Consistency in the fingerprints of projected sea level change 2015–2100CE

SUMMARY

A large ensemble of ice sheet projections to the end of the 21st century have been compiled within community-based initiatives. These ensembles allow for assessment of uncertainties in projections associated with climate forcing and a wide range of parameters governing ice sheet and shelf dynamics, including ice-ocean interactions. Herein, we compute geographically variable sea level ‘fingerprints’ associated with ∼320 simulations of polar ice sheet projections included in the Ice Sheet Model Intercomparison Project for CMIP6 and ∼180 projections of glacier mass changes from the Glacier Model Intercomparison Project. We find a strong correlation (coefficient > 0.97) between all fingerprints of Greenland Ice Sheet projections when considering a global region outside the near field of the ice sheet. Consistency in the fingerprints for the Antarctic Ice Sheet (AIS) projections is much weaker, though correlation coefficients > 0.80 were found for all projections with global mean sea level (GMSL) greater than 10 cm. The far-field variability in the fingerprints associated with the AIS is due in large part to the sea level change driven by Earth rotation changes. The size and position of the AIS on the south pole makes the rotational component of the sea level fingerprint highly sensitive to the geometry of the ice mass flux, a geometry that becomes more consistent as the GMSL associated with the ice sheet projection increases. Finally, the fingerprints of glacier mass flux show an intermediate level of consistency, with contributions from Antarctic glaciers being the primary driver of decorrelation.

INTRODUCTION

A range of geodetic observations have confirmed continuing mass loss from both the Greenland Ice Sheet (GrIS; IMBIE 2019) and Antarctic Ice Sheet (AIS; IMBIE 2018; Rignot et al. 2019), and global glaciers (Hugonnet et al. 2021) during the past 2–4 decades. From 1992 to 2018, the average mass loss from GrIS has been 0.40 ± 0.03 mm yr⁻¹ in units of equivalent global mean sea level (GMSL) rise, with approximately equal contributions from surface mass balance (SMB) and discharge from outlet glaciers (IMBIE 2019). In the period 1979–2017, the AIS had a negative mass balance of 0.36 ± 0.05 mm yr⁻¹ in GMSL units (Rignot et al. 2019), with ice streams accounting for ∼90 per cent of this discharge. Mass flux from the West Antarctic Ice Sheet (WAIS) dominates this budget, with progressively increasing contributions from the Antarctic Peninsula (AP) and East Antarctic Ice Sheet (EAIS) that combined to contribute ∼30 per cent of the total in the decade ending in 2017 (Rignot et al. 2019). Finally, from 2000 to 2019, glacial mass loss was equivalent to 0.74 ± 0.05 mm yr⁻¹ GMSL rise, about 20 per cent of the total sea level budget over the same period (Hugonnet et al. 2021).

Insights—and concerns—arising from these studies of ice sheet and glacier mass balance motivate efforts to project this mass balance and associated GMSL changes to the end of the century (e.g. Kopp et al. 2014; Hock et al. 2019; Jevrejeva et al. 2019; Goelzer et al. 2020; Marzeion et al. 2020; Seroussi et al. 2020) and beyond. A pair of recent studies report results from a large ensemble of community GrIS and AIS model simulations for 2015–2100 CE run under the auspices of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) (Goelzer et al. 2020; Seroussi et al. 2020). The goal of both sets of simulations, which were forced by a representative group of global climate models within the Coupled Model Intercomparison Project (CMIP5), was to estimate contributions of both ice sheets to GMSL across the 21^st century and quantify uncertainties associated with climate forcing, ice sheet model details, ocean-ice interactions, etc. Similar goals motivated the study of Marzeion et al. (2020), who considered a range of glacier models, GCMs and emission scenarios in their projections over the same 85 yr time period.

