Climate model projections are often aggregated into multi-model averages of all models participating in an intercomparison project, such as the Coupled Model Intercomparison Project (CMIP). The “multi-model” approach provides a sensitivity test to the models' structural choices and implicitly assumes that multiple models provide additional and more reliable information than a single model, with higher confidence being placed on results that are common to an ensemble. A first initiative of the ice sheet modeling community, SeaRISE, provided such multi-model average projections of polar ice sheets' contribution to sea-level rise. The SeaRISE Antarctic numerical experiments aggregated results from all models devoid of a priori selection, based on the capacity of such models to represent key ice-dynamical processes. Here, using the experimental setup proposed in SeaRISE, we demonstrate that correctly representing grounding line dynamics is essential to infer future Antarctic mass change. We further illustrate the significant impact on the ensemble mean and deviation of adding one model with a known bias in its ability of modeling grounding line dynamics. We show that this biased model can hardly be identified from the ensemble only based on its estimation of volume change, as ad hoc and untrustworthy parametrizations can force any modeled grounding line to retreat. However, tools are available to test parts of the response of marine ice sheet models to perturbations of climatic and/or oceanic origin (MISMIP, MISMIP3d). Based on recent projections of Pine Island Glacier mass loss, we further show that excluding ice sheet models that do not pass the MISMIP benchmarks decreases the mean contribution and standard deviation of the multi-model ensemble projection by an order of magnitude for that particular drainage basin.

The contribution of the Antarctic ice sheet to sea-level rise (SLR) has
steadily increased during the last two decades. In the early 1990s, the
amount of snow falling over the ice sheet was more or less balanced by the
total coastal discharge. Today, the ice sheet loses mass at a rate of

Current projections for mean sea-level rise in 2100 range from 0.28 to 0.98 m
depending on the Representative Concentration Pathways (RCP) scenarios, and
the contribution of ice sheets represent about a third of the total projected
SLR

Parallel to the SeaRISE initiative, specific model intercomparison exercises
(MISMIP and MISMIP3d

MISMIP: Marine Ice Sheet Model Intercomparison Project.

) have been designed to improve our understanding of grounding line dynamics (i.e., dynamics of the limit between the grounded ice sheet and the downstream floating ice shelf). These initiatives have led to the formulation of requirements regarding physics and numerical approaches to adequately simulate the flow of coastal outlet glaciers in contact with the oceanIn this paper, we assess the origin of uncertainty in recent ice sheet model
projections of Antarctic sea-level contribution for PIG, based on SeaRISE and
results due to

The basic problem in ice sheet modeling is to solve the gravity-driven flow
of an incompressible and nonlinear viscous ice mass, further extended with
a constitutive equation relating stresses to strain rates, i.e.,

Apart from the boundary conditions, which are discussed below, this model
represents the most complete mathematical description of ice sheet dynamics
and is commonly called a full-Stokes model. Owing to the considerable
computational effort, approximations to these equations are often used, such
as higher-order, shallow-shelf and shallow-ice approximations. These
approximations involve dropping terms from the momentum balance equations as
well as simplifying the strain rate definitions and boundary conditions.
Higher-order Blatter–Pattyn-type models consider the hydrostatic
approximation in the vertical direction by neglecting vertical resistive
stresses

However, the earliest and most common approximation in large-scale ice
dynamics simulations is the shallow-ice approximation (SIA). This
approximation incorporates only vertical shear stress gradients opposing the
gravitation drive, which is valid for an ice mass with a small aspect ratio
(i.e., thickness scale much smaller than length scale) in combination with a
significant traction at the bedrock. Its main advantage is that all stress
and velocity components are locally determined. The approximation is not
valid for key areas such as ice divides and grounding lines

We will not list all boundary conditions of thermomechanically coupled ice sheet models, but focus on those that are of importance for grounding line migration. These pertain to the initialization of the ice sheet and conditions at the contact of the ice sheet with the ocean boundary.

