The sea level contribution of the Antarctic ice sheet
constitutes a large uncertainty in future sea level projections. Here we
apply a linear response theory approach to 16 state-of-the-art ice sheet
models to estimate the Antarctic ice sheet contribution from basal ice shelf
melting within the 21st century. The purpose of this computation is to
estimate the uncertainty of Antarctica's future contribution to global sea
level rise that arises from large uncertainty in the oceanic forcing and the
associated ice shelf melting. Ice shelf melting is considered to be a major
if not the largest perturbation of the ice sheet's flow into the ocean.
However, by computing only the sea level contribution in response to ice
shelf melting, our study is neglecting a number of processes such as
surface-mass-balance-related contributions. In assuming linear response
theory, we are able to capture complex temporal responses of the ice sheets,
but we neglect any self-dampening or self-amplifying processes. This is
particularly relevant in situations in which an instability is dominating the
ice loss. The results obtained here are thus relevant, in particular wherever the
ice loss is dominated by the forcing as opposed to an internal instability,
for example in strong ocean warming scenarios. In order to allow for
comparison the methodology was chosen to be exactly the same as in an
earlier study (Levermann
et al., 2014) but with 16 instead of 5 ice sheet models. We include
uncertainty in the atmospheric warming response to carbon emissions (full
range of CMIP5 climate model sensitivities), uncertainty in the oceanic
transport to the Southern Ocean (obtained from the time-delayed and scaled
oceanic subsurface warming in CMIP5 models in relation to the global mean
surface warming), and the observed range of responses of basal ice shelf
melting to oceanic warming outside the ice shelf cavity. This uncertainty in
basal ice shelf melting is then convoluted with the linear response
functions of each of the 16 ice sheet models to obtain the ice flow response
to the individual global warming path. The model median for the
observational period from 1992 to 2017 of the ice loss due to basal ice
shelf melting is 10.2 mm, with a likely range between 5.2 and 21.3 mm. For
the same period the Antarctic ice sheet lost mass equivalent to 7.4 mm of
global sea level rise, with a standard deviation of 3.7 mm (Shepherd et al., 2018) including all processes,
especially surface-mass-balance changes. For the unabated warming path,
Representative Concentration Pathway 8.5 (RCP8.5), we obtain a median contribution of the Antarctic ice sheet to
global mean sea level rise from basal ice shelf melting within the 21st
century of 17 cm, with a likely range (66th percentile around the mean) between
9 and 36 cm and a very likely range (90th percentile around the mean)
between 6 and 58 cm. For the RCP2.6 warming path, which will keep the
global mean temperature below 2∘C of global warming and is thus
consistent with the Paris Climate Agreement, the procedure yields a median of
13 cm of global mean sea level contribution. The likely range for the
RCP2.6 scenario is between 7 and 24 cm, and the very likely range is
between 4 and 37 cm. The structural uncertainties in the method do not
allow for an interpretation of any higher uncertainty percentiles. We provide
projections for the five Antarctic regions and for each model and each
scenario separately. The rate of sea level contribution is highest under
the RCP8.5 scenario. The maximum within the 21st century of the median
value is 4 cm per decade, with a likely range between 2 and 9 cm per decade
and a very likely range between 1 and 14 cm per decade.
Introduction
The Antarctic ice sheet has been losing mass at an increasing rate over the
past decades (Rignot et al., 2019;
Shepherd et al., 2018). Projections of changes in ice loss from Antarctica
still constitute the largest uncertainty in future sea level projections (Bamber
et al., 2019; Bamber and Aspinall, 2013; Church et al., 2013; Schlegel et
al., 2018; Slangen et al., 2016). Evidence from paleorecords and regional
and global climate models suggests that snowfall onto Antarctica follows a
relation similar to the Clausius–Clapeyron law (Clapeyron,
1834; Clausius, 1850) of an increase by about 6 % for every degree of
global warming (Frieler
et al., 2015; Lenaerts et al., 2016; Medley and Thomas, 2019; O'Gorman et
al., 2012; Palerme et al., 2014, 2017; Previdi and Polvani, 2016). The
current snowfall onto Antarctica is of the order of 8 mm yr-1 in global sea
level equivalent; i.e. an increase in snowfall will decrease global sea
level of the order of half a millimetre for every degree of warming (van
de Berg et al., 2006; Lenaerts et al., 2012). Surface melting is likely to
play a minor role as a direct ice loss mechanism within the 21st
century, but it might initiate other ice loss processes such as
hydrofracturing and subsequent cliff calving with the potential for much
higher ice loss than any other process (DeConto and Pollard, 2016;
Pollard and DeConto, 2009). An important process of additional ice loss from
Antarctica is basal ice shelf melt and the associated acceleration of ice
flow across the grounding line (Bindschadler
et al., 2013; Jenkins et al., 2018; Nowicki et al., 2013, 2016; Reese et
al., 2018a; Rignot et al., 2013; Shepherd et al., 2004).
Here we follow a very specific procedure that is designed to estimate the
uncertainty of future ice loss from Antarctica as it can be induced by basal
ice shelf melting. We follow exactly the same procedure as in Levermann
et al. (2014) but with 16 ice sheet models instead of 3 models with a
dynamic representation of ice shelves (although five models participated in
the earlier study, only three of them had a dynamic representation of ice
shelves). At the core of the approach is a linear response theory (Good et al., 2011;
Winkelmann and Levermann, 2013), which is explained together with the models
used in more detail in Sect. 2. The ice sheet models used here all take
part in the initMIP intercomparison project for Antarctica (Seroussi et al., 2019)
within the overall ISMIP6 initiative (Goelzer et
al., 2018; Nowicki et al., 2016). Section 3 provides the hindcasting for the
observational period and Sect. 4 gives the results of the computation for
the 21st century. The last section provides conclusions and
discussions. Although we will not repeat details of the method in all
aspects and refer to the earlier publication for that, we will summarize it
in Sect. 2 in order to provide a paper that is understandable on its
own. A detailed analysis as to why the 16 different models respond differently
cannot be provided in this publication due to both space limitations and the fact that each of these analyses would constitute a full-scale
publication in itself. We provide a synthesis of the results and refer to
potential future studies by the individual modelling groups for details on
the individual model results.
The purpose of this study is to estimate the uncertainty of basal-melt-induced sea level contribution from Antarctica as it is caused by the
uncertainty in the basal melt forcing. While ice shelf melting is considered
to be a major if not the largest perturbation of the ice sheet's flow into
the ocean, the approach neglects a number of processes such as
surface-mass-balance-related contributions (Bamber et al.,
2018; Rignot et al., 2019) and their feedbacks (Levermann and Winkelmann, 2016). In assuming
linear response theory, we are able to capture complex temporal responses of
the ice sheets, but we neglect any self-dampening or self-amplifying
processes. This is particularly relevant in situations in which an instability
is dominating the ice loss. The results obtained here are thus relevant, in
particular wherever the ice loss is dominated by the forcing as opposed to
an internal instability, for example in strong warming scenarios.
In contrast to the study here, individual model simulations with specific
time series of basal ice shelf forcing for a specific ice sheet model can be
better used to understand specific processes and yield much more
precise results for this specific basal melt forcing. The main contribution
of this study is the investigation of the response of the models to the full
range of uncertain forcing and the combination of this for all the different ice sheet
models. In addition, the switch-on experiments at the basis of the analysis
allow for a comparison of the different model responses to a very simple
and generic forcing and might be used to improve the models or at least know
how one specific model compares to the others in a specific region.
It is important to note that in this study no changes in the surface mass
balance are taken into account, nor are any other ice loss processes other
than the ice dynamic discharge into the ocean as it is induced from an
increase in basal ice shelf melting. The term “Antarctic contribution to
sea level rise” is used in this study to refer to the sea-level-relevant
ice loss induced from basal ice shelf melting only.
Projecting procedure using linear response theory with forcing uncertainty
Here we follow the same procedure to project the ice loss of Antarctica in
response to basal ice shelf melting as described in Levermann
et al. (2014). In order to be able to compare to the previous results we use
the same forcing data as in the 2014 publication. The only thing that
changed is the ice sheet models that were used to compute the projections.
The model initial states are those published in the initMIP intercomparison
project for Antarctica (Seroussi et al.,
2019). All other aspects of the projections, i.e. the procedure and the data
that were used to force the models, are the same. We provide projections of
the basal-melt-induced ice discharge from Antarctica for the four different
carbon dioxide concentration scenarios (RCP2.6, RCP4.5, RCP6.0, RCP8.5; RCP is short for Representative Concentration Pathway; Moss et al.,
2010). Here the RCP8.5 scenario represents a future evolution with
increasing carbon emissions as seen in the past decades, while the RCP2.6
scenario represents one possible path that keeps the Paris Climate Agreement (United Nations, 2015) under certain conditions and thus keeps
the global mean temperature increase below 2∘C of global warming (Schleussner et al., 2016).
In a nutshell the method follows the schematic in Fig. 1: in order to
provide a statistical estimate of the basal-melt-induced sea level
contribution of Antarctica an ensemble of 20 000 basal melt forcing time
series for the ice sheet models is created. Instead of forcing each model
with each of the 20 000 forcing time series, the modelling groups carried
out a specific simulation with a constant additional basal melt forcing of
8 m yr-1, which was switched on at the beginning of the experiment after
initialization and then kept constant for 200 years. The time derivative of
the resulting sea level response of the specific ice sheet model within this
experiment was used as a response function to a delta-distribution forcing
of the ice sheet. Following the concept of a linear response theory this
response function is convoluted with each of the forcing time series in
order to estimate this ice sheet model's response to this specific forcing
time series. Thereby it is possible to provide estimates of the response of
16 ice sheet models to 20 000 different basal melt forcing time series.
Schematic of the projection procedure: global mean temperature
increase, ΔTG, is transformed
into a subsurface warming around Antarctica, ΔTO, with a scaling coefficient, αr, and a time delay, τr, both of
which are derived for each of the five Antarctic outlet regions from 19
CMIP5 models. The basal ice shelf melting rate, Δm, is then derived by multiplying the subsurface oceanic
temperature with a basal melt sensitivity β. This
sensitivity is randomly chosen from the observed interval. The basal melt
rate is then convoluted with the ice sheet response function of the specific
region, Rr, to obtain the time series of this
Antarctic outlet region.
The ensemble of basal melt forcing time series was created as follows
(Fig. 1). Each ensemble member represents three random selections. First,
a time series of the global mean temperature evolution from 1850 to 2100 is
selected from an ensemble of 600 simulations of the MAGICC 6.0 emulator.
These time series are all consistent with the observed warming path and the
future carbon concentration pathway for which the sea level projection is
computed (i.e. RCP2.6, 4.5, 6.0, or 8.5). Secondly, one of 19 CMIP5 climate
models is selected in order to obtain a relation between the global mean surface
warming and subsurface ocean warming which is forcing the Antarctic ice
sheet. The subsurface ocean warming was computed in the five different
regions around Antarctica shown in Fig. 2. In order to translate the
global warming time series into a subsurface ocean warming time series for
the different Antarctic regions a correlation coefficient in combination
with a time delay was computed for each of the CMIP5 models. Thirdly, the
subsurface ocean warming signal was multiplied with a value from the
observed interval of melting sensitivities of the ice shelves. This way each
surface warming signal is translated into a basal ice shelf melting signal
in each of the Antarctic basins.
Oceanic regions in which the basal ice shelf melting was
applied.
The random selection from 600 warming signals and 19 oceanic scaling
functions is combined with a randomly uniform selection from the observed
basal melt sensitivity interval to an ensemble of 20 000 time series for
each emission scenario. The statistics of these time series are provided in
Fig. 3.
Projected basal melt rates following Sect. 2. The
experiment used here for all the ice sheet models is the one with an
additional 8 m yr-1 of basal melting (black horizontal line in each panel). It
is the experiment that is closest to the projected basal melt rates, which
fosters the applicability of the linear response theory.
Each ensemble member of these ice sheet forcing time series is then
convoluted with the linear response function of the ice sheet model of the
respective Antarctic region to obtain an estimate of the sea level
contribution of this Antarctic sector to the global warming signal. This
procedure is carried out for each member of the ensemble to obtain
statistics of the sea level contribution of Antarctica from basal ice shelf
melting.