Goelzer et al. (2020) estimated GrIS mass loss of 90±50 mm and 32 ± 17 mm GMSL to 2100 CE for Representative Concentration Pathways (RCP) 8.5 and 2.6, relatively high and low emission scenarios respectively. Uncertainties associated with the climate and ice sheet models dominated the spread under the higher emission scenario. They also noted that limited current understanding of calving physics remained a fundamental obstacle to improving GrIS projections. The spread of predictions to year 2100 CE associated with the AIS was wider, with ranges of −78 to 300 mm GMSL under the RCP 8.5 scenario and −14 to 155 mm GMSL for RCP 2.6 (Seroussi et al. 2020). The main sources of uncertainty were related to the adopted CMIP5 forcing, the modelled physics of ice flow, the parametrization of melt in the sub ice shelf cavity and the dynamic ice sheet response to this melt. Strong regional variability in mass loss was connected to ocean forcing and the relative contributions of SMB and ice stream discharge. The balance between SMB and ice stream flux was notable across the EAIS, where net mass flux varied from −61 mm to 83 mm GMSL for RCP 8.5 scenarios, but also within the WAIS where mass loss in the Amundsen Sea sector of WAIS and in the Wilkes subglacial basin of the East Antarctic varied strongly across simulations. All figures noted above refer to ice mass changes relative to simulations with a constant climate forcing (‘control runs’) and these projections would be augmented by any future ice mass change driven by past climate forcing.

The Marzeion et al. (2020) projections of glacier mass balance included RCP scenarios 2.6, 4.5, 6.0 and 8.5. They projected mass loss of 79±56 mm and 159±86 mm GMSL equivalent change for RCP 2.6 and 8.5, respectively, from 2015 to 2100 CE. Over this time scale, uncertainty in the projections is dominated by the sensitivity to the emission scenario, whereas in the first half of the century glacier model uncertainty dominates. They also concluded that natural variability in glacier mass, while a relatively small contributor to global measures of uncertainty, can be a significant regional contributor to uncertainty.

GMSL change is a useful metric for ice sheet mass balance, but it is less useful for informing coastal adaptation since melting of ice sheets and glaciers leads to significant geographic variability in sea level change. In particular, mass flux from individual ice sheets and glaciers drives a unique geometry, or fingerprint, of sea level change (e.g. Clark & Lingle 1977; Clark & Primus 1987; Conrad & Hager 1997; Mitrovica et al. 2001, 2011; Plag & Jüttner 2001; Tamisiea et al. 2001; Plag 2006; Bamber & Riva 2010; Riva et al. 2010; Slangen et al. 2012; Spada et al. 2013; Brunnabend et al. 2015; Spada & Galassi 2016; Mitrovica et al. 2018; Adhikari et al. 2019; Moreira et al. 2021). Specifically, relative sea level (i.e. the distance between the sea-surface equipotential and the surface of the solid Earth) will fall within ∼2000 km of any rapid ice melting due to the combined effect of a loss of gravitational attraction between the ice sheet and ocean as well as an elastic rebound of the crust associated with the unloading. There will be a general increase in sea level rise at greater distance from the zone of melt, but this pattern would may be imprinted by a ‘quadrantial’ signal in sea level associated with perturbations in the orientation of Earth rotation (or polar wander) that has a spherical harmonic degree two, order one geometry (Milne & Mitrovica 1996). The latter signal (Fig. 1) approaches zero at the poles and equator and has the same sign and amplitude at sites displaced by 180°. Conservation of angular momentum indicates that the rotation axis will be perturbed towards any zone of ice melt, and this contributes a sea level drop in the two geographic quadrants towards which the local rotation axis is moving and an increase in sea level in the remaining two quadrants. This signal will play an important role in the discussion below. We note that the sign of the perturbations in sea level cited above (and directions of polar motion) will reverse in the case of ice growth.

In this paper, we compute sea level fingerprints for all GrIS and AIS simulations described in Goelzer et al. (2020) and Seroussi et al. (2020) and for a subset of global glacier projections described in Marzeion et al. (2020). Our goal is to quantify how sensitive the predicted geometries of sea level change are to uncertainties in the published projections by exploring correlations between fingerprints. We make little distinction between simulations based on different emission scenarios, but rather use the entire suite of simulations to consider geometries associated with the widest range of total mass flux.

