The fast GIC response directly affects the GMSL behavior, which results in TSLS changing between periods. Historical observations indicate a GMSL sensitivity of 3.4±0.4 mm/yr/K. Model projections indicate a greater sensitivity prior to 2050 (5.3±1.0 mm/yr/K), but smaller sensitivity post 2050 (3.0±0.4 mm/yr/K). This is in line with the central TSLS estimate derived from expert assessments for the entire 21st century (+4.2 mm/yr/K [90%: 2.6-11 mm/y/K]) (Bamber et al, 2019). The deviations between these estimates has clearly largely been mirrored from the GIC response (Fig 10), which masks the more stationary TSLS of the remainder of the sea level budget. We therefore also report the sensitivity of GMSL minus GIC (labelled ‘All but GIC’ in fig 10). This reveals a discrepancy between the sensitivity of models and estimates from historical data. Historical observations indicate a sensitivity of 3.2±0.5 mm/yr/K, which is ~30% greater than model projections. This discrepancy is hard to justify physically as models display a stationary sensitivity over the 21st century (+2.4 mm/yr/K pre-2050 vs +2.3 mm/yr/K post-2050). This suggests that models of at least one of the remaining components (steric, GrIS, or AIS) underestimates the sensitivity to warming.
We find that the steric sea level contribution from CMIP6 models have a transient sensitivity (2051-2100: 1.5±0.2 mm/yr/K) to warming which is marginally greater but compatible with the historical estimate (1.4±0.5 mm/yr/K; see fig 10). The steric contribution therefore cannot explain the ‘All but GIC’ model-data discrepancy.
Greenland ice sheet models are more sensitive to temperature change than our estimate from historical data (0.8±0.2 mm/yr/K vs 0.5±0.1 mm/yr/K). This could indicate a bias in either the model or the observational estimates, or that the transient sensitivity is increasing over time. Results from a structured expert judgement (Bamber et al., 2019) imply that experts judge that the GrIS may be more sensitive (+1.0 mm/yr/K) than models and observations imply. That increase in sensitivity would require a non-linear response to temperature that is not evident in the models (Fig 2). This suggests that experts are aware of structural uncertainties in the modeled GrIS contribution that could lead to a substantial non-linearity in the response as implied by some recent modeling and observational studies (Aschwanden et al, 2019; King et al, 2020; Sasgen et al, 2020). We conclude, therefore, that GrIS is also unlikely to be the source for the ‘All but GIC’ model-data discrepancy.
Models of the AIS display negligible sensitivity to warming (Fig. 10) in contrast to historical data which indicate that AIS has a sensitivity of +0.4±0.2 mm/yr/K. Restricting the observational estimate to the satellite era, where the AIS contribution is better constrained, increases the estimate to +0.5 mm/yr/K. This is far short of a mean centennial value as the observational record is only about 30 years. There is some evidence, however, that part of the observed behavior of the WAIS during that period is due to a forced climate signal (Holland et al, 2019). Further, experts expect a large difference in the AIS contribution between a 2℃ and a 5℃ scenario (Bamber et al, 2019) which implies a transient sensitivity of +1.2 mm/yr/K. Such an increase over the historical sensitivity indicates that experts consider a non-linearity in the AIS sensitivity to be possible. Considerable uncertainty remains regarding the role of certain processes during the 21st century for the AIS (DeConto et al., 2021; Edwards et al., 2019) and this is likely reflected in the wider range of values obtained in the expert elicitation. This behavior is not reflected in the model projections, and this partly explains the ‘All but GIC’ model-data discrepancy. The difference between the observational and model derived sensitivity of the AIS is however insufficient to fully account for the ‘All but GIC’ discrepancy.
The AIS contribution can be partitioned into dynamics and SMB, and regionally into EAIS, WAIS, and Peninsula. The EAIS and WAIS have been discussed in preceding sections. The dynamic contributions of both EAIS and WAIS show little scenario dependence in the ISMIP6 models and are thus relatively insensitive to warming (Fig. 5, Fig. 7). The model sensitivities of both ice sheets are therefore predominantly a result of the SMB response to warming. Warming tends to result in increased melt and runoff, but also increased accumulation due to the greater moisture holding capacity of the atmosphere. The SMB sensitivity to warming can therefore be both positive and negative. The accumulation response dominates over the EAIS which results in a net negative TSLS for the ice sheet (Fig. 6 and 7). Accumulation and melt is closer to balance over the WAIS, and for the most intense warming scenarios the melt response can start to dominate the SMB sensitivity in some models (Fig. 5). The net result for the WAIS is a slightly positive central estimate of the TSLS (Fig. 4). We find that models of the Antarctic Peninsula have a near zero sensitivity to warming (0.00±0.05 mm/yr/K). This is surprising considering that satellite observations show rapid and accelerating glacier mass loss in the region (Wouters et al., 2015). Further, a glacier modeling study found SMB in the region to be particularly sensitive to warming (Hock et al, 2009). Further, it has been suggested that the lack of scenario dependency in the modeled dynamic response of AIS over the 21st century is due to inadequate understanding of ice flow and sliding, which results in high uncertainty in sea level projections and thus overlap between scenarios (Lowry et al., 2021). However, over longer time scales they find that large differences between high and low emission scenarios do emerge. This conclusion is also supported by the most recent study of the AIS response when accounting for the marine ice cliff instability (Deconto et al, 2021). This could in part explain the mismatch between our observed and modeled TSLS results.
