Ice sheet numerical modeling is an important tool to estimate the dynamic
contribution of the Antarctic ice sheet to sea level rise over the coming
centuries. The influence of initial conditions on ice sheet model
simulations, however, is still unclear. To better understand this influence,
an initial state intercomparison exercise (initMIP) has been developed to
compare, evaluate, and improve initialization procedures and estimate their
impact on century-scale simulations. initMIP is the first set of experiments
of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is
the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity
focusing on the Greenland and Antarctic ice sheets. Following
initMIP-Greenland, initMIP-Antarctica has been designed to explore
uncertainties associated with model initialization and spin-up and to
evaluate the impact of changes in external forcings. Starting from the state
of the Antarctic ice sheet at the end of the initialization procedure, three
forward experiments are each run for 100 years: a control run, a run with a
surface mass balance anomaly, and a run with a basal melting anomaly beneath
floating ice. This study presents the results of initMIP-Antarctica from 25
simulations performed by 16 international modeling groups. The submitted
results use different initial conditions and initialization methods, as well
as ice flow model parameters and reference external forcings. We find a good
agreement among model responses to the surface mass balance anomaly but
large variations in responses to the basal melting anomaly. These variations
can be attributed to differences in the extent of ice shelves and their
upstream tributaries, the numerical treatment of grounding line, and the initial ocean conditions applied, suggesting that ongoing efforts to
better represent ice shelves in continental-scale models should continue.
Introduction
The Antarctic ice sheet is the largest reservoir of freshwater on Earth and
contains enough ice to raise global mean sea level by 58.3 m (Fretwell et
al., 2013). Reconstructions of past sea-level variations show that the volume
of the Antarctic ice sheet has varied significantly over time, with for
example an ice loss of up to 15 m sea level equivalent (SLE) at a rate of up
to 1 mm yr-1 during the Pliocene, around
5.3–2.6 million years before present (Miller et al., 2012). Several regions
of the Antarctic ice sheet are currently changing rapidly (Rott et al., 2002;
Scambos et al., 2004; De Angelis and Skvarca, 2003; Khazendar et al., 2013;
Mouginot et al., 2014; Rignot et al., 2014; Christie et al., 2016). These
changes have been attributed to changes in ocean circulation (e.g., Thomas et
al., 2004; Payne et al., 2004; Jenkins et al., 2010, 2018; Jacobs et al.,
2012) and atmospheric conditions (e.g., Doake and Vaughan, 1991; Vaughan and
Doake, 1996; Scambos et al., 2000). Understanding how the Antarctic ice sheet
will evolve over the coming centuries, and in particular how much it will
contribute to sea level, has therefore become a major field of research.
Projections of 21st century Antarctic ice sheet evolution, however, vary
widely, with projected upper bounds ranging from 30 cm of sea level
equivalent (Ritz et al., 2015) to over 1 m (DeConto and Pollard, 2016),
depending on model characteristics and physical processes, as well as the
climate scenarios adopted. Previous efforts from the ice sheet modeling
community for the IPCC-AR5 (Intergovernmental Panel for Climate Change Fifth
Assessment Report; Church et al., 2013) tried to estimate the ice sheet
evolution under several climate scenarios (Bindschadler et al., 2013; Nowicki
et al., 2013a, b). These results had a large spread for all scenarios, as a
consequence of differences in model characteristics and processes included,
initialization methods, and the interpretation and application of model
forcings (Nowicki et al., 2013b).
A limitation of these previous efforts was the use of climate forcing that
could be considered as outdated by the time of the experiments. For example,
the SeaRISE initiative (Sea level Response to Ice Sheet Evolution;
Bindschadler et al., 2013) used results from IPCC-AR4 scenarios, while at the
same time IPCC-AR5 climate simulations became available. In order to better
coordinate the ice sheet modeling and climate modeling communities, the Ice
Sheet Model Intercomparison Project for CMIP6 (ISMIP6) was designed to be the
primary activity within the Coupled Model Intercomparison Project Phase 6
(CMIP6) that focuses on the Greenland and Antarctic ice sheets (Nowicki et
al., 2016).
Previous ice sheet intercomparison efforts (Pattyn et al., 2012, 2013;
Bindschadler et al., 2013; Goelzer et al., 2018) highlighted the importance
of better assessing the causes of the spread in model results and separating
differences associated with model grid resolution, ice dynamics (e.g., choice
of stress balance equation), physical processes included (e.g., calving,
hydrofracture, and cliff failure), and initialization procedure (e.g., data
assimilation, spin-up, or relaxation). While the impact of many processes and
parameters can be assessed by running large ensembles (e.g., Ritz et al.,
2015; Pollard et al., 2016) or using uncertainty quantification (e.g.,
Schlegel et al., 2013, 2015, 2018), analyzing the impact of initial
conditions is more difficult. Ice sheet models rely primarily on two methods
to construct their initial state: (1) long transient simulations of ice sheet
evolution since the Last Glacial Maximum or earlier, with forcing based on
past climates (e.g., Huybrechts, 2002; Greve and Herzfeld, 2013; Aschwanden
et al., 2013; Golledge et al., 2015), or (2) data assimilation of observed
present-day conditions at a given time (e.g., Morlighem et al., 2010, 2013;
Gillet-Chaulet et al., 2012; Favier et al., 2014; Arthern et al., 2015;
Cornford et al., 2015). The first captures the climate history and ensures
that modeled variables are mutually consistent, but the simulated present-day
ice state might differ significantly from the current observed state, which
can impact the sensitivity to perturbations (Pollard and DeConto, 2012a). The
second method reproduces present-day ice sheet geometry and velocity well but
does not capture past climate evolution and current trends of ice mass, due
to inconsistencies between datasets (Seroussi et al., 2011), also impacting
the ice sheet response to perturbations. To combine the best of these two
approaches, models using long transient spin-ups have integrated simple
inverse methods to match present ice sheet geometry (Pollard and DeConto,
2012a), while models using data assimilation have run short-term relaxation
periods to limit the initial shock caused by inconsistent datasets
(Gillet-Chaulet et al., 2012). These additions are widening the spectrum of
initialization methods (see also Goelzer et al., 2018).
Since ice sheets have a slow response time, their initial conditions
influence their evolution for centuries to millennia. Understanding the
impact of initialization methods is therefore critical for projections of sea
level in the 21st century and beyond. The initMIP experiments were thus
designed as the first part of ISMIP6, with the goal of understanding the
effects of initialization procedures on model results under simplified and
relatively large climate forcings. This effort is intended to show the impact
of model initial conditions on the variations in sea level contribution from
Antarctica but not to provide improved estimates of sea level evolution. A
previous effort, initMIP-Greenland (Goelzer et al., 2018), showed that the
initial ice sheet extent has a large impact on Greenland ice sheet evolution
when anomalies in surface mass balance (SMB) are applied. Here, we describe a
similar effort for the Antarctic ice sheet, using simple climate anomalies
applied to both the SMB and to sub-ice-shelf melting rates. We analyze
25 simulations from 16 international groups in order to determine the most
relevant factors and to better understand the spread in projections of 21st
century Antarctic ice sheet contributions to sea level.
We first describe the initMIP-Antarctica experimental design in Sect. 2 and
the participating models in Sect. 3. In Sect. 4, we analyze simulation
results and the spread in model responses, and in Sect. 5 we discuss these
results and their implications for improving model initialization and
constraining sea-level projections. We conclude with remarks relevant to
future modeling efforts.
Experiments and model setup
In this section we describe in detail the initMIP-Antarctica experiments,
including model requirements and outputs. Complete documentation can be
found on the ISMIP6 wiki page
(http://www.climate-cryosphere.org/wiki/index.php?title=InitMIP-Antarctica,
last access: 7 May 2019).
Experiments description
InitMIP-Antarctica consists of an initial state,
init, describing the
initial state of the Antarctic ice sheet model, followed by three
experiments, each designed for continental-scale Antarctic simulations.
Modeling groups are asked to describe the ice sheet geometry and other
characteristics at the end of their initialization procedure, which is left
to the discretion of each group. The following three experiments are 100-year
simulations of the Antarctica ice sheet evolution under different forcing
scenarios.
In ctrl, the control run, climate forcing is assumed to be similar to
present-day conditions, so atmospheric and oceanic forcings at the end of the init
experiment are continued unchanged. The total SMB or basal melt applied to
the ice sheet can however change, due to, e.g., variations in ice extent
during the ctrl simulation.
In asmb, the SMB anomaly experiment, atmospheric forcing evolves
under a climate-change scenario associated with high greenhouse gas
emissions, similar to Representative Concentration Pathway (RCP) 8.5. The
prescribed anomaly is the average change in Antarctic SMB for six models:
five publicly available CMIP5 RCP8.5 model simulations (Taylor et al., 2012)
with large SMB changes between 2006–2010 and 2095–2100, along with one
regional model (RACMO2.1; Ligtenberg et al., 2013). As RACMO2.1 results for
RCP8.5 were not available when the anomaly field was prepared, we used
results for the A1B scenario, with SMB adjusted linearly to reflect the
additional radiative forcing (an increase of 8.5 W m-2 by 2100 in
RCP8.5, compared to 6 W m-2 in A1B). The RCP8.5 scenario increases
precipitation by up to 50 % over the Antarctic ice sheet for some climate
models (Ligtenberg et al., 2013; Palerme et al., 2016). SMB anomalies are
mostly positive over the ice sheet, with a few regions seeing a negative
anomaly due to increased surface runoff (Fig. 1a). This anomaly is applied
over the entire ice sheet.