In summary, for each emission scenario the procedure works as follows (each
of the items is described in more detail below and in Levermann
et al., 2014).
Randomly select a global mean temperature realization of the respective
RCP scenario from the 600 MAGICC 6.0 realizations constrained by the
observed temperature record. The time series start in 1850 and end in 2100.
Randomly select one of 19 CMIP5 models in order to obtain a scaling factor
and a time delay for the relation between global mean surface air
temperature and subsurface ocean warming in the respective regional sector
in the Southern Ocean.
Randomly select a melting sensitivity in order to scale the regional
subsurface warming outside the cavity of the Antarctic ice shelves onto
basal ice shelf melting.
Select an ice sheet model that is forced via its linear response function
with the time series of the forcing obtained from steps 1–3.
Compute the sea level contribution of this specific Antarctic ice sheet
sector according to linear response theory.
Repeat steps 1–5 20 000 times with different random selections in each of
the steps in order to obtain a probability distribution of the sea level
contribution of each Antarctic sector and each carbon emission scenario.
Thus, the 20 000 selections are obtained by randomly choosing one
temperature time series, one CMIP5 ocean model, one melt sensitivity, and
one ice sheet model. The procedure is also used for each of the ice sheet
models separately. In this case the random selection in step 4 is replaced
by a fixed selection of the model. The procedure is illustrated in Fig. 1.
For the computation of the total sea level contribution from all Antarctic
sectors together, the forcing is selected consistently for all sectors. That
means that for each of the 20 000 computations of the sea level contribution
one global mean temperature realization is selected, as is one ocean model for
the subsurface temperature scaling and one basal melt sensitivity. Although
there are other possibilities, this approach was chosen because it preserves
the forcing structure as provided by the ocean models. Details of steps 1–5
are given in the upcoming subsections.
Surface temperature scenario ensemble
We use the Representative Concentration Pathways (RCPs) (Meinshausen
et al., 2011; Moss et al., 2010). The range of possible changes in global
mean temperature that result from each RCP is obtained by constraining the
response of the emulator model MAGICC 6.0 (Meinshausen et
al., 2011) with the observed temperature record. This procedure has been
used in several studies and aims to cover the possible global climate
response to specific greenhouse gas emission pathways, including the carbon
cycle feedbacks (e.g. Meinshausen et
al., 2009). Here we use a set of 600 time series of global mean temperature
from the year 1900 to 2100 for each RCP that cover the full range of future
global temperature changes. Compare to Levermann
et al. (2014) for details.
Subsurface oceanic temperature scaling
We use the simulations of the Coupled Model Intercomparison phase 5
(CMIP5) (Taylor et al., 2012) to obtain a scaling
relationship between the anomalies of the global mean temperature and the
anomalies of the oceanic subsurface temperature for each model. This has
been carried out for the CMIP3 experiments (Winkelmann et al., 2012) and was
repeated for the CMIP5 climate models in Levermann
et al. (2014). The scaling approach is based on the assumption that
anomalies of the ocean temperatures resulting from global warming scale with
the respective anomalies in global mean temperature, with some time delay
between the signals. We use oceanic temperatures from the subsurface at the
mean depth of the ice shelf underside (Table 1) in each sector (Fig. 2) to
capture the conditions at the entrance of the ice shelf cavities. As a small
difference to the previous publication we modelled the Antarctic Peninsula
separately with the ice sheet models. In order to be able to keep the same
forcing we use, however, the same oceanic scaling as in the Amundsen region,
which was the approach in the previous publication. The surface warming
signal, ΔTG(t), needs to be transported to depth;
therefore, the best linear regression is found with a time delay between the
changes in global mean surface air temperature and subsurface oceanic
temperatures, i.e.
ΔTO(t)=αr⋅ΔTG(t-τ),
where τ is a CMIP5-model- and region-specific time delay.
Mean depth of ice shelves in the different regions denoted in
Fig. 2 as computed from Le Brocq et
al. (2010), consistent with the previous study (Levermann
et al., 2014) in order to make the results comparable. Oceanic temperature
anomalies were averaged vertically over a range of 100 m around these depths.
For the probabilistic projections the scaling coefficients are randomly
drawn from the 19 provided CMIP5 models. This approach does not account for
changes due to abrupt ocean circulation changes (Hellmer et al., 2012), but the assumption is
consistent with the linear response assumption underlying this study, and the
correlation coefficients obtained for the 19 CMIP5 models used here are
overall relatively high for each of the oceanic regions (Tables 2–5). In any
case it is crucial to keep this limitation in mind when interpreting the
results.
East Antarctic sector: scaling coefficients,
αr, and time delay, τr, between increases in global mean temperature and subsurface
ocean temperature anomalies.
Ross Sea sector: scaling coefficients, αr, and time delay, τr, between
increases in global mean temperature and subsurface ocean temperature
anomalies.
Amundsen Sea sector: scaling coefficients, αr, and time delay, τr, between
increases in global mean temperature and subsurface ocean temperature
anomalies.
Weddell Sea sector and Antarctic Peninsula: scaling
coefficients, αr, and time delay, τr, between increases in global mean temperature and subsurface
ocean temperature anomalies.
ModelCoeff.r2τCoeff.r2without τ(yr)with τACCESS1-00.180.77200.260.79ACCESS1-30.090.76150.120.77BNU-ESM0.280.83200.360.84CanESM20.140.74450.320.80CCSM40.140.9150.150.92CESM1-BGC0.140.9000.140.90CESM1-CAM50.160.8500.160.85CSIRO-Mk3-6-00.000.2800.000.28FGOALS-s20.180.89600.450.93GFDL-CM30.230.85250.370.89HadGEM2-ES0.250.6200.250.62INMCM40.590.8300.590.83IPSL-CM5A-MR0.020.04950.140.12MIROC-ESM-CHEM0.230.8500.230.85MIROC-ESM0.230.7800.230.78MPI-ESM-LR0.160.70400.310.73MRI-CGCM30.080.0400.080.04NorESM1-M0.120.7900.120.79NorESM1-ME0.120.68200.160.73Sensitivity of basal ice shelf melting
In order to translate the ocean temperature changes into additional basal
ice shelf melting for the five regions, we apply a basal melt sensitivity
β in a linear scaling approach, i.e.
Δm=β⋅ΔTO.
While great advances have been made in the past years bringing together
observations and measurements of Southern Ocean properties (e.g.
Schmidtko et al., 2014) as well as sub-shelf melt rates and
volume loss from Antarctic ice shelves (e.g. Paolo et al., 2015; Rignot et al.,
2013), the relation between oceanic warming and changes in basal melting is
still subject to high uncertainties (Paolo et al.,
2015).
Furthermore, some of the observed changes in sub-shelf melting are likely
caused by changes in the ocean circulation rather than warming due to
anthropogenic climate change (Hillenbrand et al., 2017;
Jenkins et al., 2018). The recently observed ice loss in the Amundsen region,
for instance, has been linked to the inflow of comparably warm circumpolar
deep water into the ice shelf cavities (e.g. Hellmer et
al., 2017; Pritchard et al., 2012). Similarly, the observed thinning in the
Totten region in East Antarctica is largely driven by changes in the
surrounding ocean circulation (Greenbaum
et al., 2015; Wouters et al., 2015).
In our simplified approach, we therefore draw the melt sensitivity parameter
with equal probability from an empirically based interval between 7 and 16 m a-1 K-1 (based on Jenkins,
1991; Payne et al., 2007). While this approach neglects the complex patterns
arising for observed basal melt rates in Antarctica, it is consistent with
the response function methodology adopted here. Note that we are applying
melt rate anomalies to derive the response functions – the ice sheet model
simulations still display a wide range of total melt rates over space, with
generally higher melting near the grounding line and lower melting or even
refreezing towards the ice shelf front. This is consistent with the vertical
overturning circulation typically found in ice shelf cavities (Lazeroms et al.,
2018; Olbers and Hellmer, 2010; Reese et al., 2018b).
Combining the global mean temperature time series of Sect. 2.1 and the
CMIP5 oceanic scaling of Sect. 2.2 with the basal melt sensitivity
described here in a probabilistic way, i.e. by choosing an ensemble of
20 000 combinations of each of these three components, yields the basal melt
time series in Fig. 3. The horizontal black line depicts the 8 m yr-1 level.
The basal melt time series are scattered around this level. For the
projections we will thus use the switch-on experiments with 8 m yr-1 of
additional basal melt as described below. This is the most balanced choice
to span the range of simulations, with 4 m yr-1 being too low for most of the
RCP8.5 scenario and 16 m yr-1 being too high for the majority of scenarios
and ensemble samples.
The reason for carrying out experiments in which a constant additional
basal melt forcing is applied for a period of 200 years is that this allows
us to easily derive linear response functions for the different ice sheet
models in the different regions as described in the next subsection.
Deriving the ice sheet response function
The core of the projections of the future sea level contribution from
Antarctic basal ice shelf melting is composed of simulations with 16 ice sheet models.
The models were forced with a constant additional basal ice shelf melting of
8 m yr-1. The forcing was applied homogeneously in each of the five oceanic
sectors separately (Fig. 2). The regions were chosen to avoid ice dynamic
interference between the regions on the timescale of this century. In order
to check this, additional simulations with all regions forced simultaneously
were carried out by some of the modelling groups (all data are provided as a
Supplement to this paper). These simulations showed that any possible
non-linear interactions between the flow of the different basins which do
exist on longer timescales (Martin et al., 2019) are
negligible on the timescale of 200 years used here and will not be
considered any further in this study. For comparison additional simulations
with 4 and 16 m yr-1 were carried out. This is discussed below. A number of
modelling groups carried out further simulations with 1, 2, and 32 m yr-1
basal melt rates. Although these simulations are highly interesting, a full
discussion of their results is beyond the scope of this publication. The
results of the 32 m yr-1 simulations are provided in Figs. S1–S4 in the Supplement. Here we aim at providing an estimate of the future sea level
contribution from Antarctic ice discharge and the uncertainty that is
associated with the external forcing.
One of the strongest assumptions of the projections computed here is that of
a linear response of the ice sheet dynamics to external forcing. This,
however, does not mean that it is assumed that the ice discharge is
increasing linearly with time. It merely assumes that increasing the
magnitude of the forcing by a specific factor will increase the magnitude of
the response of the ice sheet by the same factor. The temporal evolution of
the ice sheet is given by a temporarily varying response function. The
response function, R(t), is defined as the response of the
system to a delta-peak forcing. It could be estimated by measuring the
response of the ice sheet to a 1-year basal melt forcing of 1 m yr-1, which
would correspond to a unit forcing for a short period of time. Once the
response function is known the assumption is that the response to any given
forcing, m(t), can be obtained by linear superposition, which
in a time-continuous situation translates into a convolution of the response
function with the forcing:
S(t)=∫0tdτmτ⋅Rt-τ,
where S(t) is the sea level contribution from ice discharge
and, t is time starting from a period prior to the beginning of a
significant forcing. From Eq. (3) it is clear that the response
function can also be obtained from a Heaviside forcing whereby basal melt is
switched on to a constant value, μ, at a specific time and then kept
constant as was done here. In that case the observed response, Aμ(t), is simply the time integral of the response function:
Aμ(t)=μ⋅∫0tdτRτ.
The response functions for each of the ice sheet models use the fixed
Heaviside forcing μ=8 m yr-1 and then take the time derivative of the
response A8myr-1(t) and divide by 8 m yr-1. Due to the
relatively strong inertia of ice sheet models this approach generally yields
more robust results compared to a delta-peak approach, which is why we have
followed this path here. Another option which is often used in solid-state
physics to obtain the response functions (for example, their oscillatory
excitations) is by forcing the system with white noise.
Fourier transformation of Eq. (3) will then transform the convolution
into a simple product, and the white noise becomes a constant in Fourier
space. The Fourier transform of the response divided by this constant is
then simply the Fourier transform of the response function. This approach,
however, is not helpful to obtain a short-term response to a slow-moving
system such as an ice sheet.
