Analyzing model output
This study considers the dynamic sea level (DSL), which is defined as the mean sea level above the geoid due to ocean dynamics (Gregory et al. 2019):
ζ = η − η′. (1)
Here ζ is the variable “zos” according to the CMIP terminology (Griffies et al. 2016), η, which is named “sterodynamic sea level,” is the sea surface height relative to a reference geopotential surface, and η′ denotes a global mean (Gregory et al. 2019). Hence, DSL change (Δζ) should have a zero global mean by definition. We therefore subtracted the global mean from each input field.
As we are interested in future sea level change, our work focuses on the dynamic sea level change (Δζ) pattern, which is calculated from the difference between the DSL change in SSP5-8.5 forcing scenario (Δηs) relative to the DSL change in the historical simulation (Δηh):
Δζ = Δηs − Δηh. (2)
Considering that changes in circulation and changes in wind stress in principle are the key drivers of these changes, we also calculated changes in the barotropic streamfunction ψ, changes in surface wind stress, and variation in the meridional overturning circulation and analyzed their differences as function of model resolution.
The Sverdrup streamfunction was estimated using wind stress data based on the Sverdrup relation (Sverdrup 1947). The Sverdrup transport was integrated zonally along a latitude (y) from the eastern boundary (xe) to each zonal location (x) of the basin as follows:
ψSv = 1/(βρ) ∫^x_{xe} curl(τ) dx′, (3)
where β denotes the meridional derivative of the Coriolis parameter, ρ is the mean density of the ocean, and curl(τ) denotes the wind stress curl.
To analyze the meridional displacement of gyres, the mean latitude y of the barotropic streamfunction is calculated according to θ = ∫ψ × y dx dy / ∫ψ dx dy. (4)
We consider the zero contour as the boundary of each gyre and consider positive (negative) barotropic streamfunction values for subtropical (subpolar) gyre. The contours between the minimum and maximum transport (positive contours) in the Drake Passage were considered to calculate the mean central latitude of ACC transport.
Significance and trend
Assuming that the variance remains unchanged under climate forcing conditions, the 95% significance of the difference of changes between the resolutions ER and HR was determined according to the formula,
√(2*σ^2_{ER}/N_{ER} + 2*σ^2_{HR}/N_{HR}) × t_{95%}, with t_{95%} the Student t value, N_{ER} and N_{HR} are the respective numbers of members, and σ^2_{ER} and σ^2_{HR} are the variances of the ER and HR control simulations, respectively. The factor 2 accounts for the fact that the changes have twice the variance of the fields they are calculated from. A similar method was applied to calculate the error bar or envelope, (1/√N)√2σ^2_{ER} × t_{95%} for the ensemble mean changes [see von Storch and Zwiers (2002) for more details]. The linear least squares fitting was used to calculate the yearly average time series trend. The analyses were performed using CDO and NCL software (NCL 2019).
Commonalities of sea level changes in MPI-ESM
Over the past years, the global ocean has accounted for around 91% of anthropogenically induced Earth’s heat content increase, resulting in an observed thermal expansion and associated sea level rise of about 0.54 (0.40–0.68) mm yr−1 over the years from 1901 to 2018 (Fox-Kemper et al. 2021). In contrast, the simulated thermal expansion in IPCC AR6 leads to sea level rise of 30 (24–36) cm under SSP5-8.5 for the year 2100 relative to a baseline of 1995–2014. From the MPI- ESM model simulations we can infer a comparable global mean thermosteric sea level (GMTSL) rise (Fig. 1) of 30.30, 30.06, and 31.95 cm at the end of the twenty-first century relative to the 1950s for ER, HR, and LR, respectively. Over the period 1901–2018, changes are around 60 mm and compare well with the observed change of 63.2 mm due to thermal expansion (Fox-Kemper et al. 2021). The average simulated rate of thermosteric sea level rise due to global ocean heating for the SPP5-8.5 scenario is 3.31 mm yr−1 in ER, 3.34 mm yr−1 in HR, and 3.51 mm yr−1 in LR between 2030 and 2099.
Figure 1: Global 12-month running mean (a) sea surface temperature and (b) thermosteric sea level change for MPI-ESM-ER, MPI-ESM-HR, and MPI-ESM-LR, relative to the 1950s. The purple line in (a) represents a 12-month running mean of respective global mean HadISST values.
Figure 1 also compares the increase in thermosteric sea level rise with the respective increases in global SST. On global average, both curves suggest an equivalent increase in thermosteric sea level rise of 0.11 m per 1°C of SST increase. However, SST curves are considerable noisier and, in that sense, can only be considered a very crude proxy for thermosteric sea level rise. This holds especially for individual ensemble members and should be true also for the real world. We note that a respective correspondence cannot be expected to hold on regional scale due to the temperature dependence of the thermosteric expansion coefficient and the influence of salinity.
The common global pattern of LR, HR, and ER for the changes in DSL (in m), the barotropic streamfunction (BSF; Sv; 1 Sv ≡ 106 m3 s−1), and the wind stress (N m−2) are discussed in this section. These changes between the patterns over the SSP5-8.5 years 2080–99 relative to the historical simulation (years 1995–2014) are shown in Fig. 2. We will discuss how the models differ from one another on regional scale in the following section.
Figure 2: Anomalies of (a)–(c) dynamic sea level (m), (d)–(f) barotropic streamfunction (Sv), (g)–(i) sea surface temperature (°C), and (j)–(l) wind stress (N m−2), for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER between the SSP5-8.5 averaged over the period 2080–99 and the historical period averaged over the years 1995–2014.
The DSL is a helpful tool for analyzing the ocean processes contributing to sea level changes due to the close link between the DSL and the ocean circulation through the geostrophic relation. According to Figs. 2a–c, sea level changes are not homogeneous in the global ocean but show diverse regional patterns. At the end of the century, the respective sea level change leads to a dipole pattern in the North Atlantic with generally increasing sea level north of the Gulf Stream (in the southern part of the subpolar gyre) and a decrease in the subtropical gyre. An opposite dipole pattern exists in the North Pacific, where sea level is higher south of the Kuroshio (in the subtropical region) and lower farther to the north (in the subpolar region). In the Southern Ocean, the ridge-like pattern is associated with a sea level increase north of ∼50°S and decrease south of ∼50°S. The aforementioned sea level change patterns have also been reported previously, such as Chen et al. (2019), Church et al. (2013a,b), Couldrey et al. (2021), Fox-Kemper et al. (2021), Gregory et al. (2016), and Lyu et al. (2020), and common to all the models. As in previous studies (Prandi et al. 2012; Rose et al. 2019; Xiao et al. 2020), the highest sea level rise is also found in our models in the Arctic Ocean.


Figure 2: Anomalies of (a)–(c) dynamic sea level (m), (d)–(f) barotropic streamfunction (Sv), (g)–(i) sea surface temperature (°C), and (j)–(l) wind stress (N m−2), for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER between the SSP5-8.5 averaged over the period 2080–99 and the historical period averaged over the years 1995–2014.
The DSL is a helpful tool for analyzing the ocean processes contributing to sea level changes due to the close link between the DSL and the ocean circulation through the geostrophic relation. According to Figs. 2a–c, sea level changes are not homogeneous in the global ocean but show diverse regional patterns. At the end of the century, the respective sea level change leads to a dipole pattern in the North Atlantic with generally increasing sea level north of the Gulf Stream (in the southern part of the subpolar gyre) and a decrease in the subtropical gyre. An opposite dipole pattern exists in the North Pacific, where sea level is higher south of the Kuroshio (in the subtropical region) and lower farther to the north (in the subpolar region). In the Southern Ocean, the ridge-like pattern is associated with a sea level increase north of ∼50°S and decrease south of ∼50°S. The aforementioned sea level change patterns have also been reported previously, such as Chen et al. (2019), Church et al. (2013a,b), Couldrey et al. (2021), Fox-Kemper et al. (2021), Gregory et al. (2016), and Lyu et al. (2020), and common to all the models. As in previous studies (Prandi et al. 2012; Rose et al. 2019; Xiao et al. 2020), the highest sea level rise is also found in our models in the Arctic Ocean.
Many changes in DSL displayed in Figs. 2a–c can be associated with changes in the vertically integrated large-scale circulation as depicted by BSF (Figs. 2d–f). In the North Atlantic, circulation in subpolar regions north of the Gulf Stream and Labrador Sea and the subtropical gyre weaken, whereas the circulation southeast of Greenland strengthens (negative BSF anomalies in high latitude). The latter is accompanied by a smaller DSL. However, the opposite happens in the North Pacific, where subpolar gyre and the Kuroshio region (northern part of subtropical gyre) strengthens, while the southern part of subtropical gyre weakens. A band of positive streamfunction north of Gulf Stream could possibly indicate the poleward shift of the North Atlantic Subtropical Gyre. Moreover, Southern Ocean circulation strengthens between 40° and 50°S in all models (Figs. 2d–f).
While almost every corner in the world is heating up, a cooling temperature patch, known as warming hole (aka cold blob), is identified in the vicinity of southeast Greenland (Figs. 2g–i). This warming hole feature, however, appears to be north of the warming hole stated in earlier studies in response to warming (e.g., Chemke et al. 2020; Drijfhout et al. 2012; Gervais et al. 2018; Menary and Wood 2018). Together with the warming hole, a patch of DSL decline (Figs. 2a–c), and a reinforced high latitude circulation (Figs. 2d–f) are identified in the same subpolar region in all configurations. Numerous previous studies have discussed the occurrence of the warming hole as a result of a weakening Atlantic meridional overturning circulation (AMOC) (such as Caesar et al. 2018; Drijfhout et al. 2012; Gervais et al. 2018; Keil et al. 2020; Menary and Wood 2018; Rahmstorf et al. 2015).
The variation in the BSF field is linked to the changes in the wind stress curl field by the Sverdrup relation. However, it might also reflect the changes in the interior density gradients and/or interactions with sloping bottom bathymetry (e.g., Yeager 2015). We examine the Sverdrup relation in the North Atlantic and North Pacific Oceans later in section 4. A distinct feature of wind stress changes in the models is the strengthening of the westerly wind in the Southern Ocean at the end of the twenty-first century (Figs. 2j–l). Over most of the Pacific Ocean except the tropical North Pacific wind stress strengthens. Changes over the Atlantic are less clear, leading mostly to weakened wind stress, except for the eastern subtropical North Atlantic.
Discrepancies of regional sea level change in MPI-ESM
In the following we will discuss the detailed resolution dependence of the time mean changes from historical to SSP5-8.5 on the model resolution separately for the North Atlantic, the North Pacific, and the Southern Ocean.