In abmb, an anomaly in ocean-induced sub-ice-shelf melt rates is
applied under the floating ice to mimic future warming of ocean waters. It is
not well understood how changes in far-field ocean conditions in global
climate models transfer onto the Antarctic continental shelf and into
sub-ice-shelf cavities; this is an active area of research (Nakayama et al., 2014;
Asay-Davis et al., 2017; Donat-Magnin et al., 2017). We therefore apply a
simple forcing anomaly equivalent to the estimated present-day melt rates
under floating ice (Depoorter et al., 2013; Rignot et al., 2013). The melt
rate anomaly is the average between these two datasets and averaged over ice
shelves in each of the 20 ice sheet basins defined, so that a different mean
melt rate anomaly is specified for each of the 20 ice sheet basins, with a
spatially uniform anomaly within each basin (Fig. 1b). Thus, this melt rate
anomaly represents a doubling of present-day estimates of melting. The
anomaly is applied under all floating ice, including ice that ungrounds
during the experiment.
For the asmb and abmb experiments, anomalies in SMB and sub-shelf melt rates
are applied in addition to the forcings used in the init and ctrl
experiments. The anomalies are applied as time-dependent functions,
increasing stepwise each year over the first 40 simulation years and
remaining constant over the last 60 years:
EX(t)=EXctrl+EXanom×[t]40;for0<t<40yearsEX(t)=EXctrl+EXanom;fort>40years,
where EX(t) is the forcing at time t, EXctrl the forcing used
in the ctrl experiment, EXanom the applied anomaly (Fig. 1), and
[t] the floor function at time t.
(a) Surface mass balance anomaly (m yr-1) for the
asmb experiment and (b) basal melt rate anomaly
(m yr-1) for the abmb experiment. Black contours show the
current Antarctic ice extent.
These forcings should not be viewed as projections of climate forcing over
the coming century, but rather they represent simple perturbations with
relatively large changes for the purpose of assessing impacts on Antarctic
ice sheet evolution.
Model setup
Ice sheet models are free to use whatever initialization procedure is deemed
appropriate, given model characteristics and requirements. Submitted
simulations rely on long paleoclimate spin-ups, steady states, data
assimilation, or a combination of these methods. There is no constraint or
suggestion on forcing datasets (including SMB and sub-shelf melt rates) or on
specific physical processes and parameterizations (e.g., basal sliding laws,
ice rheology, and stress balance approximation). The initialization time
varies among models but is near the beginning of the 21st century.
Previous multi-model ice sheet studies (Bindschadler et al., 2013; Nowicki et
al., 2013a, b) showed the difficulty of separating the effects of initial
conditions, physical processes, and external forcings. In order to better
analyze the links between initial conditions and external forcings, we impose
several modeling constraints. Models are required to model floating ice
shelves and grounding line dynamics as changes in ice shelves significantly
impacted the evolution of West Antarctica in the past decades. The exact
procedure to simulate these processes, however, is left at the discretion of
the modeling groups. Ice sheet models should apply the provided SMB anomalies
without adjusting for geometric changes in forward experiments (i.e.,
surface-elevation feedback). Similarly, they should apply the basal melt rate
anomaly under floating ice as it evolves over time. Finally, bedrock
elevation adjustment, ice shelf hydrofracturing, and ice cliff failure should
not be included, while the ice front evolution is left at the discretion of
the modeling groups.
Model outputs
Modeling groups were requested to report simulation results using a standard
output format. Table A1 lists the required outputs, including both scalar and
2-D variables. Scalar variables are values describing the entire ice sheet
(e.g., ice mass, ice mass above floatation, and area-integrated SMB and basal
melting). Three kinds of 2-D outputs are requested. State variables (e.g.,
ice velocity and thickness) are snapshots reported at a given time; flux
variables are reported as temporal averages over a given period; and constant
variables do not change with time.
Scalar outputs are provided for each simulation year and corrected for area
distortion due to the projection (e.g., polar stereographic), while 2-D
variables (e.g., ice thickness, surface temperature, and basal drag) are
reported every 5 years. For 2-D variables, results are reported on prescribed
regular grids to help achieve a consistent analysis. These grids are defined
on a polar stereographic projection with standard parallel 71∘ S and
central meridian 0∘ E. Modelers are free to use one of the six
prescribed grids with the resolution closest to their native resolution. All
outputs are then regridded using a conservative interpolation scheme (Jones,
1999) onto an 8 km grid that is used for the analysis. The output grids are
identical to the grids used to provide the SMB and basal melt anomalies.
Participating models
Sixteen modeling centers participated in the initMIP-Antarctica effort and
submitted 25 simulations; each model performed the whole suite of
experiments. The list of modeling centers is shown in Table 1. Table 2 lists
the main characteristics of each simulation, including the stress balance
approximation, grid resolution, initialization procedure, initial year, and
external forcing. More details on individual models and initialization
procedures can be found in Appendix B.
The majority of models use the finite-difference method, with two models
based on finite volumes, two based on the finite-element method, and two
based on a combination of finite element and finite volume. Two simulations
use the Shallow Shelf Approximation
(SSA; MacAyeal, 1989), three use L1L2 (i.e. depth-integrated higher-order)
approximations (Hindmarsh, 2004), and two use a 3-D higher-order
approximation (Pattyn, 2003). The other models use a combination of the
Shallow Ice Approximation (SIA; Hutter, 1983) and SSA, either combining SIA
for the grounded ice with SSA for the floating ice or using SSA as a sliding
law and SIA for the internal deformation (Bueler and Brown, 2009). The grid
resolution ranges from 4 to 32 km for models based on fixed regular grids,
while models using adaptive grid refinement are able to use resolutions as
low as 0.5 km in grounding zones.
List of participants, modeling groups, and ice flow models in ISMIP6
initMIP-Antarctica.
ContributorsGroup IDIce flow modelGroupNicholas Golledge Daniel LowryARCPISMAntarctic Research Centre, Victoria University of Wellington, New ZealandThomas Kleiner Johannes Sutter Angelika HumbertAWIPISMAlfred Wegener Institute for Polar and Marine Research, Bremerhaven, GermanyStephen CornfordCPOMBISICLESSwansea University, UKChristian RodehackeDMIPISMDanish Meteorological Institute, DenmarkMatthew Hoffman Tong Zhang Stephen PriceDOEMALILos Alamos National Laboratory, USAJulien Brondex Fabien Gillet-ChauletIGEElmer/IceInstitut des Géosciences de l'Environnement, FranceRalf GreveILTSSICOPOLISInstitute of Low Temperature Science, Hokkaido University, Sapporo, JapanHeiko Goelzer Thomas Reerink Roderik van de WalIMAUIMAUICEInstitute for Marine and Atmospheric Research, Utrecht, the NetherlandsNicole Schlegel Hélène SeroussiJPLISSMJet Propulsion Laboratory, California Institute of Technology, Pasadena, USAChristophe Dumas Aurélien QuiquetLSCEGrisliLaboratoire des Sciences du Climat et de l'Environnement, Université Paris-Saclay, FranceGunter Leguy William LipscombNCARCISMNational Center for Atmospheric Research, Boulder, CO, USATorsten Albrecht Matthias Mengel Ronja Reese Ricarda WinkelmannPIKPISMPotsdam Institute for Climate Impact Research, GermanyDavid PollardPSUPSUEarth and Environmental Systems Institute, Pennsylvania State University, University Park, PA, USAMathieu Morlighem Helene SeroussiUCIJPLISSMUniversity of California, Irvine, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, USAFrank Pattyn Sainan SunULBf.ETIShUniversité libre de Bruxelles, BelgiumJonas Van Breedam Philippe HuybrechtsVUBAISMPALEOVrije Universiteit Brussel, Belgium
The initialization methods cover the spectrum of procedures used in the ice
sheet modeling community. Fourteen simulations are based on a paleoclimate
spin-up with forcings reproducing the evolution of climate during the
simulated period, and four of these simulations have a targeted ice sheet
geometry at the end of their run, similar to the method described in Pollard
and DeConto (2012a). Four models are based on a steady-state equilibrium in
which the model is run for an extended period of time, until the ice sheet
becomes close to a steady-state equilibrium, with two models also including
present-day geometry as a target (Pollard and DeConto, 2012a). The remaining
seven initializations are based on data assimilation, with three models also
including a short relaxation period after the data assimilation to limit the
impact of inconsistent datasets (Seroussi et al., 2011; Gillet-Chaulet et
al., 2012).
For the external SMB forcing, models use output from RACMO2 (Lenaerts et al.,
2012), RACMO2.3 (van Wessem et al., 2014), RACMO2.3p2 (van Wessem et al.,
2018), MAR (Agosta et al., 2019), ERA Interim (Dee et al., 2011), or Arthern
et al. (2006). Five simulations use a positive degree-day scheme (PDD; Reeh,
1991). These choices generate relatively similar initial SMB (see Sect. 4).
For sub-shelf melting, three simulations do not apply any melt rate. Four
others apply values estimated from remote sensing, extrapolated to regions
that unground during the simulation. Most models apply a parameterization
that depends linearly (Martin et al., 2011; eight simulations) or quadratically
(DeConto and Pollard, 2016; four simulations) on the ocean thermal forcing.
Three simulations adjust the melt rate using an observed thickness target,
and the remaining three simulations use the new Potsdam Ice-shelf Cavity model (PICO) parameterization (Reese
et al., 2018).