Description of the ice sheet models
The ice sheet models used here all take part in the initMIP intercomparison
project for Antarctica (Seroussi et al., 2019)
within the overall ISMIP6 initiative (Goelzer et
al., 2018; Nowicki et al., 2016). Since the description of their respective
ability to reproduce the present ice dynamics of Antarctica is a study in
its own, we refer to the corresponding model description papers and provide
only a brief description of each of the model in Appendix A.
Validity of the linearity assumption
In order to assess the validity of the linearity assumption, we plotted in
Fig. 4a–e the original simulations of each model for an 8 m yr-1 additional
basal melt forcing (black curves) which is held constant over 200 years. In
addition, we plot the outcome of the 4 m yr-1 experiment (blue solid curves)
and the 16 m yr-1 experiments (red solid curves) together with the 8 m yr-1
experiments divided by 2 (blue dashed) and multiplied by 2 (red dashed).
Generally the agreement is reasonable. The fact that the validity of the
linearity assumption can be extended all the way to a doubling and halving
of the forcing is extraordinary where it is true.
(a) Linearity check for East Antarctica. Response of ice
sheet models to additional basal melting of 8 m yr-1 (solid black line)
underneath all ice shelves in East Antarctica compared to 4 m yr-1 (solid blue
line) and 16 m yr-1 (solid red line). In order to check the linearity of the
response to the warming amplitude the dashed red line gives the times series
of the response to 8 m yr-1 of basal melt multiplied by 2 and the dashed blue
line the same but divided by 2. The dotted lines give the scaled response
with the scaling exponent α (see Eqs. 5 and 6). A positive
scaling exponent means that the ice sheet model responds super-linearly to
basal ice shelf melting in this region. A negative α indicates a
sub-linear response in this region. AISM VUB did not provide a 16 m yr-1
simulation. The black dashed line for BISI LBL represents the simulation
with 500 m horizontal resolution that is used for the projections. The
linearity is tested with a set of simulations at 1 km horizontal resolution.
(b) Linearity check for the Ross region as in panel (a). (c) Linearity check for the Amundsen region as in panel (a). (d) Linearity check for the Weddell region as in panel (a).
(e) Linearity check for the Antarctic Peninsula as in panel (a).
As a quasi-quantitative measure for the validity of the linearity assumption
we computed an exponent α such that the curves
5A4,α(t)≡4myr-18myr-11+α⋅A8(t)=2-1+α⋅A8(t)6A16,α(t)≡16myr-18myr-11+α⋅A8(t)=21+α⋅A8(t)
have the least square error to their respective target functions A4(t)
and A16(t). The values for α are provided for each model in
each sector in Fig. 4a–e together with the respective curves as dotted
lines. In the case of perfect linearity α=0. If α<0 a
doubling of A8(t) yields a curve that is higher than A16(t); i.e.
the model responds sub-linearly to basal melting. This also means that a
halving of A8(t) is an overestimation of A4(t). This was the case
for most models. As can be seen from the comparison of the curves with
α correction and the original simulations, linearity can be assumed
for the relatively short response time of 200 years and the forcing range
applied in this study.
The term “no scaling” was used when no -1<α<2
represented a valid minimum of the error; i.e. the different experiments are
not linearly related. This is only the case for very small and noisy
responses in the Antarctic Peninsula. The term “no data” means that the
modelling group did not provide the corresponding data. For the computation
of the sea level projections the 8 m yr-1 experiments were used throughout this
study.
The response function for each model and each region is given in Fig. 5a–e together with their 10-year running mean. The response function is
unitless because it is a sea level rise (m yr-1) divided by basal melt rate
(m yr-1). Note that this is the response the model would show for a short and
sudden forcing of 1 year of 1 m yr-1 additional basal ice shelf melting in the
region. While some models show an instantaneous ice loss response (e.g. in
East Antarctica the models AISM VUB, ISSM UCI, PISM VUW, and ÚA UNN), most
models exhibit a more gradual increase in the ice loss over time. The
temporal structure of the response is a result of the complexity of the ice
dynamics and its interaction with the initial condition and the bed
topography.
(a) Response function for the East Antarctica region. Response
function computed from the time derivative of the response of the ice sheet
models within the experiment with additional basal melting of 8 m yr-1 divided
by 8 m yr-1. The response function is thus unitless in this specific case.
The red line provides a 10-year running mean. For the BISI LBL model
the simulation with 1 km horizontal resolution (compared to the main
simulation with 500 m horizontal resolution that is used for the projections) is also shown. These are the light grey lines and the light red 10-year running mean. (b) Response function for the Weddell Sea region as in panel (a). (c) Response function for the Amundsen Sea region as in panel (a). (d) Response function for the Ross Sea region as in panel (a). (e) Response function for the Antarctic Peninsula region as in panel (a).
As can be seen from the basal melt projections in Fig. 3 the applied melt
rates vary strongly around 8 m yr-1. In the Supplement (Fig. S1a–e) the
results for the 32 m yr-1 switch-on experiments are provided for context for
the models that have performed these experiments. The linearity assumption
is not necessarily a good assumption in all cases, but in most cases the
assumption is a reasonable approximation of how basal melting is responding
to external forcing.
For the adaptive grid model BISI LBL, the scaling is shown for simulations
with the finest horizontal resolution of 1000 m, while the projections are carried
out with a simulation with the finest horizontal resolution of 500 m (shown as
the black dashed curve in the BISI LBL panels in Fig. 4a–e). Due to
computational constraints the linearity check had to be done at the slightly
lower resolution (1000 m). As can be seen in the Fig. 4a–e there are some
quantitative deviations between the higher- and lower-resolution simulations,
but the results are not qualitatively different.
Hindcasting the observational record
The projections of sea level contributions from Antarctica due to basal
melting underneath the ice shelves following the linear response theory were
started in the year 1900 in order to make sure that no significant global
mean temperature increase influences the outcome. Following the procedure
described above and thereby using the combined equations of Fig. 1, the sea
level contribution is computed from
Sr(t)=∫0tdτβ⋅αr⋅ΔTGτ-τr⋅Rt-τ=αrβ⋅∫0tdτΔTGτ-τr⋅Rt-τ,
with constants αr, β, and
τr derived from observations or CMIP5 model
results and the index, R, indicating the specific Antarctic
forcing region (Fig. 2). We can then hindcast the observed sea level
contribution between 1992 and 2017 and compare it to observations (Fig. 6). To this end we use the results by Shepherd et
al. (2018), which do not differ significantly from earlier estimates (Shepherd
et al., 2012). The time series of the median observed sea level contribution
is given as a white line in Figs. 6 and 7 with the uncertainty range given
in grey shading. The individual model results are given as the median
and the likely range around this median (66th percentile around the median) as
the full and dotted black lines. While individual models may deviate
strongly from the observed range, the combination of all models shows a
similar contribution for the time period 1992–2017 as was observed with a
bias towards slightly higher ice loss (Figs. 6 and 7, Table 6).
Hindcasting observed sea level contributions and modelled sea level
contribution of Antarctica from the different ice sheet models. The solid
black line represents the median contribution between 1992 and 2017 with the
66th percentile (first standard deviation) around the median. The grey shading
represents the uncertainty range of the observed contribution of Antarctica
(white solid line) following Shepherd et al. (2018).
Hindcasting of all models combined with observed sea level
contributions and modelled sea level contribution of Antarctica from the
different ice sheet models. The solid black line represents the median
contribution between 1992 and 2017 with the 66th percentile (first standard
deviation) around the median. The grey shading represents the uncertainty
range of the observed contribution of Antarctica (white solid line)
following Shepherd et al. (2018).
Likely hindcast range of historical sea level
contribution compared to the observed range.
An important issue regarding the comparison with observations (Fig. 6) is
whether the individual models or individual projections should be weighted
according to their ability to hindcast the observed contribution to global
sea level rise. One way to do this would be to compute the weight,
wi, of a specific computed time series (using a
specific atmospheric temperature time series, a specific ocean model, and
a specific melting sensitivity) as follows:
wi=1N⋅eΔSi-ΔSobs2/2σ
where ΔSobs is the observed median sea level
contribution of Antarctica between 1992 and 2017 according to Shepherd et al. (2018), and σ is the
uncertainty of this estimate according to the same publication. The
normalization factor N would depend on the sample of computations
compared. It would be chosen such that the sum over all realizations within
a set is 1. Thus, the weight for a specific realization could be different
if the contribution is computed for only one specific ice model or if it is
computed for all ice models. We have decided against this kind of weighting
for the simple reason that the comparison of a model–forcing combination to
reproduce the past does not reflect its ability to project the future. The
reason for this is that the main contribution from Antarctica to the sea
level rise since 1992 arose from a specific oceanic warming in the Amundsen
Sea sector, which cannot be easily linked to the global mean temperature
increase. It is definitely not reflected in the procedure that we apply here
to obtain the forcing underneath the ice shelves (Fig. 1). Applying such a
weighting would thus distort the results in an unjustified way.
The comparison is done here in order to illustrate the order of magnitude of
the signal that is obtained by this procedure. Compared to earlier ice sheet
models the newer generation is able to exhibit a dynamic behaviour that is
at least of the same order of magnitude compared to observations. Here only
positive temperature anomalies above the reference level are accounted for.
That is because it cannot be claimed that a linear response as described in
Eq. (7) can also capture a negative response, which would be due to
processes like refreezing. This may lead to a small positive bias in the
initial period at the beginning of the 20th century and thereby to a
small overestimation of the observed sea level contribution. Furthermore, the
observations will include changes in surface mass balance, in particular an
increase in snowfall, which is not captured by our approach. Thus, even though
the comparison with observations seems to be compelling, it is not as strong
a test as it might seem.
Projecting the 21st century sea level contribution of Antarctica from
basal ice shelf melting
Finally, we compute the projections of Antarctica's contribution to future
sea level rise using Eq. (3) following the schematic of Fig. 1 as
described in Sect. 2. The overall Antarctic projections, including all
uncertainty in basal melt forcing for each of the ice sheet models under the
atmospheric CO2 concentration path RCP2.6 and 8.5, are given in Figs. 8 and
9, respectively. The values for the median, the likely range (percentiles 16.6 and 83.3), and the very likely range (5th and 95th percentiles) are provided
in Tables 7–10 for all four RCP scenarios for the year 2100.
Projection of Antarctica's sea level contribution under the
RCP2.6 carbon concentration scenario following the procedure depicted in
Fig. 1 and detailed in Sect. 2. The white line represents the median
value, the dark shading the likely range (66th percentile around the median),
and the light shading the very likely range (90th percentile around the median).
Compare Tables 7–10 for the values and their comparison to the other
scenarios.
Projection of Antarctica's sea level contribution under the
RCP8.5 carbon concentration scenario following the procedure depicted in
Fig. 1 and detailed in Sect. 2. The white line represents the median
value, the dark shading the likely range (66th percentile around the median),
and the light shading the very likely range (90th percentile around the median).
Compare Tables 7–10 for the values and their comparison to the other
scenarios.
Percentiles of the probability distribution of the sea
level contribution of Antarctica for different ice sheet models under the
RCP2.6 climate scenario. The 50th percentile corresponds to the median;
16.6 %–83.3 % is the so-called “likely range” as denoted in the
IPCC reports. The “very likely range” is given by the 5th–95th
percentiles.
Percentiles of the probability distribution of the sea
level contribution of Antarctica for different ice sheet models under the
RCP4.5 climate scenario. The 50th percentile corresponds to the median;
16.6 %–83.3 % is the so-called “likely range” as denoted in the
IPCC reports. The “very likely range” is given by 5 %–95 %.
Percentiles of the probability distribution of the sea
level contribution of Antarctica for different ice sheet models under the
RCP6.0 climate scenario. The 50th percentile corresponds to the median; 16.6 %–83.3 % is the so-called “likely range” as denoted in the
IPCC reports. The “very likely range” is given by the 5th–95th
percentiles.
Percentiles of the probability distribution of the sea
level contribution of Antarctica for different ice sheet models under the
RCP8.5 climate scenario. The 50th percentile corresponds to the median;
16.6 %–83.3 % is the so-called “likely range” as denoted in the
IPCC reports. The “very likely range” is given by the 5th–95th
percentiles.