North Atlantic
DSL change in the subpolar gyre region is characterized by two distinct features: a decrease in the basins southeast of Greenland and an increase in the rest of the subpolar gyre (Figs. 3a–c). Statistically significant differences at 95% are marked by dots in the spatial pattern difference and by nonoverlapping error bars in the zonal averages. This DSL decrease over the basins southeast of Greenland (the Irminger Sea and Icelandic Basin) is smallest in ER and largest in LR (by the magnitude of ∼0.2 m see in Figs. 3a,c,d,e). The increase in the Labrador Sea and farther south until north of the Gulf Stream is also smaller in ER than HR and LR (by the magnitude of ∼0.16 m see in Figs. 3d,e). The changes southeast of Greenland dominate the zonal mean (north of 50°N) of DSL, indicating a prominent decrease in LR and almost no change in HR (Fig. 4a). In contrast, ER shows an overall sea level increase in the northern part of the subpolar gyre, pointing to a smaller decline in the basins southeast of Greenland (Figs. 3c,d, 4a). In the southern part of the subpolar gyre (between 40° and 50°N), the MPI-ESM models show a DSL increase with the largest rise in HR (Fig. 4a). The increase in HR can be noticed in the spatial pattern by a negative and positive sign of the difference north of the Gulf Stream (north of 40°N) in Figs. 3e and 3f, respectively.
Figure 3: North Atlantic differences of (a)–(f) dynamic sea level (m) and (g)–(l) wind stress (N m−2); panels (a)–(c) and (g)–(i) illustrate the anomalies of the SSP5-8.5 (2080–99) average relative to the historical simulation, averaged over 1995–2014 for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); panels (d)–(f) and (j)–(l) illustrate the differences of the anomalies between the models [ER minus LR in (d) and (j), ER minus HR in (e) and (k), and HR minus LR in (f) and (l)]. The contours represent the historical mean (1995–2014; contour interval is 0.1 m). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). All projections were interpolated onto the same grid prior to computing differences of the anomalies.
Figure 4: North Atlantic (a) zonal mean sea surface height (m); (b) zonal mean barotropic streamfunction (Sv); (c) zonal mean zonal wind stress (N m−2) anomalies, each for the time mean differences over historical simulation and SSP5-8.5 for ER, HR, and LR, respectively. Error bar envelopes represent two standard deviations.


Figure 3: North Atlantic differences of (a)–(f) dynamic sea level (m) and (g)–(l) wind stress (N m−2); panels (a)–(c) and (g)–(i) illustrate the anomalies of the SSP5-8.5 (2080–99) average relative to the historical simulation, averaged over 1995–2014 for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); panels (d)–(f) and (j)–(l) illustrate the differences of the anomalies between the models [ER minus LR in (d) and (j), ER minus HR in (e) and (k), and HR minus LR in (f) and (l)]. The contours represent the historical mean (1995–2014; contour interval is 0.1 m). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). All projections were interpolated onto the same grid prior to computing differences of the anomalies.
Figure 4: North Atlantic (a) zonal mean sea surface height (m); (b) zonal mean barotropic streamfunction (Sv); (c) zonal mean zonal wind stress (N m−2) anomalies, each for the time mean differences over historical simulation and SSP5-8.5 for ER, HR, and LR, respectively. Error bar envelopes represent two standard deviations.
These changes in sea level also reflect changes in circulation indicated by the vertically integrated flow (displayed in Figs. 6a–c). The cyclonic circulation in southeast of Greenland strengthens in LR and somewhat less so in HR. It is even lesser in ER (Figs. 6a–c), as does decline in sea level. Subpolar gyre circulation weakens in the Labrador Sea and the southern part of the gyre. In contrast, the weakening is considerably larger in the ER model. A weakening subpolar gyre as seen in ER was also reported for the circulation changes from the 1990s to the 2000s observed by altimetry data (Lee et al. 2010; Häkkinen and Rhines 2004, 2009), with inconclusive attribution to whether these changes remain part of natural climate variability or are already a sign of a long-term trend. Nevertheless, the circulation changes can have important consequences for the distribution of water masses as a weakening subpolar gyre can lead to an increasing transport of warm and salty Atlantic water into the Nordic seas during the historical period (Hátún et al. 2005) and significant reduction in Labrador Sea deep convection.
Many previous studies have also highlighted the relation between weakening AMOC and DSL changes in the North Atlantic (Bouttes et al. 2014; Chen et al. 2019; Fox-Kemper et al. 2021; Hu et al. 2011; Levermann et al. 2005; Lyu et al. 2020; Pardaens et al. 2011; Yin et al. 2009, 2010). The projected change of the AMOC is likely to depend on the model resolution and therefore impact DSL differently. The pattern of the AMOC change is nearly identical to its mean AMOC (Figs. 5a–c), indicating a consistent weakening of all branches from historical to SSP5-8.5 by about one-third of its strength. The overlaid contours of historical mean in Figs. 5a–c provide a comparison with its anomalies. Similar to the DSL change, the warming hole feature becomes smaller in size with improved horizontal resolution, especially in ER compared to HR (Figs. 2h,i and 3b,c), whereas the AMOC slowing (Fig. 5g) does not differ much in the final years despite the smaller trend in LR at 26°N. Although, the AMOC weakening is larger in LR than in HR and ER between 30° and 60°N centered around 1500-m depth (Figs. 5a,d,f). This puts a question mark to studies linking the strength of the warming hole directly to a slowing down of the AMOC (Caesar et al. 2018, using observations; Menary and Wood 2018; Rahmstorf et al. 2015). In this sense, Keil et al. (2020) have argued for multiple drives of the warming hole feature. During the historical period, the anthropogenically forced changes of both the gyre and overturning circulation induce heat transport increase out of the subpolar region to the Greenland–Iceland–Norwegian (GIN) Seas and then farther to the Arctic, contributing to the warming hole feature in the North Atlantic (Keil et al. 2020).
Figure 5: Anomalies of the Atlantic meridional overturning circulation streamfunction (Sv) for (a) MPI-ESM-LR, (b) MPI-ESM-HR, and (c) MPI-ESM-LR, each for the time mean differences over historical simulation and SSP5-8.5. Differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean (1995–2014; contour interval is 3 Sv). The contour colors denote solid red for the positive values, green line for the zero contour, and dash blue for the negative values. In all panels stippling indicates statistically significant differences (95% confidence level). (g) Time series of 3-yr running mean AMOC streamfunction (Sv) relative to 1950s at 1000 m and 26°N. Dashed lines represent a linear trend over the period 2030–99 for LR, HR, and ER, plotted in green, red, and blue, respectively.
In the subpolar gyre, heat transport is driven by both gyre and overturning circulation. The strengthened barotropic circulation in high latitudes, where the northern part of the subpolar region and GIN Seas (Figs. 6a–c) can similarly contribute to the development of the warming hole and the associated sea level decline. Conversely, the AMOC effect is mitigated by a weaker strengthening of the circulation in vicinity of Greenland in ER (Figs. 6c,e) leading to a smaller DSL decrease and a smaller-scale warming hole in comparison to HR. The DSL decline and strengthening subpolar circulation are larger in LR than in HR and ER (Figs. 6d,f), despite the warming hole in LR being smaller (Fig. 2g and Fig. S1 in the online supplemental material). This could be because LR has a weaker GIN Seas circulation (Figs. 6a,d,f), which could indicate smaller heat transport out of the subpolar region. Future DSL change in the subpolar North Atlantic and the formation of the warming hole are hence resolution dependent.
Figure 6: Anomalies of (a)–(c) barotropic streamfunction and (g)–(h) Sverdrup streamfunctions for the SSP5-8.5 (2080–99) average relative to the historical simulation, averaged over 1995–2014 in North Atlantic for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); the differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean [1995–2014; contour intervals are 2 Sv in (a)–(c) and 5 Sv in (g)–(h)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level.
Curry et al. (1998), Böning et al. (2006), and Häkkinen et al. (2011) show the impact of the surface wind stress on both subpolar gyre variability and the strength. The decline of the surface wind stress over the subpolar gyre region could result in the spindown of the subpolar gyre circulation, leading to sea level increase (Chafik et al. 2019; Putrasahan et al. 2019). A noticeable difference between eddy-rich and lower resolutions is that wind stress reduces in ER over the subpolar North Atlantic (50°–65°N) in contrast to LR and HR (Figs. 3j,k), for which wind stress intensify (Fig. 4c). These changes agree with the noted spindown of the subpolar gyre in ER and the strengthened gyre circulation in LR and HR (Figs. 6a–c). However, the extensive spread in zonal mean zonal wind stress anomalies implies a minor resolution dependency in subpolar gyre region (Fig. 4c) at the 95% significant level.


Figure 6: Anomalies of (a)–(c) barotropic streamfunction and (g)–(h) Sverdrup streamfunctions for the SSP5-8.5 (2080–99) average relative to the historical simulation, averaged over 1995–2014 in North Atlantic for MPI-ESM-LR in (a) and (g), MPI-ESM-HR in (b) and (h), and MPI-ESM-ER in (c) and (i); the differences of the anomalies between the models: (d) ER minus LR, (e) ER minus HR, and (f) HR minus LR. The contours represent the historical mean [1995–2014; contour intervals are 2 Sv in (a)–(c) and 5 Sv in (g)–(h)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level.
Curry et al. (1998), Böning et al. (2006), and Häkkinen et al. (2011) show the impact of the surface wind stress on both subpolar gyre variability and the strength. The decline of the surface wind stress over the subpolar gyre region could result in the spindown of the subpolar gyre circulation, leading to sea level increase (Chafik et al. 2019; Putrasahan et al. 2019). A noticeable difference between eddy-rich and lower resolutions is that wind stress reduces in ER over the subpolar North Atlantic (50°–65°N) in contrast to LR and HR (Figs. 3j,k), for which wind stress intensify (Fig. 4c). These changes agree with the noted spindown of the subpolar gyre in ER and the strengthened gyre circulation in LR and HR (Figs. 6a–c). However, the extensive spread in zonal mean zonal wind stress anomalies implies a minor resolution dependency in subpolar gyre region (Fig. 4c) at the 95% significant level.
Dynamically, the simplest concept for the barotropic circulation is the balance between wind stress curl and the advection of vorticity which is described by the Sverdrup streamfunction. For the time-mean circulation the validity of the concept has been approved for interior of the subtropical circulation (e.g., Sonnewald et al. 2019; Wunsch and Roemmich 1985; Wunsch 2011). The degree of the Sverdrup concept’s validity to describe temporal changing circulation changes was previously demonstrated (e.g., Willebrand et al. 1980; Hautala et al. 1994; Stammer 1997; Morris et al. 1996, Thomas et al. 2014) and an agreement was found even outside of the subtropics. The Sverdrup streamfunction was calculated in the North Atlantic and North Pacific (Figs. 6, 9) to quantify the impact of the wind stress curl. The weakening of the North Atlantic Subpolar Gyre between 50° and 60°N can be explained by the weakening of surface wind stress curl in ER (Fig. 6i). Despite the strengthened circulation (Figs. 6a,b, 4b) and slightly intensified surface wind stress (Fig. 4c) in LR and HR, their curl weakens in both models (Figs. 6g,h). The changes in subpolar gyre circulation do not entirely concur with the Sverdrup dynamics in HR, although HR and ER have the same T127/L95 atmospheric component.
