Using three independent ice-flow models and several satellite-based datasets, we assess the importance of correctly capturing ice-shelf breakup, shelf thinning, and reduction in basal traction from ungrounding in reproducing observed speed-up and thinning of Thwaites Glacier between 1995 and 2015. We run several transient numerical simulations applying these three perturbations individually. Our results show that ocean-induced ice-shelf thinning generates most of the observed grounding line retreat, inland speed-up, and mass loss, in agreement with previous work. We improve the agreement with observed inland speed-up and thinning by prescribing changes in ice-shelf geometry and a reduction in basal traction over areas that became ungrounded since 1995, suggesting that shelf breakups and thinning-induced reduction in basal traction play a critical role on Thwaites's dynamics, as pointed out by previous studies. These findings suggest that modeling Thwaites's future requires reliable ocean-induced melt estimates in models that respond accurately to downstream perturbations.
The reduction in basal traction due to grounding line retreat plays a critical role on Thwaites's dynamics in agreement with previous studies
Ocean-induced melt leads to a sustained acceleration and grounding line retreat consistent with observations and earlier work
Improved forecasts of Thwaites demand reliable melt estimates coupled to models that accurately reproduce the response to downstream changes
Plain Language Summary
Recent observations have shown that Thwaites Glacier, West Antarctica, has been accelerating and thinning over the past decades and its floating part is quickly breaking up. While these observations suggest that warmer ocean currents are the main factor responsible for these changes, it remains unclear which of the following processes are most important to the glacier's dynamics: (a) breakup of its floating section, (b) ice-shelf thinning, or (c) changes in the grounded-ice area. By employing three ice-sheet models and several satellite-based datasets, we find that thinning induced by ocean melting and the resulting reduction of grounded-ice area explain most of the observed flow acceleration and mass loss of Thwaites, in agreement with other studies. We also find that the breakup of the floating section plays an important role on Thwaites's dynamics. These findings suggest that improved forecasts of Thwaites's future require reliable ocean-induced melt estimates and improved model response to changes in ice-shelf thickness and geometry.
Thwaites Glacier, one of the largest ice streams in the Amundsen Sea Embayment (Figure 1), drains a large area of the West Antarctic Ice Sheet (WAIS). Its ice volume holds the equivalent of 0.65 m of sea level (Morlighem et al., 2020), and is resting on deep bedrock, a wide channel below sea level that spreads under WAIS to the Ross Sea Embayment (Fretwell et al., 2013; Holt et al., 2006). The retrograde slope of this channel makes Thwaites potentially vulnerable to marine ice sheet instability (Gudmundsson et al., 2012; Schoof, 2007; Weertman, 1974), a positive feedback of grounding line retreat and increased ice discharge which may lead ultimately to WAIS's collapse over the coming centuries (Bamber et al., 2009; Feldmann & Levermann, 2015; Joughin et al., 2014; Martin et al., 2019; Scambos et al., 2017). How fast this collapse may happen depends on internal instability mechanisms (e.g., Favier et al., 2014) and on external forcings that could drive significant mass loss of Thwaites Glacier and WAIS (e.g., Gudmundsson et al., 2019).
Recent observations have shown that Thwaites has been accelerating, thinning, and experiencing ice-shelf breakups and grounding line retreats since the 1970s (Konrad et al., 2018; Mouginot et al., 2014; Rignot et al., 2014; Shepherd et al., 2019). The pattern of ice thinning in the Amundsen Sea Sector suggests that changes in ocean conditions are likely the main external driver of ocean-induced ice-shelf thinning, increased calving rates, and changes in grounding line positions (Alley et al., 2015; Milillo et al., 2019; Seroussi et al., 2017). Although these changes are not independent, the exact chain of events that led to Thwaites's thinning and acceleration remains unclear. For instance, the increased thinning of the ice shelves may have compromised their mechanical integrity, leading to the partial collapse of Thwaites Eastern Ice Shelf (TEIS) and the complete loss of Thwaites Tongue (TT) (e.g., Miles et al., 2020; Scambos et al., 2009). These changes could have decreased the buttressing provided by the pinning point in TEIS's tip to the grounded ice (Figure 1a), inducing glacier speed-up and, as a consequence, the retreat of the grounding line (Figure 1b).
