The Antarctic ice sheet is one of the largest potential contributors to future sea level rise. Predicting its future behaviour using physically-based ice sheet models has been a bottleneck for the past decades, but major advances are ongoing

Pattyn, F.

Open Marine Archive

COMMENT
The paradigm shift in Antarctic ice
sheet modelling
Frank Pattyn 1
The Antarctic ice sheet is one of the largest potential contributors to future sea level rise.
Predicting its future behaviour using physically-based ice sheet models has been a bottleneck
for the past decades, but major advances are ongoing.
Unlike atmospheric models, ice sheet models emerged very recently. The ﬁrst numerical Ant-
arctic continental-scale ice sheet models, for instance, saw the light at the beginning of the 1990s.
Initially, such models were employed at rather coarse resolution (∼50 km) to investigate ice sheet
changes during glacial-interglacial cycles. At that time, ice sheets were believed to be a slow
component of the climate system with a highly diffusive response to palaeo-climatic changes.
This diffusive nature stems from the fact that ice sheet models were based on the so-called
'Shallow-Ice Approximation (SIA)', which is the dominant type of ice deformation for a large ice
sheet resting on a near-frozen bed and based on the premise that ice deformation is due to
shearing close to the bed. This may be valid for the bulk of ice sheet ﬂow, but breaks down near
its edges. It results in a gradual, slow response to the imposed climatology with a time lag that
increases with the size of the ice sheet due to its internal thermomechanics (cold ice deforms
slower than temperate ice).
Paradoxically, theoretical developments around the possibility of rapid continental change was
advocated several decades before1, hypothesizing a possible collapse of the West-Antarctic ice
sheet (WAIS) as a consequence of anthropogenic global warming2. The WAIS is a marine ice
sheet for which the bed lies well below sea level. As the ice thins towards the edge of the ice sheet,
ice thickness becomes equal to the buoyant thickness of ice and starts to ﬂoat, forming ice
shelves. The contact where ice starts aﬂoat is called the grounding line. The bed is also depressed
deeper in the centre of the ice sheet, making the bed slope inland from the grounding line to the
centre, hence creating a reverse or retrograde bed slope. The proposed instability, known as
Marine Ice Sheet Instability (MISI; Fig. 1a) is based on the observation that since ice ﬂux
increases with ice thickness, the location of a grounding line on a bed sloping inwards is
unstable.
Floating ice matters
MISI theory was challenged by most ice sheet models, as they considered that ice shelves were
too weak (and therefore mechanically uncoupled from the ice sheet) to affect the force balance of
the grounded ice sheet. This led to the hypothesis of neutral equilibria that were neither stable
nor unstable3. Not only were those SIA models unable to reproduce MISI, the theory was also
disputed by observations of an apparently balanced ice sheet, but that was before glaciers started
to retreat in the Amundsen Sea Embayment (ASE) of the WAIS4.
Mathematical proof of the MISI theory put forward by Weertman was ﬁnally given three
decades later5, dispelling the previous idea that ice sheets and ice shelves are mechanically
DOI: 10.1038/s41467-018-05003-z OPEN
1 Laboratoire de Glaciologie, Université libre de Bruxelles (ULB), Brussels B-1050, Belgium. Correspondence and requests for materials should be addressed to
F.P. (email: fpattyn@ulb.ac.be)
NATURE COMMUNICATIONS |  (2018) 9:2728 | DOI: 10.1038/s41467-018-05003-z | www.nature.com/naturecommunications 1
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uncoupled. This had a profound impact on ice sheet model
development, pushing models to conform to known (analytical)
solutions, which led to international model intercomparisons,
such as the Marine Ice Sheet Model Intercomparison Project
(MISMIP)6. MISMIP allowed for a collective improvement of
marine ice sheet models by adapting both their physical basis as
well as their numerical approaches. Besides being the limit of
ﬂotation, a grounding line is also the change from a shear-
dominated ice ﬂow to an ice ﬂow dominated by longitudinal
pushes and pulls (due to membrane stresses). The transition is
never sharp, but gradual, and largely depends on the processes
that govern basal motion under ice sheets within fast-ﬂowing ice
streams (basal sliding and sediment deformation). These mem-
brane stresses need to be resolved across the grounding line with
a sufﬁciently high spatial resolution, which pushed the develop-
ment of spatial grid reﬁnement in numerical models through sub-
grid interpolation schemes, the use of unconstructed grids or
adaptive mesh approaches7. It also requires the use of approx-
imations other than the SIA to the ﬂow of ice, ranging from the
Shallow-Shelf Approximation to full-Stokes models, which are
harder to solve.
Despite these theoretical and numerical advances, the devel-
oped MISI theory5 remains only valid for unconﬁned ice shelves,
i.e. ice shelves that do not exert a force on the inland ice sheet
other than the (ocean) water pressure. In reality, however, ice
shelves are bounded within embayments, thereby exerting a back
force to the grounding line, hence limiting the ﬂow speed of ice
streams and their discharge of ice through the ice shelf into the
ocean. This is commonly known as the buttressing effect of ice
shelves that act as a cork on a bottle, preventing the ice to ﬂow
out too fast. Loss of ice-shelf buttressing has effectively been
witnessed in Antarctica at the beginning of the 21st century,
where ice shelf collapse in the Antarctic Peninsula led to
increased glacier discharge8.
Ice shelf weakening happens through both atmospheric and
ocean processes, such as hydro-fracturing and sub-shelf melting.
Hydro-fracturing is a process that increases the water pressure
from surface melt on ice shelves in surface crevasses, thereby
widening them so that they become more vulnerable to calving9.
