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. We present the results of the first ice sheet model intercomparison project for higher-order and full-Stokes ice sheet models. These models are compared and verified in a series of six experiments of which one has an analytical solution obtained from a perturbation analysis. The experiments are applied to both 2-D and 3-D geometries; five experiments are steady-state diagnostic, and one has a time-dependent prognostic solution. All participating models give results that are in close agreement. A clear distinction can be made between higher-order models and those that solve the full system of equations. The full-Stokes models show a much smaller spread, hence are in better agreement with one another and with the analytical solution.

[1] Sliding velocity and basal drag are strongly influenced by changes in subglacial water pressure or subglacial water storage associated with opening and closing of water cavities in the lee of bedrock obstacles. To better understand this influence, finite-element simulations of ice flowing past bedrock obstacles with cavity formation are carried out for different synthetic periodic bedrock shapes. In the numerical model, the cavity roof is treated as an unknown free surface and is part of the solution. As an improvement over earlier studies, the cases of nonlinear ice rheology and infinite bedrock slopes are treated. Our results show that the relationship between basal drag and sliding velocity, the friction law, can be easily extended from linear to nonlinear ice rheology and is bounded even for bedrocks with locally infinite slopes. Combining our results with earlier works by others, a phenomenological friction law is proposed that includes three independent parameters that depend only on the bedrock geometry. This formulation yields an upper bound of the basal drag for finite sliding velocity and a decrease in the basal drag at low effective pressure or high velocity. This law should dramatically alter results of models of temperate glaciers and should also have important repercussions on models of glacier surges and fast glacier flows.

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.