Most models include a moving ice front, but five simulations have a fixed ice
front. Ice front migration is primarily based on strain rate in most cases
(Levermann et al., 2012; 10 simulations). Some models use ice flux divergence
and accumulated damage at the ice front (Pollard et al., 2015;
three simulations), and some have ice-front retreat based on a threshold ice
thickness (four simulations), while the others have retreat only where the ice
melts completely (three simulations).
List of initMIP-Antarctica simulations and main model
characteristics. Numerics rely on the finite-difference (FD), finite-element
(FE), or finite-volume (FV) method. Initialization methods are as follows:
spin-up (SP), spin-up with target values for the ice thickness (SP+; see
Pollard and DeConto, 2012a), data assimilation (DA), data assimilation with
short relaxation (DA+), data assimilation of ice geometry (DA*),
equilibrium state (Eq), and equilibrium state with target values for the ice
thickness (Eq+). Initial SMB is derived from the following: RACMO2 (RA2;
Lenaerts et al., 2012), RACMO2.3 (RA2.3; van Wessem et al., 2014), RACMO2.3p2
(RA2.3p2; van Wessem et al., 2018), MAR (Agosta et al., 2019), ERA Interim
(ERA; Dee et al., 2011), Arthern et al. (2006) (Art), and positive degree-day
schemes (PDD; Reeh, 1991). Basal melt rates are based on zero melting (0),
linear function of thermal forcing (Lin; Martin et al., 2011), quadratic
function of thermal forcing (Quad; DeConto and Pollard, 2016), melt rates
estimated from observations (Obs; Rignot et al., 2013; Depoorter et al.,
2013), ice shelf thickness target (SS), ice shelf thickness target with no
refreezing (SS*), and the PICO parameterization (Reese et al., 2018).
Models that have partially floating cells at the grounding line apply melting
using a sub-grid scheme (Sub-grid), a floatation condition to assess if melt
should be applied over the entire cell or not (Floating condition), or no
melt at all (No) in their partially floating cells. Ice front migration
schemes are primarily based on strain rate (StR; Levermann et al., 2012),
retreat only (RO), fixed front (Fix), minimum thickness height (MH), and
divergence and accumulated damage (Div; Pollard et al., 2015). The DMI_PISM1
and DMI_PISM0 differ by the basal melt applied under the floating ice, with
a basal melt reduced by an order of magnitude in DMI_PISM1 compared to
DMI_PISM0. Further details on all the models are given in Appendix B.
n/a: not applicable.
Resultsinit experiment
Each model reports initial ice sheet conditions at the end of the
initialization procedure (init). The total ice-covered area varies
between 1.35×107 and 1.50×107 km2, a range of
only 10.5 % among models. The ice shelf extent, on the other hand, varies
significantly among models, from 0.92×106 to 2.51×106 km2, a range of 6.4 % to 16.7 % of the total
ice-covered area. Figure 2 summarizes the initial extent of all models. Some
models have ice shelves hundreds of kilometers upstream or downstream of
their current observed location. Although models generally agree on the
location of the three largest ice shelves (Ross, Ronne–Filchner, and Amery),
the location and extent of smaller shelves vary widely, including in the
Amundsen and Bellingshausen Sea sectors. The initial ice mass above floatation
varies from 1.79×107 to 2.47×107 Gt (between 49.4 and
68.1 m of SLE), while the total ice mass varies from 2.11×107 to
2.56×107 Gt, in part because of the large discrepancy in ice
shelf extent. Table C1 details the main scalar variables in init for
all simulations.
Initial extent of ice-covered areas and ice shelves for all
participating models. All contributions are regridded onto an 8 km standard
grid. Figures indicate how many models include ice (a, b) or
floating ice (b) in each grid cell. Black lines show the observed
ice extent (a) and ice shelf extent (b) from Bedmap2
(Fretwell et al., 2013).
The ability of models to reproduce the characteristics of the present-day ice
sheet depends on their initialization procedure. The root mean square error
(RMSE) between observed (Fretwell et al., 2013) and modeled ice thickness
varies between 91.2 and 422.3 m, with generally smaller errors (between 91.2
and 320.8 m) for models using data assimilation or present-day geometry as a
target in their initialization and larger errors (between 160.0 and
422.3 m) for models using spin-up, a steady state, or long relaxation
procedures without a geometry target (Fig. 3a). The RMSE between observed
(Rignot et al., 2011a) and modeled surface velocity (Fig. 3b) also has a
large spread among models, varying from 47.5 to 308 m yr-1. These
values are significantly affected by the inclusion of observed surface
velocities during the initialization procedure: the RMSE in surface speed
varies from 47.5 to 94.5 m yr-1 for models including data assimilation
of surface velocities and from 116 to 308 m yr-1 for the other
models. Most of these errors are caused by large discrepancies in ice shelves
and a few fast-flowing ice streams: the RMSE for the logarithm of the speed,
which emphasizes the slower-moving regions, varies only between 0.62 and 1.51
(Fig. 3c), or 3 times less than the RMSE of the speed. These errors are
in part affected by the exact year of the initialization procedure, as
observations of velocity and thickness are not acquired at the same time.
However, the temporal variability of observed thickness and velocity is small
compared to the discrepancies between observations and models, so the exact
year used for the initial state has a limited impact on the RMSE calculated.
Root mean square error (RMSE) of modeled initial conditions compared
to observations for (a) initial ice thickness (m), (b)
initial ice surface velocity (m yr-1) over the ice sheet and ice shelf,
and (c) the logarithm of the initial ice surface velocity
(log(m yr-1)). Please note that the model–color relationship used in
this figure is applied in all subsequent figures. Models that assimilate
present-day conditions during their initialization process are denoted with +
if they integrate geometry and * if they integrate velocity and geometry
information.
Area-integrated external forcings (SMB and basal melt) also differ
substantially among the models (see Table C1 in the Appendix C). The total
initial SMB varies from 2015 to 3430 Gt yr-1, depending on the origin
of the SMB forcing (see Table 2) and the extent of the ice-covered areas. The
total initial ocean-induced basal melt varies from 0 to 2470 Gt yr-1,
with seven models having values of less than 150 Gt yr-1, while remote
sensing estimates of total Antarctic basal melt are ∼1400 Gt yr-1 (Rignot et al., 2013; Depoorter et al., 2013). Similar
to the SMB forcing, these differences result from the chosen melting
parameterization (Table 2) and the geometry of ice shelves.
ctrl experiment
Representing the current state of the ice sheet does not guarantee that the
current trends in ice sheet changes are correctly captured, which is what
eventually matters in sea level rise projections. In the ctrl
experiment, the Antarctic ice sheet evolves under a constant climate for
100 years. The total change of ice mass above floatation varies from a loss of
60 500 Gt to a gain of 88 100 Gt (i.e., 243 mm of SLE drop to 167 mm of
SLE rise; see Fig. 4a and Table B2), with mass loss in 8 simulations and gain
in 17 simulations. This absolute change in mass above floatation represents
less than 0.42 % of the initial volume in all cases, highlighting the
accuracy required to calculate the Antarctic evolution for sea level
projections. A spread of results is observed for all initialization methods
and model resolutions. Eleven models have an absolute change lower than 20
mm, 10 have an absolute change above 80 mm, and four have an absolute change
between 20 and 80 mm. All the models initialized with a steady-state
equilibrium but one have a sea level change lower than 20 mm, while all the
models using data assimilation to determine their initial conditions but one
have a sea level change above 80 mm. The models based on a paleoclimate
spin-up have a large spread of sea level change in the ctrl
experiment and are present in all categories. The number of models in each
category is, however, relatively small to draw definitive conclusions.
Antarctic contribution to sea level (mm of sea level equivalent).
(a) ctrl experiment, (b) difference between
asmb and ctrl experiments, and (c) difference
between abmb and ctrl experiments. Negative values of SLE
represent a growing ice sheet.
Figure 5 shows the spatial patterns of thickness and depth-average horizontal
ice speed for the ctrl experiment. Regridded results on the 8 km
standard grid are used to compute modeled mean changes and standard deviation
for these two variables. Results are reported only where at least five
simulations have ice at a given grid point. Maps of thickness and velocity
change during the ctrl experiment show that the signals are larger
along the coast than in the interior of the continent and larger in West
Antarctica compared to East Antarctica. The ice sheet mean thickness change,
averaged over all models, is equal to 1.2 m in 100 years. The standard
deviation is calculated for each grid cell of the 8 km standard grid based
on the number of models reporting results in each cell and excluding cells
where fewer than five models simulate ice. The standard deviation is much larger
than the mean changes in many places, with an average value over the
simulated area of 14.8 m. Substantial thickening and thinning (especially of
ice shelves) compensate for each other, leading to a small spatial average change
but large standard deviation. Similarly, the spatial average velocity change
is small, with a value of -1.9 m yr-1, but the standard deviation is
27.4 m yr-1. Some models have large accelerations in key regions,
while others have large slowdowns. Regions with the largest spread in model
thickness and velocity changes are generally similar.
Mean (a, b) and standard deviation (c, d) of the
change in ice thickness (a and c, in m) and depth-averaged
horizontal velocity (b and d, in m yr-1) between the
beginning and end of the ctrl experiment. Black (a, c) or
grey (b, d) lines show the observed current ice front and grounding
line positions.
