Introduction
The present-day West Antarctic Ice Sheet (WAIS) is experiencing an imbalance
between the mass it receives as snowfall and that which it loses through
discharge to the oceans
.
In several areas this has led to the persistent loss of ice amounting to
a significant contribution to sea-level rise. Continued acceleration of these
losses would imply a significant additional global sea-level rise in the coming
decades and centuries. Physically based projections of the contribution of
the WAIS to sea level rise are hampered by two main factors. The first of
these is the lack of a fully coupled climate and ice sheet model, in which
the principal forcing on the ice sheet (accumulation at the upper surface and
submarine ice shelf melt) is determined within the model. The second is the
technical difficulty involved in calculating the flow of ice across the ice
sheet's grounding line and the consequent grounding line migration. Progress
has been made in both areas
,
but the computational expense of fully-coupled ice/ocean models at sufficient
resolution and for sufficient integration times remains prohibitive.
We approximate full coupling between the ice sheet and the rest of the
climate system by imposing combinations of published meteoric accumulation
and oceanic melt rate anomaly data on the BISICLES adaptive mesh ice sheet
model . Two emission scenarios are included:
SRES E1, a mitigation scenario in which emissions are stabilized by 2050 at
500 ppm CO2, and A1B, a balanced scenario close to the center
of the SRES range. These were used to drive global climate warming in the
UKMO HadCM3 and MPI ECHAM5 global climate models, which have among the
highest skill scores in the CMIP3 model group (based on Antarctic SMB,
surface air temperature, mean sea level pressure, and height and temperature
at 500 hPa, ). The resulting global
climate projections provided boundary conditions to two high-resolution
atmosphere models: RACMO2 and LMDZ4
and two ocean models: the medium
resolution BRIOS (Bremerhaven Regional Ice–Ocean Simulations)
and the higher resolution FESOM
(Finite-element Sea ice-Ocean Model) ,
ultimately providing seven sets of meteoric accumulation data and eight sets
of oceanic melt rate data.
At the same time, we examine the response of the ice sheet model to
variability beyond the scope of the atmosphere and ocean models. The climate
projections described above tend to agree on the timing and magnitude of
future accumulation and melt rate increases, if not the distribution. We
complement them with some simplified, widespread melt rate increases, as well
as projections further into the future, in order to investigate the
additional response to more extreme scenarios. The century-scale evolution of
the ice sheet model is also sensitive to its present-day state, especially in
the Amundsen Sea Embayment, and we evaluate at least a part of this
sensitivity – which will prove to be substantial – by varying the initial
accumulation rate and hence the initial thinning rate.
In summary, the aim of this paper is to consider the response of the West
Antarctic ice streams to process-based and simplified projections of future
ocean and atmosphere warming over the 21st and 22nd centuries. We focus on
West Antarctica primarily because of constraints on available computational
resources; however these areas are also thought to be most vulnerable to
future grounding line retreat because of their deep bedrock and changes in
oceanic forcing
.
Methods
Model equations
BISICLES employs a vertically integrated ice flow model based on
which includes longitudinal and lateral
stresses and a simplified treatment of vertical shear stress which is best
suited to ice shelves and fast-flowing ice streams. Ice is assumed to be in
hydrostatic equilibrium so that given bedrock elevation b and ice thickness
h the upper surface elevation s is
s=maxh+b,1-ρiρwh,
in which ρi and ρw are the densities of
ice and ocean water.
The ice thickness h and horizontal velocity u satisfy
a two-dimensional mass transport equation
∂h∂t+∇⋅uh=a-M,
and two dimensional stress-balance equation
∇⋅ϕhμ¯2ϵ˙+2tr(ϵ˙)I+τb=ρigh∇s,
together with lateral boundary conditions. The terms on the right hand side
of Eq. (), a and M, are the meteoric accumulation rate,
applied to the upper surface of the entire ice volume, and the oceanic melt
rate, applied to the under-side of ice shelves. When Eq. () is
discretized, oceanic melt is applied only to cells whose center is floating.
As for Eq. (), ϵ˙ is the horizontal
strain-rate tensor,
ϵ˙=12∇u+∇uT
and I is the identity tensor. The vertically integrated effective
viscosity ϕhμ¯ is computed by evaluating the integral
ϕhμ¯(x,y)=ϕ∫s-hsμ(x,y,z)dz
numerically, with the ice sheet sub-divided into 10 layers, narrowing
progressively from 0.16h near the surface to 0.03h near the base. The
vertically varying effective viscosity μ(x,y,z) includes a contribution
from vertical shear and satisfies
2μA(T)(4μ2ϵ˙2+ρig(s-z)∇s2)(n-1)/2=1,
where the flow rate exponent n=3, ϕ is a stiffening factor (or,
equivalently, ϕ-n is an enhancement factor), and A(T) depends on
the ice temperature T through the Arrhenius law described by
,
A(T)=A0exp3f[Tr-T]k-QRT,
where A0=0.093 Pa-3a-1, Q/R=9.48×103 K, f=0.53 Kk, k=1.17 and Tr=273.39 K. The
coefficient ϕ is estimated by solving an inverse problem (see
Sect. ), and it is simply a convenient way to represent
several conflated factors: uncertainty in both temperature T and the form
of A(T), macroscopic damage, and fabric formation.
Finally, the basal traction is determined by a viscous law:
τb=-C|u|m-1uif ρiρwh>-b0otherwise,
with m=1. Like ϕ, C will be determined by solving an inverse
problem, as described in Sect. . Our choice of a linear
viscous law may well bias our results toward excessive grounding line
retreat: in previous work on Pine Island Glacier non-linear laws with m<1
have led to slower rates of retreat
.
We hold the fields C and ϕ constant throughout our simulations. That
is not to say that these fields ought not change over the course of one or
two centuries; for example regions of damage (low ϕ) might well
propagate with the grounding line as englacial stresses grow in regions
previously dominated by the balance between gravitational and basal shear
stress. Rather, we lack models of sufficient skill for the present, and
anticipate incorporating progress in damage models
and hydrology models
in future calculations. We note, however, that the maps of C and ϕ we
use (see Sect. ) already feature slippery beds and weak
shear margins hundreds of kilometers upstream from the grounding line.
