Thwaites Glacier (TG), West Antarctica, has experienced rapid, potentially irreversible grounding line retreat and mass loss in response to enhanced ice shelf melting. Results from recent numerical models suggest a large spread in the evolution of the glacier in the coming decades to a century. It is therefore important to investigate how different approximations of the ice stress balance, parameterizations of basal friction and ice shelf melt parameterizations may affect projections. Here, we simulate the evolution of TG using ice sheet models of varying levels of complexity, different basal friction laws and ice shelf melt to quantify their effect on the projections. We find that the grounding line retreat and its sensitivity to ice shelf melt are enhanced when a full-Stokes model is used, a Budd friction is used and ice shelf melt is applied on partially floating elements. Initial conditions also impact the model results. Yet, all simulations suggest a rapid, sustained retreat of the glacier along the same preferred pathway. The fastest retreat rate occurs on the eastern side of the glacier, and the slowest retreat occurs across a subglacial ridge on the western side. All the simulations indicate that TG will undergo an accelerated retreat once the glacier retreats past the western subglacial ridge. Combining all the simulations, we find that the uncertainty of the projections is small in the first 30 years, with a cumulative contribution to sea level rise of 5 mm, similar to the current rate. After 30 years, the contribution to sea level depends on the model configurations, with differences up to 300 % over the next 100 years, ranging from 14 to 42 mm.
Thwaites Glacier (TG), located in the Amundsen Sea Embayment
(ASE) sector of West Antarctica, is one of the largest outflows of ice in
Antarctica. It has the potential to raise global mean sea level by 0.6 m and
it is one of the largest contributors to the mass loss from Antarctica
The rapid mass loss and grounding line retreat of TG have been attributed to an increase in ice
shelf melt rate induced by warmer ocean conditions
For a marine-terminating glacier, bed topography plays a crucial role in
controlling the grounding line stability. According to the marine ice sheet
instability (MISI) theory, in 2-D, a grounding line position is stable when sitting
on a prograde bed, i.e., a bed elevation that increases in the inland
direction, and unstable when sitting on a retrograde bed
Many studies have investigated the evolution of TG with numerical ice sheet models. All of these
studies conclude that TG will experience continuous and rapid retreat, but the timing and extent of
the retreat vary significantly between models
Apart from the stress balance model, the choice of friction law and the treatment of ice shelf melt
near the grounding line may also have a significant impact on the rate of grounding line retreat and
glacier mass loss
In this study, we simulate the dynamics and evolution of TG over the next
100 years using the Ice Sheet System Model (ISSM)
We conduct numerical simulations of the ice flow of TG over its entire
drainage basin (Fig.
To solve the stress balance equations without approximation, we use a
full-Stokes (FS) model. We also use two widely used simplified models:
(1) the Higher Order (HO) model, which assumes that the horizontal gradient
of the vertical velocity and the bridging effect are negligible
We employ and compare two different friction laws. The first one is a
Weertman friction law
During the simulation, the grounding
line position lies within mesh elements. Numerical models implement ice shelf melt in these
partially floating elements differently. Some models apply melt in proportion to the floating area
fraction of each element, while others only apply melt to fully floating elements. In our
simulations, we use three types of implementations, named NMP, SEM1 and SEM2, following
The combination of stress balance models, basal friction laws and ice shelf melt implementations leads to 16 different sets of simulations.
The boundary conditions are the same in all experiments apart from the friction law. A stress-free surface is applied at the ice–atmosphere interface. At the ice–ocean interface, water pressure is applied. Along the other boundaries of the model domain, Dirichlet conditions are applied to ensure that ice velocity equals the observed velocity and the direction of ice velocity is tangential to the boundary. The calving front position is kept constant throughout our simulations; i.e. the ice shelf front is not retreating and an ice shelf is always present.
To simulate the response of TG to enhanced ice shelf melting, we run the model with seven different
ice shelf melt scenarios (Fig.
