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At present the Pine Island Glacier in West Antarctica is thinning and its grounding line has retreated. This work uses three ice-flow models to investigate the stability of the glacier and finds that the grounding line could retreat a further 40 km, which is equivalent to a rise in sea level of 3.5–10 mm over a 20 year period. Over the past 40 years Pine Island Glacier in West Antarctica has thinned at an accelerating rate 1 , 2 , 3 , so that at present it is the largest single contributor to sea-level rise in Antarctica 4 . In recent years, the grounding line, which separates the grounded ice sheet from the floating ice shelf, has retreated by tens of kilometres 5 . At present, the grounding line is crossing a retrograde bedrock slope that lies well below sea level, raising the possibility that the glacier is susceptible to the marine ice-sheet instability mechanism 6 , 7 , 8 . Here, using three state-of-the-art ice-flow models 9 , 10 , 11 , we show that Pine Island Glacier’s grounding line is probably engaged in an unstable 40 km retreat. The associated mass loss increases substantially over the course of our simulations from the average value of 20 Gt yr −1 observed for the 1992–2011 period 4 , up to and above 100 Gt yr −1 , equivalent to 3.5–10 mm eustatic sea-level rise over the following 20 years. Mass loss remains elevated from then on, ranging from 60 to 120 Gt yr −1 .

Polythermal glaciers can trap considerable volumes of liquid water with the potential to generate devastating outburst floods. This study aims to identify water‐filled subglacial reservoirs from ambient seismic noise collected by moderate‐cost surveys. The horizontal‐to‐vertical spectral ratio technique is highly sensitive to impedance contrasts at interfaces, thus commonly used to estimate glacier thickness. Here, we focus on the inverse ratio, that is, the V/H spectral ratio (VHSR), whose high values indicate a low impedance volume beneath the surface, suggesting subglacial cavities. We analyze VHSR peaks from a seismic array of 60 nodes installed on the Tête‐Rousse Glacier (Mont Blanc massif, French Alps); data were gathered over 15 days. Mapping the VHSR amplitude over the free surface reveals the main cavity locations and the basal areas affected by melting within the glacier. Results obtained in the field are supported by a conceptual model based on 3D finite‐element simulations. Plain Language Summary Considerable volumes of liquid water may be trapped within cavities in polythermal glaciers. If these cavities rupture, the resulting outburst flood has the potential to cause devastation in populated mountain areas. With the aim of testing methods to locate such cavities, we installed 60 small 3‐component seismic sensors on the Tête‐Rousse Glacier (Mont Blanc massif, French Alps), which is known to contain such cavities. We used these sensors to test a detection method based on ambient seismic noise. For 3 weeks, the sensors recorded vibrations within the glacier. On a glacier without cavities, these vibrations ought to be predominantly in the horizontal direction. In the presence of a cavity, we expect the ice above the cavity to vibrate mostly vertically—like a bridge. In this paper, we highlight areas on the glacier where vertical vibrations were stronger than horizontal vibrations. These areas fit well with the locations of the main known cavities in this glacier, and with areas affected by basal melting. We supported our field observations with modeling based on 3D simulations, paving the way to a new method to locate water‐filled cavities within glaciers. Key Points Spectral analysis from ambient seismic noise is complementary to other geophysical methods for investigating glaciers at depth Results suggest that the vertical‐to‐horizontal spectral ratio is a reliable proxy to locate subglacial cavities Experimental results were confirmed using a simplified numerical model

The stability of marine ice sheets grounded on beds that slope upwards in the overall direction of flow is investigated numerically in two horizontal dimensions. We give examples of stable grounding lines on such retrograde slopes illustrating that marine ice sheets are not unconditionally unstable in two horizontal dimensions. Retrograde bed slopes at the grounding lines of marine ice sheets, such as the West Antarctic Ice Sheet (WAIS), do not per se imply an instability, nor do they imply that these regions are close to a threshold of instability. We therefore question those estimates of the potential near-future contribution of WAIS to global sea level change based solely on the notion that WAIS, resting on a retrograde slope, must be inherently unstable.

Calving of icebergs is a major negative component of polar ice-sheet mass balance. Here we present a new calving model relying on both continuum damage mechanics and linear elastic fracture mechanics. This combination accounts for both the slow sub-critical surface crevassing and the rapid propagation of crevasses when calving occurs. First, damage to the ice occurs over long timescales and enhances the viscous flow of ice. Then brittle fractures propagate downward, at very short timescales, when the ice body is considered as an elastic medium. The model was calibrated on Helheim Glacier, Southeast Greenland, a well-monitored glacier with fast-flowing outlet. This made it possible to identify sets of model parameters to enable a consistent response of the model and to produce a dynamic equilibrium in agreement with the observed stable position of the Helheim ice front between 1930 and today.

Abstract Basal sliding of glaciers and ice sheets remains a source of uncertainty in simulating the long‐term evolution of ice masses. In particular, the response of ice flow to changes in driving stress depends strongly on the value of the exponent m in nonlinear friction laws (e.g., Weertman's law), which is poorly constrained by observations. Here we constrain the friction law at a natural scale on Argentière Glacier (French Alps, hard‐bed), taking advantage of well‐resolved observations of glacier mass balance, geometry and basal sliding over time spans that include large changes in driving stress. By combining three different independent methods based on (a) surface velocity inversion, (b) transient length change modeling, and (c) direct local sliding measurements, we consistently find a value of m = 3.1 ± 0.3. We suggest that Weertman's law is suitable for modeling the long‐term evolution of hard‐bedded glaciers and ice sheets.