This eventually leads to ice shelf collapse if sufﬁcient melt water
and cracks are available. Hydro-fracturing is also considered a
precursor for a new emerging mechanism in ice sheet modelling,
the concept of Marine Ice Cliff Instability (MICI; Fig. 1b), i.e.,
that once ice shelves have collapsed ice cliffs become unstable and
fall down if higher than ∼90 m above sea level, leading to
accelerated collapse of ice sheets10. MICI is a process that facil-
itates and enhances MISI and relies on the assumption of perfect
plastic rheology to represent failure. However, these crucial pro-
cesses of ice shelf breakup (hydro-fracturing) and calving front/
cliff stability still need to be further explored. While such
mechanisms aid at explaining past changes in the Antarctic ice
sheet, they do show a higher sensitivity to forcing, and hence lead
to a signiﬁcant larger mass loss10.
Sub-shelf melting is responsible for more than half of the ice
mass loss at the margins of the Antarctic ice sheet11. As with
calving due to hydro-fracturing, sub-shelf melting decreases the
buttressing capacity of ice shelves via loss of pinning points and
weakening of the ice shelf through thinning. This has presumably
been the trigger of the observed acceleration of large Antarctic
outlet glaciers in the ASE during the last decade. However, sub-
shelf melt is particularly determined by ocean circulation within
the ice shelf cavity, which, in turn, requires high-resolution ocean
circulation models to link large-scale ocean circulation to sub-
shelf melt. While such ongoing and future developments require
increased computer power, intermediate solutions can be
obtained through physically based parametrisations of sub-shelf
melt based on sub-shelf ocean circulation12.
Towards decadal predictability of ice sheets?
A key aspect of projecting future Antarctic mass loss with
dynamical ice sheet models is related to the initial state of the
model. Since ice sheet models were initially applied for palaeo-
climatic studies on long time scales, initialisation was generally
obtained from a long spin-up time leading to a steady-state ice
sheet (both in terms of geometry and thermodynamics). How-
ever, for predictions on shorter time scales (decades to centuries),
a stable spin-up generally leads to an ice sheet geometry far dif-
ferent from the one currently observed, which is one of the rea-
sons why such ice sheet models may respond differently than
observations suggest13. Moreover, using a steady-state for initi-
alising the ice sheet prevents models from properly accounting for
the dynamical mass losses observed over the last decade, as the
present-day ice sheet is not in steady state. Motivated by the
increasing ice sheet imbalance of the ASE glaciers over the last 20
years, and supported by the recent boom in satellite data avail-
ability, data-assimilation methods are progressively used to
evaluate unknown ﬁelds using time-evolving states accounting for
the transient nature of observations and the model dynamics14.
Antarctic ice sheet modelling has taken a big step forward
based on an improved understanding of key processes and the
development of assimilation methods leading to the ability to
reproduce observed ice sheet changes and by making reﬁned
future projections. From a theoretical viewpoint, we now have the
ability to verify marine ice sheet models, albeit that certain effects,
such as buttressing, are not yet quantiﬁed/veriﬁed accurately, but
Ice sheet
Ocean
Antarctic bedRetrogra
de slope
MISI: retrograde slope
Grounding line
MICI: pro/retrograde slopes
Pro/retrograde slope
Flux at the grounding line
Heat
Retreating grounding line
Cliff failure 
Hydro-fracturing
Grounding line
a
b
Fig. 1 Instability scenarios. a Marine Ice Sheet Instability versus b Marine
Ice Cliff Instability (MICI). Ice discharge generally increases with increasing
ice thickness at the grounding line. For a bed sloping down towards the
interior this may lead to unstable groundingline retreat (MISI), as increased
ﬂux (due to reduced buttressing) leads to thinning and eventually ﬂotation,
which moves the grounding line into deeper water where the ice is thicker.
Thicker ice results in increased ice ﬂux, which further thins the ice, which
results in further retreat into deeper water (and thicker ice), and so on.
MICI is the result of collapse of exposed ice cliffs (after the ice shelf
collapses due to hydro-fracturing) under their own weight. MISI applies for
a retrograde slope bed, while MICI can also apply for prograde slopes
COMMENT NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05003-z
2 NATURE COMMUNICATIONS |  (2018) 9:2728 | DOI: 10.1038/s41467-018-05003-z | www.nature.com/naturecommunications
new analytical tools are becoming available15. The increase in
computational efﬁciency enabling high spatial resolution model-
ling, high-resolution datasets of bedrock topography and surface
velocity, longer time series on ice sheet changes, and the
improved initialisation of ice sheet models are now allowing ice
sheet modelling to move away from the slow-diffusive response
over millennium time scales towards robust predictions on dec-
adal time scales, hindcasting and potentially reanalysis.
Received: 26 May 2018 Accepted: 8 June 2018
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Acknowledgements
F.P. thanks Lionel Favier for the preparation of the ﬁgure. This comment is a con-
tribution to the PARAMOUR project ‘Decadal predictability and variability of polar
climate: the role of atmosphere-ocean-cryosphere multiscale interactions’ supported by
the Fonds de la Recherche Scientiﬁque–FNRS under Grant number O0100718F (EOS ID
30454083).
Author contributions
F.P. solely contributed to the writing of this piece.
Additional information
Competing interests: The author declares no competing interests.
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© The Author(s) 2018
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The paradigm shift in Antarctic ice sheet modelling

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The paradigm shift in Antarctic ice sheet modelling

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