In the other six scenarios, we change the maximum ice shelf melt rate and the
depth at which the maximum melt occurs. To constrain the range of ice shelf
melt rates, we calculate the ice shelf melt rate with mass conservation as in
Ice shelf melt rate parameterization for the seven ocean thermal forcing scenarios.
In total, we run 112 simulations: seven ice shelf melt scenarios for 16 models. We name our simulations
from the combination of ice shelf melt scenario, stress balance equation, ice shelf melt treatment
and friction law. For instance, Exp. 80_1000_FS_Budd_NMP represents the experiment conducted
with a maximum of 80 m yr
The mesh is constructed using an anisotropic metric based on ice surface velocity and distance to
the grounding line over the entire drainage basin of TG. The horizontal mesh spacing is 300 m in the
grounding line region, progressively increasing to 10 km in the interior of the ice sheet.
Vertically, the domain is divided into eight layers that are denser at the bottom. This is the maximum
number of layers that we can have to ensure a high horizontal resolution and to keep the model
numerically affordable. We validated the number of layers by running the MISMIP3d and MISMIP+
experiments and found that the results did not change significantly when using eight or more layers and
were in agreement with other models
To relax the model while maintaining a good fit with surface observations, we adopt the following
procedure. We first solve an inverse problem to estimate the basal friction coefficient over
grounded ice and the ice viscosity parameter over floating ice to best match the modeled surface
velocity with the observed surface velocity
FS is more sensitive to mesh resolution than HO and SSA; hence it requires a higher mesh resolution in
the interior than other models to converge. To avoid the computational cost of high-resolution FS
modeling over the entire drainage basin, we use a tiling method to apply FS within 150 km of the
grounding line and HO in the interior
The inversion results are shown in Fig.
Inversion results.
In transient simulations, the results display a consistent, general pattern of retreat, with different magnitudes of mass loss and rates of grounding line retreat. Overall, the grounding line retreats faster on the eastern side of the glacier and tends to remain more stable on the western side. A sustained mass loss is obtained for all simulations.
The evolution of the grounding line positions for all 16 models with the 80_1000 and 160_700 melt
rate scenarios is shown in Fig.
Grounding line evolution of Thwaites Glacier, West Antarctica, from 16 models with the 80_1000 and 160_700 ice shelf melt scenarios, overlaid on the bed elevation map. Each panel is one simulation. Within each panel, the grounding line positions are plotted every 5 years.
The mass loss is significant and rapid in all simulations (Fig.
The response of TG to ice shelf melt differs with different stress balance models, ice shelf melt implementations and friction laws. Among the three stress balance models, FS shows consistently more grounding line retreat than HO and SSA, except in the Weertman_SEM1 experiments, where HO retreats the most. In the Budd_NMP and Budd_SEM1 experiments, FS produces 5–40 % more grounded area loss than HO and SSA. In the Weertman_SEM1 experiments, FS has 10 % less retreat than HO and 15 % more than SSA. In the SEM2 experiments, HO displays 10–20 % more retreat than SSA. In terms of VAF loss, the three models are closer to each other. SSA shows more VAF loss in the Budd experiments, while FS shows more VAF loss in the Weertman experiments. The overall differences between these simulations are within 20 %.
The choice of friction law has a significant impact on the results. The Budd friction law produces more grounding line retreat (10–50 %) and more VAF loss (15–90 %) than the Weertman friction law. The Budd experiments also display a higher sensitivity to ocean thermal forcing than the Weertman experiments. The grounding line retreat rate is significantly reduced in the NMP experiments compared to the SEM experiments. The total grounded area loss is reduced by 35–65 % and the VAF loss is reduced by 15–40 % with the NMP experiments.