The results for RCP8.5 for each of the five Antarctic regions are provided
in Fig. 10a–e. The results differ between the different models. Overall,
median contributions of around 5 cm come from the Weddell Sea sector and the East
Antarctic, while the Ross and Amundsen Sea sectors have a median contribution
of around 2 cm, and the peninsula has the lowest median contribution. Although
the largest median contributions arise from the Weddell Sea sector, the largest
95th percentile is found in the East Antarctic sector (Fig. 11). This is
because the forcing onto the ice sheet is transported not with a particular
oceanic current but is mainly mixed to the ice shelves due to the overall
coarse resolution of the CMIP5 climate models. It thus arrives everywhere,
and the East Antarctic Ice Sheet has the most ice catchment area that is in
direct contact with the ocean due to its size. In East Antarctica four
of the models have a stronger contribution than the others (PISM VUW,
ÚA UNN, IMAU UU, and ISSM UCI). For the three West Antarctic outlet regions
the model results are more similar than for East Antarctica. Overall the
models show quite similar responses to the forcing, and overall the
uncertainty in the sea level response is dominated by the uncertainty in the
forcing.
(a) Projection of East Antarctica's sea level contribution under the
RCP8.5 carbon concentration scenario following the procedure depicted in
Fig. 1 and detailed in Sect. 2. The white line represents the median
value, the dark shading the likely range (66th percentile around the median),
and the light shading the very likely range (90th percentile around the median).
(b) Projection of the Ross sector's sea level contribution under the
RCP8.5 carbon concentration scenario as in panel (a).
(c) Projection of the Amundsen sector's sea level contribution under the
RCP8.5 carbon concentration scenario as in panel (a).
(d) Projection of the Weddell sector's sea level contribution under the
RCP8.5 carbon concentration scenario as in panel (a).
(e) Projection of the Antarctic Peninsula's sea level contribution
under the RCP8.5 carbon concentration scenario as in panel (a).
Projections from all models of the future sea level contribution
of the different Antarctic sectors following the procedure depicted in
Fig. 1 and detailed in Sect. 2. The white line represents the median
value, the dark shading the likely range (66th percentile around the median),
and the light shading the very likely range (90th percentile around the median).
There are a number of different reasons for relatively weak responses of
some models in some regions. These reasons are as diverse as the models.
It is beyond the scope of this article to provide a detailed analysis of the
causes for the model response differences. Here we discuss possible reasons
for the deviations of the different models from the median in order to give
some information that is specific to the different models and to provide
some guidance on reading the results.
For the spin-up of the GRIS LSC model, an inversion procedure
(Le clec'h et al., 2019b) was used to infer a map of the basal
drag coefficient that minimizes the ice thickness mismatch with respect to
the observations and the drift over a 200-year equilibrium simulation. The
procedure is iterative and computationally cheap. Some errors compared to
the observed state remain. The procedure resulted in a relatively large
positive ice thickness drift in the Amundsen region. The GRIS LSC model is
thus almost insensitive to the basal melting rate anomaly in this region as the
error in the grounded ice is too large. Conversely, there are relatively low
errors in the Ross region and the response to the oceanic perturbation is
stronger there. In addition, in some regions there are compensating errors
(positive bias in some places and negative bias in others) which complicate
the analysis of the response curve in terms of sea level. In addition, as for
the initMIP-Antarctica experiments, a homogeneous sub-shelf basal melting
rate was used for each individual IMBIE 2016 basin (Rignot and Mouginot, 2016). The value for each basin was
computed as the basin-averaged sub-shelf basal melting rates that
ensure a minimal ice shelf thickness Eulerian derivative in a forward
experiment with constant climate forcing and a fixed grounding-line position.
The spatial average is needed in order to smooth the otherwise noisy melt
rates, and it also provides melt rates for a changing ice shelf geometry.
Nonetheless, in computing the spatial average the model tends to overestimate
the melt away from the grounding line and underestimate it in its vicinity,
where it has the largest impact on ice dynamics.
The response of the PISM AWI model is slightly lower than the median response
across all models. This can be partially understood by breaking down the
response to the individual sectors and their discrepancy between modelled
spin-up and observed state. In the Weddell Sea sector the initial grounding-line position is already retreated inland, lowering this sector's potential
sea level contribution in the forward runs. This could explain the
relatively low sensitivity to the melt perturbation compared to other
models. While the initial grounding line in the Amundsen Sea sector is
captured well compared to observations, the corresponding ice shelf area is
overestimated, leading to a stronger buttressing and therefore a limited
drainage via Pine Island and Thwaites glacier. Basel melt anomalies above
8 m yr-1 are required to eliminate the additional ice shelf area in this
region and thus have less influence on the sea level contribution. A
small basal melt anomaly of 1 m yr-1 is already sufficient to melt away large portions
of the Ronne and Ross Ice Shelf with only a minor impact on the grounding-line
position on the timescales considered here.
The sea level contribution from AISM VUB is also somewhat below the median
of the 16 state-of-the-art ice sheet models. It has a median of 0.06 m for
RCP2.6 (all-model median mean is 0.13 m) and a median of 0.13 m for RCP8.5
(all-model median mean is 0.17 m). Experiments with the high 16 m yr-1 basal
melt anomaly were not performed because most of the ice shelves are lost
after 200 years, and the model does not include a proper treatment for
calving at a moving margin or for the specific force balance of a calving
front at the grounding line. Possible reasons for differences with the other
models are most likely the various approximations made to simulate
grounding-line mechanics, and it seems fair to state that no model does this
perfectly. Additionally, AISM VUB is run at a resolution of 20 km over the
entire model domain, which is rather course. Sub-grid-scale mechanisms are
not described, and this may affect the model sensitivity. Another difference
is that AISM VUB has a freely evolving grounding line in the spin-up at the
expense of a slight mismatch of the ice sheet geometry compared to the
observations. In contrast to many of the other models, AISM VUB represents
the hindcast of the historical contribution to sea level rise very well
using the linear response functions.
Also, CISM NCA is one of the less sensitive models, with median sea level
contributions ranging from 0.07 m for RCP2.6 (Table 7) to 0.10 m for RCP8.5
(Table 10) compared to all-model means of 0.13 and 0.17 m, respectively.
The largest responses are in the East Antarctic, Weddell, and Ross sectors,
with little change in the Amundsen sector and Antarctic Peninsula. One
reason for the low sensitivity may be the multi-millennial spin-up
procedure, during which the ice was nudged toward present-day thickness by
adjusting basal sliding coefficients (beneath grounded ice) and basal melt
rates (beneath floating ice). There was no attempt to match recent mass
loss, and the spun-up ice sheet has considerable inertia. In multi-century
CISM NCA simulations substantial thinning and retreat in the Thwaites basin is
seen, driven largely by MISI. The retreat, however, only begins after several
decades of increased basal melting. Apart from MISI, CISM NCA, like all models in
this intercomparison, has no special mechanisms (e.g. hydrofracture) to
promote fast grounding-line retreat.
The ISSM JPL model shows a relatively weak sensitivity to basal ice shelf
melt. By comparison the ISSM UCI version of the model shows a medium
to strong response. The main difference between the two ISSM models is the
different mesh resolution over the ice shelves and especially close to the
grounding lines. The ISSM JPL model has a finer resolution over all the ice
shelves (less than 5 km for all the floating ice at the beginning of the
simulation), while the ISSM UCI models has a slightly coarser resolution in some
parts of the ice shelves as the resolution is mostly refined in regions with
large gradients of velocities. Otherwise, most parameters and
parameterizations are similar, including the friction law and the exclusion
of melt on partially grounded cells.
In order to understand the response of FETI ULB in a more global context,
especially the relatively weak response in the Amundsen Sea sector compared to
other regions such as the Weddell sector, we can add that this is most
likely related to underestimating the present-day peak melt rates near the
grounding line in this sector. This is due to both the applied spatial
resolution and the use of the PICO model (Potsdam Ice-shelf Cavity mOdel; Reese et al., 2018b)
(and associated temperature and salinity data in front of the ice shelf).
For the Amundsen region, the PICO model leads to peak melt rates below 20 m a-1, and adding even 32 m a-1 to this still remains to the low side compared
to observed. Improvements on this sector are currently on the way in order
to improve the match with present-day and glacier mass losses. The same
applies to the Weddell sector, where sub-shelf melting may be
overestimated.
The MALI DOE model response is also overall less sensitive than the model
mean. For some Antarctic sectors (e.g. the Ross and Amundsen Sea sectors),
average sea level trends or the shape of sea level curves from MALI DOE
compare well with those from other higher-order
Here, by
higher-order, we mean those that are formally a higher-order approximation
of the Stokes equations, e.g. 1st-order (Blatter–Pattyn) or L1L2, as
opposed to “hybrid” models which are a more ad hoc approximation to formally
higher-order models.
models (e.g. BISI LBL and ISSM UCI). For other
sectors (Weddell and EAIS), MALI DOE response functions compare well with
only one other model (BISI LBL and SICO ILTS, respectively). In general, there is
no obvious correlation between the only two three-dimensional, formally
higher-order models in the study (MALI DOE and ISSM UCI), which suggests
that something other than model dynamics is responsible for the differences
in model response functions seen here (e.g. choice of model physics or
model initialization procedure). For the hindcasting experiments,
approximately half of the models compare reasonably well with observed
trends in Antarctic mass loss, while the other half are biased towards the
high side of mass loss (both in terms of mean trends and upper bounds).
MALI DOE is within the former group (Fig. 6), initially overestimating then
underestimating mass loss trends in the middle part of the observational
record, but in good agreement in terms of both the mean trend and range in
the latter part of the record. For experiments under the RCP scenarios, 7–10
models are (visually) in agreement regarding the mean and bounds on future
sea level rise from Antarctica for most of the Antarctic sectors
investigated. MALI DOE is generally within this group. An exception to this
can be found for the Amundsen Sea sector (ASE) under RCP8.5, in which MALI DOE is slightly on the
high side (for both the mean trends and upper bounds) relative to other
models. This is likely an expression of MALI DOE already exhibiting a trend
towards significant mass loss from the ASE in its unperturbed initial
condition (see e.g. Fig. 4a in Seroussi et al.,
2019). While this trend is largely removed by differencing with the control
run, the unstable and non-linear nature of the retreat in ASE likely
increases the magnitude of mass loss forced under RCP scenarios.
The strongly sub-linear response of PISM PIK to the additional basal melt
forcing in the Ross region (Fig. 4b) is likely to result partially from
the applied spin-up procedure. In order to best match present-day
observations in the most sensitive part of the West Antarctic Ice Sheet
(mainly the Amundsen Sea sector) and due to computational costs, PISM PIK was
initialized with a transient spin-up at the end of a 600-year run forced by
present-day climatic boundary conditions that is not in equilibrium. This
allows us to reproduce recent change rates in the Amundsen sector, but trends
in other regions (e.g. Siple Coast) can exceed present rates and superpose
the ice sheet's response to the forcing in the experiments. Another reason
for PISM PIK's sub-linear behaviour in this region is likely related to ice
shelf break-up in the forcing experiments as a result of the interplay of
strong melting near the grounding line and the applied calving mechanism
(“eigencalving”; Levermann et al.,
2012). For all additional sub-shelf melt rates, disintegration of the Ross Ice
Shelf is initiated near the grounding line, which is rather unrealistic. As
the ice shelf remainders exert almost no buttressing onto the grounded ice
stream flow, there is almost no response of the sea-level-relevant ice volume
to the magnitude of melt forcing applied. The peninsula region, where
in the initial state almost no ice shelves are present, also shows no
significant response. In contrast to the Ross region and peninsula, PISM PIK
shows slightly super-linear scaling in the Weddell region. Although large
portions of the Filchner–Ronne Ice Shelf melt and calve off, a small part
pinned to the Korff and Henry ice rises remains in the forcing experiments and
exerts buttressing. For higher melt rates, those ice shelf remainders exert
decreasing buttressing on grounded ice sheet flow, which is associated with
enhanced sea level contributions.