5 Conclusions
We have examined how the contributions to the sea level budget relate to global mean surface temperature from both models and data. We approximate AR6 model projections (Fox-Kemper et al. 2021) by using weighted CMIP6 models and the output of an ice emulator (Edwards et al., 2021) using ISMIP6 (Goelzer et al., 2020; Seroussi et al., 2020) and GlacierMIP (Marzeion et al., 2020). We find the rate of the individual contributions to be near linear in average temperature, and quantify the slope as the transient sea level sensitivity. We thus focus our attention on the response sensitivity to a change in warming, rather than the total sea level contribution which is also affected by drift.
Models of all contributors, apart from GIC, show little change in TSLS over the 21st century. A comparison between the historical sensitivity estimated from observations, and the sensitivity implied by model projections can therefore serve as a sanity check on the model response for most contributors. GIC shows a marked change in TSLS over the 21st century (Fig. 8), which is expected as many glaciers have decadal scale response times. The TSLS concept is therefore of limited utility for the GIC contribution. While GIC only contributes a fraction to GMSL, this limits how closely we should expect 21st century TSLS to match the historical GMSL sensitivity (3.4±0.4 mm/yr/K). We therefore also examine the residual response after removing the GIC contribution, and identify a substantial discrepancy between the sensitivity inferred from models vs historical data. The historical estimate of the ‘All but GIC’ sensitivity (3.2±0.5 mm/yr/K) is 30% greater than the model sensitivity (Fig. 10). This strongly suggests that at least one of the ice sheets, or the steric contribution has an overly muted response to warming. The sensitivity of GrIS and steric show a closer correspondence with historical estimates. We find that the AIS is the most likely candidate as most models have low to negative sensitivity to warming in contrast to our historical estimate of 0.4±0.2 mm/yr/K (Fig.10). We speculate the WAIS and Antarctic Peninsula to be the source of the discrepancy based on recent mass loss trends in the region (Shepherd et al., 2018; Wouters et al., 2015).
A recent study found that the ice sheet models were unable to reproduce recent observed trends in mass loss (specifically from GrIS) and argued that this raises concerns regarding model skill (Aschwanden et al., 2021). This is a separate issue from the TSLS discrepancy we identify in this paper which suggests that AIS model sensitivity is biased low. The TSLS quantifies how mass loss accelerates under warming and is unaffected by how well it captures present day trends. Modeling protocols such as removing a control run, or how the model is spun-up will influence long term trends. An imperfect initial state in a model with a long response time can result in an unforced long term model drift. Model drift is a challenging issue in all models with a very long response time, and so affects both ice sheets (Goelzer et al., 2018) and steric models (Slangen et al., 2016). A reasonable match to the present-day rate is therefore not a sufficient validation of models of components with long response times, and vice versa. This is perhaps best illustrated by the ensemble of GrIS models (Fig. 2) which is unable to match present-day trends (Aschwanden et al., 2021; vertical offset in fig. 2), while having a TSLS that is in good agreement with historical records (Fig 2. and Fig 10). Model intercomparison projects such as ISMIP6 and CMIP6 are crucial to assessing model skill. A limitation of the TSLS comparison in this paper is that we compare past to future response and some models were not run for the historical period. We therefore recommend that the protocol for future ice sheet model intercomparisons is inspired by CMIP6 to include historical runs starting in 1850, to enable stronger validation against data. However, this is not feasible for model initialization methods that rely on the assimilation of high-quality ice-sheet wide observations from satellites, for example inverting for model parameters by matching observed velocities. It is a challenge to critically assess the sensitivity in models without a past, but TSLS comparisons to historical estimates remain a viable option.
The near-stationary sensitivity of most contributors has practical implications for coastal planners and decision-makers. Regional sea level rise projections are usually constructed by modeling the impact of the mass loss from individual contributors on the static equilibrium of the sea surface (due to e.g. gravitational redistribution of mass), and change due to dynamical sea level is then accounted for. Often it is assumed that the dynamical sea level scales with global mean steric expansion. In practice, this means that the local sea level is a weighted sum of all the individual contributors. If we explicitly account for GIC, local vertical land motion, weather and tidal variability (e.g. following Frederikse et al., 2016) then we are left with a residual that responds near linearly to warming according to models. This can potentially be leveraged to make local relative sea level projections by extrapolation. Further study is needed to assess the feasibility of this approach.
Beyond the year 2100, we expect feedbacks to play an increasing role in the ocean heat uptake and ice sheet mass loss. We therefore expect the TSLS of these contributors to start deviating from historical values and from a linear trend. Eventually the response can no longer meaningfully be considered transient, and it will be more useful to consider the equilibrium sensitivity to warming and sea level commitment (Clark et al., 2016, Fox-Kemper et al, 2022); i.e. how many metres can we ultimately expect for a given forcing? Here paleo records, rather than historical records, can serve as an important constraint for models. We note that a credible equilibrium response does not guarantee a credible transient sensitivity as the equilibrium can be approached at different speeds (Gilford et al., 2020). Finally, we associate SLR since the start of the 20th century with anthropogenic global warming.