All three resolutions show a weakening subtropical gyre (Figs. 6a–c), associated with a negative DSL, and just north of the Gulf Stream a band of positive DSL (Figs. 3a–c) that signifies the reduction of Gulf Stream transport associated with the weakening subtropical gyre and the declining AMOC (Fig. 5g). The weakening of the Gulf Stream under warming conditions during the twenty-first century (Yang et al. 2016) could be related to the sea level changes in the North Atlantic associated with higher sea level rise north of the Gulf Stream (Bouttes et al. 2014; Chen et al. 2019; Levermann et al. 2005; Yin et al. 2009). The argument requires that the DSL is lower than the global mean such that a relaxation locally leads to a DSL rise; the same applies to the barotropic streamfunction.
ER shows the largest DSL reduction in the subtropical gyre (Figs. 3d,e), although a weakening of wind stress is smaller south of 40°N (Figs. 3j,k, 4c). However, the spindown of the subtropical gyre is larger in the ER compared to HR and LR (Figs. 6d,e, 4b). There is no considerable difference in the AMOC slowdown (Figs. 5e,g) between HR and ER. The AMOC deceleration is larger by 0.25 Sv in ER than in HR and 1.25 Sv than in LR (Fig. 5g) by 2100 at 26°N. The AMOC linear trend, calculated over 1995–2099, amounts to −0.061 Sv yr−1 for ER, −0.059 Sv yr−1 for HR, and −0.052 Sv yr−1 for LR. Despite the similar magnitude of AMOC decline at 26°N in HR and ER, spindown of the subtropical gyre and the DSL reduction is larger in ER than in HR.
In addition to the effect of AMOC slowdown, changes in wind stress could also be responsible for the sea level reduction in the subtropical gyre south of the Gulf Stream (40°N), as suggested by Bouttes et al. (2012). The Sverdrup circulation of the North Atlantic Subtropical Gyre weakens dramatically in all three models. Moreover, the wind stress weakens south of 40°N in the zonal mean, with a stronger decline in HR and LR relative to the ER (Fig. 4c). The associated Sverdrup circulation is illustrated in Figs. 6g–i for comparison with the gyre changes as illustrated by the barotropic streamfunction (Figs. 6a–c, 4b). Additionally, the contours representing the present-day state are superimposed over the streamfunction anomalies to better visualize the shifting and changing of gyres. The wind stress curl changes tend to weaken the gyre circulation in the southern part of the North Atlantic Subtropical Gyre, whereas the northern part experiences a strengthening in all model versions (Figs. 6g–i). This suggests a poleward shift of the weakening subtropical gyre and Gulf Stream (Figs. 6a–c).
North Pacific
In contrast to the North Atlantic, in ER the DSL increases south of the Kuroshio Extension (over the subtropical gyre) and decreases farther to the north (in the subpolar gyre, Fig. 7a). This characteristic North Pacific dipole pattern is opposite to that in the North Atlantic and its axis is located along the steep DSL gradient associated with the Kuroshio causing further steepening of the frontal zone. In the southern part of the subpolar gyre, the DSL reduction is much greater in ER and HR than in LR (Figs. 7d,f), though there is no substantial difference between HR and ER (Fig. 7e). The DSL decreases in the lower resolutions along the eastern boundary of the North Pacific (Figs. 7a,b), while ER shows an increase in the Gulf of Alaska (Figs. 7c). The discrepancies between the models are negligible in the northern part of the subpolar gyre (Figs. 7d–f). In the subtropical gyre, the DSL increase is larger in ER compared to the LR and HR (Figs. 7d,e), and in HR than in LR (Fig. 7f), along with a significant increase east of Japan in the eddy-rich model (Fig. 8a).
Figure 7: As in Fig. 3, but for the North Pacific.
Figure 8: As in Fig. 4, but for the North Pacific.


North Pacific
In contrast to the North Atlantic, in ER the DSL increases south of the Kuroshio Extension (over the subtropical gyre) and decreases farther to the north (in the subpolar gyre, Fig. 7a). This characteristic North Pacific dipole pattern is opposite to that in the North Atlantic and its axis is located along the steep DSL gradient associated with the Kuroshio causing further steepening of the frontal zone. In the southern part of the subpolar gyre, the DSL reduction is much greater in ER and HR than in LR (Figs. 7d,f), though there is no substantial difference between HR and ER (Fig. 7e). The DSL decreases in the lower resolutions along the eastern boundary of the North Pacific (Figs. 7a,b), while ER shows an increase in the Gulf of Alaska (Figs. 7c). The discrepancies between the models are negligible in the northern part of the subpolar gyre (Figs. 7d–f). In the subtropical gyre, the DSL increase is larger in ER compared to the LR and HR (Figs. 7d,e), and in HR than in LR (Fig. 7f), along with a significant increase east of Japan in the eddy-rich model (Fig. 8a).
Figure 7: As in Fig. 3, but for the North Pacific.
Figure 8: As in Fig. 4, but for the North Pacific.
In HR and ER, the subpolar gyre strengthens (Figs. 9a,b), but in LR, the barotropic streamfunction field exhibits only minor change (Fig. 9c). Although the subpolar gyre is stronger in ER than in LR, the differences in subpolar gyre circulation between the models are relatively insignificant (Figs. 9d–f). The changes in the subtropical gyre indicate a pattern with a positive north and negative south parts of the gyre (Figs. 9a–c). The northern part of subtropical gyre (the Kuroshio region) strengthens; here ER displays a considerable amplification (30°–35°N; Fig. 8b). In the same region, we also noticed the high rate of DSL changes (Fig. 8a). Although the streamfunction differences are significant between the eddy-rich and eddy parameterized models in the northern part of the subtropical gyre (Figs. 9d,e), weakening southern part shows minor changes (Figs. 9d,e). The differences between LR and HR are significant (insignificant) in the southern (northern) part of the subtropical gyre circulation (Fig. 9f).
Figure 9: As in Fig. 6, but for the North Pacific.
In comparison to the DSL change, changes of the barotropic circulation (Figs. 9a–c) show some distinctively different patterns in the tropical regions. Although, the DSL changes across the Kuroshio Extension front are still reflected by similar albeit much weaker streamfunction changes, the strengthening of the subtropical gyre encompasses only the region 30°–40°N, while for DSL it reaches down to 20°N. The negative DSL change south of 20°N covers the entire tropical region, while for the streamfunction it reaches down to only 15°N, where the pattern continues southward by a positive signal. Streamfunction and DSL are therefore inconsistent in the region north of the equator until 30°N, a region where the Pacific and the Indian Ocean are connected by the Indonesian Throughflow passages (Zhang et al. 2014).
Because of the absence of deep-water formation and deep convection in the North Pacific, similar changes seen in CMIP5 models were mainly attributed to changes in the wind field (Sakamoto et al. 2005; Yin et al. 2010). Merrifield (2011) has shown the relevance of off-equatorial wind changes for explaining the features of the large observed sea level trend in the western tropical Pacific during the 1990s and early 2000s. Figure 8c depicts the zonally averaged zonal wind stress changes for three models, showing an increase north of about 38°–45°N and a decrease to the south. Although differences in wind stress change between the models are not significant at the 95% confidence interval of the multimember mean, ER shows less weakening in the subtropical and more strengthening in the subpolar in comparison to HR and LR (Figs. 7j,k, 8c).
Changes in wind stress curl were found to explain the intensification of the subtropical gyre in the South Pacific since the early 1990s (Roemmich et al. 2007, 2016), which were also shown by Köhl and Stammer (2008) to explain the sea level trends during the longer time scale 1960–2001 over much of the Pacific Ocean. We will therefore again examine the wind-driven component of the circulation by the Sverdrup streamfunction (Figs. 9g–i).
Consistent with the barotropic streamfunction, the Sverdrup circulation changes show that the southern part of the North Pacific Subtropical Gyre weakens in all models, while the northern part of the gyre (north of 30°N) indicates a strengthening (Figs. 9g–i). Cheon et al. (2012) argue that this pattern (positive north part and negative south part) observed in the subtropical gyre indicates a poleward shift rather than a strengthening of the gyre under a warming future. Yin et al. (2010) further corroborate this hypothesis of the subtropical gyre poleward shift, resulting from the poleward shift of subtropical high in the western Pacific and the associated wind system. These characteristic patterns of DSL change in the western North Pacific because of the poleward shift and intensification of the Kuroshio have also been studied earlier in earlier CMIP models (e.g., Church et al. 2013a,b; Fox-Kemper et al. 2021; Sueyoshi and Yasuda 2012; Suzuki and Tatebe 2020; Terada and Minobe 2018; Yin 2012; Zhang et al. 2014). However, whether this pattern in the Sverdrup and barotropic streamfunction indicates a poleward shift of the subtropical gyre or a strengthening of the Kuroshio is debatable (see section 4d). Different from the other resolutions, in LR, Sverdrup circulation weakens in the southern part of the North Pacific Subpolar Gyre, while the northern part shows a strengthening (Fig. 9g). It significantly strengthens in ER, and crosses the present-day zero contour (Fig. 9i), while HR shows no considerable change (Fig. 9h).
Previous studies have emphasized that increased model resolution is necessary for the representation of accurate western boundary currents such as Gulf Stream, Kuroshio, and East Australian Currents (e.g., Chassignet and Xu 2017; Chassignet et al. 2020; Griffies et al. 2015; Hewitt et al. 2017, 2020; Roberts et al. 2018; Small et al. 2014). Similarly, Hurlburt et al. (1996) and Nishikawa et al. (2020) demonstrate that eddy-rich horizontal resolution can realistically represent the Oyashio–Kuroshio fronts. Therefore, the strong, narrow current, noted in the DSL and barotropic streamfunction fields (Figs. 7, 9) east of Japan, denotes the more accurately represented Kuroshio in the eddy-rich model, which alters the characteristics of the Kuroshio–Oyashio front by representing a significant number of mesoscale activities in comparison to eddy parameterized models. The Kuroshio, between 30° and 35°N, is significantly intensified in the ER model but slightly strengthens in the high-resolution and the low-resolution climate models.
The Southern Ocean
Like in the North Atlantic and North Pacific, a north–south gradient of DSL change is found in the Southern Ocean for all resolutions (Figs. 10a–c), with increasing sea level north to ∼50°S and decreasing south of ∼50°S, which has been described as a belt-like pattern (Yin et al. 2010). The increase (decrease) of DSL north (south) of the ACC is smaller in ER than in HR and LR at the end of the twenty-first century (Figs. 11a,b, 12a). In earlier studies, the strengthening and poleward shift of Southern Hemisphere westerlies have been shown to induce such a pattern of DSL changes, although it was also noted that it is not sufficient to explain all of the projected changes (Thompson and Solomon 2002; Bouttes et al. 2012; Frankcombe et al. 2013).


