TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-2623-2016Dynamic influence of pinning points on marine ice-sheet
stability:
a numerical study in Dronning Maud Land, East AntarcticaFavierLionellionel.favier@ulb.ac.behttps://orcid.org/0000-0002-5392-3031PattynFrankhttps://orcid.org/0000-0003-4805-5636BergerSophiehttps://orcid.org/0000-0003-4095-9323DrewsReinhardhttps://orcid.org/0000-0002-2328-294XLaboratoire de Glaciologie, DGES, Université libre de Bruxelles, Brussels, BelgiumLionel Favier (lionel.favier@ulb.ac.be)9November2016106262326356June201616June201626September201622October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/10/2623/2016/tc-10-2623-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/2623/2016/tc-10-2623-2016.pdf
The East Antarctic ice sheet is likely more stable than its West Antarctic
counterpart because its bed is largely lying above sea level. However, the
ice sheet in Dronning Maud Land, East Antarctica, contains marine sectors
that are in contact with the ocean through overdeepened marine basins
interspersed by grounded ice promontories and ice rises, pinning and
stabilising the ice shelves. In this paper, we use the ice-sheet model
BISICLES to investigate the effect of sub-ice-shelf melting, using a series
of scenarios compliant with current values, on the ice-dynamic stability of
the outlet glaciers between the Lazarev and Roi Baudouin ice shelves over the
next millennium. Overall, the sub-ice-shelf melting substantially impacts the
sea-level contribution. Locally, we predict a short-term rapid grounding-line
retreat of the overdeepened outlet glacier Hansenbreen, which further induces
the transition of the bordering ice promontories into ice rises. Furthermore,
our analysis demonstrated that the onset of the marine ice-sheet retreat and
subsequent promontory transition into ice rise is controlled by small pinning
points, mostly uncharted in pan-Antarctic datasets. Pinning points have a
twofold impact on marine ice sheets. They decrease the ice discharge by
buttressing effect, and they play a crucial role in initialising marine ice sheets
through data assimilation, leading to errors in ice-shelf rheology when
omitted. Our results show that unpinning increases the sea-level rise by
10 %, while omitting the same pinning point in data assimilation decreases it by
10 %, but the more striking effect is in the promontory transition time,
advanced by two centuries for unpinning and delayed by almost half a
millennium when the pinning point is missing in data assimilation. Pinning
points exert a subtle influence on ice dynamics at the kilometre scale, which
calls for a better knowledge of the Antarctic margins.
Introduction
The marine ice-sheet instability (MISI)
hypothesis states that a marine ice sheet with its grounding line – the
boundary between grounded and floating ice – resting on an upsloping bed
towards the sea is potentially unstable. A prior retreat of the grounding
line (e.g. ocean-driven) resting on such an upsloping bed thickens the ice at
the grounding line, which increases the ice flux and induces further retreat,
etc., until a downsloping bed is reached, provided that upstream snowfall
balances local flux at the grounding line. The MISI hypothesis has been
verified using the boundary layer theory developed by and
simulated with numerical studies e.g.. Because most of
the West Antarctic ice sheet (WAIS) rests on an upsloping bed, the potential
retreat of its grounding line is widespread. Therefore, the vulnerability of
the WAIS to current climate change has been extensively studied
e.g.. On the other hand, the East
Antarctic ice sheet (EAIS) is less vulnerable to retreat on short timescales,
and its stability has therefore been less debated. However, a recent
numerical study investigating ice-sheet instability in Antarctica through a
statistical approach pointed out the likeliness for unstable
retreat of grounding lines in Dronning Maud Land (DML), East Antarctica, over
the next two centuries. Moreover, the EAIS hosts 10 times more ice than the
WAIS, and therefore its future stability needs to be more investigated.
In DML, the floating margins of outlet glaciers are buttressed by numerous
topographic highs, which attach to the otherwise floating ice shelves from
beneath and form icy pinning points protruding through ice. Pinning points
are either called ice rises or ice rumples. The former exhibit a local-flow
regime, while the latter are still overridden by the main ice flow. Ice
promontories are ice rises that are connected to the mainland through a
grounded saddle. Most ice rumples and a significant number of ice rises are
smaller than 10 km2. Even though they are common
features in DML, they are often missing in the bathymetry because airborne
radar data are not spaced closely enough. This issue was recently pointed out
in two studies revealing a series of uncharted pinning points from ice-sheet
modelling and observations .
The back stress induced by pinning points – even small ones, i.e. a few kilometres
squared in area – buttresses ice shelves, hampering ice discharge towards the ocean.
Because simulating pinning points requires accurate treatment of
grounding-line dynamics, they have only recently been considered in ice-sheet
models: and investigated the transient
effect of pinning points for idealised geometry, using ice-sheet models of
varying complexity. In both studies, including a pinning point beneath an ice
shelf in steady state significantly slows down the ice flow, inducing a
grounding-line advance until the grounded ice sheet fully covers the pinning
point. The development of an ice rise over a deglaciation and its further
stability among an ice sheet/shelf system in steady state were recently
simulated by , even though the stability of ice rises has
been known for decades . also
demonstrated that ice promontories are transient features transitioning into
ice rises during ice-sheet deglaciation.
