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.