Model domains and boundary conditions
We carried out calculations on three rectangular domains, shown in
Fig. . The largest of these (RISFRIS) covers the Ross and
Filchner–Ronne ice shelves and their tributary ice streams, while two
smaller domains cover the Amundsen Sea Embayment (ASE) and Marie-Byrd Land
(MBL). Each of the rectangular domains is split into an active region
ΩV, where ice is permitted to flow, and a quiescent region
ΩQ where ice is taken to be stationary. For example, in the
RISFRIS domain, ΩV covers the present-day drainage basins of
the Ross and Filchner–Ronne ice shelves, and the ice shelves themselves,
while ΩQ covers the Amundsen Sea Embayment, Marie-Byrd Land,
and part of the Antarctic Peninsula. Likewise, inside the ASE domain
ΩV spans the drainage basin of Pine Island, Thwaites, Smith,
Pope, and Kohler glaciers. This construction assumes that the ice divides
will not stray from their current configuration, and so limits us to
simulations over a few centuries.
West Antarctica divided into three computational
domains. Simulations are carried out in three rectangular model domains:
RISFRIS, ASE and MBL. Each of these has an active region ΩV bounded
by the dashed contours and the calving front (black), while the remaining
area ΩQ is made quiescent. Integration of, say, volume above
flotation is carried out only over the active regions. Sea level rise results
are given separately for the Filchner–Ronne Ice Shelf (FRIS) and Ross Ice
Shelf (RIS) regions, but the simulations are carried out on a domain joining
both regions together (RISFRIS). The Amundsen Sea Embayment (ASE) and
Marie-Byrd Land (MBL)
are simulated separately.
Model initial state.
Panels show (a) the ice flow speed |u|, (b)
the difference between observed and model speed |uo|-|u|,
(c) the basal traction coefficient c,
(d) the vertically averaged effective viscosity ϕμ¯,
(e) the synthetic mass balance a0(x,y)-M0(x,y,t=0),
and (f), the thickening rate ∂h∂t, all at the start of the prognostic
calculations. Data from all three domains are shown, with a magnified inset
showing the ASE data in more detail.
Reflection boundary conditions were applied at the edge of each domain.
If n is normal to a boundary and t is parallel to it,
u⋅n=0,t⋅∇u⋅n=0,∇h⋅n=0.
In practice, these boundary conditions are unimportant because of the
presence of quiescent regions and calving fronts inside the domain. In the
quiescent regions, we set the basal traction coefficient to a large value, C=105Pam-1a so that at the interface between
ΩV and ΩQ,
u≈0anduh≈0,
while at the calving front (which is fixed), we impose the usual conditions
on the normal and transverse stress:
n⋅ϕhμ¯2ϵ˙+2tr(ϵ˙)I=12ρig1-ρiρwh2n.
These boundary conditions, and indeed, Eq. () alone for
a problem whose entire boundary is a fixed calving front, are sufficient
provided that h(x,y,t=0) is given and that the basal friction coefficient
C(x,y) is non-zero in at least part of the ice sheet.
Adaptive mesh refinement
Fine horizontal resolution, or other careful treatment, is held to be crucial
when simulating grounding line migration
(; ). Indeed, the BISICLES ice sheet
model was designed primarily with this in mind, and discretizes the stress
and mass balance Eqs. () and () on block-structured
meshes built from rectangular subsets of uniform grids with resolution
Δxℓ, with 0≤ℓ≤L and 2Δxℓ+1=Δxℓ. While restrictive in some senses – all model domains must
be rectangular, for example – these meshes have a signal advantage: it is
straightforward to generate new meshes as the ice sheet evolves, and to
transfer the previous time-step's ice thickness data to the new mesh in
a conservative fashion. It is also relatively easy to study convergence with
mesh resolution by running the same experiment for successive values of L
and verifying that the differences between, say, the volume above flotation
calculated in each case converge to zero at the expected rate. We regard such
a convergence study as a pre-requisite for any ice dynamics simulation, since
there is no general proof that any particular mesh resolution is adequate. We
include the relevant results in appendix , where we show
that sub-kilometer resolution around the grounding line is necessary and
adequate in all of West Antarctica, but that finer resolution is needed in
the Amundsen Sea Embayment, where we employ a mesh with 250m≤Δxℓ≤4000m, than in the Ronne-Filchner and Ross
ice shelf catchments; there we find that a mesh with 625m≤Δxℓ≤5000m is sufficient.
There is a relationship between horizontal mesh spacing, ice velocity and
time-step. Since the advection scheme chosen to evolve Eq. () is
explicit, we re-compute the time-step periodically so that a
Courant-Friedrichs-Lewy (CFL) condition Δt<0.25Δxl|u| is satisfied everywhere in the domain. In practice, this
leads to as many as 128 time-steps per year in the ASE domain, where the mesh
is finest and the flow is fastest.
Model data requirements
Time-dependent simulations require initial ice thickness data h0(x,y) as
well as accumulation rates a(x,y,t) and melt rates M(x,y,t) for
Eq. (), together with a bedrock elevation map b(x,y), a basal
friction coefficient field C(x,y), a temperature field T(x,y,z) and
a stiffening factor ϕ(x,y) to solve Eq. (). Bedrock
elevation and initial ice thickness data for the RISFRIS and MBL domains were
taken from the ALBMAP DEM . ALBMAP is provided
at a lower resolution (5 km) than the more recent Bedmap2
(1 km) , but the model is less
sensitive to finer-scale variations in bedrock and
in any case the distance between the flight-lines measuring ice thickness for
both DEMs is typically not finer than 5 km. A custom map of bedrock
elevation and ice thickness set on a 1 km grid was used for the ASE
domain: it is close to the Bedmap2 data, and was used before for studies of
Pine Island Glacier . It was prepared in a similar
manner to ALBMAP, but includes extra data from high-resolution airborne radar
and submarine surveys
. It also includes a pinning point at the
tip of Thwaites Glacier's slower flowing eastern ice shelf, a feature that is
clearly visible in the velocity data
, that corresponds to peak one of
the two described in , but is absent in the
bathymetry data. We raised the bathymetry by 120 m to ground the ice
in that region. Ice temperature data are provided by a three-dimensional
thermo-mechanical model and is held fixed in
time.
