caps; SMB: surface mass balance.
We construct separate projections for three representative concentration pathways (RCPs): RCP 2.6, RCP 4.5, and RCP 8.5 [Meinshausen et al., 2011], which correspond respectively to likely global mean temperature increases in 2081 – 2100 of 1.9-2.3˚C, 2.0-3.6˚C, and 3.2-5.4˚C above 1850-1900 levels [Intergovernmental Panel on Climate Change, 2013]. We do not consider RCP 6.0, as 21st-century sea-level rise projections for this pathway are nearly identical to those for RCP 4.5, and few CMIP Phase 5 (CMIP5) model runs for RCP 6.0 extend beyond 2100 [Taylor et al., 2012]. The RCPs do not represent socioeconomic scenarios but can be compared to emissions in no-policy socioeconomic projections such as the Shared Socioeconomic Pathways (SSPs) [O’Neill et al., 2014]. Radiative forcing in RCP 6.0 in the second half of the century is comparable to that in the lowest emissions SSP (SSP 1), while RCP 8.5 is above four of the SSPs but below the highest-emission SSP [Riahi, 2013]. Thus, RCP 8.5 can be viewed as corresponding to high-end business-as-usual emissions and RCP 4.5 as a moderate mitigation policy scenario. RCP 2.6 requires net-negative global emissions in the last quarter of the 21st century, implying a combination of intensive greenhouse gas mitigation and at least modest active carbon dioxide removal.
Ice Sheets
Our projections of 21st-century changes in mass balance of GIS and the Antarctic ice sheet (AIS) are generated by combining the projections of AR5 and the expert elicitation of Bamber and Aspinall [2013] [BA13]. AR5 is used to characterize median and likely ranges of sea-level change, while BA13 is used to calibrate the shape of the tails (Supporting Information Figure S1 and Table S1).
Figure S1:  Exceedance probabilities for GIS (left) and AIS (right) mass loss between 2000 and 2100 in RCP 8.5, in meters equivalent sea level. Green curves are derived from Bamber and Aspinall [2013], blue curves from the median and likely range of AR5, and red curves are a hybrid based on the green curves but shifted and scaled to match the median and likely range of AR5.
Table S1: Ice sheet mass loss in sensitivity cases (cm equivalent sea level, RCP 8.5 in 2100)
cm
GIS
AIS
50
17-83
5-95
0.5-99.5
99.9
50
17-83
5-95
0.5-99.5
99.9
Default
14
8-25
5-39
3-70
<95
4
-8-15
-11-33
-14-91
<155
AR5
14
8-25
5-39
3-68
<95
4
-8-15
-16-23
-26-35
<40
BA
14
10-21
9-29
7-48
<65
14
2-41
-2-84
-4-220
<375
Alt. Corr.
14
8-25
5-39
3-70
<95
4
-8-15
-12-33
-14-85
<185
AR5 separately assesses AIS and GIS mass balance changes driven by SMB and ice sheet dynamics. For ice sheet dynamics, AR5 determined that there was insufficient knowledge to differentiate between RCP 2.6 and 4.5 (and 8.5 for AIS). Projections of total ice sheet mass loss – given as a likely cumulative sea-level rise contribution – are thus partially scenario-independent. BA13 probed more deeply into the tail of ice sheet mass loss projections, inquiring into the 5th-95th percentile ranges of GIS, EAIS, and WAIS. However, BA13 does not differentiate between SMB and ice sheet dynamics or between RCPs.
We reconcile the projections as described in the Supporting Information. For AIS, the reconciled RCP 8.5 projections (median/likely/very likely [90% probability] of 4/−8 to 15/−11 to 33 cm) are significantly reduced in range relative to BA13 (median/likely/very likely of 13/2 to 41/−2 to 83 cm); for GIS, the reconciled projections are almost identical to those based directly on AR5 and have a likely range (8 – 25 cm) close to the very likely range estimated from BA13 (9-29 cm) (Supporting Information Table S1).