SEA LEVEL MODELLING

Our predictions of sea level fingerprints are based on the so-called Sea Level Equation (see below) and require, on input, models of ice mass changes from 2015 to 2100 CE and a model for the elastic structure of the Earth. For the latter, we adopt the Preliminary Reference Earth Model (Dziewonski & Anderson 1981) which provides 1-D, depth-varying profiles of density and elastic constants. Lateral variations in these quantities are of the order of a few per cent and neglecting them has negligible effect on the computed sea level fingerprints (Mitrovica et al. 2011). Our set of ∼160 projections for each of the GrIS and AIS are adopted from Goelzer et al. (2020) and Seroussi et al. (2020), respectively, and we consider 178 projections of global glaciers from Marzeion et al. (2020), as tabulated by Edwards et al. (2021). The GrIS simulations involved 14 groups working with 10 ice sheet models, while the AIS simulations included 13 groups and 10 ice sheet models. The glacier simulations were based on 7 different glacier models and include peripheral Greenland and Antarctic glaciers. Comprehensive details of the simulations are provided in these references, including discussions of the multiple experiments performed with each ice model to assess sensitivity to climate forcings and model parameters.

Our sea level calculations are based on a theory that extends the classic treatment of Farrell & Clark (1976) to accurately account for the advance or retreat of grounded, marine-based sectors, shoreline migration due to local onlap or offlap of water and the signal in sea level associated with (ocean plus water) load induced perturbations in Earth rotation (Milne & Mitrovica 1996; Kendall et al. 2005; Mitrovica et al. 2005). The calculations were all performed up to spherical harmonic degree and order 512. Maps of sea level fingerprints shown below will be normalized by dividing by the GMSL change associated with each simulation. For this purpose, GMSL is the sea level rise computed by spreading the total volume of meltwater associated with each simulation uniformly over the present-day ocean geometry after any depressions vacated by grounded, marine-based ice are filled. In practice, this number is computed by repeating each sea level calculation for the case of a non-rotating, rigid Earth with no gravitational effects.

The solution of the Sea Level Equation is performed using the elastic special case of the pseudo-spectral algorithm described in detail in Kendall et al. (2005). The algorithm requires iterative improvement to a first guess for the sea level change, and we have found that sufficient convergence is established after 3–4 iterations. Our adoption of an elastic Earth model is based on an assumption that viscous effects on the century time scale we are considering are small, and on this basis, given our goal of predicting the sea level change from 2015 to 2100 CE, we only need to consider a single time step defined by change in the ice model between the initial (2015 CE) and final (2100 CE) time step of each ISMIP6 simulation. The neglect of viscous effects in the case of the AIS fingerprints requires some justification given the relatively low viscosity (∼10¹⁸ Pa s) below some areas of the West Antarctic (Barletta et al. 2018; Pan et al. 2021). We address this issue below. We note that our use of the term ‘sea level’ in the manuscript always refers to relative sea level, as defined above. In a later section of the manuscript, we consider predictions of changes in the height of the sea-surface equipotential, as would be measured by altimeters, and in that case we use the distinguishing term ‘absolute sea level’.

RESULTS AND DISCUSSION

As an illustration, Fig. 2 shows normalized sea level fingerprints for three scenarios which yielded the highest values of GMSL change associated with net mass loss from the GrIS, AIS and global glaciers (16.6, 31.1 and 16.5 cm, respectively, in units of equivalent GMSL rise). All maps show the main elements of a sea level fingerprint discussed above: a zone of radius ∼2000 km surrounding the mass loss associated with the weakening gravitational pull of the ice sheet and crustal uplift; a general trend towards higher sea level rise at further distance from the mass flux, but with a superimposed quadrantial pattern associated with rotational effects (evident in the GrIS and AIS cases); and an ocean loading signal apparent, for example, in the shoreline-parallel orientation of contours of North America in Fig. 2(a). In the GrIS simulation, the rotation axis is perturbed towards Greenland, and this contributes a sea level fall centred over the North Atlantic and (in the opposite quadrant) Australia, and a sea level rise over southern South America and the northwest Pacific (Fig. 2b). The polar motion in the AIS simulation is towards the West Antarctic and this reorientation contributes a rise in sea level in the northeast Pacific and Indian Ocean (notice the dip south of contours in this ocean) and a fall in the southeast Pacific and the Asian continent (the latter is obscured by the continental mask applied to the maps). The rotational feedback signal is not discernible in Fig. 2(c) because in that particular simulation the glacier mass flux drives a relatively small polar wander. In any event, the question arises: Do all fingerprints computed by adopting all simulations of either the GrIS, AIS or glacier mass flux have a consistent geographical pattern?