Different ice shelf melt scenarios have a significant impact on the behavior of TG. On the one hand, a
higher ice shelf melt rate always leads to more retreat. On the other hand, the sensitivity to
changes in ice shelf melt rate varies among the models. The SEM experiments with FS or HO and Budd
friction law are more sensitive to ocean thermal forcing than the NMP experiments with SSA and
Weertman friction law. Between the SEM1 and SEM2 experiments, however, the differences are limited
and typically within 5 %, except for the 160_700_Budd experiments. This result is consistent with
previous studies on idealized geometry
Grounded area loss
In our simulations, the stress balance models produce
different results due to both physical and mathematical reasons. With the inclusion of vertical shear
and bridging effects in the stress field, the ice viscosity in FS is lowered, which leads to a
larger acceleration as the grounding line retreats. In the MISMIP3D experiments, using the same
initial setting, the modeled ice velocity of FS is faster than HO by 0–5 %, and HO is faster than
SSA by another 0–5 %
In terms of mathematical implementation, the inversions are conducted separately for each model to
make sure that they best fit the observations. Hence, the initial conditions are slightly different
for each model, which sets them up on different trajectories. In transient simulations, small
differences in initial conditions accumulate with time and may lead to significant differences
in the model outcomes. Here, SSA has a higher rate of VAF loss than grounded area loss compared to
HO and FS due to the higher thinning rate in the interior. This sensitivity to the initial
conditions indicates that we need better constraints for the inversion process. For instance, it
would be useful to infer the basal friction coefficient and ice viscosity parameter from a time
series of observed velocities, as in
In summary, the FS model includes more complex physics and leads to faster grounding line retreat, especially over subglacial ridges, compared to SSA or HO models. The difference between FS and simplified models varies with bed topography. Meanwhile, initial conditions are also critical to consider when comparing model results.
The limitation of FS is mostly computational. FS is 10 times slower than HO and 100 times slower than SSA. In our results, we find that the impact of choosing stress balance model is smaller than the impact of choosing ice shelf melt treatment and friction law.
The introduction of an effective pressure term in the Budd friction law produces more retreat and mass loss compared to the Weertman experiments. With the Budd friction law, the basal drag is reduced when the ice is thinning, which in turn accelerates the retreat and thinning, forming a positive feedback. In our results, the difference between Weertman and Budd experiments is larger in VAF loss than grounded area loss due to the differences in the interior. Once the friction is reduced with the Budd friction law, ice thinning increases and propagates inland to produce more VAF loss than in the Weertman case. This result indicates that the difference in grounding line retreat between these two sets of experiments diverges with time as the upstream thinning evolves.
The underlying assumption for the Budd friction law is the existence of a subglacial drainage
system. Previous studies have revealed that such systems exist in West Antarctica and are connected
to the ocean
Several new friction laws have been proposed recently.
Our results show that if we apply ice shelf melt over the floating area of
partially floating elements (SEM1 and SEM2), the retreat changes
significantly, which is consistent with previous studies
Despite the differences between these
models, the overall results are similar; i.e., the glacier retreats along essentially the same
preferred paths. The major difference between the models is the time it takes for each model to
overcome ridges in the bed topography along the pathway of the retreat. In all simulations, TG
experiences grounding line retreat and mass loss over the entire period, which is consistent with
previous studies
There is a subglacial trough between the second and third ridge that connects PIG and TG. If the grounding line of TG retreats into this region (SEM experiments with high
melt), the grounding line of TG will connect with the grounding line of PIG, and the two drainage
basins will merge into one. The flow of ice could be significantly impacted if this merge takes
place. In this study, we did not account for this scenario as it would require the
entire ASE to be simulated
The subglacial ridge that has the strongest stabilizing effect is the western subglacial ridge where the grounding line is currently anchored. In the NMP experiments, the grounding lines are stable in the west. In the Weertman_SEM1 experiments, only the FS model with the highest ice shelf melt rate has its grounding line retreat over the ridge at year 95. In the Budd_SEM experiments, the grounding line retreats over this ridge for the three high ice shelf melt scenarios (160_700, 160_1000, 120_700). Further upstream, the bed slope of TG is retrograde up until the ice divide and the subglacial channel widens inland. Once the grounding line retreats past the western ridge, our model results do not suggest that the retreat can be stopped.