Over the last two decades, the Greenland ice sheet (GrIS) has been losing mass at an increasing rate, enhancing its contribution to sea-level rise (SLR). The recent increases in ice loss appear to be due to changes in both the surface mass balance of the ice sheet and ice discharge (ice flux to the ocean). Rapid ice flow directly affects the discharge, but also alters ice-sheet geometry and so affects climate and surface mass balance. Present-day ice-sheet models only represent rapid ice flow in an approximate fashion and, as a consequence, have never explicitly addressed the role of ice discharge on the total GrIS mass balance, especially at the scale of individual outlet glaciers. Here, we present a new-generation prognostic ice-sheet model which reproduces the current patterns of rapid ice flow. This requires three essential developments: the complete solution of the full system of equations governing ice deformation; a variable resolution unstructured mesh to resolve outlet glaciers and the use of inverse methods to better constrain poorly known parameters using observations. The modelled ice discharge is in good agreement with observations on the continental scale and for individual outlets. From this initial state, we investigate possible bounds for the next century ice-sheet mass loss. We run sensitivity experiments of the GrIS dynamical response to perturbations in climate and basal lubrication, assuming a fixed position of the marine termini. We find that increasing ablation tends to reduce outflow and thus decreases the ice-sheet imbalance. In our experiments, the GrIS initial mass (im)balance is preserved throughout the whole century in the absence of reinforced forcing, allowing us to estimate a lower bound of 75 mm for the GrIS contribution to SLR by 2100. In one experiment, we show that the current increase in the rate of ice loss can be reproduced and maintained throughout the whole century. However, this requires a very unlikely perturbation of basal lubrication. From this result we are able to estimate an upper bound of 140 mm from dynamics only for the GrIS contribution to SLR by 2100.

The stability of marine ice sheets and outlet glaciers is mostly controlled by the dynamics of their grounding line, i.e., where the bottom contact of the ice changes from bedrock or till to ocean water. The last report of the Intergovernmental Panel on Climate Change has clearly underlined the poor ability of models to capture the dynamics of outlet glaciers. Here we present computations of grounding line dynamics on the basis of numerical solutions of the full Stokes equations for ice velocity, coupled with the evolution of the air ice– and sea ice–free interfaces. The grounding line position is determined by solving the contact problem between the ice and a rigid bedrock using the finite element code Elmer. Results of the simulations show that marine ice sheets are unstable on upsloping beds and undergo hysteresis under perturbation of ice viscosity, confirming conclusions from boundary layer theory. The present approach also indicates that a 2‐D unconfined marine ice sheet sliding over a downsloping bedrock does not exhibit neutral equilibrium. It is shown that mesh resolution around the grounding line is a crucial issue. A very fine grid size (<100 m spacing) is needed in order to achieve consistent results.

Increase in ice‐shelf melting is generally presumed to have triggered recent coastal ice‐sheet thinning. Using a full‐Stokes finite element model which includes a proper description of the grounding line dynamics, we investigate the impact of melting below ice shelves. We argue that the influence of ice‐shelf melting on the ice‐sheet dynamics induces a complex response, and the first naive view that melting inevitably leads to loss of grounded ice is erroneous. We demonstrate that melting acts directly on the magnitude of the buttressing force by modifying both the area experiencing lateral resistance and the ice‐shelf velocity, indicating that the decrease of back stress imposed by the ice‐shelf is the prevailing cause of inland dynamical thinning. We further show that feedback from melting and buttressing forces can lead to nontrivial results, as an increase in the average melt rate may lead to inland ice thickening and grounding line advance.

Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving \"shelfy stream\" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.

The West Antarctic ice sheet is confined by a large area of ice shelves, fed by inland ice through fast flowing ice streams. The dynamics of the grounding line, which is the line-boundary between grounded ice and the downstream ice shelf, has a major influence on the dynamics of the whole ice sheet. However, most ice sheet models use simplifications of the flow equations, as they do not include all the stress components, and are known to fail in their representation of the grounding line dynamics. Here, we present a 3-D full Stokes model of a marine ice sheet, in which the flow problem is coupled with the evolution of the upper and lower free surfaces, and the position of the grounding line is determined by solving a contact problem between the shelf/sheet lower surface and the bedrock. Simulations are performed using the open-source finite-element code Elmer/Ice within a parallel environment. The model's ability to cope with a curved grounding line and the effect of a pinning point beneath the ice shelf are investigated through prognostic simulations. Starting from a steady state, the sea level is slightly decreased to create a contact point between a seamount and the ice shelf. The model predicts a dramatic decrease of the shelf velocities, leading to an advance of the grounding line until both grounded zones merge together, during which an ice rumple forms above the contact area at the pinning point. Finally, we show that once the contact is created, increasing the sea level to its initial value does not release the pinning point and has no effect on the ice dynamics, indicating a stabilising effect of pinning points.