The ice extent is relatively temporally stable in all ctrl
simulations, with less than 1.3 % change in the most sensitive
simulations. Some simulations, however, have large temporal changes in ice
shelf extent, ranging from a reduction of 13 % to an increase of
14 %. The area-integrated SMB varies by up to 6 % for the simulations
that experience the largest change in SMB (Fig. 6b). The area-integrated
basal melting varies by more than 5 % for 15 models, with a maximum
change of 29 %, in response to changes in ice shelf extent and thickness
(Fig. 6c).
Evolution of Antarctic ice sheet mass above floatation and external
forcings in the ctrl experiment. (a) Total mass of ice
above floatation (Gt), (b) total SMB applied at the ice surface
(Gt yr-1), and (c) total basal melting rate (Gt yr-1).
asmb experiment
In the asmb experiment, an SMB anomaly (Fig. 1a) is added to the SMB
used in the ctrl experiment. This anomaly leads to an increase in
ice mass above floatation compared to ctrl, with the mass gain
ranging from 4.51×104 to 6.72×104 Gt (125–186 mm
decrease in SLE; see Fig. 4b). The differences among models (Fig. 7a, b) are
linked to the extent of the ice-covered areas, as well as ice shelf extent.
For most models there is a small increase in grounded area, as some floating
areas near grounding lines thicken and reground due to the positive SMB
anomaly.
Evolution of the Antarctic ice sheet and external forcings in the
asmb (a and b) and abmb (c and d)
experiments compared to the ctrl experiment. Total amount of ice above
floatation for asmb minus ctrl (a) and abmb minus ctrl (c)
(in Gt). Evolution of SMB applied at the ice surface for asmb minus ctrl
(b, in Gt yr-1) and total basal melting applied in abmb minus ctrl
(d, in Gt yr-1).
Figure 8 shows the mean and standard deviation of the impact of this SMB
anomaly on the ice thickness and depth-averaged horizontal velocity. Figure 8
is similar to Fig. 5 but for the difference between the end of the
asmb experiment and the end of the ctrl experiment. As
expected from the SMB anomaly spatial pattern (Fig. 1a), there is a
thickening of 3.6 m on average over Antarctica, with the largest changes
happening along the West Antarctic coasts and the Antarctic Peninsula
(Fig. 8a). The standard deviation map (Fig. 8c) shows that model differences
are again concentrated along the West Antarctica coast and on the Antarctic Peninsula.
The average standard deviation over the continent is 5.2 m for this anomaly.
The SMB anomaly has a small impact on ice dynamics, as shown in Fig. 8b, with
a spatial average speed increase of 1.5 m yr-1 over 100 years and a
standard deviation of 17.6 m yr-1. Regions where models disagree are
similar to those for the ctrl experiment. Figure 9a compares for
each model the difference in mass between the end of the asmb
experiment and the end of the ctrl experiment with the cumulative
SMB anomaly of the asmb experiment integrated over the entire ice sheet.
It confirms that the additional SMB is the primary cause of mass change: the
SMB anomaly explains between 97 % and 130 % of the total mass change.
The difference between the cumulative SMB anomaly and the change in mass is
caused by thicker and faster ice (see Fig. 8) that increases the calving flux,
as well as feedbacks on ice shelf basal melt.
Mean (a, b) and standard deviation (c, d) of the
ice thickness (a and c, in m) and depth-averaged horizontal
velocity (b and d, in m yr-1) between the end of the
asmb experiment and the end of the ctrl experiment. Black
(a, b) or grey (c, d) lines show the current observed ice
front and grounding line positions.
(a) Difference in mass (Gt) between the end of the asmb
experiment and the end of the ctrl experiment and the cumulative SMB anomaly
(Gt) of the asmb experiment integrated over the entire ice sheet for the 25
simulations. (b) Difference in mass (Gt) between the end of the abmb
experiment and the end of the ctrl experiment and the cumulative basal melt
anomaly (Gt) of the abmb experiment integrated over the entire ice sheet for
the 25 simulations. Black dashed lines show mass change equal to cumulative
anomaly change.
abmb experiment
In the abmb experiment, an anomaly is applied to the basal melting
rate of floating ice shelves, in addition to the basal melting used in the
ctrl experiment. The basal melt anomaly is uniform within each
region (see Fig. 1b) and largest in the Amundsen Sea, where an additional
ocean-induced melt of 13.2 m yr-1 is applied. This additional melting
leads to a thinning of ice shelves, a reduction of the buttressing they
provide to grounded ice, an acceleration of the ice streams feeding the
shelves, and a retreat of grounding lines. However, unlike what is observed
for the asmb experiment, the abmb response varies
significantly among models.
Differences can be attributed in part to different treatments of basal melt
in model cells near the grounding line. Some models have no melting in
partially floating cells, others
apply melt in partially floating cells based on the fraction of floating area,
and two models apply melt over the entire cell if it satisfies a floatation
criterion (see Table 2). The spread in ice mass loss above floatation
compared to the end of the ctrl experiment varies by 2 orders of magnitude,
from 4.7×103 to 1.5×105 Gt (or 13–427 mm of SLE; see
Fig. 4c and Table B2 in Appendix B), even though the additional melt is
applied only to floating ice and therefore does not contribute directly to
sea level rise. The grounded area is reduced for all the models (between
0.10 % and 1.7 % reduction) as grounding lines retreat. The change in
ice shelf extent varies from a reduction of 25 % to an increase of
12 %, as some ice shelves calve during this experiment, depending on the
choice made for ice front evolution (see Table 2).
Figure 10 shows that the modeled mean and standard deviation for the ice
thickness and depth-averaged velocity changes are concentrated on the ice
shelves and near grounding lines. Ice thinning is 10.7 m on average, and the
standard deviation is 12.4 m. The dynamic impact of such variations is not
limited to the ice shelves but propagates upstream of the grounding line,
especially in the Amundsen Sea Basin, where the largest anomalies are
applied. The Ross and Filchner–Ronne ice shelves have acceleration near the
grounding line but also a slowdown near the ice front. The modeled mean
velocity change over the ice sheet is a small slowdown of 3.3 m yr-1;
this signal is small compared to the standard deviation of
29.6 m yr-1. Regions where models show a large spread of thickness and
velocity changes are different from the ctrl and asmb simulations. Large
deviations among models extend upstream from the present-day grounding lines and over the ice streams
feeding the ice shelves, reflecting
different model responses to this oceanic forcing. Figure 9b compares for
each model the difference in mass between the end of the abmb experiment and
the end of the ctrl experiment, with the cumulative basal melt anomaly of the
abmb experiment integrated over the entire ice sheet. It shows that the
additional basal melt only accounts for a fraction of the mass change: the
basal melt anomaly explains between 5 % and 125 % of the total mass
change. The difference between the cumulative basal melt anomaly and the
change in mass is mainly caused by thinner and slower ice shelves (see
Fig. 10) that reduce the calving flux.
Mean (a, b) and standard deviation (c, d) of the
change in ice thickness (a and c, in m) and depth-averaged
horizontal velocity (b and d, in m yr-1) between the
end of the abmb experiment and the end of the ctrl
experiment. Black (a, b) or grey (c, d) lines show the
current observed ice front and grounding line positions.
Discussion
The initMIP-Antarctica experiments are designed to analyze the impact of ice
sheet model initial conditions on the evolution of the Antarctic ice sheet
and its response to simple climate forcings. For this exercise, 16 groups
submitted 25 simulations, more than 4 times the number of Antarctic
simulations submitted for the SeaRISE project (Bindschadler et al., 2013),
highlighting the importance and the fast evolution of this research field
(Pattyn et al., 2017). The
simulations represent a large diversity of initialization methods, forcing
datasets, and model parameters, and the results show a large spread in the
mass balance and dynamic evolution of this ice sheet in century-scale
simulations.
The initial ice volume above floatation varies from 1.8 to 2.5×107
Gt, or almost 32 %, which is much larger than the spread of about 8 %
in SeaRISE (Nowicki et al., 2013b). This is not surprising given the larger
number of model contributions. On the other hand, the largest drifts in the
ctrl experiment are reduced compared to the SeaRISE project. For
initMIP-Antarctica, the ctrl sea level contribution varies between
-243 and +167 mm of sea level equivalent for the 25 simulations of
ISMIP6, while its evolution varied between -256 and +1 mm over the first
100 years for the six simulations of SeaRISE. Specifically, four models
participated in both SeaRISE and initMIP-Antarctica, and the large drift that
two of them experienced in SeaRISE has been reduced in the initMIP-Antarctica
ctrl experiment.
The asmb and abmb experiments are designed to analyze the
ice sheet response to simple anomalies in SMB and basal melting under the ice
shelves. Unlike initMIP-Greenland, where Goelzer et al. (2018) observed a
large spread of 118 % in the responses in the asmb experiment,
the response to the SMB anomaly in initMIP-Antarctica is similar among all
the models, with a 39 % variation in the response to this anomaly between
the models. The differences can be attributed to the larger spread in initial
ice sheet extent and the pattern of the SMB anomaly in initMIP-Greenland. In
Greenland, large ablation rates are applied at the ice sheet periphery,
leading to significant ice loss for the models with the largest initial
extents (Goelzer et al., 2018). The Antarctic SMB anomaly has less spatial
variability, and the initial extent of the ice sheet is closer for the
different simulations, which leads to more consistent responses to this
perturbation.
While the response to the SMB anomaly has limited variations among models,
the impact of the basal melting anomaly varies significantly among models,
with a spread in sea level contribution from 13 mm to more than 400 mm.
