Plain Language Summary
The planet is warming, and sea levels are rising as oceans expand and ice on land melts. The warmer the Earth gets, the faster the seas will rise. Projecting future sea level rise using numerical models has proved extremely challenging and, as a consequence, estimates carry a large uncertainty. How good are the models of ocean expansion and mass loss from glaciers and ice sheets? We tackle this question by comparing how the models react to future warming with how sea level reacted in the past. The models for glaciers, Greenland, and the oceans are compatible with observations. For the largest ice mass on the planet, the Antarctic Ice Sheet, the models do not agree with the observations. As a result, projections of global sea level rise may be an underestimate.
1 Introduction
Despite recent advances in both observations and numerical modeling, sea level rise (SLR) projections remain highly uncertain due, in large part, to inadequate understanding of how the ice sheets covering Antarctica and Greenland will respond to climate forcing. Various approaches have been developed to attempt to address this uncertainty including community-based model intercomparison projects (Goelzer et al., 2020; Nowicki et al., 2016; Seroussi et al., 2020), emulator studies (Edwards et al., 2021), structured expert judgement (Bamber and Aspinall, 2013; Bamber et al., 2019) and, what have been termed, semi-empirical models (SEMs). This latter approach correlates changes in global surface temperature with global mean sea level (GMSL) based on how these two variables have evolved in the past (Moore et al., 2013). Various approaches have been used to account for the different time constants for the response of the components of the climate system that contribute to SLR, such as thermal expansion of the oceans, and mass loss from glaciers and ice caps and the Greenland and Antarctic ice sheets. The different approaches mentioned above have produced markedly different estimates for future SLR, especially for the upper tail of the distributions and depending on the climate forcing scenario used (Fox-Kemper et al, 2022). The ice sheets have the longest response time of any component of the climate system and their behavior for a given year does not, therefore, reflect the climate forcing for that year, or preceding decade but the cumulative forcing over a longer time period. To account for this delayed response and to provide a scenario-independent metric for SLR, Grinsted and Christensen developed the concept of the transient sea level sensitivity (TSLS) (Grinsted and Christensen, 2021). This is analogous to the notion of a transient climate sensitivity, which defines the mean temperature response of a GCM to a doubling in CO2 concentrations. In the case of the TSLS, however, the definition accounts for the slow response of the ice sheets and ocean by using a century-average temperature to determine the transient sea level response at the end of the 100-year period. Hence, the TSLS provides an estimate of the instantaneous rate of SLR per century per centigrade change in time-averaged temperature (Grinsted and Christensen, 2021). This is a useful metric because it is i) scenario independent and ii) it is not the equilibrium SLR that is critical for adaptation planning but the rate over some time period (Oppenheimer, 2019).
An important conclusion of the study that introduced the concept of the TSLS was that projections for SLR presented in the Fifth Assessment Report (AR5) of the IPCC and their Special Report on Oceans Cryosphere and Climate (SROCC) had weaker sensitivities than indicated by the observational and proxy sea level record (Grinsted and Christensen, 2021). This suggests that the model-based projections in the AR5 and SROCC likely underestimate future SLR when compared to observations. This conclusion is supported by studies using structured expert judgement (Bamber et al., 2019) and from simple extrapolation of the present-day, forced SLR trends from satellite altimeter observations (Fasullo et al, 2018). The difference was significant and, assuming a linear relationship between TSLS and the centennial-average temperature change, the observations lie closer to expert judgement median projections than to the numerical model estimates. This is likely due to smaller ice sheet contributions from the numerical models although an investigation of the sensitivity of each component of the sea level budget was not undertaken (Grinsted and Christensen, 2021). This raises two interesting and important questions. First, there is evidence suggesting that CMIP6 models have a higher climate sensitivity compared to their predecessors (Forster et al., 2020) and, indeed, this has lead to the conclusion that the Greenland Ice Sheet (GrIS) produces a larger contribution to SLR compared to their predecessors when forced by these models (Hofer et al., 2020) and that the steric contribution is about 10% greater than in CMIP5 (Jevrejeva et al., 2020). It is possible, therefore, that the TSLS for CMIP6 simulations lies closer to the observational trend relative to CMIP5 and the AR5 values. Second, data are available for each component of the sea level budget for CMIP6 simulations making it possible to examine the transient sensitivity of each of these and to compare them with whatever suitable observational data are available. This would permit identification of which modeled components are less sensitive with respect to observations and to quantitatively assess the origin for the discrepancy between the observations and modeled TSLS identified in Grinsted and Christensen 2021. Those two questions are addressed in this study: namely an examination of the TSLS of the GrIS, West and East Antarctic Ice Sheets (WAIS, EAIS), glaciers and ice caps (GIC) and ocean thermal expansion separately based on the CMIP6 model runs used in the Sixth Assessment Report (AR6) of the IPCC (Fox-Kemper et al., 2021) and an evaluation of the CMIP6 TSLS against observations and previous modeled SLR trends.