We investigate the effect of each of these physical processes on numerical modeling of Thwaites's dynamics between 1995 and 2015. We perform several numerical simulations using three independent ice sheet models (Úa, ISSM, and STREAMICE) for which we prescribe changes in calving front position, ice-shelf thickness, and basal traction due to grounding line retreat, and we quantify their impacts on upstream flow. The resulting changes in ice speed and thickness are compared with satellite-based measurements. The misfit between modeled and observed ice velocities in each case provides estimates of the relative importance of all those observed changes on the glacier flow.
2 Data and Methods
The three models are initialized to 1995 conditions and are run forward in time until 2015. The 1995 digital elevation model (DEM) is derived from the European Remote Sensing (ERS-1) radar altimetry (Bamber, 2000). The 2015 DEM is the Reference Elevation Model of Antarctica, REMA (Howat et al., 2019), included in BedMachine Antarctica v2 (Morlighem et al., 2020). We employ the most recent bed elevation product derived from mass conservation and a recent survey in Thwaites (Hogan et al., 2020; Jordan et al., 2020; Morlighem et al., 2020). Ice velocities and grounding line positions of the initial (1995) and final (2015) states are derived from interferometric synthetic aperture radar data (InSAR, Mouginot et al., 2014; Rignot et al., 2014).
As described in Section 2.3, we impose perturbations based on satellite measurements. Changes in calving-front extension are derived from Landsat imagery (MacGregor et al., 2012). Ice-shelf thinning rates are estimated by radar altimetry (Paolo et al., 2015). Grounding line retreat is measured by InSAR data (Rignot et al., 2014). We compare the modeled velocity change and thinning rates with observations of speed change and ice thinning derived from InSAR and radar/laser altimetry data, respectively (Mouginot et al., 2014; Shepherd et al., 2019; Smith et al., 2020). The basal melting is parameterized by a depth-dependent relationship based on observations and ice-ocean-coupling simulations (Milillo et al., 2019; Nakayama et al., 2019; Rignot et al., 2013; Seroussi et al., 2017). The surface mass balance is derived from the Regional Climate Model (RACMO v2.3; Van Wessem et al., 2014).
Landsat imagery shows a rift propagating between TEIS and TT from the 1980s to 2010/2011 when the main part of TT calved off (MacGregor et al., 2012). Based on the hypothesis of non-negligible shear stress between TEIS and TT prior to 2006 (Miles et al., 2020; Mouginot et al., 2014), likely due to mélange formation that could act as a granular ice shelf (Burton et al., 2018) into that rifted zone, we start all the experiments in 1995 with TEIS and TT mechanically connected. To set up this connection, we remove this rift from the 1995 Landsat-derived ice-front contour, allowing transfer of stresses across the region where the rift later developed. The model initialization (inversion, see Section 2.2) adjusts the rheological parameter of the ice into that rifted zone to model the speed differences between TEIS and TT (Figure 1a). We keep the 1995 shelf-front position fixed in time, except where otherwise stated (see Section 2.3).
2.2 Ice Sheet Models
Each model performs its own inversion procedure to infer the spatial distributions of the basal drag coefficient , and an ice rheological parameter, commonly denoted as , in Glen's flow law, using 1995 data (DEM and ice velocity; Bamber, 2000; Mouginot et al., 2014) and ice temperatures calculated by other studies (Seroussi et al., 2019; Van Liefferinge & Pattyn, 2013). All three models invert for over grounded ice. Úa and STREAMICE invert for the ice rheological parameter over the entire domain (with STREAMICE penalizing variations from a ‘prior’ temperature-based estimate in grounded ice), while ISSM inverts for only on floating ice. Technical details of the model inversions are described in Barnes et al. (2021). The resulting spatial distributions, that is, and , are kept constant over the transient runs (except for the experiments where we manually decrease in specific areas; Section 2.3).
The models set the basal traction to a negligible value downstream of the 1995 grounding-line position, which helps to prevent the grounding line from advancing beyond its initial state. The grounding line is based on hydrostatic equilibrium (Seroussi et al., 2014) and is free to migrate in all experiments.