The basal friction and stiffening coefficients are chosen by solving an
inverse problem similar to those of ,
and . A detailed
description is given in Appendix , but in summary, we
construct smooth fields C(x,y) and ϕ(x,y) that minimize the mismatch
between the modeled speed and the published InSAR observations. For the
RISFRIS and MBL domains we use InSAR observations made between 2007 to 2009
. For the ASE domain, which has accelerated over
the last decade, we use measurements made in 1996 .
However, the observed speeds are not entirely compatible with the thickness
and bedrock data. Notably, computing the flux divergence from the thickness
and velocity data results in a region of 100 ma-1 thickening
across Pine Island Glacier's grounding line. Others have noted this strong
thickening, and address it by imposing a large synthetic mass balance
, by constraining the ice viscosity and
accepting a worse match to the observed velocity ,
or by modifying the bed to give acceptable thickening rates while matching
the observed velocity field . Here,
we soften the ice around the grounding line by reducing the stiffening
factor relative to the field in the inverse problem.
Accumulation anomalies integrated over each
region.
The atmosphere models provide enhanced accumulation only for the A1B emission scenarios.
Melt rate anomalies integrated over each region.
In contrast with the atmosphere models, the ocean models provide similarly
growing melt rates in both A1B and E1 scenarios. Note that the Amundsen Sea
Embayment and Marie-Byrd Land melt rate anomalies are not given directly by
the ocean models, which do not resolve the smaller ice shelves, but are
characterized in terms of nearby Circumpolar Deep Water temperatures.
The accumulation and melt rates are computed by adding future climate
anomalies, described in Sect. , to initial
accumulation and melt rates a0 and M0 chosen to hold the ice sheet
close to equilibrium. Determination of a0 and M0 – especially M0 –
is somewhat involved, and is described in more detail in
Appendix . Essentially, we evolve the ice sheet geometry for 50
years while holding the ice shelf constant in order to dampen
short-wavelength, large-amplitude fluctuations in the flux divergence. At the
end of this relaxation period, we compute a0 and M0 from ∇⋅uh, with M0 parametrized as a function of time and
space so that peak melt rates follow the grounding line as it migrates. Since
a synthetic mass balance along the lines of a0 will tend to counter the
thinning that is already evident in the ASE, we carry out some additional
experiments where a0 is replaced by an accumulation pattern derived from
the RACMO atmosphere model.
Initial state
Figure illustrates the state of the three regional models
at the end of the initialization procedure. The large ice streams flowing
into the Amundsen Sea, through the Filchner–Ronne Ice Shelf, and through the
Ross Ice Shelf are apparent in both the flow field and the basal traction
field C. The flow field itself is close to the observed speed, with the
largest mismatch due to the softening in Pine Island Glacier described above,
and within 200ma-1 of the observations elsewhere. Regions of
fast flow are fringed by weak shear margins that are due to both the shear
thinning action of Glen's flow law and localized low stiffening factor
ϕ. Note that the observed velocity field cannot be matched with ϕ=1, whatever the basal traction. For example the shear margins in Pine Island
Glacier and the division between the western and eastern portions of Thwaites
Glacier's ice shelf require ϕ∼0.1.
Accumulation data, oceanic melt rate data, and
duration for all 22 experiments. Each experiment is named for its
climate forcing data, which are specified by combinations of GCM, emission
scenario, high-resolution atmosphere model and high-resolution ocean model.
Synthetic
Mass balance anomalies
Experiment
accumulation
GCM
Emissions
Atmosphere
Ocean
Final year
control
a0(x,y)
–
–
–
–
2200
control′′
a0′′(x,y)
–
–
–
–
2200
H/A/R/F
a0(x,y)
HadCM3
A1B
RACMO2
FESOM
2200
H/A/R/B
a0(x,y)
HadCM3
A1B
RACMO2
BRIOS
2200
H/A/L/F
a0(x,y)
HadCM3
A1B
LMDZ4
FESOM
2200
H/A/L/B
a0(x,y)
HadCM3
A1B
LMDZ4
BRIOS
2200
H/E/R/F
a0(x,y)
HadCM3
E1
RACMO2
FESOM
2150
H/E/R/B
a0(x,y)
HadCM3
E1
RACMO2
BRIOS
2200
H/E/L/F
a0(x,y)
HadCM3
E1
LMDZ4
FESOM
2150
H/E/L/B
a0(x,y)
HadCM3
E1
LMDZ4
BRIOS
2200
E/A/R/F
a0(x,y)
ECHAM5
A1B
RACMO2
FESOM
2100
E/A/R/B
a0(x,y)
ECHAM5
A1B
RACMO2
BRIOS
2100
E/E/R/F
a0(x,y)
ECHAM5
E1
RACMO2
FESOM
2100
E/E/R/B
a0(x,y)
ECHAM5
E1
RACMO2
BRIOS
2100
E/E/L/F
a0(x,y)
ECHAM5
E1
LMDZ4
FESOM
2100
E/E/L/B
a0(x,y)
ECHAM5
E1
LMDZ4
BRIOS
2100
H/A/0/F
a0(x,y)
HadCM3
A1B
–
FESOM
2300
H/A/0′/F
a0′(x,y)
HadCM3
A1B
–
FESOM
2200
H/A/0′′/F
a0′′(x,y)
HadCM3
A1B
–
FESOM
2200
0/U16
a0(x,y)
–
–
–
16 ma-1
2200
0/U8
a0(x,y)
–
–
–
8 ma-1
2200
0′′/U16
a0′′(x,y)
–
–
–
16 ma-1
2200
The thickening rate (given a0 and M0) is between -5 and
5ma-1 except at calving fronts. Integrating this thickening
rate leads to an annual loss of volume above flotation of
3 km3a-1 in the ASE, 7 km3a-1 in the
Filchner–Ronne ice shelf basin and 7 km3a-1 in the Ross ice
shelf basin. The synthetic accumulation a0 used to obtain this thickening
rate does include some unrealistic large-amplitude short-wavelength features,
with the largest values in mountainous regions with steep slopes: the
ring-shaped features in the ASE surround isolated peaks, for example. Strong
ablation is limited to the ice shelves, with a0 between -5 and
5ma-1: in particular there is no region of ∼100m a-1 ablation needed to counter the flux arriving at the Pine
Island Glacier grounding line.