Fig. 3 shows the GMSL change to year 2100 CE associated with all ISMIP6 ice sheet simulations described in Goelzer et al. (2020) and Seroussi et al. (2020), and the glacier projections of Marzeion et al. (2020). In each case, colours distinguish the various emission scenarios. The GrIS simulations have values that range from 1.6 to 16.6 cm, with the RCP 2.6 simulations providing lower bound values. (We do not include a single simulation with a GMSL of −0.4 cm in the analysis.) The range in the AIS simulations is −8.6 to 31.1 cm, and in this case extreme values of both signs are generated with RCP 8.5 simulations. As described by Seroussi et al. (2020), the EAIS experiences a wide range of responses in the RCP 8.5 scenarios, with mass gain associated with an increase in SMB in some simulations contributing significantly to the lower bound GMSL values in Fig. 3(a). Finally, the glacier simulations have a GMSL range of 2.7 to 26.3 cm, with increasing emission scenarios showing higher values within this range.

Maps of the standard deviation for all the AIS, GrIS and glacier simulations provide a direct measure of the level of consistency between the normalized fingerprints (Figs 4a–c). The maps for GrIS and glacier simulations are characterized by standard deviations less than 0.2 (or 20 per cent of the normalized global average) outside regions in the near vicinity of the ice mass flux, Greenland in the former case, and Alaska, Greenland, the Arctic, West Antarctica, Patagonia, etc., in the latter. In contrast, in the AIS case (Fig. 4a; note the different colour scale) standard deviations fall below 0.5 only within a thin band on the equator and reach significantly higher values at higher latitudes in both hemispheres.

As an integrated measure of consistency across the simulations, we have computed a correlation coefficient (Fig. 5) between all fingerprints and the fingerprints generated by the simulation with the largest GMSL change to 2100 CE (Fig. 2). (Correlation coefficients are not impacted by normalization of the fingerprints and thus they are equally a measure of the correlation between the raw, i.e. unnormalized fingerprints.) In the case of the GrIS and glacier simulations, the correlation was limited to the region in which the standard deviation in the associated maps of Fig. 4 was less than 0.2 (the lightest blue contour in these maps), whereas in the case of the AIS, the correlation only included points north of 55° S. The sampling of these regions was performed on a grid of equal area to avoid sampling bias. The results of the correlation analysis are shown as solid dots in Fig. 5.

Outside the excluded region closest to the GrIS, all simulations show very strong correlation, with the minimum correlation coefficient found to be 0.97 (Fig. 5b). In contrast, the geographic variability in AIS sea level fingerprints north of 55° S is far more significant, varying from close to −1 (perfect anti-correlation) to + 1 (Fig. 5a). However, we note that the correlation (and anti-correlation) increases with increasing magnitude of GMSL change associated with the simulation. For example the correlation coefficient exceeds 0.8 for all simulations in which GMSL change is above 10 cm. The spread of correlations in the glacier case is intermediate to these two results, with only ∼10 per cent of the coefficients falling below 0.9 spread over a relatively wide range of GMSL values.

As we noted in the Introduction, the feedback into sea level of Earth rotation changes will act to introduce a large-scale signal in sea level well away from the location of mass flux. To consider the impact of this contribution on the correlations in Fig. 5, we repeated all simulations with the feedback process turned off and the results are shown by the open circles in Fig. 5. In both the AIS and glacier cases the removal of the rotational signature in the sea level simulations improves the correlation coefficients indicating that the feedback mechanism is contributing to the decorrelation of the fingerprints. (In the case of the AIS simulations with a net mass increase from 2015 to 2100 CE, removing the rotational signal increases the level of anti-correlation.) This raises the question of why the same feedback signal—which is clear in Fig. 2(b)—has negligible impact on the correlations computed in the full GrIS simulations (i.e. the solid dots in Fig. 5b). Since Greenland sits further from the pole than the AIS (or WAIS) it might be expected to have a stronger rotational feedback signal. Moreover, the distribution of glaciers is such that the net displacement of the pole and the associated sea level feedback would tend to be smaller, as was noted in the context of Fig. 2(c).