A number of models scatter quite closely around the median model sensitivity
when measured in the total ice sheet response. In general, the BISI LBL
model falls within the median group of models but is generally on the
more responsive side in that grouping. This has much to do with the
initialization of the model – the BISI LBL runs use the initial condition
from the initMIP exercise; since BISI LBL falls in the median group of
models in that exercise, it is unsurprising that it also falls in the median
group in this context. It is well known that models with
insufficient resolution will generally tend to underestimate marine ice
sheet response, which is borne out in the results here, in which the
coarser-resolution (1 km resolution) BISI LBL is less responsive than the
finer-resolution runs (500 m); however, the differences are small in this
case because both cases are sufficiently resolved to capture the dynamics
in play. The BISI LBL response function appears to be on the higher side in
regions with no appreciable present-day grounding-line retreat (like East
Antarctica), possibly because it is able to better capture the onset of new
retreat and deploy sufficient resolution there. BISI LBL appears more
in line with other models for the Amundsen Sea sector, possibly because
substantial retreat and loss is already underway in that sector, so the
actual dynamics remain relatively unchanged with increased sub-shelf melting.
One possibility distinguishing the PS3D PSU model is the boundary layer
parameterization of ice flux across grounding lines (Schoof, 2007) imposed as a condition on
ice velocity across the grounding line. This enables grounding-line
migration to be simulated reasonably well without much higher grid
resolution. The sub-grid grounding-line treatment also ensures no
substantial oceanic melt upstream of the grounding line, in contrast to some
models. Note that the recently proposed mechanisms of hydrofracturing by
surface meltwater and structural failure of large ice cliffs (DeConto and Pollard, 2016) are not enabled for the
LARMIP experiments. Without these, previous studies with this model have
found little retreat in East Antarctic basins with moderate sub-ice ocean
melting alone, consistent with the generally smaller response for East
Antarctica in the experiments here.
Similarly to the less sensitive models, the models which have an overall
stronger response to basal ice shelf melting have similarly diverse reasons
for their dynamics. The sea level contribution of IMAU UU is in the upper
half of the ensemble and most similar to the ISSM UCI model as well as to some extent
PISM DMI and PISM VUW (Figs. 6, 8, 9, 10a–d, Tables 6–10). The only exception
is the Antarctic Peninsula region (Fig. 10e), where IMAU UU has the lowest
response in the ensemble. This may be attributed to the relatively low
horizontal grid resolution of the model (32×32 km), which prevents the
resolution of small-scale features important for this region.
Compared to other models in the ensemble, PISM VUW yields a hindcast
sea level contribution that is above observed values and a large spread in
the projected contribution by 2100 under RCP8.5 (less than 0.2 m up to ca.
1 m). Model differences appear to be spatially variable. For example,
PISM VUW projects SL contributions from the Ross Sea sector that are very
consistent with most other models in the ensemble, as well as contributions from
the Antarctic Peninsula and from the Amundsen Sea embayment that lie
consistently between the highest and lowest models. It is primarily the
contributions from the Weddell Sea sector that are very much higher than
most other models, and since the combined East Antarctic contributions from
PISM VUW appear to be similarly skewed, it is reasonable to infer that the
large Weddell Sea contributions are principally sourced from the Recovery
Basin in the eastern part of the sector. It seems reasonable that the
different modelled response here arises from the way in which basal
conditions are parameterized: for example, the basal substrate yield
strength that determines the propensity of ice in this area to stream.
The set-up used for the LARMIP simulations with SICO ILTS is the same as
that used for the ISMIP6 projections (http://tinyurl.com/ismip6-wiki-ais, last access: 6 January 2020;
publication in preparation; see also Appendix A15). In most regions, the
results show a rather high sensitivity to the applied ice shelf basal
melting anomalies. This is probably because any grid cell for which the
centre point is floating is assigned the full ice shelf basal melting rate,
even if the grid cell is near the grounding line and parts of it might be
detectable as grounded via a sub-grid interpolation technique. Relative to
the other models, the sensitivity is largest for the Ross region. This
correlates with the fact that for this region, in particular the West
Antarctic part including the Siple Coast ice streams, the regional basal
sliding inversion (Appendix A15) produces the largest values for the basal
sliding coefficient.
Out of all the models the ÚA UNN model has the overall highest
projection for future sea level contribution for Antarctica as a whole. This
can mostly be attributed to the high amount of future sea level rise the
model projects for East Antarctica as this region is the single largest
contributor to future sea level rise. The model also projects a relatively
strong contribution from the Amundsen and Antarctic Peninsula sectors, with
more average projections when compared to the rest of the model ensemble
from the Ross and Weddell sector. One possible explanation for this is that
the ÚA UNN model overestimates the past Antarctic sea level rise when
compared to observations (Fig. 6). This would likely predispose the model
to have a relatively large projection for the future contribution of
Antarctic sea level rise when compared to other models that more accurately
match the hindcast.
Across all models one can say that even though the temperature difference
between the scenarios is significant, the difference in the Antarctic ice
sheet response is existent but percentage-wise smaller. Table 11 gives a
summary across the scenarios for all ice sheet models combined. The
corresponding time series are given in Fig. 12. The relative warming
difference between RCP8.5 and RCP2.6 within this century (according to the
median values) is about (3.7–1.0 K) / 1.0 K = 270 % (Stocker et
al., 2013). For comparison the Antarctic sea level contribution is
(according to Table 11) about (0.17–0.13 m) / 0.13 m = 31 %. One reason for
this is the time delay between the surface forcing and the subsurface
oceanic forcing that is experienced by the ice shelves. The relative
difference in global mean temperature increase between the scenarios also
increases with time during this century. However, the strongly reduced
relative sea level difference between the scenarios mainly reflects the
inertia in the ice sheet dynamics, which responds to the forcing in a time-delayed way as can be seen from the response functions in Fig. 5a–e. For
the upper end of the very likely range (95th percentile) this ratio is larger at
(0.58–0.37 m) / 0.37 m = 57 % but still lower than the scenario ratio of
the warming. This does not hold for the rate of change in sea level (Fig. 13, Table 12), which is (4.4–2.2 mm yr-1) / 2.2 mm yr-1= 100 %.
Sea level contributions from basal ice shelf melting from
Antarctica within the 21st century from all models for the different
emission scenarios in metres.
Projections from all models of the future sea level contribution
of the Antarctic ice sheet under different atmospheric carbon concentration
scenarios following the procedure depicted in Fig. 1 and detailed in
Sect. 2. The white line represents the median value, the dark shading the
likely range (66th percentile around the median), and the light shading the
very likely range (90th percentile around the median).
Projections from all models of the rate of future sea level
contribution of the Antarctic ice sheet under different atmospheric carbon
concentration scenarios following the procedure depicted in Fig. 1 and
detailed in Sect. 2. The white line represents the median value, the dark
shading the likely range (66th percentile around the median), and the light
shading the very likely range (90th percentile around the median).
Sea level rate contributions from basal ice shelf melting
from Antarctica in 2100 from all models for the
different emission scenarios in millimetres per year or centimetres per decade.
Due to increasing interest of society and by extension of the
Intergovernmental Panel on Climate Change, we also provide the sea level
contributions of Antarctica due to basal ice shelf melting until the middle of
the 21st century (Table 13), the associated rate of sea level
contribution (Table 14), and the contribution of Antarctica within the next
30 years (Table 15). There is practically no scenario dependence in these
numbers. This is to be expected since the global warming signal only differs
significantly between scenarios for time periods beyond 2040. It is found
that in the next 30 years the median contribution of Antarctica to global
sea level rise from basal ice shelf melting is 3 cm, with a likely range
between 1 and 6 cm. The applicability of these numbers is strongly limited by
the caveats of the method as described in the next section.
Sea level contributions from basal ice shelf melting from
Antarctica until the middle of the 21st century (year 2050) from all
models for the different emission scenarios in metres. The projections are
scenario independent until 2050, with the uncertainty of the forcing and
across ice sheet models determining the uncertainty in the future.
Sea level rate contributions from basal ice shelf melting
from Antarctica in the middle of the 21st century (year 2050) from all
models for the different emission scenarios in metres. Different from the
sea level rise, the rate of sea level rise already depends on the scenario
even in the first half of the century. Note that in RCP4.5, although it ends
up lower in radiative forcing in the year 2100, it rises more quickly in the
beginning of the century, which leads to a slightly higher contribution of
Antarctica to the rate of sea level rise until 2050 compared to RCP6.0.
Sea level contributions from basal ice shelf melting from
Antarctica between 2020 and 2050.
Scenario5 %16.6 %50 %83.3 %95 %RCP2.60.010.010.030.050.09RCP4.50.010.010.030.060.09RCP6.00.010.010.030.050.09RCP8.50.010.010.030.060.10Discussion and conclusions
The projections of the Antarctic contribution to future sea level rise have
to be seen in comparison with other studies. The fifth assessment report of
the Intergovernmental Panel on Climate Change (IPCC AR5) only had limited
process-based model simulations available (Gladstone et al., 2012) and thus estimated
a likely range for the ice dynamical contribution of the Antarctic ice sheet
of -1 to 16 cm (Church
et al., 2013). This estimate was largely based on statistical considerations (Little et al.,
2013a, b) which do not represent a response to future warming but
merely estimate the possible statistical range of responses based on
variations in observed discharge velocities. Thus, these estimates are
scenario independent as was the projection by the IPCC AR5. The IPCC AR5,
however, added a footnote saying that the likely range could increase by
“several decimetres” if the West Antarctic Ice Sheet becomes unstable. The
following special reports of the IPCC that addressed sea level rise (Masson-Delmotte
et al., 2018; Pörtner et al., 2019) included the estimates obtained with
the same procedure applied here but for earlier ice sheet models (Levermann
et al., 2014). A mere extrapolation of observed ice dynamic contributions
from Antarctica constrained by its future sea level commitment yields a
likely range of 9 to 19 cm for the end of the 21st century under RCP8.5 (Mengel et al., 2016). Similar values are
obtained with more elaborated statistical methods (Kopp et al., 2014,
2017).
In the meantime a number of other studies have shed light on the importance
of process-based projections of Antarctica (e.g. Arthern
et al., 2015; Favier et al., 2014; Gong et al., 2014; Joughin et al., 2014).
For example, it was shown that feedbacks between the Antarctic ice sheet and
the surrounding ocean and atmosphere can strongly increase the ice loss from
Antarctica (Golledge et al., 2019). In a model (Pollard and DeConto, 2009) that was able
to reproduce paleo-evidence of the grounding-line retreat in a location in
Antarctica (Naish
et al., 2009), it was shown that the inclusion of additional physical
surface processes (Pollard et al., 2015) yields more
than a doubling of the previous high estimate of the ice loss considered
possible from Antarctica (DeConto and Pollard, 2016).
Although it was shown that the paleo-constraints used in these simulations
were insufficient to properly constrain future projections (Edwards et al., 2019), it cannot be ruled out
that these processes are significant. Consequently there is large
uncertainty in the ice sheet community regarding the possible contribution
of Antarctica to future sea level rise, as can be seen from two separate
expert elicitations before (Bamber and Aspinall,
2013) and after the IPCC AR5 (Bamber et al., 2019). These
expert elicitations include all known and unknown uncertainties of possible
responses of the Antarctic ice sheet to future warming, and thus the likely
and in particular the very likely ranges found in the elicitations are wider
than those found with the procedure described here. By comparison the likely
and very likely ranges found in the earlier estimate based on the
linear response theory are the largest ranges if no additional processes such
as hydrofracturing and cliff calving are included.
The latest assessment of the Intergovernmental Panel on Climate Change based
on the literature published after IPCC AR5 was carried out in the special
report on the ocean and cryosphere (Oppenheimer et al., 2019). The author team
estimated the Antarctic contribution within the 21st century under the
RCP8.5 scenario to be 10 cm, with a likely range of 2 to 23 cm. In this study
the likely range for RCP8.5 of 9 to 36 cm is slightly higher compared
to the earlier studies with a likely range of 4 to 21 cm (Table 6 in Levermann
et al., 2014, “Shelf models with time delay”). The same is true for the
very likely range over which the current study finds 6 to 58 cm, while the study
with only three ice sheet models found 1 to 37 cm. The 2014 study even
found a lower estimate for the very likely range if the time delay was
omitted and the atmospheric warming was translated immediately into a scaled
subsurface ocean warming (very likely range between 0.04 and 0.43 m).