Ice sheet mass balance changes do not cause globally uniform sea-level rise. To account for the differing patterns of static-equilibrium sea-level rise caused by land ice mass loss, we apply sea-level fingerprints, calculated after Mitrovica et al. [2011] (Supporting Information Figure S2). These ﬁngerprints assume mass loss from each ice sheet is uniform; in most regions, the error introduced by this assumption is minimal [Mitrovica et al., 2011].
Figure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.
Glacier and Ice Caps
For each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).
The projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.
Oceanographic Processes
Projections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.


Figure S2: Static equilibrium sea-level fingerprints employed for (a) GIS, (b) EAIS, (c) WAIS, and (d) median glaciers and ice cap mass loss. Units are meters of local sea level change per meter global sea level change.
Glacier and Ice Caps
For each RCP, we generate mass balance projections for 17 different source regions of glaciers and ice caps (described in the Supporting Information). For each source region, we employ a multivariate t-distribution of ice mass change with a mean and covariance estimated from the process model results of Marzeion et al. [2012]. Each source region has a distinct static-equilibrium sea-level fingerprint, calculated in the same fashion as for ice sheet mass loss (Supporting Information Figure S2).
The projections based on Marzeion et al. [2012] are modestly narrower and have a slightly higher median than those of AR5: a likely range of 9-15 cm from non-Antarctic glaciers by 2100 for RCP 2.6 (vs. 4-16 cm for AR5) and 14-21 cm for RCP 8.5 (vs. 9-23 cm for AR5). We opt for the Marzeion et al. [2012] projections because of the availability of disaggregated output representing projections based on a suite of global climate models (GCMs) for each source region.
Oceanographic Processes
Projections of changes in GSL due to thermal expansion and in LSL due to regional steric and dynamic effects are based upon the CMIP5 GCMs. In particular, we employ a t-distribution with the mean and covariance of a multi-model ensemble constructed from the CMIP5 archive (Supporting Information Figures S3 and S4, Table S2). Values used are 19-year running averages. For each model, we use a single realization. The sea-level change at each tide-gauge location is assumed to be represented by the nearest ocean grid cell value of each GCM.
Figure S3: CMIP5 thermal expansion projections (left) and after smoothing and drift correction (right). Black = GSL curve of Church and White [2011]. Dashed = mean/max/min of GSL with glacier and ice cap projections removed.
Figure S4: Map of (top) median and (middle) width of likely range of ocean dynamic contribution to sea-level rise between 2000 and 2100 for RCP 8.5 (not including the contribution of global mean thermal expansion). (Bottom) Number of model projections retained at each site in RCP 8.5.
Table S2: CMIP5 models used for thermal expansion and oceanographic processes
The horizontal resolution of the CMIP5 ocean models is ~1 degree. In these coarse-resolution models, sea level at the coast may differ from the open ocean due to local biases driven by unresolved processes (e.g., coastal currents) and bathymetry [Holt et al., 2009] or via the influence of small-scale processes (e.g., eddies) on larger-scale steric and dynamic changes [Penduff et al., 2010, 2011]. Although there is some evidence that climate-forced trends in sea level are not sensitive to resolution [Penduff et al., 2011; Suzuki et al., 2005], higher-resolution coastal modeling is required to determine whether the probabilities estimated at the GCM grid scale are significantly changed by sub-grid processes.
GCM projections exhibit a range of late nineteenth-century sea-level behavior largely attributable to model drift. Uncorrected GCM-based estimates of the rate of mean global sea-level change from 1861 to 1900 range from −0.4 to +1.1 mm/yr. To correct for global-mean model drift, we apply a linear correction term to each model. The linear correction adjusts the rate of GSL rise over 1861-1900 to match a rate of thermal expansion estimated by removing the multi-model average of GIC mass loss from Marzeion et al. [2012] from the GSL curve of Church and White [2011]. After correction, the rate of thermal expansion over 1861–1900 is 0.3 ± 0.9 (2σ) mm/yr (Supporting Information Figure S3).