Several factors explain the wide range of abmb responses. First, models vary
in their treatment of basal melting near the grounding line. Elements and
grid cells crossed by the grounding line are considered partially floating. Some
models have no melting in partially floating cells, others apply melt in partially floating cells
based on the fraction of floating area, and two models apply melt over the
entire cell if it satisfies a floatation criterion (see Table 2). These
different treatments can have a significant impact on grounding line
evolution, as highlighted by previous studies (Arthern and Williams, 2017;
Seroussi and Morlighem, 2018). This is especially important for
continental-scale simulations that have a resolution varying between several
kilometers and several tens of kilometers, as is the case in
initMIP-Antarctica. The four largest sea level contributions in the abmb
experiment (> 200 mm) come from four models that apply sub-grid
melt in partially floating cells and have a resolution of 8 km or coarser (see
Tables 2 and B2). Additionally, two of these models were run without
(ARC_PISM1 and ARC_PISM3) and with (ARC_PISM2 and ARC_PISM4) a sub-grid
melt scheme in partially floating cells (see Table 2), which resulted in an
additional sea level rise of 90 and 124 mm when the sub-grid melt scheme was
used.
Second, the total ice shelf extent varies by more than 100 % among the
different models, and their extent within different basins also varies
significantly (see Fig. 2 and Table B1). As the basal melting anomaly is
applied only under floating ice, the spatial extent and amount of the applied
anomaly therefore vary significantly from one model to the next. Ice shelf
extent also varies during the ctrl and abmb experiments, so
that the applied melt anomaly evolves differently between the simulations. As
shown in Fig. 11, floating ice areas stay relatively constant in some models,
increase because of grounding line retreat in others, and decrease as ice
shelves thin significantly and calve in the remaining ones.
Third, while the SMB applied in init and ctrl is relatively
similar among the different models, the basal melting varies from zero melt
to 2140 Gt yr-1. The latter value is about 50 % larger than values
derived from remote sensing observations (Rignot et al., 2013; Depoorter et
al., 2013) (see Fig. 7). The applied basal melting anomaly therefore
represents about half the initial basal melting for some models but a drastic
increase for others. The impact on ice shelf thickness evolution and dynamic
response is therefore very different, as shown by Fig. 10.
Finally, surface-elevation feedback processes were not allowed in
asmb, ensuring that a similar SMB anomaly was applied by all models
at a given location. In abmb, no such constraint was prescribed,
which introduces feedbacks between ice shelf and basal melting for some
parameterizations. For example, if an ice shelf thins and the grounding line
retreats in a given model, the newly floating ice experiences basal melting
that can drive further thinning and retreat. The effective basal melting
anomaly therefore varies between the simulations (see Fig. 7d). These results
highlight the need for further modeling studies and observations on basal
melting patterns near the grounding line.
Evolution of Antarctic ice shelf extent for the (a)
ctrl and (b) abmb experiments.
One objective of ISMIP6 and initMIP-Antarctica is to gather a large and
diverse ice sheet modeling community. To facilitate participation of a large
number of models, only two constraints were imposed: (1) the inclusion of
both grounded and floating ice and (2) the simulation of dynamic grounding
line migration. This lack of constraints complicates the analysis of the
simulation differences, since model parameters, input forcing, initialization
techniques, and physical processes vary widely among models. Initialization
methods that are based on the assimilation of present-day conditions usually
have lower RMSE in the initial ice thickness and velocity compared to
observations (Fig. 3) but larger trends in the ctrl experiment
(Fig. 4a), while the opposite is true for models relying on paleoclimate
spin-up or a steady-state solution. This is similar to what was previously
observed by Nowicki et al. (2013a, b) and Goelzer et al. (2018). As the two
approaches are complementary, models are starting to combine them by either
following data assimilation with short relaxation periods or by assimilating
surface elevation during transient initialization to have an initial geometry
more consistent with observations (Pollard and DeConto, 2012a). Combining the
best of both approaches is an active field of research. Assimilating
observations over longer time periods looks like a promising option, despite
the technical challenges (Larour et al., 2014; Goldberg et al., 2015).
Representation of ice shelves and their connection to glaciers upstream is
an outstanding cause of differences among models. Ice shelves are directly
affected by variations in oceanic (Jacobs et al., 2011; Pritchard et al.,
2012; Greenbaum et al., 2015; Wouters et al., 2015) and atmospheric (Scambos
et al., 2000; Banwell et al., 2013; Munneke et al., 2014; Bassis and Ma,
2015) conditions, which impacts grounding line and ice front evolution
(Favier et al., 2014; Joughin et al., 2014; Rignot et al., 2014; Bassis and
Ma, 2015; Scheuchl et al., 2016; Christie et al., 2016; Seroussi et al.,
2017). Ice shelf evolution over the past few decades has been complex, with
large spatial and temporal variability (Depoorter et al., 2013; Rignot et
al., 2013; Paolo et al., 2015; Christie et al., 2018) that is not fully
understood and typically is not included in numerical models. Representation
of ice shelves varies among models: the ice shelf extent, spatial location,
and thickness differ significantly between the simulations, resulting in
large deviations in ice shelf flow. Another major source of disagreement is
the boundary condition at the ice–ocean interface, with ocean-induced basal
melting applied under the floating ice and its temporal evolution based on a
wide range of parameterizations. Significant progress was made over the past
decade (Pattyn et al., 2017), but continued improvement of ice shelf
representation in continental-scale models should remain a research priority
so that ice shelf representation in continental-scale ice sheet models is in
better agreement with observations of the current state of the Antarctic ice
sheet.
The results presented in this study rely on simple atmospheric and oceanic
forcings that are only loosely based on RCP scenarios. Furthermore, many
participating models did not use their full capabilities. To reduce model
differences, for example, participants were asked to turn off
surface-elevation feedback schemes, bedrock adjustment capabilities, and ice
cliff failure. As a result, the initMIP-Antarctica simulations are not
projections of Antarctic evolution over the coming century and should not be
compared with previous Antarctic simulations aiming to simulate this
evolution (e.g., Ritz et al., 2015; Golledge et al., 2015). The next step of
ISMIP6 will be the assessment of Antarctic evolution under different scenarios
forced with oceanic and atmospheric conditions derived from CMIP climate
models; experiments are now being designed. The initMIP-Antarctic
simulations do, however, illustrate the spread in ice sheet evolution (hence
sea level) that is due to ice sheet model initial state and modeling choices
(e.g., grounding line numerics, calving laws) and provide insight into
uncertainty in simulations of sea level change.
Conclusions
The initMIP-Antarctica experiment, part of the Ice Sheet Model
Intercomparison Project for CMIP6 (ISMIP6), had broad participation, with
25 model simulations submitted from 16 groups. Results are improved compared
to previous similar exercises of continental-scale modeling of the Antarctic
ice sheet, with enhanced representation of present-day conditions and ice
mass loss trend. A first experiment performed with a simple surface mass
balance anomaly forcing produces relatively robust results across the models,
while a second experiment with a simple perturbation in basal melting rate
under the ice shelves creates very large discrepancies in the ice sheet
response. Variations in the representation of ice shelves (e.g., spatial
extent, thickness), ice shelf basal melting, and numerical treatment of
grounding lines cause this significant spread of results between the
simulations. Including accurate representations of ice shelves that are
consistent with observations of the current Antarctic ice sheet in
continental-scale models should therefore remain an important research
subject in the coming years. All the experiments performed as part of
initMIP-Antarctica are based on simplified anomaly forcings. Future
projections of the Antarctic ice sheet evolution under different climate
scenarios are currently being designed and will be the subject of future
ISMIP6 modeling experiments.
Data availability
The model output from the simulations described in this
paper and forcing data sets will be made publicly available with a digital object identifier
https://doi.org/10.5281/zenodo.2651652. In order to document CMIP6's
scientific impact and enable ongoing support of CMIP, users are asked to
acknowledge CMIP6, ISMIP6, and the participating modeling groups.
Outputs and output format
initMIP-Antarctica participants are required to provide output variables
according to the data request plan. Three types of 2-D fields are reported by
modeling groups at 5-year intervals: state variables, flux variables, and
constants. Also, scalar outputs (e.g., total ice mass, ice mass above
floatation, SMB, basal melt) are reported every simulation year. Table A1
provides the complete list of requested variables. In addition to model
output results, a README file describing model characteristics and details of
the initialization procedure was requested from modeling groups for each
simulation.
Data requests for initMIP-Antarctica. ST: state variable. FX: flux
variable. CST: constant.