The median estimates in both studies are also very different, with 9 cm in the
2014 and 17 cm in the present study for RCP8.5.
The projections of the Antarctic ice sheet's mass loss presented here have
strong limitations. First of all they represent only the contribution from basal
ice shelf melt. Any calving that might be incorporated in the modelling does
not reflect atmospheric or even specific oceanic processes that may enhance
calving in a warming world. Hydrofracturing and cliff calving are not
explicitly accounted for. The approach neglects a number of processes
such as surface-mass-balance-related contributions and mechanisms. There is
no mass gain due to additional snowfall or any responses to such a mass
addition. In assuming linear response theory, we are able to capture complex
temporal responses of the ice sheets, but we neglect any self-dampening or
self-amplifying processes. This is particularly relevant in situations in which
an instability is dominating the ice loss. This is particularly important
for the Marine Ice Sheet Instability (MISI) (Pattyn et
al., 2012; Pattyn and Durand, 2013; Weertman, 1974) that might have already been
triggered in the Amundsen Sea sector (Favier et
al., 2014; Joughin et al., 2014; Rignot et al., 2014) and might lead to the
eventual discharge of the entire marine ice sheet in West Antarctica over a
multi-centennial to multi-millennial timescale (Feldmann and Levermann, 2015). The results obtained here
are thus relevant, in particular wherever the ice loss is dominated by the
forcing as opposed to an internal instability, for example in strong warming
scenarios. The study also does not include any feedbacks between the ice
sheet and its surroundings. Although feedbacks between the surface mass
balance and the ice dynamics are expected to be small (Cornford et al., 2015)
there might be significant feedbacks with the ocean circulation both locally
and globally (Golledge et al., 2019;
Swingedouw et al., 2008). Basal melt rate anomalies are added to the
background run of the different ice sheet models. However, as melting
parameterizations in ice sheet models vary, the sub-shelf melt
rates respond differently to the evolving geometry. This is a feedback that
is captured in the approach but might be quite different across the models.
These strong caveats that are associated with the approach presented here
may either lead to an overestimation or an underestimation of the ice loss from basal
ice shelf melting compared to what might occur in reality. In any case the
median contribution from basal ice shelf melting of Antarctica under any
scenario is found to be higher within the 21st century than it was in
the last century. The values obtained here for the basal ice shelf
contribution from Antarctica are slightly larger than other probabilistic
estimates of the ice loss with (Bakker et al., 2017; Ruckert et
al., 2017) and without climate change (Little et al., 2013b). They are much
lower than the values that may be obtained if additional processes such as
the marine cliff instability and hydrofracturing are included (DeConto and Pollard, 2016). Whether these high
estimates, however, can be well constrained by paleo-evidence is still under
intense debate (Edwards et al., 2019).
However, due to the very large potential sea level contribution of Antarctica
and its high sea level commitment compared to the other contributions (Levermann et al., 2013), the rate of
change increases strongly over the century. Under the RCP8.5 scenario the
median rate of sea level contribution by the end of the 21st century
from basal-melt-induced ice loss from Antarctica alone is with 4.1 mm yr-1
larger than the mean rate of sea level rise observed at the beginning of
this century (Dangendorf
et al., 2019; Hay et al., 2015; Oppenheimer et al., 2019).
Although the method described here has a large number of caveats it provides
an estimate of the role of the uncertainty in the oceanic forcing for the
uncertainty in Antarctica's future contribution to sea level rise. By
comparison with the earlier study using the same method but only three ice
sheet models of an earlier model generation, we find a shift of
the sea level contribution to higher values and an increase in the
ranges of uncertainty. We thus have to conclude that uncertainty with
respect to the ice dynamic contribution of Antarctica due to future warming is
still increasing and thus that coastal planning has to take into account
that multi-decadal sea level projections are likely to change with
an increasing understanding of the ice dynamics and their representation in ice
sheet models. This study provides an estimate of the uncertainty in the
future contribution of Antarctica to global sea level rise only based on
known ice dynamics but including the full range of forcing uncertainty. It
substantiates the result of the previous study that Antarctica can become
the largest contributor to global sea level rise in the future, in
particular if carbon emissions are not abated.
Brief description of ice sheet models
The model initialization was carried out according to the initMIP protocol
and is described together with the models and their set-up in Seroussi et al. (2019).
The Antarctic ice sheet model AISM VUB derives from a coarse-resolution
version used mainly in simulations of the glacial cycles (Huybrechts, 1990,
2002). The version used here is identical to the VUB AISMPALEO model
participating in initMIP-Antarctica (Seroussi et al.,
2019). It considers thermomechanically coupled flow in both the ice sheet
and the ice shelf using the respective shallow-ice approximation and
shallow-ice-shelf approximation coupled across a one-grid-cell-wide
transition zone. Basal sliding is calculated using a Weertman relation
inversely proportional to the height above buoyancy wherever the ice is at
the pressure melting point. The horizontal resolution is 20 km and there are
31 layers in the vertical. The model is initialized with a freely evolving
geometry until steady state is reached using observed climatologies for the
surface mass balance. The sub-shelf basal melt rate is parameterized as a
function of local mid-depth (485–700 m) ocean water temperature above the
freezing point (Beckmann and Goosse, 2003). A distinction is
made between protected ice shelves (Ross and Filchner–Ronne) with a low melt
factor and all other ice shelves with a higher melt factor. Ocean
temperatures are derived from the LOVECLIM climate model (Goelzer et al., 2016) and parameters are
chosen to reproduce observed average melt rates (Depoorter et al., 2013). Heat
conduction is calculated in a slab bedrock of 4 km thick underneath the ice
sheet. Isostatic compensation is based on an elastic lithosphere floating on
a viscous asthenosphere (ELRA model), but this feature is not allowed to
evolve further in the current experiments. The LARMIP basal melting rates
are applied on top of the present-day melt rates used for the
initialization.
BISI LBL: BISICLES
The finite-volume BISICLES model (Cornford et al., 2013) is
used with a modified L1L2 scheme (Schoof and Hindmarsh, 2010)
over the entire Antarctic ice sheet. The model employs adaptive mesh
refinement (AMR) to vary resolution between a finest resolution (either
1000 or 500 m, depending on the run) near grounding lines and shear margins
and 8 km in the interior of the domain. Basal sliding follows a
Coulomb-limited friction law (Tsai et al., 2015), resulting in
power-law sliding (with a spatially varying friction coefficient) across the
majority of the ice sheet with and Coulomb sliding in regions close to
flotation. Ice viscosity is computed following Cuffey and
Paterson (2010), assuming a prescribed temperature and an enhancement
factor. The basal friction coefficient and the enhancement factor are chosen
to best match observed surface velocity (Rignot et al.,
2011) using a gradient-based, Tikhonov-regularized optimization scheme (Cornford et al., 2015). The
grounding-line position is determined using hydrostatic equilibrium, with
sub-cell treatment of the friction and a modified driving stress (Cornford et al., 2016). The melt rate is applied only for
fully floating cells (as in Seroussi and Morlighem, 2018) and
is composed of a base rate and the anomalies specified in the individual
experiments. The base melt rate is time varying and designed to prevent ice
shelf thickening but permit thinning where flux divergence in the shelf is
positive. The surface mass balance is from Arthern
et al. (2006). The ice front position is fixed at the extent of the
present-day ice sheet. After initialization, the model is relaxed for 2 years, with the base melt rate only applied. For more details on the model
and the initialization procedure, we refer to Cornford et al. (2015).
CISM NCA: Community Ice Sheet Model – NCAR
For LARMIP, the Community Ice Sheet Model (Lipscomb et al.,
2019) uses finite-element methods to solve a depth-integrated higher-order
approximation (Goldberg, 2011) over the entire Antarctic
ice sheet. The model uses a structured rectangular grid with a uniform
horizontal resolution of 4 km and five vertical σ-coordinate levels.
The ice sheet is initialized with present-day geometry and an idealized
temperature profile, then spun up for 30 000 years using 1979–2016
climatological surface mass balance and surface air temperature from RACMO2 (Lenaerts
et al., 2012; van Wessem et al., 2018). During the spin-up, basal friction
parameters (for grounded ice) and sub-shelf melt rates (for floating ice)
are adjusted to nudge the ice thickness during present-day observations.
This method is a hybrid approach between assimilation and spin-up, similar
to that described by Pollard and DeConto (2012a). The
geothermal heat flux is taken from Le
Brocq et al. (2010). The basal sliding is similar to that of Schoof (2005), combining power-law and Coulomb behaviour. The
grounding-line location is determined using hydrostatic equilibrium and
sub-element parameterization (Gladstone
et al., 2010; Leguy et al., 2014). The calving front is initialized from
present-day observations and thereafter is allowed to retreat but not
advance. See Lipscomb et al. (2019) for more information
about the model.
FETI ULB: fast Elementary Thermomechanical Ice Sheet model (f.ETHISh v1.2)
The f.ETISh (fast Elementary Thermomechanical Ice Sheet) model (Pattyn, 2017) is a vertically integrated hybrid (SSA for
basal sliding; SIA for grounded ice deformation) finite-difference ice
sheet–ice shelf model with vertically integrated thermomechanical coupling.
The transient englacial temperature field is calculated in a 3-D fashion. The
marine boundary is represented by a grounding-line flux condition according
to Schoof (2007), coherent with power-law
basal sliding (power-law coefficient of 2). Model initialization is based on
an adapted iterative procedure based on Pollard and
DeConto (2012a) to fit the model as close as possible to present-day
observed thickness and flow field (Pattyn, 2017). The model
is forced by present-day surface mass balance and temperature (van Wessem et al., 2014) based on the output of the regional
atmospheric climate model RACMO2 for the period 1979–2011. The
mass balance–elevation feedback is taken into account and a positive degree day (PDD) model for
surface melt was employed. Isostatic adjustment was included using an
elastic lithosphere–relaxed asthenosphere (ELRA) model. The PICO model (Reese et al., 2018b) was employed to calculate sub-shelf melt
rates based on present-day observed ocean temperature and salinity
(Schmidtko et al., 2014) on which the LARMIP forcings for the
different basins are added. The model is run on a regular grid of 16 km with
time steps of 0.1 years.
GRIS LSC: Grenoble Ice Sheet and Land Ice (GRISLI)
The GRISLI model is a three-dimensional thermomechanically coupled ice
sheet model originating from the coupling of the inland ice model of Ritz (1992) and Ritz et al. (1997) and the ice shelf model of
Rommelaere and Ritz (1996), extended to the case of ice streams
treated as dragging ice shelves (Ritz et al., 2001). In the
version used here, over the whole domain, the velocity field consists of the
superposition of the shallow-ice approximation (SIA) velocities for ice flow
due to vertical shearing and the shallow-shelf approximation (SSA)
velocities used as a sliding law (Bueler and Brown, 2009).
For the LARMIP experiments, we used the GRISLI version 2.0 (Quiquet et al., 2018), which includes the analytical
formulation of Schoof (2007) to compute
the flux at the grounding line. Basal drag is computed with a power-law
basal friction (Weertman, 1957). For this study, we use an
iterative inversion method to infer a spatially variable basal drag
coefficient that ensures an ice thickness as close as possible to
observations with a minimal model drift (Le clec'h et al.,
2019a). The basal drag is assumed to be constant for the forward experiments.
The model uses finite differences on a staggered Arakawa C grid in the
horizontal plane at 16 km resolution with 21 vertical levels. Atmospheric
forcing, namely near-surface air temperature and surface mass balance, is
taken from the 1979–2014 climatological annual mean computed by the RACMO2.3
regional atmospheric model (van Wessem et al., 2014). Initial
sub-shelf basal melting rates are the regionally averaged basal melting
rates that ensure a minimal ice shelf thickness Eulerian derivative in a
forward experiment with constant climate and a fixed grounding-line position.