2 Data
2.1 Ice and ocean observations and paleo sea level proxies
The observations and their errors are based on the assessment of the historical sea level budget in AR6 (Fox-Kemper et al., 2021). From this we extract the rates in four distinct periods (1901-1970, 1971-1992, 1993-2005, 2006-2018) for the steric, AIS, GrIS, and GIC contributors and for GMSL. The AR6 represents a synthesis of all relevant knowledge, but the data sources are similar to a recent study that demonstrated closure of the sea level budget components when compared to the integral as inferred from sea surface height data (Frederikse et al., 2020). This study includes satellite and in-situ assessments starting in 1960 for GIC, 1970s for the GrIS and 1992 for the AIS. modeled and/or observational estimates for both the GrIS and GIC extend back to 1900 but not for the AIS, which is assumed to have made a small contribution based on geodetic observations of polar motion (Adhikari et al., 2018). These older (pre satellite) observations, however, have a significantly larger uncertainty associated with them. The thermosteric component of the sea level budget was obtained from three different compilations of in-situ observations from 1957-2018 combined with a reconstruction based on more limited historical data extending back to 1871 (Zanna et al., 2019). Thus we have reconstructed or observational estimates from 1901-2018 for all components except the AIS. For the preindustrial 1850-1900 period we use estimates for GMSL from Kopp et al. (Kopp et al., 2016) and estimates for GIC using an update of (Leclercq et al., 2011) rates (Marzeion et al., 2015). The AR6 only reports the historical contribution for the entire Antarctic ice sheet, and we therefore supplement with estimates for the WAIS, EAIS and Antarctic Peninsula (PEN) from IMBIE2 (Shepherd et al., 2018) for the period from 1992-2017. The observations of sea level rates are paired with corresponding estimates of Global Mean Surface Temperature (GSMT) based on HadCRUT5 (Morice et al., 2021). Throughout, we report temperatures as anomalies relative to a 1995–2014 baseline for both observations and models.
2.2 CMIP6 Data
The sixth phase of the Coupled Model Intercomparison Project (CMIP6) brings together an advanced set of participating climate models compared to CMIP5. CMIP6 models were forced by an updated set of emissions scenarios, utilizing the Shared Socioeconomic Pathways (SSPs), creating a broader selection of possible futures. For the first time, CMIP6 included an ice sheet modeling intercomparison (Goelzer et al., 2020; Nowicki et al., 2016; Seroussi et al., 2020) and experiments investigated the effects of higher ocean resolution (e.g. HighResMIP). Since CMIP5, greater understanding of physical processes (e.g. glacier and ice-shelf calving and grounding line evolution) have driven developments in glacier and ice sheet models, and the representation of ocean processes has improved with increased resolution (e.g. ocean eddies in a number of models). The closure of the global energy and ocean mass budget after removing drift has also improved in CMIP6 (Irving et al., 2021).