Previous studies have emphasized that increased model resolution is necessary for the representation of accurate western boundary currents such as Gulf Stream, Kuroshio, and East Australian Currents (e.g., Chassignet and Xu 2017; Chassignet et al. 2020; Griffies et al. 2015; Hewitt et al. 2017, 2020; Roberts et al. 2018; Small et al. 2014). Similarly, Hurlburt et al. (1996) and Nishikawa et al. (2020) demonstrate that eddy-rich horizontal resolution can realistically represent the Oyashio–Kuroshio fronts. Therefore, the strong, narrow current, noted in the DSL and barotropic streamfunction fields (Figs. 7, 9) east of Japan, denotes the more accurately represented Kuroshio in the eddy-rich model, which alters the characteristics of the Kuroshio–Oyashio front by representing a significant number of mesoscale activities in comparison to eddy parameterized models. The Kuroshio, between 30° and 35°N, is significantly intensified in the ER model but slightly strengthens in the high-resolution and the low-resolution climate models.
The Southern Ocean
Like in the North Atlantic and North Pacific, a north–south gradient of DSL change is found in the Southern Ocean for all resolutions (Figs. 10a–c), with increasing sea level north to ∼50°S and decreasing south of ∼50°S, which has been described as a belt-like pattern (Yin et al. 2010). The increase (decrease) of DSL north (south) of the ACC is smaller in ER than in HR and LR at the end of the twenty-first century (Figs. 11a,b, 12a). In earlier studies, the strengthening and poleward shift of Southern Hemisphere westerlies have been shown to induce such a pattern of DSL changes, although it was also noted that it is not sufficient to explain all of the projected changes (Thompson and Solomon 2002; Bouttes et al. 2012; Frankcombe et al. 2013).
Figure 10: Anomalies of (a)–(c) dynamic sea level, (d)–(f) barotropic streamfunction, and (g)–(i) wind stress for the SSP5-8.5 (2080–99) average relative to the historical simulation, averaged over 1995–2014 in Southern Ocean for (left) MPI-ESM-LR, (center) MPI-ESM-HR, and (right) MPI-ESM-ER. The contours represent the historical mean [1995–2014; contour intervals are 0.1 m in (a)–(c) and 2 Sv in (d)–(f)]. The contour colors denote solid red for the positive values, green line for the zero contour, and blue dashed for the negative values. The stippling indicates the statistically significant regions at the 95% confidence level. In (a), W stands for Weddell Sea and R stands for Ross Sea.
Figure 11: Differences of the anomalies between the models [(left) ER minus LR, (center) ER minus HR, and (right) HR minus LR] for (a)–(c) dynamic sea level, (d)–(f) barotropic streamfunction, and (g)–(i) wind stress in Southern Ocean. The stippling indicates the statistically significant regions at the 95% confidence level.
Figure 12: As in Fig. 4, but for the Southern Ocean.
The projected wind stress change shows a decrease north of the ACC, with a peak around 38°S, and an increase to the south centered around 58°S (Figs. 10g–i, 12c). This dipole-type pattern in the zonal component of the wind stress is interpreted by Fyfe and Saenko (2006) as the strengthening and poleward shift. The differences in wind stress between ER and HR are minor (Figs. 11h, 12c). The changes in LR are considerably larger than both ER and HR (Figs. 11g,i, 12c).
The pattern of DSL reflects circulation changes characterized by similar patterns of barotropic streamfunction change (Figs. 10d–f). The intriguing feature of the projected circulation change is an intensifying region centered around 45°S (Fig. 12b). This strengthening could be caused by a potential southerly shift of subtropical gyres, and as horizontal resolution improves, the magnitude of the strengthening decreases. The poleward shift in sea surface height contours is consistent with regional sea level rise patterns (Gille 2014). Therefore, understanding gyre shift is crucial for sea level change studies. The historical mean contours overlaid over the anomalies can further explain this poleward movement (Figs. 10a–e). Positive dynamic sea level anomalies and negative anomalies in the barotropic streamfunction field both cross the present-day zero contour, which indicates a poleward shift. This poleward shift of subtropical gyres, interpreted as the belt-like pattern, is less pronounced in ER than in HR and LR (Figs. 10d,e). Similarly, ER reflects a thinner belt of DSL increase compared to HR and LR (Figs. 10a,b).
A dipole-like pattern of changes in the southern Indian Ocean and South Atlantic Ocean is revealed by changes in streamfunction for the Southern Ocean (Figs. 10d–f). The southern (northern) part of the Indian Ocean Gyre is shown to be strengthening (weakening) by around 18 Sv (10 Sv) in the ER. The southern part of the South Atlantic Gyre is also strengthening by about 13 Sv (Fig. 10f). However, the South Pacific Gyre weakens in all the projections by about 6 Sv. When the changes in subpolar gyres are taken into account, we found that all projections show a weakening Weddell Gyre (Fig. 10d–f), which is more pronounced in HR than in LR and ER (Figs. 11e,f). With a larger acceleration in ER (Fig. 11d), the Ross Gyre strengthens in LR and ER (Figs. 10d,f), whereas it weakens in HR (Fig. 10e).
Eddies are omnipresent in the Southern Ocean, especially along the ACC (e.g., Constantinou and Hogg 2019; Frenger et al. 2015). These eddies are crucial for establishing the stratification in the presence of wind and buoyancy forcing (Karsten et al. 2002). The intensified Southern Hemisphere westerlies enhance the Southern Ocean eddy activity, leading to the phenomenon known as eddy saturation (Straub 1993) and eddy compensation. As a result, the strength of the ACC, the isopycnal slope, and the meridional circulation of the Southern Ocean become less sensitive to the enhanced wind forcing. Studies using higher-resolution ocean models (e.g., Farneti et al. 2010; Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006) or observations (Böning et al. 2008; Chidichimo et al. 2014; Firing et al. 2011) have shown the insensitivity of ACC or the Southern Ocean meridional overturning circulation to the enhanced westerlies. They stated that the non-eddy-resolving models respond with an accelerated ACC, steeper isopycnals, and robust meridional overturning circulation to wind intensification forcing changes.
To evaluate the response of ACC to the intensified westerly wind stress, we investigated the Drake Passage transport independently for the two time periods (Fig. 13a). Even though the studies cited above oppose the ACC’s sensitivity to changing westerly winds, we discovered an accelerating ACC particularly in our eddy-rich model (Fig. 13b). With a substantial increase in ER, the strength of the ACC increases in ER and LR (Fig. 13a). The LR reveals increased transport between 60° and 68°S, with no changes north of 60°S. The transport in HR remains unchanged until 64°S, south of which it begins to weaken (Fig. 13a), reflecting its insensitivities to accelerated southern westerlies. Furthermore, Shi et al. (2021) and Swart et al. (2018) show that factors other than wind influence the Southern Ocean circulation. Warming in the upper ocean generates a density change, accelerating the ACC. Heat and freshwater fluxes at the surface could also cause changes observed in ER.
Figure 13: (a) Time mean transport through Drake Passage; the dashed line for the time mean future (2080–99) transport and the solid line indicates the historical (1995–2014) transport (Sv). (b) Time series of ACC transport through Drake Passage relative to 1950s mean at 65°W. The green, red, and blue lines represent MPI-ESM-LR, MPI-ESM-HR, and MPI-ESM-ER, respectively. The positive barotropic streamfunction values were considered for the calculation.


To evaluate the response of ACC to the intensified westerly wind stress, we investigated the Drake Passage transport independently for the two time periods (Fig. 13a). Even though the studies cited above oppose the ACC’s sensitivity to changing westerly winds, we discovered an accelerating ACC particularly in our eddy-rich model (Fig. 13b). With a substantial increase in ER, the strength of the ACC increases in ER and LR (Fig. 13a). The LR reveals increased transport between 60° and 68°S, with no changes north of 60°S. The transport in HR remains unchanged until 64°S, south of which it begins to weaken (Fig. 13a), reflecting its insensitivities to accelerated southern westerlies. Furthermore, Shi et al. (2021) and Swart et al. (2018) show that factors other than wind influence the Southern Ocean circulation. Warming in the upper ocean generates a density change, accelerating the ACC. Heat and freshwater fluxes at the surface could also cause changes observed in ER.
Figure 13: (a) Time mean transport through Drake Passage; the dashed line for the time mean future (2080–99) transport and the solid line indicates the historical (1995–2014) transport (Sv). (b) Time series of ACC transport through Drake Passage relative to 1950s mean at 65°W. The green, red, and blue lines represent MPI-ESM-LR, MPI-ESM-HR, and MPI-ESM-ER, respectively. The positive barotropic streamfunction values were considered for the calculation.
The stronger DSL increase relative to HR and LR is significant in ER in the South Pacific (25°–60°S), especially east of Australia (Figs. 11a,b). The East Australian Current system strengthens as DSL rises in the ER model (Figs. 11d,e). This intensified circulation represented by the barotropic streamfunction field is more significant in ER than in HR and LR. Lower-resolution models poorly simulate the western boundary current system due to unresolved mesoscale processes, whereas the East Australian Current is adequately simulated in ER. Increasing southward transport of the East Australia Current in a warming climate was shown to be a response to the intensified South Pacific wind stress curl (Goyal et al. 2021; Roemmich et al. 2007), which can be seen in ER. We also found the enormously increased sea surface temperature in southeastern Australia in ER as indicated in previous studies (Wu et al. 2012; Hobday and Pecl 2014), which causes this region to be a global warming hotspot.
The DSL decreases in southern Indian Ocean and the Pacific (north of 30°S), though it increases in the Atlantic (Figs. 10a–c). The increase in the South Atlantic is larger in LR than in HR as well as ER (Figs. 11a,c). In the south Indian Ocean, the DSL decreases, in order of decreasing the reduction, in HR, LR, and ER (Figs. 11a–c), similarly in the South Pacific.
Displacement of major ocean gyres
The poleward shift of major ocean gyres, which secondarily drives sea level change, was previously discussed by Yang et al. (2020). To comprehend how differences in poleward shift affect different DSL responses, we have calculated the change in position of major ocean gyres in the three versions of MPI-ESM and quantified the linear trend from 2030 to 2100 in Fig. 14. Most gyres shift toward the poles (except for the North Pacific), indicating a statistically significant poleward gyre displacement as a response to a warmer climate.
Figure 14: Time series of 3 yr running mean latitudinal variations of the ocean gyres relative to the 1950s mean (°). The position is calculated based on the barotropic streamfunction weighted center of each gyre, and the contours between the minimum and maximum eastward transport in the Drake passage were considered to calculate the mean central latitude of ACC transport. Abbreviations in each panel are North Atlantic Subpolar Gyre (NASPG), North Atlantic Subtropical Gyre (NASTG), North Pacific Subpolar Gyre (NPSPG), North Pacific Subtropical Gyre (NPSTG), and Antarctic Circumpolar Current (ACC). The linear trend is indicated by the dashed lines between 2030 and 2099 for LR, HR, and ER in green, red, and blue, respectively. The related linear trends are presented in the box (° yr−1).