The initial ice sheet geometry, bedrock, and ice thickness are taken from the
Bedmap2 dataset (Fretwell
et al., 2013), and the geothermal heat flux is from Shapiro
and Ritzwoller (2004).
IMAU UU: IMAUICE – IMAU/Utrecht University
The finite-difference model (de Boer et al., 2014) uses a
combination of SIA and SSA solutions, with velocities added over grounded
ice to model basal sliding (Bueler and Brown, 2009). The
model grid at 32 km horizontal resolution covers the entire Antarctic ice
sheet and surrounding ice shelves. The grounded ice margin is freely
evolving, while the shelf extends to the grid margin and a calving front is
not explicitly determined. We use the Schoof flux boundary condition (Schoof, 2007) at the grounding line with
a heuristic rule following Pollard and DeConto (2012b).
For the LARMIP experiments, the sea level equation is not solved or coupled
(de Boer et al., 2014).
We run the thermodynamically coupled model with constant present-day
boundary conditions to determine a thermodynamic steady state. The model is
first initialized for 100 kyr using the average 1979–2014 surface mass balance (SMB) and
surface ice temperature from RACMO2.3 (van Wessem et al.,
2014). Bedrock elevation is fixed in time with data taken from the Bedmap2
dataset (Fretwell
et al., 2013), and geothermal heat flux data are from Shapiro and Ritzwoller (2004). We then run for 30 kyr with
constant ice temperature from the first run to get to a dynamic steady
state, which is our initial condition. Model set-up, parameter settings, and
initialization are identical to the IMAUICE submission to
initMIP-Antarctica.
ISSM JPL: Ice Sheet System Model – JPL
The finite-element Ice Sheet System Model (Larour et al., 2012) is used with the
two-dimensional shelfy-stream approximation (MacAyeal, 1989) over
the entire Antarctic ice sheet. The model resolution varies between 1 km
along the coast and 50 km in the interior of the domain, with the resolution of
the ice shelves below 8 km. The model is initialized to match present-day
conditions. On grounded ice, the viscosity is derived from a steady-state
temperature that does not vary during the simulation, following Cuffey and Paterson (2010). The basal friction and the
viscosity of floating ice are inferred to best match observed surface
velocity (Rignot et al., 2011) using data assimilation (Morlighem et al., 2010). The basal sliding law follows
a Budd friction law (Budd et al., 1979) that depends on the
ice effective parameterization. The grounding-line position is determined
using hydrostatic equilibrium, with sub-element parameterization of the
friction (Seroussi et al., 2014). The melt rate
is applied only for fully floating elements (Seroussi and
Morlighem, 2018) and is initialized using mean rates of ocean estimates over
the 2004–2015 period (Schodlok et al., 2016)
that are kept constant with time. The surface mass balance is from the RACMO2.1
1979–2010 mean (Lenaerts
et al., 2012). The ice front position is fixed at the extent of the
present-day ice sheet. After initialization, the model is relaxed for 2 years so that the geometry and grounding lines can adjust (Seroussi et al., 2011). For more
details on the model and the initialization procedure, we refer to Schlegel et al. (2018), as we used a similar procedure here.
ISSM UCI: Ice Sheet System Model – UCI
We use the Ice Sheet System Model (ISSM; Larour et al., 2012) with a higher-order
stress balance (Pattyn, 2003). The model resolution varies
from 3 km around the coast to 50 km in the interior of the ice sheet,
vertically extruded into 10 layers using a smaller spacing near the bed.
The model is initialized using data assimilation of present-day conditions (Morlighem et al., 2013). We perform the
inversion of basal friction assuming that the ice is in thermomechanical
steady state based on a Budd friction law (Budd et al.,
1979). The ice temperature is updated as the basal friction and internal
deformation changes, and the ice viscosity is changed accordingly. At the
end of the inversion, basal friction, ice temperature, and stresses are all
consistent. After that, the model is run forward assuming that the
temperature does not change. We use the surface mass balance from
the RACMO2.1 1979–2010 mean (Lenaerts
et al., 2012). The grounding line is parameterized using a sub-element
friction scheme (Seroussi et al., 2014) and no
melt in partially floating elements (Seroussi and Morlighem,
2018). The ice front is fixed through time. More details on the model are
available in the ISMIP6 iniMIP-Antarctica study (Seroussi et al., 2019).
MALI DOE: model for prediction across scales – Albany Land Ice
MPAS-Albany Land Ice (MALI) (Hoffman
et al., 2018) uses a three-dimensional, 1st-order Stokes approximation
(Blatter–Pattyn) momentum balance solver using finite-element methods.
Ice velocity is solved on a two-dimensional, map plane triangulation
extruded vertically to form tetrahedra. Mass and tracer transport occur on
the Voronoi dual mesh using a mass-conserving, finite-volume, 1st-order
upwinding scheme. To ensure that the grounding line is captured by adequate
spatial resolution even under full retreat of West Antarctica (or large
parts of East Antarctica), mesh resolution is 2 km along grounding lines,
in all marine regions of West Antarctica, and in marine regions of East
Antarctica where present-day ice thickness is less than 2500 m. Mesh
resolution coarsens to 20 km in the ice sheet interior and is no greater
than 6 km within the large ice shelves. The horizontal mesh has 1.6 million
cells. The mesh uses 10 vertical layers that are finest near the bed (4 %
of total thickness) and coarsen towards the surface (23 % of total
thickness). Ice temperature is based on results from Van
Liefferinge and Pattyn (2013) and held fixed in time. The model uses a
linear basal friction law with a spatially varying basal friction coefficient.
The basal friction of grounded ice and the viscosity of floating ice are
inferred to best match observed surface velocity (Rignot et al., 2011) using an adjoint-based
optimization method (Perego et al., 2014) and then kept
constant in time. The grounding-line position is determined using
hydrostatic equilibrium, with a sub-element parameterization of the friction
(analogous to SE3 from Seroussi et al., 2014).
Sub-ice-shelf melt rates come from Rignot et al. (2013) and are extrapolated across the entire model domain to provide
non-zero ice shelf melt rates after grounding-line retreat. The surface mass
balance is the 1979–2010 mean from RACMO2.1 (Lenaerts
et al., 2012). Maps of surface and basal mass balance forcing are kept
constant with time. The ice shelf calving front positions are fixed at the
extent of their present-day observations. To minimize large, non-physical
transients resulting from the optimization procedure, the model is first
relaxed by integrating forward in time for a century under steady forcing.
During this time the model velocities, geometry, and grounding lines are
free to adjust as needed.
PISM AWI: Parallel Ice Sheet Model – AWI
The Parallel Ice Sheet Model (Bueler and Brown,
2009; Winkelmann et al., 2011) in the hybrid shallow approximation is
applied at 16 km resolution over the entire Antarctic ice sheet. The model
is initialized via a 100 kyr equilibrium-type spin-up with steady present-day
climate and fixed bedrock topography. The initial geometry is Bedmap2 (Fretwell
et al., 2013). Basal friction is parameterized by the water content in the
till and the depth of the ice base. Basal sliding is calculated via a
pseudo-plastic friction law (Bueler and Brown,
2009; Winkelmann et al., 2011) depending on the yield strength of the till
and the stored basal water. The grounding line is determined by hydrostatic
equilibrium with a sub-grid parameterization of basal conditions (Feldmann et al., 2014). Both
the grounding line and ice shelf front can freely evolve in the spin-up and the
projections. Calving is governed by strain rate
(eigencalving; Levermann et al., 2012) and
ice shelf thickness (thickness calving). Calving is further applied if the
ice extends over the continental shelf (sea floor below -2000 m). The melt
rate underneath ice shelves is applied only to fully floating cells (no
sub-grid basal melt) and calculated via the local difference between ocean
temperature and pressure melting point. In the Amundsen and Bellingshausen
Sea as well as underneath the Filchner Ice Shelf melt rates are modified by
a scaling factor to better fit present-day patterns. Local ocean temperature
is derived via extrapolation of 3-D ocean temperature fields from the World
Ocean Atlas 2009 (Locarnini et al., 2013) for the present day.
Present-day surface mass balance and ice surface temperature are from
RACMO2.3 (van Wessem et al., 2014).
PISM DMI: Danish Meteorological Institute's Parallel Ice Sheet Model
The Parallel Ice Sheet Model (PISM version 0.7) utilizes a hybrid
system (Bueler and Brown, 2009) combining the shallow-ice
approximation (SIA) and shallow-shelf approximation (SSA) on an equidistant
polar stereographic grid of 16 km. The basal resistance is described as
plastic till for which the yield stress is given by a Mohr–Coulomb formula (Bueler and Brown, 2009; Schoof, 2006).
Assuming an ocean temperature of -1.7∘C and constant melting
factor (Fmelt=0.001) sub-shelf melting follows Eq. (7) in
Martin et al. (2011) and occurs only for
fully floating grid points, while the grounding-line position is determined
on a sub-grid space (Feldmann et al., 2014). The calving
parameterization incorporates three sub-schemes: at the ice shelf margin
calving occurs when the thickness is less than 150 m; ice shelves that
extend into the depth ocean disintegrate; the stress field evaluates
the eigencalving parameterization with the proportionality constant of
5×1017 (Levermann et al.,
2012). Monthly atmospheric forcing deduced from sub-daily ERA-Interim
reanalysis products (Berrisford et
al., 2011; Dee et al., 2011) covers the period 1979–2012. Its 2 m air
temperature determines the ice surface temperature, while the total
precipitation is considered to be snow accumulation due to negligible surface
melting in Antarctica. This forcing has been applied to match present-day
conditions during spin-up, in which grounded ice margins, grounding lines, and
calving fronts evolve freely.
PISM PIK: Potsdam Parallel Ice Sheet Model
The Parallel Ice Sheet Model (Winkelmann et al.,
2011) (PISM, dev version c10a3a6e from 3 June 2018, based on v1.0, with added basal melt modifier, see documentation at https://pism-docs.org/wiki/doku.php, last access: 6 January 2020) uses a hybrid of the shallow-ice
approximation (SIA) and the two-dimensional shelfy-stream approximation of
the stress balance (SSA; Bueler and Brown, 2009;
MacAyeal, 1989) over the entire Antarctic ice sheet. Here we use a plastic
sliding law, which is independent of ice base sliding velocity. The model
domain is discretized on a regular rectangular grid with 4 km horizontal
resolution and a vertical resolution between 48 m at the top of the domain
at 6000 and 7 m at the base of the ice. The model is initialized from
Bedmap2 geometry (Fretwell
et al., 2013) with model parameters (e.g. enhancement factors for SIA and
SSA both equal 1 here) that minimize dynamic changes over 600 years of
constant present-day climatic conditions (no equilibrium spin-up). PISM is a
thermomechanically coupled (polythermal) model based on the
Glen–Paterson–Budd–Lliboutry–Duval flow law (Aschwanden
et al., 2012) such that the enthalpy can evolve freely for given boundary
conditions. Basal meltwater is stored in the till. The Mohr–Coulomb
criterion relates the yield stress by parameterizations of till material
properties to the effective pressure on the saturated till (Bueler and van Pelt, 2015).
The till friction angle is a shear strength parameter for the till material
property and is optimized iteratively in the grounded region such that
mismatch of equilibrium and modern surface elevation (8 km) is minimized
(analogous to the friction coefficient in Pollard and
DeConto, 2012a). The grounding-line position is determined using
hydrostatic equilibrium, with sub-grid interpolation of the friction (Feldmann et al., 2014). The melt
rate is not interpolated across the grounding line and is calculated with
the Potsdam Ice-shelf Cavity mOdel (PICO; Reese et al.,
2018b), which calculates melt patterns underneath the ice shelves for given
ocean conditions; here this includes mean values over the observational period 1975–2012 (Schmidtko et al., 2014). The basin mean ocean temperature in
the Amundsen region of 0.46 ∘C has been corrected to a lower
value of -0.37∘C as an average from the neighbouring Getz Ice
Shelf basin, assuming that colder conditions were prevalent in the
pre-industrial period. In the experiments basal melt offsets are added to
the evolving PICO melt rate pattern, while basal melt is only for
fully floating grid cells. The near-surface climate, surface mass balance, and
ice surface temperature are from the RACMO2.3p2 1986–2005 mean (van Wessem et al., 2018) remapped from 27 km resolution. The
calving front position can freely evolve using the eigencalving
parameterization (Levermann et al., 2012)
with K=1×1017 m s and a terminal thickness threshold of 200 m.