Studies have found that some CMIP6 GCMs have higher equilibrium climate sensitivity compared to CMIP5 (Forster et al., 2020), attributed to improved representation of clouds. This translates into higher projections of global mean surface temperature change (Hermans et al., 2021) and impacts projections of regional sea-level change, such as dynamic sea-level change in the North Atlantic and Arctic (Lyu et al., 2020). The AR6, however, did not rely solely on CMIP6 simulations and used emulators, calibrated to an assessed range of climate sensitivity from paleoclimate, observations, and physical process models. This reduced the higher warming found in some CMIP6 models.
2.3 Steric model output
The thermosteric sea-level change is obtained from either the CMIP6 direct output of global average thermosteric sea level change (zostoga) or calculated based on potential temperature and salinity in CMIP6 output. For historical outputs, the thermosteric sea-level change time series are divided into four periods which are: 1850-1900, 1900-1950, 1950-2000, and 1992-2014. For the future climate scenario, we have investigated SSP1-2.6, SSP2-4.5, and SSP5-8.5, for two time periods: 2016-2050, and 2051-2100. Table S1 shows the CMIP6 models and variants used in this study. It should be noted that individual model runs could produce negative rates of thermosteric sea-level change due to model drift. We therefore correct for model drift by applying a constant rate bias adjustment that sets the 1958-2015 steric rate to exactly match an observational estimate of 0.54 mm/yr (Frederikse et al., 2020). This constant rate adjustment will not affect the sensitivity to a change in temperature.
2.4 Land ice model output
The ice sheet and GIC contributions to sea level rise have been the focus of two model intercomparison projects — ISMIP6 and GlacierMIP. Edwards et al. (2021) emulated glacier simulations from GlacierMIP Phase 2 (Marzeion et al., 2020), ensuring any peripheral glacier overlap with ice sheets was minimal. The models in these intercomparison projects were driven by a relatively small subset of CMIP5 (Goelzer et al., 2020; Seroussi et al., 2020) and CMIP6 models (Payne et al., 2021). Edwards et al. (2021) constructed an emulator tuned to reproduce these MIPs, and used this to project ice mass loss for a modern set of scenarios. Temperatures are projected by a reduced complexity climate model (Smith et al., 2018), allowing for uncertainty in climate sensitivity in a manner that approximates the AR6. In this paper we use a published sample of 500 simulations from the emulator. Each sample from the emulator models the contributions from GrIS, GIC, EAIS, WAIS, and the Antarctic Peninsula, and each sample has been run for six different SSP scenarios. The emulator model projections were pre-processed with a first order Savitzky-Golay filter with a window length of 15 years to reduce interannual variability. Neither ISMIP6, nor the emulator, has hindcasts that can be used to assess model drift. A constant drift can be considered an unforced contribution to sea level rise and will therefore not affect estimates of the transient sensitivity to a temperature change.
Mass loss from the ice sheets can be partitioned into ice dynamic and surface mass balance (SMB) components. To make an assessment as to which of these components is driving the ice sheet’s TSLS, we used the output from the ISMIP6 ice sheet models that were forced by CMIP6 models, reported in Payne et al. (2021). The CMIP6 models used to drive the ice sheet models were limited to those available to the ISMIP6 project at the time – these consist of four models for SSP5-8.5 and one for SSP1-2.6. The models are all at the upper end of the CMIP6 ensemble in terms of their transient climate sensitivity (Payne et al., 2021). The ice dynamic sea level contribution is calculated by subtracting the SMB, integrated over the grounded ice sheet area, from the total sea level contribution.