Both studies of and used ice-sheet models
of sufficient complexity to accurately quantify the stress pattern in the
pinning point's vicinity: ice is compressed along-flow upstream of the
pinning point, sheared when flowing around it, and stretched along-flow
farther downstream. The levels of extensive stress computed were higher than
what can be accommodated by ice creep, which in reality leads to brittle
fracturing and rifting . Pinning points thus affect ice
rheology by increasing local-scale deformability, which further impacts
surface velocities.
Initialisation of transient simulations relies on data assimilation methods
e.g.. These are applied to observed ice geometry and
surface velocity to infer poorly known parameters such as basal friction and
ice stiffening/softening, the latter mostly accounting for crevasse weakening
and ice anisotropy. These parameters are inferred by minimising a cost
function, which sums the mismatch between observed and modelled surface
velocities and Tikhonov regularisation terms for each inferred parameter, the
latter terms being tuned to provide continuous fields and avoid overfitting.
Even though regularisation remains subjective, a sound trade-off between
reducing velocity mismatch and overfitting can be achieved using the L-curve
method e.g..
In areas where ice/bed geometry and surface velocity are not correctly
resolved, the inferred parameters are likely flawed. Recently,
investigated the band of floating ice that can safely calve
off without increasing ice discharge to the ocean. This result stems from a
static analysis of the force balance between ocean pressure and ice internal
stress state, which can flaw further transient simulations if pinning points
are not accounted for . demonstrated
through a diagnostic study that omitting the contact between a topographic
high and the ice-shelf base during data assimilation yields excessive
ice-shelf stiffening, which compensates for the lack of basal friction in
order to match observed surface velocities. However, it remains unclear how
such erroneous initialisation impacts the transient behaviour of the
ice-sheet/shelf system, which is a question we address here.
Unpinning may occur over various timescales due to progressive ice-shelf
thinning , erosion, rising sea level, tidal
uplift , or through the developments of rifts
. However, unpinning of Antarctic ice shelves has been
poorly documented so far. According to , the best
explanation for the acceleration of the eastern ice shelf of Thwaites Glacier
in the Amundsen Sea sector since 2008 might be reduced buttressing from the
pinning point at its terminus also hypothesised in, even
though other mechanisms such as sub-ice-shelf melting may also be at play. In
Larsen C ice shelf, the unpinning of the Bawden and Gipps ice rises was
simulated diagnostically (i.e. without ice geometry changes) by manually
decreasing the basal drag , which substantially
accelerated the ice flow by up to 200 m a-1 over an extent of about
100 km upstream. However, the transient evolution of ice geometry and
velocity after unpinning has not been investigated so far. We also address
this question in this paper.
Computational domain with the extended flow field from
in the background. The thick black lines show the grounding
line and the calving front. The thin black lines show ice surface elevation
contours every 500 m. The white, light grey, and dark grey lines are bed
elevation contours of -500, -750, and -1000 m, respectively. The yellow
line shows the central trench of the bathymetry excavation
(Sect. ), and the green triangle the supporting bathymetric
data (K. Leonard, personal communication, 2012). The dashed box shows the
domain of interest shown from Figs. to and in Figs. S2 the Supplement. LIS: Lazarev Ice
Shelf; UG: unnamed glacier; TB: Tussebreen; HB: Hansenbreen; HB/WRG:
promontory in between HB and WRG; TB/HB: promontory in between TB and HB;
DIR: Derwael Ice Rise; RBIS: Roi Baudouin Ice Shelf; WRG: West Ragnhild
Glacier; ERG: East Ragnhild Glacier. We also name a group of two pinning
points PPhs located at the front of HB and the pinning point PPw at the
front of WRG.
The studied area is situated between the Lazarev and Roi Baudouin ice shelves
in DML and contains a number of ice streams flowing around the Sør Rondane
mountain range to the west and the Yamato mountain range to the east. The
coastal belt comprises a series of ice rumples, ice rises, and promontories
buttressing the ice shelves. From west to east, the three outlet glaciers of
Tussebreen (TB), Hansenbreen (HB), and West Ragnhild (WRG) are potentially
unstable because their beds lie below sea level and dip towards the interior
of the ice sheet. The grounded area is well constrained in the Antarctic-wide
bed elevation datasets as the latter incorporate
airborne radio-echo sounding data collected during the Austral summer of
2010/2011 . TB and HB are separated by the
TB/HB promontory, HB and WRG by the HB/WRG promontory. The calving front of
HB is in contact with two pinning points, hereafter called PPhs, and the
calving front of WRG with another pinning point, hereafter called PPw
(Fig. ).
The pinning point PPw strongly buttresses the ice shelf of WRG
. However, Antarctic-wide datasets do not correctly resolve
surface velocities and ice/bed geometry
in the vicinity of PPw. This has been improved by
who modified the corresponding datasets in the surroundings
of PPw with field-based data of ice thickness and velocity
. The modified datasets are used here for model
initialisation.