Figs 6(a) and (b) show the predicted angle and (normalized) magnitude of polar wander for all GrIS simulations, where the latter has units of meters of pole displacement per meter of GMSL equivalent ice mass loss. Both quantities show remarkable consistency, with the former being constrained to a few degrees within ∼40° W and the latter falling within the range of 120–140 m m⁻¹ GMSL. Thus, the high correlation across all simulations in Fig. 5(b) reflects a consistency in both the direction and magnitude of polar wander. The origin of this consistency is explored in Fig. 6(c), which shows the centres of ice mass flux (triangles, melt zones; crosses, zones of ice growth) for all 163 GrIS projections. These symbols fall within a remarkably narrow geographic band that is consistent with the concordant predictions of polar wander angles (Fig. 6a) and magnitude (Fig. 6b).

Next, we turn to the AIS simulations. As noted earlier, the rotational feedback signal contributes to the reduction in correlation evident in Fig. 5(a), and this issue is considered in more detail in Fig. 7(a) where the predicted angle of polar wander is shown for all AIS simulations. These angles vary over the full 360° range of longitude, with simulations characterized by a net mass loss (GMSL > 0) having a polar wander tending towards West Antarctica and those with a net mass gain (GMSL < 0) tending to move away from West Antarctica (and towards East Antarctica). The former is expected since simulations with a mass loss are dominated by melting from WAIS and Antarctic Peninsula, while the latter is typically driven by net mass gain across the same two regions. The high level of variability in the angle of polar wander reflects the equally broad variability in the location of centres of ice mass flux (Figs 7c and d). The location of the Antarctic on the south pole makes the orientation of the sea level signal associated with polar motion highly sensitive to small shifts in the geographic location of the mass flux since these can represent large shifts in longitude. However, we note that as the net mass loss increases in the AIS, the variability in the geometry of ice mass flux becomes less pronounced and the correlation improves (Fig. 5a).

To further illustrate the physical effects that control the level of consistency between sea level fingerprints of projected AIS mass flux, Fig. 8 shows ice height changes for four simulations, the associated normalized sea level fingerprint for each, and a decomposition of this fingerprint into the non-rotating case and a rotation signal. The top row is the simulation with the highest GMSL case treated in Fig. 2(a), while the remaining three rows involve simulations with GMSL values of ∼2–3 cm, but widely varying correlations factors of (from second to fourth row) 0.98, 0.81 and 0.44 (see Fig. 5a, green circles). The decomposition for the high GMSL case shows that the contribution to the fingerprint from rotational effects is relatively muted, indicating that the distribution of melt is sufficiently widespread across the perimeter of the AIS that the net rotational forcing is small. The second simulation has a much smaller volume of ice melt, but the distribution of this melt is similar to the first case, and so our normalization by GMSL yields an almost identical normalized fingerprint, and high correlation. The ice mass change is much more concentrated in WAIS and significant ice loss occurs in the AP in the third simulation and while the orientation of the rotation signal remains the same as in the first two cases, the polar motion and amplitude of the associated (normalized) signal is increased by a factor of 3. This amplified signal leads to a strong quadrantial imprint in the normalized fingerprint, with peaks over North America and the Indian Ocean, and troughs over the southeast Pacific and Asia; this rotation signal, and the more extensive near field expression of mass loss in the Southern Ocean, reduce the correlation coefficient to 0.81. Finally, the distribution of ice mass changes in the 4^th case is far different from the first three and extends from the Amundsen Sea in the West Antarctic to Aurora basin in the East Antarctic, and this leads to a high amplitude rotation signal that is oriented 90° from the signal in the first three cases (polar motion towards the Wilkes Basin). This leads to a highly distinct sea level fingerprint from the first 3 cases across the entire globe, with peaks over the northern Pacific and southernmost Atlantic and troughs centred over Europe and New Zealand. In this case, the correlation coefficient between this fingerprint and that for the highest GMSL case (Figs 2a and 5a) is only 0.44.

The rotational feedback into sea level is responsible for only part of the decorrelation between the AIS fingerprints (Fig. 5a). To investigate the origin of the remaining level of decorrelation, Fig. 4(d) repeats the standard deviation calculation of Fig. 4(a) with the exception that the normalized AIS fingerprints do not include the rotational feedback signal. In this case, the variability in the normalized sea level fingerprints originates from deformational and gravitational effects that are sensitive to the detailed geometry of ice mass flux. This variability extends significantly farther north than the cut-off angle of 55°S used in the correlation analysis of Fig. 5(a). Furthermore, removing the rotational signal significantly improves the correlation of the normalized fingerprints in the far field of the AIS.

