Currently Pine Island Glacier (PIG) is responsible for 20% of the total ice loss offdischarge from the West Antarctic Ice Sheet (WAIS) ([22]; [30]). The accelerated thinning observed since the 1980s has essentially been attributed to enhanced sub-ice shelf melting [21] induced by the recent alteration of Circumpolar Deep Water circulation [10]. This has reduced the buttressing exerted by the ice shelf, leading to the acceleration of the ice stream and the ongoing retreat of the grounding line (GL) along the glacier's trunk observed since 1992 [17]. Today the GL lies over bedrock that has a steep retrograde slope [29] (Figure 1c) raising the possibility that PIG may already be engaged in an irrevocable retreat. ProvidedAssuming that ice flow is dominated * durand@lgge.obs.ujf-grenoble.fr 2 by basal sliding and lateral variation can be ignored, grounding lines located on retrograde slopes are always unstable [24,3], but in realistic, three-dimensional geometries lateral drag and buttressing in the ice shelf can act to prevent unstable retreat [9]. Assessing the stability of PIG therefore requires numerical models that accurately represent these additional forces.Models designed to study the evolution of PIG have been reported, though limited to flowline geometries [7] or extreme forcings [11]. Overall, the short-term behaviour of PIG is not well understood, and projections vary wildly, ranging from modest retreat to almost full collapse of the main trunk within a century [11,7].Here, we evaluate the potential instability of PIG and its short-term contribution to sea-level rise (SLR) using state-of-the-art ice flow models. To decide whether PIG is subject to Marine Ice Sheet Instability (MISI) at present, we must answer two questions: (i) to what extent is the dynamic response of PIG to changes in its ice shelf dictated by the bedrock topography rather than the type and amplitude of the perturbation, and, (ii) can the GL be stabilized on the retrograde slope? Confidence in the answers we propose is of course affected by the accuracy of both the physics implemented in the models that we use and our estimates of poorly constrained parameters. We addressed these questions using three different ice-flow models: the full Stokes For all three models, the geometry is relaxed over 15 years to remove unphysical surface undulations induced by remaining uncertainties in the model initial conditions [6]. Surface accumu-3 lation is given by the regional atmospheric model RACMO (1980RACMO ( -2004) and sub-ice shelf melting is imposed as a piecewise linear function of the lower surface elevationwater depth with a maximum melting rate of 100 m a −1 below -800 m depth, linearly decreasing to no melt above -400 m. This melt-rate parametrisation, which we will refer to as m0 control, is in reason- The recent retreat of PIG is now firmly attributed to acceleration of the glacier in response to sub-ice shelf melting. To evaluate the consequences of melting on PIG dynamics, fivefour different melt-rate perturbations are tested. These ar...

Abstract. The Fourth IPCC Assessment Report concluded that ice sheet flow models, in their current state, were unable to provide accurate forecast for the increase of polar ice sheet discharge and the associated contribution to sea level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice flow models, and as a result a significant number of new ice sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the opensource multi-physics code Elmer. It was one of the first fullStokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger-scale problems, earning the status of an ice sheet model. Here, we summarise almost 10 yr of development performed by different groups. Elmer/Ice solves the full-Stokes equations, for isotropic but also anisotropic ice rheology, resolves the grounding line dynamics as a contact problem, and contains various basal friction laws. Derived fields, like the age of the ice, the strain rate or stress, can also be computed. Elmer/Ice includes two recently proposed inverse methods to infer badly known parameters. Elmer is a highly parallelised code thanks to recent developments and the implementation of a block preconditioned solver for the Stokes system. In this paper, all these components are presented in detail, as well as the numerical performance of the Stokes solver and developments planned for the future.

Abstract. 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.

Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view 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 buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (<500 m), or subgrid interpolation of the grounding line. The latter still requires nominal grid sizes of <5 km. For larger grid spacings, appropriate parameterizations for ice flux may be imposed at the grounding line, but the short-time transient behaviour is then incorrect and different from models that do not incorporate grounding-line parameterizations. The numerical error associated with predicting grounding-line motion can be reduced significantly below the errors associated with parameter ignorance and uncertainties in future scenarios.