3 Methods
The major contributors to sea level rise can be viewed as large reservoirs. The ice sheets and GIC are reservoirs of freshwater, and the ocean is a reservoir of heat. Any change in the stock of these reservoirs will result in a change in sea level. A steady state is characterized by a balance in the fluxes to and from these reservoirs, for example, gains from snow fall must be balanced by losses from melt and discharge. The initial impact of a change in climate will be a shift in the flux balance of every reservoir, and thus a change in the corresponding sea level rates. However, the fluxes to and from reservoirs are not only influenced by external forcing but will also depend on the stock in the reservoir. The long wave radiation losses from the ocean surface will depend on sea surface temperature and be connected to the ocean heat, and total melt losses from GIC will depend on the remaining glaciated area. This leads to a feedback between the stock in the reservoir and the net fluxes. The reservoir will keep leaking or gaining or leaking until it finds a new equilibrium with the imposed climate. The equilibration process can be characterized by an e-folding timescale. The ocean and ice sheets are giant reservoirs that change size slowly and have multi-centennial equilibrium response times. GIC, however, come in many sizes — every glacier or ice cap with its own response time. Often glacier response times are counted in decades.
In this paper, we focus on the century scale response of the primary contributors to the sea level budget. The chosen time frames are relatively short compared to the response times we expect from most contributors. Thus we will be focusing on the initial ‘transient’ response. We use global mean surface temperature as an indicator for the intensity of the climate forcing, and investigate how sensitive the transient response is to a change in forcing intensity, i.e. mean temperature. As we are primarily concerned with changes in the response rather than absolute values, we disregard small quasi-constant components of the sea level budget such as the effect of glacial isostatic adjustment (order 0.1 mm/yr) (Vishwakarma et al., 2020), the deep steric term (order 0.1 mm/yr) or land hydrology (order -0.15 mm/yr) (Fox-Kemper et al, 2022).
The Transient Sea Level Sensitivity (TSLS) is defined as the increase in the rate of sea level rise to an increase in global mean surface air temperature (Grinsted and Christensen, 2021). We aim to determine the TSLS for each of the major contributors to the sea level budget from both models and observations. The TSLS concept inherently represents a linearization of the response to warming. This is an approximation with a limited range of applicability, as discussed later. We therefore determine the TSLS in three different periods (historical, early 21st century, and late 21stcentury). Future projections span a range of scenarios with different warming pathways. This allows us to estimate the TSLS by regressing the temporal average GMST against the average rate of the modeled contribution to sea level rise. The regression intercept is the sea level rate associated with a temperature anomaly of zero. The intercept can be reformulated in terms of a balance temperature — the temperature change necessary to stop that sea level component from contributing to sea level rise (Grinsted and Christensen, 2021). For the historical period we only have a single warming pathway, and thus cannot estimate the sensitivity to warming at a particular point in time. We can, however, examine how the sea level contribution has accelerated over time as warming has progressed.
For every model we calculate the temporal average rate of sea level contribution, and the corresponding average GMST in a set of target periods. We have chosen four historical periods (1850–1900, 1900–1950, 1950–2000, and 1992–2014) and two projection periods (2016–2050, and 2051–2100). The steric contribution is based on CMIP6, and thus covers the entire set of target periods. However, the ice emulator only provides estimates for the future contribution. This is a limitation inherited from the ISMIP6 protocol. We require at least three points in every regression, and reject all poorly constrained TSLS estimates with a standard error greater than 3 mm/yr/K. This quality filter is particularly useful for the 2016–2050 period where the GMST for the different scenarios has not yet deviated by much. We use a different set of periods when we estimate the historical TSLS from observations as we are limited by data availability.
In order to estimate the TSLS we regress GMST against the rate in the sea level contribution. We simply use linear least squares regression for model data. However, for observational estimates we use weighted least squares regression as not all data are equally certain. We weight every data point by the inverse of the estimated standard error in the sea level rate. Confidence intervals in the historical TSLS estimates are determined using a Monte Carlo approach where we perturb the estimated rate and temperature according to the reported standard errors. These perturbations are independent, and thus we are assuming no error covariance between the estimated rates in different periods. Fully covariant errors in the sea level rates would only affect the estimated intercept but not the slope. We therefore argue that this assumption will have minimal impact on the estimated TSLS confidence intervals.