2.3 Numerical Experiments
2.3.1 Control Experiment
We first run a “control” simulation forced by ice-shelf melting only. None of the observed changes in geometry are imposed during the transient runs, and the ice-shelf thickness and the position of the grounding line are therefore free to evolve in response to this ice-shelf melting. Note that in this control simulation the models may not necessarily reproduce the observed ice-shelf thinning and grounding line retreat since those are unconstrained in this experimental setup.
We apply melt only to elements/cells containing fully floating ice (Seroussi & Morlighem, 2018). The parameters in Equation 2 are kept fixed during the simulations, although the spatial distribution of basal melting varies in time with the evolving thickness and extent (due to grounding line migration) of the ice shelf.
2.3.2 Imposed Change Experiments Overview
Since the grounding line and ice-shelf thickness evolve freely in the control experiments, we expect that the agreement with observed speed and thickness changes will be improved if we constrain front geometry, ice-shelf thinning, and loss of basal drag in the models, all according to observed changes. Prescribing these changes individually allows their respective impacts on the modeled evolution to be quantified and compared. For example, if applying the observed change in the ice-front position improves the agreement with observations, it would suggest that calving dynamics played a role on the behavior of Thwaites. Comparing the response of the models will also shed light on the processes that have the strongest effect on Thwaites's dynamics.
We run simulations where we apply observed changes to the control setup in (a) ice-front position, (b) ice-shelf thickness, and (c) basal traction downstream of the 2015 grounding line, all based on observations. We force the models to follow these changes individually by prescribing these observed changes directly in the models. We also run (d) an all-external-drivers experiment, where (a), (b), (c), and melt are all applied. We expect the results of experiment (d) to be more consistent with observations. All experiments employ basal melt as given by Equation 2 unless otherwise specified.
2.3.3 Ice-Front Change Experiment
The observed retreat and rift propagation on Thwaites's floating ice are imposed on a yearly basis at the ice-ocean boundary, following Landsat imagery (MacGregor et al., 2012). Any dynamic effect from ice-shelf rifting or collapse is captured in this simulation. We apply these changes only to regions downstream of the 1995 grounding-line position. We keep TEIS and TT mechanically connected until 2005, following the hypothesis mentioned in Section 2.1. To this end, we remove the rift between TEIS and TT from the Landsat-derived ice-front contours for all years between 1996 and 2005. From 2006 to 2015, we impose the original Landsat-based contours, disconnecting TEIS and TT (MacGregor et al., 2012). We do not consider any healing of that link after 2006 (Miles et al., 2020; Mouginot et al., 2014) since TT calved off in 2010/2011 (MacGregor et al., 2012). The basal melt is applied to all floating ice.
2.3.4 Ice-Shelf Thinning Experiment
The 1995 shelf thickness is manually decreased according to satellite-measured thinning rates (e.g., Paolo et al., 2015; Smith et al., 2020). The 1995 shelf thickness is proportionally changed at each time step from 1995 to 2015. This setup simulates the effect of decreasing ice-shelf buttressing on grounded ice following the observed shelf thinning. The imposed thinning "overrides" melting except in newly ungrounded ice where the thinning is not applied, that is, the melt is only applied to areas upstream of the 1995 grounding line that becomes ungrounded during the transient runs. Imposing the thinning manually recovers the observed shelf-thickness change, which would probably not be perfectly reproduced by our parameterized basal melt in the control experiment (see Figures S3 and S6 in Supporting Information S1).
2.3.5 Loss of Basal Traction Experiment
Due to the lack of spatial and temporal data availability and the technical challenge of preserving hydrostatic equilibrium at the grounding line, we cannot directly prescribe the grounding line positions in transient runs. Instead, we simulate the effect of observed grounded ice retreat by linearly decreasing with time from its 1995-inverted value to 0 between 1995 and 2015. The value of the basal drag coefficient, , is reduced only in the region that was grounded in 1995 but floating in 2015 (Rignot et al., 2014). This setup simulates a thinning-induced reduction in basal traction: as the ice approaches flotation, the effective pressure declines, reducing the basal traction. Note that the control experiment would not necessarily be reproducing this physical process and the observed grounding line retreat. The basal melt applies to all floating ice.
2.3.6 All-External-Drivers Experiment
The setup imposes the three observed changes together. These changes are the same as those imposed in the experiments described in Sections 2.3.3–2.3.5-2.3.3–2.3.5. The melt is applied only to areas upstream of the 1995 grounding line that become floating over the simulations.