The impact of ocean thermal forcing is most significant in the Budd_SEM experiments and is small in the NMP experiments. The difference is due to the grounding line retreat rate. In the scenarios where the grounding line is constantly retreating, a higher ice shelf melt rate will remove ice in the newly ungrounded area more rapidly and reduces the buttressing force on the inland ice faster, which leads to further retreat. If the grounding line position is relatively stable, however, a higher ice shelf melt rate will only act over floating ice and has no impact over grounded ice. The removal of ice becomes limited, the ice bottom reaches a steady shape and the reduction in buttressing is minimal.
In our simulations, the effect of changing the depth of maximum melt from 1000 to 700 m is similar
to increasing the maximum ice shelf melt rate by 50 % (80_700 vs. 120_1000 and 120_700
vs. 160_1000). This is because the bed elevation between the current grounding line and the upstream
subglacial ridges is between 800 and 500 m, which makes the melt rate at this depth particularly
important. If warm ocean water intrudes at 700 m depth, as observed on PIG, or
above, the retreat of TG will be more rapid, even without increasing the maximum ice shelf melt
rate. Indeed, the bathymetry in
The contribution to global sea level rise
revealed by our simulations spread from 14 to 42 mm in the next 100 years. However, in the first
30 years, all models suggest a global sea level rise of 5 mm, or 0.18 mm yr
One major limitation of this model study is the ice
shelf melt rate parameterization. We estimate the ice shelf melt rate from observations and try to
cover both cold and warm scenarios. In reality, the melt rate could have large spatial and temporal
variability, especially as the grounding line retreats. These variabilities are likely to affect the
evolution of TG. Coupled ice–ocean models indicate that warm ocean water has more limited access to
newly formed cavities as the ice sheet retreats
Another limitation is that the ice shelf front migration is not included in our simulations. We assume
that the ice shelf front position of TG remains fixed; i.e., all ice passing the ice shelf front
calves immediately. Densely distributed crevasses along the ice shelf of TG, however, make the ice
shelf conducive to rapid calving
We simulate the response of Thwaites Glacier, West Antarctica, to varying model configurations and ice shelf melt scenarios. We find that the stress balance approximations, the friction law, the treatment of ice shelf melt near the grounding line and the ice shelf melt rate parameterization all affect the retreat of TG significantly. Different model configurations affect the results mainly through the timing for the grounding line to retreat past subglacial ridges; different ice shelf melt rates mainly affect the retreat rate when the grounding line is retreating along retrograde portions of the bed. Despite the differences, however, all models follow similar trajectories and concur to indicate that TG will continue to retreat at a rapid rate over the next century, under both cold and warm ocean water scenarios. The retreat is controlled by the bed topography. Subglacial ridges on the eastern side will moderately delay the retreat, whereas the western ridge provides the most stability for the glacier, for at least the next several decades. Once the grounding line retreats past the western subglacial ridge, our simulations suggest that there will be no further stabilization of the glacier and the retreat will become unstoppable for the next 100 years. Our simulations project a 5 mm global mean sea level contribution from TG in the next 30 years and 14–42 mm in the next 100 years.
The ice flow model ISSM can be found and downloaded at
Volume above floatation loss in two sensitivity experiments
All authors contributed to the design of the experiments. HY conducted them and wrote the paper with the help of ER, MM, and HS.
The authors declare that they have no conflict of interest.
This work was carried out at the University of California Irvine and at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the Cryosphere Science Program of the National Aeronautics and Space Administration. We thank the reviewers Stephen Cornford and Lionel Favier for their constructive comments on the manuscript. Edited by: Nanna Bjørnholt Karlsson Reviewed by: Stephen Cornford and Lionel Favier