Initialization of ice sheet models to reproduce the current ice sheet state
is commonly done through long-term paleo simulations (paleo spin-up). This
has the advantage of establishing a reasonable temperature regime within the
ice column

It has long been hypothesized that grounding line migration may provoke
unstable behavior when the ice sheet rests on a retrograde bed slope below
sea level

A verification of ice sheet models became feasible due to a boundary layer
theory developed by

In a more recent paper,

Essential characteristics of Antarctic SeaRISE models together with
SISM. More details on the numerics can be fund in

To demonstrate the importance of the proper inclusion of a marine boundary in
large-scale ice sheet models, we developed a simple (but in terms of marine
conditions – wrong) ice sheet model. The simplified ice sheet model (SISM)
is a numerical ice sheet model based on the physics inherent to well-known
ice sheet models

Contrary to the SeaRISE experiments, climate forcing is not applied and the
present climate conditions are retained during the whole run (see Appendix A
for details). Note that models with a similar degree of physical complexity
in the description of ice flow have been included in the SeaRISE multi-model
ensemble

Grounding line dynamics are not explicitly included in SISM. However, melting
at the grounding line is introduced by subtracting the amount of basal melt
from the surface mass balance at the last grounded grid point. Ice thickness
becomes zero when the ice thickness in that grid point – determined from
ice advected from upstream and the local mass balance – becomes zero (or
negative). Therefore, grounding line retreat is purely due to melting and not
due to any physical process operating at the grounding line. Hence, a marine ice
sheet instability (retreat of the grounding line on a retrograde slope in
absence of melt perturbation and significant buttressing) is not simulated
with this simplified model

Using SISM, we perform a number of the Antarctic SeaRISE experiments and investigate the impact of including a model with a known bias on the ensemble projection.

The SeaRISE initiative led to the first attempt to evaluate multi-ice sheet
models ensembles. It is important to note that at the time the experiments
were designed, circa 2008, SeaRISE's primary goal was to investigate the
sensitivity of ice sheet models to external forcing. Its baseline hypothesis
presumed that there was no “best” ice sheet model around and that ensemble
modeling would potentially lead to a better understanding of ice sheet
models

The SeaRISE experiments all start from an initial present-day ice sheet,
which is built up using either a paleo spin-up or assimilation methods.
Perturbations in boundary conditions are then imposed for 500 years and
compared to a control run to remove the long-term drift. Climate forcing
experiments refer to the ensemble mean of AR4 A1B changes in temperature and
precipitation being imposed for 94 years and held constant at the values of year 94
for the remainder of the 500-year runs. An amplification factor of 1,
1.5 and 2, respectively, is applied in order to simulate warmer climate
scenarios (experiments C1, C2 and C3, respectively). Subsequently, basal
sliding perturbations are implemented through a uniform increase of basal
sliding (amplified by a factor 2, 2.5 and 3, respectively, for experiments
S1, S2 and S3, respectively) and the sensitivity of Antarctic ice shelves to
sub-ice shelf melt was performed by applying a uniform melt rate at the base
of floating ice (2, 20 and 200 m yr

While SeaRISE focussed on modeling the whole Antarctic ice sheet, a number of
studies have simulated the effect of ice shelf melting at the basin scale.
Pine Island Glacier

All models presented above will be compared below for the PIG basin. However, we start the analysis with an evaluation of the importance of marine processes on ice sheet response on a pan-Antarctic scale.

Change in grounded area vs. contribution to SLR after 200 years for
all models participating in the SeaRISE Antarctic experiments. For reference,
a loss of 4.0469

Evolution of the Antarctic grounded area as computed by the five
models which participated in the SeaRISE experiment M3

Figure

Large differences in model response are essentially due to two factors:
models that correctly implement melting under the ice shelves will fail to
produce a significant retreat if the grounding line area is not properly
sampled (spatial resolution below 500 m), when using a physical approximation
based on SSA, or lacking a parametrization of grounding line dynamics based
on the boundary layer theory due to

Since the number of models participating in the Antarctic SeaRISE experiments
is rather limited, we may expect that adding a model (e.g., SISM) to the
sample will significantly impact on the ensemble mean projections, thereby
questioning its relevance. Its effect is illustrated in Fig.