Next, we return to the normalized sea level fingerprints of glacier mass flux. It is important to note that Antarctic glaciers are included in our calculations and that their relative contribution to the net GMSL values in Fig. 3(c) varies significantly across the simulations. As an example, Fig. 9(a) shows the normalized sea level fingerprint of a simulation in which Antarctic glaciers account for 69 per cent (5.2 cm) of the total GMSL change (7.6 cm). No other glacier accounts for more than 8 per cent of total in this simulation. This Antarctic mass flux is clearly the main driver of both the near- and far-field geometry of the sea level change, where the latter is imprinted with the strong quadrantial signal associated with polar wander. In Fig. 9(b), we compare the correlation coefficients computed using the full glacier data base (solid dots, reproduced from Fig. 5c) with coefficients computed for glacier simulations in which the Antarctic glaciers are removed from the analysis. The results indicate that the decorrelation evident in Fig. 5(c) is primarily due to the global sea level signal contributed by the Antarctic glaciers.

To this point, we have focused on the consistency between fingerprints of relative sea level change. In Figs 10(a)–(c), we show normalized fingerprints analogous to Fig. 2 with the exception that we are now considering absolute sea level changes as would be observed, for example, by satellite altimetry. These results are similar to their relative sea level analogues in Fig. 2, with a strong rotational signal evident, in particular, for the AIS and GrIS fingerprints, and near field sea level fall in areas of ice mass loss. Figs 10(d)–(f) provide a comparison of the correlations reproduced from Fig. 5 (solid dots) and correlations based on the analogous fingerprints of absolute sea level (open circles). A general observation is that the latter correlations are degraded relative to the former in the case of AIS and glacier simulations, consistent with earlier work showing that the rotational feedback signal is larger in predictions of absolute versus relative sea level (Tamisiea et al.2001).

Our maps of normalized sea level fingerprints have highlighted differences in the geometries of the fingerprints rather than differences between the raw (i.e. unnormalized) projections of sea level change. The latter will be important in a wide range of studies, for example, assessments of uncertainty in projections of local or regional sea level change. As a final investigation, useful to such studies, we have repeated the calculations of the standard deviations in Figs 4(a)–(c) using the raw projections of sea level change and the result is shown in Fig. 11. (The figure also includes mean values for the simulations.) As expected, the variability peaks in the near field of the ice mass flux, where deformational and gravitational effects dominate the fingerprints. Outside this region, the variability reflects the signal associated with the gravitational migration of water away from the ice flux and, in the case of the AIS and GrIS simulations, this pattern is clearly imprinted by the signal due to rotational feedback. The peak variation in the far-field is 7.7, 4.5 and 5.9 cm for the AIS, GrIS and glacier simulations, respectively.

CONCLUSIONS

Community efforts have emerged to provide projections of polar ice sheet mass balance to the end of the 21st century across a wide range of ice models with a focus on quantifying uncertainties associated with climate forcing, the details of the ice sheet model, including treatments of ice-ocean interactions, ice shelf dynamics, etc. It is common in such studies to quote the net mass balance in terms of the equivalent GMSL change, but a long history of sea level research has emphasized the geographic variability inherent to sea level changes driven by ice mass fluctuations. The goal of this study has been to quantify, for the first time, the consistency of so-called sea level fingerprints associated with the large ensemble of polar ice sheet and glacier projections. That is, our focus has been directed towards answering the following question: How similar are the geometries of sea level fingerprints computed within each of the set of AIS, GrIS and glacier simulations? To this end, the global maps have been normalized by GMSL to remove amplitude information. (As noted earlier, correlation coefficients are independent of a simple scaling of the fingerprints.)