To assess the relative impact of each imposed change on the models, we compute correlations and root mean square errors (RMSE) between observed and modeled speed and thickness changes. The correlations measure the agreement between spatial patterns, while the RMSE quantifies the magnitude of the misfits.
3.1 Ice Velocity Changes
The observed acceleration of Thwaites Glacier has not been spatially uniform (Mouginot et al., 2014). The ice velocity increased by up to 25 m/yr per year in the vicinity of the grounding line (Figure 1b). Most of the main trunk and the western ice stream has been accelerating markedly up to 100 km upstream of the glacier's margin. The eastern part of the glacier has not changed significantly, except around the eastern margin of TEIS (see L1 in Figure 2a1) which accelerated by up to 20 m/yr per year. Most of the regions that sped up coincide with the regions where the grounding line retreated during this period (Figure 1b). Only a small area at the terminus of the western ice stream (see L2, Figure 2a1) decelerated between 1995 and 2015. At this location, the grounding line has not changed since the 1990s. The ice flux at the 2011 grounding line of Thwaites increased 30–335 Gt/yr over the 1994/1996–2013 period (Mouginot et al., 2014) (see Table S2 in Supporting Information S1).
The control experiment produces grounding line retreat and inland speed-up with moderate correlations in comparison to other experiments (Figures 2b1–2b3, and Table 1). The modeled increase in ice flux is also comparable to observations and varies from 20 Gt/yr (ISSM) to 30 Gt/yr (STREAMICE) (Table S2 in Supporting Information S1). Applying observed changes individually produces some differences among the model responses, with some simulations producing substantially better improvements in misfit and correlation for some models (e.g., ice-front change for Úa and ice-shelf thinning for STREAMICE) than for others. In Úa, prescribing ice-shelf thinning appears to introduce numerical inconsistencies at the boundary of the area for which thickness is enforced, which explains the differences in the shape of the grounding line compared to other experiments (Figure 2d1). As expected, the all-external-drivers experiment reproduces the overall pattern of observed speed change with the least error, including the localized changes at L1 and L2 (Figures 2f1–2f3). Changes in L2 are not captured by STREAMICE because the grounding line retreats in this region with this model. Overall, the final modeled grounding line positions obtained with the all-external-drivers experiment are also in good agreement with observations. STREAMICE overestimates grounding line retreat along the western side of the grounding line “bight” in front of western Thwaites (location “A” of Milillo et al., 2019). This overestimated retreat coincides with overestimated acceleration in the western part of Thwaites (Figure 2, panels from b3 to f3, and Figure 3, transect C-C’), which contributes to the higher RMSE and glacier flux compared to Úa and ISSM (Table 1 and Table S2 in Supporting Information S1, respectively). The increase in glacier flux varies from 15 Gt/yr (ISSM) to 30 Gt/yr (STREAMICE) (Table S2 in Supporting Information S1).
3.2 Ice Thinning
The observed thinning of Thwaites followed the observed ice speed-up, extending tens of kilometers over the interior of the glacier (Figure S9a1 in Supporting Information S1). The margins of the main trunk and western ice streams as well as the eastern part of TEIS (L1) thinned the most (up to 45 m over the 2003–2019 period; Smith et al., 2020). To compare with our results, we use two different datasets of observed thickness changes (Shepherd et al., 2019; Smith et al., 2020), since they employ an acquisition period different from the period considered here (see Table 1).
|Thickness change (a)||Correlation||RMSE (m)|
|Thickness change (b)||Correlation||RMSE (m)|
- Note. The correlations and root mean square errors (RMSE) for thickness change are calculated using two different data sets: (a) From Shepherd et al. (2019), whose time period is 1992–2017, and (b) From Smith et al. (2020), whose time period is 2003–2019. We apply a Gaussian filter to the modeled thickness changes with kernel size equal to 35 km and km, following Smith et al. (2020). All correlation coefficients and RMSE are obtained considering Thwaites's basin and inland extension as given by transect A-A’ portrayed on panel (b) of Figure 1. Legend: CR (control experiment), IF (ice-front change experiment), IS (ice-shelf thinning experiment), BT (loss of basal traction experiment), and AD (all-external-drivers experiment).