The poleward shift of the North Atlantic Subtropical Gyre is almost identical in all projections, showing a magnitude of 0.0138°, 0.0112°, and 0.0161° per year in ER, HR, and LR, respectively (Fig. 14b). The North Atlantic Subpolar Gyre, on the other hand, responds differently in each projection, with the highest displacement in ER and trends of 0.0129°, 0.0125°, and 0.0085° per year in ER, HR, and LR, respectively (Fig. 14a), from 2030 to 2099.
Periods over which trends occur are also not very consistent. While HR shows no trend until the last few decades, poleward trends start in the early to mid-twenty-first century for LR and ER, respectively, but it seems to cease after 2070 for ER pointing to considerable influence of climate variability. The North Pacific Subpolar Gyre behaves contrarily to the North Atlantic in ER, which shows a southward shift, indicated by a negative trend of 0.0088° per year, while northward shifts are small with 0.0067 per year in HR and 0.0011° per year in LR (Fig. 14c). Similarly, North Pacific Subtropical Gyre displacements are also relatively small in HR and LR, with linear trends of 0.0028° and 0.0010° yr−1, respectively (Fig. 14d). Both poleward shifts of the ocean gyres in the North Pacific are not statistically significant in LR, and in ER, the subtropical gyre is experiencing a statistically insignificant downward trend of 0.0026° year−1.
The displacements of the North Pacific Subpolar and Subtropical Gyres are negligible when compared to interannual variability in all configurations (Figs. 14c,d). Consistent with the changes of the barotropic streamfunction (Figs. 9c), the boundary of the negative circulation anomaly crossing the zero contour of present day (solid green line) in the Sverdrup circulation implies that the North Pacific Subpolar Gyre strengthens and moves southward in ER (Fig. 9i). Thus, ER shows a strengthening Kuroshio due to the stronger wind rather than a poleward displacement (Fig. 14d), despite the interpretation of earlier CMIP5 model investigations that the changes in the Sverdrup streamfunction indicates a northward movement of the subtropical gyre (Cheon et al. 2012). It is worth mentioning that the latitudinal variations observed in the North Atlantic Subtropical Gyre are consistent with a pattern of positive north and negative south parts of the gyre in the Sverdrup streamfunction field (Figs. 6g–i) and barotropic circulation (Figs. 6a–c).
Our results indicate a distinct poleward shift of the ACC (Fig. 14e), which has been linked to climate change in many earlier studies (e.g., Morrow et al. 2008; Yang et al. 2020). Interestingly, the eddy-rich model shows less poleward migration of the ACC with induced transport increase in comparison to the high- and low-resolution models. Between 2030 and 2100, the HR has the highest trend of 0.0044° yr−1, whereas the LR has the lowest trend of 0.0024° yr−1, while ER’s linear trend lies with 0.0028° yr−1 in between. In ER, the latitudinal displacement of the ACC is less than in HR and LR (Fig. 14e), and we also observed the smallest poleward shift of the ACC in the barotropic streamfunction (Figs. 11c,d) and sea surface height field (Figs. 11a,b).


The displacements of the North Pacific Subpolar and Subtropical Gyres are negligible when compared to interannual variability in all configurations (Figs. 14c,d). Consistent with the changes of the barotropic streamfunction (Figs. 9c), the boundary of the negative circulation anomaly crossing the zero contour of present day (solid green line) in the Sverdrup circulation implies that the North Pacific Subpolar Gyre strengthens and moves southward in ER (Fig. 9i). Thus, ER shows a strengthening Kuroshio due to the stronger wind rather than a poleward displacement (Fig. 14d), despite the interpretation of earlier CMIP5 model investigations that the changes in the Sverdrup streamfunction indicates a northward movement of the subtropical gyre (Cheon et al. 2012). It is worth mentioning that the latitudinal variations observed in the North Atlantic Subtropical Gyre are consistent with a pattern of positive north and negative south parts of the gyre in the Sverdrup streamfunction field (Figs. 6g–i) and barotropic circulation (Figs. 6a–c).
Our results indicate a distinct poleward shift of the ACC (Fig. 14e), which has been linked to climate change in many earlier studies (e.g., Morrow et al. 2008; Yang et al. 2020). Interestingly, the eddy-rich model shows less poleward migration of the ACC with induced transport increase in comparison to the high- and low-resolution models. Between 2030 and 2100, the HR has the highest trend of 0.0044° yr−1, whereas the LR has the lowest trend of 0.0024° yr−1, while ER’s linear trend lies with 0.0028° yr−1 in between. In ER, the latitudinal displacement of the ACC is less than in HR and LR (Fig. 14e), and we also observed the smallest poleward shift of the ACC in the barotropic streamfunction (Figs. 11c,d) and sea surface height field (Figs. 11a,b).
The differences between the anomalies seen in the Arctic Ocean are not thoroughly covered in a separate section. Thus, the discrepancies found are outlined here at the end of the section 4. We noted a dipole pattern of the difference in the DSL changes between ER and the lower-resolution models in the Arctic Ocean (Fig. S5). The ER reveals no changes to the north of Greenland, where we diagnose strong sea level increase in HR and LR (Fig. 2c and Fig. S2i). As expected, the model differences of the freshwater content change show a similar behavior to the differences of sea level change (Fig. S6). Although the Beaufort Gyre weakens (Figs. 2d,e and Figs. S3d,e) at the end of the twenty-first century, our models, HR and LR, show a DSL increase in the Canada Basin (Figs. 2a,b) associated with freshwater accumulation (Fig. S7). Furthermore, we do not find any considerable changes in the wind stress field, except for its increase in the Chukchi Sea in ER (Fig. 2j and Fig. S4). The induced anticyclonic circulation in ER (Fig. 2f) causes the increase in DSL (Fig. 2c) and freshwater content (Fig. S7i) in the Canada Basin.
Summary and concluding remarks
By analyzing model simulations from eddy-rich (ER), high-resolution (HR), and low-resolution (LR) versions of MPI-ESM run under the SSP5-8.5 scenario forcing, we found substantial DSL change differences in the global ocean among the different resolutions. We note that HR and ER have the same atmospheric component, whereas LR also has a lower-resolution atmosphere. However, when comparing LR and HR, we cannot fully discriminate between the effects of resolution changes versus intrinsic changes of surface forcing in either simulation. This is because the response to changes in external forcing is a complex coupled phenomenon that depends on details of the surface boundary condition formulation. Because of this, even ocean models coupled to the same atmosphere (Semmler et al. 2021) show different regional or global expressions of such change as soon as ocean surface fields are different. Nevertheless, in many cases we can link the responses in sea level change to the different ocean resolution, in particular comparing the HR and ER versions of the model.
All models simulate a meridional dipole pattern of sea level change in the North Atlantic. This dipole pattern is identified by a larger sea level rise relative to the global mean in the subpolar region and sea level decrease in the subtropical region. However, southeast of Greenland, we identify a patch of sea level decline, which shrinks with the enhanced horizontal resolution. The warming hole feature is also located in the same area as the sea level decline, indicating a similar pattern of behavior, particularly in HR and ER. We have mainly focused on the changes in the circulation to examine the causes of these differences, since the long-term changes in sea level are linked to the changes in the circulation.
In HR and LR, the subpolar gyre strengthens in the barotropic streamfunction field, although its component driven by the wind stress curl weakens. The strengthening circulation in the subpolar region, on the one hand, can induce the heat transport out of the region into the GIN Seas and then farther north to the Arctic, forming NA warming hole. However, in this region the changes in wind stress curl in the subpolar region do not agree with the change in circulation in the eddy permitting models.
In the ER model, the subpolar gyre weakens in both barotropic and Sverdrup fields, as well as the region of the sea level decline becomes small. Furthermore, the magnitude of the sea level decline is also smaller in ER compared to HR and LR. The sea level increase over the rest of the subpolar gyre has been simulated by all the models. This increase becomes smaller in the eddy-rich model, indicating lower sea level in the Labrador Sea and north of Gulf Stream. This lower increase is caused by lower freshwater content in ER than in HR and LR. Previous studies have widely reported the relation between the uncertainty in twenty-first century sea level change in the North Atlantic and the variability in projected weakening of AMOC (Yin et al. 2009; Bouttes et al. 2014). We observed a significant AMOC decline in all the versions. This decrease is very similar in HR and ER at 26°N. However, the DSL changes in the North Atlantic are considerably different between these models. These results indicate that the North Atlantic DSL change is not responding as we anticipated to the weakening AMOC. The sea level decline in the subtropical region is larger in ER compared to HR and LR, caused by the larger weakening of the circulation in ER.
The poleward shift of North Atlantic Subtropical Gyre, which is also observed in the Sverdrup field as a pattern of positive north and negative south parts of the gyre, is considerable in all the models. However, the differences between models are not significant.
Interestingly, a pattern of positive north and negative south parts of the gyre identified in the Sverdrup streamfunction most likely indicates the strengthening of Kuroshio rather than the poleward shift of the subtropical gyre in the ER simulation, because the gyres in the North Pacific show a negligible poleward displacement. It is further explained by identifying a significant DSL change, robust circulation, and less reduction of wind stress in the Kuroshio region (30°–35°N). These robust changes are identified only in the eddy-rich model, because of the realistically represented western boundary currents.
It is well known that in the Southern Ocean changes in sea level correspond to changes in ACC and barotropic circulation (e.g., van Westen and Dijkstra 2021). Southern Ocean sea level change is smaller in ER, indicating a minor poleward shift of the ACC in comparison to HR and LR. The ACC, as in earlier studies, is known to be insensitive to the strengthening westerlies in the higher-resolution models that explicitly resolve eddies. One interesting result is that ACC strengthens in ER, but remains unchanged or slightly weakened in HR. The findings indicate that ER, as opposed to HR, appears to be more sensitive to strong westerlies.
The general understanding is that many low-lying coastal areas experience substantial threats from sea level rise due to their relatively low elevation above sea level. Figure 1 by Magnan et al. (2022) provides a detailed overview of the low-lying islands and coasts of the world. However, we have not included in-depth discussion about low lying coastal areas that are located in the Indian Ocean and southwest Pacific due to small model differences of DSL anomalies (maximum around ±40 mm; see supplemental Figs. S8–S13). Interesting to note is that the differences of DSL change between HR and ER is significant in these regions and larger than the difference between LR and ER.


The poleward shift of North Atlantic Subtropical Gyre, which is also observed in the Sverdrup field as a pattern of positive north and negative south parts of the gyre, is considerable in all the models. However, the differences between models are not significant.