To address the above question, we have computed the normalized fingerprints of a set of ∼160 simulations of ice sheet mass balance for both the GrIS (Goelzer et al. 2020) and AIS (Seroussi et al. 2020), each relative to the appropriate control run at constant climate, compiled under the auspices of the ISMIP6 for CMIP6. All simulations were forced using climate output generated through CMIP5. Outside the near-field of the GrIS, which we defined as the region characterized by a standard deviation less than 0.2 in Fig. 4(b), we have found strong correlation (coefficient > 0.97) across all GrIS fingerprints, regardless of the associated GMSL of the ISMIP6 projection, a reflection of the notable consistency in the centres of ice mass flux across all the GrIS simulations (Fig. 6). We conclude that projections of sea level changes due to GrIS mass flux—which are likely to show similar ice mass distributions—need only consider a single normalized fingerprint scaled by the appropriate GMSL change of the GrIS model. The situation for AIS fingerprints is significantly more complex. Given the position of the Antarctic straddling the south pole, small changes in the distribution of a mass flux can lead to significant changes in the orientation of the global signal of Earth rotation changes in sea level. Furthermore, the geometry of mass flux varies significantly across the suite of simulations we have considered (Figs 7b and c), leading to highly discordant sea level predictions that extend well north of the Antarctic (Figs 4a and d). These near- and far-field effects lead to major inconsistencies amongst the normalized sea level fingerprints of projected AIS mass flux. Nevertheless, we have noted that the consistency in these fingerprints increases as the GMSL change associated with the projected ice change increases. For GMSL changes greater than 10 cm to year 2100 CE, we find correlation coefficients > 0.80. For simulations satisfying this lower bound it may be possible, depending on the level of accuracy required in a sea level projection, to adopt one of the high-GMSL fingerprints described herein. Finally, the sea level fingerprints computed using projections of glacier mass change to 2100 CE show consistencies at a level intermediate to the GrIS and AIS cases and any decorrelation is largely due to the near- and far-field signal associated with projected mass changes within the Antarctic glacier system.

Our sea level projections have assumed that the Earth's response to ice mass flux may be modelled as a purely elastic phenomenon. Viscous effects, and in particular the migration of water out of marine-based areas exposed by retreating ice, have been shown to be important contributors to multi-century sea level projections associated with AIS mass flux given the relatively low mantle viscosity beneath some areas of the West Antarctic (Pan et al. 2021). However, the relatively short duration of our sea level projections, and our focus on consistency outside the near field of the ice mass change, reduce the importance of viscous effects. As an example, we repeated the AIS simulation shown in Fig. 2(a) using the 3-D viscosity model V3D_RH described in Pan et al. (2021) and found that the correlation coefficient between this simulation and the purely elastic calculation using the same ice sheet simulation was 0.998.

The term ‘fingerprint’ emphasizes that each distinct geometry of ice melt will drive a unique geometry of sea level change and as a result the geographic variability in observed sea level provides information regarding the source of the meltwater. The consistency between normalized fingerprint projections in the far-field of the ice sheets for all the GrIS simulations, and for AIS simulations with the highest GMSL values, has the advantage of reducing uncertainty in projections of geographically variable sea level change driven by polar ice mass flux to the year 2100 CE. However, the consistency in these cases also indicates that distinguishing between various geometries of GrIS mass flux, or of high-GMSL AIS mass flux, would ultimately require observations of sea level change in the near field of the ice sheets, where the consistency breaks down.

Of course, any study assessing the risk of sea level changes to the end of the current century must also consider a range of other processes that contribute to geographic variability in these changes and to GMSL. These processes include ongoing glacial isostatic adjustment, changes in continental water storage, ocean dynamic and steric effects (Hamlington et al. 2020). Over the past few decades, there is unequivocal evidence for accelerating mass flux from both polar ice sheets (Fox-Kemper et al. 2021) suggesting that their contribution to the sea level budget of the 21st century will become increasingly important.

Acknowledgement

We thank the Editor (Bert Vermeersen) and two anonymous reviewers for their constructive comments regarding earlier versions of the manuscript. We thank the Climate and Cryosphere (CliC) effort which supported ISMIP6 and acknowledge the World Climate Research Programme which coordinated and promoted CMIP5 and CMIP6. We also thank the various climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the CMIP data and providing access, the University at Buffalo for ISMIP6 data distribution and upload, and the multiple funding agencies who support CMIP5 and CMIP6 and ESGF.

FUNDING

This work was supported by the  MacArthur Foundation and Harvard University.

Data Availability

All sea level modelling software used in this study and modelling results are available at the publicly accessible online site doi.org/10.5281/zenodo.7949464.

References