The three ice sheet models produce patterns of ice thinning similar to observations in all experiments, as seen by the relatively high correlations (Table 1), although some thickening appears in regions around the glacier's basin likely due to thickness adjustments during the transient runs (Figure S9 in Supporting Information S1). The inland thickening produced by Úa in the ice-shelf experiment is likely caused by the numerical inconsistencies described above.
The control experiment generates a pattern of thickness change comparable to observations, as noted by the relatively high correlation of 0.81. The thinning rates obtained with all-external-drivers and loss of basal traction experiments show the highest correlation coefficients (0.88 and 0.86, respectively), followed by ice-front change (0.85) and ice-shelf thinning (0.78) experiments.
The control experiment produces upstream acceleration, thinning, and grounding line migration comparable to observations. Our parameterized melt is not necessarily in balance with the ice-shelf flow (e.g., Rignot et al., 2013), which produces some shelf thinning (Figure S6 in Supporting Information S1). As a consequence, the melt sustains thinning of newly-ungrounded ice upstream of the 1995 grounding line as downstream changes (i.e., shelf thinning) induce a loss of buttressing on upstream flow (e.g., in the vicinity of the grounding line along the main trunk and the western ice stream), causing inland speed-up, thinning, and grounding line retreat. This mechanism may be enhanced by local reverse-slope bedrock, where the grounding line may retreat faster (Joughin et al., 2014; Morlighem et al., 2020; Rignot et al., 2014; Schoof, 2007; Seroussi et al., 2017). The observed mass loss over the last decades in the Amundsen Sea Sector is therefore likely associated with increasing ocean-induced melt (e.g., Hoffman et al., 2019; Jenkins et al., 2016; Joughin et al., 2014; Martin et al., 2019; Milillo et al., 2019; Pritchard et al., 2012; Robel et al., 2019; Seroussi et al., 2017).
In the experiments where we impose observed changes instead of letting the model evolve freely, we find that forcing the geometry of the ice shelf and basal traction increases the correlations in both speed change and ice thinning. These findings suggest that rifting propagation between TEIS and TT and thinning-induced reduction in basal traction play an important role on Thwaites's dynamics, as pointed out by previous studies (e.g., Joughin et al., 2014; Miles et al., 2020; Mouginot et al., 2014; Nias et al., 2016). Given its importance, the evolution of basal drag as the grounding line retreats may therefore need to be further improved in ice-sheet models (De Rydt et al., 2021; Nias et al., 2016). For instance, we employ here Weertman's sliding law with an exponent and we invert for the drag coefficient (). The resulting spatial distribution of is then kept fixed in all simulations (except for the loss of basal traction setup). Other sliding laws that reduce the basal traction as the grounding line migrates could potentially generate a different upstream response to ice thinning/front retreat (Brondex et al., 2017, 2019; De Rydt et al., 2021; Joughin et al., 2019). Also, it remains unclear whether a "mechanical link" between TEIS and TT could be reinstated in the future, or whether the mechanical integrity of TEIS will be compromised due to structural weakening (e.g., Miles et al., 2020). Thus, enhanced calving dynamics may also improve the accuracy of numerical simulations of Thwaites (e.g., Crawford et al., 2021).
Our parameterized basal melt is based on observations and ocean simulations, and similar parameterizations have been used in other studies of Thwaites Glacier (Depoorter et al., 2013; Hoffman et al., 2019; Joughin et al., 2014; Milillo et al., 2019; Nakayama et al., 2018, 2019; Rignot et al., 2013; Seroussi et al., 2017). At the end of the control experiments, the integrated melt is, on average, 110 Gt/yr, which is slightly greater than satellite-based (97.57 Gt/yr, Rignot et al., 2013) and simulation-based (80–120 Gt/yr, Seroussi et al., 2017) estimates (see Table S1 and Figure S10 in Supporting Information S1). Depth-dependent melt parameterizations tend to overestimate grounding line retreat in comparison to ice-ocean simulations in longer runs (Seroussi et al., 2017). The parameters in Equation 2 were kept constant over the transient runs, although ocean conditions have likely changed over the last decades, which could have affected the response of the models. For instance, rerunning the control experiment in ISSM with the parameterized melt multiplied by 4, the model overestimates the inland acceleration (the resulting RMSE is 28.58 m/yr. See also Figure S5b in Supporting Information S1) and the integrated melt along the entire transient run (Figure S10 in Supporting Information S1), although the spatial pattern of the response is similar to observations (correlation of 0.78). To improve the forecast of Thwaites's future, reliable estimates of melt rates are required, especially close to the grounding line, where thinning-induced reduction in basal traction is critical.