Interestingly, a pattern of positive north and negative south parts of the gyre identified in the Sverdrup streamfunction most likely indicates the strengthening of Kuroshio rather than the poleward shift of the subtropical gyre in the ER simulation, because the gyres in the North Pacific show a negligible poleward displacement. It is further explained by identifying a significant DSL change, robust circulation, and less reduction of wind stress in the Kuroshio region (30°–35°N). These robust changes are identified only in the eddy-rich model, because of the realistically represented western boundary currents.
It is well known that in the Southern Ocean changes in sea level correspond to changes in ACC and barotropic circulation (e.g., van Westen and Dijkstra 2021). Southern Ocean sea level change is smaller in ER, indicating a minor poleward shift of the ACC in comparison to HR and LR. The ACC, as in earlier studies, is known to be insensitive to the strengthening westerlies in the higher-resolution models that explicitly resolve eddies. One interesting result is that ACC strengthens in ER, but remains unchanged or slightly weakened in HR. The findings indicate that ER, as opposed to HR, appears to be more sensitive to strong westerlies.
The general understanding is that many low-lying coastal areas experience substantial threats from sea level rise due to their relatively low elevation above sea level. Figure 1 by Magnan et al. (2022) provides a detailed overview of the low-lying islands and coasts of the world. However, we have not included in-depth discussion about low lying coastal areas that are located in the Indian Ocean and southwest Pacific due to small model differences of DSL anomalies (maximum around ±40 mm; see supplemental Figs. S8–S13). Interesting to note is that the differences of DSL change between HR and ER is significant in these regions and larger than the difference between LR and ER.
It is expected that the eddy-rich models improve the representation of the eddy activities, providing more accurate and informative sea level change patterns over the following decades. In general, the DSL change pattern and dynamics are similar in eddy-rich compared to the coarser-resolution climate models in each ocean basin, suggesting that the coarser-resolution models will remain valid in understanding the sea level change patterns. On the other hand, the detailed, quantitative responses depend on the resolution. The robust changes found in MPI-ESM-ER suggest that improved resolution will have an impact on the interpretation of regional sea level change in the following decades. Therefore, the sea level projections of coarse-resolution models should be interpreted with caution, predominantly in the eddy active regions such as Kuroshio, ACC, Gulf Stream, and East Australian Current, and one should consider restrictions associated with limited climate model horizontal resolutions, when planning future adaptation and mitigation investments.


DeConto et al. (2021)
Title:
The Paris Climate Agreement and future sea-level rise from Antarctica
Corresponding author:
Robert M. DeConto
Citation:
DeConto, R. M., Pollard, D., Alley, R. B., Velicogna, I., Gasson, E., Gomez, N., et al. (2021). The Paris Climate Agreement and future sea-level rise from Antarctica. Nature, 593(7857), 83–89. doi: 10.1038/s41586-021-03427-0
URL:
https://www.nature.com/articles/s41586-021-03427-0
Abstract
The Paris Agreement aims to limit global mean warming in the twenty-first century to less than 2 degrees Celsius above preindustrial levels, and to promote further efforts to limit warming to 1.5 degrees Celsius [1]. The amount of greenhouse gas emissions in coming decades will be consequential for global mean sea level (GMSL) on century and longer timescales through a combination of ocean thermal expansion and loss of land ice [2]. The Antarctic Ice Sheet (AIS) is Earth’s largest land ice reservoir (equivalent to 57.9 metres of GMSL) [3], and its ice loss is accelerating [4]. Extensive regions of the AIS are grounded below sea level and susceptible to dynamical instabilities [5,6,7,8] that are capable of producing very rapid retreat [8]. Yet the potential for the implementation of the Paris Agreement temperature targets to slow or stop the onset of these instabilities has not been directly tested with physics-based models. Here we use an observationally calibrated ice sheet–shelf model to show that with global warming limited to 2 degrees Celsius or less, Antarctic ice loss will continue at a pace similar to today’s throughout the twenty-first century. However, scenarios more consistent with current policies (allowing 3 degrees Celsius of warming) give an abrupt jump in the pace of Antarctic ice loss after around 2060, contributing about 0.5 centimetres GMSL rise per year by 2100—an order of magnitude faster than today [4]. More fossil-fuel-intensive scenarios [9] result in even greater acceleration. Ice-sheet retreat initiated by the thinning and loss of buttressing ice shelves continues for centuries, regardless of bedrock and sea-level feedback mechanisms [10,11,12] or geoengineered carbon dioxide reduction. These results demonstrate the possibility that rapid and unstoppable sea-level rise from Antarctica will be triggered if Paris Agreement targets are exceeded.
Introduction
Most of the AIS terminates in the ocean, with massive ice shelves (floating extensions of glacial ice) providing resistance (buttressing) to the seaward flow of the grounded ice upstream [13]. About a third of the AIS rests on bedrock hundreds to thousands of metres below sea level [3], and in places where subglacial bedrock slopes downwards away from the ocean (reverse-sloped), the ice margin is susceptible to a marine ice-sheet instability (MISI) [5,6] and possibly a marine ice-cliff instability (MICI) [7,8]. The West Antarctic Ice Sheet (WAIS), which has the potential to cause about 5 m of GMSL rise, is particularly vulnerable. The WAIS is losing ice faster than other Antarctic sectors [4] and it sits in a deep basin >2.5 km below sea level in places [3].
Marine ice instabilities
MISI and MICI can be triggered by the thinning or loss of buttressing ice shelves in response to a warming ocean, atmosphere or both [14]. MISI is related to a self-sustaining positive feedback between seaward ice flux across the grounding line (the boundary between grounded and floating ice) and ice thickness [5,6]. If buttressing is lost and retreat is initiated on a reverse-sloped bed, the retreating grounding line will encounter thicker ice, strongly increasing ice flow. Retreat will continue until the grounding line reaches forward-sloping bedrock, or sufficient resistive stress is restored by the regrowth of a buttressing ice shelf that is confined within coastal embayments or is thick enough to ‘pin’ on shallow bedrock features. Grounding lines on reverse-sloped bedrock are conditionally unstable15 and retreat at a rate determined by the complex interplay between ice flow and stress fields, bedrock conditions, surface mass balance and other factors that make model-ling these dynamics difficult.
MICI is also theorized to be triggered where buttressing ice shelves disappear or become too small to provide substantial back stress [7,8]. At unsupported grounding lines where ice thickness exceeds a critical value, the weight of ice above sea level can produce deviatoric stresses that exceed the material yield strength of the ice. This causes structural failure [16,17], possibly manifest as repeated slumping and calving events17. Once initiated, failure can continue until the collapsing ice front backs into shallow water, where subaerial cliff heights and the associated stresses drop below their critical values, viscous deformation lowers the cliff, or sufficient buttressing is restored by an ice shelf.
In undamaged ice, with small grain sizes and without large bubbles or pre-existing weaknesses, slowly emerging subaerial ice cliffs could exceed 500 m in height before failing [18]. However, natural glacial ice is typically damaged, especially near crevassed calving fronts and in fast-flowing ice upstream [19]. Assuming ice properties representative of glaciers, stress-balance calculations [16] point to maximum sustainable cliff heights of around 200 m. This value is reduced to about 100 m or less [8,16] where deep surface and basal crevasses effectively thin the supportive ice column (increasing the stress), possibly explaining why the tallest ice cliffs observed today are about 100 m tall. Recent modelling [18] using values of fracture toughness and pre-existing flaw size appropriate for damaged ice fronts [17] and consistent with field observations [19] indicates that tensile fracturing can occur at cliffs as low as 60 m. This reinforces the argument for including ice-cliff calving in ice-sheet models [20], despite current uncertainties in ice properties and the lack of observations which make ice-cliff calving laws difficult to formulate.
Thick, marine-terminating glaciers such as Jakobshavn Isbræ in Greenland demonstrate how efficient calving can deliver ice to the ocean. The terminus of Jakobshavn is about 10 km wide, 1,000 m thick and flows seawards at about 12 km yr−1 (ref. 21). Since the glacier lost its ice shelf in the late 1990s, the ice front (with an intermittent ~100-m ice cliff) has retreated >12 km into the thicker ice upstream, albeit with a recent re-advance coincident with regional ocean cooling [22]. The average effective calving rate (flow speed + retreat) between 2002 and 2015 is estimated at 13.2 ± 0.9 km yr−1 (1σ; ref. 21).
Calving in narrow fjord settings such as Jakobshavn is controlled by a complex combination of ductile and brittle processes, as well as buoyancy. After calving, subsequent fracture-driven failure is delayed until accelerated flow thins the terminus to near-flotation, allowing tidal flexure, basal crevassing, slumping or other processes to initiate the next event17,23. Resistive stresses from lateral shear along fjord walls, as well as thick mélange strengthened by sea ice, slow calving in winter, but annual ice loss remains high.
Jakobshavn-style calving is not widespread in Antarctica today, because most marine-terminating grounding lines with comparable ice thickness are supported by the resistive back stress of ice shelves. Crane Glacier, previously buttressed by the Larsen B ice shelf on the Antarctic Peninsula, is an exception. When the ice shelf suddenly collapsed in 2002 after becoming covered in meltwater, the glacier sped up by a factor of three24. A persistent 100-m ice cliff formed at the terminus25 and the calving front retreated into its narrow fjord. The drainage of Crane Glacier was too small to contribute substantially to sea level, but similar events could become widespread in Antarctica if temperatures continue to rise.
Importantly, some Antarctic glaciers are vastly larger than their Greenland counterparts. For example, Thwaites Glacier in West Antarctica terminates in the open Amundsen Sea rather than in a narrow fjord. The main trunk of Thwaites Glacier is about 120 km wide, widening upstream into the heart of the WAIS. Today, the heavily crevassed grounding zone of Thwaites Glacier is minimally buttressed and retreating on reverse-sloped bedrock at >1 km yr−1 in places26, possibly owing to MISI. The terminus currently sits in water too shallow (about 600 m deep) to produce an unstable cliff face, but if retreat continues into deeper bedrock and thicker ice, a calving face taller than that of Jakobshavn could appear, with stresses and strain rates exceeding thresholds for brittle failure16,17,18. Similar vulnerabilities exist at other Antarctic glaciers, particularly where buttressing ice shelves are already thinning from contact with warm sub-surface waters14.


Calving in narrow fjord settings such as Jakobshavn is controlled by a complex combination of ductile and brittle processes, as well as buoyancy. After calving, subsequent fracture-driven failure is delayed until accelerated flow thins the terminus to near-flotation, allowing tidal flexure, basal crevassing, slumping or other processes to initiate the next event17,23. Resistive stresses from lateral shear along fjord walls, as well as thick mélange strengthened by sea ice, slow calving in winter, but annual ice loss remains high.