Prognostic experiments
Twenty-two simulations were performed for one or more of the three model
domains. Each simulation makes use of the same initial geometry, basal
traction coefficient, and stiffness coefficient, but differs from the others
in terms of the meteoric accumulation and oceanic melt rates imposed. Each
experiment is named after these forcing data, and falls into one of three
groups: two control calculations, which are subject to a constant climate,
fourteen experiments forced by combinations of time-dependent climate model
data, and six melt rate anomaly experiments, which are subject to
constant-in-time accumulation. The experiments are summarized in
Table and described in detail below.
Net change in volume above flotation over the course
of the combined anomaly experiments.
Only the Amundsen Sea Embayment experiences a net loss (ΔV) in all of the combined experiments.
Nonetheless, the result is a net loss over West Antarctica as a whole.
Note that Thwaites glacier does not retreat in the combined anomaly experiments (which use the synthetic accumulation), and the ASE
could contribute an extra 9×103km3 loss by 2100 and 40×103km3 by 2200.
A magnified version of this figure, covering the period 1980-2100, is included in the supplement, as is a .csv file
of the data.
Combined anomaly experiments
Future climate forcings were derived from the atmosphere and ocean models by
computing space- and time-dependent anomalies with respect to the 1980–1989
mean, and adding them to a0(x,y) and M0(x,y,t). By combining the seven
atmosphere projections with the eight ocean projections, we have fourteen
experiments, as shown in Table . These are named after the
anomalies: for example, the experiment named H/A/R/F combines the
HadCM3/A1B/RACMO2 accumulation anomalies with the HadCM3/A1B/FESOM melt rate
anomalies. Given the fourteen forcing combinations, the ice sheet model was
evolved, starting from its initial state in 1980 to at least 2100 and on to
2150 or 2200 if the forcing data were available. The HadCM3/A1B/FESOM ocean
data, both sets of HadCM3/A1B/BRIOS ocean data and all of the HadCM3/A1B
atmosphere projections were sufficient to run the ice sheet model until 2200,
the HadCM3/E1/FESOM data run to 2150, and the ECHAM5 data to 2100.
Neither ocean model produced substantial melt rate increases in the ASE or
MBL domains, presumably because they are not able to resolve the small ice
shelves along those coasts. We computed melt rates in those regions from
projections of nearby ocean temperatures. The melt rates and consequent
thinning experienced by small ice shelves, such as Pine Island Glacier, is
thought to be forced by changes in the temperature of near-coast water masses
. We compute a local
ocean temperature anomaly ΔT(t) by averaging the projected ocean
temperature over volume bounded laterally between the contemporary ice front,
the sector boundaries, and the 1000 m bathymetric contour and
vertically between depths of 200 and 800 m, on the grounds that water
contributing to melting must be deep enough to interact with the base of an
ice shelf but shallow enough to cross the continental shelf break. Finally,
a melt rate anomaly ΔM(t)=16ΔT(t) ma-1K-1
was chosen to be at the upper end of the range of observational and modeling
studies .
The accumulation and melt rate anomalies, plotted in Figs.
and , have a notable feature. The A1B atmosphere models
project increased accumulation during the 21st century, and a further
increase during the 22nd century, over and above the E1 models. Although the
two atmosphere models distribute snowfall differently, with RACMO2
concentrating its increased accumulation over the Amundsen Sea Embayment and
Filchner–Ronne Ice Shelf drainage basins and LMDZ4 heaping mass over
Marie-Byrd Land and the Ross Ice Shelf drainage basin, both models project
a threefold increase for A1B over E1. At the same time, the A1B and E1 ocean
models both provide enhanced melt rates from 2100, with the most obvious
difference between trends being the choice of FESOM or BRIOS. Even before
carrying out any simulations, we can expect to see similar dynamic thinning
in the two emissions scenarios, which, coupled with the extra accumulation in
A1B, means that we expect to simulate more sea level rise for E1 (mitigation)
emissions than A1B (business as usual) emissions.
Melt rate anomaly experiments
The climate-forced experiments outlined above present a rather limited view
of future change. Since both the ocean and atmosphere models project similar
futures, they cannot provide much information about the response to earlier
or more widely distributed ice shelf thinning. At the same time, the
assumption that the ice sheet was in steady state at the end of the 20th
century does not allow us to examine changes that may already be under way.
A number of experiments with melt rate anomalies but no accumulation
anomalies were carried out to address these limitations.
Parts of the ice sheet model might be on the brink of dramatic change in
2200, so we ran a longer set of calculations, starting in 1980 and running
until 2300, based on the HadCM3/A1B/FESOM melt rates. This experiment has
only the synthetic accumulation field, so we label it H/A/0/F. The
HadCM3/A1B/FESOM melt rates were chosen because they run up to 2200, produce
enhanced melting in all of the basins, and rise constantly from 2050 onward
to give the largest melt rates at the end of the 22nd century. From 1980 to
2200 we applied the melt rate anomalies as before, and applied the 2200 melt
rate anomaly for the remainder of the simulation.