Variable nameTypeStandard nameUnitIce sheet thicknessSTland_ice_thicknessmIce sheet surface elevationSTsurface_altitudemIce sheet base elevationSTbase_altitudemBedrock elevationSTbedrock_altitudemGeothermal heat fluxCSTupward_geothermal_heat_flux_at_ground_levelW m-2Surface mass balance fluxFLland_ice_surface_specific_mass_balance_fluxkg m-2 s-1Basal mass balance fluxFLland_ice_basal_specific_mass_balance_fluxkg m-2 s-1Ice thickness imbalanceFLtendency_of_land_ice_thicknessm s-1Surface velocity in x directionSTland_ice_surface_x_velocitym s-1Surface velocity in y directionSTland_ice_surface_y_velocitym s-1Surface velocity in z directionSTland_ice_surface_upward_velocitym s-1Basal velocity in x directionSTland_ice_basal_x_velocitym s-1Basal velocity in y directionSTland_ice_basal_y_velocitym s-1Basal velocity in z directionSTland_ice_basal_upward_velocitym s-1Mean velocity in x directionSTland_ice_vertical_mean_x_velocitym s-1Mean velocity in y directionSTland_ice_vertical_mean_y_velocitym s-1Ice surface temperatureSTtemperature_at_ground_level_in_snow_or_firnKIce basal temperatureSTland_ice_basal_temperatureKMagnitude of basal dragSTmagnitude_of_land_ice_basal_dragPaLand ice calving fluxFLland_ice_specific_mass_flux_due_to_calvingkg m-2 s-1Grounding line fluxFLland_ice_specific_mass_flux_due_at_grounding_linekg m-2 s-1Land ice area fractionSTland_ice_area_fraction1Grounded ice sheet area fractionSTgrounded_ice_sheet_area_fraction1Floating ice sheet area fractionSTfloating_ice_sheet_area_fraction1Total ice sheet massSTland_ice_masskgTotal ice sheet mass above floatationSTland_ice_mass_not_displacing_sea_waterkgArea covered by grounded iceSTgrounded_land_ice_aream2Area covered by floating iceSTfloating_ice_shelf_aream2Total SMB fluxFLtendency_of_land_ice_mass_due_to_surface_mass_balancekg s-1Total BMB fluxFLtendency_of_land_ice_mass_due_to_basal_mass_balancekg s-1Total calving fluxFLtendency_of_land_ice_mass_due_to_calvingkg s-1Total grounding line fluxFLtendency_of_grounded_ice_masskg s-1Model description and initialization
Below are descriptions of the ice flow models and the initialization
procedure performed by the different groups.
ARC_PISM
We use the Parallel Ice Sheet Model (PISM) version 0.7.1. PISM is a hybrid
ice sheet–ice shelf model that combines shallow approximations of the flow equations that compute
gravitational flow and flow by horizontal stretching (Bueler and Brown,
2009). We perform two sets of experiments with different initialization
procedures. In the first set (PISM-1,2), the simulations are initialized from
the end of a 120 000-year spin-up using paleoclimate forcing, whereas in the
second set (PISM-3,4), the simulations are initialized from the end of a
100 000-year spin-up using a constant climate forcing. Both procedures
result in a present-day ice sheet configuration that is in a thermally and
dynamically evolved state, with a “present-day” sea-level equivalent volume
of 58.35 and 56.38 m, respectively. The combined stress balance of PISM
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, for PISM-1,2, and 2.8 and
0.5, respectively, for PISM-3,4), which allow us to adjust creep and sliding
velocities using simple coefficients. By doing so we are able to optimize
simulations such that modeled behavior is consistent with observed behavior.
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. We run
duplicate experiments with the sub-grid melt turned off (PISM-1,3) or on
(PISM-2,4) in order to quantify the effect of this scheme. SMB 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
Olber (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 modeled ice sheet to evolve in response to
this.
AWI_PISM
The simulations are performed with PISM version 0.7.3. For the 220 ka-long
spin-up simulations with paleoclimatic forcing (PISM1Pal), time slice
anomalies for the Last Interglacial (LIG) and the Last Glacial Maximum (LGM)
from the Earth System Model COSMOS (Pfeiffer and Lohmann, 2016; Zhang et al.,
2014) are used in addition to datasets for present-day (PD) Antarctic climate
(RACMO2.3, van Wessem et al., 2014; WOA09, Locarnini et al., 2010).
Time-dependent and spatially variable climate anomaly fields are interpolated
during the PISM run between LIG, LGM, and PD climate time slices with a
glacial index method (Sutter et al., 2016), where the glacial index is
derived from Dome C deuterium depletion (Jouzel et al., 2007). For the SMB,
PISM's positive degree-day (PDD) scheme is used. Relative sea level forcing
(Waelbroeck et al., 2002) and bed deformation (Bueler et al., 2007) are
applied during the paleo spin-up. In addition to the paleo
spin-up, a 100 ka-long
equilibrium-type spin-up (PISM1Eq) with steady present-day climate (ocean and
atmosphere) and sea level is carried out with isostatic bed deformation.
Instead of precipitation and 2 m air temperature (PISM1Pal), SMB and skin
temperature from RACMO2.3 are directly applied without the PDD scheme. The
initial geometry for both spin-ups is Bedmap2 (Fretwell et al., 2013), and
the geothermal flux is from Shapiro and Ritzwoller (2004). Basal shelf melt
rates are calculated via a quadratic form of the melt rate formula in
Beckmann and Goosse (2003) using the extrapolated 3-D ocean temperatures at
the depth of the ice shelf base. PISM's sub-grid grounding line scheme for
basal sliding (Feldmann et al., 2014) is used in all simulations.
CPOM_BISICLES
CPOM_BISICLES_A_500m is a block structured adaptive mesh finite-element
model based on a vertically integrated stress balance model (Cornford et al.,
2013, 2016) and the basal friction physics of Tsai et al. (2015). Here, we
make use of the adaptive mesh to maintain a resolution of 8 km in the
slow-moving interior, 1 km in ice streams, and 500 m at the grounding line.
The initial state is based on ice thickness and bedrock elevation from
Bedmap2 (Fretwell et al., 2013), modified according to mass conservation
close to the grounding line to avoid the large unphysical thickening rates
that would otherwise occur, especially in the Amundsen Sea Embayment. Ice
temperature is taken from Pattyn (2010) and is held constant in time over the
course of the simulations. Effective viscosity φ(x,y) and effective
drag coefficients β2(x,y) are estimated by minimizing the mismatch
between modeled speed the observed speed of Rignot et al. (2011b), following
the methods described in Cornford et al. (2015) The background ocean melt
rate M0(x,y,t) is defined so that the thinning rate is zero across the ice
shelf and varies in time accordingly, so that when a melt rate anomaly Ma(x,y,t) is applied, the ice shelf thinning rate is Ma(x,y,t).
CPOM_BISICLES_B is similar to CPOM_BISICLES_A but does not allow
accumulation onto the lower surface of the ice shelf, so that the ice sheet
thins where div(uh) > 0, even with no anomaly.
DMI_PISM
The Parallel Ice Sheet Model (PISM; version 0.7) used utilizes a hybrid
system (Bueler and Brown, 2009) combining the Shallow Ice Approximation (SIA)
and Shallow Shelf Approximation (SSA)
on a polar stereographic grid of 16 km. Monthly atmospheric forcing is
deduced from sub-daily ERA-Interim reanalysis products (Berrisford et al.,
2011; Dee et al., 2011) covering the period 1979–2012. Its 2 m air
temperature drives the ice surface temperature, while the total precipitation
is considered as snow accumulation due to negligible surface melting in
Antarctica. Starting from the contemporary ice sheet geometry, both ice
internal enthalpy and temperature evolve for 150 000 years for a fixed ice
geometry due to surface and geothermal heat fluxes. Afterward the model runs
freely for 25 000 years, so that the model updates grounded ice margins,
grounding lines, and calving fronts continuously. The calving parametrization
exploits three sub-schemes for grid points at the ice shelf margins: the
eigencalving parameterization (Levermann et al., 2012), which utilizes the
stress field divergence with the proportionality constant of 5×1017, the ice shelf margin with a thickness of less than 150 m calve,
and ice shelves that extend into the depth ocean calve. Assuming a constant
ocean temperature of -1.7 ∘C and melting factor (Fmelt=0.001), sub-shelf melting follows Eq. (5) 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 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). In
DMI_PISM1 the basal melting rate of ice shelves is increased by an order of
magnitude compared to DMI_PISM0.
DOE_MALI
MPAS-Albany Land Ice (MALI) (Hoffman et al., 2018) uses a three-dimensional,
first-order Blatter–Pattyn momentum balance solver solved using finite-element methods. Ice velocity is solved on a two-dimensional map plane
triangulation extruded vertically to form tetrahedra. Mass and tracer
transport occurs on the Voronoi dual mesh using a mass-conserving finite-volume first-order upwind scheme. Mesh resolution is 2 km along grounding
lines and in all marine regions of West Antarctica and in marine regions of
East Antarctica where present-day ice thickness is less than 2500 m to
ensure that the grounding line remains in the fine-resolution region, even
under full retreat of West Antarctica and large parts of East Antarctica.
Mesh resolution coarsens to 20 km in the ice sheet interior and no greater
than 6 km in 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 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., 2011b) 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
sub-element parameterization of the friction. 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
SMB is from RACMO2.1 1979–2010 mean (Lenaerts et al., 2012). Maps of SMB and
basal mass balance forcing are kept constant with time. The ice front
position is fixed at the extent of the present-day ice sheet. After
initialization, the model is relaxed for 99 years, so that the geometry and
grounding lines can adjust.
IGE_Elmer-Ice
For the momentum equations, we solve the Shelfy-Stream Approximation. Using
the methodology presented in Fürst et al. (2015, 2016), we rely on
inverse methods to initialize the model to present-day conditions. We use the
present-day ice sheet topography and assimilate observed horizontal surface
velocities to tune the basal friction coefficient and ice viscosity. The cost
function also includes the mismatch between flux divergence and SMB and basal
mass balance. The initial friction coefficient and viscosity fields are kept
constant during the forward simulations. The model is relaxed with a constant
forcing for 20 years after the initialization. For the control experiment the
SMB comes from the regional atmospheric model MAR (Agosta et al., 2019) and
is an averaged SMB between 1979 and 2015. The basal melt rate depends on the
difference between ocean temperature and ocean freezing point and is a
parameterization by sector based on Pollard and DeConto (2012a). The bedrock
topography is taken from Bedmap2 (Fretwell et al., 2013), except that we
include two pinning points in contact with the bottom surface of Thwaites ice
shelf using the bathymetry of Millan et al. (2017). The mesh is fixed, and the
resolution has been adapted to equidistribute the interpolation error of the
observed velocities and thickness with an additional criterion based on
grounding line proximity. The horizontal resolution ranges between 1 km and
50 km.