Jakobshavn-style calving is not widespread in Antarctica today, because most marine-terminating grounding lines with comparable ice thickness are supported by the resistive back stress of ice shelves. Crane Glacier, previously buttressed by the Larsen B ice shelf on the Antarctic Peninsula, is an exception. When the ice shelf suddenly collapsed in 2002 after becoming covered in meltwater, the glacier sped up by a factor of three24. A persistent 100-m ice cliff formed at the terminus25 and the calving front retreated into its narrow fjord. The drainage of Crane Glacier was too small to contribute substantially to sea level, but similar events could become widespread in Antarctica if temperatures continue to rise.
Importantly, some Antarctic glaciers are vastly larger than their Greenland counterparts. For example, Thwaites Glacier in West Antarctica terminates in the open Amundsen Sea rather than in a narrow fjord. The main trunk of Thwaites Glacier is about 120 km wide, widening upstream into the heart of the WAIS. Today, the heavily crevassed grounding zone of Thwaites Glacier is minimally buttressed and retreating on reverse-sloped bedrock at >1 km yr−1 in places26, possibly owing to MISI. The terminus currently sits in water too shallow (about 600 m deep) to produce an unstable cliff face, but if retreat continues into deeper bedrock and thicker ice, a calving face taller than that of Jakobshavn could appear, with stresses and strain rates exceeding thresholds for brittle failure16,17,18. Similar vulnerabilities exist at other Antarctic glaciers, particularly where buttressing ice shelves are already thinning from contact with warm sub-surface waters14.
Because of the very strong dependency of crack growth with increasing stress17,27, a previously unseen style of calving and ice failure might emerge at unbuttressed Antarctic ice fronts with higher freeboard than glaciers on Greenland7,8. The potential pace of fracturing in such settings remains uncertain20, but once a calving front backs into thicker ice upstream, brittle failure could outpace viscous flow, inhibiting the growth of a new shelf. Complete, sustained loss of an ice shelf is not required for structural failure16. If a small floating shelf survives or reforms without providing substantial buttressing, the grounding zone would remain under sufficient stress for collapse. Re-emerging ice shelves would remain vulnerable to warm ocean waters and surface meltwater, as evidenced at Jakobshavn and Crane glaciers; despite fast flow and mélange buttressing, persistent ice tongues have not reformed and calving continues.
Extensive loss of buttressing ice shelves (prerequisite for both MISI and MICI) represents a possible tipping point in Antarctica’s future. This is concerning, because ice shelves are vulnerable to both oceanic melt from below14 and surface warming above28. Rain and meltwater can deepen crevasses28 and cause flexural stresses29, leading to hydrofracturing and ice-shelf collapse. Vulnerability to surface meltwater is enhanced where firn (the transitional layer between surface snow and underlying ice) becomes saturated and where ocean-driven thinning is already underway28. Air temperatures above Antarctica’s largest ice shelves remain too cold to produce sustained meltwater rates associated with collapse30,31; however, given sufficient future warming, this could change.
Modelling the AIS response to warming
We build on previous work [8] by improving a hybrid ice sheet–shelf model that includes viscous ice processes related to MISI and brittle processes related to MICI. The model allows conditionally unstable grounding lines (MISI) on reverse-sloped bedrock in response to flow and stress fields, bed conditions and surface mass balance. The model accounts for oceanic sub-ice melt and meltwater-driven hydrofracturing of ice shelves, leading to ice-cliff calving at thick, marine-terminating ice fronts where stresses exceed ice strength (MICI). Model improvements and extensions described in Methods and Supplementary Information include new formulations of ice-shelf buttressing, hydrofracturing and coupling with a comprehensive Earth–sea-level model, as well as ice–climate (meltwater) feedback mechanisms using the NCAR Community Earth System Model. Parametric uncertainty is assessed using modern and geological observations and statistical emulation. Regional climate model (RCM) forcing used in future ice-sheet ensembles is substantially improved relative to ref. 8, with the trajectory of warming being comparable to that of other studies30 (Supplementary Information).
We test the future response of the AIS to scenarios representing +1.5 °C and +2 °C global warming limits, a +3 °C scenario representing current policies [32] and extended RCP emissions scenarios9. We consider recently proposed negative feedback mechanisms that could slow the pace of future ice loss, and emissions scenarios allowing a temporary overshoot of Paris Agreement temperature targets followed by rapid carbon dioxide reduction (CDR), assuming that such geoengineering is possible. The results identify emissions-forced climatic thresholds capable of triggering rapid retreat of the AIS.
Calibrated model ensembles
To account for the current uncertainty in key parameters controlling (1) the sensitivity of crevasse penetration to surface melt and rainwater (hydrofracturing) and (2) the ice-cliff calving rate, we run 196 ice-sheet simulations for each climate scenario described below. Each ensemble member uses a unique combination of parameter values (Extended Data Table 1), scored using a binary history-matching approach [8,33]. Scoring is based on the model’s ability to simulate the observed ice loss, d𝑀¯/d𝑡, between 1992 and 2017 (IMBIE) [4], and Antarctica’s contribution to sea level in the last interglacial period (LIG) [34] and the mid-Pliocene epoch [35,36] (Methods). Ensemble members falling outside the likely range of observations are discarded, and only parameter combinations within the bounds of all three constraints are included in future projections. Both modern and geological constraints contain considerable uncertainty with poorly known sample distributions, so weighting of individual model outcomes is avoided. In Supplementary Information we compare our ensemble scoring to a more rigorous Gaussian process emulation approach [33,37] to verify that the central estimates of our calibrated ensembles are robust.
Comparing simulated and IMBIE estimates of d𝑀¯/d𝑡 (Extended Data Fig. 1a) eliminates 33 ensemble members (n = 163). The effect of replacing IMBIE with alternative (narrower) ranges of d𝑀¯/d𝑡 on the basis of solely GRACE data from 2002–2017 [38] (Methods) is shown in Extended Data Fig. 2. The model performs well over the IMBIE interval with and without hydrofracturing and ice-cliff calving enabled. Although IMBIE provides guidance on processes that cause contemporary mass change (surface mass balance, oceanic-shelf thinning and grounding-line dynamics), it does not sufficiently test the brittle-ice processes theorized to become important in a warmer climate [7,8]. Furthermore, the 25-year IMBIE record is very short relative to the dynamical response time of an ice sheet, and interdecadal and longer variability is not captured. Collectively, these issues motivate our use of geological records from past warm periods as additional training constraints.
Adding the LIG constraint (3.1–6.1 m; 129–128 kyr ago) to IMBIE eliminates 44 additional parameter combinations (n = 119), but only at the lower bound of the parameter range. Without MICI, the model is incapable of simulating realistic LIG ice loss. Even at the top of the parameter range, simulated rates of GMSL rise remain below 1 cm yr−1, slower than indicated by some LIG proxy records39 (Extended Data Fig. 1b, c). Adding a warm mid-Pliocene test (11–21 m; 3.26–3.03 Ma) further reduces the ensemble to n = 109 by eliminating some of the highest-valued parameter combinations. Similar to the LIG, hydrofracturing and ice-cliff calving must be included to satisfy Pliocene geological observations, including regional retreat into East Antarctic basins40 (Extended Data Figs. 1d, 3). The model’s ability to simulate current rates of ice loss without ice-cliff calving, while failing to simulate past retreat under warmer climate conditions (Extended Data Figs. 1, 3), is at odds with the findings of ref. 33, which assumed a lower range of Pliocene sea-level constraints than the more recent data35,36 used here.


Adding the LIG constraint (3.1–6.1 m; 129–128 kyr ago) to IMBIE eliminates 44 additional parameter combinations (n = 119), but only at the lower bound of the parameter range. Without MICI, the model is incapable of simulating realistic LIG ice loss. Even at the top of the parameter range, simulated rates of GMSL rise remain below 1 cm yr−1, slower than indicated by some LIG proxy records39 (Extended Data Fig. 1b, c). Adding a warm mid-Pliocene test (11–21 m; 3.26–3.03 Ma) further reduces the ensemble to n = 109 by eliminating some of the highest-valued parameter combinations. Similar to the LIG, hydrofracturing and ice-cliff calving must be included to satisfy Pliocene geological observations, including regional retreat into East Antarctic basins40 (Extended Data Figs. 1d, 3). The model’s ability to simulate current rates of ice loss without ice-cliff calving, while failing to simulate past retreat under warmer climate conditions (Extended Data Figs. 1, 3), is at odds with the findings of ref. 33, which assumed a lower range of Pliocene sea-level constraints than the more recent data35,36 used here.
Processes other than ice-cliff calving could be invoked to improve geological model–data comparisons. For example, Pliocene retreat in East Antarctica has been simulated in a model without MICI, using a sub-ice melt scheme allowing the presence of melt beneath grounded ice upstream of the grounding line41. Tidally driven seawater intrusion and non-zero melt beneath discontinuous sectors of grounding zones has been observed26; however, model treatments used so far41 have been questioned on physical grounds42. Alternative (Coulomb) sub-glacial sliding laws have been proposed43 that can substantially increase the rate of ice loss in models with ice shelves removed44, but they have not been tested with realistic palaeoclimate forcing. We stress that hydrofracturing and ice-cliff calving processes incorporated here are observed phenomena, tested under both modern and geological settings.
Ice loss in both LIG and Pliocene ensembles saturates at the upper range of parameter values (Extended Data Fig. 1). The LIG is sufficiently warm to cause complete WAIS retreat, but not warm enough to trigger retreat into East Antarctic basins, even if our nominal ice-cliff calving limit (13,000 m yr−1) is doubled. Similarly, maximum ice loss in the Pliocene ensemble reflects the loss of most marine-based ice, as supported by observations35, but not more. As such, the geological constraints do not rule out the possibility of faster Antarctic ice-cliff calving rates than those observed on Greenland today, which would substantially increase our future projections while remaining consistent with geological observations.
Implications of the Paris Agreement
We run ensembles of the transient response of the AIS to future greenhouse gas emissions scenarios (Methods) representing global mean warming limits of +1.5 °C, +2 °C and +3 °C (similar to current policies and Nationally Determined Contributions, NDCs32), as well as RCP2.6, RCP4.5 and RCP8.59. Only simulations with validated parameter combinations (Extended Data Fig. 4d) are included in the analysis. The +1.5 °C, +2 °C and +3 °C scenarios assume that there is no overshoot in temperature; once these global mean temperatures are reached in 2040, 2060 and 2070, respectively, atmosphere and ocean forcings are held constant.
In the +1.5 °C and +2 °C ensembles, Antarctic ice loss continues at a pace similar to today’s throughout the 21st century (Fig. 1, Table 1). The median contribution to sea level in 2100 is 8 cm with +1.5 °C warming and 9 cm with +2 °C. By contrast, about 10% of the ensemble members in the +3 °C scenario produce onset of major WAIS retreat before 2100. This skews the upper bound of the +3 °C distribution (33 cm at the 90th percentile), substantially increasing the ensemble median (15 cm in 2100) relative to the +1.5 °C and +2 °C scenarios. The jump in late 21st century ice loss at +3 °C is mainly caused by retreat of Thwaites Glacier (Fig. 2; Extended Data Fig. 5), which destabilizes the entire WAIS in some ensemble members.