In this study, we use the adaptive-mesh ice-sheet model BISICLES to
investigate the following: (i) the future behaviour of these outlet glaciers (see previous
paragraph) with respect to potential instabilities, (ii) their dynamic
response to PPw unpinning, (iii) the dependency of the transient results on
the model initialisation, using datasets either resolving PPw
('s high-resolution dataset), or not correctly resolving PPw
('s velocities in combination with ice/bed geometry from
), and (iv) the effect of two sliding laws and six
sub-ice-shelf melting parametrisations comparable to observed values. The three
distinct initial conditions stemming from (ii) and (iii) are used to run
transient simulations forced by the different melting parametrisations, over
the next millennium. The 36 resulting simulations give a comprehensive
overview of future ice dynamics in DML and testify to the importance of
including even small pinning points in the observational datasets.
Datasets and methodsInput data
Each experiment consists of an initialisation by data assimilation and a
subsequent set of transient simulations. The initialisation requires surface
velocity, ice thickness, bed elevation, englacial temperatures, and two
initial fields for ice stiffening factor and basal friction coefficient. The
transient simulations require ice thickness, bed elevation, initial englacial
temperatures, two fields for ice stiffening factor and basal friction
coefficient (the latter two computed by the data assimilation), surface mass
balance, and basal mass balance of the ice shelves.
The computational domain covers an area of about 40 000 km2 and is
illustrated in Fig. . Two distinct datasets for flow-field
and ice/bed geometry were employed. The standard dataset comprises
surface velocities from and ice/bed geometry from
(the Bedmap2 dataset). The high-resolution
dataset uses the observations of on the WRG ice shelf,
which account for PPw in both surface velocities and ice/bed geometry (the
latter called mBedmap2). These two datasets only differ for the WRG ice shelf
and are otherwise identical.
Modelling grounding-line advance as a response to ocean-induced perturbation
is very sensitive to sub-ice-shelf bathymetry, which is roughly interpolated
in our studied domain and thus largely uncertain. As a
consequence, the water column beneath ice shelves is very shallow in places,
which can cause spurious ice-shelf regrounding. In order to make the
bathymetry more coherent with both bed elevation at the grounding line and
(unpublished) measurements near the ice-shelf front, we lowered the bed
elevation beneath the ice shelves in a two-step procedure. First, we
excavated a uniform layer 250 m thick 30 km away from the grounding line,
ensuring a smooth connection with the grounded area with a 1-D Gaussian
function. The second part of the excavation is based on unpublished
bathymetric data collected during a 2011 oceanographic survey (K. Leonard,
personal communication, 2012), which shows a trough more than 850 m deep
cutting through the continental shelf between PPw and Derwael Ice Rise (DIR)
(Fig. ). This feature may be the relict of past ice sheet
erosion from the WRG ice stream when the grounding line was closer to the
continental shelf break . We therefore assume the
presence of a narrow trough cutting through the bathymetry beneath the ice
shelf linked to the deepest section at the grounding line (yellow line in
Fig. ). The second excavation was done across-flow using a
1-D Gaussian-shaped function (its half-width is 15 km based on the ice-stream
cross-section extent). Both excavations are included in the standard
as well as the high-resolution datasets.
The surface mass balance was derived by , who combined
in situ measurements (most of them between 1950 and 1990) and satellite
observations of passive microwave (from 1982 to 1997) using a geostatistical
approach, and it is constant in time.
For the ice-shelf basal mass balance, we applied two melt-rate
parametrisations, Mb1 and Mb2, based on and
, respectively. The former is a scheme that allows the
highest melt rates to follow the grounding-line migration, using a combined
function of ice thickness and distance to the grounding line, defined as
Mb1=Hα(pG+(1-p)A),
where H is the ice thickness, and G and A are tuning parameters to
constrain melt rates at the grounding line, and away from the grounding line,
respectively. The value of p decreases exponentially with distance to the
grounding line, taking the value of 1 at the grounding line and 0 away from
it Appendix B2, and α is a tuning parameter.
The Mb2 parametrisation is based on the difference between the freezing
point of water and ocean temperature near the continental shelf break
as developed in. The virtual temperature Tf at
which the ocean water freezes at the depth zb below the ice shelf is
defined as
Tf=273.15+0.0939-0.057SO+7.64×10-4zb,
where SO is the ocean salinity set at 34.5 psu fromconfirmed by K.
Leonard, personal communication, 2012. The melt rates
Mb2 are prescribed as
Mb2=ρwcpOγTFmelt(TO-Tf)Liρi,
where ρw is the density of water, cpO the specific capacity of
the ocean mixed layer, γT the thermal exchange velocity, TO the
ocean temperature set at -1.5 ∘C fromand K.
Leonard, personal communication, 2012, Li the latent heat
capacity of ice, ρi the density of ice (Table for
the value of parameters), and Fmelt a tuning parameter.
Ice temperature data are provided by a 3-D thermo-mechanical
model updated from and are constant in time.
Model parameters.