ILTS_SICOPOLIS
We use SICOPOLIS version 3.3-dev with either shallow-ice dynamics
(ILTS_SICOPOLIS1) or hybrid shallow-ice–shelfy-stream dynamics
(ILTS_SICOPOLIS2; Bernales et al., 2017) for grounded ice and shallow-shelf
dynamics for floating ice. Ice thermodynamics is treated with the melting-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-type sliding law, with sub-melt sliding in the form of Sato and
Greve (2012). The model is initialized 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
the 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), runoff is modeled by the
positive degree-day method with the parameters by Sato and Greve (2012), the
bed topography is Bedmap2 (Fretwell et al., 2013), and the geothermal heat
flux is by Purucker (2012). Present-day ice shelf basal melting is
parameterized as a function of both the depth of ice below mean sea level and
ocean temperatures outside the ice shelf fronts at 500 m depth, tuned
differently for eight Antarctic sectors (Greve and Galton-Fenzi, 2017).
IMAU_IMAUICE
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 initMIP
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 SMB and surface
ice temperature from RACMO2.3 (van Wessem et al., 2014) and mapped with
OBLIMAP (Reerink et al., 2010, 2016). 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) and mapped with OBLIMAP
(Reerink et al., 2010, 2016). 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.
JPL_ISSM
Model setup, as follows, is adapted from Schlegel et
al. (2018). The model domain covers the present-day Antarctic ice sheet, and
its geometry is interpolated from the Bedmap2 dataset (Fretwell et al.,
2013), with additional refinement in
the Amundsen Sea sector, Recovery Ice Stream, and Totten Glacier, from Morlighem et al. (2011)
and Rignot et al. (2014). The forward simulations rely on a 2-D Shelfy-Stream
Approximation (MacAyeal, 1989) for stress balance, with a mesh resolution
varying between 1 km at the domain boundary and within the shear margins and
50 km in the interior and a resolution of 8 km or finer within the boundary
of all initial ice shelves. To estimate land ice viscosity, we compute the
ice temperature based on a thermal steady state with 15 vertical layers
(Seroussi et al., 2013), using three-dimensional higher-order (Blatter, 1995;
Pattyn, 2003) stress balance equations, observations of surface velocities
(Rignot et al., 2011b), and basal friction inferred from surface elevations
(Morlighem et al., 2010). Thermal boundary conditions are geothermal heat
flux from Maule et al. (2005) and surface temperatures from Lenaerts et
al. (2012). Steady-state ice temperatures are vertically averaged, used as
inputs in the ice flow law, and held constant over time. To infer the unknown
basal friction coefficient over grounded ice and the ice viscosity of the
floating ice, we use data assimilation (MacAyeal, 1993; Morlighem et al.,
2010) to reproduce observed surface velocities from Rignot et al. (2011b).
Then, we run the model forward for 2 years, allowing the grounding line
position and ice geometry to relax (Seroussi et al., 2011; Gillet-Chaulet et
al., 2012). The grounding line evolves assuming hydrostatic equilibrium and
following a sub-element grid scheme (SEP2 in Seroussi et al., 2014). The ice
front remains fixed in time during all simulations performed, and we impose a
minimum ice thickness of 1 m everywhere in the domain. The SMB and the ice
shelf basal melt rates used in the control experiment are respectively from
the 1979–2010 mean of RACMO2.1 (Lenaerts et al., 2012) and from the
2004–2013 mean from Schodlok et
al. (2016).
LSCE_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 (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 in 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 initMIP-Antarctica 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 insures an ice thickness as close as possible to
observations with a minimal model drift (Le clec'h et al., 2018). 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 SMB, is taken from the
1979–2014 climatological annual mean computed by the MAR version 3.6.4
regional atmospheric model (Agosta et al., 2019). 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 fixed grounding line position. The initial ice sheet
geometry, bedrock and ice thickness, is taken from the Bedmap2 dataset
(Fretwell et al., 2013), and the geothermal heat flux is from Shapiro and
Ritzwoller (2004).
NCAR_CISM
The Community Ice Sheet Model (CISM; 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 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 SMB and surface air temperature
from RACMO2.3p2 (van Wessem et al., 2018; Lenaerts et al., 2012). During the
spin-up, basal friction parameters (for grounded ice) and sub-shelf melt
rates (for floating ice) are adjusted to nudge the ice surface elevation
toward 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 behavior. The grounding line location is determined
using hydrostatic equilibrium and sub-element parameterization (Gladstone et
al., 2010; Leguy et al., 2014). Basal melt is applied in grid cells that
satisfy a floatation condition based on cell thickness and bed elevation; this
includes some but not all cells intersected by the grounding line. 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.
PIK_PISM
With the Parallel Ice Sheet Model (PISM; Winkelmann et al., 2011;
http://www.pism-docs.org; version 9ae1674 from 2 August 2017), we
performed a paleoclimatic spin-up and an equilibrium simulation on a regular
rectangular grid with 16 and 8 km horizontal resolution, respectively. The
vertical resolution increases from 130 m at the top of the domain to 20 m
at the (ice) base, with a domain height of 6000 m. PISM uses a hybrid of the
Shallow-Ice Approximation (SIA) and the two-dimensional Shelfy-Stream
Approximation of the stress balance (SSA; MacAyeal, 1989; Bueler and Brown,
2009) over the entire Antarctic ice sheet. The grounding line position is
determined using hydrostatic equilibrium, with sub-grid interpolation of the
friction at the grounding line (Feldmann et al., 2014). The calving front
position can freely evolve using the eigencalving parameterization (Levermann
et al., 2012). PISM is a thermomechanically coupled (polythermal) model based
on the Glen–Paterson–Budd–Lliboutry–Duval flow law (Aschwanden et al.,
2012). The three-dimensional enthalpy field can evolve freely for given
boundary conditions.
The model is initialized from Bedmap2 geometry (Fretwell et al., 2013), with
precipitation from RACMOv2.3 1986–2005 mean (van Wessem et al., 2014)
remapped from 27 km resolution and a parameterized ice surface temperature
using the positive degree-day scheme (PDD; Huybrechts and de Wolde, 1999,
modified by Martin et al., 2011) for PIK_PISM3PAL. In contrast,
PIK_PISM4EQUI uses SMB and temperature directly from RACMOv2.3p2 (van Wessem
et al., 2018) without PDD. The geothermal heat flux is from Shapiro and
Ritzwoller (2004). We use the Potsdam Ice-shelf Cavity model (PICO; Reese et
al., 2018) to calculate basal melt rate patterns underneath the ice shelves.
We use observed ocean temperature and salinity mean values over the period
1975–2012 (Schmidtko et al., 2014) to drive PICO. 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). Till friction angle is a shear strength parameter for the till
material property and is optimized iteratively in the grounded-ice region
such that the mismatch of equilibrium and modern surface elevation is
minimized. This is analogous to the friction-coefficient optimization in
Pollard and DeConto (2012a).
PSU_PSUICE
The Penn State University 3-D ice sheet model (PSUICE3-D) is described 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. 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 modeled 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 using an inverse
method (Pollard and DeConto, 2012a), iteratively matching ice surface
elevations to modern observations. Atmospheric temperatures and precipitation
are obtained from the ALBMAP climatology (Le Brocq et al., 2010), with an
imposed sinusoidal cycle for monthly air temperatures, interpolated to the
ice sheet grid for SMB calculations. Oceanic melting at the base of ice
shelves depends on the squared difference between nearby 400 m depth
climatological ocean temperature (Levitus, 2012) and the melt point at the
bottom of the ice. “Standard” calving of ice shelves is included. InitMIP
experiments are run without recently proposed mechanisms of hydrofracturing
by surface meltwater and structural failure of large ice cliffs (Pollard et
al., 2015; DeConto and Pollard, 2016). The model grid size is 16 km, and two
types of initialization are used: (i) spun up to modern equilibrium (for
60 kyr) with constant invariant model climate forcing and (ii) run from
40 ka to modern time using paleoclimate forcing, and the model state at the end of that run is used.
UCIJPL_ISSM
We rely on inverse modeling to initialize the model to present-day
conditions, following Morlighem et al. (2013). The mesh horizontal resolution
varies from 3 km along the coast (in the vicinity of grounding lines and in
shear margins) to 30 km inland and is extruded vertically in 10 layers. We
use a higher-order stress balance (Pattyn, 2003) and an enthalpy-based
thermal model (Aschwanden et al., 2012; Seroussi et al., 2013). We first
perform an inversion of ice shelf viscosity and then an inversion of basal
drag under grounded ice, assuming a
thermomechanical steady state. Our geometry is primarily based on Bedmap-2
(Fretwell et al., 2013), with local improvements based on mass conservation
in the Amundsen Sea Embayment, along the coast of Wilkes Land, and on
Recovery Ice Stream (Morlighem et al., 2011; Millan et al., 2017). The
thermal model is constrained by surface temperatures from Comiso (2000) and
the geothermal heat flux from Shapiro and Ritzwoller (2004), both included in
the SeaRISE dataset (Nowicki et al., 2013b). The SMB used in the control
experiment is from RACMO2.3 (van Wessem et al., 2014).