PISM VUW: Parallel Ice Sheet Model – VUW
We use the Parallel Ice Sheet Model (PISM) version 0.7.1. PISM is a “hybrid”
ice sheet–shelf model that combines shallow approximations of the flow
equations that compute gravitational flow and flow by horizontal stretching
(Bueler and Brown, 2009). The combined stress balance allows
for a treatment of ice sheet flow that is consistent across non-sliding
grounded ice to rapidly sliding grounded ice (ice streams) and floating ice
(shelves). As with most continental-scale ice sheet models, we use flow
enhancement factors for the shallow-ice and shallow-shelf components of the
stress regime (3.5 and 0.5, respectively), which allow us to adjust creep and
sliding velocities using simple coefficients. By doing so we are able to
optimize simulations such that modelled behaviour is consistent with
observed behaviour. The junction between grounded and floating ice is
refined by a sub-grid-scale parameterization (Feldmann et al., 2014) that smooths
the basal shear stress field and tracks an interpolated grounding-line
position through time. This allows for much more realistic grounding-line
motion, even with relatively coarse spatial grids, such as the 16 km grid
used in our experiments. Surface mass balance is calculated using a positive
degree day model that takes as inputs air temperature and precipitation from
RACMO2.1 (Lenaerts
et al., 2012). In previous simulations (e.g. Golledge et al., 2015) we
have derived evolving melt beneath ice shelves from the thermodynamic
three-equation model of Hellmer and Olbers (1989), in which the
melt rate is primarily controlled by salinity and temperature gradients
across the ice–ocean interface. For the simplified experiments presented
here, however, we set a spatially uniform melt rate as an initial condition
and allow our modelled ice sheet to evolve in response to this. All of our
simulations are initialized from a thermally and dynamically evolved state
that represents the present-day ice sheet configuration and has a sea level
equivalent volume of 58.35 m. We also run a control experiment, in which no
additional basal melt is applied and which increases in volume by 0.05 m
over 200 years.
PS3D PSU: Penn State University 3-D ice sheet model (PSUICE3D)
The model is described in detail in Pollard and DeConto (2012b), with updates in Pollard et al. (2015). The
dynamics use a hybrid combination of vertically averaged SIA and SSA
scaling. Floating ice shelves and grounding-line migration are included,
with sub-grid interpolation for grounding-line position. The Schoof (2007) boundary layer formulation
is imposed as a condition on ice velocity across the grounding line, which
enables grounding-line migration to be simulated reasonably accurately
without much higher grid resolution. The model includes standard equations
for the evolution of ice thickness and internal ice temperatures with 10
unevenly spaced vertical layers. Bedrock deformation under the ice load is
modelled as an elastic lithospheric plate above local isostatic relaxation
(ELRA). Basal sliding follows a Weertman-type power law, occurring only
where the bed is close to the melt point. Basal sliding coefficients are
determined by an inverse method (Pollard and DeConto,
2012a), iteratively matching ice surface elevations to modern observations.
Calving of ice shelves depends on combined depths of surface and basal
crevasses relative to the ice shelf thickness. Crevasse depths depend
primarily on the divergence of the ice velocity. The recently proposed
mechanisms of hydrofracturing by surface meltwater and structural failure
of large ice cliffs (DeConto and Pollard,
2016; Pollard et al., 2015) are not enabled for the LARMIP experiments.
Oceanic melting at the base of ice shelves depends on the squared difference
between nearby 400 m depth climatological ocean temperature (Levitus et al., 2012) and the melt point at the bottom of
the ice. Atmospheric temperatures and precipitation are obtained from the
ALBMAP climatology (Le Brocq et al.,
2010), with an imposed sinusoidal cycle for monthly air temperatures. A
simple box model based on positive degree days is used to compute annual
surface mass balance, allowing for refreezing of meltwater. For the LARMIP
experiments the model grid size is 16 km, and the control is spun up to
equilibrium using perpetual modern climate forcing.
SICO ILTS: SICOPOLIS (SImulation COde for POLythermal Ice Sheets)
The model SICOPOLIS version 5.1 (http://www.sicopolis.net, last access: 6 January 2020) is applied to the
Antarctic ice sheet with hybrid shallow-ice–shelfy-stream dynamics for
grounded ice (Bernales et al., 2017) and shallow-shelf
dynamics for floating ice. Ice thermodynamics are treated with the
melting cold–temperate transition surface (CTS) enthalpy method (ENTM) by Greve and Blatter (2016). The ice surface is assumed to be traction-free. Basal sliding under
grounded ice is described by a Weertman–Budd-type sliding law with sub-melt
sliding (Sato and Greve, 2012) and subglacial hydrology (Calov et al., 2018; Kleiner
and Humbert, 2014). The basal sliding coefficient is chosen differently for
the 18 IMBIE 2016 basins (Rignot and Mouginot, 2016) to optimize the
agreement between simulated and observed present-day surface velocities
(Greve et al., 2019). The model is initialized to the reference year 1990 by
a paleoclimatic spin-up over 140 000 years, forced by Vostok δD
converted to ΔT (Petit et al., 1999), in which
the topography is nudged towards the present-day topography to enforce a
good agreement. In the future climate simulations, the ice topography
evolves freely. For the last 2000 years of the spin-up and all future
climate simulations, a regular (structured) grid with 8 km resolution is
used. In the vertical, we use terrain-following coordinates with 81 layers
in the ice domain and 41 layers in the thermal lithosphere layer below. The
present-day surface temperature is parameterized (Fortuin and
Oerlemans, 1990), the present-day precipitation is by Arthern et al. (2006) and
Le Brocq et al. (2010), and runoff is
modelled by the positive degree day method with the parameters by Sato and Greve (2012). The 1960–1989 average SMB correction
that results diagnostically from the nudging technique is used as a
prescribed SMB correction for the future climate simulations. The bed
topography is Bedmap2 (Fretwell
et al., 2013), the geothermal heat flux is by Martos et
al. (2017), and isostatic adjustment is included using an
elastic lithosphere–relaxing asthenosphere (ELRA) model (parameters by
Sato and Greve, 2012). Present-day ice shelf basal melting is
parameterized by the ISMIP6 standard approach, a non-local quadratic melting
parameterization that depends on the thermal forcing (ocean temperature
minus freezing temperature) at the ice–ocean interface, and is tuned
separately for the IMBIE 2016 basins (http://tinyurl.com/ismip6-wiki-ais). The
LARMIP forcings (1, 2, 4, 8, 16, and 32 m yr-1) for the five oceanic sectors
are added to this parameterization.
ÚA UNN: University of Northumbria, Newcastle upon Tyne, UK
ÚA is a finite-element ice flow model
(https://github.com/GHilmarG/UaSource/, last access: 6 January 2020) that solves the momentum and mass
conservation equations in a vertically integrated form using the shallow-ice-stream approximation (SSA) (Gudmundsson et
al., 2012). The transient evolution of the geometry is solved in a fully
implicit manner, i.e. implicitly with respect to both velocities and ice
thickness. The model uses automated mesh refinement and coarsening based on
user-specified criteria. In the runs used in the study, mesh resolution
ranged from about 1 to 40 km. The Weertman sliding law and Glen's flow law
were used to describe basal sliding and ice rheology, respectively. Here the
stress exponents of both laws were set to 3. Spatial variations in the sliding
coefficient (C in the Weertman sliding law) and rate factor (A in Glen's flow
law) were determined by conducting an inversion using the adjoint method
with horizontal velocities as measurements using Tikhonov regularization on
both amplitudes and second spatial derivatives. The ocean model MIT GCM
(Massachusetts Institute of Technology general circulation model;
http://mitgcm.org/, last access: 6 January 2020) has recently been coupled to ÚA (De Rydt et al., 2016). All runs presented were
conducted by the co-author Jim Jordan.
Code and data availability
Data and analysis software can be obtained from the corresponding author upon request. The data can also be downloaded directly from http://www.pik-potsdam.de/~anders/larmip (Levermann, 2020a) and the analysis software from https://github.com/ALevermann/Larmip2019 (Levermann, 2020b).
The supplement related to this article is available online at: https://doi.org/10.5194/esd-11-35-2020-supplement.
Author contributions
AL designed and coordinated the study and computed the projections. All other authors contributed their model simulations as well as to the writing of the paper and the discussion of the results.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
We would like to thank two anonymous reviewers and Daniel Gilford for
extremely helpful comments on the paper.
Support for Daniel Martin, Tong Zhang, Matthew J. Hoffman, Mauro Perego, Stephen F. Price, and Esmond Ng was provided through the
Scientific Discovery through Advanced Computing (SciDAC) programme funded by
the US Department of Energy (DOE), Office of Science, Biological and
Environmental Research, and Advanced Scientific Computing Research programmes.
Their contributions relied on computing resources from the National Energy
Research Scientific Computing Center, a DOE Office of Science user facility
supported by the Office of Science of the US Department of Energy under
contract no. DE-AC02-05CH11231.
Christian Rodehacke has received funding from the European Research Council under the
European Community's Seventh Framework Programme (FP7/2007–2013)/ERC grant
agreement 610055 as part of the Ice2Ice project.
Heiko Goelzer has received funding from the programme of the Netherlands Earth System
Science Centre (NESSC), financially supported by the Dutch Ministry of
Education, Culture and Science (OCW) under grant no. 024.002.001.
A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Helene Seroussi and Nicole-Jeanne Schlegel were supported by grants from the NASA Cryospheric Science, Sea Level Change Team, and Modeling Analysis and Prediction programmes.
Ralf Greve was supported by the Japan Society for the Promotion of Science (JSPS) under
KAKENHI grant nos. JP16H02224, JP17H06104, and JP17H06323.
The work of Thomas Kleiner and Angelika Humbert has been conducted in the framework of the PalMod
project (FKZ: 01LP1511B), supported by the German Federal Ministry of
Education and Research (BMBF) as a Research for Sustainability initiative
(FONA).
The material provided for the CISM model is based upon work supported by the
National Center for Atmospheric Research, which is a major facility
sponsored by the National Science Foundation under cooperative agreement no. 1852977. Computing and data storage resources, including the Cheyenne
supercomputer (https://www2.cisl.ucar.edu/resources/computational-systems/cheyenne, last access: 6 January 2020), were provided by the Computational and
Information Systems Laboratory (CISL) at NCAR.
Torsten Albrecht was supported by the Deutsche Forschungsgemeinschaft (DFG) in the
framework of the priority programme “Antarctic Research with comparative
investigations in Arctic ice areas” by grants LE1448/6-1 and LE1448/7-1. Julius Garbe
acknowledges funding from the Leibniz Association (project DominoES).
Jonas Van Breedam and Philippe Huybrechts acknowledge support from the iceMOD project funded by the
Research Foundation – Flanders (FWO-Vlaanderen).
Malte Meinshausen received funding from the National Science Foundation (NSF grant
no. 1739031) through the PROPHET project, a component of the International
Thwaites Glacier Collaboration (ITGC).
Financial support
This research has been supported by the U.S. Department of Energy (grant no. DE-AC02-05CH11231), the European Research Council (ICE2ICE (grant no. 610055)), the Dutch Ministry of Education, Culture and Science (grant no. 024.002.001), the Japan Society for the Promotion of Science (grant nos. JP16H02224, JP17H06104, and JP17H06323), the German Federal Ministry of Education and Research (BMBF) FONA (grant no. 01LP1511B), the German Research Foundation (grant nos. LE1448/6-1 and LE1448/7-1), and the National Science Foundation (grant no. 1852977).The article processing charges for this open-access publication were covered by the Potsdam Institute for Climate Impact Research (PIK).
Review statement
This paper was edited by Yun Liu and reviewed by Daniel Gilford and two anonymous referees.
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