Figure 1: Antarctic contribution to future GMSL rise. a–h, The fan charts show the time-evolving uncertainty and range around the median ensemble value (black line) in 10% increments. a, c, e, g, Ensemble results from 2000–2100, including median rates of GMSL rise (red line). b, d, f, h The same as a, c, e, g, extended to 2300. a, b, Emissions consistent with a +1.5.°C global mean warming scenario. c, d, Emissions consistent with +2.0.°C. e, f, Emissions consistent with +3.0.°C. g, h, RCP8.5. In h, two additional RCP8.5 simulations are shown with average calibrated parameter values (Methods) but with atmosphere and ocean forcing provided by the NCAR CESM1.2.2 GCM with (blue line) and without (red line) Antarctic meltwater feedback46. Note the expanded vertical axes in g and h.
Table 1: Antarctic sea-level contributions. Ensemble medians (top six rows) using IMBIE, LIG and Pliocene observational constraints, reported in metres, relative to 2000. Values in parentheses are the 17th–83rd percentiles (likely range). Scenarios refer to the maximum global mean temperature reached relative to pre-industrial (1850) or following RCPs. Alternative ensemble outcomes using more restrictive ranges of ice-cliff calving parameters are provided in Extended Data Table 2. Model simulations corresponding to Fig. 3 (bottom 12 rows) use average calibrated parameter values (Extended Data Table 1). NDC simulations follow the standard +3 °C emissions scenario or consider CDR beginning in 2200, 2150, 2100, 2090, 2080, 2070, 2060, 2050, 2040 or 2030. An alternative scenario maintains the atmosphere and ocean climate forcing at 2020 (with no additional future warming). Note that the +3.0 °C ensemble median (third row) differs from the corresponding +3.0 °C (NDCs) simulation using average model parameter values (seventh row) owing to the skewness of the ensembles (Fig. 1).
Figure 2: Ice-sheet evolution following the +3 °C global warming emissions trajectory. A single +3 °C ensemble member with average hydrofracturing and ice-cliff calving parameters. Transient atmosphere and ocean forcing follows the +3 °C scenario, roughly consistent with current policies (NDCs). Floating and grounded ice thickness is shown in blue. The grounding line position is shown with a black line. The red square over the Thwaites Glacier (TG) and Pine Island Glacier (PIG) sector of West Antarctica corresponds to the high-resolution (1,000 m) nested model domain in Extended Data Fig. 5. a, Initial ice-sheet conditions. b, Model ice sheet in 2100, showing the onset of major retreat of Thwaites Glacier. c, Change in ice thickness in 2100. d, The ice sheet in 2300, with Thwaites Glacier retreat leading to the loss of the WAIS. e, Change in ice thickness in 2300.
With more extreme RCP8.5 warming, thinning and hydrofracturing of buttressing ice shelves becomes widespread, triggering marine ice instabilities in both West and East Antarctica. The RCP8.5 median contribution to GMSL is 34 cm by 2100. This is substantially less than reported by ref. 8 (64–105 cm), owing to a combination of improved model physics and revised atmospheric forcing (Methods) that delays the onset of surface melt by about 25 years. Nonetheless, the median contribution to GMSL reaches 1 m by 2125 and rates exceed 6 cm yr−1 by 2150 (Extended Data Figs. 6, 7). By 2300, Antarctica contributes 9.6 m of GMSL rise under RCP8.5, almost 10 times more than simulations limiting warming to +1.5 °C.


Figure 2: Ice-sheet evolution following the +3 °C global warming emissions trajectory. A single +3 °C ensemble member with average hydrofracturing and ice-cliff calving parameters. Transient atmosphere and ocean forcing follows the +3 °C scenario, roughly consistent with current policies (NDCs). Floating and grounded ice thickness is shown in blue. The grounding line position is shown with a black line. The red square over the Thwaites Glacier (TG) and Pine Island Glacier (PIG) sector of West Antarctica corresponds to the high-resolution (1,000 m) nested model domain in Extended Data Fig. 5. a, Initial ice-sheet conditions. b, Model ice sheet in 2100, showing the onset of major retreat of Thwaites Glacier. c, Change in ice thickness in 2100. d, The ice sheet in 2300, with Thwaites Glacier retreat leading to the loss of the WAIS. e, Change in ice thickness in 2300.
With more extreme RCP8.5 warming, thinning and hydrofracturing of buttressing ice shelves becomes widespread, triggering marine ice instabilities in both West and East Antarctica. The RCP8.5 median contribution to GMSL is 34 cm by 2100. This is substantially less than reported by ref. 8 (64–105 cm), owing to a combination of improved model physics and revised atmospheric forcing (Methods) that delays the onset of surface melt by about 25 years. Nonetheless, the median contribution to GMSL reaches 1 m by 2125 and rates exceed 6 cm yr−1 by 2150 (Extended Data Figs. 6, 7). By 2300, Antarctica contributes 9.6 m of GMSL rise under RCP8.5, almost 10 times more than simulations limiting warming to +1.5 °C.
In alternative ensembles, the upper bound of the maximum calving rate (VCLIFF) is reduced from 13 km yr−1 to 11 km yr−1 or 8 km yr−1 to reflect Jakobshavn’s recent slowdown22, but the effect on the calibrated ensemble medians is small (Extended Data Table 2). The main ensembles (Fig. 1, Table 1) use 13 km yr−1 as the upper bound because LIG and Pliocene responses saturate above these values and observations at Jakobshavn demonstrate that such rates are indeed possible. Future simulations excluding hydrofracturing and ice-cliff calving produce less GMSL rise than our ensemble medians (Extended Data Fig. 6). Similar to other models without ice-cliff calving45, enhanced precipitation in East Antarctica partially compensates for MISI-driven retreat in West Antarctica, but these simulations are excluded from the future projections because they fail to reproduce the LIG and Pliocene.
Negative feedback mechanisms slowing ice loss
Because our model includes hydrofracturing, the onset of major retreat is sensitive to the pace of future atmospheric warming. We compare our RCM/CCSM4-driven RCP8.5 ensemble to two alternative simulations, with atmosphere and ocean forcing supplied by the NCAR CESM1.2.2 GCM. Both CESM-forced simulations follow RCP8.5, but one includes Antarctic meltwater feedback (Methods) by adding time-evolving liquid-water and solid-ice discharge at the appropriate ocean grid cells in the GCM46.
Including meltwater discharge in CESM expands Southern Ocean sea ice, stratifies the upper ocean, and warms the subsurface (400 m water depth) by 2–4 °C around most of the Antarctic margin in the early 22nd century46. Conversely, expanded sea ice suppresses surface atmospheric warming by more than 5 °C, slowing the onset of surface melt and hydrofracturing in the ice-sheet model. The net result of competing sub-surface ocean warming (enhanced sub-shelf melt) and atmospheric cooling (reduced surface melt) produces a substantial negative feedback on the pace of ice-sheet retreat (Fig. 1h). This contrasts ref. 41, which found a net positive (ocean-driven) meltwater feedback using an ice-sheet model without hydrofracturing. The CESM-driven simulations bracket our RCM/CCSM4-driven ensembles, supporting the timing of retreat in our main ensembles. Our RCM and CESM1.2.2 climate forcings are evaluated relative to independent CMIP5 and CMIP6 GCMs in Supplementary Information.
We test two additional negative-feedback mechanisms proposed to provide a stabilizing influence on marine ice-sheet retreat. First, the potential for channelized supraglacial runoff to delay or stop ice-shelf hydrofracturing47 is examined by reducing meltwater-enhanced surface crevassing in regions of compressional ice-shelf flow (Supplementary Information). Despite a reduced influence of meltwater, we find that hydrofracturing in a warming climate still occurs near ice-shelf calving fronts, where the ice is thinnest, convergence and buttressing are minimal13 and air temperatures (melt rates) are highest. Once initiated, meltwater-enhanced calving near the shelf edge reduces compressional flow in ice upstream and calving propagates. As a result, reduced wet crevassing in compressional flow does little to protect buttressing ice shelves48 and the impact on our simulations is minimal (Supplementary Fig. 3).
Second, we examine the potential for rapid bedrock uplift and ice–ocean gravitational effects to lower relative sea level and reduce ice loss at retreating grounding lines12. Exceptionally fast uplift rates due to low mantle viscosities in the Amundsen Sea sector of West Antarctica have been invoked to slow future retreat of the WAIS10. This is tested by replacing the model’s standard Elastic Lithosphere/Relaxed Asthenosphere representation of deforming bedrock with a more complete viscoelastic (Maxwell) Earth model combining a radially varying, depth-dependent lithosphere and viscosity structure with gravitationally self-consistent sea-level calculations (Methods)12. Simulations assuming the lowest upper mantle viscosity10 with rapid bedrock uplift under all of West Antarctica show limited potential for ice–Earth feedback mechanisms to slow retreat over the next approximately two centuries (Extended Data Fig. 8). This finding is consistent with other recent studies11,12,49, although future work should explore these effects at higher resolution and with a three-dimensional Earth structure50 including lateral heterogeneity of viscoelastic properties under West and East Antarctica.
Implications of delayed mitigation
An additional set of simulations was run using a single combination of ice-model parameters representing calibrated ensemble averages (Extended Data Table 1). The simulations either maintain current (2020) atmosphere and ocean conditions without any future warming, or begin to follow the +3 °C emissions pathway, except assuming that CDR mitigation is initiated at different times in the future, beginning in 2030, 2040, 2050, 2060, 2070, 2080, 2090, 2100, 2150 or 2200. We optimistically assume that CDR technologies will be capable of reducing CO2 atmospheric mixing ratios with an e-folding time of one century (Fig. 3a).
Figure 3: AIS thresholds and commitments to GMSL rise with delayed mitigation. a, Greenhouse gas (GHG) emissions scenarios that initially follow the +3 °C (NDCs) scenario, followed by CDR (carbon dioxide reduction/negative emissions), assuming relaxation towards preindustrial levels with an e-folding time of 100 years. The timing when CDR commences is shown in b. The solid black line is the same +3 °C simulation shown in Fig. 2 and Extended Data Fig. 5. The dashed black line assumes there is no additional GHG increase or warming after 2020. GHG concentrations are shown in CO2 equivalent, in units of preindustrial atmospheric level (PAL; 280 ppm). b, GMSL contributions from Antarctica, corresponding to the scenarios in a, over the 21st century. All simulations use identical model physics and average hydrofracturing and ice-cliff calving parameters. Note the sharp increase in late-21st-century ice loss when CDR is delayed until 2070. c, The same as b, but extended to 2500 (see Table 1). Note the long-term dependence of GMSL rise on the timing when mitigation begins. All scenarios exceed 1 m by 2500, and no scenario shows recovery of the ice sheet, including those returning to near-preindustrial levels of GHGs by about 2300.