ParameterSymbolValueUnitIce densityρi917kg m-3Water densityρw1028kg m-3Gravitational accelerationg9.81m s-2Glen's exponentn3Basal friction exponentm(1, 1/3)Grid resolution4000 down to 500mSpecific heat capacity of ocean mixed layercpO3974J kg-1 K-1Thermal exchange velocityγT10-4m s-1Temperature of the oceanTO271.65 (-1.5 ∘C)KSalinity of the oceanSO34.5psuLatent heat capacity of iceLi3.35 × 105J kg-1Tuning parameter for Mb1α3Tuning parameter for Mb1G(25, 50, 100) × 10-9Tuning parameter for Mb1A0Tuning parameter for Mb2Fmelt(0.01, 0.02, 0.03)Ice-sheet modelling
The simulations were performed using the finite volume ice-sheet model
BISICLES (http://BISICLES.lbl.gov). The model solves the shallow shelf
approximation (SSA) and includes vertical shearing in the effective strain
rate the model is fully detailed in, which makes the
ice softer than the traditional SSA approach at the grounding line, and
it induces similar ice sheet behaviour compared to full-Stokes models
when using sub-kilometric resolution at the grounding
line. We assessed the sensitivity to the grid resolution at the grounding
line, between 250 and 4000 m (Fig. S2 in the Supplement). The contribution to
sea-level change and grounding-line migration converge below 500 m. We thus
used 500 m resolution at the grounding line for all the transient
simulations, up to 4000 m farther inland (Table ). The
equations are solved on an adaptive horizontal 2-D grid rendered by the
Chombo framework. Data assimilation is performed by a control method that
solves the adjoint system of equations, as described in Appendix B1 of
. The relationship between stresses and strain rates is
given by Glen's flow law:
S=2ϕηε˙,
where S is the deviatoric stress tensor,
ε˙ is the strain rate tensor, η is the
effective viscosity (depending on englacial temperatures and effective strain
rate), and ϕ is a stiffening factor representing non-thermal viscosity
effects, such as crevasse weakening and ice anisotropy. The basal friction
between the grounded ice sheet and the bed is governed by a Weertman-type
sliding law :
τb=-C|ub|m-1ubifρiρwH>-b0otherwise,
where τb is the basal traction, C is the friction coefficient,
m is the friction exponent, and ub is the basal velocity. Initial
fields of C and ϕ were both inferred (simultaneously and over the
entire computational domain) using the control method applied to ice/bed
geometry and surface velocities, using the same procedure as described in
, as well as the results obtained for the C and ϕ
fields.
Description of the experimentsInitialisation
Three sets of initialisations with both linear (m=1) and non-linear
(m=1/3) sliding were performed for C, ϕ (both inferred with the
control method), and the initial ice/bed geometry.
Be/S: The control method and the transient simulations use the high-resolution dataset (PPw is included in model initialisation and evolution).
Be/U: This is a variant of Be/S in which transient simulations start from bed elevation and ice
thickness without resolving PPw – we use Bedmap2 instead of mBedmap2 – in order to simulate unpinning.
RF/S: The control method and the transient simulations use the standard dataset (PPw is excluded from initialisation and evolution).
Because there is no friction beneath ice shelves, we set the value of the
friction coefficient C in case of further ice-shelf regrounding during
transient simulations at 500 Pa m-1 a. This number causes high basal
sliding (comparable to sliding beneath ice streams), which reflects the idea
of a sediment-filled bathymetry, and it is motivated by the sediment layer
inferred from airborne radar and ice-sheet modelling upstream of the WRG
grounding line .
After model initialisation, the ice-sheet geometry was relaxed for 50 years
prior to the transient simulations in the same manner as the first stage of
relaxation in , which was enough to decrease the ice-flux
divergence due to artefacts of interpolation and other sources of geometry
errors. To relax the ice sheet, we thus applied sub-ice-shelf melt rates
computed from mass conservation assuming steady state, which gives values in
line with current observations . However,
applying such melt rates beneath the HB ice shelf leads to a rapid retreat of
the grounding line induced by MISI during the time span of the relaxation.
We solved this issue by applying a positive basal mass balance (i.e. accretion) of 1 m a-1 during the relaxation, which helps to stabilise
the ice shelf, but it leads to a few kilometres' advance of the grounding line
stabilising the ice sheet during relaxation can also be done by fixing
the ice-shelf thickness, such as inand .
Surface elevation change rates (and their spatial gradients) drop by an order
of magnitude (Fig. ) during relaxation.
Surface
elevation change rates after relaxation of Be/S and Be/U(a) and RF/S(b) initialisations, for linear sliding.
Set-up of all 36 experiments. The name of each experiment
reflects the dataset used for initialisation, its initial ice/bed geometry,
the form of sliding law, and the type and amplitude of the melt rates.