Imposing a synthetic accumulation field to hold the ice sheets close to
steady state given the present-day geometry and velocity is a questionable
choice in the Amundsen Sea Embayment, where observations over the last
decades show extensive thinning. Furthermore, the synthetic mass balance
field a0(x,y), which we constructed to hold Thwaites Glacier in steady
state during the control experiment, includes a spot of unrealistic –
5 ma-1 – accumulation close to the Thwaites Glacier grounding
line (see Fig. ). In light of these issues, we carried out
three additional simulations. None of these experience accumulation anomalies
but the first, H/A/0′/F, has a synthetic accumulation field
a0′(x,y) with the 5 ma-1 accumulation spot removed,
and the second and third, H/A/0′′/F and
control′′ do not make use of a synthetic accumulation field at
all, but employ the HadCM3/E1/RACMO2 1990–1999 temporal mean, which we will
call a0′′(x,y), from 1980 onward. H/A/0′/F and
H/A/0′′/F are subject (like H/A/0/F) to the HadCM3/A1B/FESOM
melt rate anomaly data, while the control′′ experiment
maintains the same melt rate parametrization as the control experiment, that
is M0(x,y,t).
As none of the melt rate anomalies in the ASE exceed 10 ma-1
until after 2050, we also examined the model's response to earlier ocean
warming. Two simulations, 0/U16 and 0′′/U16, were performed,
with melt rate anomalies of 16 ma-1 applied across all floating
ice from 1980 onward. 0/U16 used the synthetic accumulation field
a0(x,y), while 0′′/U16 used the HadCM3/E1/RACMO2 1990–2000
mean accumulation field a0′′(x,y).
Both FESOM and BRIOS ocean models produce similar melt rate anomalies, with
enhanced melt rates concentrated around Berkner Island in the Filchner–Ronne
ice shelf, and around Roosevelt Island in the Ross Ice Shelf. Those similar
patterns are due to the physics of ocean circulation in the two models, but
it makes sense to consider ice sheet sensitivity to melt rates that cover
a greater extent. At the same time, as in the ASE, melt rates begin to grow
around 2100 in all of the drainage basins, so we need to consider our
sensitivity to earlier warming. With those aims in mind, we carried out
a pair of uniform melt rate experiments (0/U8,0/U16) in the RISFRIS
domain, applying melt rate anomalies of 8 and 16 ma-1 across the
entire extent of floating ice starting from 1980.
Results and discussion
Combining melt rate and accumulation anomalies leads to essentially the same
patterns of dynamic thinning and grounding line retreat as melt rate
anomalies alone. For example, the H/A/R/F and H/A/L/F simulations exhibit
similar grounding line retreat to the H/A/0/F results. With that in mind, we
will discuss the variation in volume above flotation between the combined
anomaly experiments in Sect. before discussing grounding line
migration in the context of the melt rate anomaly experiments in
Sect. .
Dynamic change in volume above flotation over the
course of the combined anomaly experiments. Dynamic losses (computed by
subtracting the accumulation anomaly from the net loss)
occur in all regions, and are nearly independent of the accumulation anomalies,
so that the net change in (for example) the H/A/R/F
simulation is much the same as the sum of the volume change computed for the
ocean-forced H/A/0/F simulation and the HadCM3/A1B/RACMO2 accumulation anomaly.
Note that Thwaites glacier does not retreat in the combined anomaly experiments (which use the synthetic accumulation), and the ASE
could contribute an extra 9×103km3 loss by 2100 and 40×103km3 by 2200. A magnified version of this figure, covering the period 1980-2100, is included in the supplement, as is a .csv file
of the data.
Combined anomaly experiments
Only the Amundsen Sea Embayment experiences a net loss of volume above
flotation (ΔV) in all of the combined anomaly experiments
(Fig. ). Both the Ross Ice Shelf drainage basin and Marie-Byrd
Land show a positive imbalance, while the Filchner–Ronne Ice Shelf drainage
basin remains close to balance. Adding all four trends together, West
Antarctica sees a net loss of 0–8×103km3 by 2100 and
3–23×103km3 by 2200. Note that Thwaites Glacier does
not retreat in these combined calculations, as they all apply the synthetic
accumulation. When Thwaites glacier does retreat the ASE model loses an extra
9×103km3 by 2100 and 40×103km3 by
2200, based on the difference between the H/A/0/F and
H/A/0′′/F melt rate anomaly experiments (see
Sect. ).
Grounding line migration and bedrock elevation in
the melt rate anomaly (no accumulation anomaly) experiments. Bedrock (b)
contours are drawn every 400 from 1200 m below to 1200 m
above sea level Pine Island Glacier and the ice streams feeding the Dotson
and Crosson Ice Shelves retreat throughout the 21st, 22nd, and 23rd century
CE in all simulations apart from the control. Thwaites Glacier retreats over
200 km during the 21st and 22nd centuries when subjected to the 1990s
HadCM3/A1B/RACMO2 accumulation
(H/A/0′′/F,0′′/U16), and still retreats by more
than 100 km in the control′′ experiment when no melt
rate anomaly is applied, but its retreat is delayed when subjected to
a synthetic accumulation field (H/A/0/F,0/U16). In the Filchner–Ronne Ice
shelf region, the Möller, Institute, and Evans Ice Streams begin to
retreat during the 22nd century when forced by the HadCM3/A1B/FESOM (H/A/0/F)
melt rates, and their retreat accelerates in the following century, but all
three ice streams, along with the Foundation and Rutford Ice Streams and
Carlson inlet, retreat during the 21st century if uniform
16 ma-1 melt rates are applied (0/U16). Along the Siple coast,
Whillans Ice Stream, and to a lesser extent Mercer Ice Stream, retreat over
the 21st and 22nd century in both the H/A/0/F and control simulations, but
their grounding lines have merely swept over a lightly grounded area between
the model initial state and the present-day state. The MacAyeal and
Bindschadler Ice Streams are driven to retreat 100 km during the 22nd
century by the H/A/0/F melt rates but all four streams retreat more than
200 km in the 0/U16 experiment.