Even if anthropogenic warming were constrained to less than 2°C above pre-industrial, the Greenland and Antarctic ice sheets will continue to lose mass this century, with rates similar to those observed over the last decade. However, nonlinear responses cannot be excluded, which may lead to larger rates of mass loss. Furthermore, large uncertainties in future projections still remain, pertaining to knowledge gaps in atmospheric (Greenland) and oceanic (Antarctica) forcing. On millennial time scales, both ice sheets have tipping points at or slightly above the 1.5-2.0°C threshold; for Greenland, this may lead to irreversible mass loss due to 1 the surface mass balance-elevation feedback, while for Antarctica, this could result in a collapse of major drainage basins due to ice-shelf weakening.Projecting future sea-level rise (SLR, Box 1) is primarily hampered by our incomplete knowledge of the contributions of the Greenland and the Antarctic Ice Sheets (GrIS and AIS, respectively), Earth's largest ice masses. In this paper we review the potential contribution of both ice sheets under a strongly mitigated climate change scenario that limits the rise in global near-surface temperature to less than 2°C above pre-industrial (targeting 1.5°C), as agreed at the 21st UNFCCC climate conference in Paris. We base the review on both present-day observed/modelled changes and future forcings according to the RCP2.6 scenario. We use RCP2.6, the most conservative of the four Representative Concentration Pathways of greenhouse gas concentration trajectories adopted by the IPCC for its Fifth Assessment Report, because it is the scenario in the published literature that best approximates to the above warming range. Ice-sheet mass balance is defined as the net result of all mass gains and losses, and surface mass balance (SMB) as the net mass balance at the ice-sheet surface (where a negative mass balance means mass loss), including the firn layer. Hence, SMB does not include dynamical mass loss associated with ice flow at the ice-sheet margin or melting at the ice-ocean interface. Increased ice flow accounts for about one third of the recent GrIS mass loss 1 . For Antarctica, where mass lost through ice discharge past the grounding line (the limit between the grounded ice sheet and floating ice shelf) is roughly evenly shared between oceanic basal melt before reaching the ice front and iceberg calving, increased ice flow accounts for all of the recent mass loss 2,3 .In the following sections we synthesize: (i) the latest available evidence of GrIS and AIS mass balance changes together with possible climate forcings from the atmosphere/ocean; (ii) the expected responses of the ice sheets under conditions of limited (1.5°C) global warming by 2100. In the concluding section, we highlight outstanding issues that require urgent attention by the research community in order to improve projections. Greenland forcing and mass-balance changesGreenland has warmed by ∼5°C in winter and ∼2°C in summer since the mid-1990s 4 , which is more than d...

The Fourth IPCC Assessment Report concluded that ice-sheet flow models are unable to forecast the current increase of polar ice sheet discharge and the associated contribution to sea-level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice-flow models, and as a result, a significant number of new ice-sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger scale problems, earning the status of an ice-sheet model. Here, we summarise almost 10 yr of development performed by different groups. We present the components already included in Elmer/Ice, its numerical performance, selected applications, as well as developments planned for the future

Abstract. Oceanic melting beneath ice shelves is the main driver of the current mass loss of the Antarctic ice sheet and is mostly parameterised in stand-alone ice-sheet modelling. Parameterisations are crude representations of reality, and their response to ocean warming has not been compared to 3-D ocean–ice-sheet coupled models. Here, we assess various melting parameterisations ranging from simple scalings with far-field thermal driving to emulators of box and plume models, using a new coupling framework combining the ocean model NEMO and the ice-sheet model Elmer/Ice. We define six idealised one-century scenarios for the far-field ocean ranging from cold to warm, and representative of potential futures for typical Antarctic ice shelves. The scenarios are used to constrain an idealised geometry of the Pine Island glacier representative of a relatively small cavity. Melt rates and sea-level contributions obtained with the parameterised stand-alone ice-sheet model are compared to the coupled model results. The plume parameterisations give good results for cold scenarios but fail and underestimate sea level contribution by tens of percent for warm(ing) scenarios, which may be improved by adapting its empirical scaling. The box parameterisation with five boxes compares fairly well to the coupled results for almost all scenarios, but further work is needed to grasp the correct number of boxes. For simple scalings, the comparison to the coupled framework shows that a quadratic as opposed to linear dependency on thermal forcing is required. In addition, the quadratic dependency is improved when melting depends on both local and non-local, i.e. averaged over the ice shelf, thermal forcing. The results of both the box and the two quadratic parameterisations fall within or close to the coupled model uncertainty. All parameterisations overestimate melting for thin ice shelves while underestimating melting in deep water near the grounding line. Further work is therefore needed to assess the validity of these melting parameteriations in more realistic set-ups.

Abstract. 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.