Dataset for Sub-ice-shelf melt rates Experiment namedata assimilationinitial geometrymTypeAmplitudeBe/S/L/Mbi/Ajhigh-resolutionhigh-resolution1Be/S/NL/Mbi/Aj1/3Be/U/L/Mbi/Ajhigh-resolutionstandard1i= (1,2) forj= (l,m,h) forBe/U/NL/Mbi/Aj1/3Mb1 or Mb2(low, medium, high)RF/S/L/Mbi/Ajstandardstandard1RF/S/NL/Mbi/Aj1/3Transient scenarios
Each initialisation is followed by 12 different transient simulations,
applying either linear or non-linear sliding together with 6 different
prescribed sub-ice-shelf melt rates, Mb1 and Mb2, each with 3
different amplitudes – low, medium, and high – set by tuning the parameters
α, G, and A for Mb1, and Fmelt for Mb2
(Table ). The naming convention adopted for transient
simulations and the corresponding parameters are given in
Table .
The sum of initial medium melt rates over the ice shelves yields values that
are comparable to current values and M. Depoorter, personal
communication, 2016; Table S1 in the Supplement. The sum
of low and high melt rates represent approximately half and twice the sum of
medium melt rates, respectively. Initial melt rates Mb1 and Mb2 of
medium amplitude are shown in Fig. for the Be/S
initialisation. For similar amplitudes, Mb1 causes much higher melt
rates than Mb2 close to the grounding line, where melt rates are always
the highest whatever the type of melt rates.
Initial fields
of medium Mb1(a) and Mb2(b) sub-ice-shelf melt rates for the
Be/S initialisation. The sum of melt rates over the computational domain,
written at the top right of panels, is comparable to current values
and M. Depoorter, personal communication, 2016; Table S1.
ResultsData assimilation
Results of the
control method for B/S and B/U(a–c) and RF/S(d–f)
initialisations, for linear sliding. Vertically averaged effective viscosity
(a, d), basal friction coefficient (b, e) (for current ice shelves, the value
of C= 500 Pa m-1 a is prescribed for transient simulations) and
difference between modelled and observed velocities (c, f). The circles
indicate PPw (c, f). The dashed box (f) marks the large mismatches that are
discussed in the text and shown in more detail in Fig. S1 in the Supplement.
The L-curve analysis performed by to optimise
regularisation still holds for our extended domain and non-linear sliding,
even though it was originally applied to a smaller domain and linear sliding.
The root mean square error between modelled and observed velocities after
data assimilation is ≈ 14 m a-1 for Be/S and Be/U
initialisations and ≈ 13 m a-1 for RF/S initialisation, and
it is independent of the applied sliding law. Such mismatches are similar to
what was already computed by control methods applied to the Antarctic ice
sheet e.g.. The largest mismatches are found
at the calving front, on ice rises and promontories, as well as upstream of
the TB/HB promontory (Fig. ). We attribute the latter to
the poor consistency between the high observed surface slope and thickness
combined with low surface velocities (Fig. S1), as high
driving stresses should induce high velocities. The control method cannot
deal with such a nonphysical combination for a steady-state ice sheet: it
decreases the friction during the first iterations, and it further attempts to
catch up with the consequent mismatch through ice stiffening during the
following iterations.
A significant difference between the two datasets appears in the vicinity of
PPw (Fig. ), where the mismatch is lower when using the
high-resolution dataset. There, omitting PPw in the control method
leads to an excessive ice stiffening Fig. 5 inand hereafter in
Fig. .
The central parts of ice shelves are comparatively more viscous, except
within rifting areas, where the viscosity can be few orders of magnitudes
smaller. The friction coefficient is comparatively small beneath the ice
streams of WRG, HB, and TB, and few orders of magnitude higher where ice
velocity is small, such as in between ice streams and beneath ice
promontories and rises. We show these results in Fig.
with linear sliding.
Initial speed up after unpinning
Speed up due to
unpinning after 50 a for medium melt rates Mb1 and linear sliding.
Absolute velocity differences (m a-1) between Be/U/L/Mb1/Am and
Bu/U/L/Mb1/Am.
Unpinning (for Be/U initialisation) induces an instantaneous acceleration
of the WRG ice shelf by up to 300 m a-1 at the former location of PPw.
After 50 a, the acceleration has propagated over almost the entire ice shelf
up to the grounding line, but none of the neighbouring ice shelves of HB and
East Ragnhild Glacier are affected by unpinning (Fig. ).
The central flow line of the WRG ice stream migrates westward, and it relocates at
an almost equal distance from the HB/WRG promontory and DIR within a few
years. The velocities at the ice-shelf front are ≈ 20 % larger than
for Be/S initialisation. Overall, the comparatively faster ice shelf
induces a less advanced grounding line at the end of simulations (about
10 km). The velocity increase near the HB/WRG promontory leads to thinning of
its eastward side, causing its saddle area to be afloat and turning it into an ice
rise more rapidly than for Be/S and RF/S initialisations.
Main steps of grounding-line migration
Grounding-line migration for the Be/S/L/Mb1/Am experiment.
(a) The bed elevation is in the background, grounding lines are shown every
100 years (colour scale shown in b), and the dashed line shows the central
flow line of HB. (b) Ice velocity profiles along the central flow line of HB,
shown every 100 years. The grounding-line position is marked by the limit
between solid and dashed parts of profiles.