An alternative version of this figure, intended for larger displays, is included in the Supplement.
The differences between responses to the ocean models are quantitative rather
than qualitative, with the higher BRIOS melt rates leading to faster retreat
along the same paths. Figure shows the volume above flotation
trends for the combined anomaly experiments where, with everything else held
equal, the BRIOS simulations exhibit a 10×103km3 greater
loss (-ΔV) by the end of the 22nd century than the FESOM simulations.
Around half of this difference is concentrated in the Amundsen Sea Embayment,
with the remainder divided between the Filchner–Ronne Ice Shelf region and
Marie-Byrd Land.
The difference between RACMO2 and LMDZ4 simulations with a given ocean model
and the A1B scenario is as large as the difference between both ocean models
across emission scenarios. Although the H/A/R/F and H/A/L/F grounding line
retreat is essentially the same, the decrease in volume above flotation over
West Antarctica as a whole differs by 10×103km3, with
the majority of that difference accounted for by the larger LMDZ4
accumulation over the drainage basin of the Ross Ice Shelf. The H/A/R/B and
H/A/L/B experiments differ in the same way. Variation between the atmosphere
models for the E1 scenario is smaller, with all of the E1 models having
similar mass loss trends.
The choice of GCM and emission scenario leads to the largest variation
between the combined anomaly experiments. Melt rates grow over time in both
A1B and E1 scenarios, but accumulation grows much less in the E1 scenario.
The four HadCM3 E1 experiments produce a net volume loss between 6 and
10×103km3 during the 21st century, and around 20×103km3 by the end of the 22nd century (assuming that the
E1/FESOM experiments follow the same trend from 2150 onward). Of the A1B
simulations, only H/A/R/B results in a similar trend, with H/A/R/B and
H/A/L/F giving rise to around 10×103km3 loss by 2200 and
H/A/R/B less than 5×103km3. The ECHAM5 E1 and A1B
simulations are generally closer to balance, but do not run beyond 2100 when
the majority of HadCM3 imbalance occurs.
Despite the wide variation in accumulation anomalies, we see little
interaction between atmosphere model and ice dynamics.
Figure shows the loss of volume above flotation due to ice
dynamics, ΔVd. For a given region Ω, ΔVd is the difference between the net change in volume above
flotation and the cumulative, integrated accumulation anomaly:
ΔVd(t)=ΔV(t)-∫t′=1980t′=t∫ΩΔadΩdt′.
In each case the difference between curves is dominated by the difference in
ocean anomaly. The H/A/R/F and H/A/L/F curves lie close to one another (and
to the H/A/0/F curve), each resulting in ΔVd≈10×103km3 (25 mm SLE) across the whole of West
Antarctica by 2100 and around 30×103km3(75 mm
SLE) by 2200. The H/A/R/B and H/A/L/B trends are also close to one another,
but lead to rather more excess discharge – around 40×103km3(100 mm SLE) by 2200. Overall, the net ΔV(t) for a simulation with accumulation anomaly Δa(t) and melt rate
anomaly ΔM(t) can be estimated rather precisely from the result,
ΔV′(t), of a simulation with the same ocean anomaly and a different
(or no) accumulation anomaly Δa′(t):
ΔV(t)≈ΔV′(t)+∫t′=1980t′=t∫ΩΔa-Δa′dΩdt′.
This result is valid for the Amundsen Sea Embayment and the Filchner–Ronne
and Ross ice shelf drainage basins, and only breaks down in Marie-Byrd Land,
which contributes little to the projections. We account for it by noting
that, in these century scale simulations, increased melt rates lead to large
amplitude but localized thinning, whereas increased accumulation causes low
amplitude but widely distributed thickening.
Melt rate anomaly experiments
The melt rate anomaly experiments (that is, the experiments with no
accumulation anomalies) all exhibit grounding line retreat in excess of the
control simulation. Figure depicts this retreat for the
H/A/0/F experiment, alongside RISFRIS and ASE uniform melt rate simulations
(0/U16) and ASE simulations with no synthetic accumulation
(control′′,H/A/0′′/F and
0′′/U16). Provided that melt rates are sufficient, deep bedded
glaciers flowing into the Filchner–Ronne and Ross Ice Shelves see their
grounding lines retreat by as much as 100 km in a century, as do Pine
Island and Thwaites Glaciers. However, while the ASE retreats during the
21st, 22nd, and 23rd century in both the FESOM and uniform melt experiments,
the RISFRIS glaciers do not show significant retreat until the 22nd century
when driven by FESOM melt rates (which do not start to grow until the late
21st century). Animations showing several of the melt rate anomaly
experiments are included in the supplement.
Change in volume above flotation (ΔV(t)) in the Amundsen Sea Embayment during the melt rate anomaly
experiments. The ASE discharges an excess volume between 5 × 103
and 20 × 103 km3 by 2100, and between 20 × 103
and 60 × 103 km3 by 2200. The difference is dominated by the
onset of retreat in Thwaites Glacier and Pine Island Glacier. Pine Island
Glacier begins its retreat around 2000 in all simulations, apart from the
control and control′′ experiment, as do the glaciers feeding
Dotson Ice Shelf and Crosson Ice Shelf. Thwaites Glacier, on the other hand,
begins to retreat immediately in the H/A/0′′/F,
control′′ and 0′′/U16 experiments, in around
2100 in the H/A/0′/F and 0′/U16,
and after 2200 in the H/A/0′/F and O′/U16 experiments.
Amundsen Sea Embayment
The Amundsen Sea Embayment thins throughout the melt rate anomaly
simulations, losing 5–14×103km3
(15–40 mm SLE) volume above flotation between 2000 and 2100 and
20–70×103km3 (50–190 mm SLE) by 2200
(Fig. ). Pine Island Glacier and the ice streams feeding
the Crosson and Dotson Ice Shelves experience ∼1kma-1
grounding line retreat from the present day onward in all of the experiments
apart from control and control′′, while Thwaites Glacier sees
its retreat delayed in some simulations. The major distinction between
simulations is the onset of retreat in Thwaites Glacier: experiments in which
its grounding line begins to retreat around 2000 lose volume at more than
twice the rate of those in which retreat begins around 2200.