Global sea-level increase (cm) projected by SISM after a 1000-year spin-up, together with
mean and standard deviation projected by the SeaRISE models extended with SISM
(described in Sect.

Evolution of the contribution to SLR for all the models participating in SeaRISE experiments S1, S2, S3, M1 M2 and M3 (gray lines). SLR contribution computed by SISM for similar perturbations are presented in black, after a 1000- and 100-year spin-up (continuous and dashed line, respectively).

Compared to other models, the contribution to SLR with SISM is close to the SeaRISE ensemble mean for sliding experiments and is amongst the largest for melting perturbations, but it is not a striking outlier. As a reminder, SISM is based on simple model physics, isothermal and a surface mass balance set to present-day conditions and not evolving following any RCP scenario. Taking SISM into account in the ensemble unweighted mean leads to two distinct impacts. When considering melt perturbation, adding SISM to the ensemble usually increases both the mean and standard deviation of the ensemble projections. The increase in mean is substantial, up to 20 % for experiments M2 after 100 years. We can anticipate that adding a biased model which would present a limited capacity of grounding line retreat would lead to a decrease of the ensemble mean contribution to SLR together with an increase in the related standard deviation, as the sample size increases. The particular case of sliding experiments and experiment M3 is instructive: the projected contribution of SISM is fortuitously close to the SeaRISE ensemble mean. Including the SISM in the ensemble mean projections slightly affects the mean but also decreases the standard deviation. Ironically, in the particular situation where a biased model projection is coincidentally close to the ensemble mean, introducing such a model may be wrongly interpreted as improving the confidence in the ensemble projection.

The SeaRISE experiments were rerun with SISM, starting from a different
spinup (100 years instead of 1000 years; Fig.

In view of the small SeaRISE sample, we extended the sample with recent
regional studies (basin-scale), focused on Pine Island Glacier

Figure

A striking feature of Fig.

Most models in the SeaRISE sample have a coarse spatial grid size (

Evolution of the cumulated contribution of Pine Island Glacier to
SLR until 2050 as computed by models participating in SeaRISE experiment M3
(blue lines), SISM for the SeaRISE M3 forcing (purple line), together with
estimations from

Models that capture grounding line dynamics are within the dark gray envelope
in Fig.

It is peculiar to note that the models due to

The SeaRISE initiative has been the first multi-ice-sheet model ensemble
projection to evaluate the future contribution of Antarctica to SLR. Results
of all participating model results were taken into account, irrespective of
the inherent difference in complexity between the models. A similar approach
is used in AOGCMs (Atmosphere-Ocean General Circulation Models) community

Benchmark experiments to evaluate the ability of models to cope with
grounding line dynamics have been recently developed and others will emerge (MISMIP

SISM (simplified ice sheet model) is an isothermal two-dimensional ice sheet
model based on the shallow-ice approximation (SIA), using Glen's flow law as
a constitutive equation. The vertical mean horizontal ice velocities in the
grounded ice sheet are calculated from the local ice geometry

The model is numerically solved on a finite-difference grid with a spatial
resolution of 15 km. BEDMAP2 data

Initialization of the model is based on a relaxation of the surface
elevation, starting from the BEDMAP2 present-day ice sheet geometry, for a
period of 1000 and 100 years, respectively. Surface mass balance is obtained
from

Similar to the SeaRISE experiments, the model is forced according to three
basal sliding and three basal melt scenarios and for a period of 200 years,
during which the basal sliding factor is multiplied by 2, 2.5 and 3,
respectively, and basal melting at the grounding line is set to 2, 20, and
200 m yr

This study was funded by the French National 960 Research Agency (ANR) under the SUMER (Blanc SIMI 6) 2012 project referenced as ANR-12-BS06-0018. This research is also a contribution to the Belgian Federal Research Project “IceCon” (Constraining Antarctic ice mass change) BELSPO, contract number SD/CA/06A. Edited by: G. H. Gudmundsson