The grounding line migrates similarly for medium-melt-rate experiments with
linear sliding (Fig. ) and non-linear sliding. Here we
present the common successive steps of all scenarios regarding grounding-line
migration and ice dynamics (Fig. and Movie S1 in the
Supplement).
The HB ice shelf/sheet system is by far the most dynamic of the three
glaciers. During the first century, its grounding line retreats relatively
slowly and the pinning points PPhs (Fig. ) detach from the
ice-shelf base. The subsequent unpinning of PPhs is followed by an
acceleration of the grounding-line retreat over the deepest part of the bed,
along with a speed up of ice increasing from ≈ 20 to 100 % in 100 years or so. During these rapid changes, two sudden jumps (the second
being less strong than the first) in velocity and grounding-line retreat
rates occur when the grounding line retreats over two consecutive troughs
imprinting the bed. During the following years, the grounding line and
velocities of HB stabilise progressively as the grounding line gets closer to
the downsloping part of the bed. By the end of the simulations, the two
saddles linking the TB/HB and HB/WRG promontories to the main ice sheet
get successively afloat until the two promontories transition into ice rises, and
the grounding line of HB has retreated by up to 100 km. The consequent loss
of buttressing eventually produces a small retreat of the TB grounding line
for the highest melt-rate scenarios.
The Be/U initialisation produces faster retreat of grounding lines than
the Be/S initialisation, which produces faster retreat than the RF/S
initialisation. In particular, the saddle of the HB/WRG promontory gets
afloat the most rapidly. The grounding lines of TB and WRG re-advance over up
to tens of kilometres for low-melt scenarios.
Grounding-line migration for medium melt rates and linear sliding.
Melt rates Mb1(a–c) and Mb2(d–f). Experiments
Be/S/L/Mb1/Am(a), Be/U/L/Mb1/Am(b), RF/S/L/Mb1/Am(c),
Be/S/L/Mb2/Am(d), Be/U/L/Mb2/Am(e), and RF/S/L/Mb2/Am(f). Grounding lines are shown every 100 years. In (a–c) the stiffening
factor field is shown in the background, and a dashed line window is drawn to
point out the area where excessive stiffening occurs when omitting PPw in
data assimilation.
Discussion
Most of the continental shelf beneath the WAIS lies below sea level, making
the ice sheet prone to undergo MISI .
With respect to the bed topography, the EAIS appears more stable, but its
volume of ice is 10 times larger than its western counterpart. It is
therefore crucial to investigate a potential unstable retreat of grounding
lines that may further affect the ice-sheet stability. Here, our simulations
systematically show an unstable retreat of HB over the first few hundreds
years regardless of the applied sub-ice-shelf melt rates, sliding laws, and
initialisations (Fig. and Movie S1 in the Supplement). Half
of the simulations also predict the retreat of the neighbouring glacier TB
for melt rates comparable to current observations. Overall, the contribution
of the studied area to sea-level rise is 30±10 mm for the next
millennium, which needs to be put in perspective with the comparatively small
domain (representing about 1 % of the Antarctic ice sheet) and the
possible non-linear effects due to future oceanic forcing that are neglected
in this study.
After a century, the HB grounding-line retreat reaches its highest speed,
1 km a-1, for the Be/S/L/Mb1/Am experiment and 500 m a-1 for
the Be/S/L/Mb2/Am experiment, further inducing after a couple of
decades a peak in ice-shelf velocities, attaining 700 m a-1 for the
latter two experiments when the grounding line retreats over the deepest part
of the bed (Fig. ). The retreat is thus influenced by the
type and amplitude of melt rates (Fig. ). We also evaluated
the MISI part on the retreat of HB, by switching off the sub-ice-shelf
melting during the Be/S/L/Mb1/Am when the grounding line retreats over
the upsloping part of the bed, without altering the melt rates beneath the
other ice shelves. The experiment, shown in Fig. S3,
demonstrates that the grounding-line retreat is substantially affected by MISI, even
though not entirely. However, none of the simulations show a
retreat of the WRG grounding line, despite the presence of an incised valley
of about 1200 m deep beneath the ice upstream of the grounding line
(Fig. ). This valley is also narrow and starts tens of
kilometres upstream of the current grounding line, while the depression
beneath the HB grounded ice is wider and starts closer to the grounding line.
This is in accordance with the ideal simulations of , who
showed that a wider trough upstream of a grounding line reduces the
buttressing exerted by the ice shelf, which enhances the grounding-line
retreat rate.
During the retreat of HB, the ice-shelf thickness is halved compared to
initial conditions. Meanwhile, the thickness of the WRG ice shelf remains
almost constant in time near the east side of the HB/WRG promontory. The
consequence is an increase of the ice flux coming from the promontory's
saddle and going towards the HB ice shelf, reducing the width of the saddle
from its western side and eventually transiting the HB/WRG promontory into an
ice rise when its saddle becomes afloat. The retreat of TB depends on the
melt-rate type and amplitude. All the low-amplitude and the Mb2
medium-amplitude melt rates lead to an advance of its grounding line, while the
other scenarios lead to a retreat. However, this contrasting behaviour only
slightly modulates the time span by which the saddle of the TB/HB promontory
gets afloat, for which the substantial thinning of the HB ice shelf is the
major driver.