Consistent with AR5’s judgment that the 5th-95th percentile of CMIP5 output represents a likely (67% probability) range for global mean thermal expansion, we multiply the standard deviation of the t-distribution for oceanographic processes by 1.7.
Land Water Storage
Following the approach of Rahmstorf et al. [2012], we estimate GSL change due to changes in water storage on land based upon the relationship between such changes and population (Supporting Information Figure S5). For changes in reservoir storage, we use the historical cumulative impoundment estimate of Chao et al. [2008]. We assume that reservoir construction is a sigmoidal function of population:
\[I = a \times \mathrm{erf}\left(\frac{{P(t) - b}}{{c}}\right) + I_0\]
where I is impoundment expressed in mm equivalent sea level (esl), P(t) is world population as a function of time, and the remaining variables are constants. The results imply a maximum additional impoundment of 6 mm (esl) on top of the current 30 mm; based on the discrepancy between the “nominal” and “actual” impoundment estimated by Chao et al. [2008], we conservatively allow a 2σ error in this estimate of ±50 %.
For the rate of groundwater depletion, we fit the estimates of Wada et al. [2012] and Konikow [2011] as linear functions of population, forced through the origin. The estimate of Wada et al. [2012] is based on fluxes estimated from a global hydrological model of groundwater recharge and a global database of groundwater abstraction, while that of Konikow [2011] uses a range of approaches depending on the data available for each aquifer. We take the mean and standard deviation of the two slopes estimated (0.06 ± 0.02 mm/yr/billion people) and allow an additional 2 error of ±50%, a level based upon the errors estimated by the authors of the two impoundment studies. In our main calculation, we do not include the water resource assessment model-based estimate of Pokhrel et al. [2012], which is about a factor of three higher than the other two estimates; we include this estimate in a sensitivity case.
We employ population projections derived from United Nations Department of Economics and Social Aﬀairs [2014]. We treat population as distributed following a triangular distribution, with the median, minimum, and maximum values corresponding to the middle, low, and high U.N. scenarios (10.9, 6.8, and 16.6 billion people in 2100, respectively). For scenarios in which population declines, we allow some reduction in impoundment, but do not allow impoundment to decrease below its year 2000 level.
Glacial Isostatic Adjustment, Tectonics, and Other Non-Climatic Local Effects
GIA, tectonics, and other non-climatic local effects that can be approximated as linear trends over the twentieth century are assumed to continue unchanged in the 21st and 22nd centuries. This is a good assumption for GIA, but imperfect for other processes. Tectonic processes can operate unsteadily, and a linear trend estimated from the historical record may be inaccurate. LSL rise related to fluid withdrawal is subject to engineering, resource depletion, market factors and policy controls, and might either increase or decrease in the future relative to historical levels. In addition, the trend estimates can encompass slow ocean dynamic changes that are close to constant over the historical record but could change in the future. Nonetheless, for a global analysis, assuming the continuation of observed historical changes offers the best currently feasible approach.
We estimate historical rates using a spatiotemporal Gaussian process model akin to that employed by Kopp [2013]. Sea level as recorded in the tide-gauge records (Permanent Service for Mean Sea Level, Tide-gauge data, retrieved from http://www.psmsl.org/data/obtaining/, accessed January 2014) is represented as the sum of three Gaussian processes: (1) a globally uniform process, (2) a regionally varying, temporally linear process, and (3) a regionally varying, temporally autocorrelated non-linear process. We allow for spatial non-stationarity in the Gaussian process prior by optimizing the hyperparameters separately for each of 15 regions (Supporting Information Table S4 and Figure S6). The posterior estimate of the second (linear) process at each site is used for forward projections. Mathematical details are provided in the Supporting Information.
Table S4: Optimized model hyperparameters by region
Figure S6: Tide gauge sites and regions used in background rate calculation.
Post-2100 Projections