The differences between the models' results may be caused by several factors: stress balance approximation, inversion procedure, mesh resolution, numerical issues caused by imposed forcings, etc. (e.g., Barnes et al., 2021; Cornford et al., 2020). STREAMICE had a more extensive retreat in the western part of the Thwaites grounding line than that of Úa or ISSM, which might be the reason for the larger acceleration in this region and resulting in higher RMSE. The difference may arise from differing treatment of a small ice rise in TT arising from a topographic high in the bathymetry data (see Supporting Information S1), or from resolution in the vicinity of the grounding line which may be too coarse (Cornford et al., 2020). Deceleration can be seen upstream in some Úa results, particularly evident across transect F-F’ in Figure S8 in Supporting Information S1, due to slight differences in the inverted basal sliding and rate factor fields compared to the other models. These factors all play an important role on transient simulations and shall be investigated in future work. Our results also illustrate how challenging reproducibility is in the field of ice sheet modeling (e.g., Seroussi et al., 2020), which calls for further numerical developments and model inter-comparison initiatives.
Uncertainties in the data and inversion procedures may have an impact on our results. For example, the mass loss observed over the last decades could be part of an already existing dynamic imbalance prior to 1995, and our inversions were not able to capture this early loss trend. Also, using a previous bed elevation version (BedMachine v1), artificial "bumps" downstream of the 2015 grounding line (and close to the 1995 grounding line) prevented inland acceleration and grounding line retreat in most of the experiments. These results highlight the need for further improvements in bed topography data, as noted by others (e.g., Durand et al., 2011; Nias et al., 2016).
By conducting time-dependent numerical simulations of Thwaites Glacier between 1995 and 2015 with three independent ice sheet models and several satellite-based datasets, we find that thinning induced by ocean melting and the resulting grounding line retreat explain much of the observed speed-up of Thwaites. The models also suggest that changes in the ice-shelf geometry, especially the rifting propagation between the Eastern Ice Shelf and Thwaites Tongue, improve the agreement with observations. The results suggest that improved forecasts of Thwaites's future require reliable ocean-induced melt estimates and improved model response to downstream perturbations, particularly thinning-induced reduction in basal traction.
This work is from the PROPHET project, a component of the International Thwaites Glacier Collaboration (ITGC). Support from National Science Foundation (NSF: Grant #1739031) and Natural Environment Research Council (NERC: Grants NE/S006745/1 and NE/S006796/1). ITGC Contribution No. ITGC-023.
Data Availability Statement
All of the data sets and source codes used in this study are publicly available. The Ice-sheet and Sea-level System Model can be accessed at https://issm.jpl.nasa.gov (we used version 4.18). STREAMICE is a module of MITgcm and can be download at https://mitgcm.org/source-code/. The source code of Úa can be downloaded at http://doi.org/10.5281/zenodo.3706623. BedMachine Antarctica is available at NSIDC (http://nsidc.org/data/nsidc-0756). The 1995 Antarctic 5 km DEM is also available at NSIDC (https://nsidc.org/data/nsidc-0076). InSAR-Based ice velocity of the Amundsen Sea Embayment is found at NSIDC (https://nsidc.org/data/NSIDC-0545). Coastal and terminus history of Thwaites (shapefile format) is found at NSIDC (https://nsidc.org/data/NSIDC-0522). Grounding line positions are found at NSIDC (https://nsidc.org/data/NSIDC-0498). Maps of thickness changes are found at Nasa's EarthData (https://sealevel-nexus.jpl.nasa.gov/data/ice_shelf_dh_v1/), University of Washington's digital repository (https://digital.lib.washington.edu/researchworks/handle/1773/45388), and at CPOM (http://www.cpom.ucl.ac.uk/csopr). The Antarctic surface mass balance (RACMO 2.3) is available at https://www.projects.science.uu.nl/iceclimate/models/antarctica.php.
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