Projections of retreat in Thwaites Glacier are strongly affected by initial
conditions, with some simulations showing little retreat and others shedding
between 100 and 210 km3a-1 volume above flotation over the 21st
and 22nd centuries. In calculations with the synthetic mass balance a0:
H/A/0/F, 0/U16, and the control experiment 0/U0), the grounding line remains
close to the present-day position until after 2200, despite the near complete
removal of its ice shelf by that time in H/A/0/F and 0/U16. It seems that
even with the isolated promontory in the slowly flowing eastern section, the
ice shelf exerts little back-pressure on the ice stream and so its loss is
not felt strongly. The majority of the grounding line retreat only begins
after 2200, triggered by the retreat of the small stream which diverts from
Thwaites glacier to flow into the south-western corner of Pine Island Glacier
and from then on the grounding line retreats at a rate of
1 kma-1 until 2300. In contrast, the glacier begins to retreat
around 2100 in the H/A/0′/F experiment, and around 2000 in the
H/A/0′′/F, 0′′/U16 and even the
control′′ experiments. In these last three simulations, marine
ice sheet instability is already acting at the beginning of the simulation,
and at no point does the ice shelf provide enough buttressing to prevent it.
Provided that retreat is initiated, the higher melt rates applied in
H/A/0′′/F, 0′′/U16 do result in faster retreat
(∼ 200km3a-1) than in the control′′
(∼ 100km3a-1).
Both mass loss and grounding line migration in Thwaites Glacier accelerate
during the second century of retreat. For the H/A/0′′/F
simulation, volume above flotation decreases at a mean rate of
75km3a-1 (0.2mma-1SLE) between 2000
and 2100, while the grounding line retreats at a rate ∼1kma-1 across a region featuring a broad area less than
800 m below sea level and a narrow trough between 800 and
1200 m below sea level. Over the following century, the grounding
line crosses a widening region of deeper bedrock (>1200 m below sea
level), so that the greater rate of flow associated with thicker ice at the
grounding line is integrated over a broadening front. The average rate of
grounding line retreat grows to ∼2kma-1, and the rate of
loss of volume above flotation to 320km3a-1
(0.9mma-1SLE). A similar calculation of accelerating
mass loss, with losses of less than 0.25mma-1SLE
during the 21st century and up to 1mma-1SLE
thereafter was reported by .
Variation between the remaining ASE projections, dominated by Pine Island
Glacier, is due to both ocean forcing and initial conditions. Neither the
control nor the control′′ simulations exhibit as much
grounding line retreat in Pine Island Glacier as those with enhanced melt
rates, with the control grounding line holding its initial position and the
control′′ grounding line retreating by around 50 km
over 200 years. In contrast, the FESOM-forced simulations all see the
grounding line retreat by 60 km in the 21st century and a further
160 km in the 22nd century. The H/A/0′′F simulation,
which employs the RACMO2 surface mass balance rather than a synthetic mass
balance, loses volume above flotation at a rate rising from
70 km3a-1 over the 21st century, comparable to rates computed
in other modeling studies
, and present-day
observations . Grounding line retreat slows
toward the end of the 21st century around a bedrock rise and stronger bed
60 km upstream from the present-day position
, after which increase in melt rates from
around 2100 drives the grounding line over this stabilizing region and into
the deeper beds upstream. From then on, volume above flotation losses
increase to 150 km3a-1. Applying uniform melt rates of
16ma-1 pushes the glacier over this region earlier, but the
mean rate of volume loss still increases, from 110 to
170 km3a-1 in the 0′′/U16 experiment.
Change in volume above flotation (ΔV(t)) in the Filchner–Ronne and Ross ice shelf regions during the melt
rate anomaly experiments. The FESOM-forced simulations (H/A/0/F) lose little
volume before 2100, in contrast to the uniform melt rate calculations 0/U8
and 0/U16. All three simulations feature a period where volume is lost from
the Filchner–Ronne region at a rate of more than 200km3a-1
– starting immediately for the uniform melt rate experiments but delayed
until 2200 for H/A/0/F – which corresponds to the retreat of the Möller
and Institute Ice Streams across the Robin Sub-glacial Basin and the
flotation of Bungenstock ice rise, which abates after a century.
The Ross region, on the other hand, tends to see its rate of mass loss increase throughout the simulation.
Filchner–Ronne Ice Shelf
The Weddell Sea ice streams feeding the Filchner–Ronne Ice Shelf speed up
and lose mass in response to the FESOM melt rates from the mid 21st century,
thinning faster in the 22nd century and faster still in the 23rd. The H/A/0/F
experiment sees 22nd-century grounding line retreat in the Evans, Möller,
Institute and Foundation Ice Streams, with the remaining ice streams starting
to retreat only after 2200. Figure shows the
corresponding loss of volume above flotation, increasing from
20km3a-1 (5 mm SLE per century) over the 21st
century through 60km3a-1 (15 mm SLE per century)
over the 22nd – a rate comparable to Pine Island Glacier in the 21st
century. Although the melt rate anomaly is held at its late-22nd century
values over the 23rd century, the rate of retreat continues to increase,
reaching 210km3a-1 (50 mm SLE per century).
All of the ice streams respond immediately to the higher melt rates imposed
in the uniform melt rate experiments. Grounding line retreat is most apparent
in the Evans, Möller and Institute Ice Streams, but even the narrow
Rutford Ice Stream and Carlson Inlet see grounding line migration over
50 km or more by 2200. Rates of retreat in the Evans, Möller and
Institute Ice streams are comparable to rates of retreat, given the same
forcing, in Thwaites and Pine Island Glacier, while volume loss in the two
regions is similar over the 21st century: 220 vs.