The spread between CMIP6 runs should not be interpreted as representative of the uncertainty distribution. Some earth system models have been run multiple times, and this can lead to a bias if all CMIP6 runs are treated as equally probable samples from an uncertainty distribution. We therefore average all the model runs from an individual Earth System Model (ESM), with the only exception being to models with perturbed physics which are treated as if it was a different ESM. In this study, CanESM5 is the only model with two different perturbed physics members. Given that there exists substantial difference between different perturbed physics members of CanESM5 in volume-averaged ocean temperature (Swart et al., 2019), it is sensible to treat it as two different ESMs. The approach we use here is inline with the standard practice of combining multi-model climate ensembles (Knutti et al., 2010).
There is not a simple one-to-one relationship between the ESMs used for the steric model, and the model samples from the ice emulator. It is therefore not trivial to produce a fully consistent model estimate of GMSL. However, it is clear that at the very least we must ensure that only models with similar climate sensitivity are paired. We therefore pair each ice emulator sample (i ) with the steric estimate from a random sample from the CMIP6 ensemble where each run (j ) has been assigned a probability weight. The weight is designed to account for how well temperatures match. We write
\(w_{\text{ij}}=e^{-\frac{1}{2}\ \left(\frac{T_{i}-T_{j}}{0.2\ K}\right)^{2}}\), Equation 1
where the 0.2K is a standard deviation to allow for a small misfit between the two temperatures. This is necessary as we are dealing with finite samples and is similar to the bin width in a histogram. A randomly selected model run (k ) based on these weights will therefore have a small temperature misfit. We make a first order adjustment to the steric rate (\({\dot{S}}_{k}\)) to account for this misfit as follows
\({\dot{S}}_{adjusted,k}={\dot{S}}_{k}+\left(T_{k}-T_{i}\right)\cdot TSLS_{k}\)Equation 2
where TSLSk is the sensitivity estimated for k -th model. This is a small adjustment as the model weights ensure that the temperature misfit is small. This combination strategy ensures that the CMIP6 ensemble is weighed such that it is consistent with future temperatures used by the ice emulator and consequently AR6 as the emulator was designed to be consistent with the AR6.
The TSLS estimates are, by design, near independent of GMST and thus climate sensitivity (Grinsted and Christensen, 2021). We therefore directly combine TSLS estimates from the different contributors, where we simply combine each set of TSLS from an ice emulator sample with the steric TSLS from a random CMIP6 model.
4 Results and discussion
The results and discussion is divided into subsections for each component followed by a subsection examining the integral, i.e. GMSL. This is followed by a summary subsection with TSLS estimates for all components as a function of temperature. The results of each component are discussed in the relevant subsection. When TSLS ranges are included, they are quoted as the two sigma, 90 percentile range.
4.1 Steric
Although there is significant model spread, it is evident that the assumption of a linear relationship between the averaged temperature and sea level rate for the thermosteric component is valid and that the gradient of the linear fit for CMIP6 models and the observations are broadly consistent (Figure 1). This is not surprising as thermal expansion of the oceans is a linear function of ocean heat content to first order. It is, nonetheless, reassuring that the models and observational data are broadly consistent, despite the relatively limited steric data available for the first half of the Twentieth century.
The linear regression is best constrained for the period 2051-2100 which spans the largest temperature range between scenarios. For this period, we find that models have a sensitivity of 1.5±0.2 mm/yr/K. The median estimates for the earlier periods (1850-2015 and 2015-2050) are consistent (1.7±0.5 mm/yr/K and 2.1±0.8 mm/yr/K) but show substantially more scatter as the data span a smaller temperature range and, consequently, is less well constrained. The observations indicate a sensitivity of 1.4±0.5 mm/yr/K.
The observational data imply a balance temperature of -1.1K which is close to the pre-industrial value. This suggests that to mitigate sea level rise in the future would require a substantial reduction in present-day GMST. We cannot extract a meaningful estimate of balance temperature from the models as it is necessary to apply a drift correction to CMIP6 models, as mentioned earlier. This drift correction is a vertical offset in figure 1 which will affect the balance temperature.