ULB_f.ETISh
The f.ETISh (fast Elementary Thermomechanical Ice Sheet) model (Pattyn, 2017)
version 1.3 is a vertically integrated hybrid finite-difference (SSA for
basal sliding; SIA for grounded ice deformation) 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 SMB and temperature (van Wessem et al., 2014),
based on the output of the regional atmospheric climate model RACMO2 for the
period 1979–2011. The PICO model (Reese et al., 2018) was employed to
calculate sub-shelf melt rates, based on present-day observed ocean
temperature and salinity (Schmidtko et al., 2014) on which the initMIP
forcings for the different basins are added. The model is run on a regular
grid of 16 km with time steps of 0.05 year.
VUB_AISMPALEO
The Antarctic ice sheet model from the Vrije Universiteit Brussel is derived
from the coarse-resolution version used mainly in simulations of the glacial
cycles (Huybrechts, 1990, 2002). It considers thermomechanically coupled flow
in both the ice sheet and the ice shelf, using the shallow ice
approximation–shallow ice
shelf approximation coupled across a
transition zone one grid cell wide. 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 a steady state is
reached. The precipitation pattern is based on the Giovinetto and
Zwally (2000) compilation used in Huybrechts et al. (2000), updated with
accumulation rates obtained from shallow ice cores during the EPICA pre-site
surveys (Huybrechts et al., 2007). Surface melting is calculated over the
entire model domain with the PDD scheme, including meltwater retention by
refreezing and capillary forces in the snowpack (Janssens and Huybrechts,
2000). 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 of bedrock 4 km thick underneath the ice
sheet. Isostatic compensation is based on an elastic lithosphere floating on
a viscous asthenosphere (ELRA model) but is not allowed to evolve further in
line with the initMIP-Antarctica experiments.
Modeled initial conditions
Simulated Antarctic initial ice-covered extent, ice shelf extent,
ice mass, ice mass above floatation, total SMB, and total basal melt.
Model nameIce extentIce shelf extentIce massIce mass aboveSurface massBasal melt(106 km2)(106 km2)(107 Gt)floatation (107 Gt)balance (Gt)(Gt)ARC_PISM113.6961.23482.52892.465626860ARC_PISM213.6961.23482.52892.465626860ARC_PISM313.5791.14662.33022.2785249350ARC_PISM413.5791.14632.33022.2785249349AWI_PISM1Eq14.1121.38852.44822.097926721233AWI_PISM1Pal14.6691.43642.56022.154430611581CPOM_BISICLES_A13.6541.53382.41182.073421442141CPOM_BISICLES_B13.6541.53382.41182.073421442141DMI_PISM014.2702.04082.10681.78733427152DMI_PISM114.2702.04112.10681.78733427451DOE_MALI13.5951.46232.37942.04672415562IGE_ELMER13.5901.34562.38852.05232515784ILTS_SICOPOLIS113.6091.19422.40502.07812020456ILTS_SICOPOLIS213.5911.26432.40922.08542015508IMAU_IMAUICE3214.1741.23182.35352.057327060JPL1_ISSM13.9051.45222.43822.10742337986LSCE_GRISLI13.9561.19912.45042.108126021565NCAR_CISM13.5001.18502.36402.042224691125PIK_PISM3PAL14.5561.22732.35742.00693191583PIK_PISM4EQUI14.2300.91682.39932.04662795304PSU_EQNOMEC15.0432.27002.49621.877226391278PSU_GLNOMEC15.0032.50632.49701.888826791417UCIJPL_ISSM13.7841.32172.42892.11422519683ULB_FETISH113.8891.63282.39722.061226602468VUB_AISMPALEO14.2411.21672.50072.16032435278Modeled sea level contribution for all experiments
Antarctic contribution to sea level (mm sea level equivalent,
positive for sea level increase) at the end of the 100-year simulation for
the three experiments and all submissions.
Model namectrlasmbabmbARC_PISM1-112.9-287.166.5ARC_PISM2-115.0-300.6154.7ARC_PISM3-5.5-151.388.6ARC_PISM4-2.4-154.9215.4AWI_PISM1Eq-22.1-172.322.7AWI_PISM1Pal-48.4-213.0-4.5CPOM_BISICLES_A26.9-110.4105.3CPOM_BISICLES_B83.3-54.3169.1DMI_PISM00.8-140.194.4DMI_PISM1-4.1-140.0108.8DOE_MALI167.3-26.6249.9IGE_ELMER-111.5-255.6-98.3ILTS_SICOPOLIS1-107.5-251.8-84.9ILTS_SICOPOLIS2-115.3-262.7-80.0IMAU_IMAUICE320.1-146.7108.9JPL1_ISSM-80.7-236.87.4LSCE_GRISLI-167.6-324.6-149.6NCAR_CISM4.1-137.439.3PIK_PISM3PAL-12.2-167.8365.7PIK_PISM4EQUI-19.8-181.4407.0PSU_EQNOMEC12.7-112.047.5PSU_GLNOMEC16.2-108.950.7UCIJPL_ISSM-243.6-400.0-178.5ULB_FETISH1-47.4-209.7-22.0VUB_AISMPALEO-9.4-169.579.7Competing interests
The authors declare that they have no conflict of
interest.
Special issue statement
This article is part of the special issue “The Ice Sheet Model
Intercomparison Project for CMIP6 (ISMIP6)”. It is not associated with a
conference.
Acknowledgements
We acknowledge the Climate and Cryosphere (CliC) project and the World
Climate Research Programme (WCRP) for their guidance, support, and
sponsorship. We thank the CMIP6 panel members for their continuous leadership
of the CMIP6 effort and the Working Group on Coupled Modeling (WGCM)
Infrastructure Panel (WIP) for overseeing the CMIP6 and ISMIP6 infrastructure
and data request. Research was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration (80NM0018D0004).
Hélène Seroussi, Nicole-Jeanne Schlegel, Eric Larour, Sophie Nowicki, and Erika Simon are
supported by grants from the NASA Cryospheric Science, Sea Level Change Team, and Modeling
Analysis and Prediction Program. Material 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 for CISM
simulations, including the Cheyenne supercomputer (10.5065/D6RX99HX),
were provided by the Computational and Information Systems Laboratory (CISL)
at NCAR. Ralf Greve was supported by the Japan Society for the Promotion of
Science (JSPS) KAKENHI grant numbers JP16H02224, JP17H06104, and JP17H06323.
Christian Rodehacke (DMI) has received funding from the European Research
Council under the European Community's Seventh Framework Programme (FP7) for
research, and Theme 6 Environment as part of the NACLIM (North Atlantic
Climate) project (grant agreement 308299), as well as the Nordic Centers of
Excellence eSTICC (eScience Tool for Investigating Climate Change at High
Northern Latitudes) funded by Nordforsk (grant 57001). Support for
Matthew J. Hoffman, Stephen F. Price, and Tong Zhang was provided through the
Scientific Discovery through Advanced Computing (SciDAC) program funded by
the US Department of Energy Office of Science, Biological and Environmental
Research and Advanced Scientific Computing Research programs. This research
used resources of 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. The Ministry of
Education, Culture and Science (OCW), in the Netherlands, provided financial
support for this study via the program of the Netherlands Earth System
Science Centre (NESSC). 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
Research for Sustainability initiative (FONA). Aurélien Quiquet
acknowledges funding from the European Research Council grant ACCLIMATE
no. 339108. Fabien Gillet-Chaulet and Julien Brondex (IGE) have received
funding from the French National Research Agency (ANR) under the TROIS-AS
project (ANR-15-CE01-0005-01). IGE-ELMER simulations were performed using HPC
resources from GENCI-CINES (grant 2017-016066) and using the Froggy platform
of the CIMENT infrastructure, which is supported by the Rhone-Alpes region
(grant CPER07_13 CIRA), the OSUG@2020 laBex (reference ANR10 LABX56), and
the Equip@Meso project (reference ANR-10-EQPX-29-01). Torsten Albrecht was
supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of
the priority program “Antarctic Research with comparative investigations in
Arctic ice areas” by grant LE1448/6-1 and LE1448/7-1. Matthias Mengel was
supported by the DFG in the same framework by grant WI 4556/4-1. Development
of PISM is supported by NASA grant NNX17AG65G and NSF grants PLR-1603799 and
PLR-1644277. The authors gratefully acknowledge the European Regional
Development Fund (ERDF), the German Federal Ministry of Education and
Research, and the Land Brandenburg for supporting this project by providing
resources on the high-performance computer system at the Potsdam Institute
for Climate Impact Research. Computer resources for this project have also
been provided by the Gauss Centre for Supercomputing/Leibniz Supercomputing
Centre under Project-ID pr94ga. Mathieu Morlighem was supported by a grant
from the National Science Foundation, Office of Polar Programs (OPP; grant
no. 1443229). Sainan Sun was supported by the FRS-FNRS MEDRISM project and
the BELSPO MIMO project (Stereo III). Philippe Huybrechts and
Jonas Van Breedam acknowledge support from the iceMOD project funded by the
Research Foundation – Flanders (FWO-Vlaanderen). Daniel Lowry acknowledges
support from the Antarctica New Zealand Doctoral Scholarship program and the
New Zealand Ministry of Business, Innovation and Employment (grant
15-VUW-131).
Review statement
This paper was edited by Kenichi Matsuoka and reviewed by
Jesse Johnson and one anonymous referee.
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