180km3a-1 and somewhat lower in the 22nd century: 340 vs.
500km3a-1.
The Möller and Institute Ice Streams exhibit a century-long period of
accelerated retreat in all of our simulations, though its onset varies
considerably. The H/A/0/F experiment shows some retreat from 2100–2200 in
response to the FESOM projection of increased melt rates under the
Filchner–Ronne ice shelf, but from 2200 onward the grounding lines of the
two ice streams merge and then migrate across the bulk of the deep-bedded
Robin Sub-glacial Basin in a single century to reach down-sloping beds by
2300 CE (Fig. ). At the same time, the Bungenstock ice rise
is isolated and then floats. Compared to that, retreat begins right away in
the 0/U16 experiment, reaches the down-sloping bed by 2100 CE, and retreats
little more after that, while the 0/U8 calculation produces a similar period
of retreat starting in 2050. Figure shows the change
in volume above flotation for each of these simulations: all three sustain
a maximum rate of volume loss, approximately 210km3a-1, for
the hundred-year period corresponding to this retreat. These streams, it
would seem, are close to marine ice sheet instability as seen in
and can be forced into unstable retreat by
physically plausible (FESOM) melt rates. We compute faster retreat here than
simply because the melt rates are greater.
Ross Ice Shelf and Siple Coast
The Siple coast ice streams feeding the Ross Ice Shelf lose up to
50 mm SLE by 2100 and 150 mm SLE by 2200 in response to
increased melt rates, but respond less to melt rates derived from FESOM.
Figure shows the mass loss trend for the control,
H/A/0/F, 0/U16 and U/08 experiments, and grounding lines are shown for the
first three in Fig. . The MacAyeal, Bindschadler, Mercer and
Whillans ice streams all flow over retrograde beds and exhibit ∼1kma-1 grounding line retreat in the 0/U16 and U/08
experiments and lose volume above flotation at a rate of around ∼200km3a-1. Although the Mercer and Whillans ice streams do
retreat in response to the H/A/0/F experiment, they retreat in a similar
fashion in the control experiment. Both the H/A/0/F and control grounding
lines sweep across an area which is lightly grounded in the model's initial
state but just floating in (for example) Bedmap2
. The MacAyeal and Bindschadler ice streams do
start to retreat around 2150, when the FESOM melt rates grow to
10ma-1 in the region of Roosevelt Island; that retreat is
sustained, and accelerates, until the end of the experiment in 2300. The
accompanying loss of volume above flotation amounts to about
60km3a-1. There is little retreat apparent in the inactive
Kamb ice stream in any of the experiments.
Marie-Byrd Land
Marie-Byrd Land shows little sign of retreat in the H/A/0/F experiments,
amounting to around 0.5×103km3 (1.5 mm SLE),
despite the elevated melt rates imposed from 2100 onward. Even when uniform
16ma-1 melt rates are imposed across the ice shelves, the
grounding line retreats by only a few kilometers over the 200 years,
with an accompanying loss of volume above flotation of 1.6×103km3 (5 mm SLE). It is apparent in
Fig. that the present-day grounding line in this region runs
perpendicular to a down-sloping bed, with much of the bed above sea level, so
there is no possibility of marine ice sheet instability. As a result, we
might not expect to see century-scale retreat. On the other hand, all of the
glaciers in this region are rather narrow, which leaves the possibility that
they are under-resolved even at Δxmin=625m, and
their beds are inevitably under-resolved by the sparse bedrock data in this
region .
Conclusions
Our most extreme simulation of widespread dynamic thinning in West
Antarctica's fast-flowing ice streams results in 200 mm of eustatic
sea level rise by 2100 and 475 mm by 2200. Pine Island and Thwaites
Glaciers see their grounding lines retreat by hundreds of kilometers, as do
the Möller, Institute, Evans, MacAyeal, Bindschadler, Whillans and Mercer
ice streams and to a lesser extent Carlson Inlet and the Rutford Ice Stream.
All of these ice streams flow along beds that deepen inland, and so can be
subject to marine ice sheet instability. Some of the ice streams appear to be
on the edge of critical change; for example Pine Island Glacier and the
Möller, Institute and Evans ice streams remain close to their present-day
configurations unless melt rates are increased. Our model of Thwaites
Glacier, on the other hand, depends strongly on its initial state: either it
remains steady for up to 200 years after its ice shelf has all but
disappeared, or it retreats rapidly, raising sea level by at least
25 mm each century, even if its ice shelf remains in place.
Wholesale retreat occurs only if enhanced oceanic melt rates are imposed
across all the ice shelves, but neither the FESOM nor the BRIOS ocean
circulation models project substantial warming beneath the Filchner–Ronne or
Ross ice shelves until after 2050. Simulations based upon these more
realistic projections also result in significant dynamic losses in the
Amundsen Sea Embayment: up to 50 mm SLE by 2100 and 150 mm
SLE by 2200 provided that Thwaites Glacier retreats. On the other hand, there
is little retreat in the Filchner–Ronne or Siple Coast ice streams until
after 2100, and only around 30 mm SLE of thinning by 2200. The
Möller and Institute ice streams do exhibit accelerated retreat
immediately after 2200, increasing their contribution from 20 mm SLE
in 2200 to 75 mm SLE by 2300.
Both the RACMO2 and LMDZ4 atmosphere models project increasing snowfall given
the A1B emissions scenario, which partly offsets any dynamic thinning. We
found that the effect of increasing accumulation could be separated from the
effect of increasing melt rates, with the ice sheet model responding to the
two perturbations independently. Up to 20 mm SLE of extra
accumulation by 2100 and as much as 75 mm by 2200 is dispersed across
West Antarctica, sufficient to balance the FESOM- or BRIOS-driven
contribution of Pine Island Glacier and the Möller and Institute ice
streams – but not Thwaites Glacier – over the same period. The E1
projections do not show increased accumulation, and in those cases the
dynamic thinning, which varies much less between emissions scenarios, is
offset by no more than 20 mm SLE by 2200.