The observed grounding lines that are currently fringed and buttressed by ice
promontories (such as for HB) are stable in the studied area, even resting on
the upsloping bed also shown byfor synthetic numerical
experiments. However, small amounts of sub-ice-shelf
melting clearly induce rapid grounding-line retreat and transition of the
promontories into ice rises. Such a quick transition is corroborated by
, showing that promontories are transient features of
grounding-line retreat, when they are characterised by an overdeepening
upstream of the pinned area.
Most low- and several medium-melt-rate scenarios lead to an advance of the
WRG grounding line upstream of DIR (Fig. ), even though we
excavated the area beneath the ice shelf. Because the bathymetry of ice-shelf
cavities is poorly constrained, advancing grounding lines must be cautiously
interpreted, and this potentially spurious effect on sea level thus calls for
a better knowledge of bathymetry beneath ice shelves.
Contribution to sea level for all transient simulations. Linear
sliding (a–c) and non-linear sliding (d–f) experiments.
Experiments using Be/S(a, d), Be/U(b, e), and RF/S(c, f) initialisations. Solid and dashed
lines show Mb1 and Mb2 melt rates, respectively. The
brighter the line, the higher the melt-rate amplitude. The circles (in
Mb1 lines) and triangles (in Mb2 lines) indicate the time
by which the HB/WRG promontory transitions into an ice rise, which is also
marked by a vertical line (solid or dashed) for the medium-melt-rate
experiments. The two numbers shown at the top right of each panel indicate
the contribution to sea-level change in millimetres after 500 a of
medium-melt-rate experiments (mtot1 for Mb1 and
mtot2 for Mb1).
Unpinning of the WRG ice shelf mildly affects the global contribution to sea
level, increasing it by 10 % compared to the Be/S
initialisations (Fig. ). However, the decrease of buttressing
stemming from unpinning thins the WRG ice shelf and accelerates the retreat
of the HB/WRG promontory's saddle from its eastern side: the saddle gets
afloat two centuries earlier (Fig. ). This indicates a large
sensitivity of promontories' deglaciation to a loss of buttressing, similarly
to the unstable retreat pointed out in . The loss of
buttressing induced by unpinning also cancels the advance of the WRG
grounding line simulated by the experiments using Be/S
initialisations (Fig. b), but it does not have enough effect
to induce an unstable retreat over the upsloping bed area upstream of the
grounding line. On the west side of the HB/WRG promontory, unpinning of PPhs
occurring after less than 100 years of simulation precedes the acceleration
of the ongoing retreat of the HB grounding line by a few years (Movie S1 in
the Supplement). However, quantifying the contribution of PPhs unpinning to
the grounding-line retreat is not straightforward since unpinning is
effective when the HB grounding line retreats over the deepest part of the
bed, hence with the largest potential for inducing MISI.
Besides the MISI-driven consequences on sea level, sub-ice-shelf melting is
the other main driver of the retreat. Different behaviours emerge from the
two types of melt-rate parametrisations. During the first few hundreds of
years, sea-level contribution is more or less a linear function of melt-rate
amplitude. The form of Mb1 induces high melt rates at the grounding line
when it retreats over the deep trough beneath HB. The contribution to sea
level is then a function of pure melting and dynamic thinning, inducing peaks
of sea-level contribution after about a century. In the case of Mb2 melt
rates, this peak is replaced by a milder bump in sea-level contribution
(Fig. ) since the pure melting contribution is lower. After
500 a, the retreat of the HB grounding line is less rapid, and the
contribution to sea level is then mostly due to melting, and to a lesser
extent it is due to dynamic thinning. Since the Mb1 melt rates induce more
melting at large depth and almost no melting closer to the surface compared
to the Mb2 of similar amplitudes, the Mb1 melt rates become lower
compared to the Mb2 melt rates, except for the lowest melt rates where
this is the opposite. After ≈ 800 a, a sudden increase in sea-level
contribution occurs for non-linear sliding and the high Mb2 melt rates
(Fig. e, f), which is due to ungrounding of the promontory
saddle between Lazarev Ice Shelf and the unnamed glacier
(Fig. ). This peculiar behaviour that does not occur for
the other experiments is the reason why we indicate the sea-level
contribution after 500 a of transient simulation (Fig. ).
Compared to linear sliding, non-linear sliding (with m=1/3) should enhance
basal sliding when ice velocity increases. The acceleration of HB during its
retreat consequently yields higher velocities and faster retreat rates of the
grounding line for the non-linear case, hence leading to a higher contribution
to sea level from HB. At the scale of the domain, this is, however, difficult
to distinguish the differences between the two sliding laws, since they
induce similar contributions after 500 a.
As already shown by , omitting the pinning point PPw in data
assimilation induces erroneous ice stiffening nearby
(Fig. ). Initialising transient simulations with such
stiffening leads to a spurious decrease in sea-level contribution by 10 %
compared to the experiments using Be/S initialisation. The transient
evolution of the WRG grounding line looks similar to the unpinning
experiments, pointing out the spatially limited effects of the excessively
stiffened ice. However, the stiffening effect largely alters the timing of
deglaciation of the HB/WRG promontory (Fig. ) and delays it by
approximately 500 a. Moreover, any further local change in the boundary
condition between the pinning points and the ice shelf, including the extreme
– but possible – event of unpinning for instance induced by a
substantial thinning of ice shelves;, cannot be simulated by the
model if the pinning point is omitted in the first place.
Since the early 2000s, uncertainties of ice-sheet modelling outputs have been
reduced by substantial numerical improvements, enabling key processes to be grasped more
accurately such as grounding-line migration . This improvement was also made possible by the
increasing computational power. We are now able to simulate the behaviour of
the WAIS using higher-order models at a high spatial resolution in the
relevant areas for a wide range of scenarios over the next centuries
, which was not feasible a few years ago. Nevertheless,
the lack of knowledge of essential parameters still affects simulations of
the Antarctic ice sheet behaviour, hence preventing further decrease of
uncertainties in sea-level predictions. Sub-ice-shelf melting is a major
driver of ice-sheet retreat and sea-level contribution
(Fig. ). Even though forcing the ice sheet with parametrised
melt rates (such as in this study) gives qualitative and informative insights
on future sea-level contribution, the lack of knowledge of the cavity beneath
ice shelves prevents the use of more advanced assessment based on ocean
modelling such as in. Moreover, the
ill-constrained shape of the ice-shelf cavity dictates how and if the
grounding line advances, which also biases future sea-level predictions.
Here, we demonstrates that sea-level predictions and timing of deglaciation
can be substantially affected by too shallow a bathymetry and the absence of
small pinning points, which all affect ice-sheet initialisation. In addition, the
exact representation of pinning points (ice rumples, rises, and promontories)
in the observational datasets, even if they are small, is key for more
accurate predictions of future sea-level change and timing of ice-sheet
retreat. Therefore, improving these predictions by the use of ice-sheet
modelling relies on future improvements of our knowledge of the bathymetry
beneath ice shelves and (small) pinning points.
Conclusions
We use the ice-sheet model BISICLES to evaluate the contribution of the
outlet glaciers between the Lazarev and Roi Baudouin ice shelves in East
Antarctica to future sea-level rise, with two different input datasets,
including or excluding an observed small pinning point (PPw) at the calving
front. We also investigate the influence of various sub-ice-shelf melt-rate
parametrisation and two types of Weertman-type sliding law (linear and non-linear). Our results suggest an unstable retreat of the Hansenbreen (HB)
glacier within the next century. This retreat is equally driven by sub-ice-shelf melting and marine ice sheet instability (MISI), while the other
outlet glaciers are relatively stable over the next millennium. Where the bed
is downsloping towards the sea (no potential for MISI), sub-ice-shelf
melting exclusively controls sea-level contribution. Unpinning of PPw
increases the sea-level contribution by 10 % but substantially affects the
timing of ice-sheet retreat in the most sensitive parts, such as the HB/WRG
promontory, which transitions into an ice rise 200 a in advance. On the other
hand, omitting PPw during the initialisation of the ice sheet yields local
excessive ice-shelf stiffening, which decreases the sea-level contribution by
10 % and delays the HB/WRG promontory transition by 500 a in transient
simulations. Even small pinning points should be accounted for in ice-sheet
modelling because they affect transient ice-dynamical behaviour and
grounding-line retreat. This study calls for a better knowledge of Antarctic
ice sheet margins, including the bathymetry beneath ice shelves and the
characteristics – ice velocity and ice/bed geometry – of even the smallest
pinning points, in order to improve our ability of predicting future Antarctic
ice sheet margins.
Data availability
The high-resolution velocity dataset, which was also used in the previous
publication of , is available upon request, and will be
shortly made publicly available to the community.
The Supplement related to this article is available online at doi:10.5194/tc-10-2623-2016-supplement.
Acknowledgements
This paper forms a contribution to the Belgian Research Programme on the
Antarctic (Belgian Federal Science Policy Office), project SD/CA/06A
(Constraining Ice Mass Change in Antarctica, IceCon). R. Drews was partially
supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of
the priority programme “Antarctic Research with comparative investigations
in Arctic ice areas” by the grant MA 3347/10-1. BISICLES development is led
by D. F. Martin at Lawrence Berkeley National Laboratory, California, USA,
and S. L. Cornford at the University of Bristol, UK, with financial support
provided by the US Department of Energy and the UK Natural Environment
Research Council. Simulations were carried out using the computational
facilities of the HPC Computing Center at Université libre de Bruxelles.
S. Berger is supported by a FRS-FNRS (Fonds de la Recherche Scientifique) PhD
fellowship. We are grateful to M. Depoorter for providing us with current
sub-ice-shelf melt rates. We thank Robert J. Arthern and an anonymous
reviewer for their insightful comments that helped to improve the manuscript.
Edited by: H. Gudmundsson
Reviewed by: R. Arthern and one anonymous referee
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